Abstract:
  We propose a reduced-form benchmark predictive model (BPM) for fixed-target
forecasting of Arctic sea ice extent, and we provide a case study of its
real-time performance for target date September 2020. We visually detail the
evolution of the statistically-optimal point, interval, and density forecasts
as time passes, new information arrives, and the end of September approaches.
Comparison to the BPM may prove useful for evaluating and selecting among
various more sophisticated dynamical sea ice models, which are widely used to
quantify the likely future evolution of Arctic conditions and their two-way
interaction with economic activity.


Abstract:
  We demonstrate the underwater quantum key distribution (UWQKD) over a
10.4-meter Jerlov type III seawater channel by building a complete UWQKD system
with all-optical transmission of quantum signals, synchronization signal and
classical communication signal. The wavelength division multiplexing and the
space-time-wavelength filtering technology are applied to ensure that the
optical signals do not interfere with each other. The system is controlled by
FPGA, and can be easily integrated into watertight cabins to perform field
experiment. By using the decoy-state BB84 protocol with polarization encoding,
we obtain a secure key rate of 1.82Kbps and an error rate of 1.55% at the
attenuation of 13.26dB. We prove that the system can tolerate the channel loss
up to 23.7dB, therefore may be used in the 300-meter-long Jerlov type I clean
seawater channel.


Abstract:
  The formulas for local root numbers of abelian varieties of dimension one are
known. In this paper we treat the simplest unknown case in dimension two by
considering a curve of genus 2 defined over a $5$-adic field such that the
inertia acts on the first $\ell$-adic cohomology group through the largest
possible finite quotient, isomorphic to $C_5\rtimes C_8$. We give a few
criteria to identify such curves and prove a formula for their local root
numbers in terms of invariants associated to a Weierstrass equation.


Abstract:
  The low lying spectrum of the massless overlap Dirac operator coupled to
abelian fields in three dimensions with three different measures are shown to
exhibit two phases: a strong coupling gapped phase and a weak coupling gapless
phase. The vanishing of the gap from the strong coupling side with a Maxwell
and a conformal measure is governed by a Gaussian exponent. Contrary to this
result, the vanishing of the gap from the strong coupling side with a compact
Thirring measure is not consistent with a Gaussian exponent. The low lying
spectrum with a non-compact Thirring measure does not exhibit a simple
non-monotonic behavior as a function of the lattice size on the weak coupling
side. Our combined analysis suggests exploring the possibility of a strongly
coupled continuum theory starting from a compact lattice Thirring model where a
compact U(1) gauge field with a single link action is coupled to even number of
flavors of massless overlap Dirac fermions.


Abstract:
  We report observations of the total solar eclipse of 14 December 2020, during
which a coronal mass ejection can be see n propagating. A comprehensive set of
photographs covering a high dynamic range of exposure allow to characterize its
dimensions. The displacement of the front can be seen occurring during the few
minutes of totality.


Abstract:
  Ferroelectricity in hafnia is often regarded as a breakthrough discovery in
ferroelectrics, potentially able to revolutionize the whole field. Despite
increasing interests, a comprehensive understanding of the many factors driving
the ferroelectric stabilization is still lacking. We here address the phase
transition in terms of a Landau-theory-based approach, by analyzing
symmetry-allowed distortions connecting the high-symmetry paraelectric
tetragonal phase to the low-symmetry polar orthorhombic phase. By means of
first-principles simulations, we find that the $\Gamma_{3-}$ polar mode is only
weakly unstable, whereas the other two symmetry-allowed distortions, non-polar
Y$_{2+}$ and anti-polar Y$_{4-}$ are hard modes. None of the modes, taken alone
or combined with one other mode, is able to drive the transition: the key
factor in stabilizing the polar phase is identified as the strong trilinear
coupling among the three modes. Furthermore, the experimentally acknowledged
importance of substrate-induced effects in the growth of HfO$_2$ ferroelectric
thin films, along with the lack of a clear order parameter in the transition,
suggested the extension of our analysis to strain effects. Our findings suggest
a complex behaviour of the Y$_{2+}$ mode, which become unstable under certain
strain conditions and an overall unstable behaviour for the $\Gamma_{3-}$ polar
mode for all the strain states. A robust result emerges from our analysis:
independently of the different applied strain (compressive or tensile, applied
along orthorhombic axes), the need of a simultaneous excitation of the three
coupled modes remain unaltered. Finally, when applied to mimic experimental
growth conditions under strain, our analysis show a further stabilization of
the ferroelectric phase with respect to the unstrained case, in agreeement with
experimental findings.


Abstract:
  Scaling blockchain efficiency is crucial to its widespread usage in which the
payment channel is one of the most prominent approaches. With payment channels
and the network they construct, two users can move some transactions off-chain
in a predetermined duration to avoid expensive and time-consuming on-chain
settlements. Existing work is devoted to designing high-throughput payment
channel networks (PCNs) or efficient PCN routing policies to reduce the fee. In
this paper, we investigate the PCN routing from a different perspective by
answering whether the routing fee of transactions can be saved by being a bit
more patient. The key idea is to reorder the processing sequence of atomic
transactions, other than to handle each of them separately and immediately. We
present two mechanisms, one is periodic transaction processing assisted by a
PCN broker and the other is purely strategic waiting. In the former, all the
incoming transactions in a short time interval are processed collectively. We
formulate an optimization model to minimize their total routing fee and derive
the optimal permutation of processing transactions as well as the routing
policy for each of them. A Shapley value based scheme is presented to
redistribute the benefit of reordering among the transactions efficiently and
fairly. In the latter, we model the waiting time of a strategic transaction on
a single payment channel as the first passage time problem in queueing theory
when the transaction value is higher than the edge capacity upon its arrival.
By capturing the capacity dynamics, we are able to calculate the recursive
expression of waiting for time distribution that is useful to gauge a user's
cost of patience. Experimental results manifest that our cost redistribution
mechanism can effectively save routing fees for all the transactions, and the
waiting time distribution coincides with the model well.


Abstract:
  We show that Steklov eigenfunctions in a bounded Lipschitz domain have
wavelength dense nodal sets near the boundary, in contrast to what can happen
deep inside the domain. As a converse, in a two-dimensional Lipschitz domain
$\Omega$, we prove that any nodal domain of a Steklov eigenfunction contains a
half-ball centered at $\partial\Omega$ of radius $c_{\Omega}/\lambda$.


Abstract:
  Spinal codes are known to be capacity achieving over both the additive white
Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). Over
wireless channels, Spinal encoding can also be regarded as an
adaptive-coded-modulation (ACM) technique due to its rateless property, which
fits it with mobile communications. Due to lack of tight analysis on error
probability of Spinal codes, optimization of transmission scheme using Spinal
codes has not been fully explored. In this work, we firstly derive new tight
upper bounds of the frame error rate (FER) of Spinal codes for both the AWGN
channel and the BSC in the finite block-length (FBL) regime. Based on the
derived upper bounds, we then design the optimal transmission scheme.
Specifically, we formulate a rate maximization problem as a nonlinear integer
programming problem, and solve it by an iterative algorithm for its dual
problem. As the optimal solution exhibits an incremental-tail-transmission
pattern, we propose an improved transmission scheme for Spinal codes. Moreover,
we develop a bubble decoding with memory (BD-M) algorithm to reduce the
decoding time complexity without loss of rate performance. The improved
transmission scheme at the transmitter and the BD-M algorithm at the receiver
jointly constitute an "encoding-decoding" system of Spinal codes. Simulation
results demonstrate that it can improve both the rate performance and the
decoding throughput of Spinal codes.


Abstract:
  Human-Object Interaction (HOI) detection is an important problem to
understand how humans interact with objects. In this paper, we explore
interactiveness knowledge which indicates whether a human and an object
interact with each other or not. We found that interactiveness knowledge can be
learned across HOI datasets and bridge the gap between diverse HOI category
settings. Our core idea is to exploit an interactiveness network to learn the
general interactiveness knowledge from multiple HOI datasets and perform
Non-Interaction Suppression (NIS) before HOI classification in inference. On
account of the generalization ability of interactiveness, interactiveness
network is a transferable knowledge learner and can be cooperated with any HOI
detection models to achieve desirable results. We utilize the human instance
and body part features together to learn the interactiveness in hierarchical
paradigm, i.e., instance-level and body part-level interactivenesses.
Thereafter, a consistency task is proposed to guide the learning and extract
deeper interactive visual clues. We extensively evaluate the proposed method on
HICO-DET, V-COCO, and a newly constructed PaStaNet-HOI dataset. With the
learned interactiveness, our method outperforms state-of-the-art HOI detection
methods, verifying its efficacy and flexibility. Code is available at
https://github.com/DirtyHarryLYL/Transferable-Interactiveness-Network.


Abstract:
  Actin and spectrin are important constituents of axonal cytoskeleton.
Periodic actin and spectrin structures are found in dendrites, initial segment
of axon, and main axon. Actin and spectrin periodicity has been hypothesized to
be manipulating the axon stability and mechanical behavior. Several
experimental and computational studies have been performed focusing on the
mechanical behavior of actin, spectrin, and actin and spectrin network.
However, most of the actin studies focus on typical long F actin and do not
provide quantitative comparison between the mechanical behavior of short and
long actin filaments. Also, most of the spectrin studies focus on erythrocytic
spectrin and do not shed light on the behavior of structurally different axonal
spectrin. Only a few studies have highlighted forced unfolding of axonal
spectrin which are relevant to brain injury scenario. A comprehensive, strain
rate dependent mechanical study is still absent in the literature. Moreover,
the current opinions regarding periodic actin and spectrin network structure in
axon are disputed due to conflicting results on actin ring organization as
argued by recent superresolution microscopy studies. This review summarizes the
ongoing limitations in this regard and provides insights on possible approaches
to address them. This study will invoke further investigation into relevant
high strain rate response of actin, spectrin, and actin and spectrin network
shedding light into brain pathology scenario such as traumatic brain injury.


Abstract:
  This paper generalizes the concept of Bayes correlated equilibrium (Bergemann
and Morris, 2016) to multi-stage games. We demonstrate the power of our
characterization results by applying them to a number of illustrative examples
and applications.


Abstract:
  We derive a Matern Gaussian process (GP) on the vertices of a hypergraph.
This enables estimation of regression models of observed or latent values
associated with the vertices, in which the correlation and uncertainty
estimates are informed by the hypergraph structure. We further present a
framework for embedding the vertices of a hypergraph into a latent space using
the hypergraph GP. Finally, we provide a scheme for identifying a small number
of representative inducing vertices that enables scalable inference through
sparse GPs. We demonstrate the utility of our framework on three challenging
real-world problems that concern multi-class classification for the political
party affiliation of legislators on the basis of voting behaviour,
probabilistic matrix factorisation of movie reviews, and embedding a hypergraph
of animals into a low-dimensional latent space.


Abstract:
  Experiments involving optical traps often require careful control of the ac
Stark shifts induced by strong confining light fields. By carefully balancing
light shifts between two atomic states of interest, optical traps at the magic
wavelength have been especially effective at suppressing deleterious effects
stemming from such shifts. Highlighting the power of this technique, optical
clocks today exploit Lamb-Dicke confinement in magic-wavelength optical traps,
in some cases realizing shift cancellation at the ten parts per billion level.
Theory and empirical measurements can be used at varying levels of precision to
determine the magic wavelength where shift cancellation occurs. However, lasers
exhibit background spectra from amplified spontaneous emission or other lasing
modes which can easily contaminate measurement of the magic wavelength and its
reproducibility in other experiments or conditions. Indeed, residual light
shifts from laser background have plagued optical lattice clock measurements
for years. In this work, we develop a simple theoretical model allowing
prediction of light shifts from measured background spectra. We demonstrate
good agreement between this model and measurements of the background light
shift from an amplified diode laser in an Yb optical lattice clock.
Additionally, we model and experimentally characterize the filtering effect of
a volume Bragg grating bandpass filter, demonstrating that application of the
filter can reduce background light shifts from amplified spontaneous emission
well below the $10^{-18}$ fractional clock frequency level. This demonstration
is corroborated by direct clock comparisons between a filtered amplified diode
laser and a filtered titanium:sapphire laser.


Abstract:
  Let $F$ be a Bedford-McMullen carpet defined by independent integer
exponents. We prove that for every line $\ell \subseteq \mathbb{R}^2$ not
parallel to the major axes, $$ \dim_H (\ell \cap F) \leq \max \left\lbrace 0,\,
\frac{\dim_H F}{\dim^* F} \cdot (\dim^* F-1) \right\rbrace$$ and $$ \dim_P
(\ell \cap F) \leq \max \left\lbrace 0,\, \frac{\dim_P F}{\dim^* F} \cdot
(\dim^* F-1) \right\rbrace$$ where $\dim^*$ is Furstenberg's star dimension
(maximal dimension of microsets). This improves the state of art results on
Furstenberg type slicing Theorems for affine invariant carpets.


Abstract:
  Unmanned aerial vehicles (UAVs) are now beginning to be deployed for
enhancing the network performance and coverage in wireless communication.
However, due to the limitation of their on-board power and flight time, it is
challenging to obtain an optimal resource allocation scheme for the
UAV-assisted Internet of Things (IoT). In this paper, we design a new
UAV-assisted IoT systems relying on the shortest flight path of the UAVs while
maximising the amount of data collected from IoT devices. Then, a deep
reinforcement learning-based technique is conceived for finding the optimal
trajectory and throughput in a specific coverage area. After training, the UAV
has the ability to autonomously collect all the data from user nodes at a
significant total sum-rate improvement while minimising the associated
resources used. Numerical results are provided to highlight how our techniques
strike a balance between the throughput attained, trajectory, and the time
spent. More explicitly, we characterise the attainable performance in terms of
the UAV trajectory, the expected reward and the total sum-rate.


Abstract:
  After averaging over fermion couplings, SYK has a collective field
description that sometimes has "wormhole" solutions. We study the fate of these
wormholes when the couplings are fixed. Working mainly in a simple model, we
find that the wormhole saddles persist, but that new saddles also appear
elsewhere in the integration space -- "half-wormholes." The wormhole
contributions depend only weakly on the specific choice of couplings, while the
half-wormhole contributions are strongly sensitive. The half-wormholes are
crucial for factorization of decoupled systems with fixed couplings, but they
vanish after averaging, leaving the non-factorizing wormhole behind.


Abstract:
  We investigate fully self-consistent multiscale quantum-classical algorithms
on current generation superconducting quantum computers, in a unified approach
to tackle the correlated electronic structure of large systems in both quantum
chemistry and condensed matter physics. In both of these contexts, a strongly
correlated quantum region of the extended system is isolated and
self-consistently coupled to its environment via the sampling of reduced
density matrices. We analyze the viability of current generation quantum
devices to provide the required fidelity of these objects for a robust and
efficient optimization of this subspace. We show that with a simple error
mitigation strategy and optimization of compact tensor product bases to
minimize the number of terms to sample, these self-consistent algorithms are
indeed highly robust, even in the presence of significant noises on quantum
hardware. Furthermore, we demonstrate the use of these density matrices for the
sampling of non-energetic properties, including dipole moments and Fermi liquid
parameters in condensed phase systems, achieving a reliable accuracy with
sparse sampling. It appears that uncertainties derived from the iterative
optimization of these subspaces is smaller than variances in the energy for a
single subspace optimization with current quantum hardware. This boosts the
prospect for routine self-consistency to improve the choice of correlated
subspaces in hybrid quantum-classical approaches to electronic structure for
large systems in this multiscale fashion.


Abstract:
  Previous calculations of the dielectric and optical properties of 2D
materials often overlooked or circumvented the influence of vacuum spacing
introduced in periodic calculations, which gave rise to mispredictions of the
intrinsic properties of 2D materials or merely qualitative results. We first
elucidate the relationship between the vacuum spacing and the dielectric and
optical properties of 2D materials in periodic calculations, and then bring
forward an effective method to accurately predict the dielectric and optical
properties of 2D materials by restoring the intrinsic dielectric functions of
2D materials independent of the additional vacuum spacing. As examples, the
intrinsic dielectric and optical properties of ultrathin h-BN and MoS2 from
monolayer to pentalayer, including dielectric functions, optical absorption
coefficients, refraction indexes, reflectivities, extinction coefficients, and
energy loss functions, have been calculated by our method. Our calculations
reveal that the out-of-plane optical dielectric constants, static refraction
indexes, and static reflectivities of 2D h-BN and MoS2 increase as the number
of layers increases, while the in-plane counterparts remain unchanged.
Excitonic frequency-dependent optical properties of h-BN and MoS2 from
monolayer to bulk are also calculated by solving the Bethe-Salpeter equation
and show strong anisotropy. In better agreement with experimental results than
previous calculations, the presented method demonstrates enormous potential to
investigate the dielectric and optical properties of other 2D materials
extensively and quantitively.


Abstract:
  Model-based fault injection methods are widely used for the evaluation of
fault tolerance in safety-critical control systems. In this paper, we introduce
a new model-based fault injection method implemented as a highlycustomizable
Simulink block called FIBlock. It supports the injection of typical faults of
essential heterogeneous components of Cyber-Physical Systems, such as sensors,
computing hardware, and network. The FIBlock GUI allows the user to select a
fault type and configure multiple parameters to tune error magnitude, fault
activation time, and fault exposure duration. Additional trigger inputs and
outputs of the block enable the modeling of conditional faults. Furthermore,
two or more FIBlocks connected with these trigger signals can model chained
errors. The proposed fault injection method is demonstrated with a lower-limb
EXO-LEGS exoskeleton, an assistive device for the elderly in everyday life. The
EXO-LEGS model-based dynamic control is realized in the Simulink environment
and allows easy integration of the aforementioned FIBlocks. Exoskeletons, in
general, being a complex CPS with multiple sensors and actuators, are prone to
hardware and software faults. In the case study, three types of faults were
investigated: 1) sensor freeze, 2) stuck-at-0, 3) bit-flip. The fault injection
experiments helped to determine faults that have the most significant effects
on the overall system reliability and identify the fine line for the critical
fault duration after that the controller could no longer mitigate faults.


Abstract:
  Excitons, quasiparticles of electrons and holes bound by Coulombic
attraction, are created transiently by light and play an important role in
optoelectronics, photovoltaics and photosynthesis. While they are also
predicted to form spontaneously in a small gap semiconductor or a semimetal,
leading to a Bose-Einstein condensate at low temperature, their material
realization has been elusive without any direct evidence. Here we detect the
direct photoemission signal from spontaneously formed excitons in a debated
excitonic insulator candidate Ta2NiSe5. Our symmetry-selective angle-resolved
photoemission spectroscopy reveals a characteristic excitonic feature above the
transition temperature, which provides detailed properties of excitons such as
anisotropic Bohr radius. The present result evidences so called preformed
excitons and guarantees the excitonic insulator nature of Ta2NiSe5 at low
temperature. Direct photoemission can be an important tool to characterize
steady-state excitons.


Abstract:
  We establish an explicit asymptotic formula for the number of rational
solutions of intrinsic Diophantine inequalities on simply-connected simple
algebraic groups, at arbitrarily small scales.


Abstract:
  This paper studies construction of above-ground biomass (AGB) prediction maps
from synthetic aperture radar (SAR) intensity images. The purpose is to improve
traditional regression models based on SAR intensity, trained with a limited
amount of AGB in situ measurements. Although it is costly to collect, data from
airborne laser scanning (ALS) sensors are highly correlated with AGB.
Therefore, we propose using AGB predictions based on ALS data as surrogate
response variables for SAR data in a sequential modelling fashion. This
increases the amount of training data dramatically. To model the regression
function between SAR intensity and ALS-predicted AGB we propose to utilise a
conditional generative adversarial network (cGAN), i.e. the Pix2Pix
convolutional neural network. This enables the recreation of existing ALS-based
AGB prediction maps. The generated synthesised ALS-based AGB predictions are
evaluated qualitatively and quantitatively against ALS-based AGB predictions
retrieved from a traditional non-sequential regression model trained in the
same area. Results show that the proposed architecture manages to capture
characteristics of the actual data. This suggests that the use of ALS-guided
generative models is a promising avenue for AGB prediction from SAR intensity.
Further research on this area has the potential of providing both large-scale
and low-cost predictions of AGB.


Abstract:
  We calculate the extremal cross sectional areas and cyclotron masses for the
Fermi-surface pockets in Dirac and Weyl topological semimetals. The calculation
is carried out for the most general form of the electron energy bands in the
vicinity of the Weyl and Dirac points. Using the obtained formulas, one can
find parameters characterizing the Dirac and Weyl electrons in the topological
semimetals from appropriate experimental data. As an example, we consider the
W1 electrons in TaAs.


Abstract:
  Training deep networks with limited labeled data while achieving a strong
generalization ability is key in the quest to reduce human annotation efforts.
This is the goal of semi-supervised learning, which exploits more widely
available unlabeled data to complement small labeled data sets. In this paper,
we propose a novel framework for discriminative pixel-level tasks using a
generative model of both images and labels. Concretely, we learn a generative
adversarial network that captures the joint image-label distribution and is
trained efficiently using a large set of unlabeled images supplemented with
only few labeled ones. We build our architecture on top of StyleGAN2, augmented
with a label synthesis branch. Image labeling at test time is achieved by first
embedding the target image into the joint latent space via an encoder network
and test-time optimization, and then generating the label from the inferred
embedding. We evaluate our approach in two important domains: medical image
segmentation and part-based face segmentation. We demonstrate strong in-domain
performance compared to several baselines, and are the first to showcase
extreme out-of-domain generalization, such as transferring from CT to MRI in
medical imaging, and photographs of real faces to paintings, sculptures, and
even cartoons and animal faces. Project Page:
\url{https://nv-tlabs.github.io/semanticGAN/}


Abstract:
  We present the largest systematic, HST-based search to date for luminous
$z\gtrsim8$ galaxy candidates using $\sim$1267 arcmin$^{2}$ of (pure-)parallel
observations from a compilation of 288 random sightlines with ACS and WFC3
observations, derived from the SuperBoRG data set and together representing a
factor $\sim1.12\times$ larger than existing space-based data sets. Using NIR
color cuts and careful photo-$z$ analyses, we find 31 $z\gtrsim8$ galaxy
candidates over 29 unique sightlines, and derive global galaxy properties such
as UV magnitudes and continuum slopes, sizes, and rest-frame optical properties
(e.g., SFRs, stellar masses, $A_{\rm v}$). Taking advantage of the
(pure-)parallel nature of our data set - making it one of the most
representative thus far - and derived SFRs, we evaluate the cosmic star
formation rate density for the bright end of the UV luminosity function at
$z\sim8-10$ and test the validity of luminosity function-derived results using
a conversion factor. We find our method yields comparable results to those
derived with luminosity functions. Furthermore, we present follow up
observations of 5 (Super)BoRG targets with Keck/MOSFIRE, finding no evidence of
Ly$\alpha$ in $>3$ hrs of $Y-$band observations in either, consistent with a
largely neutral medium at $z\sim8$. Our results offer a definitive HST legacy
on the bright end of the luminosity function and provide a valuable benchmark
as well as targets for follow up with JWST.


Abstract:
  Frequency perspective recently makes progress in understanding deep learning.
It has been widely verified in both empirical and theoretical studies that deep
neural networks (DNNs) often fit the target function from low to high
frequency, namely Frequency Principle (F-Principle). F-Principle sheds light on
the strength and the weakness of DNNs and inspires a series of subsequent
works, including theoretical studies, empirical studies and the design of
efficient DNN structures etc. Previous works examine the F-Principle in
gradient-descent-based training. It remains unclear whether
gradient-descent-based training is a necessary condition for the F-Principle.
In this paper, we show that the F-Principle exists stably in the training
process of DNNs with non-gradient-descent-based training, including
optimization algorithms with gradient information, such as conjugate gradient
and BFGS, and algorithms without gradient information, such as Powell's method
and Particle Swarm Optimization. These empirical studies show the universality
of the F-Principle and provide hints for further study of F-Principle.


Abstract:
  For a generalized soliton $(g,\xi,\eta,\beta,\gamma,\delta)$, we provide
necessary and sufficient conditions for the dual $1$-form $\xi^{\flat}$ of the
potential vector field $\xi$ to be a solution of the Schr\"{o}dinger-Ricci
equation, a harmonic or a Schr\"{o}dinger-Ricci harmonic form. We also
characterize the $1$-forms orthogonal to $\xi^{\flat}$, underlying the results
obtained for the Ricci and Yamabe solitons. Further, we formulate the results
for the case of gradient generalized solitons. Several applications and
examples are also presented.


Abstract:
  In the standard framework of self-consistent many-body perturbation theory,
the skeleton series for the self-energy is truncated at a finite order $N$ and
plugged into the Dyson equation, which is then solved for the propagator $G_N$.
For two simple examples of fermionic models -- the Hubbard atom at half filling
and its zero space-time dimensional simplified version -- we find that $G_N$
converges when $N\to\infty$ to a limit $G_\infty\,$, which coincides with the
exact physical propagator $G_{\rm exact}\ \,$ at small enough coupling, while
$G_\infty \neq G_{\rm exact}\ \,$ at strong coupling. We also demonstrate that
it is possible to discriminate between these two regimes thanks to a criterion
which does not require the knowledge of $G_{\rm exact}\ \,$, as proposed in
[Rossi et al., PRB 93, 161102(R) (2016)].


Abstract:
  We consider structural vector autoregressions subject to 'narrative
restrictions', which are inequality restrictions on functions of the structural
shocks in specific periods. These restrictions raise novel problems related to
identification and inference, and there is currently no frequentist procedure
for conducting inference in these models. We propose a solution that is valid
from both Bayesian and frequentist perspectives by: 1) formalizing the
identification problem under narrative restrictions; 2) correcting a feature of
the existing (single-prior) Bayesian approach that can distort inference; 3)
proposing a robust (multiple-prior) Bayesian approach that is useful for
assessing and eliminating the posterior sensitivity that arises in these models
due to the likelihood having flat regions; and 4) showing that the robust
Bayesian approach has asymptotic frequentist validity. We illustrate our
methods by estimating the effects of US monetary policy under a variety of
narrative restrictions.


Abstract:
  Inspired by our serendipitous discovery of six AGNs with varying broad-Halpha
fluxes over years out of our searching for intermediate-mass black holes
(IMBHs), we conduct a systematic investigation of changing-look (CL) and
large-variability AGNs. We collect all the CL AGNs at z<0.15 and the
reverberation mapped AGNs with strongly variable broad Halpha, and perform
careful decomposition fittings to both their images and spectra. We find two
observational facts: (1) The host galaxies of local CL and large-variability
AGNs, mainly being Seyferts, are in the red (gas-poor) tail of the general
Seyfert galaxy population. (2) In contrast, there is a significant trend that
their more luminous counterparts namely CL and extremely variable quasars (CLQs
and EVQs) are different: CLQs are generally in blue galaxies; in terms of the
diagram of SFR and M* local CL Seyfert galaxies are located in the green
valley, whereas CLQ hosts are in the star-forming main sequence. We propose
explanations for those strongly variable Seyferts and quasars, respectively,
under the thought that accretion disks broadly depend on nuclear fueling modes.
Local large-variability and CL Seyferts are in nuclear famine mode, where
cold-gas clumps can be formed stochastically in the fueling flow, and their
episodic infall produces sharp peaks in the accretion-rate curve. CLQs and EVQs
are in feast fueling mode, which may account for both their preference to blue
galaxies and their variability pattern (high-amplitude tail of the continuous
distribution). Lastly, we propose a new thinking: to search for IMBHs by
optical variability in red galaxies.


Abstract:
  We design a proof system for propositional classical logic that integrates
two languages for Boolean functions: standard conjunction-disjunction-negation
and binary decision trees. We give two reasons to do so. The first is
proof-theoretical naturalness: the system consists of all and only the
inference rules generated by the single, simple, linear shape of the recently
introduced subatomic logic. Thanks to this regularity, cuts are eliminated via
a natural construction. The second reason is that the system generates
efficient proofs. Indeed, we show that a certain class of tautologies due to
Statman, which cannot have better than exponential cut-free proofs in the
sequent calculus, have polynomial cut-free proofs in our system. We achieve
this by using the same construction that we use for cut elimination. In
summary, by expanding the language of propositional logic, we make its proof
theory more regular and generate more proofs, some of which are very efficient.
  That design is made possible by considering propositional variables as
superpositions of their truth values, which are connected by self-dual,
non-commutative connectives. A proof can then be projected via each
propositional variable into two proofs, one for each truth value, without a
need for cuts. Those projections are semantically natural and are at the heart
of all the constructions in this paper. To accommodate self-dual
non-commutativity, we compose proofs by deep inference.


Abstract:
  Primitive recursion is a mature, well-understood topic in the theory and
practice of programming. Yet its dual, primitive corecursion, is
underappreciated and still seen as exotic. We aim to put them both on equal
footing by giving a foundation for primitive corecursion based on computation,
giving a terminating calculus analogous to the original computational
foundation of recursion. We show how the implementation details in an abstract
machine strengthens their connection, syntactically deriving corecursion from
recursion via logical duality. We also observe the impact of evaluation
strategy on the computational complexity of primitive (co)recursive
combinators: call-by-name allows for more efficient recursion, but
call-by-value allows for more efficient corecursion.


Abstract:
  We prove the existence of a crepant sdlt model for slc pairs whose
irreducible components are normal in codimension one.


Abstract:
  Regular variations of the pulse period of Her X-1 with X-ray flux observed by
Fermi-GBM are examined. We argue that these regular variations result from the
free precession of the neutron star in Her X-1.


Abstract:
  We study photon orbits in the background of $(1+3)$-dimensional static,
spherically symmetric geometries. In particular, we have obtained exact
analytical solutions to the null geodesic equations for light rays in terms of
the Weierstra{\ss} function for space-times arising in the context of
scale-dependent gravity. The trajectories in the $(x-y)$ plane are shown
graphically, and we make a comparison with similar geometries arising in
different contexts. The light deflection angle is computed as a function of the
running parameter $\xi$, and an upper bound for the latter is obtained.


Abstract:
  Deep neural networks for natural language processing are fragile in the face
of adversarial examples -- small input perturbations, like synonym substitution
or word duplication, which cause a neural network to change its prediction. We
present an approach to certifying the robustness of LSTMs (and extensions of
LSTMs) and training models that can be efficiently certified. Our approach can
certify robustness to intractably large perturbation spaces defined
programmatically in a language of string transformations. Our evaluation shows
that (1) our approach can train models that are more robust to combinations of
string transformations than those produced using existing techniques; (2) our
approach can show high certification accuracy of the resulting models.


Abstract:
  A promising trend in deep learning replaces traditional feedforward networks
with implicit networks. Unlike traditional networks, implicit networks solve a
fixed point equation to compute inferences. Solving for the fixed point varies
in complexity, depending on provided data and an error tolerance. Importantly,
implicit networks may be trained with fixed memory costs in stark contrast to
feedforward networks, whose memory requirements scale linearly with depth.
However, there is no free lunch -- backpropagation through implicit networks
often requires solving a costly Jacobian-based equation arising from the
implicit function theorem. We propose Jacobian-Free Backpropagation (JFB), a
fixed-memory approach that circumvents the need to solve Jacobian-based
equations. JFB makes implicit networks faster to train and significantly easier
to implement, without sacrificing test accuracy. Our experiments show implicit
networks trained with JFB are competitive with feedforward networks and prior
implicit networks given the same number of parameters.


Abstract:
  We study distributed estimation of a high-dimensional static parameter vector
through a group of sensors whose communication network is modeled by a fixed
directed graph. Different from existing time-triggered communication schemes,
an event-triggered asynchronous scheme is investigated in order to reduce
communication while preserving estimation convergence. A distributed estimation
algorithm with a single step size is first proposed based on an event-triggered
communication scheme with a time-dependent decaying threshold. With the
event-triggered scheme, each sensor sends its estimate to neighbor sensors only
when the difference between the current estimate and the last sent-out estimate
is larger than the triggering threshold. We prove that the proposed algorithm
has mean-square and almost-sure convergence respectively, under an integrated
condition of sensor network topology and sensor measurement matrices. The
condition is satisfied if the topology is a balanced digraph containing a
spanning tree and the system is collectively observable. Moreover, we provide
estimates for the convergence rates, which are related to the step size as well
as the triggering threshold. Furthermore, as an essential metric of sensor
communication intensity in the event-triggered distributed algorithms, the
communication rate is proved to decay to zero with a certain speed almost
surely as time goes to infinity. We show that given the step size, adjusting
the decay speed of the triggering threshold can lead to a tradeoff between the
convergence rate of the estimation error and the decay speed of the
communication rate. Specifically, increasing the decay speed of the threshold
would make the communication rate decay faster, but reduce the convergence rate
of the estimation error. Numerical simulations are provided to illustrate the
developed results.


Abstract:
  Previous studies have demonstrated that commonly studied (vanilla)
touch-based continuous authentication systems (V-TCAS) are susceptible to
population attack. This paper proposes a novel Generative Adversarial Network
assisted TCAS (G-TCAS) framework, which showed more resilience to the
population attack. G-TCAS framework was tested on a dataset of 117 users who
interacted with a smartphone and tablet pair. On average, the increase in the
false accept rates (FARs) for V-TCAS was much higher (22%) than G-TCAS (13%)
for the smartphone. Likewise, the increase in the FARs for V-TCAS was 25%
compared to G-TCAS (6%) for the tablet.


Abstract:
  In the currently favored cosmological paradigm galaxies form hierarchically
through the accretion of numerous satellite galaxies. Since the satellites are
much less massive than the host halo, they occupy a small fraction of the
volume in action space defined by the potential of the host halo. Since actions
are conserved when the potential of the host halo changes adiabatically, stars
from an accreted satellite are expected to remain clustered in action space as
the host halo evolves. In this paper, we identify accreted satellites in three
Milky Way like disk galaxies from the cosmological baryonic FIRE-2 simulations
by tracking satellite galaxies through simulation snapshots. We then try to
recover these satellites by applying the cluster analysis algorithm Enlink to
the orbital actions of accreted star particles in the present-day snapshot. We
define several metrics to quantify the success of the clustering algorithm and
use these metrics to identify well-recovered and poorly-recovered satellites.
We plot these satellites in the infall time-progenitor mass (or stellar mass)
space, and determine the boundaries between the well-recovered and
poorly-recovered satellites in these two spaces with classification tree
method. The groups found by Enlink are more likely to correspond to a real
satellite if they have high significance, a quantity assigned by Enlink. Since
cosmological simulations predict that most stellar halos have a population of
insitu stars, we test the ability of Enlink to recover satellites when the
sample is contaminated by 10-50% of insitu star particles, and show that most
of the satellites well-recovered by Enlink in the absence of insitu stars, stay
well-recovered even with 50% contamination. We thus expect that, in the future,
cluster analysis in action space will be useful in upcoming data sets (e.g.
Gaia) for identifying accreted satellites in the Milky Way.


Abstract:
  Mobile edge computing pushes computationally-intensive services closer to the
user to provide reduced delay due to physical proximity. This has led many to
consider deploying deep learning models on the edge -- commonly known as edge
intelligence (EI). EI services can have many model implementations that provide
different QoS. For instance, one model can perform inference faster than
another (thus reducing latency) while achieving less accuracy when evaluated.
In this paper, we study joint service placement and model scheduling of EI
services with the goal to maximize Quality-of-Servcice (QoS) for end users
where EI services have multiple implementations to serve user requests, each
with varying costs and QoS benefits. We cast the problem as an integer linear
program and prove that it is NP-hard. We then prove the objective is equivalent
to maximizing a monotone increasing, submodular set function and thus can be
solved greedily while maintaining a (1-1/e)-approximation guarantee. We then
propose two greedy algorithms: one that theoretically guarantees this
approximation and another that empirically matches its performance with greater
efficiency. Finally, we thoroughly evaluate the proposed algorithm for making
placement and scheduling decisions in both synthetic and real-world scenarios
against the optimal solution and some baselines. In the real-world case, we
consider real machine learning models using the ImageNet 2012 data-set for
requests. Our numerical experiments empirically show that our more efficient
greedy algorithm is able to approximate the optimal solution with a 0.904
approximation on average, while the next closest baseline achieves a 0.607
approximation on average.


Abstract:
  We propose a method for extracting physics-based biomarkers from a single
multiparametric Magnetic Resonance Imaging (mpMRI) scan bearing a glioma tumor.
We account for mass effect, the deformation of brain parenchyma due to the
growing tumor, which on its own is an important radiographic feature but its
automatic quantification remains an open problem. In particular, we calibrate a
partial differential equation (PDE) tumor growth model that captures mass
effect, parameterized by a single scalar parameter, tumor proliferation,
migration, while localizing the tumor initiation site. The single-scan
calibration problem is severely ill-posed because the precancerous, healthy,
brain anatomy is unknown. To address the ill-posedness, we introduce an
ensemble inversion scheme that uses a number of normal subject brain templates
as proxies for the healthy precancer subject anatomy. We verify our solver on a
synthetic dataset and perform a retrospective analysis on a clinical dataset of
216 glioblastoma (GBM) patients. We analyze the reconstructions using our
calibrated biophysical model and demonstrate that our solver provides both
global and local quantitative measures of tumor biophysics and mass effect. We
further highlight the improved performance in model calibration through the
inclusion of mass effect in tumor growth models -- including mass effect in the
model leads to 10% increase in average dice coefficients for patients with
significant mass effect. We further evaluate our model by introducing novel
biophysics-based features and using them for survival analysis. Our preliminary
analysis suggests that including such features can improve patient
stratification and survival prediction.


Abstract:
  Conformal defects describe the universal behaviors of a conformal field
theory (CFT) in the presence of a boundary or more general impurities. The
coupled critical system is characterized by new conformal anomalies which are
analogous to, and generalize those of standalone CFTs. Here we study the
conformal $a$- and $c$-anomalies of four dimensional defects in CFTs of general
spacetime dimensions greater than four. We prove that under unitary defect
renormalization group (RG) flows, the defect $a$-anomaly must decrease, thus
establishing the defect $a$-theorem. For conformal defects preserving minimal
supersymmetry, the full defect symmetry contains a distinguished $U(1)_R$
subgroup. We derive the anomaly multiplet relations that express the defect
$a$- and $c$-anomalies in terms of the defect (mixed) 't Hooft anomalies for
this $U(1)_R$ symmetry. Once the $U(1)_R$ symmetry is identified using the
defect $a$-maximization principle which we prove, this enables a
non-perturbative pathway to the conformal anomalies of strongly coupled
defects. We illustrate our methods by discussing a number of examples including
boundaries in five dimensions and codimension-two defects in six dimensions. We
also comment on chiral algebra sectors of defect operator algebras and
potential conformal collider bounds on defect anomalies.


Abstract:
  In the presence of attraction, the jamming transition of packings of
frictionless particles corresponds to the rigidity percolation. When the range
of attraction is long, the distribution of the size of rigid clusters, $P(s)$,
is continuous and shows a power-law decay. For systems with short-range
attractions, however, $P(s)$ appears discontinuous. There is a power-law decay
for small cluster sizes, followed by a low probability gap and a peak near the
system size. We find that this appearing ``discontinuity'' does not mean that
the transition is discontinuous. In fact, it signifies the coexistence of two
distinct length scales, associated with the largest cluster and smaller ones,
respectively. The comparison between the largest and second largest clusters
indicates that their growth rates with system size are rather different.
However, both cluster sizes tend to diverge in the large system size limit,
suggesting that the jamming transition of systems with short-range attractions
is still continuous. In the framework of the two-scale scenario, we also derive
a generalized hyperscaling relation. With robust evidence, our work challenges
the former single-scale view of the rigidity percolation.


Abstract:
  This paper is concerned with the existence of positive solutions for a
fractional population model with the homogeneous Dirichlet condition on the
exterior of a bounded domain. The approach is based on the sub-super solutions
method. Our results generalize some recent results in the literature.


Abstract:
  The distribution of liquid water in ice-free clouds determines their
radiative properties, a significant source of uncertainty in weather and
climate models. Evaporation and turbulent mixing cause a cloud to display large
variations in droplet-number density, but quite small variations in droplet
size [Beals et al. (2015)]. Yet direct numerical simulations of the joint
effect of evaporation and mixing near the cloud edge predict quite different
behaviors, and it remains an open question how to reconcile these results with
the experimental findings. To infer the history of mixing and evaporation from
observational snapshots of droplets in clouds is challenging because clouds are
transient systems. We formulated a statistical model that provides a reliable
description of the evaporation-mixing process as seen in direct numerical
simulations, and allows to infer important aspects of the history of observed
droplet populations, highlighting the key mechanisms at work, and explaining
the differences between observations and simulations.


Abstract:
  In 2018, XMM-Newton observed the awakening in X-rays of the Be/X-ray binary
(Be/XRB) A0538-66. It showed bright and fast flares close to periastron with
properties that had never been observed in other Be/XRBs before. We report the
results from the observations of A0538-66 collected during the first all-sky
survey of eROSITA, an X-ray telescope (0.2-10 keV) on board the
Spektrum-Roentgen-Gamma (SRG) satellite. eROSITA caught two flares within one
orbital cycle at orbital phases $\phi = 0.29$ and $\phi = 0.93$ (where $\phi=0$
corresponds to periastron), with peak luminosities of $\sim 2-4 \times 10^{36}$
erg/s (0.2-10 keV) and durations of $42 \leq \Delta t_{\rm fl} \leq 5.7\times
10^4$ s. The flare observed at $\phi \approx 0.29$ shows that the neutron star
can accrete considerably far from periastron, although it is expected to be
outside of the circumstellar disk, thus providing important new information
about the plasma environment surrounding the binary system. We also report the
results from the photometric monitoring of A0538-66 carried out with the REM,
OGLE, and MACHO telescopes from January 1993 until March 2020. We found that
the two sharp peaks that characterize the orbital modulation in the optical
occur asymmetrically in the orbit, relative to the position of the donor star.


Abstract:
  A coastal eddy is modelled as a barotropic vortex propagating along a coastal
shelf. If the vortex speed matches the phase speed of any coastal trapped shelf
wave modes, a shelf wave wake is generated leading to a flux of energy from the
vortex into the wave field. Using a simply shelf geometry, we determine
analytic expressions for the wave wake and the leading order flux of wave
energy. By considering the balance of energy between the vortex and wave field,
this energy flux is then used to make analytic predictions for the evolution of
the vortex speed and radius under the assumption that the vortex structure
remains self similar. These predictions are examined in the asymptotic limit of
small rotation rate and shelf slope and tested against numerical simulations.
  If the vortex speed does not match the phase speed of any shelf wave, steady
vortex solutions are expected to exist. We present a numerical approach for
finding these nonlinear solutions and examine the parameter dependence of their
structure.


Abstract:
  Scarcity of parallel data causes formality style transfer models to have
scarce success in preserving content. We show that fine-tuning pre-trained
language (GPT-2) and sequence-to-sequence (BART) models boosts content
preservation, and that this is possible even with limited amounts of parallel
data. Augmenting these models with rewards that target style and content -- the
two core aspects of the task -- we achieve a new state-of-the-art.


Abstract:
  We present ten different characterizations of functions satisfying a weak
reverse H\"older inequality on an open subset of a metric measure space with a
doubling measure. Among others, we describe these functions as a class of weak
$A_\infty$ weights, which is a generalization of Muckenhoupt weights that
allows for nondoubling weights. Although our main results are modeled after
conditions that hold true for Muckenhoupt weights, we also discuss two
conditions for Muckenhoupt $A_\infty$ weights that fail to hold for weak
$A_\infty$ weights.


Abstract:
  Given a D-brane background in string theory (or equivalently boundary
conditions in a two-dimensional conformal field theory), classical solutions of
open string field theory equations of motion are conjectured to describe new
D-brane backgrounds (boundary conditions). In this thesis, we study these
solutions in bosonic open string field theory using the level truncation
approach, which is a numerical approach where the string field is truncated to
a finite number of degrees of freedom.
  We start with a review of the theoretical background and numerical methods
which are needed in the level truncation approach and then we discuss solutions
on several different backgrounds. First, we discuss universal solutions, which
do not depend on the open string background, then we analyze solutions of the
free boson theory compactified on a circle or on a torus, then marginal
solutions in three different approaches and finally solutions in theories which
include the A-series of Virasoro minimal models. In addition to known D-branes,
we find so-called exotic solutions which potentially describe yet unknown
boundary states.
  This paper is based on my doctoral thesis submitted to the Faculty of
Mathematics and Physics at Charles University in Prague.


Abstract:
  The tight correlations between the mass of supermassive black holes ($M_{\rm
BH}$) and their host-galaxy properties have been of great interest to the
astrophysical community, but a clear understanding of their origin and
fundamental drivers still eludes us. The local relations for active galaxies
are interesting in their own right and form the foundation for any evolutionary
study over cosmic time. We present Hubble Space Telescope optical imaging of a
sample of 66 local active galactic nuclei (AGNs); for 14 objects, we also
obtained Gemini near-infrared images. We use state of the art methods to
perform surface photometry of the AGN host galaxies, decomposing them in
spheroid, disk and bar (when present) and inferring the luminosity and stellar
mass of the components. We combine this information with spatially-resolved
kinematics obtained at the Keck Telescopes to study the correlations between
$M_{\rm BH}$ (determined from single-epoch virial estimators) and host galaxy
properties. The correlations are uniformly tight for our AGN sample, with
intrinsic scatter 0.2-0.4 dex, smaller than or equal to that of quiescent
galaxies. We find no difference between pseudo and classical bulges or barred
and non-barred galaxies. We show that all the tight correlations can be
simultaneously satisfied by AGN hosts in the 10$^7$-10$^9$ $M_{\odot}$ regime,
with data of sufficient quality. The MBH-$\sigma$ relation is also in agreement
with that of AGNs with $M_{\rm BH}$ obtained from reverberation mapping,
providing an indirect validation of single-epoch virial estimators of $M_{\rm
BH}$.


Abstract:
  We present Syntroids, a case study for the automatic synthesis of hardware
from a temporal logic specification. Syntroids is a space shooter arcade game
realized on an FPGA, where the control flow architecture has been completely
specified in Temporal Stream Logic (TSL) and implemented using reactive
synthesis. TSL is a recently introduced temporal logic that separates control
and data. This leads to scalable synthesis, because the cost of the synthesis
process is independent of the complexity of the handled data.
  In this case study, we report on our experience with the TSL-based
development of the Syntroids game and on the implementation quality obtained
with synthesis in comparison to manual programming. We also discuss solved and
open challenges with respect to currently available synthesis tools.


Abstract:
  Topological phases such as polar skyrmions have been a fertile playground for
ferroelectric oxide superlattices, with exotic physical phenomena such as
negative capacitance. Herein, using phase-field simulations, we demonstrate the
local control of the skyrmion phase with electric potential applied through a
top electrode. Under a relatively small electric potential, the skyrmions
underneath the electrode can be erased and recovered reversibly. A
topologically protected transition from the symmetric to asymmetric skyrmion
bubbles is observed at the edge of the electrode. While a topological
transition to a labyrinthine domain requires a high applied potential, it can
switch back to the skyrmion state with a relatively small electric potential.
The topological transition from +1 to 0 occurs before the full destruction of
the bubble state. It is shown that the shrinking and bursting of the skyrmions
leads to a large reduction in the dielectric permittivity, the magnitude of
which depends on the size of the electrode.


Abstract:
  We consider solutions of the 2D Toda lattice hierarchy which are elliptic
functions of the zeroth time t_0=x. It is known that their poles as functions
of t_1 move as particles of the elliptic Ruijsenaars-Schneider model. The goal
of this paper is to extend this correspondence to the level of hierarchies. We
show that the Hamiltonians which govern the dynamics of poles with respect to
the m-th hierarchical times t_m and \bar t_m of the 2D Toda lattice hierarchy
are obtained from expansion of the spectral curve for the Lax matrix of the
Ruijsenaars-Schneider model at the marked points.


Abstract:
  This paper proposes a general framework for nonperturbatively defining
continuum quantum field theories. Unlike most such frameworks, the one offered
here is finitary: continuum theories are defined by reducing large but finite
quantum systems to subsystems with conserved entanglement patterns at short
distances. This makes it possible to start from a lattice theory and use rather
elementary mathematics to isolate the entire algebraic structure of the
corresponding low-energy continuum theory.
  The first half of this paper illustrates this approach through a persnickety
study of (1 + 1)D continuum theories that emerge from the $\mathbb{Z}_K$ clock
model at large $K$. This leads to a direct lattice derivation of many known
continuum results, such as the operator product expansion of vertex operators
in the free scalar CFT. Many new results are obtained too. For example,
self-consistency of the lattice-continuum correspondence leads to a rich, novel
proposal for the symmetry breaking structure of the clock model at weak
coupling, deep in the BKT regime. This also makes precise what one means by
"continuous" when saying that continuous symmetries cannot be broken in (1+1)D.
  The second half of this paper is devoted to path integrals for continuum
theories of bosons and fermions defined in this finitary formalism. The path
integrals constructed here have both nonperturbative lattice definitions and
manifest continuum properties, such as symmetries under infinitesimal rotations
or dilatations. Remarkably, this setup also makes it possible to generalize
Noether's theorem to discrete symmetries.


Abstract:
  We study the average behaviour of the Iwasawa invariants for Selmer groups of
elliptic curves. These results lie at the intersection of arithmetic statistics
and Iwasawa theory. We obtain unconditional lower bounds for the density of
rational elliptic curves with prescribed Iwasawa invariants.


Abstract:
  The goal of this paper is to characterize Gaussian-Process optimization in
the setting where the function domain is large relative to the number of
admissible function evaluations, i.e., where it is impossible to find the
global optimum. We provide upper bounds on the suboptimality (Bayesian simple
regret) of the solution found by optimization strategies that are closely
related to the widely used expected improvement (EI) and upper confidence bound
(UCB) algorithms. These regret bounds illuminate the relationship between the
number of evaluations, the domain size (i.e. cardinality of finite domains /
Lipschitz constant of the covariance function in continuous domains), and the
optimality of the retrieved function value. In particular, we show that even
when the number of evaluations is far too small to find the global optimum, we
can find nontrivial function values (e.g. values that achieve a certain ratio
with the optimal value).


Abstract:
  We consider flows $(X,T)$, given by actions $(t, x) \to tx$, on a compact
metric space $X$ with a discrete $T$ as an acting group. We study a new class
of flows - the \textsc{Strongly Rigid} ($ \mathbf {SR} $) \ flows, that are
properly contained in the class of distal ($ \mathbf D $) flows and properly
contain the class of all equicontinuous ($ \mathbf {EQ} $) flows. Thus,
$\mathbf {EQ} \ \text{flows} \subsetneqq \mathbf {SR} \ \text{flows}
\subsetneqq \mathbf{ D} \ \text{flows}$.
  The concepts of equicontinuity, strong rigidity and distality coincide for
the induced flow $(2^X,T)$. We observe that strongly rigid $(X,T)$ gives
distinct properties for the induced flow $(2^X,T)$ and its enveloping semigroup
$E(2^X)$. We further study strong rigidity in case of particular semiflows
$(X,S)$, with $S$ being a discrete acting semigroup.


Abstract:
  This paper describes an image based visual servoing (IBVS) system for a
nonholonomic robot to achieve good trajectory following without real-time robot
pose information and without a known visual map of the environment. We call it
trajectory servoing. The critical component is a feature-based, indirect SLAM
method to provide a pool of available features with estimated depth, so that
they may be propagated forward in time to generate image feature trajectories
for visual servoing. Short and long distance experiments show the benefits of
trajectory servoing for navigating unknown areas without absolute positioning.
Trajectory servoing is shown to be more accurate than pose-based feedback when
both rely on the same underlying SLAM system.


Abstract:
  This paper shows that not only do the codimension one spurious poles of $N^k
MHV$ tree level diagrams in N=4 SYM theory cancel in the tree level amplitude
as expected, but their vanishing loci have a geometric interpretation that is
tightly connected to their representation in the positive Grassmannians. In
general, given a positroid variety, $\Sigma$, and a minimal matrix
representation of it in terms of independent variable valued matrices,
$M_{\mathcal{V}}$, one can define a polynomial, $R({\mathcal{V}})$ that is
uniquely defined by the Grassmann necklace, ${\mathcal{I}}$, of the positroid
cell. The vanishing locus of $R({\mathcal{V}})$ lies on the boundary of the
positive variety $\overline{\Sigma} \setminus \Sigma$, but not all boundaries
intersect the vanishing loci of a factor of $R({\mathcal{V}})$. We use this to
show that the codimension one spurious poles of N=4 SYM, represented in twistor
space, cancel in the tree level amplitude.


Abstract:
  From physics to engineering, biology and social science, natural and
artificial systems are characterized by interconnected topologies whose
features - e.g., heterogeneous connectivity, mesoscale organization, hierarchy
- affect their robustness to external perturbations, such as targeted attacks
to their units. Identifying the minimal set of units to attack to disintegrate
a complex network, i.e. network dismantling, is a computationally challenging
(NP-hard) problem which is usually attacked with heuristics. Here, we show that
a machine trained to dismantle relatively small systems is able to identify
higher-order topological patterns, allowing to disintegrate large-scale social,
infrastructural and technological networks more efficiently than human-based
heuristics. Remarkably, the machine assesses the probability that next attacks
will disintegrate the system, providing a quantitative method to quantify
systemic risk and detect early-warning signals of system's collapse. This
demonstrates that machine-assisted analysis can be effectively used for policy
and decision making to better quantify the fragility of complex systems and
their response to shocks.


Abstract:
  We provide a comprehensive quantitative analysis of localized and extended
topological defects in the steady state of 2D passive and active repulsive
Brownian disk systems. We show that, both in and out-of-equilibrium, the
passage from the solid to the hexatic is driven by the unbinding of
dislocations, in quantitative agreement with the KTHNY singularity. Instead,
although disclinations dissociate as soon as the liquid phase appears, extended
clusters of defects largely dominate below the solid-hexatic critical line. The
latter percolate in the liquid phase very close to the hexatic-liquid
transition, both for continuous and discontinuous transitions, in the
homogeneous liquid regime. At critical percolation the clusters of defects are
fractal with statistical and geometric properties that, within our numerical
accuracy, are independent of the activity and compatible with the universality
class of uncorrelated critical percolation. We also characterize the spatial
organization of different kinds of point-like defects and we show that the
disclinations are not free, but rather always very near more complex defect
structures. At high activity, the bulk of the dense phase generated by
Motility-Induced Phase Separation is characterized by a density of point-like
defects, and statistics and morphology of defect clusters, set by the amount of
activity and not the packing fraction. Hexatic domains within the dense phase
are separated by grain-boundaries along which a finite network of topological
defects resides, interrupted by gas bubbles in cavitation. The fractal
dimension of this network diminishes for increasing activity. This structure is
dynamic in the sense that the defect network allows for an unzipping mechanism
that leaves free space for gas bubbles to appear, close, and even be released
into the dilute phase.


Abstract:
  The Strict Avalanche Criterion (SAC) is a property of vectorial Boolean
functions that is used in the construction of strong S-boxes. We show in this
paper how to generalize the concept of SAC to address possible c-differential
attacks, in the realm of finite fields. We define the concepts of c-Strict
Avalanche Criterion (c-SAC) and c-Strict Avalanche Criterion of order m
(c-SAC(m)), and generalize results of (Li and Cusick, 2005). We also show
computationally how the new definition is not equivalent to the existing
concepts of c-bent1-ness (Stanica et al., 2020), nor (for n = m) PcN-ness
(Ellingsen et al., 2020)


Abstract:
  Spectral reconstructions provide rigorous means to remove the Gibbs
phenomenon and accelerate the convergence of spectral solutions in non-smooth
differential equations. In this paper, we show the concurrent emergence of
truncated convolution errors could entirely disrupt the performance of most
reconstruction techniques in the vicinity of discontinuities. They arise when
the Fourier coefficients of the product of two discontinuous functions, namely
$f=gh$, are approximated via truncated convolution of the corresponding Fourier
series, i.e. $\hat{f}_k\approx \sum_{|\ell|\leqslant
N}{\hat{g}_\ell\hat{h}_{k-\ell}}$. Nonetheless, we numerically illustrate and
rigorously prove that the classical Gegenbauer method remains exceptionally
robust against this phenomenon, with the reconstruction error still diminishing
proportional to $\mathcal{O}(N^{-1})$ for the Fourier order $N$, and
exponentially fast regardless of a constant. Finally, as a case study and a
problem of interest in grating analysis whence the phenomenon initially was
noticed, we demonstrate the emergence and practical resolution of truncated
convolution errors in grating modes, which constitute the basis of Fourier
modal methods.


Abstract:
  Peters' formula is an analytical estimate of the time-scale of gravitational
wave (GW)-induced coalescence of binary systems. It is used in countless
applications, where the convenience of a simple formula outweighs the need for
precision. However, many promising sources of the Laser Interferometer Space
Antenna (LISA), such as supermassive black hole binaries and extreme mass-ratio
inspirals (EMRIs), are expected to enter the LISA band with highly eccentric
($e \gtrsim$ 0.9) and highly relativistic orbits. These are exactly the two
limits in which Peters' estimate performs the worst. In this work, we expand
upon previous results and give simple analytical fits to quantify how the
inspiral time-scale is affected by the relative 1.5 post-Newtonian (PN)
hereditary fluxes and spin-orbit couplings. We discuss several cases that
demand a more accurate GW time-scale. We show how this can have a major
influence on quantities that are relevant for LISA event-rate estimates, such
as the EMRI critical semi-major axis. We further discuss two types of
environmental perturbations that can play a role in the inspiral phase: the
gravitational interaction with a third massive body and the energy loss due to
dynamical friction and torques from a surrounding gas medium ubiquitous in
galactic nuclei. With the aid of PN corrections to the time-scale in vacuum, we
find simple analytical expressions for the regions of phase space in which
environmental perturbations are of comparable strength to the effects of any
particular PN order, being able to qualitatively reproduce the results of much
more sophisticated analyses.


Abstract:
  Transfer learning with pre-training on large-scale datasets has played an
increasingly significant role in computer vision and natural language
processing recently. However, as there exist numerous application scenarios
that have distinctive demands such as certain latency constraints and
specialized data distributions, it is prohibitively expensive to take advantage
of large-scale pre-training for per-task requirements. In this paper, we focus
on the area of object detection and present a transfer learning system named
GAIA, which could automatically and efficiently give birth to customized
solutions according to heterogeneous downstream needs. GAIA is capable of
providing powerful pre-trained weights, selecting models that conform to
downstream demands such as latency constraints and specified data domains, and
collecting relevant data for practitioners who have very few datapoints for
their tasks. With GAIA, we achieve promising results on COCO, Objects365, Open
Images, Caltech, CityPersons, and UODB which is a collection of datasets
including KITTI, VOC, WiderFace, DOTA, Clipart, Comic, and more. Taking COCO as
an example, GAIA is able to efficiently produce models covering a wide range of
latency from 16ms to 53ms, and yields AP from 38.2 to 46.5 without whistles and
bells. To benefit every practitioner in the community of object detection, GAIA
is released at https://github.com/GAIA-vision.


Abstract:
  Efficient characterization of quantum devices is a significant challenge
critical for the development of large scale quantum computers. We consider an
experimentally motivated situation, in which we have a decent estimate of the
Hamiltonian, and its parameters need to be characterized and fine-tuned
frequently to combat drifting experimental variables. We use a machine learning
technique known as meta-learning to learn a more efficient optimizer for this
task. We consider training with the nearest-neighbor Ising model and study the
trained model's generalizability to other Hamiltonian models and larger system
sizes. We observe that the meta-optimizer outperforms other optimization
methods in average loss over test samples. This advantage follows from the
meta-optimizer being less likely to get stuck in local minima, which highly
skews the distribution of the final loss of the other optimizers. In general,
meta-learning decreases the number of calls to the experiment and reduces the
needed classical computational resources.


Abstract:
  In this paper we consider utilizing a residual neural network (ResNet) to
solve ordinary differential equations. Stochastic gradient descent method is
applied to obtain the optimal parameter set of weights and biases of the
network. We apply forward Euler, Runge-Kutta2 and Runge-Kutta4 finite
difference methods to generate three sets of targets training the ResNet and
carry out the target study. The well trained ResNet behaves just as its
counterpart of the corresponding one-step finite difference method. In
particular, we carry out (1) the architecture study in terms of number of
hidden layers and neurons per layer to find the optimal ResNet structure; (2)
the target study to verify the ResNet solver behaves as accurate as its finite
difference method counterpart; (3) solution trajectory simulation. Even the
ResNet solver looks like and is implemented in a way similar to forward Euler
scheme, its accuracy can be as high as any one step method. A sequence of
numerical examples are presented to demonstrate the performance of the ResNet
solver.


Abstract:
  There has been increasing interest in modeling survival data using deep
learning methods in medical research. In this paper, we proposed a Bayesian
hierarchical deep neural networks model for modeling and prediction of survival
data. Compared with previously studied methods, the new proposal can provide
not only point estimate of survival probability but also quantification of the
corresponding uncertainty, which can be of crucial importance in predictive
modeling and subsequent decision making. The favorable statistical properties
of point and uncertainty estimates were demonstrated by simulation studies and
real data analysis. The Python code implementing the proposed approach was
provided.


Abstract:
  The pre-trained neural models have recently achieved impressive performances
in understanding multimodal content. However, it is still very challenging to
pre-train neural models for video and language understanding, especially for
Chinese video-language data, due to the following reasons. Firstly, existing
video-language pre-training algorithms mainly focus on the co-occurrence of
words and video frames, but ignore other valuable semantic and structure
information of video-language content, e.g., sequential order and
spatiotemporal relationships. Secondly, there exist conflicts between video
sentence alignment and other proxy tasks. Thirdly, there is a lack of
large-scale and high-quality Chinese video-language datasets (e.g., including
10 million unique videos), which are the fundamental success conditions for
pre-training techniques.
  In this work, we propose a novel video-language understanding framework named
VICTOR, which stands for VIdeo-language understanding via Contrastive
mulTimOdal pRe-training. Besides general proxy tasks such as masked language
modeling, VICTOR constructs several novel proxy tasks under the contrastive
learning paradigm, making the model be more robust and able to capture more
complex multimodal semantic and structural relationships from different
perspectives. VICTOR is trained on a large-scale Chinese video-language
dataset, including over 10 million complete videos with corresponding
high-quality textual descriptions. We apply the pre-trained VICTOR model to a
series of downstream applications and demonstrate its superior performances,
comparing against the state-of-the-art pre-training methods such as VideoBERT
and UniVL. The codes and trained checkpoints will be publicly available to
nourish further developments of the research community.


Abstract:
  Existing graph neural networks (GNNs) largely rely on node embeddings, which
represent a node as a vector by its identity, type, or content. However, graphs
with unattributed nodes widely exist in real-world applications (e.g.,
anonymized social networks). Previous GNNs either assign random labels to nodes
(which introduces artefacts to the GNN) or assign one embedding to all nodes
(which fails to explicitly distinguish one node from another). Further, when
these GNNs are applied to unattributed node classification problems, they have
an undesired equivariance property, which are fundamentally unable to address
the data with multiple possible outputs. In this paper, we analyze the
limitation of existing approaches to node classification problems. Inspired by
our analysis, we propose a generalized equivariance property and a Preferential
Labeling technique that satisfies the desired property asymptotically.
Experimental results show that we achieve high performance in several
unattributed node classification tasks.


Abstract:
  Gradient estimation and vector space projection have been studied as two
distinct topics. We aim to bridge the gap between the two by investigating how
to efficiently estimate gradient based on a projected low-dimensional space. We
first provide lower and upper bounds for gradient estimation under both linear
and nonlinear projections, and outline checkable sufficient conditions under
which one is better than the other. Moreover, we analyze the query complexity
for the projection-based gradient estimation and present a sufficient condition
for query-efficient estimators. Built upon our theoretic analysis, we propose a
novel query-efficient Nonlinear Gradient Projection-based Boundary Blackbox
Attack (NonLinear-BA). We conduct extensive experiments on four image datasets:
ImageNet, CelebA, CIFAR-10, and MNIST, and show the superiority of the proposed
methods compared with the state-of-the-art baselines. In particular, we show
that the projection-based boundary blackbox attacks are able to achieve much
smaller magnitude of perturbations with 100% attack success rate based on
efficient queries. Both linear and nonlinear projections demonstrate their
advantages under different conditions. We also evaluate NonLinear-BA against
the commercial online API MEGVII Face++, and demonstrate the high blackbox
attack performance both quantitatively and qualitatively. The code is publicly
available at https://github.com/AI-secure/NonLinear-BA.


Abstract:
  Non-von Neumann computational hardware, based on neuron-inspired, non-linear
elements connected via linear, weighted synapses -- so-called neuromorphic
systems -- is a viable computational substrate. Since neuromorphic systems have
been shown to use less power than CPUs for many applications, they are of
potential use in autonomous systems such as robots, drones, and satellites, for
which power resources are at a premium. The power used by neuromorphic systems
is approximately proportional to the number of spiking events produced by
neurons on-chip. However, typical information encoding on these chips is in the
form of firing rates that unarily encode information. That is, the number of
spikes generated by a neuron is meant to be proportional to an encoded value
used in a computation or algorithm. Unary encoding is less efficient (produces
more spikes) than binary encoding. For this reason, here we present
neuromorphic computational mechanisms for implementing binary two's complement
operations. We use the mechanisms to construct a neuromorphic, binary matrix
multiplication algorithm that may be used as a primitive for linear
differential equation integration, deep networks, and other standard
calculations. We also construct a random walk circuit and apply it in Brownian
motion simulations. We study how both algorithms scale in circuit size and
iteration time.


Abstract:
  We report gamma ray spectroscopy measurements of trinitite samples and
analogous samples obtained from detonation sites in Nevada and Semipalatinsk,
as well as in situ measurements of topsoil at the Trinity site. We also report
the first isotopic composition measurements of trinitite using the novel
forensics technique of decay energy spectroscopy (DES) as a complement to
traditional forensics techniques. Our measurements are compared to other
published results.


Abstract:
  In adversarial training (AT), the main focus has been the objective and
optimizer while the model has been less studied, so that the models being used
are still those classic ones in standard training (ST). Classic network
architectures (NAs) are generally worse than searched NAs in ST, which should
be the same in AT. In this paper, we argue that NA and AT cannot be handled
independently, since given a dataset, the optimal NA in ST would be no longer
optimal in AT. That being said, AT is time-consuming itself; if we directly
search NAs in AT over large search spaces, the computation will be practically
infeasible. Thus, we propose a diverse-structured network (DS-Net), to
significantly reduce the size of the search space: instead of low-level
operations, we only consider predefined atomic blocks, where an atomic block is
a time-tested building block like the residual block. There are only a few
atomic blocks and thus we can weight all atomic blocks rather than find the
best one in a searched block of DS-Net, which is an essential trade-off between
exploring diverse structures and exploiting the best structures. Empirical
results demonstrate the advantages of DS-Net, i.e., weighting the atomic
blocks.


Abstract:
  In asynchronous games, Melli{\`e}s proved that innocent strategies are
positional: their behaviour only depends on the position, not the temporal
order used to reach it. This insightful result shaped our understanding of the
link between dynamic (i.e. game) and static (i.e. relational) semantics. In
this paper, we investigate the positionality of innocent strategies in the
traditional setting of Hyland-Ong-Nickau-Coquand pointer games. We show that
though innocent strategies are not positional, total finite innocent strategies
still enjoy a key consequence of positionality, namely positional injectivity:
they are entirely determined by their positions. Unfortunately, this does not
hold in general: we show a counterexample if finiteness and totality are
lifted. For finite partial strategies we leave the problem open; we show
however the partial result that two strategies with the same positions must
have the same P-views of maximal length.


Abstract:
  Many problems related to the quality of requirements arise during elicitation
and specification activities since they are written in natural language. The
flexibility and inherent nature of language make requirements prone to
inconsistencies, redundancies, and ambiguities, and consequently, this
influences negatively the later phases of the software life cycle. To address
this problem, this paper proposes an innovative approach that combines natural
language processing techniques and recurrent neural networks to automatically
assess the quality of software requirements. Initially, the analysis of
singular, complete, correct, and appropriate quality properties defined in the
IEEE 29148: 2018 standard is addressed. The proposed neural models are trained
with a data set composed of 1000 software requirements. The proposal provides
an average accuracy of 75%. These promising results were a motivation to
explore its application in the evaluation of other quality properties


Abstract:
  Computing the similarity of two point sets is a ubiquitous task in medical
imaging, geometric shape comparison, trajectory analysis, and many more
settings. Arguably the most basic distance measure for this task is the
Hausdorff distance, which assigns to each point from one set the closest point
in the other set and then evaluates the maximum distance of any assigned pair.
A drawback is that this distance measure is not translational invariant, that
is, comparing two objects just according to their shape while disregarding
their position in space is impossible.
  Fortunately, there is a canonical translational invariant version, the
Hausdorff distance under translation, which minimizes the Hausdorff distance
over all translations of one of the point sets. For point sets of size $n$ and
$m$, the Hausdorff distance under translation can be computed in time $\tilde
O(nm)$ for the $L_1$ and $L_\infty$ norm [Chew, Kedem SWAT'92] and $\tilde O(nm
(n+m))$ for the $L_2$ norm [Huttenlocher, Kedem, Sharir DCG'93].
  As these bounds have not been improved for over 25 years, in this paper we
approach the Hausdorff distance under translation from the perspective of
fine-grained complexity theory. We show (i) a matching lower bound of
$(nm)^{1-o(1)}$ for $L_1$ and $L_\infty$ (and all other $L_p$ norms) assuming
the Orthogonal Vectors Hypothesis and (ii) a matching lower bound of
$n^{2-o(1)}$ for $L_2$ in the imbalanced case of $m = O(1)$ assuming the 3SUM
Hypothesis.


Abstract:
  Breakthrough advances in reinforcement learning (RL) research have led to a
surge in the development and application of RL. To support the field and its
rapid growth, several frameworks have emerged that aim to help the community
more easily build effective and scalable agents. However, very few of these
frameworks exclusively support multi-agent RL (MARL), an increasingly active
field in itself, concerned with decentralised decision-making problems. In this
work, we attempt to fill this gap by presenting Mava: a research framework
specifically designed for building scalable MARL systems. Mava provides useful
components, abstractions, utilities and tools for MARL and allows for simple
scaling for multi-process system training and execution, while providing a high
level of flexibility and composability. Mava is built on top of DeepMind's Acme
\citep{hoffman2020acme}, and therefore integrates with, and greatly benefits
from, a wide range of already existing single-agent RL components made
available in Acme. Several MARL baseline systems have already been implemented
in Mava. These implementations serve as examples showcasing Mava's reusable
features, such as interchangeable system architectures, communication and
mixing modules. Furthermore, these implementations allow existing MARL
algorithms to be easily reproduced and extended. We provide experimental
results for these implementations on a wide range of multi-agent environments
and highlight the benefits of distributed system training.


Abstract:
  End-to-end speech translation models have become a new trend in research due
to their potential of reducing error propagation. However, these models still
suffer from the challenge of data scarcity. How to effectively use unlabeled or
other parallel corpora from machine translation is promising but still an open
problem. In this paper, we propose Cross Speech-Text Network (XSTNet), an
end-to-end model for speech-to-text translation. XSTNet takes both speech and
text as input and outputs both transcription and translation text. The model
benefits from its three key design aspects: a self-supervised pre-trained
sub-network as the audio encoder, a multi-task training objective to exploit
additional parallel bilingual text, and a progressive training procedure. We
evaluate the performance of XSTNet and baselines on the MuST-C En-X and
LibriSpeech En-Fr datasets. In particular, XSTNet achieves state-of-the-art
results on all language directions with an average BLEU of 28.8, outperforming
the previous best method by 3.2 BLEU. Code, models, cases, and more detailed
analysis are available at https://github.com/ReneeYe/XSTNet.


Abstract:
  In this paper, we describe how the electronic rolling shutter in CMOS image
sensors can be exploited using a bright, modulated light source (e.g., an
inexpensive, off-the-shelf laser), to inject fine-grained image disruptions. We
demonstrate the attack on seven different CMOS cameras, ranging from cheap IoT
to semi-professional surveillance cameras, to highlight the wide applicability
of the rolling shutter attack. We model the fundamental factors affecting a
rolling shutter attack in an uncontrolled setting. We then perform an
exhaustive evaluation of the attack's effect on the task of object detection,
investigating the effect of attack parameters. We validate our model against
empirical data collected on two separate cameras, showing that by simply using
information from the camera's datasheet the adversary can accurately predict
the injected distortion size and optimize their attack accordingly. We find
that an adversary can hide up to 75% of objects perceived by state-of-the-art
detectors by selecting appropriate attack parameters. We also investigate the
stealthiness of the attack in comparison to a na\"{i}ve camera blinding attack,
showing that common image distortion metrics can not detect the attack
presence. Therefore, we present a new, accurate and lightweight enhancement to
the backbone network of an object detector to recognize rolling shutter
attacks. Overall, our results indicate that rolling shutter attacks can
substantially reduce the performance and reliability of vision-based
intelligent systems.


Abstract:
  We analyze the charmonium states by testing a phenomenological
nonrelativistic potential and propose a new set of parameters. This new set of
parameters are fixed using only the lowest lying S-wave states of charmonia
where the spin-orbit and tensor interactions will not contribute. After fitting
the parameters we analyze the whole fine structure of charmonium states taking
into account the spin-orbit and tensor interactions too. Calculations showed
that the nonrelativistic potential model with the phenomenologically defined
parameters is indeed well approximation for describing the charmonium states.


Abstract:
  This work presents the dynamic properties of charged test particles
influenced by the gravitational and electromagnetic fields. Accordingly, we
concentrate on the simplest static and axially symmetric metric in this work,
which contains two quadrupole parameters. One relates to the central object,
and another relates to the distortion parameter, which is linked to the
external distribution of matter. This metric may associate the observable
effects to these parameters as dynamical degrees of freedom. The astrophysical
motivation for choosing such fields is the possibility to constitute a
reasonable model for a real situation occurring in these objects' vicinity. To
test the role of large-scale magnetic fields in accretion processes, we start
by analyzing different bound orbits of timelike orbits under the influence of
the system's different parameters. In particular, studying the influence of the
strength of the magnetic field. This leads to the examine their stability
concerning radial and/or vertical oscillations. The final goal is to discuss
the oscillation modes' resonant phenomena using different resonant models for
disk-oscillation modes.


Abstract:
  The capacity of multiple-input multiple-output additive white Gaussian noise
channels is investigated under peak amplitude constraints on the norm of the
input vector. New insights on the capacity-achieving input distribution are
presented. Furthermore, it is provided an iterative algorithm to numerically
evaluate both the information capacity and the optimal input distribution of
such channel.


Abstract:
  We consider the problems of sampling and counting edges from a graph on $n$
vertices where our basic access is via uniformly sampled vertices. When we have
a vertex, we can see its degree, and access its neighbors. Eden and Rosenbaum
[SOSA 2018] have shown it is possible to sample an edge $\epsilon$-uniformly in
$O(\sqrt{1/\epsilon}\frac{n}{\sqrt{m}})$ vertex accesses. Here, we get down to
expected $O(\log(1/\epsilon)\frac{n}{\sqrt{m}})$ vertex accesses. Next, we
consider the problem of sampling $s>1$ edges. For this we introduce a model
that we call hash-based neighbor access. We show that, w.h.p, we can sample $s$
edges exactly uniformly at random, with or without replacement, in
$\tilde{O}(\sqrt{s} \frac{n}{\sqrt{m}} + s)$ vertex accesses. We present a
matching lower bound of $\Omega(\sqrt{s} \frac{n}{\sqrt{m}} + s)$ which holds
for $\epsilon$-uniform edge multi-sampling with some constant $\epsilon>0$ even
though our positive result has $\epsilon=0$.
  We then give an algorithm for edge counting. W.h.p., we count the number of
edges to within error $\epsilon$ in time $\tilde{O}(\frac{n}{\epsilon\sqrt{m}}
+ \frac{1}{\epsilon^2})$. When $\epsilon$ is not too small (for $\epsilon \geq
\frac{\sqrt m}{n}$), we present a near-matching lower-bound of
$\Omega(\frac{n}{\epsilon \sqrt{m}})$. In the same range, the previous best
upper and lower bounds were polynomially worse in $\epsilon$.
  Finally, we give an algorithm that instead of hash-based neighbor access uses
the more standard pair queries (``are vertices $u$ and $v$ adjacent''). W.h.p.
it returns $1+\epsilon$ approximation of the number of edges and runs in
expected time $\tilde{O}(\frac{n}{\epsilon \sqrt{m}} + \frac{1}{\epsilon^4})$.
This matches our lower bound when $\epsilon$ is not too small, specifically for
$\epsilon \geq \frac{m^{1/6}}{n^{1/3}}$.


Abstract:
  In this paper, we build on the work from our previous paper
(arXiv:2002.01556) to show that periodic rational $G$-equivariant topological
$K$-theory has a unique genuine-commutative ring structure for $G$ a finite
abelian group. This means that every genuine-commutative ring spectrum whose
homotopy groups are those of $KU_{\mathbb{Q},G}$ is weakly equivalent, as a
genuine-commutative ring spectrum, to $KU_{\mathbb{Q},G}$. In contrast, the
connective rational equivariant $K$-theory spectrum does not have this type of
uniqueness of genuine-commutative ring structure.


Abstract:
  We establish new Liouville-type theorems for the two-dimensional stationary
magneto-hydrodynamic incompressible system assuming that the velocity and
magnetic field have bounded Dirichlet integral. The key tool in our proof is
observing that the stream function associated to the magnetic field satisfies a
simple drift-diffusion equation for which a maximum principle is available.


Abstract:
  Although much progress has been made recently in 3D face reconstruction, most
previous work has been devoted to predicting accurate and fine-grained 3D
shapes. In contrast, relatively little work has focused on generating
high-fidelity face textures. Compared with the prosperity of photo-realistic 2D
face image generation, high-fidelity 3D face texture generation has yet to be
studied. In this paper, we proposed a novel UV map generation model that
predicts the UV map from a single face image. The model consists of a UV
sampler and a UV generator. By selectively sampling the input face image's
pixels and adjusting their relative locations, the UV sampler generates an
incomplete UV map that could faithfully reconstruct the original face. Missing
textures in the incomplete UV map are further full-filled by the UV generator.
The training is based on pseudo ground truth blended by the 3DMM texture and
the input face texture, thus weakly supervised. To deal with the artifacts in
the imperfect pseudo UV map, multiple partial UV map discriminators are
leveraged.


Abstract:
  This paper develops a new method for identifying and estimating production
functions with partially latent inputs. Such data structures arise naturally
when data are collected using an "input-based sampling" strategy, e.g., if the
sampling unit is one of multiple labor input factors. We show that the latent
inputs can be nonparametrically identified, if they are strictly monotone
functions of a scalar shock a la Olley & Pakes (1996). With the latent inputs
identified, semiparametric estimation of the production function proceeds
within an IV framework that accounts for the endogeneity of the covariates. We
illustrate the usefulness of our method using two applications. The first
focuses on pharmacies: we find that production function differences between
chains and independent pharmacies may partially explain the observed
transformation of the industry structure. Our second application investigates
skill production functions and illustrates important differences in child
investments between married and divorced couples.


Abstract:
  Atom-in-jellium calculations of the Einstein frequency in condensed matter
and of the equation of state were used to predict the variation of shear
modulus from zero pressure to ~$10^7$ g/cm$^3$, for several elements relevant
to white dwarf (WD) stars and other self-gravitating systems. This is by far
the widest range reported electronic structure calculation of shear modulus,
spanning from ambient through the one-component plasma to extreme relativistic
conditions. The predictions were based on a relationship between Debye
temperature and shear modulus which we assess to be accurate at the o(10%)
level, and is the first known use of atom-in-jellium theory to calculate a
shear modulus. We assessed the overall accuracy of the method by comparing with
experimental measurements and more detailed electronic structure calculations
at lower pressures.