Abstract:
  We present 87 candidates for RR Lyrae variable stars in binary systems, based
on our new search using the light-travel time effect (LTTE) and observed -
calculated ($O-C$) diagrams in the Galactic bulge time-series photometry of the
Optical Gravitational Lensing Experiment. Out of these, 61 are new candidates,
while 26 have been announced previously. Furthermore, 12 stars considered as
binary candidates in earlier works are discarded from the list, either as they
were found to have $O-C$ diagrams incompatible with the LTTE or because their
long-term periodicity is definitely caused by the Blazhko effect. This sample
of RR Lyrae binary candidates allows us to draw the first firm conclusions
about the population of such objects: no candidate has an orbital period below
1000 days, while their occurrence rate steadily increases with increasing
period, and peaks between 3000 and 4000 days; however, the decrease in the
number of stars toward even longer periods is probably the result of
observational biases. The eccentricities show a very significant concentration
between 0.25 and 0.3, with a quarter of candidates found in this single bin,
overlaid on an otherwise flat distribution between 0.05 and 0.6. Only six stars
have higher inferred eccentricities above 0.6. Lastly, the distribution of the
mass functions is highly peculiar, exhibiting strong trimodality. We interpret
these modes as the presence of three distinct groups of companions, with
typical inferred masses of $\sim0.6$, $\sim0.2$, and
$\sim0.067\,\mathrm{M}_\odot$, which can be associated with populations of
white dwarf and main sequence, red dwarf, and brown dwarf companions,
respectively.


Abstract:
  In this review, we discuss critical dynamics of simple nonequilibrium models
on large connectomes, obtained by diffusion MRI, representing the white matter
of the human brain. In the first chapter, we overview graph theoretical and
topological analysis of these networks, pointing out that universality allows
selecting a representative network, the KKI-18, which has been used for
dynamical simulation. The critical and sub-critical behaviour of simple, two-
or three-state threshold models is discussed with special emphasis on
rare-region effects leading to robust Griffiths Phases (GP). Numerical results
of synchronization phenomena, studied by the Kuramoto model, are also shown,
leading to a continuous analog of the GP, termed frustrated synchronization.
The models presented here exhibit dynamical scaling behaviour with exponents in
agreement with brain experimental data if local homeostasis is provided.


Abstract:
  In the whole space $R^d$, $d\ge 2$, we study homogenization of a divergence
form elliptic fourth-order operator $A_\varepsilon$ with measurable
$\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter.
For the resolvent $(A_\varepsilon+1)^{-1}$, acting as an operator from $L^2$ to
$H^2$, we find an approximation with remainder term of order $O(\varepsilon^2)$
as $\varepsilon$ tends to $0$. Relying on this result, we construct the
resolvent approximation with remainder of order $O(\varepsilon^3)$ in the
operator $L^2$-norm. We employ two-scale expansions that involve smoothing.


Abstract:
  In this paper, we consider a wireless multihop device-to-device (D2D) based
mobile edge computing (MEC) system, where the destination wireless device (WD)
is scheduled to compute nomographic functions. Under the MapReduce framework
and motivated by reducing communication resource overhead, we propose a new
multi-level over-the-air (OTA) aggregation scheme for the destination WD to
collect the individual partially aggregated intermediate values (IVAs) for
reduction from multiple source WDs in the data shuffling phase. For OTA
aggregation per level, the source WDs employ a channel inverse structure
multiplied by their individual transmit coefficients in transmission over the
same time frequency resource blocks, and the destination WD finally uses a
receive filtering factor to construct the aggregated IVA. Under this setup, we
develop a unified transceiver design framework that minimizes the mean squared
error (MSE) of the aggregated IVA at the destination WD subject to the source
WDs' individual power constraints, by jointly optimizing the source WDs'
individual transmit coefficients and the destination WD's receive filtering
factor. First, based on the primal decomposition method, we derive the
closed-form solution under the special case of a common transmit coefficient.
It shows that all the source WDs' common transmit is determined by the minimal
transmit power budget among the source WDs. Next, for the general case, we
transform the original problem into a quadratic fractional programming problem,
and then develop a low-complexity algorithm to obtain the (near-) optimal
solution by leveraging Dinkelbach's algorithm along with the Gaussian
randomization method.


Abstract:
  In this paper we develop a concrete and fully implementable approach to the
optimization of functionally generated portfolios in stochastic portfolio
theory. The main idea is to optimize over a family of rank-based portfolios
parameterized by an exponentially concave function on the unit interval. This
choice can be motivated by the long term stability of the capital distribution
observed in large equity markets, and allows us to circumvent the curse of
dimensionality. The resulting optimization problem, which is convex, allows for
various regularizations and constraints to be imposed on the generating
function. We prove an existence and uniqueness result for our optimization
problem and provide a stability estimate in terms of a Wasserstein metric of
the input measure. Then, we formulate a discretization which can be implemented
numerically using available software packages and analyze its approximation
error. Finally, we present empirical examples using CRSP data from the US stock
market, including the performance of the portfolios allowing for dividends,
defaults, and transaction costs.


Abstract:
  Contrastive learning is a family of self-supervised methods where a model is
trained to solve a classification task constructed from unlabeled data. It has
recently emerged as one of the leading learning paradigms in the absence of
labels across many different domains (e.g. brain imaging, text, images).
However, theoretical understanding of many aspects of training, both
statistical and algorithmic, remain fairly elusive.
  In this work, we study the setting of time series -- more precisely, when we
get data from a strong-mixing continuous-time stochastic process. We show that
a properly constructed contrastive learning task can be used to estimate the
transition kernel for small-to-mid-range intervals in the diffusion case.
Moreover, we give sample complexity bounds for solving this task and
quantitatively characterize what the value of the contrastive loss implies for
distributional closeness of the learned kernel. As a byproduct, we illuminate
the appropriate settings for the contrastive distribution, as well as other
hyperparameters in this setup.


Abstract:
  In this paper we propose the first deep unsupervised approach in human body
reconstruction to estimate body surface from a sparse set of landmarks, so
called DeepMurf. We apply a denoising autoencoder to estimate missing
landmarks. Then we apply an attention model to estimate body joints from
landmarks. Finally, a cascading network is applied to regress parameters of a
statistical generative model that reconstructs body. Our set of proposed loss
functions allows us to train the network in an unsupervised way. Results on
four public datasets show that our approach accurately reconstructs the human
body from real world mocap data.


Abstract:
  Two-dimensional (2D) Van Hove singularities (VHSs) associated with the saddle
points or extrema of the energy dispersion usually show logarithmic divergences
in the density of states (DOS). However, recent studies find that the VHSs
originating from higher-order saddle-points have faster-than-logarithmic
divergences, which can amplify electron correlation effects and create exotic
states such as supermetals in 2D materials. Here we report the existence of
'high-order' VHSs in the cuprates and related high-Tc superconductors and show
that the anomalous divergences in their spectra are driven by the electronic
dimensionality of the system being lower than the dimensionality of the
lattice. The order of VHS is found to correlate with the superconducting Tc
such that materials with higher order VHSs display higher Tc's. We further show
that the presence of the normal and higher-order VHSs in the electronic
spectrum can provide a straightforward marker for identifying the propensity of
a material toward correlated phases such as excitonic insulators or
supermetals. Our study opens up a new materials playground for exploring the
interplay between high-order VHSs, superconducting transition temperatures and
electron correlation effects in the cuprates and related high-Tc
superconductors.


Abstract:
  Higher rank symmetry and higher moment conservation have been drawn
considerable attention from, e.g., subdiffusive transport to fracton
topological order. In this paper, we perform a one-loop renormalization group
(RG) analysis and show how these phenomena emerge at low energies. We consider
a $d$-dimensional model of interacting bosons of d components. At
higher-rank-symmetric points with conserved angular moments, the $a$-th bosons
have kinetic energy only along the $x^a$ direction. Therefore, the symmetric
points look highly anisotropic and fine-tuned. By studying RG in a wide
vicinity of the symmetric points, we find that symmetry-disallowed kinetic
terms tend to be irrelevant within the perturbative regime, which potentially
leads to emergent higher-rank symmetry and higher-moment conservation at the
deep infrared limit. While non-perturbative analysis is called for in the
future, by regarding higher-rank symmetry as an emergent phenomenon, the RG
analysis presented in this paper holds alternative promise for realizing
higher-rank symmetry and higher-moment conservation in experimentally
achievable systems.


Abstract:
  Simulation models are widely used in practice to facilitate decision-making
in a complex, dynamic and stochastic environment. But they are computationally
expensive to execute and optimize, due to lack of analytical tractability.
Simulation optimization is concerned with developing efficient sampling schemes
-- subject to a computational budget -- to solve such optimization problems. To
mitigate the computational burden, surrogates are often constructed using
simulation outputs to approximate the response surface of the simulation model.
In this tutorial, we provide an up-to-date overview of surrogate-based methods
for simulation optimization with continuous decision variables. Typical
surrogates, including linear basis function models and Gaussian processes, are
introduced. Surrogates can be used either as a local approximation or a global
approximation. Depending on the choice, one may develop algorithms that
converge to either a local optimum or a global optimum. Representative examples
are presented for each category. Recent advances in large-scale computation for
Gaussian processes are also discussed.


Abstract:
  In this paper we study algebras of modular forms on unitary groups of
signature $(n,1)$. We give a necessary and sufficient condition for an algebra
of unitary modular forms to be free in terms of the modular Jacobian. As a
corollary we obtain a criterion that guarantees in many cases that, if $L$ is
an even lattice with complex multiplication and the ring of modular forms for
its orthogonal group is a polynomial algebra, then the ring of modular forms
for its unitary group is also a polynomial algebra. We prove that a number of
rings of unitary modular forms are freely generated by applying these criteria
to Hermitian lattices over the rings of integers of $\mathbb{Q}(\sqrt{d})$ for
$d=-1,-2,-3$. As a byproduct, our modular groups provide many explicit examples
of finite-covolume reflection groups acting on complex hyperbolic space.


Abstract:
  In bidisperse particle mixtures varying in size or density alone, large
particles rise (driven by percolation) and heavy particles sink (driven by
buoyancy). When the two particle species differ from each other in both size
and density, the two segregation mechanisms either enhance (large/light and
small/heavy) or oppose (large/heavy and small/light) each other. In the latter
case, an equilibrium condition exists in which the two segregation mechanisms
balance and the particles no longer segregate. This leads to a methodology to
design non-segregating particle mixtures by specifying particle size ratio,
density ratio, and mixture concentration to achieve the equilibrium condition.
Using DEM simulations of quasi-2D bounded heap flow, we show that segregation
is significantly reduced for particle mixtures near the equilibrium condition.
In addition, the rise-sink transition for a range of particle size and density
ratios matches the combined size and density segregation model predictions.


Abstract:
  Age estimation is an essential challenge in computer vision. With the
advances of convolutional neural networks, the performance of age estimation
has been dramatically improved. Existing approaches usually treat age
estimation as a classification problem. However, the age labels are ambiguous,
thus make the classification task difficult. In this paper, we propose a simple
yet effective approach for age estimation, which improves the performance
compared to classification-based methods. The method combines four
classification losses and one regression loss representing different class
granularities together, and we name it as Age-Granularity-Net. We validate the
Age-Granularity-Net framework on the CVPR Chalearn 2016 dataset, and extensive
experiments show that the proposed approach can reduce the prediction error
compared to any individual loss. The source code link is
https://github.com/yipersevere/age-estimation.


Abstract:
  In the analysis and control of discrete-time linear systems, the spectral
radius of the system state matrix plays an essential role. Usually, it is
assumed that the system matrices are known, from which the spectral radius can
be directly computed. Instead, we consider the setting where the linear system
is affected by process noises, and one has only finitely many samples of system
input and state measurements. We provide two methods for estimating the
spectral radius and derive error bounds that hold with high probability.
Moreover, we show how to use the derived results to test stabilizability for
networked control systems (NCSs) with lossy channels when only finitely many
samples of system input, state, and the packet drop sequence are available.


Abstract:
  We propose a new model of Early Dark Energy (EDE) as a solution to the Hubble
tension in cosmology, the apparent discrepancy between local measurements of
the Hubble constant $H_0\simeq 74$ km s$^{-1}$ Mpc$^{-1}$ and $H_0\simeq 67$ km
s$^{-1}$ Mpc$^{-1}$ inferred from the Cosmic Microwave Background (CMB). In
Chain EDE, the Universe undergoes a series of first order phase transitions,
starting at a high energy vacuum in a potential, and tunneling down through a
chain of every lower energy metastable minima. As in all EDE models, the
contribution of the vacuum energy to the total energy density of the universe
is initially negligible, but reaches $\sim 10\%$ around matter-radiation
equality, before cosmological data require it to redshift away quickly -- at
least as fast as radiation. We indeed obtain this required behavior with a
series of $N$ tunneling events, and show that for $N>600$ the phase transitions
are rapid enough to allow fast percolation and thereby avoid large scale
anisotropies in the CMB. We construct a specific example of Chain EDE featuring
a scalar field in a quasiperiodic potential (a tilted cosine), which is
ubiquitous in axion physics and, therefore, carries strong theoretical
motivation. Interestingly, the energy difference between vacua can be roughly
the size of today's Dark Energy (meV scale). Therefore, the end result of Chain
EDE could provide a natural explanation of Dark Energy, if the tunneling
becomes extremely slow in the final step before the field reaches zero (or
negative) energy. We discuss a simple mechanism which can stop the scalar field
in the desired minimum. Thus Chain EDE offers the exciting prospect to explain
EDE and Dark Energy by the same scalar field.


Abstract:
  The development of silicon anodes to replace conventional graphite in efforts
to increase energy densities of lithium-ion batteries has been largely impeded
by poor interfacial stability against liquid electrolytes. Here, stable
operation of 99.9 weight% micro-Si (uSi) anode is enabled by utilizing the
interface passivating properties of sulfide based solid-electrolytes. Bulk to
surface characterization, as well as quantification of interfacial components
showed that such an approach eliminates continuous interfacial growth and
irreversible lithium losses. In uSi || layered-oxide full cells, high current
densities at room temperature (5 mA cm 2), wide operating temperature
(-20{\deg}C to 80{\deg}C) and high loadings (>11 mAh cm-2) were demonstrated
for both charge and discharge operations. The promising battery performance can
be attributed to both the desirable interfacial property between uSi and
sulfide electrolytes, as well as the unique chemo-mechanical behavior of the
Li-Si alloys.


Abstract:
  Great achievements in last five years, such as record-efficient
amorphous/crystalline silicon heterojunction (SHJ) solar cells and cutting-edge
perovskite/SHJ tandem solar cells, place hydrogenated amorphous silicon
(a-Si:H) at the forefront of emerging photovoltaics. Due to the extremely low
doping efficiency of trivalent boron (B) in amorphous tetravalent silicon,
light harvesting of aforementioned devices are limited by their fill factors
(FF), which is a direct metric of the charge carrier transport. It is
challenging but crucial to develop highly conductive doped a-Si:H for
minimizing the FF losses. Here we report intensive light soaking can
efficiently boost the dark conductance of B-doped a-Si:H "thin" films, which is
an abnormal Staebler-Wronski effect. By implementing this abnormal effect to
SHJ solar cells, we achieve a certificated power conversion efficiency (PCE) of
25.18% (26.05% on designated area) with FF of 85.42% on a 244.63-cm2 wafer.
This PCE is one of the highest reported values for total-area "top/rear"
contact silicon solar cells. The FF reaches 98.30 per cent of its
Shockley-Queisser limit.


Abstract:
  In this work, we analyse the properties of the Maupertuis' action as a tool
to reveal the phase space structure for Hamiltonian systems. We construct a
scalar field with the action's values along the trajectories in the phase
space. The different behaviour of the trajectories around important phase space
objects like unstable periodic orbits, their stable and unstable manifolds, and
KAM islands generate characteristic patterns on the scalar field constructed
with the action. Using these different patterns is possible to identify the
skeleton of the phase space and understand the dynamics. Also, we present a
simple argument based on the conservation of the energy and the behaviour of
the trajectories to understand the values of their actions. In order to show
how this tool reveals the phase space structures and its effectiveness, we
compare the scalar field constructed with the actions with Poincare maps for
the same set of initial conditions in the phase space of an open Hamiltonian
system with 2 degrees of freedom.


Abstract:
  Imperfect labels limit the quality of predictions learned by deep neural
networks. This is particularly relevant in medical image segmentation, where
reference annotations are difficult to collect and vary significantly even
across expert annotators. Prior work on mitigating label noise focused on
simple models of mostly uniform noise. In this work, we explore biased and
unbiased errors artificially introduced to brain tumour annotations on MRI
data. We found that supervised and semi-supervised segmentation methods are
robust or fairly robust to unbiased errors but sensitive to biased errors. It
is therefore important to identify the sorts of errors expected in medical
image labels and especially mitigate the biased errors.


Abstract:
  In this paper, we consider the motion of incompressible magnetohydrodynamics
(MHD) with resistivity in a domain bounded by a free surface. The free boundary
problem for MHD is an important problem not only for mathematical fluid
dynamics but also some application to the field of engineering In fact, when a
thermonuclear reaction is caused artificially, a high-temperature plasma is
sometimes subjected to a magnetic field and held in the air, and the boundary
of the fluid at this time is a free one. In this paper, an electromagnetic
field generated by some currents in an external domain keeps an MHD flow in a
bounded domain. On the free surface, free boundary conditions for MHD flow and
transmission conditions for electromagnetic fields are imposed. We proved the
local well-posedness in the general setting of domains from a mathematical
point of view. The solutions are obtained in the maximal regularity class, and
in particular, the regularity class of velocity fields is one more higher than
the regularity class of magnetic fields. To prove our main result, we use Lp-Lq
maximal regularity theorem for the Stokes equations with free boundary
conditions and for the magnetic field equations with transmission conditions.


Abstract:
  Interface of transition metal dichalcogenide (TMDC) and high-k dielectric
transition metal oxides (TMO) had triggerred umpteen discourses due to the
indubitable impact of TMO in reducing the contact resistances and restraining
the Fermi-level pinning for the metal-TMDC contacts. In the present work, we
focus on the unresolved tumults of large-area TMDC/TMO interfaces, grown by
adopting different techniques. Here, on a pulsed laser deposited (PLD) MoS2
thin film, a layer of TiO2 is grown by using both atomic layer deposition (ALD)
and PLD. These two different techniques emanate TiO2 layers with different
crystalline properties, thicknesses and interfacial morphologies, subsequently
influencing the electronic and optical properties of the interfaces. In
addition, they manifest a boost in the extent of p-type doping with increasing
thickness of TiO2, as emerged after analyzing the core-level shifts of the
X-ray photoelectron spectra (XPS). Density functional analysis of the
MoS2/Anatase-TiO2 interfaces, for pristine and in presence of a wide range of
interfacial defects, could explain the interdependence of doping and the
terminating atomic-surface of TiO2 on MoS2. The optical properties of the
interface, encompassing the photoluminescence, transient absorption and z-scan
two-photon absorption indicate the presence of defect-induced localized mid-gap
levels in MoS2/TiO2 (PLD), resulting quenched exciton signals. On the contrary,
the relatively defect-free interface in MoS2/TiO2 (ALD) demonstrates a clear
presence of both A and B excitons of MoS2. From the investigation of optical
properties, we indicate that MoS2/TiO2 (PLD) interface may act as a promising
saturable absorber. Moreover, MoS2/TiO2 (PLD) interface had resulted a better
photo-transport. A potential application of MoS2/TiO2 (PLD) is demonstrated by
the fabrication of a p-type photo-transistor with the ionic-gel top gate.


Abstract:
  Massive stars die an explosive death as a core-collapse supernova (CCSN). The
exact physical processes that cause the collapsing star to rebound into an
explosion are not well-understood, and the key in resolving this issue may lie
in the measurement of the shape of CCSNe ejecta. Spectropolarimetry is the only
way to perform this measurement for CCSNe outside of the Milky Way and
Magellanic Clouds. We present an infrared (IR) spectropolarimetric detection of
a CCSN, enabled by the new highly sensitive WIRC+Pol instrument at Palomar
Observatory, that can observe CCSNe (M = -17 mags) out to 20 Mpc to ~0.1%
polarimetric precision. IR spectropolarimetry is less affected than optical by
dust scattering in the circumstellar and interstellar media, thereby providing
a more unbiased probe of the intrinsic geometry of the SN ejecta. SN 2018hna, a
SN 1987A-like explosion, shows 2.0+-0.3% continuum polarization in the J band
oriented at ~160 degree on-sky at 182 d after the explosion. Assuming prolate
geometry like in SN 1987A, we infer an ejecta axis ratio of <0.48 with the axis
of symmetry pointing at 70 degree position angle. The axis ratio is similar to
that of SN 1987A suggesting that they may share intrinsic geometry and
inclination angle. Our data do not rule out oblate ejecta. We also observe one
other core-collapse and two thermonuclear SNe in the J band. SN 2020oi, a
stripped-envelope Type Ic SN in Messier 100 has p = 0.37+-0.09% at peak light,
indicative of either a 10% asymmetry or host interstellar polarization. The SNe
Ia, 2019ein and 2020ue have p < 0.33% and < 1.08% near peak light, indicative
of asymmetries of less than 10% and 20%, respectively.


Abstract:
  We study large uniform random maps with one face whose genus grows linearly
with the number of edges. They can be seen as a model of discrete hyperbolic
geometry. In the past, several of these hyperbolic geometric features have been
discovered, such as their local limit or their logarithmic diameter. In this
work, we show that with high probability such a map contains a very large
induced subgraph that is an expander.


Abstract:
  We propose and explore a physical mechanism for the stabilization of the
complex spatiotemporal dynamics in arrays (bars) of broad area laser diodes
taking advantage of the symmetry breaking in non-Hermitian potentials. We show
that such stabilization can be achieved by specific pump and index profiles
leading to a PT-symmetric coupling between nearest neighboring lasers within
the semiconductor bar. A numerical analysis is performed using a complete
(2+1)-dimensional space-temporal model, including transverse and longitudinal
spatial degrees of freedom and temporal evolution of the electric field and
carriers. We show regimes of temporal stabilization and light emission spatial
redistribution and enhancement. We also consider a simplified (1+1)-dimensional
model for an array of lasers holding the proposed non-Hermitian coupling with a
global axisymmetric geometry. We numerically demonstrate a two-fold benefit:
the control over the temporal dynamics over the EELs bar and the field
concentration on the central lasers leading to a brighter output beam,
facilitating a direct coupling to an optical fiber.


Abstract:
  A particular case of the fundamental Sz.-Nagy--Foias functional model for a
contraction states that a pure contraction always dilates to a pure isometry.
We are interested in the similar question for pairs, more precisely: does a
pair of commuting pure contractions always dilate to a pair of commuting pure
isometries? The purpose of this article is to identify pairs of commuting pure
contractions for which the above question has an affirmative answer. Our method
is based on an explicit structure of isometric dilation for pure pairs of
commuting contractions obtained in a recent work by Das, Sarkar and the author.


Abstract:
  Spin systems such as silicon or nitrogen vacancy centers in diamond, quantum
dots and quantum dot molecules coupled to optical cavities appear as key
elements for creating quantum networks as not only constituting the nodes of
the network, but also assisting the creation of photonic networks. Here we
study deterministic preparation of arbitrary size $W$ states with spin systems.
We present an efficient operation on three qubits, two being the logical qubits
and one being the ancillary qubit, where no interaction between the logical
qubits are required. The proposed operation can create a $W$-type
Einstein-Podolsky-Rosen (EPR) pair from two separable qubits, and expand that
EPR pair or an arbitrary size $W$ state by one, creating a $W$-like state.
Taking this operation as the fundamental building block, we show how to create
a large scale $W$ state out of separable qubits, or double the size of a $W$
state. Based on this operation and focusing on nitrogen vacancy (NV) centers in
diamond as an exemplary spin system, we propose a setup for preparing $W$
states of circularly polarized photons, assisted by a single spin qubit, where
no photon-photon interactions are required. Next, we propose a setup for
preparing $W$ states of spin qubits of spatially separated systems, assisted by
a single photon. We also analyze the effects of possible imperfections in
implementing the gates on the fidelity of the generated $W$ states. In our
setups, neither post-measurement, nor post-processing on the states of spin or
photonic qubit is required. Our setups can be implemented with current
technology, and we anticipate that they contribute to quantum science and
technologies.


Abstract:
  Route choice models in public transport have been discussed for a long time.
The main factor why a passenger chooses a specific path is usually based on its
length or travel time. However, also the ticket price that passengers have to
pay may influence their decision since passengers prefer cheaper paths over
more expensive ones. In this paper, we deal with the cheapest ticket problem
which asks for a cheapest ticket to travel between a pair of stations. The
complexity and the algorithmic approach to solve this problem depend crucially
on the underlying fare structure, e.g., it is easy if the ticket prices are
proportional to the distance traveled (as in distance tariff fare structures),
but may become NP-complete in zone tariff fare structures. We hence discuss the
cheapest ticket problem for different variations of distance- and zone-based
fare structures. We start by modeling the respective fare structure
mathematically, identify its main properties, and finally provide a polynomial
algorithm, or prove NP-completeness of the cheapest ticket problem. We also
provide general results on the combination of two fare structures, which is
often observed in practice.


Abstract:
  Ensuring a faithful interaction with data and its representation for
humanities can and should depend on expert-constructed ground truths.


Abstract:
  Celebrated theorems of Roth and of Matou\v{s}ek and Spencer together show
that the discrepancy of arithmetic progressions in the first $n$ positive
integers is $\Theta(n^{1/4})$. We study the analogous problem in the
$\mathbb{Z}_n$ setting. We asymptotically determine the logarithm of the
discrepancy of arithmetic progressions in $\mathbb{Z}_n$ for all positive
integer $n$. We further determine up to a constant factor the discrepancy of
arithmetic progressions in $\mathbb{Z}_n$ for many $n$. For example, if $n=p^k$
is a prime power, then the discrepancy of arithmetic progressions in
$\mathbb{Z}_n$ is $\Theta(n^{1/3+r_k/(6k)})$, where $r_k \in \{0,1,2\}$ is the
remainder when $k$ is divided by $3$. This solves a problem of Hebbinghaus and
Srivastav.


Abstract:
  We study a nonlocal parametric problem driven by the fractional Laplacian
operator combined with a Kirchhoff-type coefficient and involving a critical
nonlinearity term in the sense of Sobolev embeddings. Our approach is of
variational and topological nature. The obtained results can be viewed as a
nontrivial extension to the nonlocal setting of some recent contributions
already present in the literature.


Abstract:
  Canonical quantization covers a broad class of classical systems, but that
does not include all the problems of interest. Affine quantization has the
benefit of providing a successful quantization of many important problems
including the quantization of half-harmonic oscillators [1] nonrenormalizable
scalar fields, such as $(\varphi^{12})_3$ [2], and $(\varphi^4)_4$ [3], as well
as the quantum theory of Einstein's general relativity [4]. The features that
distinguish affine quantization are emphasized, especially, that affine
quantization differs from canonical quantization only by the choice of
classical variables promoted to quantum operators. Coherent states are used to
ensure proper quantizations are physically correct. While quantization of
nonrenormalizable covariant scalars and gravity are difficult, we focus on
appropriate ultralocal scalars and gravity which are fully soluble while, in
that case, implying that affine quantization is the proper procedure to ensure
the validity of affine quantizations for nonrenormalizable covariant scalar
fields and Einstein's gravity.


Abstract:
  There is a growing interest in developing computer vision methods that can
learn from limited supervision. In this paper, we consider the problem of
learning to predict camera viewpoints, where obtaining ground-truth annotations
are expensive and require special equipment, from a limited number of labeled
images. We propose a semi-supervised viewpoint estimation method that can learn
to infer viewpoint information from unlabeled image pairs, where two images
differ by a viewpoint change. In particular our method learns to synthesize the
second image by combining the appearance from the first one and viewpoint from
the second one. We demonstrate that our method significantly improves the
supervised techniques, especially in the low-label regime and outperforms the
state-of-the-art semi-supervised methods.


Abstract:
  A number of auditory models have been developed using diverging approaches,
either physiological or perceptual, but they share comparable stages of signal
processing, as they are inspired by the same constitutive parts of the auditory
system. We compare eight monaural models that are openly accessible in the
Auditory Modelling Toolbox. We discuss the considerations required to make the
model outputs comparable to each other, as well as the results for the
following model processing stages or their equivalents: outer and middle ear,
cochlear filter bank, inner hair cell, auditory nerve synapse, cochlear
nucleus, and inferior colliculus. The discussion includes some practical
considerations related to the use of monaural stages in binaural frameworks.


Abstract:
  Bayesian inference provides a uniquely rigorous approach to obtain principled
justification for uncertainty in predictions, yet it is difficult to articulate
suitably general prior belief in the machine learning context, where
computational architectures are pure abstractions subject to frequent
modifications by practitioners attempting to improve results. Parsimonious
inference is an information-theoretic formulation of inference over arbitrary
architectures that formalizes Occam's Razor; we prefer simple and sufficient
explanations. Our universal hyperprior assigns plausibility to prior
descriptions, encoded as sequences of symbols, by expanding on the core
relationships between program length, Kolmogorov complexity, and Solomonoff's
algorithmic probability. We then cast learning as information minimization over
our composite change in belief when an architecture is specified, training data
are observed, and model parameters are inferred. By distinguishing model
complexity from prediction information, our framework also quantifies the
phenomenon of memorization.
  Although our theory is general, it is most critical when datasets are
limited, e.g. small or skewed. We develop novel algorithms for polynomial
regression and random forests that are suitable for such data, as demonstrated
by our experiments. Our approaches combine efficient encodings with prudent
sampling strategies to construct predictive ensembles without cross-validation,
thus addressing a fundamental challenge in how to efficiently obtain
predictions from data.


Abstract:
  Electronic degrees of freedom and their coupling to lattice vibrations in
semiconductors can be strongly modified by doping. Accordingly, the addition of
surplus charge carriers to chirality-mixed carbon nanotube samples has
previously been found to give rise to a Drude-type plasmon feature as well as
Fanotype antiresonances in the far- to mid-infrared spectral range (FIR/MIR).
Here we investigate the FIR/MIR response of redox-chemically doped
semiconducting (6,5) carbon nanotubes (s-SWNTs). We find that, contrary to
expectations, the Drude-type plasmon shifts to lower wavenumbers with
increasing doping level. By means of Monte-Carlo simulations of the optical
response, we attribute this behavior to the confinement of excess charge
carriers at low doping levels and their progressive delocalization when
approaching degenerate doping. The coupling of vibrational modes to intraband
excitations in the doped s-SWNTs can be probed via a double resonance process
similar to that responsible for the Raman D-band. The resulting Fano
antiresonances shed new light onto the character and coupling of electronic and
vibrational degrees of freedom in these one-dimensional semiconductors.


Abstract:
  We study dense packings of a large number of congruent non-overlapping
circles inside a square by looking for configurations which maximize the
packing density, defined as the ratio between the area occupied by the disks
and the area of the square container. The search for these configurations is
carried out with the help of two algorithms that we have devised: a first
algorithm is in charge of obtaining sufficiently dense configurations starting
from a random guess, while a second algorithm improves the configurations
obtained in the first stage. The algorithms can be used sequentially or
independently. The performance of these algorithms is assessed by carrying out
numerical tests for configurations with a large number of circles.


Abstract:
  In this paper, we propose HOME, a framework tackling the motion forecasting
problem with an image output representing the probability distribution of the
agent's future location. This method allows for a simple architecture with
classic convolution networks coupled with attention mechanism for agent
interactions, and outputs an unconstrained 2D top-view representation of the
agent's possible future. Based on this output, we design two methods to sample
a finite set of agent's future locations. These methods allow us to control the
optimization trade-off between miss rate and final displacement error for
multiple modalities without having to retrain any part of the model. We apply
our method to the Argoverse Motion Forecasting Benchmark and achieve 1st place
on the online leaderboard.


Abstract:
  Engineering materials to include nanoscale porosity or other nanoscale
structures has become a well-established strategy for enhancing the
thermoelectric performance of dielectrics. However, the approach is only
considered beneficial for materials where the intrinsic phonon mean-free path
is much longer than that of the charge carriers. As such, the approach would
not be expected to provide significant performance gains in polycrystalline
semiconducting alloys, such as SixGe1-x, where mass disorder and grains provide
strong phonon scattering. In this manuscript, we demonstrate that the addition
of nanoscale porosity to even ultrafine-grained Si0.8Ge0.2 may be worthwhile.
The semiclassical Boltzmann transport equation was used to model electrical and
phonon transport in polycrystalline Si0.8Ge0.2 containing prismatic pores
perpendicular to the transport current. The models are free of tuning
parameters and were validated against experimental data. The models reveal that
a combination of pores and grain boundaries suppresses phonon conductivity to a
magnitude comparable with the electronic thermal conductivity. In this regime,
ZT can be further enhanced by reducing carrier concentration to the electrical
and electronic thermal conductivity and simultaneously increasing thermopower.
Although increases in ZT are modest, the optimal carrier concentration is
significantly lowered, meaning semiconductors need not be so strongly
supersaturated with dopants.


Abstract:
  To plan safe and comfortable trajectories for automated vehicles on highways,
accurate predictions of traffic situations are needed. So far, a lot of
research effort has been spent on detecting lane change maneuvers rather than
on estimating the point in time a lane change actually happens. In practice,
however, this temporal information might be even more useful. This paper deals
with the development of a system that accurately predicts the time to the next
lane change of surrounding vehicles on highways using long short-term
memory-based recurrent neural networks. An extensive evaluation based on a
large real-world data set shows that our approach is able to make reliable
predictions, even in the most challenging situations, with a root mean squared
error around 0.7 seconds. Already 3.5 seconds prior to lane changes the
predictions become highly accurate, showing a median error of less than 0.25
seconds. In summary, this article forms a fundamental step towards downstreamed
highly accurate position predictions.


Abstract:
  Can we make undergraduate engineering education easier and more fun? This
research aims to see if we can answer the ambitious question! The digital
game-based learning (DGBL) has been found to increase the efficacy of learning
when applied in engineering classes thanks to its ability to make students feel
easy and fun. However, the state-of-the-art DGBL schemes still observe
challenges in various aspects including cost, efficacy, readiness of
instructors and students, etc. Motivated from the challenges, this research
proposes to design a DGBL platform that features visualized and systematic
views. Specifically, we identify the blockchain applied to wireless
communications and networking systems as a key ecosystem that we capitalize the
benefit of the proposed platform.. As such, in this paper, we lay out a
comprehensive DGBL pedagogy that includes (i) creation of relevant assignment
activities and class materials in a relevant course and (ii) evaluation of the
pedagogical efficacy. In a long-term view, a successful delivery of this
research will increase the confidence of undergraduate engineering students on
the "in-concert" dynamics of various factors determining the performance of a
blockchain system built on a wireless network.


Abstract:
  We reveal intrinsic topological vector potentials underlying the nonlinear
waves governed by one-dimensional nonlinear Schr\"{o}dinger equations by
investigating the Berry connection of the linearized Bogoliubov-de-Gennes (BdG)
equations in an extended complex coordinate space. Surprisingly, we find that
the density zeros of these nonlinear waves exactly correspond to the degenerate
points of the BdG energy spectra and can constitute monopole fields with a
quantized magnetic flux of elementary $\pi$. Such a vector potential consisting
of paired monopoles with opposite charges can completely capture the essential
characteristics of nonlinear wave evolution. As an application, we investigate
rogue waves and explain their exotic property of ``appearing from nowhere and
disappearing without a trace'' by means of a monopole collision mechanism. The
maximum amplification ratio and multiple phase steps of a high-order rogue wave
are found to be closely related to the number of monopoles. Important
implications of the intrinsic topological vector potentials are discussed.


Abstract:
  Chaotic quantum many-body dynamics typically lead to relaxation of local
observables. In this process, known as quantum thermalization, a subregion
reaches a thermal state due to quantum correlations with the remainder of the
system, which acts as an intrinsic bath. While the bath is generally assumed to
be unobserved, modern quantum science experiments have the ability to track
both subsystem and bath at a microscopic level. Here, by utilizing this
ability, we discover that measurement results associated with small subsystems
exhibit universal random statistics following chaotic quantum many-body
dynamics, a phenomenon beyond the standard paradigm of quantum thermalization.
We explain these observations with an ensemble of pure states, defined via
correlations with the bath, that dynamically acquires a close to random
distribution. Such random ensembles play an important role in quantum
information science, associated with quantum supremacy tests and device
verification, but typically require highly-engineered, time-dependent control
for their preparation. In contrast, our approach uncovers random ensembles
naturally emerging from evolution with a time-independent Hamiltonian. As an
application of this emergent randomness, we develop a benchmarking protocol
which estimates the many-body fidelity during generic chaotic evolution and
demonstrate it using our Rydberg quantum simulator. Our work has wide ranging
implications for the understanding of quantum many-body chaos and
thermalization in terms of emergent randomness and at the same time paves the
way for applications of this concept in a much wider context.


Abstract:
  We introduce a domain decomposition-based nonlinear preconditioned iteration
for solving nonlinear, nonsmooth elliptic optimal control problems, with a
nonlinear reaction term, $L^1$ regularization and box constraints on the
control function. The method is obtained by applying semismooth Newton to the
fixed-point equation of the parallel optimized Schwarz iteration. As a proof of
concept, numerical experiments are performed on two subdomains, as well as on a
multi-subdomain test case. The results show that it is possible to obtain
substantial improvements in robustness and efficiency with the new method,
relative to semismooth Newton applied directly to the full optimization
problem, provided appropriate Robin parameters and a good continuation strategy
are chosen.


Abstract:
  State-of-the-art temporal action detectors to date are based on two-stream
input including RGB frames and optical flow. Although combining RGB frames and
optical flow boosts performance significantly, optical flow is a hand-designed
representation which not only requires heavy computation, but also makes it
methodologically unsatisfactory that two-stream methods are often not learned
end-to-end jointly with the flow. In this paper, we argue that optical flow is
dispensable in high-accuracy temporal action detection and image level data
augmentation (ILDA) is the key solution to avoid performance degradation when
optical flow is removed. To evaluate the effectiveness of ILDA, we design a
simple yet efficient one-stage temporal action detector based on single RGB
stream named DaoTAD. Our results show that when trained with ILDA, DaoTAD has
comparable accuracy with all existing state-of-the-art two-stream detectors
while surpassing the inference speed of previous methods by a large margin and
the inference speed is astounding 6668 fps on GeForce GTX 1080 Ti. Code is
available at \url{https://github.com/Media-Smart/vedatad}.


Abstract:
  Approximate Bayesian inference methods that scale to very large datasets are
crucial in leveraging probabilistic models for real-world time series. Sparse
Markovian Gaussian processes combine the use of inducing variables with
efficient Kalman filter-like recursions, resulting in algorithms whose
computational and memory requirements scale linearly in the number of inducing
points, whilst also enabling parallel parameter updates and stochastic
optimisation. Under this paradigm, we derive a general site-based approach to
approximate inference, whereby we approximate the non-Gaussian likelihood with
local Gaussian terms, called sites. Our approach results in a suite of novel
sparse extensions to algorithms from both the machine learning and signal
processing literature, including variational inference, expectation
propagation, and the classical nonlinear Kalman smoothers. The derived methods
are suited to large time series, and we also demonstrate their applicability to
spatio-temporal data, where the model has separate inducing points in both time
and space.


Abstract:
  This article describes research on claim verification carried out using a
multiple GAN-based model. The proposed model consists of three pairs of
generators and discriminators. The generator and discriminator pairs are
responsible for generating synthetic data for supported and refuted claims and
claim labels. A theoretical discussion about the proposed model is provided to
validate the equilibrium state of the model. The proposed model is applied to
the FEVER dataset, and a pre-trained language model is used for the input text
data. The synthetically generated data helps to gain information which helps
the model to perform better than state of the art models and other standard
classifiers.


Abstract:
  In this paper, we prove Sp\"ath's Character Triple Conjecture for
$p$-solvable groups. This is a conjecture proposed by Sp\"ath during the
reduction process of Dade's Projective Conjecture to quasisimple groups. In
addition, as suggested by Isaacs and Navarro, we take into account the
$p$-residue of characters.


Abstract:
  We construct a gauge theory based in the supergroup $G=SU(2,2|2)$ that
generalizes MacDowell-Mansouri supergravity. This is done introducing an
extended notion of Hodge operator in the form of an outer automorphism of
$su(2,2|2)$-valued 2-form tensors. The model closely resembles a Yang-Mills
theory -- including the action principle, equations of motion and gauge
transformations -- which avoids the use of the otherwise complicated component
formalism. The theory enjoys $H=SO(3,1)\times \mathbb{R} \times U(1)\times
SU(2)$ off-shell symmetry whilst the broken symmetries $G/H$, translation-type
symmetries and supersymmetry, can be recovered on surface of integrability
conditions of the equations of motion, for which it suffices the
Rarita-Schwinger equation and torsion-like constraints to hold. Using the
\textit{matter ansatz} -- projecting the $1 \otimes 1/2$ reducible
representation into the spin-$1/2$ irreducible sector -- we obtain (chiral)
fermion models with gauge and gravity interactions.


Abstract:
  Subspace methods are essential to high-resolution environment sensing in the
emerging unmanned systems, if further combined with the millimeter-wave
(mm-Wave) massive multi-input multi-output (MIMO) technique. The estimation of
signal/noise subspace, as one critical step, is yet computationally complex and
presents a particular challenge when developing high-resolution yet
low-complexity automotive radars. In this work, we develop a fast
randomized-MUSIC (R-MUSIC) algorithm, which exploits the random matrix
sketching to estimate the signal subspace via approximated computation. Our new
approach substantially reduces the time complexity in acquiring a high-quality
signal subspace. Moreover, the accuracy of R-MUSIC suffers no degradation
unlike others low-complexity counterparts, i.e. the high-resolution angle of
arrival (AoA) estimation is attained. Numerical simulations are provided to
validate the performance of our R-MUSIC method. As shown, it resolves the
long-standing contradiction in complexity and accuracy of MIMO radar signal
processing, which hence have great potentials in real-time super-resolution
automotive sensing.


Abstract:
  The amount of data, manpower and capital required to understand, evaluate and
agree on a group of symptoms for the elementary prognosis of pandemic diseases
is enormous. In this paper, we present FedPandemic, a novel noise
implementation algorithm integrated with cross-device Federated learning for
Elementary symptom prognosis during a pandemic, taking COVID-19 as a case
study. Our results display consistency and enhance robustness in recovering the
common symptoms displayed by the disease, paving a faster and cheaper path
towards symptom retrieval while also preserving the privacy of patient's
symptoms via Federated learning.


Abstract:
  In this paper we analyze some interesting features of the thermodynamics of
the rotating BTZ black hole from the Carath\'{e}odory axiomatic postulate, for
which, we exploit the appropriate Pfaffian form. The allowed adiabatic
transformations are then obtained by solving the corresponding Cauchy problem,
and are studied accordingly. Furthermore, we discuss the implications of our
approach, regarding the the second and third laws of black hole thermodynamics.
In particular, the merging of two extremal black holes is studied in detail.


Abstract:
  Preregistration refers to the practice of specifying what you are going to
do, and what you expect to find in your study, before carrying out the study.
This practice is increasingly common in medicine and psychology, but is rarely
discussed in NLP. This paper discusses preregistration in more detail, explores
how NLP researchers could preregister their work, and presents several
preregistration questions for different kinds of studies. Finally, we argue in
favour of registered reports, which could provide firmer grounds for slow
science in NLP research. The goal of this paper is to elicit a discussion in
the NLP community, which we hope to synthesise into a general NLP
preregistration form in future research.


Abstract:
  Lecture-notes: introducing and discussing basic kp concepts related to bands
interaction at an elementary level to beginners


Abstract:
  In this paper, we consider the evolution of spacelike graphic hypersurfaces
defined over a convex piece of hyperbolic plane $\mathscr{H}^{n}(1)$, of center
at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space
$\mathbb{R}^{n+1}_{1}$ along an anisotropic inverse mean curvature flow with
the vanishing Neumann boundary condition, and prove that this flow exists for
all the time. Moreover, we can show that, after suitable rescaling, the
evolving spacelike graphic hypersurfaces converge smoothly to a piece of
hyperbolic plane of center at origin and prescribed radius, which actually
corresponds to a constant function defined over the piece of $\mathscr{H}^{n}
(1)$, as time tends to infinity. Clearly, this conclusion is an extension of
our previous work [2].


Abstract:
  Multi-armed Bandit (MAB) algorithms identify the best arm among multiple arms
via exploration-exploitation trade-off without prior knowledge of arm
statistics. Their usefulness in wireless radio, IoT, and robotics demand
deployment on edge devices, and hence, a mapping on system-on-chip (SoC) is
desired. Theoretically, the Bayesian approach-based Thompson Sampling (TS)
algorithm offers better performance than the frequentist approach-based Upper
Confidence Bound (UCB) algorithm. However, TS is not synthesizable due to Beta
function. We address this problem by approximating it via a pseudo-random
number generator-based approach and efficiently realize the TS algorithm on
Zynq SoC. In practice, the type of arms distribution (e.g., Bernoulli,
Gaussian, etc.) is unknown and hence, a single algorithm may not be optimal. We
propose a reconfigurable and intelligent MAB (RI-MAB) framework. Here,
intelligence enables the identification of appropriate MAB algorithms for a
given environment, and reconfigurability allows on-the-fly switching between
algorithms on the SoC. This eliminates the need for parallel implementation of
algorithms resulting in huge savings in resources and power consumption. We
analyze the functional correctness, area, power, and execution time of the
proposed and existing architectures for various arm distributions, word-length,
and hardware-software co-design approaches. We demonstrate the superiority of
the RI-MAB over TS and UCB only architectures.


Abstract:
  Accurate and precise terrain estimation is a difficult problem for robot
locomotion in real-world environments. Thus, it is useful to have systems that
do not depend on accurate estimation to the point of fragility. In this paper,
we explore the limits of such an approach by investigating the problem of
traversing stair-like terrain without any external perception or terrain models
on a bipedal robot. For such blind bipedal platforms, the problem appears
difficult (even for humans) due to the surprise elevation changes. Our main
contribution is to show that sim-to-real reinforcement learning (RL) can
achieve robust locomotion over stair-like terrain on the bipedal robot Cassie
using only proprioceptive feedback. Importantly, this only requires modifying
an existing flat-terrain training RL framework to include stair-like terrain
randomization, without any changes in reward function. To our knowledge, this
is the first controller for a bipedal, human-scale robot capable of reliably
traversing a variety of real-world stairs and other stair-like disturbances
using only proprioception.


Abstract:
  Several aspects influence corrosive processes in RC structures, such as
environmental conditions, structural geometry, and mechanical properties. Since
these aspects present large randomnesses, probabilistic models allow a more
accurate description of the corrosive phenomena. On the other hand, the
definition of limit states, applied in the reliability assessment, requires a
proper mechanical model. In this context, this study proposes an accurate
methodology for the mechanical-probabilistic modelling of RC structures
subjected to reinforcements' corrosion. To this purpose, an improved damage
approach is proposed to define the limit states for the probabilistic
modelling, considering three main degradation phenomena: concrete cracking,
rebar yielding, and rebar corrosion caused either by chlorides or carbonation
process. The stochastic analysis is evaluated by the Monte Carlo simulation
method due to the computational efficiency of the LDMC. The proposed
mechanical-probabilistic methodology is implemented in a computational
framework and applied to the analysis of a simply supported RC beam, and a 2D
RC frame. Curves illustrate the probability of failure over a service life of
50 years. Moreover, the proposed model allows drawing the probability of
failure map and then identify the critical failure path for progressive
collapse analysis. Collapse path changes caused by the corrosion phenomena are
observed.


Abstract:
  Recently, the importance of weather parameters and location information to
better understand the context of the communication of children with profound
intellectual and multiple disabilities (PIMD) or severe motor and intellectual
disorders (SMID) has been proposed. However, an investigation on whether these
data can be used to classify their behavior for system optimization aimed for
predicting their behavior for independent communication and mobility has not
been done. Thus, this study investigates whether recalibrating the datasets
including either minor or major behavior categories or both, combining location
and weather data and feature selection method training (Boruta) would allow
more accurate classification of behavior discriminated to binary and multiclass
classification outcomes using eXtreme Gradient Boosting (XGB), support vector
machine (SVM), random forest (RF), and neural network (NN) classifiers.
Multiple single-subject face-to-face and video-recorded sessions were conducted
among 20 purposively sampled 8 to 10 -year old children diagnosed with
PIMD/SMID or severe or profound intellectual disabilities and their caregivers.


Abstract:
  There are two puzzles surrounding the Pleiades, or Seven Sisters. First, why
are the mythological stories surrounding them, typically involving seven young
girls being chased by a man associated with the constellation Orion, so similar
in vastly separated cultures, such as the Australian Aboriginal cultures and
Greek mythology? Second, why do most cultures call them "Seven Sisters" even
though most people with good eyesight see only six stars? Here we show that
both these puzzles may be explained by a combination of the great antiquity of
the stories combined with the proper motion of the stars, and that these
stories may predate the departure of most modern humans out of Africa around
100,000 BC.


Abstract:
  The method of covariant perturbation theory allowed for the computation of
the kernel of the evolution equation on a spin Riemannian manifold. The
proposed axiomatic definition of the covariant effective action introduces the
universal scale parameter, with the length square dimensionality, into a
dimensionless mathematical theory. It is shown that this geometrical result has
a physical meaning of the action of field theory, including gravity. Two lowest
tensor order terms of this functional are independent of a spin group and
local. They reproduce the action of general relativity with the cosmological
constant. The current value of the universal scale can be determined with the
measured Hubble constant. This scale parameter considered as a physical
variable can let us build cosmological theories axiomatically.


Abstract:
  In this work, we provide an asymptotic analysis of the solutions to an
elliptic integro-differential equation. This equation describes the
evolutionary equilibria of a phenotypically structured population, subject to
selection, mutation, and both local and non-local dispersion in a spatially
heterogeneous, possibly patchy, environment. Considering small effects of
mutations, we provide an asymptotic description of the equilibria of the
phenotypic density. This asymptotic description involves a Hamilton-Jacobi
equation with constraint coupled with an eigenvalue problem. Based on such
analysis, we characterize some qualitative properties of the phenotypic density
at equilibrium depending on the heterogeneity of the environment. In
particular, we show that when the heterogeneity of the environment is low, the
population concentrates around a single phenotypic trait leading to a unimodal
phenotypic distribution. On the contrary, a strong fragmentation of the
environment leads to multi-modal phenotypic distributions.


Abstract:
  General equilibrium macroeconomic models are a core tool used by policymakers
to understand a nation's economy. They represent the economy as a collection of
forward-looking actors whose behaviours combine, possibly with stochastic
effects, to determine global variables (such as prices) in a dynamic
equilibrium. However, standard semi-analytical techniques for solving these
models make it difficult to include the important effects of heterogeneous
economic actors. The COVID-19 pandemic has further highlighted the importance
of heterogeneity, for example in age and sector of employment, in macroeconomic
outcomes and the need for models that can more easily incorporate it. We use
techniques from reinforcement learning to solve such models incorporating
heterogeneous agents in a way that is simple, extensible, and computationally
efficient. We demonstrate the method's accuracy and stability on a toy problem
for which there is a known analytical solution, its versatility by solving a
general equilibrium problem that includes global stochasticity, and its
flexibility by solving a combined macroeconomic and epidemiological model to
explore the economic and health implications of a pandemic. The latter
successfully captures plausible economic behaviours induced by differential
health risks by age.


Abstract:
  In a new Weyl 2-spinor approach to Non abelian Gauge Theories, starting with
the local U(1) Gauge group of a previous work, we study now the SU(3) case
corresponding to quarks (antiquarks) interacting with color fields. The
principal difference with the conventional approach is that particle-field
interactions are not described by means of potentials but by the field strength
magnitudes. Some analytical expressions showing similarities with
electrodynamics are obtained. Classical equations that describe the behavior of
quarks under gluon fields might be in principle applied to the quark-gluon
plasma phase existing during the first instants of the Universe.


Abstract:
  This paper studies the nonlinear stability of capillary-gravity waves
propagating along the interface dividing two immiscible fluid layers of finite
depth. The motion in both regions is governed by the incompressible and
irrotational Euler equations, with the density of each fluid being constant but
distinct. A diverse collection of small-amplitude solitary wave solutions for
this system have been constructed by several authors in the case of strong
surface tension (as measured by the Bond number) and slightly subcritical
Froude number. We prove that all of these waves are (conditionally) orbitally
stable in the natural energy space. Moreover, the trivial solution is shown to
be conditionally stable when the Bond and Froude numbers lie in a certain
unbounded parameter region. For the near critical surface tension regime, we
prove that one can infer conditional orbital stability or orbital instability
of small-amplitude traveling waves solutions to the full Euler system from
considerations of a dispersive PDE model equation.
  These results are obtained by reformulating the problem as an
infinite-dimensional Hamiltonian system, then applying a version of the
Grillakis--Shatah--Strauss method recently introduced by Varholm, Wahl\'en, and
Walsh. A key part of the analysis consists of computing the spectrum of the
linearized augmented Hamiltonian at a shear flow or small-amplitude wave. For
this, we generalize an idea used by Mielke to treat capillary-gravity water
waves beneath vacuum.


Abstract:
  The Continuous Spontaneous Localisation (CSL) theory in the cosmological
context is subject to uncertainties related to the choice of the collapse
operator. In this paper, we constrain its form based on generic arguments. We
show that, if the collapse operator is even in the field variables, it is
unable to induce the collapse of the wavefunction. Instead, if it is odd, we
find that only linear operators are such that the outcomes are distributed
according to Gaussian statistics, as required by measurements of the cosmic
microwave background. We discuss implications of these results for previously
proposed collapse operators. We conclude that the cosmological CSL collapse
operator should be linear in the field variables.


Abstract:
  An adaptive variational quantum imaginary time evolution (AVQITE) approach is
introduced that yields efficient representations of ground states for
interacting Hamiltonians on near-term quantum computers. It is based on
McLachlan's variational principle applied to imaginary time evolution of
variational wave functions. The variational parameters evolve deterministically
according to equations of motions that minimize the difference to the exact
imaginary time evolution, which is quantified by the McLachlan distance. Rather
than working with a fixed variational ansatz, where the McLachlan distance is
constrained by the quality of the ansatz, the AVQITE method iteratively expands
the ansatz along the dynamical path to keep the McLachlan distance below a
chosen threshold. This ensures the state is able to follow the quantum
imaginary time evolution path in the system Hilbert space rather than in a
restricted variational manifold set by a predefined fixed ansatz. AVQITE is
used to prepare ground states of H$_4$, H$_2$O and BeH$_2$ molecules, where it
yields compact variational ans\"atze and ground state energies within chemical
accuracy. Polynomial scaling of circuit depth with system size is demonstrated
through a set of AVQITE calculations of quantum spin models. Finally, it is
shown that quantum Lanczos calculations can also be naturally performed
alongside AVQITE without additional quantum resource costs.


Abstract:
  Estimating the features of noise is the first step in a chain of protocols
that will someday lead to fault tolerant quantum computers. The randomized
benchmarking (RB) protocol is designed with this exact mindset, estimating the
average strength of noise in a quantum processor with relative ease in
practice. However, RB, along with most other benchmarking and characterization
methods, is limited in scope because it assumes that the noise is temporally
uncorrelated (Markovian), which is increasingly evident not to be the case.
Here, we combine the RB protocol with a recent framework describing
non-Markovian quantum phenomena to derive a general analytical expression of
the average sequence fidelity (ASF) for non-Markovian RB with the Clifford
group. We show that one can identify non-Markovian features of the noise
directly from the ASF through its deviations from the Markovian case, proposing
a set of methods to collectively estimate these deviations, non-Markovian
memory time-scales, and diagnose (in)coherence of non-Markovian noise in an RB
experiment. Finally, we demonstrate the efficacy of our proposal by means of
several proof-of-principle examples. Our methods are directly implementable and
pave the pathway to better understanding correlated noise in quantum
processors.


Abstract:
  We write down the Algebraic Bethe Ansatz for string theory on
$\mbox{AdS}_3\times\mbox{S}^3\times\mbox{T}^4$ and
$\mbox{AdS}_3\times\mbox{S}^3\times\mbox{K3}$ in its orbifold limits. We use it
to determine the wave-functions of protected closed strings in these
backgrounds and prove that their energies are protected to all orders in
$\alpha'$. We further apply the ABA to find the wave functions of protected
states of $\mbox{AdS}_3\times\mbox{S}^3\times\mbox{S}^3\times \mbox{S}^1$ and
its $\mathbf{Z}_2$ orbifold. Our findings match with protected spectrum
calculations from supergravity, $\mbox{Sym}^N$ orbifolds and apply to the
complete moduli space of these theories, excluding orbifold blow-up modes for
which further analysis is necessary.


Abstract:
  Low temperature optical spectroscopy in applied magnetic fields provides
clear evidence of magnetoelastic coupling in the spin ice material Ho2Ti2O7. In
IR measurements, we observe field dependent features around 61, 72 and 78 meV,
energies corresponding to crystal electronic field doublets. Calculating the
electronic band structure based on the crystal field Hamiltonian allows
determination of crystal field energies, values for the crystal field
parameters, and confirmation that the observed features in IR are consistent
with magnetic-dipole-allowed transitions between 5I8 CEF levels. Additionally,
we identify a weak field-dependent feature near one of the CEF doublets, which
we associate with a vibronic bound state that was previously observed by others
in inelastic neutron measurements.


Abstract:
  Recent work suggests that convolutional neural networks of different
architectures learn to classify images in the same order. To understand this
phenomenon, we revisit the over-parametrized deep linear network model. Our
asymptotic analysis, assuming that the hidden layers are wide enough, reveals
that the convergence rate of this model's parameters is exponentially faster
along directions corresponding to the larger principal components of the data,
at a rate governed by the singular values. We term this convergence pattern the
Principal Components bias (PC-bias). We show how the PC-bias streamlines the
order of learning of both linear and non-linear networks, more prominently at
earlier stages of learning. We then compare our results to the simplicity bias,
showing that both biases can be seen independently, and affect the order of
learning in different ways. Finally, we discuss how the PC-bias may explain
some benefits of early stopping and its connection to PCA, and why deep
networks converge more slowly when given random labels.


Abstract:
  This report gives the reasoning for the setting of the target queue delay
parameter in the reference Linux implementation of PI$^2$ Active Queue
Management (AQM)


Abstract:
  "Transcription bottlenecks", created by a shortage of effective human
transcribers are one of the main challenges to endangered language (EL)
documentation. Automatic speech recognition (ASR) has been suggested as a tool
to overcome such bottlenecks. Following this suggestion, we investigated the
effectiveness for EL documentation of end-to-end ASR, which unlike Hidden
Markov Model ASR systems, eschews linguistic resources but is instead more
dependent on large-data settings. We open source a Yolox\'ochitl Mixtec EL
corpus. First, we review our method in building an end-to-end ASR system in a
way that would be reproducible by the ASR community. We then propose a novice
transcription correction task and demonstrate how ASR systems and novice
transcribers can work together to improve EL documentation. We believe this
combinatory methodology would mitigate the transcription bottleneck and
transcriber shortage that hinders EL documentation.


Abstract:
  Since being launched in 2014, Alexa, Amazon's versatile cloud-based voice
service, is now active in over 100 million households worldwide. Alexa's
user-friendly, personalized vocal experience offers customers a more natural
way of interacting with cutting-edge technology by allowing the ability to
directly dictate commands to the assistant. Now in the present year, the Alexa
service is more accessible than ever, available on hundreds of millions of
devices from not only Amazon but third-party device manufacturers.
Unfortunately, that success has also been the source of concern and
controversy. The success of Alexa is based on its effortless usability, but in
turn, that has led to a lack of sufficient security. This paper surveys various
attacks against Amazon Alexa ecosystem including attacks against the frontend
voice capturing and the cloud backend voice command recognition and processing.
Overall, we have identified six attack surfaces covering the lifecycle of Alexa
voice interaction that spans several stages including voice data collection,
transmission, processing and storage. We also discuss the potential mitigation
solutions for each attack surface to better improve Alexa or other voice
assistants in terms of security and privacy.


Abstract:
  In a recent paper, Madritsch and Tichy established Diophantine inequalities
for the fractional parts of polynomial-like functions. In particular, for
$f(x)=x^k+x^c$ where $k$ is a positive integer and $c>1$ is a non-integer, and
any fixed $\xi\in [0,1]$ they obtained \[\min_{2\leq p\leq X} \Vert \xi \lfloor
f(p)\rfloor \Vert\ll_{k,c,\epsilon} X^{-\rho_1(c,k)+\epsilon}\] for
$\rho_1(c,k)>0$ explicitly given. In the present note, we improve upon their
results in the case $c>k$ and $c>4$.


Abstract:
  In this paper, I reply to the recent article by Jeffery and Verheijen (2020)
'A new soil health policy paradigm: Pay for practice not performance!'. While
expressing support for their call for a more pronounced role of soil protection
in agri-environmental policy, I critically discuss the two main elements of
their specific proposal: its emphasis of the concept of soil health and the
recommendation to use action-based payments as the main policy instrument. I
argue for using soil functions as a more established concept (and thus more
adequate for policy purposes), which is also informationally richer than soil
health. Furthermore, I provide a more differentiated discussion of the relative
advantages and disadvantages of result-based and action-based payments, while
addressing the specific criticisms towards the former that Jeffery and
Verheijen voice. Also, I suggest an alternative approach (a hybrid model-based
scheme) that addresses the limitations of both Jeffery and Verheijen's own
proposal and the valid criticisms they direct at result-based payments.


Abstract:
  White matter fiber clustering (WMFC) enables parcellation of white matter
tractography for applications such as disease classification and anatomical
tract segmentation. However, the lack of ground truth and the ambiguity of
fiber data (the points along a fiber can equivalently be represented in forward
or reverse order) pose challenges to this task. We propose a novel WMFC
framework based on unsupervised deep learning. We solve the unsupervised
clustering problem as a self-supervised learning task. Specifically, we use a
convolutional neural network to learn embeddings of input fibers, using
pairwise fiber distances as pseudo annotations. This enables WMFC that is
insensitive to fiber point ordering. In addition, anatomical coherence of fiber
clusters is improved by incorporating brain anatomical segmentation data. The
proposed framework enables outlier removal in a natural way by rejecting fibers
with low cluster assignment probability. We train and evaluate our method using
200 datasets from the Human Connectome Project. Results demonstrate superior
performance and efficiency of the proposed approach.


Abstract:
  Controllable strong interactions between a nanocavity and a single emitter is
important to manipulating optical emission in a nanophotonic systems but
challenging to achieve. Here a three-dimensional DNA origami, named as DNA rack
(DR) is proposed and demonstrated to deterministically and precisely assemble
single emitters within ultra-small plasmonic nanocavities formed by closely
coupled gold nanorods (AuNRs). The DR uniquely possesses a saddle shape with
two tubular grooves that geometrically allows a snug fit and linearly align two
AuNRs with a bending angle <10{\deg}. It also includes a spacer at the saddle
point to maintain the gap between AuNRs as small as 2-3 nm, forming a
nanocavity estimated to be 20 nm3 and an experimentally measured Q factor of
7.3. A DNA docking strand is designed at the spacer to position a single
fluorescent emitter at nanometer accuracy within the cavity. Using Cy5 as a
model emitter, a ~30-fold fluorescence enhancement and a significantly reduced
emission lifetime (from 1.6 ns to 670 ps) were experimentally verified,
confirming significant emitter-cavity interactions. This DR-templated assembly
method is capable of fitting AuNRs of variable length-to-width aspect ratios to
form anisotropic nanocavities and deterministically incorporating different
single emitters, thus enabling flexible design of both cavity resonance and
emission wavelengths to tailor light-matter interactions at nanometer scale.


Abstract:
  In machine learning we often encounter structured output prediction problems
(SOPPs), i.e. problems where the output space admits a rich internal structure.
Application domains where SOPPs naturally occur include natural language
processing, speech recognition, and computer vision. Typical SOPPs have an
extremely large label set, which grows exponentially as a function of the size
of the output. Existing generalization analysis implies generalization bounds
with at least a square-root dependency on the cardinality $d$ of the label set,
which can be vacuous in practice. In this paper, we significantly improve the
state of the art by developing novel high-probability bounds with a logarithmic
dependency on $d$. Moreover, we leverage the lens of algorithmic stability to
develop generalization bounds in expectation without any dependency on $d$. Our
results therefore build a solid theoretical foundation for learning in
large-scale SOPPs. Furthermore, we extend our results to learning with weakly
dependent data.


Abstract:
  Background: The neutron skin thickness $R_{\rm skin}^{\rm PV}$ of PREX-II is
presented in Phys. Rev. Lett. {\bf 126}, 172502 (2021). The reaction cross
section $\sigma_R$ is useful to determine the matter radius $R_m$ and $R_{\rm
skin}$. For proton scattering, the reaction cross section $\sigma_R$ are
available for $E_{\rm in} > 400$ MeV.
  Method and results: We determine $R_n^{\rm exp}=5.727 \pm 0.071$ fm and
$R_m^{\rm exp}=5.617 \pm 0.044$ fm from $R_p^{\rm exp}$ = 5.444 fm and $R_{\rm
skin}^{\rm PV}$. The $R_p^{\rm GHFB}$ calculated with D1S-GHFB with the angular
momentum projection (AMP). agrees with $R_p^{\rm exp}$. The neutron density
calculated with GHFB+AMP is scaled so as to $R_n^{\rm scaling}=5.727$ fm. The
Love-Franey $t$-matrix model with the scaled densities reproduces the data on
$\sigma_R$.
  Aim: Our aim is to find the $\sigma_R$ of proton scattering consistent with
$R_{\rm skin}^{\rm PV}$.
  Conclusion: The $\sigma_R$ of proton scattering consistent with $R_{\rm
skin}^{\rm PV}$ are $\sigma_R^{\rm exp}$ at $E_{\rm in} = 534.1, 549, 806$ MeV.


Abstract:
  Deep Learning networks have established themselves as providing state of art
performance for semantic segmentation. These techniques are widely applied
specifically to medical detection, segmentation and classification. The advent
of the U-Net based architecture has become particularly popular for this
application. In this paper we present the Dense Recurrent Residual
Convolutional Neural Network(Dense R2U CNN) which is a synthesis of Recurrent
CNN, Residual Network and Dense Convolutional Network based on the U-Net model
architecture. The residual unit helps training deeper network, while the dense
recurrent layers enhances feature propagation needed for segmentation. The
proposed model tested on the benchmark Lung Lesion dataset showed better
performance on segmentation tasks than its equivalent models.


Abstract:
  In this paper, we present a novel implicit glyph shape representation, which
models glyphs as shape primitives enclosed by quadratic curves, and naturally
enables generating glyph images at arbitrary high resolutions. Experiments on
font reconstruction and interpolation tasks verified that this structured
implicit representation is suitable for describing both structure and style
features of glyphs. Furthermore, based on the proposed representation, we
design a simple yet effective disentangled network for the challenging one-shot
font style transfer problem, and achieve the best results comparing to
state-of-the-art alternatives in both quantitative and qualitative comparisons.
Benefit from this representation, our generated glyphs have the potential to be
converted to vector fonts through post-processing, reducing the gap between
rasterized images and vector graphics. We hope this work can provide a powerful
tool for 2D shape analysis and synthesis, and inspire further exploitation in
implicit representations for 2D shape modeling.


Abstract:
  In this paper we present a new approach to tackle complex routing problems
with an improved state representation that utilizes the model complexity better
than previous methods. We enable this by training from temporal differences.
Specifically Q-Learning is employed. We show that our approach achieves
state-of-the-art performance for autoregressive policies that sequentially
insert nodes to construct solutions on the CVRP. Additionally, we are the first
to tackle the MDVRP with machine learning methods and demonstrate that this
problem type greatly benefits from our approach over other ML methods.


Abstract:
  We demonstrate the occurrence of nodal non-Hermitian (NH) phases featuring
exceptional degeneracies in chiral-symmetric disordered quantum wires, where NH
physics naturally arises from the self-energy in a disorder-averaged Green's
function description. Notably, we find that at least two nodal points in the
clean Hermitian system are required for exceptional points to be effectively
stabilized upon adding disorder. We identify and study experimental signatures
of our theoretical findings both in the spectral functions and in mesoscopic
quantum transport properties of the considered systems. Our results are
quantitatively corroborated and exemplified by numerically exact simulations on
a microscopic lattice model. The proposed setting provides a conceptually
minimal framework for the realization and study of topological NH phases in
quantum many-body systems.


Abstract:
  We adapt to global fields of positive characteristic the contents of the book
by Labesse and Waldspurger on the Twisted Trace Formula after the Friday
Morning Seminar.


Abstract:
  Atmospheric turbulence generally limits free-space optical (FSO)
communications, and this problem is severely exacerbated when implementing
highly sensitive and spectrally efficient coherent detection. Specifically,
turbulence induces power coupling from the transmitted Gaussian mode to
higher-order Laguerre-Gaussian (LG) modes, resulting in a significant decrease
of the power that mixes with a single-mode local oscillator (LO). Instead, we
transmit a frequency-offset Gaussian pilot tone along with the data signal,
such that both experience similar turbulence and modal power coupling.
Subsequently, the photodetector (PD) optoelectronically mixes all corresponding
pairs of the beams' modes. During mixing, a conjugate of the turbulence
experienced by the pilot tone is automatically generated and compensates the
turbulence experienced by the data, and nearly all orders of the same
corresponding modes efficiently mix. We demonstrate a 12-Gbit/s
16-quadrature-amplitude-modulation (16-QAM) polarization-multiplexed (PolM) FSO
link that exhibits resilience to emulated turbulence. Experimental results for
turbulence D/r_0~5.5 show up to ~20 dB reduction in the mixing power loss over
a conventional coherent receiver. Therefore, our approach automatically
recovers nearly all the captured data power to enable high-performance coherent
FSO systems.


Abstract:
  Users install many apps on their smartphones, raising issues related to
information overload for users and resource management for devices. Moreover,
the recent increase in the use of personal assistants has made mobile devices
even more pervasive in users' lives. This paper addresses two research problems
that are vital for developing effective personal mobile assistants: target apps
selection and recommendation. The former is the key component of a unified
mobile search system: a system that addresses the users' information needs for
all the apps installed on their devices with a unified mode of access. The
latter, instead, predicts the next apps that the users would want to launch.
Here we focus on context-aware models to leverage the rich contextual
information available to mobile devices. We design an in situ study to collect
thousands of mobile queries enriched with mobile sensor data (now publicly
available for research purposes). With the aid of this dataset, we study the
user behavior in the context of these tasks and propose a family of
context-aware neural models that take into account the sequential, temporal,
and personal behavior of users. We study several state-of-the-art models and
show that the proposed models significantly outperform the baselines.


Abstract:
  Airborne transmission is now believed to be the primary way that COVID-19
spreads. We study the airborne transmission risk associated with holding
in-person classes on university campuses. We utilize a model for airborne
transmission risk in an enclosed room that considers the air change rate for
the room, mask efficiency, initial infection probability of the occupants, and
also the activity level of the occupants. We introduce, and use for our
evaluations, a metric $R_0^{eff}$ that represents the ratio of new infections
that occur over a week due to classroom interactions to the number of infected
individuals at the beginning of the week. This can be seen as a surrogate for
the well-known $R_0$ reproductive number metric, but limited in scope to
classroom interactions and calculated on a weekly basis. The simulations take
into account the possibility of repeated in-classroom interactions between
students throughout the week. We presented model predictions were generated
using Fall 2019 and Fall 2020 course registration data at a large US
university, allowing us to evaluate the difference in transmission risk between
in-person and hybrid programs. We quantify the impact of parameters such as
reduced occupancy levels and mask efficacy. Our simulations indicate that
universal mask usage results in an approximately $3.6\times$ reduction in new
infections through classroom interactions. Moving 90% of the classes online
leads to about $18\times$ reduction in new cases. Reducing class occupancy to
20%, by having hybrid classes, results in an approximately $2.15-2.3\times$
further reduction in new infections.


Abstract:
  High speed microfluidic jets can be generated by a thermocavitation process:
from the evaporation of the liquid inside a microfluidic channel, a rapidly
expanding bubble is formed and generates a jet through a flow focusing effect.
Here, we study the impact and traversing of such jets on a pendant liquid
droplet. Upon impact, an expanding cavity is created, and, above a critical
impact velocity, the jet traverses the entire droplet. We predict the critical
traversing velocity (i) from a simple energy balance and (ii) by comparing the
Young-Laplace and dynamic pressures in the cavity that is created during
impact. We contrast the model predictions against experiments, in which we vary
the liquid properties of the pendant droplet and find good agreement. In
addition, we asses how surfactants and viscoelastic effects influence the
critical impact velocity. Our results are relevant for the study of needle-free
injections, where jets of similar velocities and dimensions are being used.
Given the simplicity of our system we can systematically vary the target
properties and unravel their effect on the impact dynamics, a true challenge
when injecting into real skin.


Abstract:
  Defending computer networks from cyber attack requires coordinating actions
across multiple nodes based on imperfect indicators of compromise while
minimizing disruptions to network operations. Advanced attacks can progress
with few observable signals over several months before execution. The resulting
sequential decision problem has large observation and action spaces and a long
time-horizon, making it difficult to solve with existing methods. In this work,
we present techniques to scale deep reinforcement learning to solve the cyber
security orchestration problem for large industrial control networks. We
propose a novel attention-based neural architecture with size complexity that
is invariant to the size of the network under protection. A pre-training
curriculum is presented to overcome early exploration difficulty. Experiments
show in that the proposed approaches greatly improve both the learning sample
complexity and converged policy performance over baseline methods in
simulation.


Abstract:
  This study was aimed to consider the NG-group that consisting of
transformations on a nonempty set A has no bijection as its element. In
addition, it tried to find the maximal order of these groups. It found the
order of NG-group not greater than n. Our results proved by showing that any
kind of NG-group in the theorem be isomorphic to a permutation group on a
quotient set of A with respect to an equivalence relation on A.


Abstract:
  Logical reasoning tasks over symbols, such as learning arithmetic operations
and computer program evaluations, have become challenges to deep learning. In
particular, even state-of-the-art neural networks fail to achieve
\textit{out-of-distribution} (OOD) generalization of symbolic reasoning tasks,
whereas humans can easily extend learned symbolic rules. To resolve this
difficulty, we propose a neural sequence-to-grid (seq2grid) module, an input
preprocessor that automatically segments and aligns an input sequence into a
grid. As our module outputs a grid via a novel differentiable mapping, any
neural network structure taking a grid input, such as ResNet or TextCNN, can be
jointly trained with our module in an end-to-end fashion. Extensive experiments
show that neural networks having our module as an input preprocessor achieve
OOD generalization on various arithmetic and algorithmic problems including
number sequence prediction problems, algebraic word problems, and computer
program evaluation problems while other state-of-the-art sequence transduction
models cannot. Moreover, we verify that our module enhances TextCNN to solve
the bAbI QA tasks without external memory.


Abstract:
  Based on the continuous interpretation of deep learning cast as an optimal
control problem, this paper investigates the benefits of employing B-spline
basis functions to parameterize neural network controls across the layers.
Rather than equipping each layer of a discretized ODE-network with a set of
trainable weights, we choose a fixed number of B-spline basis functions whose
coefficients are the trainable parameters of the neural network. Decoupling the
trainable parameters from the layers of the neural network enables us to
investigate and adapt the accuracy of the network propagation separated from
the optimization learning problem. We numerically show that the spline-based
neural network increases robustness of the learning problem towards
hyperparameters due to increased stability and accuracy of the network
propagation. Further, training on B-spline coefficients rather than layer
weights directly enables a reduction in the number of trainable parameters.


Abstract:
  We are concerned here with an exact solution to the governing equations for
geophysical fluid dynamics in spherical coordinates which incorporates
discontinuous fluid stratification. This solution represents a steady,
purely--azimuthal equatorial flow with an associated free-surface and an
interface separating two fluid regions, each of which having its own continuous
distribution of density. However, the two density functions do not match along
the interface. Following the derivation of the solution we demonstrate that
there is a well-defined relationship between the imposed pressure at the
free-surface and the resulting distortion of the surface's shape. Moreover,
imposing the continuity of the pressure along the interface generates an
equation that describes (implicitly) the shape of the interface. Interestingly,
it turns out that the interface defining function has infinite regularity.


Abstract:
  Let $\mathcal{T}^*$ be the semi-group maximal function associated to the
Schr\"odinger operator $-\Delta+V(x)$ with $V$ satisfying an appropriate
reverse H\"{o}lder inequality. In this paper, we show that the commutator of
$\mathcal{T}^*$ is a compact operator on $L^p(w)$ for $1<p<\infty$ if $b\in
\text{CMO}_\theta(\rho)(\mathbb{R}^n)$ and $w\in
A_p^{\rho,\theta}(\mathbb{R}^n)$. Here $\text{ CMO}_\theta(\rho)(\mathbb{R}^n)$
denotes the closure of $\mathcal{C}_c^\infty(\mathbb{R}^n)$ in the
$\text{BMO}_\theta(\rho)(\mathbb{R}^n)$ (which is larger than the classical
$\text{BMO}(\mathbb{R}^n)$ space) topology. The space where $b$ belongs and the
weighs class $w$ belongs are more larger than the usual
$\text{CMO}(\mathbb{R}^n)$ space and the Muckenhoupt $A_p$ weights class,
respectively.


Abstract:
  We present a context classification pipeline to allow a robot to change its
navigation strategy based on the observed social scenario. Socially-Aware
Navigation considers social behavior in order to improve navigation around
people. Most of the existing research uses different techniques to incorporate
social norms into robot path planning for a single context. Methods that work
for hallway behavior might not work for approaching people, and so on. We
developed a high-level decision-making subsystem, a model-based context
classifier, and a multi-objective optimization-based local planner to achieve
socially-aware trajectories for autonomously sensed contexts. Using a context
classification system, the robot can select social objectives that are later
used by Pareto Concavity Elimination Transformation (PaCcET) based local
planner to generate safe, comfortable, and socially-appropriate trajectories
for its environment. This was tested and validated in multiple environments on
a Pioneer mobile robot platform; results show that the robot was able to select
and account for social objectives related to navigation autonomously.


Abstract:
  We study learning algorithms for the classical Markovian bandit problem with
discount. We explain how to adapt PSRL [24] and UCRL2 [2] to exploit the
problem structure. These variants are called MB-PSRL and MB-UCRL2. While the
regret bound and runtime of vanilla implementations of PSRL and UCRL2 are
exponential in the number of bandits, we show that the episodic regret of
MB-PSRL and MB-UCRL2 is $\tilde O(S\sqrt{nK})$ where $K$ is the number of
episodes, n is the number of bandits and S is the number of states of each
bandit (the exact bound in $S$, $n$ and $K$ is given in the paper). Up to a
factor $\sqrt S$, this matches the lower bound of $\Omega(\sqrt{SnK}$) that we
also derive in the paper. MB-PSRL is also computationally efficient: its
runtime is linear in the number of bandits. We further show that this linear
runtime cannot be achieved by adapting classical non-Bayesian algorithms such
as UCRL2 or UCBVI to Markovian bandit problems. Finally, we perform numerical
experiments that confirm that MB-PSRL outperforms other existing algorithms in
practice, both in terms of regret and of computation time.


Abstract:
  Whilst there are perhaps only a few scientific methods, there seem to be
almost as many artistic methods as there are artists. Artistic processes appear
to inhabit the highest order of open-endedness. To begin to understand some of
the processes of art making it is helpful to try to automate them even
partially. In this paper, a novel algorithm for producing generative art is
described which allows a user to input a text string, and which in a creative
response to this string, outputs an image which interprets that string. It does
so by evolving images using a hierarchical neural Lindenmeyer system, and
evaluating these images along the way using an image text dual encoder trained
on billions of images and their associated text from the internet. In doing so
we have access to and control over an instance of an artistic process, allowing
analysis of which aspects of the artistic process become the task of the
algorithm, and which elements remain the responsibility of the artist.


Abstract:
  We have explored an extended seesaw model accommodating a keV sterile
neutrino adopting $U(1)_{B-L}$ symmetry. This model provides a natural platform
for achieving resonant leptogenesis to account for the observed baryon
asymmetry of the Universe. The required lepton asymmetry is sourced by the CP
violating decay of the lightest heavy right handed neutrino to Standard Model
leptons and Higgs. The presence of the light sterile neutrino in the model
brings out an enhancement in the final lepton asymmetry through an additional
self-energy contribution. Adopting a proper treatment for all the washout
processes this framework strictly favours a strong washout regime thereby
protecting the low energy neutrino mass parameters in agreement with the
present neutrino and cosmology data. This framework of extended seesaw scheme
offers the source of matter-antimatter asymmetry without any severe fine tuning
of the Yukawa couplings governing the tiny neutrino mass. We also comment on
the half-life period for the neutrino less double beta decay process in the
background of having a keV sterile neutrino satisfying all the constraints
which guide the explanation for the observed baryon asymmetry of the Universe.