Abstract:
  We analyse the gas content evolution of infalling haloes in cluster
environments from THE THREE HUNDRED project, a collection of 324 numerically
modelled galaxy clusters. The haloes in our sample were selected within
$5R_{200}$ of the main cluster halo at $z=0$ and have total halo mass
$M_{200}\geq10^{11} h^{-1} M_{\odot}$. We track their main progenitors and
study their gas evolution since their crossing into the infall region, which we
define as $1-4R_{200}$. Studying the radial trends of our populations using
both the full phase space information and a line-of-sight projection, we
confirm the Arthur et al. (2019) result and identify a characteristic radius
around $1.7R_{200}$ in 3D and at $R_{200}$ in projection at which infalling
haloes lose nearly all of the gas prior their infall. Splitting the trends by
subhalo status we show that subhaloes residing in group-mass and low-mass host
haloes in the infall region follow similar radial gas-loss trends as their
hosts, whereas subhaloes of cluster-mass host haloes are stripped of their gas
much further out. Our results show that infalling objects suffer significant
gaseous disruption that correlates with time-since-infall, cluster-centric
distance and host mass, and that the gaseous disruption they experience is a
combination of subhalo pre-processing and object gas depletion at a radius
which behaves like an accretion shock.


Abstract:
  Eddington-inspired Born-Infeld gravity is an important modification of
Einstein's general relativity, which can give rise to non-singular cosmologies
at the classical level, and avoid the end-stage singularity in a gravitational
collapse process. In the Newtonian limit, this theory gives rise to a modified
Poisson's equation, as a consequence of which stellar observables acquire model
dependent corrections, compared to the ones computed in the low energy limit of
general relativity. This can in turn be used to establish astrophysical
constraints on the theory. Here, we obtain such a constraint using
observational data from cataclysmic variable binaries. In particular, we
consider the tidal disruption limit of the secondary star by a white dwarf
primary. The Roche lobe filling condition of this secondary star is used to
compute stellar observables in the modified gravity theory in a numerical
scheme. These are then contrasted with the values obtained by using available
data on these objects, via a Monte Carlo error progression method. This way, we
are able to constrain the theory within $5\sigma$ confidence level.


Abstract:
  Nearest Neighbor Search (NNS) is a central task in knowledge representation,
learning, and reasoning. There is vast literature on efficient algorithms for
constructing data structures and performing exact and approximate NNS. This
paper studies NNS under Uncertainty (NNSU). Specifically, consider the setting
in which an NNS algorithm has access only to a stochastic distance oracle that
provides a noisy, unbiased estimate of the distance between any pair of points,
rather than the exact distance. This models many situations of practical
importance, including NNS based on human similarity judgements, physical
measurements, or fast, randomized approximations to exact distances. A naive
approach to NNSU could employ any standard NNS algorithm and repeatedly query
and average results from the stochastic oracle (to reduce noise) whenever it
needs a pairwise distance. The problem is that a sufficient number of repeated
queries is unknown in advance; e.g., a point maybe distant from all but one
other point (crude distance estimates suffice) or it may be close to a large
number of other points (accurate estimates are necessary). This paper shows how
ideas from cover trees and multi-armed bandits can be leveraged to develop an
NNSU algorithm that has optimal dependence on the dataset size and the
(unknown)geometry of the dataset.


Abstract:
  Question generation (QG) is to generate natural and grammatical questions
that can be answered by a specific answer for a given context. Previous
sequence-to-sequence models suffer from a problem that asking high-quality
questions requires commonsense knowledge as backgrounds, which in most cases
can not be learned directly from training data, resulting in unsatisfactory
questions deprived of knowledge. In this paper, we propose a multi-task
learning framework to introduce commonsense knowledge into question generation
process. We first retrieve relevant commonsense knowledge triples from mature
databases and select triples with the conversion information from source
context to question. Based on these informative knowledge triples, we design
two auxiliary tasks to incorporate commonsense knowledge into the main QG
model, where one task is Concept Relation Classification and the other is Tail
Concept Generation. Experimental results on SQuAD show that our proposed
methods are able to noticeably improve the QG performance on both automatic and
human evaluation metrics, demonstrating that incorporating external commonsense
knowledge with multi-task learning can help the model generate human-like and
high-quality questions.


Abstract:
  This paper considers decentralized stochastic optimization over a network of
$n$ nodes, where each node possesses a smooth non-convex local cost function
and the goal of the networked nodes is to find an $\epsilon$-accurate
first-order stationary point of the sum of the local costs. We focus on an
online setting, where each node accesses its local cost only by means of a
stochastic first-order oracle that returns a noisy version of the exact
gradient. In this context, we propose a novel single-loop decentralized hybrid
variance-reduced stochastic gradient method, called GT-HSGD, that outperforms
the existing approaches in terms of both the oracle complexity and practical
implementation. The GT-HSGD algorithm implements specialized local hybrid
stochastic gradient estimators that are fused over the network to track the
global gradient. Remarkably, GT-HSGD achieves a network topology-independent
oracle complexity of $O(n^{-1}\epsilon^{-3})$ when the required error tolerance
$\epsilon$ is small enough, leading to a linear speedup with respect to the
centralized optimal online variance-reduced approaches that operate on a single
node. Numerical experiments are provided to illustrate our main technical
results.


Abstract:
  The magnetic activity of the Sun directly impacts the Earth and human life.
Likewise, other stars will have an impact on the habitability of planets
orbiting these host stars. The lack of information on the magnetic field in the
higher atmospheric layers hampers our progress in understanding solar magnetic
activity. Overcoming this limitation would allow us to address four paramount
long-standing questions: (1) How does the magnetic field couple the different
layers of the atmosphere, and how does it transport energy? (2) How does the
magnetic field structure, drive and interact with the plasma in the
chromosphere and upper atmosphere? (3) How does the magnetic field destabilise
the outer solar atmosphere and thus affect the interplanetary environment? (4)
How do magnetic processes accelerate particles to high energies? New
ground-breaking observations are needed to address these science questions. We
suggest a suite of three instruments that far exceed current capabilities in
terms of spatial resolution, light-gathering power, and polarimetric
performance: (a) A large-aperture UV-to-IR telescope of the 1-3 m class aimed
mainly to measure the magnetic field in the chromosphere by combining high
spatial resolution and high sensitivity. (b) An extreme-UV-to-IR coronagraph
that is designed to measure the large-scale magnetic field in the corona with
an aperture of about 40 cm. (c) An extreme-UV imaging polarimeter based on a 30
cm telescope that combines high throughput in the extreme UV with polarimetry
to connect the magnetic measurements of the other two instruments. This mission
to measure the magnetic field will unlock the driver of the dynamics in the
outer solar atmosphere and thereby greatly advance our understanding of the Sun
and the heliosphere.


Abstract:
  In this work, we investigate the near horizon and asymptotic symmetries of
static and rotating hairy$-$AdS black hole in the framework of general minimal
massive gravity. We obtain energy, angular momentum and entropy of the
solutions. Then we show that our results for these quantities are consistent
with the first law of black hole thermodynamics. By considering the near
horizon geometry of black hole, we find near horizon conserved charges and
their algebra. By writing the algebra of conserved charges in terms of Fourier
modes we have obtained the conserved charges in terms of zero modes.


Abstract:
  We propose a novel framework for modeling multiple multivariate point
processes, each with heterogeneous event types that share an underlying space
and obey the same generative mechanism. Focusing on Hawkes processes and their
variants that are associated with Granger causality graphs, our model leverages
an uncountable event type space and samples the graphs with different sizes
from a nonparametric model called {\it graphon}. Given those graphs, we can
generate the corresponding Hawkes processes and simulate event sequences.
Learning this graphon-based Hawkes process model helps to 1) infer the
underlying relations shared by different Hawkes processes; and 2) simulate
event sequences with different event types but similar dynamics. We learn the
proposed model by minimizing the hierarchical optimal transport distance
between the generated event sequences and the observed ones, leading to a novel
reward-augmented maximum likelihood estimation method. We analyze the
properties of our model in-depth and demonstrate its rationality and
effectiveness in both theory and experiments.


Abstract:
  The Secured Overnight Funding Rate (SOFR) is becoming the main Risk-Free Rate
benchmark in US dollars, thus interest rate term structure models need to be
updated to reflect the key features exhibited by the dynamics of SOFR and the
forward rates implied by SOFR futures. Historically, interest rate term
structure modelling has been based on rates of substantially longer time to
maturity than overnight, but with SOFR the overnight rate now is the primary
market observable. This means that the empirical idiosyncrasies of the
overnight rate cannot be ignored when constructing interest rate models in a
SOFR-based world.
  As a rate reflecting transactions in the Treasury overnight repurchase
market, the dynamics of SOFR are closely linked to the dynamics of the
Effective Federal Funds Rate (EFFR), which is the interest rate most directly
impacted by US monetary policy target rate decisions. Therefore, these rates
feature jumps at known times (Federal Open Market Committee meeting dates), and
market expectations of these jumps are reflected in prices for futures written
on these rates. On the other hand, forward rates implied by Fed Funds and SOFR
futures continue to evolve diffusively. The model presented in this paper
reflects the key empirical features of SOFR dynamics and is calibrated to
futures prices. In particular, the model reconciles diffusive forward rate
dynamics with piecewise constant paths of the target short rate.


Abstract:
  I discuss the strong link between the transmission line (TL) equation and the
TL circuit model for the charging of an electrolyte-filled pore of finite
length. In particular, I show how Robin and Neumann boundary conditions to the
TL equation, proposed by others on physical grounds, also emerge in the TL
circuit subject to a stepwise potential. The pore relaxes with a timescale
$\tau$, an expression for which consistently follows from the TL circuit, TL
equation, and from the pore's known impedance. An approximation to $\tau$
explains the numerically determined relaxation time of the stack-electrode
model of Lian et al. [Phys. Rev. Lett. 124, 076001 (2020), arXiv:1911.09924].


Abstract:
  We study the dynamics of a cosmological model with a perfect fluid and
$\mathcal{N}$ fields on a hyperbolic field space interacting via a symmetric
potential. We list all late-time solutions, investigate their stability and
briefly discuss predictions of the theory. Moreover, for the case of two scalar
fields and an exponential potential we prove that the field equations are
Liouville integrable and we provide for the first time the general solution for
a region of the parameter space.


Abstract:
  We prove foundational results about the set of homomorphisms from a finitely
generated group to the collection of all fundamental groups of compact
3-manifolds and answer questions of Reid-Wang-Zhou and Agol-Liu.


Abstract:
  For every positive integer $r$, we solve the modular Schwarzian differential
equation $\{h,\tau\}=2\pi^2r^2E_4$, where $E_4$ is the weight 4 Eisenstein
series, by means of equivariant functions on the upper half-plane. This paper
supplements previous works \cite{forum, ramanujan}, where the same equation has
been solved for infinite families of rational values of $r$. This also leads to
the solutions to the modular differential equation $y''+r^2\pi^2E_4\,y=0$ for
every positive integer $r$. These solutions are quasi-modular forms for
$\mbox{SL}_2(\mathbb Z)$ if $r$ is even or for the subgroup of index 2,
$\mbox{SL}_2(\mathbb Z)^2$, if $r$ is odd.


Abstract:
  Context. Direct observation of gamma-ray emission from the decay of $^{18}$F
ejected in classical nova outbursts remains a major focus of the nuclear
astrophysics community. However, modeling the abundance of ejected $^{18}$F,
and thus the predicted detectability distance of a gamma-ray signal near 511
keV emitted from these transient thermonuclear episodes, is hampered by
significant uncertainties in our knowledge of the key $^{18}$F(p,$\alpha$)
reaction rate. Aims. We analyze uncertainties in the most recent nuclear
physics experimental results employed to calculate the $^{18}$F(p,$\alpha$)
reaction rate. Our goal is to determine which uncertainties have the most
profound influence on the predicted abundance of $^{18}$F ejected from novae,
in order to guide future experimental works. Methods. We calculated a wide
range of $^{18}$F(p,$\alpha$) reaction rates using R-Matrix formalism, allowing
us to take into account all interference effects. Using a selection of 16
evenly-spaced rates over the full range, we performed 16 new hydrodynamic nova
simulations. Results. We performed one of the most thorough theoretical studies
of the impact of the $^{18}$F(p,$\alpha$) reaction in classical novae to date.
The $^{18}$F(p,$\alpha$) rate remains highly uncertain at nova temperatures,
resulting in a factor ~10 uncertainty in the predicted abundance of $^{18}$F
ejected from nova explosions. We also found that the abundance of $^{18}$F may
be strongly correlated with that of $^{19}$F. Conclusions. Despite numerous
nuclear physics uncertainties affecting the $^{18}$F(p,$\alpha$) reaction rate,
which are dominated by unknown interference signs between 1/2$^+$ and 3/2$^+$
resonances, future experimental work should focus on firmly and precisely
determining the directly measurable quantum properties of the subthreshold
states in the compound nucleus $^{19}$Ne near 6.13 and 6.29 MeV.


Abstract:
  We study uncloneable quantum encryption schemes for classical messages as
recently proposed by Broadbent and Lord. We focus on the information-theoretic
setting and give several limitations on the structure and security of these
schemes: Concretely, 1) We give an explicit cloning-indistinguishable attack
that succeeds with probability $\frac12 + \mu/16$ where $\mu$ is related to the
largest eigenvalue of the resulting quantum ciphertexts. 2) For a uniform
message distribution, we partially characterize the scheme with the minimal
success probability for cloning attacks. 3) Under natural symmetry conditions,
we prove that the rank of the ciphertext density operators has to grow at least
logarithmically in the number of messages to ensure uncloneable security. 4)
The \emph{simultaneous} one-way-to-hiding (O2H) lemma is an important technique
in recent works on uncloneable encryption and quantum copy protection. We give
an explicit example which shatters the hope of reducing the multiplicative
"security loss" constant in this lemma to below 9/8.


Abstract:
  Over the past two decades, CNN architectures have produced compelling models
of sound perception and cognition, learning hierarchical organizations of
features. Analogous to successes in computer vision, audio feature
classification can be optimized for a particular task of interest, over a wide
variety of datasets and labels. In fact similar architectures designed for
image understanding have proven effective for acoustic scene analysis. Here we
propose applying Transformer based architectures without convolutional layers
to raw audio signals. On a standard dataset of Free Sound 50K,comprising of 200
categories, our model outperforms convolutional models to produce state of the
art results. This is significant as unlike in natural language processing and
computer vision, we do not perform unsupervised pre-training for outperforming
convolutional architectures. On the same training set, with respect mean
aver-age precision benchmarks, we show a significant improvement. We further
improve the performance of Transformer architectures by using techniques such
as pooling inspired from convolutional net-work designed in the past few years.
In addition, we also show how multi-rate signal processing ideas inspired from
wavelets, can be applied to the Transformer embeddings to improve the results.
We also show how our models learns a non-linear non constant band-width
filter-bank, which shows an adaptable time frequency front end representation
for the task of audio understanding, different from other tasks e.g. pitch
estimation.


Abstract:
  Automatic code synthesis from natural language descriptions is a challenging
task. We witness massive progress in developing code generation systems for
domain-specific languages (DSLs) employing sequence-to-sequence deep learning
techniques in the recent past. In this paper, we specifically experiment with
\textsc{AlgoLisp} DSL-based generative models and showcase the existence of
significant dataset bias through different classes of adversarial examples. We
also experiment with two variants of Transformer-based models that outperform
all existing \textsc{AlgoLisp} DSL-based code generation baselines. Consistent
with the current state-of-the-art systems, our proposed models, too, achieve
poor performance under adversarial settings. Therefore, we propose several
dataset augmentation techniques to reduce bias and showcase their efficacy
using robust experimentation.


Abstract:
  We use combined South Pole Telescope (SPT)+Planck temperature maps to analyze
the circumgalactic medium (CGM) encompassing 138,235 massive, quiescent 0.5
$\leq$ z $\leq$ 1.5 galaxies selected from data from the Dark Energy Survey
(DES) and Wide-Field Infrared Survey Explorer (WISE). Images centered on these
galaxies were cut from the 1.85 arcmin resolution maps with frequency bands at
95, 150, and 220 GHz. The images were stacked, filtered, and fit with a
gray-body dust model to isolate the thermal Sunyaev-Zel'dovich (tSZ) signal,
which is proportional to the total energy contained in the CGM of the galaxies.
We separate these $M_{\star} = 10^{10.9} M_\odot$ - $10^{12} M_\odot$ galaxies
into 0.1 dex stellar mass bins, detecting tSZ per bin up to $5.6\sigma$ and a
total signal-to-noise ratio of $10.1\sigma$. We also detect dust with an
overall signal-to-noise ratio of $9.8\sigma$, which overwhelms the tSZ at
150GHz more than in other lower-redshift studies. We correct for the $0.16$ dex
uncertainty in the stellar mass measurements by parameter fitting for an
unconvolved power-law energy-mass relation, $E_{\rm therm} = E_{\rm therm,peak}
\left(M_\star/M_{\star,{\rm peak}} \right)^\alpha$, with the peak stellar mass
distribution of our selected galaxies defined as $M_{\star,{\rm peak}}= 2.3
\times 10^{11} M_\odot$. This yields an $E_{\rm therm,peak}=
5.98_{-1.00}^{+1.02} \times 10^{60}$ erg and $\alpha=3.77_{-0.74}^{+0.60}$.
These are consistent with $z \approx 0$ observations and within the limits of
moderate models of active galactic nuclei (AGN) feedback. We also compute the
radial profile of our full sample, which is similar to that recently measured
at lower-redshift by Schaan et al. (2021).


Abstract:
  Spontaneous scalarization is a gravitational phenomenon in which deviations
from general relativity arise once a certain threshold in curvature is
exceeded, while being entirely absent below that threshold. For black holes,
scalarization is known to be triggered by a coupling between a scalar and the
Gauss-Bonnet invariant. A coupling with the Ricci scalar, which can trigger
scalarization in neutron stars, is instead known to not contribute to the onset
of black hole scalarization, and has so far been largely ignored in the
literature when studying scalarized black holes. In this paper, we study the
combined effect of both these couplings on black hole scalarization. We show
that the Ricci coupling plays a significant role in the properties of
scalarized solutions and their domain of existence. This work is an important
step in the construction of scalarization models that evade binary pulsar
constraints and have general relativity as a cosmological late-time attractor,
while still predicting deviations from general relativity in black hole
observations.


Abstract:
  This paper studies the problem of multi-agent computation under the
differential privacy requirement of the agents' local datasets against
eavesdroppers having node-to-node communications. We first propose for the
network equipped with public-private networks. The private network is sparse
and not even necessarily connected, over which communications are encrypted and
secure along with the intermediate node states; the public network is connected
and may be dense, over which communications are allowed to be public. In this
setting, we propose a multi-gossip PPSC mechanism over the private network,
where at each step, randomly selected node pairs update their states in such a
way that they are shuffled with random noise while maintaining summation
consistency. We show that this mechanism can achieve any desired differential
privacy level with any prescribed probability. Next, we embed this mechanism in
distributed computing processes, and propose privacy-guarantee protocols for
three basic computation tasks, where an adaptive mechanism adjusts the amount
of noise injected in PPSC steps for privacy protection, and the number of
regular computation steps for accuracy guarantee. For average consensus, we
develop a PPSC-Gossip averaging consensus algorithm by utilizing the
multi-gossip PPSC mechanism for privacy encryption before an averaging
consensus algorithm over the public network for local computations. For network
linear equations and distributed convex optimization, we develop two respective
distributed computing protocols by following the PPSC-Gossip averaging
consensus algorithm with an additional projection or gradient descent step
within each step of computation. Given any privacy and accuracy requirements,
it is shown that all three proposed protocols can compute their corresponding
problems with the desired computation accuracy, while achieving the desired
differential privacy.


Abstract:
  Zr and Mo macrosegregations were investigated in Ti6246 titanium alloy
industrial-scale ingotby vacuum arc remelting. The formation mechanism of Zr
and Mo macrosegregations was studied during the solidification process. Zr
macrosegregation was characterized by low content in the equiaxed grain zone
and high content in the hot top zone. Mo exhibits an opposite trend with Zr.
The macrosegregations of Zr and Mo were the most pronounced, with a statistic
segregation degree higher than Al and Sn. It could be concluded that
temperature gradient and solidification rate dominated the macrosegregation
formations during the solidification process. The thermal buoyancy made the
negative segregation Zr be continuously discharged to the front of the
solid-liquid interface. Mo was enriched in the solid phase at the solid-liquid
interface as the positive segregation.


Abstract:
  In the Demand Strip Packing problem (DSP), we are given a time interval and a
collection of tasks, each characterized by a processing time and a demand for a
given resource (such as electricity, computational power, etc.). A feasible
solution consists of a schedule of the tasks within the mentioned time
interval. Our goal is to minimize the peak resource consumption, i.e. the
maximum total demand of tasks executed at any point in time.
  It is known that DSP is NP-hard to approximate below a factor 3/2, and
standard techniques for related problems imply a (polynomial-time)
2-approximation. Our main result is a (5/3+eps)-approximation algorithm for any
constant eps>0. We also achieve best-possible approximation factors for some
relevant special cases.


Abstract:
  This paper focuses on error-correcting codes that can handle a predefined set
of specific error patterns. The need for such codes arises in many settings of
practical interest, including wireless communication and flash memory systems.
In many such settings, a smaller field size is achievable than that offered by
MDS and other standard codes. We establish a connection between the minimum
alphabet size for this generalized setting and the combinatorial properties of
a hypergraph that represents the prespecified collection of error patterns. We
also show a connection between error and erasure correcting codes in this
specialized setting. This allows us to establish bounds on the minimum alphabet
size and show an advantage of non-linear codes over linear codes in a
generalized setting. We also consider a variation of the problem which allows a
small probability of decoding error and relate it to an approximate version of
hypergraph coloring.


Abstract:
  The complexity of cyberattacks in Cyber-Physical Systems (CPSs) calls for a
mechanism that can evaluate the operational behaviour and security without
negatively affecting the operation of live systems. In this regard, Digital
Twins (DTs) are revolutionizing the CPSs. DTs strengthen the security of CPSs
throughout the product lifecycle, while assuming that the DT data is trusted,
providing agility to predict and respond to real-time changes. However,
existing DTs solutions in CPS are constrained with untrustworthy data
dissemination among multiple stakeholders and timely course correction. Such
limitations reinforce the significance of designing trustworthy distributed
solutions with the ability to create actionable insights in real-time. To do
so, we propose a framework that focuses on trusted and intelligent DT by
integrating blockchain and Artificial Intelligence (AI). Following a hybrid
approach, the proposed framework not only acquires process knowledge from the
specifications of the CPS, but also relies on AI to learn security threats
based on sensor data. Furthermore, we integrate blockchain to safeguard product
lifecycle data. We discuss the applicability of the proposed framework for the
automotive industry as a CPS use case. Finally, we identify the open challenges
that impede the implementation of intelligence-driven architectures in CPSs.


Abstract:
  We extend the notion of singular vectors in the context of Diophantine
approximation of real numbers with elements of a totally real number field $K$.
For $m\geq1$, we establish a version of Dani correspondence in number fields
and prove that under a class of `friendly measures' in $K_S^m$, the set of
singular vectors has measure zero. Tackling the inheritance question, we show
the existence of nondegenerate divergent orbits on manifolds in $K_S^m$ under
the action of a certain one parameter subgroup of $\mathrm{SL}_{m+1}(K_S)$.


Abstract:
  The Louvain algorithm is currently one of the most popular community
detection methods. This algorithm finds communities by maximizing a quantity
called modularity. In this work, we describe a metric space of clusterings,
where clusterings are described by a binary vector indexed by the vertex-pairs.
We extend this geometry to a hypersphere and prove that maximizing modularity
is equivalent to minimizing the angular distance to some modularity vector over
the set of clustering vectors. This equivalence allows us to view the Louvain
algorithm as a nearest-neighbor search that approximately minimizes the
distance to this modularity vector. By replacing this modularity vector by a
different vector, many alternative community detection methods can be obtained.
We explore this wider class and compare it to existing modularity-based
methods. Our experiments show that these alternatives may outperform
modularity-based methods. For example, when communities are large compared to
vertex neighborhoods, a vector based on numbers of common neighbors outperforms
existing community detection methods. While the focus of the present work is
community detection in networks, the proposed methodology can be applied to any
clustering problem where pair-wise similarity data is available.


Abstract:
  Based on the recently formulated chiral radiation transport theory for
left-handed neutrinos, we study the chiral transport of neutrinos near thermal
equilibrium in core-collapse supernovae. We first compute the near-equilibrium
solution of the chiral radiation transport equation under the relaxation time
approximation, where the relaxation time is directly derived from the effective
field theory of the weak interaction. By using such a solution, we
systematically derive analytic expressions for the nonequilibrium corrections
of the neutrino energy-momentum tensor and neutrino number current induced by
magnetic fields via the neutrino absorption on nucleons. In particular, we find
the nonequilibrium neutrino energy current proportional to the magnetic field.
We also discuss its phenomenological consequences such as the possible relation
to pulsar kicks.


Abstract:
  Recent advances in self-supervised learning with instance-level contrastive
objectives facilitate unsupervised clustering. However, a standalone datum is
not perceiving the context of the holistic cluster, and may undergo sub-optimal
assignment. In this paper, we extend the mainstream contrastive learning
paradigm to a cluster-level scheme, where all the data subjected to the same
cluster contribute to a unified representation that encodes the context of each
data group. Contrastive learning with this representation then rewards the
assignment of each datum. To implement this vision, we propose twin-contrast
clustering (TCC). We define a set of categorical variables as clustering
assignment confidence, which links the instance-level learning track with the
cluster-level one. On one hand, with the corresponding assignment variables
being the weight, a weighted aggregation along the data points implements the
set representation of a cluster. We further propose heuristic cluster
augmentation equivalents to enable cluster-level contrastive learning. On the
other hand, we derive the evidence lower-bound of the instance-level
contrastive objective with the assignments. By reparametrizing the assignment
variables, TCC is trained end-to-end, requiring no alternating steps. Extensive
experiments show that TCC outperforms the state-of-the-art on challenging
benchmarks.


Abstract:
  Second harmonic generation (SHG) spectroscopy ubiquitously enables the
investigation of surface chemistry, interfacial chemistry as well as symmetry
properties in solids. Polarization-resolved SHG spectroscopy in the visible to
infrared regime is regularly used to investigate electronic and magnetic orders
through their angular anisotropies within the crystal structure. However, the
increasing complexity of novel materials and emerging phenomena hamper the
interpretation of experiments solely based on the investigation of hybridized
valence states. Here, polarization-resolved SHG in the extreme ultraviolet
(XUV-SHG) is demonstrated for the first time, enabling element-resolved angular
anisotropy investigations. In non-centrosymmetric LiNbO$_3$, elemental
contributions by lithium and niobium are clearly distinguished by energy
dependent XUV-SHG measurements. This element-resolved and symmetry-sensitive
experiment suggests that the displacement of Li ions in LiNbO$_3$, which is
known to lead to ferroelectricity, is accompanied by distortions to the Nb ion
environment that breaks the inversion symmetry of the NbO$_{6}$ octahedron as
well. Our simulations show that the measured second harmonic spectrum is
consistent with Li ion displacements from the centrosymmetric position by
$\sim$0.5 Angstrom while the Nb-O bonds are elongated/contracted by
displacements of the O atoms by $\sim$0.1 Angstrom. In addition, the
polarization-resolved measurement of XUV-SHG shows excellent agreement with
numerical predictions based on dipole-induced SHG commonly used in the optical
wavelengths. This constitutes the first verification of the dipole-based SHG
model in the XUV regime. The findings of this work pave the way for future
angle and time-resolved XUV-SHG studies with elemental specificity in condensed
matter systems.


Abstract:
  A subset $X$ of a finite group $G$ is said to be prime-power-independent if
each element in $X$ has prime power order and there is no proper subset $Y$ of
$X$ with $\langle Y, \Phi(G)\rangle = \langle X, \Phi(G)\rangle$, where
$\Phi(G)$ is the Frattini subgroup of $G$. A group $G$ is $\mathcal{B}_{pp}$ if
all prime-power-independent generating sets for $G$ have the same cardinality.
We prove that, if $G$ is $\mathcal{B}_{pp}$, then $G$ is solvable. Pivoting on
some recent results of Krempa and Stocka, this yields a complete classification
of $\mathcal{B}_{pp}$-groups.


Abstract:
  Projective monomial curves correspond to rings generated by monomials of the
same degree in two variables. Such rings always have finite Macaulayfication.
We show how to characterize the Buchsbaumness and the Castelnuovo-Mumford
regularity of these rings by means of their finite Macaulayfication, and we use
this method to study the Buchsbaumness and to estimate the Castelnuovo-Mumford
regularity of large classes of non-smooth monomial curves in terms of the given
monomials.


Abstract:
  Context: The analytical results of Chandrasekhar's semi-infinite diffuse
reflection problem is crucial in the context of stellar or planetary
atmosphere. However, the atmospheric emission effect was not taken into account
in this model, and the solutions are applicable only for diffusely scattering
atmosphere in absence of emission.
  Aim: We extend the model of semi-infinite diffuse reflection problem by
including the effects of thermal emission B(T ), and present how this affects
Chandrasekhar's analytical end results. Hence, we aim to generalize
Chandrasekhar's model to provide a complete picture of this problem.
  Method: We use Invariance Principle Method to find the radiative transfer
equation accurate for diffuse reflection in presence of B(T ). Then we derive
the modified scattering function S(${\mu},{\phi}; {\mu}_0 , {\phi}_0$ ) for
different kind of phase functions.
  Results: We find that, the scattering function S(${\mu}, {\phi}; {\mu}_0 ,
{\phi}_0$ ) as well as diffusely reflected specific intensity $I(0, {\mu};
{\mu}_0 )$ for different phase functions are modified due to the emission
$B(T)$ from layer ${\tau} = 0$. In both cases, B(T) is added to the results of
only scattering case derived by Chandrasekhar, with some multiplicative
factors. Thus the diffusely reflected spectra will be enriched and carries the
temperature information of ${\tau} = 0$ layer. As the effects are additive in
nature, hence our model reduces to the sub-case of Chandrasekhar's scattering
model in case of $B(T) = 0$. We conclude that our generalized model provides
more accurate results due to the inclusion of the thermal emission effect in
Chandrasekhar's semi-infinite atmosphere problem.


Abstract:
  In this paper, the notions of nonnil-injective modules and
nonnil-FP-injective modules are introduced and studied. Especially, we show
that a $\phi$-ring $R$ is an integral domain if and only if any
nonnil-injective (resp., nonnil-FP-injective) module $R$-module is injective
(resp., FP-injective). Some new characterizations of $\phi$-von Neumann regular
rings, nonnil-Notherian rings and nonnil-coherent rings are given. We finally
characterize $\phi$-Dedekind rings and $\phi$-\Prufer\ rings in terms of
$\phi$-flat modules, nonnil-injective modules and nonnil-FP-injective modules.


Abstract:
  Few-shot segmentation has been attracting a lot of attention due to its
effectiveness to segment unseen object classes with a few annotated samples.
Most existing approaches use masked Global Average Pooling (GAP) to encode an
annotated support image to a feature vector to facilitate query image
segmentation. However, this pipeline unavoidably loses some discriminative
information due to the average operation. In this paper, we propose a simple
but effective self-guided learning approach, where the lost critical
information is mined. Specifically, through making an initial prediction for
the annotated support image, the covered and uncovered foreground regions are
encoded to the primary and auxiliary support vectors using masked GAP,
respectively. By aggregating both primary and auxiliary support vectors, better
segmentation performances are obtained on query images. Enlightened by our
self-guided module for 1-shot segmentation, we propose a cross-guided module
for multiple shot segmentation, where the final mask is fused using predictions
from multiple annotated samples with high-quality support vectors contributing
more and vice versa. This module improves the final prediction in the inference
stage without re-training. Extensive experiments show that our approach
achieves new state-of-the-art performances on both PASCAL-5i and COCO-20i
datasets.


Abstract:
  In this review paper, we present an elaborate discussion on wavelength
selective switches and their demonstrations. We also review packaging and
electronic photonic integration of switches; a topic neglected in other review
papers. We also cover wavelength locking which is paramount in switching
networks with many tunable filters.


Abstract:
  Following Benjamin et al., a matrix with entries being sums of two
neighbouring Catalan numbers is considered. Its LU-decomposition is given, by
guessing the results and later prove it by computer algebra, with lots of human
help. Specializing a parameter, the determinant turns out to be a Fibonacci
number with odd index, confirming earlier results, obtained back then by
combinatorial methods.


Abstract:
  We present the discovery of rapid photometric variability in three ultra-cool
dwarfs from long-duration monitoring with the Spitzer Space Telescope. The T7,
L3.5, and L8 dwarfs have the shortest photometric periods known to date:
${1.080}^{+0.004}_{-0.005}$ h, ${1.14}^{+0.03}_{-0.01}$ h, and
${1.23}^{+0.01}_{-0.01}$ h, respectively. We confirm the rapid rotation through
moderate-resolution infrared spectroscopy, which reveals projected rotational
velocities between 79 and 104 km s$^{-1}$. We compare the near-infrared spectra
to photospheric models to determine the objects' fundamental parameters and
radial velocities. We find that the equatorial rotational velocities for all
three objects are $\gtrsim$100 km s$^{-1}$. The three L and T dwarfs reported
here are the most rapidly spinning and likely the most oblate field ultra-cool
dwarfs known to date. Correspondingly, all three are excellent candidates for
seeking auroral radio emission and net optical/infrared polarization. As of
this writing, 78 L-, T-, and Y-dwarf rotation periods have now been measured.
The clustering of the shortest rotation periods near 1 h suggests that brown
dwarfs are unlikely to spin much faster.


Abstract:
  We show that, for a (not necessarily continuous) weakly contractive mean-type
mapping $\mathbf{M} \colon I^p\to I^p$ (where $I$ is an interval and $p \in
\mathbb{N}$), the functional equation $K \circ \mathbf{M}=K$ has at most one
solution in the family of continuous means $K \colon I^p \to I$.
  Some general approach to the latter equation is also given.


Abstract:
  Turning principles into practice is one of the most pressing challenges of
artificial intelligence (AI) governance. In this article, we reflect on a novel
governance initiative by one of the world's largest AI conferences. In 2020,
the Conference on Neural Information Processing Systems (NeurIPS) introduced a
requirement for submitting authors to include a statement on the broader
societal impacts of their research. Drawing insights from similar governance
initiatives, including institutional review boards (IRBs) and impact
requirements for funding applications, we investigate the risks, challenges and
potential benefits of such an initiative. Among the challenges, we list a lack
of recognised best practice and procedural transparency, researcher opportunity
costs, institutional and social pressures, cognitive biases, and the inherently
difficult nature of the task. The potential benefits, on the other hand,
include improved anticipation and identification of impacts, better
communication with policy and governance experts, and a general strengthening
of the norms around responsible research. To maximise the chance of success, we
recommend measures to increase transparency, improve guidance, create
incentives to engage earnestly with the process, and facilitate public
deliberation on the requirement's merits and future. Perhaps the most important
contribution from this analysis are the insights we can gain regarding
effective community-based governance and the role and responsibility of the AI
research community more broadly.


Abstract:
  The covariance matrix $\boldsymbol{\Sigma}$ of non-linear clustering
statistics that are measured in current and upcoming surveys is of fundamental
interest for comparing cosmological theory and data and a crucial ingredient
for the likelihood approximations underlying widely used parameter inference
and forecasting methods. The extreme number of simulations needed to estimate
$\boldsymbol{\Sigma}$ to sufficient accuracy poses a severe challenge.
Approximating $\boldsymbol{\Sigma}$ using inexpensive but biased surrogates
introduces model error with respect to full simulations, especially in the
non-linear regime of structure growth. To address this problem we develop a
matrix generalization of Convergence Acceleration by Regression and Pooling
(CARPool) to combine a small number of simulations with fast surrogates and
obtain low-noise estimates of $\boldsymbol{\Sigma}$ that are unbiased by
construction. Our numerical examples use CARPool to combine GADGET-III $N$-body
simulations with fast surrogates computed using COmoving Lagrangian
Acceleration (COLA). Even at the challenging redshift $z=0.5$, we find variance
reductions of at least $\mathcal{O}(10^1)$ and up to $\mathcal{O}(10^4)$ for
the elements of the matter power spectrum covariance matrix on scales
$8.9\times 10^{-3}<k_\mathrm{max} <1.0$ $h {\rm Mpc^{-1}}$. We demonstrate
comparable performance for the covariance of the matter bispectrum, the matter
correlation function and probability density function of the matter density
field. We compare eigenvalues, likelihoods, and Fisher matrices computed using
the CARPool covariance estimate with the standard sample covariance estimators
and generally find considerable improvement except in cases where $\Sigma$ is
severely ill-conditioned.


Abstract:
  We introduce the notion of a g-atomic subspace for a bounded linear operator
and construct several useful resolutions of the identity operator on a Hilbert
space using the theory of g-fusion frames. Also we shall describe the concept
of frame operator for a pair of g-fusion Bessel sequences and some of their
properties.


Abstract:
  Recently, atomically thin PdSe$_2$ semiconductors with rare pentagonal
Se-Pd-Se monolayers were synthesized and were also found to possess superior
properties such as ultrahigh air stability, and high carrier mobility, thus
offering a new family of two-dimensional (2D) materials for exploration of 2D
semiconductor physics and for applications in advanced opto-electronic and
nonlinear photonic devices. In this work, we systematically study the nonlinear
optical (NLO) responses [namely, bulk photovoltaic effect (BPVE),
second-harmonic generation (SHG) and linear electric-optic (LEO) effect] of
noncentrosymmetric bilayer (BL) and four-layer (FL) PdS$_2$ and PdSe$_2$ by
applying the first-principles density functional theory with the generalized
gradient approximation plus scissors-correction. First of all, the shift
current conductivity is in the order of 130 $\mu$A/V$^2$, being very high
compared to known BPVE materials. Similarly, their injection current
susceptibilities are in the order of 100$\times$10$^8$A/V$^2$s, again being
large. Secondly, the SHG coefficients ($\chi^{(2)}$) of these materials are
also large, being one order higher than that of the best-known few-layer group
6B transition metal dichalcogenides. For example, the maximum magnitude of
$\chi^{(2)}$ can reach 1.4$\times$10$^3$ pm/V for BL PdSe$_2$ at 1.9 eV and
1.2$\times$10$^3$ pm/V at 3.1 eV for BL PdS$_2$. Thirdly we find significant
LEO coefficients for these structures in the low photon energy. All these
indicate that 2D PdX$_2$ semiconductors will find promising NLO applications.
Fourthly, we find that the large BPVE and SHG of the few-layer PdX$_2$
structures are due to strong intralayer directional covalent bonding and also
2D quantum confinement.


Abstract:
  Borromean ring refers to a peculiar structure where three rings are linked
together while any two of them are unlinked. Here we propose the realization of
its quantum mechanical analog in a many-body system of three-component
ultracold bosons. Namely, we identify the {\it Borromean droplet}, where only
the ternary bosons can form a self-bound droplet while any binary subsystems
cannot. Its formation is facilitated by an additional attractive force induced
by the density fluctuation of a third component, which enlarges the mean-field
collapse region in comparison to the binary case and renders the formation of
Borromean droplet after incorporating the repulsive force from quantum
fluctuations. Outside the Borromean regime, the competition between ternary and
binary droplets leads to an interesting phenomenon of droplet phase separation,
manifested by double plateaus in the density profile. We further show that the
transition between different droplets and gas phase can be conveniently tuned
by boson numbers and interaction strengths. The study reveals the possibility
of Borromean binding in the many-body world and sheds light on more intriguing
many-body bound state formed in multi-component systems.


Abstract:
  Observing a set of images and their corresponding paragraph-captions, a
challenging task is to learn how to produce a semantically coherent paragraph
to describe the visual content of an image. Inspired by recent successes in
integrating semantic topics into this task, this paper develops a plug-and-play
hierarchical-topic-guided image paragraph generation framework, which couples a
visual extractor with a deep topic model to guide the learning of a language
model. To capture the correlations between the image and text at multiple
levels of abstraction and learn the semantic topics from images, we design a
variational inference network to build the mapping from image features to
textual captions. To guide the paragraph generation, the learned hierarchical
topics and visual features are integrated into the language model, including
Long Short-Term Memory (LSTM) and Transformer, and jointly optimized.
Experiments on public dataset demonstrate that the proposed models, which are
competitive with many state-of-the-art approaches in terms of standard
evaluation metrics, can be used to both distill interpretable multi-layer
topics and generate diverse and coherent captions.


Abstract:
  We give an inductive procedure for finding the extremal rays of the
equivariant Littlewood-Richardson cone, which is closely related to the
solution space to S. Friedland's majorized Hermitian eigenvalue problem. In so
doing, we solve the "rational version" of a problem posed by C. Robichaux, H.
Yadav, and A. Yong. Our procedure is a natural extension of P. Belkale's
algorithm for the classical Littlewood-Richardson cone. The main tools for
accommodating the equivariant setting are certain foundational results of D.
Anderson, E. Richmond, and A. Yong. We also study two families of special rays
of the cone and make observations about the Hilbert basis of the associated
lattice semigroup.


Abstract:
  Recent developments in Machine Learning and Deep Learning depend heavily on
cloud computing and specialized hardware, such as GPUs and TPUs. This forces
those using those models to trust private data to cloud servers. Such scenario
has prompted a large interest on Homomorphic Cryptography and Secure
Multi-Party Computation protocols that allow the use of cloud computing power
in a privacy-preserving manner.
  When comparing the efficiency of such protocols, most works in literature
resort to complexity analysis that gives asymptotic higher-bounding limits of
computational cost when input size tends to infinite. These limits may be very
different from the actual cost or execution time, when performing such
computations over small, or average-sized datasets.
  We argue that Monte Carlo methods can render better computational cost and
time estimates, fostering better design and implementation decisions for
complex systems, such as Privacy-Preserving Machine Learning Frameworks.


Abstract:
  We develop a non-perturbative analysis of the electro-production of heavy
vector mesons ($\phi$, $J/\Psi$) from threshold to high energy. We use the
holographic construction with bulk confinement enforced through a soft wall.
Using Witten diagrams, we evaluate the pertinent cross sections for heavy
vector mesons ($\phi$, $J/\Psi$) production and study their dependence on both
the incoming virtual photon polarization as well as the outgoing polarization
of the heavy meson. Our results for $J/\Psi$ electro-production compares well
with the available HERA data at low and intermediate $Q^2$, and for a wide
range of momentum transfer. We also predict the quasi-real electro-production
of $J/\Psi$ near threshold.


Abstract:
  In a recent paper~[Nature Catalysis 3, 573 (2020)], Robatjazi {\em et al.}
demonstrate hydrodefluorination on Al nanocrystals decorated by Pd islands
under illumination and under external heating. They conclude that
photocatalysis accomplishes the desired transformation \ce{CH3F + D2 -> CH3D +
DF} efficiently and selectively due to "hot" electrons, as evidenced by an
illumination-induced reduction of the activation energy.
  Although some of the problems identified in prior work by the same group have
been addressed, scrutiny of the data in~[Nature Catalysis 3, 573 (2020)] raises
doubts about both the methodology and the central conclusions. First, we show
that the thermal control experiments in~[Nature Catalysis 3, 573 (2020)] do not
separate thermal from "hot electron" contributions, and therefore any
conclusions drawn from these experiments are invalid. We then show that an
improved thermal control implies that the activation energy of the reaction
does not change, and that an independent purely thermal calculation (based
solely on the sample parameters provided in the original manuscript) explains
the measured data perfectly. For the sake of completeness, we also address
technical problems in the calibration of the thermal camera, an unjustifiable
disqualification of some of the measured data, as well as concerning aspects of
the rest of the main results, including the mass spectrometry approach used to
investigate the selectivity of the reaction, and claims about the stoichiometry
and reaction order. All this shows that the burden of proof for involvement of
hot electrons has not been met.


Abstract:
  We propose a framework where a phase transition associated with a gauge
symmetry breaking that occurs (not far) above the electroweak scale sets a
stage for baryogenesis similar to the electroweak baryogenesis in the Standard
Model. A concrete realization utilizes the breaking of $SU(2)_R \times U(1)_X
\rightarrow U(1)_Y$. New chiral fermions charged under the extended gauge
symmetry have nonzero lepton numbers, which makes the $B-L$ symmetry anomalous.
The new lepton sector contains a large flavor-dependent CP violation, similar
to the Cabibbo-Kobayashi-Maskawa phase, without inducing sizable electric
dipole moments of the Standard Model particles. A bubble wall dynamics
associated with the first-order phase transition and $SU(2)_R$ sphaleron
processes generate a lepton asymmetry, which is transferred into a baryon
asymmetry via the ordinary electroweak sphaleron process. Unlike the Standard
Model electroweak baryogenesis, the new phase transition can be of the strong
first order and the new CP violation is not significantly suppressed by Yukawa
couplings, so that the observed asymmetry can be produced. The model can be
probed by collider searches for new particles and the observation of
gravitational waves. One of the new leptons becomes a dark matter candidate.
The model can be also embedded into a left-right symmetric theory to solve the
strong CP problem.


Abstract:
  Question Answering (QA) models over Knowledge Bases (KBs) are capable of
providing more precise answers by utilizing relation information among
entities. Although effective, most of these models solely rely on fixed
relation representations to obtain answers for different question-related KB
subgraphs. Hence, the rich structured information of these subgraphs may be
overlooked by the relation representation vectors. Meanwhile, the direction
information of reasoning, which has been proven effective for the answer
prediction on graphs, has not been fully explored in existing work. To address
these challenges, we propose a novel neural model, Relation-updated
Direction-guided Answer Selector (RDAS), which converts relations in each
subgraph to additional nodes to learn structure information. Additionally, we
utilize direction information to enhance the reasoning ability. Experimental
results show that our model yields substantial improvements on two widely used
datasets.


Abstract:
  Here we numerically solve the equations derived in part I of this two-part
series and verify their validity. In particular we use the functional
Renormalisation Group (fRG) flow equations to obtain effective potentials for
initially highly anharmonic and non-polynomial potentials, including potentials
with multiple trapping wells and barriers, and at different temperatures. The
numerical computations determining the effective action are much faster than
the direct simulation of the stochastic dynamics to which we compare our fRG
results. We benchmark our numerical solutions to the flow equations by
comparing the first two equilibrium cumulants from the fRG against the
Boltzmann distribution. We obtain excellent agreement between the two methods
demonstrating that numerical solutions for the effective potential can be
accurately obtained in all the highly unharmonic cases we examined. We then
assess the utility of the effective potential to describe the equilibrium
2-point correlation function $\langle x(0)x(t) \rangle$ and the relevant
correlation time. We find that when Wavefunction Renormalisation is also
utilized, these are obtained to percent accuracy for temperatures down to the
typical height of the potentials' barriers but accuracy is quickly lost for
lower temperatures. We also show how the fRG can offer strong agreement with
direct numerical simulation of the nonequilibrium evolution of average position
and variance. Also, the fRG solution represents the whole ensemble average,
further adding to its convenience over other techniques, such as direct
numerical simulations or solving the Fokker-Planck diffusion equation, which
require multiple solutions with different initial conditions to construct
averages over an ensemble.


Abstract:
  In this article we prove large deviations principles for high minima of
Gaussian processes with nonnegatively correlated increments on arbitrary
intervals. Furthermore, we prove large deviations principles for the increments
of such processes on intervals $[a,b]$ where $b-a$ is either less than the
increment or twice the increment, assuming stationarity of the increments. As a
chief example, we consider fractional Brownian motion and fractional Gaussian
noise for $H\geq 1/2$.


Abstract:
  The last decade has witnessed an experimental revolution in data science and
machine learning, epitomised by deep learning methods. Indeed, many
high-dimensional learning tasks previously thought to be beyond reach -- such
as computer vision, playing Go, or protein folding -- are in fact feasible with
appropriate computational scale. Remarkably, the essence of deep learning is
built from two simple algorithmic principles: first, the notion of
representation or feature learning, whereby adapted, often hierarchical,
features capture the appropriate notion of regularity for each task, and
second, learning by local gradient-descent type methods, typically implemented
as backpropagation.
  While learning generic functions in high dimensions is a cursed estimation
problem, most tasks of interest are not generic, and come with essential
pre-defined regularities arising from the underlying low-dimensionality and
structure of the physical world. This text is concerned with exposing these
regularities through unified geometric principles that can be applied
throughout a wide spectrum of applications.
  Such a 'geometric unification' endeavour, in the spirit of Felix Klein's
Erlangen Program, serves a dual purpose: on one hand, it provides a common
mathematical framework to study the most successful neural network
architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand,
it gives a constructive procedure to incorporate prior physical knowledge into
neural architectures and provide principled way to build future architectures
yet to be invented.


Abstract:
  In this paper, we study the existence of limit cycles in continuous and
discontinuous planar piecewise linear Hamiltonian differential systems with two
or three zones separated by straight lines and such that the linear systems
that define the piecewise one have isolated singular points, i.e. centers or
saddles. In this case, we show that if the planar piecewise linear Hamiltonian
differential system is either continuous or discontinuous with two zones, then
it has no limit cycles. Now, if the planar piecewise linear Hamiltonian
differential system is discontinuous with three zones, then it has at most one
limit cycle, and there are examples with one limit cycle. More precisely,
without taking into account the position of the singular points in the zones,
we present examples with the unique limit cycle for all possible combinations
of saddles and centers.


Abstract:
  Many cell membrane proteins that bind to actin form dynamic clusters driven
by contractile flows generated by the actomyosin machinery at the cell cortex.
Recent evidence suggests that a necessary condition for the generation of these
protein clusters on the membrane is the stratified organization of the active
agents -formin-nucleated actin, myosin-II minifilaments, and ARP2/3-nucleated
actin mesh -within the cortex. Further, the observation that these clusters
dynamically remodel, requires that the components of this active machinery
undergo turnover. Here we develop a coarse-grained agent-based Brownian
dynamics simulation that incorporates the effects of stratification, binding of
myosin minifilaments to multiple actin filaments and their turnover. We show
that these three features of the active cortical machinery -stratification,
multivalency and turnover -are critical for the realisation of a nonequilibrium
steady state characterised by contractile flows and dynamic orientational
patterning. We show that this nonequilibrium steady state enabled by the above
features of the cortex, can facilitate multi-particle encounters of membrane
proteins that profoundly influence the kinetics of bimolecular reactions at the
cell surface.


Abstract:
  This master's thesis contains an introduction to $A_\infty$-algebras and
homological perturbation theory. We then discuss the formality of compact
K\"ahler manifolds and present a direct proof of a homotopy transfer principle
of $A_\infty$-algebras, also known as Kadeishvili's Theorem.


Abstract:
  We consider the problem of learning stabilizer states with noise in the
Probably Approximately Correct (PAC) framework of Aaronson (2007) for learning
quantum states. In the noiseless setting, an algorithm for this problem was
recently given by Rocchetto (2018), but the noisy case was left open. Motivated
by approaches to noise tolerance from classical learning theory, we introduce
the Statistical Query (SQ) model for PAC-learning quantum states, and prove
that algorithms in this model are indeed resilient to common forms of noise,
including classification and depolarizing noise. We prove an exponential lower
bound on learning stabilizer states in the SQ model. Even outside the SQ model,
we prove that learning stabilizer states with noise is in general as hard as
Learning Parity with Noise (LPN) using classical examples. Our results position
the problem of learning stabilizer states as a natural quantum analogue of the
classical problem of learning parities: easy in the noiseless setting, but
seemingly intractable even with simple forms of noise.


Abstract:
  We introduce DIVE, an end-to-end speaker diarization algorithm. Our neural
algorithm presents the diarization task as an iterative process: it repeatedly
builds a representation for each speaker before predicting the voice activity
of each speaker conditioned on the extracted representations. This strategy
intrinsically resolves the speaker ordering ambiguity without requiring the
classical permutation invariant training loss. In contrast with prior work, our
model does not rely on pretrained speaker representations and optimizes all
parameters of the system with a multi-speaker voice activity loss. Importantly,
our loss explicitly excludes unreliable speaker turn boundaries from training,
which is adapted to the standard collar-based Diarization Error Rate (DER)
evaluation. Overall, these contributions yield a system redefining the
state-of-the-art on the standard CALLHOME benchmark, with 6.7% DER compared to
7.8% for the best alternative.


Abstract:
  The challenge of each organization is how they adapt to the shift of more
complex technology such as mobile, big data, interconnected world, and the
Internet of things. In order to achieve their objective, they must understand
how to take advantage of the interconnected individuals inside and outside the
organization. Learning organization continues to transform by listening and
maintain the connection with their counterparts. Customer relationship
management is an important source for business organizations to grow and to
assure their future. The complex social network, where interconnected peoples
get information and get influenced very quickly, certainly a big challenge for
business organizations. The combination of these complex technologies provides
intriguing insight such as the capabilities to listen to what the markets want,
to understand their market competition, and to understand their market
segmentation. In this paper, as a part of organization transformation, we show
how a business organization mine online conversational in Twitter related to
their brand issue and analyze them in the context of customer relationship
management to extract several insights regarding their market.


Abstract:
  There are a large number of optimization problems in physical models where
the relationships between model parameters and outputs are unknown or hard to
track. These models are named as black-box models in general because they can
only be viewed in terms of inputs and outputs, without knowledge of the
internal workings. Optimizing the black-box model parameters has become
increasingly expensive and time consuming as they have become more complex.
Hence, developing effective and efficient black-box model optimization
algorithms has become an important task. One powerful algorithm to solve such
problem is Bayesian optimization, which can effectively estimates the model
parameters that lead to the best performance, and Gaussian Process (GP) has
been one of the most widely used surrogate model in Bayesian optimization.
However, the time complexity of GP scales cubically with respect to the number
of observed model outputs, and GP does not scale well with large parameter
dimension either. Consequently, it has been challenging for GP to optimize
black-box models that need to query many observations and/or have many
parameters. To overcome the drawbacks of GP, in this study, we propose a
general Bayesian optimization algorithm that employs a Neural Process (NP) as
the surrogate model to perform black-box model optimization, namely, Neural
Process for Bayesian Optimization (NPBO). In order to validate the benefits of
NPBO, we compare NPBO with four benchmark approaches on a power system
parameter optimization problem and a series of seven benchmark Bayesian
optimization problems. The results show that the proposed NPBO performs better
than the other four benchmark approaches on the power system parameter
optimization problem and competitively on the seven benchmark problems.


Abstract:
  Quantum-access security, where an attacker is granted superposition access to
secret-keyed functionalities, is a fundamental security model and its study has
inspired results in post-quantum security. We revisit, and fill a gap in, the
quantum-access security analysis of the Lamport one-time signature scheme (OTS)
in the quantum random oracle model (QROM) by Alagic et al.~(Eurocrypt 2020). We
then go on to generalize the technique to the Winternitz OTS. Along the way, we
develop a tool for the analysis of hash chains in the QROM based on the
superposition oracle technique by Zhandry (Crypto 2019) which might be of
independent interest.


Abstract:
  The accuracy of smartphone-based positioning methods using WiFi usually
suffers from ranging errors caused by non-line-of-sight (NLOS) conditions.
Previous research usually exploits several statistical features from a long
time series (hundreds of samples) of WiFi received signal strength (RSS) or
WiFi round-trip time (RTT) to achieve a high identification accuracy. However,
the long time series or large sample size attributes to high power and time
consumption in data collection for both training and testing. This will also
undoubtedly be detrimental to user experience as the waiting time of getting
enough samples is quite long. Therefore, this paper proposes a new real-time
NLOS/LOS identification method for smartphone-based indoor positioning system
using WiFi RTT and RSS. Based on our extensive analysis of RSS and RTT
features, a machine learning-based method using random forest was chosen and
developed to separate the samples for NLOS/LOS conditions. Experiments in
different environments show that our method achieves a discrimination accuracy
of about 94% with a sample size of 10. Considering the theoretically shortest
WiFi ranging interval of 100ms of the RTT-enabled smartphones, our algorithm is
able to provide the shortest latency of 1s to get the testing result among all
of the state-of-art methods.


Abstract:
  We present a pioneering estimate of the global yearly greenhouse gas
emissions of a large-scale Astrophysics experiment over several decades: the
Giant Array for Neutrino Detection (GRAND). The project aims at detecting
ultra-high energy neutrinos with a 200,000 radio antenna array over
200,000\,km$^2$ as of the 2030s. With a fully transparent methodology based on
open source data, we calculate the emissions related to three unavoidable
sources: travel, digital technologies and hardware equipment. We find that
these emission sources have a different impact depending on the stages of the
experiment. Digital technologies and travel prevail for the small-scale
prototyping phase (GRANDProto300), whereas hardware equipment (material
production and transportation) and data transfer/storage largely outweigh the
other emission sources in the large-scale phase (GRAND200k). In the mid-scale
phase (GRAND10k), the three sources contribute equally. This study highlights
the considerable carbon footprint of a large-scale astrophysics experiment, but
also shows that there is room for improvement. We discuss various lines of
actions that could be implemented. The GRAND project being still in its
prototyping stage, our results provide guidance to the future collaborative
practices and instrumental design in order to reduce its carbon footprint.


Abstract:
  We report a systematic study of the $5d$-electron-doped system
Ce(Fe$_{1-x}$Ir$_x$)$_2$Al$_{10}$ ($0 \leq x \leq 0.15$). With increasing $x$,
the orthorhombic $b$~axis decreases slightly while accompanying changes in $a$
and $c$ leave the unit cell volume almost unchanged. Inelastic neutron
scattering, along with thermal and transport measurements, reveal that for the
Kondo semiconductor CeFe$_2$Al$_{10}$, the low-temperature energy gap which is
proposed to be a consequence of strong $c \mhyphen f$ hybridization, is
suppressed by a small amount of Ir substitution for Fe, and that the system
adopts a metallic ground state with an increase in the density of states at the
Fermi level. The charge or transport gap collapses (at $x=$~0.04) faster than
the spin gap with Ir substitution. Magnetic susceptibility, heat capacity, and
muon spin relaxation measurements demonstrate that the system undergoes
long-range antiferromagnetic order below a N\'eel temperature,
$T_{\mathrm{N}}$, of 3.1(2)~K for $x = 0.15$. The ordered moment is estimated
to be smaller than 0.07(1)~$\mu_\mathrm{B}$/Ce although the trivalent state of
Ce is confirmed by Ce L$_3$-edge x-ray absorption near edge spectroscopy. It is
suggested that the $c \mhyphen f$ hybridization gap, which plays an important
role in the unusually high ordering temperatures observed in Ce$T_2$Al$_{10}$
($T$ = Ru and Os), may not be necessary for the onset of magnetic order with a
low $T_{\mathrm{N}}$ seen here in Ce(Fe$_{1-x}$Ir$_x$)$_2$Al$_{10}$.


Abstract:
  In this chapter we review recent results concerning localized and extended
dissipative solutions of the discrete complex Ginzburg-Landau equation. In
particular, we discuss discrete diffraction effects arising both from linear
and nonlinear properties, the existence of self-localized dissipative solitons
in the presence of cubic-quintic terms and modulational instability induced by
saturable nonlinearities. Dynamical stability properties of localized and
extended dissipative discrete solitons are also discussed.


Abstract:
  There is a growing privacy concern due to the popularity of social media and
surveillance systems, along with advances in face recognition software.
However, established image obfuscation techniques are either vulnerable to
re-identification attacks by human or deep learning models, insufficient in
preserving image fidelity, or too computationally intensive to be practical. To
tackle these issues, we present DeepBlur, a simple yet effective method for
image obfuscation by blurring in the latent space of an unconditionally
pre-trained generative model that is able to synthesize photo-realistic facial
images. We compare it with existing methods by efficiency and image quality,
and evaluate against both state-of-the-art deep learning models and industrial
products (e.g., Face++, Microsoft face service). Experiments show that our
method produces high quality outputs and is the strongest defense for most test
cases.


Abstract:
  The murder of George Floyd by police in May 2020 sparked international
protests and renewed attention in the Black Lives Matter movement. Here, we
characterize ways in which the online activity following George Floyd's death
was unparalleled in its volume and intensity, including setting records for
activity on Twitter, prompting the saddest day in the platform's history, and
causing George Floyd's name to appear among the ten most frequently used
phrases in a day, where he is the only individual to have ever received that
level of attention who was not known to the public earlier that same week.
Further, we find this attention extended beyond George Floyd and that more
Black victims of fatal police violence received attention following his death
than during other past moments in Black Lives Matter's history. We place that
attention within the context of prior online racial justice activism by showing
how the names of Black victims of police violence have been lifted and
memorialized over the last 12 years on Twitter. Our results suggest that the
2020 wave of attention to the Black Lives Matter movement centered past
instances of police violence in an unprecedented way, demonstrating the impact
of the movement's rhetorical strategy to "say their names."


Abstract:
  Nonlinear metasurface holography shows the great potential of metasurfaces to
control the phase, amplitude, and polarization of light while simultaneously
converting the frequency of the light. The possibility of tailoring the
scattering properties of a coherent beam, as well as the scattering properties
of nonlinear signals originating from the meta-atoms facilitates a huge degree
of freedom in beam shaping application. Recently, several approaches showed
that virtual objects or any kind of optical information can be generated at a
wavelength different from the laser input beam. Here, we demonstrate a
single-layer nonlinear geometric-phase metasurface made of plasmonic
nanostructures for a simultaneous second and third harmonic generation.
Different from previous works, we demonstrate a two-color hologram with
dissimilar types of nanostructures that generate the color information by
different nonlinear optical processes. The amplitude ratio of both harmonic
signals can be adapted depending on the nanostructures' resonance as well as
the power and the wavelength of the incident laser beam. The two-color
holographic image is reconstructed in the Fourier space at visible wavelengths
with equal amplitudes using a single near-infrared wavelength. Nonlinear
holography using multiple nonlinear processes simultaneously provides an
alternative path to holographic color display applications, enhanced optical
encryption schemes, and multiplexed optical data-storage.


Abstract:
  A lot of attention has been paid to a quantum-sensing network for detecting
magnetic fields in different positions. Recently, cryptographic quantum
metrology was investigated where the information of the magnetic fields is
transmitted in a secure way. However, sometimes, the positions where non-zero
magnetic fields are generated could carry important information. Here, we
propose an anonymous quantum sensor where an information of positions having
non-zero magnetic fields is hidden after measuring magnetic fields with a
quantum-sensing network. Suppose that agents are located in different positions
and they have quantum sensors. After the quantum sensors are entangled, the
agents implement quantum sensing that provides a phase information if non-zero
magnetic fields exist, and POVM measurement is performed on quantum sensors.
Importantly, even if the outcomes of the POVM measurement is stolen by an
eavesdropper, information of the positions with non-zero magnetic fields is
still unknown for the eavesdropper in our protocol. In addition, we evaluate
the sensitivity of our proposed quantum sensors by using Fisher information
when there are at most two positions having non-zero magnetic fields. We show
that the sensitivity is finite unless these two (non-zero) magnetic fields have
exactly the same amplitude. Our results pave the way for new applications of
quantum-sensing network.


Abstract:
  We present the prospects for the pre-merger detection and localization of
binary neutron star mergers with third generation gravitational-wave
observatories. We consider a wide variety of gravitational-wave networks which
may be operating in the 2030's and beyond; these networks include up to two
Cosmic Explorer sites, the Einstein Telescope, and continued observation with
the existing second generation ground-based detectors. For a fiducial local
merger rate of 300 Gpc$^{-3}$yr$^{-1}$, we find that the Einstein Telescope on
its own is able to detect 6 and 2 sources per year at 5 and 30 minutes before
merger, respectively, while providing a localization of $<10~\textrm{deg}^2$. A
single Cosmic Explorer would detect but be unable to localize sources on its
own. A two-detector Cosmic Explorer network, however, would detect 22 and 0.4
mergers per year using the same criteria. A full three-detector network with
the operation of dual Cosmic Explorers and the Einstein Telescope would allow
for $<1~\textrm{deg}^2$ source localization at 5 minutes before merger for
$\sim7$ sources per year. Given the dramatic increase in localization and
detection capabilities, third generation observatories will enable the regular
observation of the prompt emission of mergers by a broad array of observatories
including gamma-ray, x-ray, and optical telescopes. Moreover, sub-degree
localizations minutes before merger, combined with narrow-field-of-view
high-energy telescopes, could strongly constrain the high-energy pre-merger
emission models proposed in the last decade.


Abstract:
  We investigate the Cauchy problem for the focusing inhomogeneous nonlinear
Schr\"odinger equation $i \partial_t u + \Delta u = - |x|^b |u|^{p-1} u$ in the
radial Sobolev space $H^1_{\text{rad}}(\mathbb{R}^N)$, where $b>0$ and $p>1$.
We show the global existence and energy scattering in the inter-critical
regime, i.e., $p>\frac{N+4+2b}{N}$ and $p<\frac{N+2+2b}{N-2}$ if $N\geq 3$. We
also obtain blowing-up solutions for the mass-critical and mass-supercritical
nonlinearities. The main difficulty, coming from the spatial growing
nonlinearity, is overcome by refined Gagliardo-Nirenberg type inequalities. Our
proofs are based on improved Gagliardo-Nirenberg inequalities, the
Morawetz-Sobolev approach of Dodson and Murphy, radial Sobolev embeddings, and
localized virial estimates.


Abstract:
  We are concerned with zeros of random power series with coefficients being a
stationary, centered, complex Gaussian process. We show that the expected
number of zeros in every smooth domain in the disk of convergence is less than
that of the hyperbolic GAF with i.i.d. coefficients. When coefficients are
finitely dependent, i.e., the spectral density is a trigonometric polynomial,
we derive precise asymptotics of the expected number of zeros inside the disk
of radius $r$ centered at the origin as $r$ tends to the radius of convergence,
in the proof of which we clarify that the negative contribution to the number
of zeros stems from the zeros of the spectral density.


Abstract:
  Context: Galaxy interactions and mergers can lead to supermassive black hole
(SMBH) binaries which become active galactic nuclei (AGN) pairs when the SMBHs
start accreting mass. If there is a third galaxy involved in the interaction,
then a triple AGN system can form. Aims: Our goal is to investigate the nature
of the nuclear emission from the galaxies in the interacting pair
NGC\,7733--NGC\,7734 using archival VLT/MUSE Integral field spectrograph data
and study its relation to the stellar mass distribution traced by near-infrared
(NIR) observations from the South African Astronomical Observatory (SAAO).
Methods:We conducted near-infrared observations using the SAAO and identified
the morphological properties of bulges in each galaxy. We used MUSE data to
obtain a set of ionized emission lines from each galaxy and studied the
ionization mechanism. We also examined the relation of the galaxy pair with any
nearby companions with Far-UV observations using the UVIT. Conclusions: The
emission line analysis from the central regions of NGC\,7733 and NGC\,7734 show
Seyfert and LINER type AGN activity. The galaxy pair NGC\,7733--34 also shows
evidence of a third component, which has Seyfert-like emission. Hence, the
galaxy pair NGC\,7733--34 forms a triple AGN system. We also detected an
Extended Narrow-line region (ENLR) associated with the nucleus of NGC\,7733.


Abstract:
  We distinguish two general modes of testing for Deep Neural Networks (DNNs):
Offline testing where DNNs are tested as individual units based on test
datasets obtained without involving the DNNs under test, and online testing
where DNNs are embedded into a specific application environment and tested in a
closed-loop mode in interaction with the application environment. Typically,
DNNs are subjected to both types of testing during their development life cycle
where offline testing is applied immediately after DNN training and online
testing follows after offline testing and once a DNN is deployed within a
specific application environment. In this paper, we study the relationship
between offline and online testing. Our goal is to determine how offline
testing and online testing differ or complement one another and if offline
testing results can be used to help reduce the cost of online testing? Though
these questions are generally relevant to all autonomous systems, we study them
in the context of automated driving systems where, as study subjects, we use
DNNs automating end-to-end controls of steering functions of self-driving
vehicles. Our results show that offline testing is less effective than online
testing as many safety violations identified by online testing could not be
identified by offline testing, while large prediction errors generated by
offline testing always led to severe safety violations detectable by online
testing. Further, we cannot exploit offline testing results to reduce the cost
of online testing in practice since we are not able to identify specific
situations where offline testing could be as accurate as online testing in
identifying safety requirement violations.


Abstract:
  The balancing domain decomposition methods (BDDC) are originally introduced
for symmetric positive definite systems and have been extended to the
nonsymmetric positive definite system from the linear finite element
discretization of advection-diffusion equations. In this paper, the convergence
of the GMRES method is analyzed for the BDDC preconditioned linear system from
advection-diffusion equations with the hybridizable discontinuous Galerkin
(HDG) discretization. Compared to the finite element discretizations, several
additional norms for the numerical trace have to be used and the equivalence
between the bilinear forms and norms needs to be established. For large
viscosity, if the subdomain size is small enough, the number of iterations is
independent of the number of subdomains and depends only slightly on the
sudomain problem size. The convergence deteriorates when the viscosity
decreases. These results are similar to those with the finite element
discretizations. Moreover, the effects of the additional primal constraints
used in the BDDC algorithms are more significant with the higher degree HDG
discretizations. The results of two two-dimensional examples are provided to
confirm our theory.


Abstract:
  For a positive integer $b\ge2$, the $b$-symbol code is a new coding framework
proposed to combat $b$-errors in $b$-symbol read channels. Especially, a
$2$-symbol code is called a symbol-pair code. Remarkably, a classical maximum
distance separable (MDS) code is also an MDS $b$-symbol code. Recently, for any
MDS code $\mathcal{C}$, Ma and Luo determined the symbol-pair weight
distribution for $\mathcal{C}$. In this paper, by calculating the number of
codewords in $\mathcal{C}$ with special shape, we obtain the $b$-weight
distribution for $\mathcal{C}$, and then generalize Theorem $1$ in \cite{ML}.


Abstract:
  Genuine multipartite entanglement underlies correlation experiments
corroborating quantum mechanics and it is an expedient empowering many quantum
technologies. One of many counterintuitive facets of genuine multipartite
entanglement is its ability to exhibit an emergent character, that is, one can
infer its presence in some multipartite states merely from a set of its
separable marginals. Here, we show that the effect can be found also in the
context of Gaussian states of bosonic systems. Specifically, we construct
examples of multimode Gaussian states carrying genuine multipartite
entanglement which can be verified solely from separable nearest-neighbour
two-mode marginals. The key tool of our construction is a genuine multipartite
entanglement witness acting only on some two-mode reductions of the global
covariance matrix, which we find by a numerical solution of a semi-definite
programme. We also propose an experimental scheme for preparation of the
simplest three-mode state, which requires interference of three correlatively
displaced squeezed beams on two beam splitters. Besides revealing the concept
of emergent genuine multipartite entanglement in the Gaussian scenario and
bringing it closer to experimentally testable form, our results pave the way to
effective diagnostics methods of global properties of multipartite states
without complete tomography.


Abstract:
  We derive a new interior solution for stellar compact objects in
$f\mathcal{(R)}$ gravity assuming a differential relation to constrain the
Ricci curvature scalar. To this aim, we consider specific forms for the radial
component of the metric and the first derivative of $f\mathcal{(R)}$. After,
the time component of the metric potential and the form of $f(\mathcal R)$
function are derived. From these results, it is possible to obtain the radial
and tangential components of pressure and the density. The resulting interior
solution represents a physically motivated anisotropic neutron star model. It
is possible to match it with a boundary exterior solution. From this matching,
the components of metric potentials can be rewritten in terms of a compactness
parameter $C$ which has to be $C=2GM/Rc^2 <<0.5$ for physical consistency.
Other physical conditions for real stellar objects are taken into account
according to the solution. We show that the model accurately bypasses
conditions like the finiteness of radial and tangential pressures, and energy
density at the center of the star, the positivity of these components through
the stellar structure, and the negativity of the gradients. These conditions
are satisfied if the energy-conditions hold. Moreover, we study the stability
of the model by showing that Tolman-Oppenheimer-Volkoff equation is at
hydrostatic equilibrium. The solution is matched with observational data of
millisecond pulsars with a withe dwarf companion and pulsars presenting
thermonuclear bursts.


Abstract:
  Cyber-physical systems (CPS) have been increasingly attacked by hackers.
Recent studies have shown that CPS are especially vulnerable to insider
attacks, in which case the attacker has full knowledge of the systems
configuration. To better prevent such types of attacks, we need to understand
how insider attacks are generated. Typically, there are three critical aspects
for a successful insider attack: (i) Maximize damage, (ii) Avoid detection and
(iii) Minimize the attack cost. In this paper we propose a Stealthy Attack
GEneration (SAGE) framework by formulizing a novel optimization problem
considering these three objectives and the physical constraints of the CPS. By
adding small worst-case perturbations to the system, the SAGE attack can
generate significant damage, while remaining undetected by the systems
monitoring algorithms. The proposed methodology is evaluated on several anomaly
detection algorithms. The results show that SAGE attacks can cause severe
damage while staying undetected and keeping the cost of an attack low. Our
method can be accessed in the supplementary material of this paper to aid
researcher and practitioners in the design and development of resilient CPS and
detection algorithms.


Abstract:
  ASASSN-14ms may represent the most luminous Type Ibn supernova (SN~Ibn) ever
detected, with an absolute U-band magnitude brighter than -22.0 mag and a total
bolometric luminosity >1.0x10^{44} erg/s near maximum light. The early-time
spectra of this SN are characterized by a blue continuum on which are
superimposed narrow P~Cygni profile lines of He I, suggesting the presence of
slowly moving (~1000 km/s), He-rich circumstellar material (CSM). At 1--2
months after maximum brightness, the He I line profiles become only slightly
broader, with blueshifted velocities of 2000--3000 km/s, consistent with the
CSM shell being continuously accelerated by the SN light and ejecta. Like most
SNe~Ibn, the light curves of ASASSN-14ms show rapid post-peak evolution,
dropping by ~7 mag in the V band over three months. Such a rapid post-peak
decline and high luminosity can be explained with interaction between SN ejecta
and helium-rich CSM of 0.9~M_{\odot} at a distance of~10^{15} cm. The CSM
around ASASSN-14ms is estimated to originate from a pre-explosion event with a
mass-loss rate of 6.7~M_\odot /yr (assuming a velocity of ~1000 km/s), which is
consistent with abundant He-rich material violently ejected during the late
Wolf-Rayet (WN9-11 or Opfe) stage. After examining the light curves for a
sample of SNe~Ibn, we find that the more luminous ones tend to have slower
post-peak decline rates, reflecting that the observed differences may arise
primarily from discrepancies in the CSM distribution around the massive
progenitors.


Abstract:
  Compact varifocal lenses are essential to various imaging and vision
technologies. However, existing varifocal elements typically rely on
mechanically-actuated systems with limited tuning speeds and scalability. Here,
an ultrathin electrically controlled varifocal lens based on a liquid crystal
(LC) encapsulated semiconductor metasurface is demonstrated. Enabled by the
field-dependent LC anisotropy, applying a voltage bias across the LC cell
modifies the local phase response of the silicon meta-atoms, in turn modifying
the focal length of the metalens. In a numerical implementation, a
voltage-actuated metalens with continuous zoom and up to 20% total focal shift
is demonstrated. The concept of LC-based metalens is experimentally verified
through the design and fabrication of a bifocal metalens that facilitates
high-contrast switching between two discrete focal lengths upon application of
a 3.2 V$_{\rm pp}$ voltage bias. Owing to their ultrathin thickness and
adaptable design, LC-driven semiconductor metasurfaces open new opportunities
for compact varifocal lensing in a diversity of modern imaging applications.


Abstract:
  In this research, we study biological networks at different scales: a gene
autoregulatory network at the single-cell level and the gut microbiota at the
population level.
  Proteins are the main actors in cells, they are the building blocks, act as
enzymes and antibodies. The production of proteins is mediated by transcription
factors. In some cases, a protein acts as its own transcription factor, this is
called autoregulation. It is known that autorepression speeds up the response
and that autoactivation can lead to multiple stable equilibria. In this thesis,
we study the effects of the combination of activation and repression in
autoregulation, as a case study we investigate the possible dynamics of the
leucine responsive protein B of the archaeon Sulfolobus solfataricus (Ss-LrpB),
a protein that regulates itself in a unique and non-monotonic way via three
binding boxes. We examine for which conditions this type of network leads to
oscillations or bistability.
  In the second part, much larger biological systems are considered. Ecological
systems, among which the human gut microbiome, are characterized by
heavy-tailed abundance profiles. We study how these distributions can arise
from population-based models by adding saturation effects and linear noise.
Moreover, we examine different characteristics of experimental time series of
microbial communities, such as the noise color and neutrality of the
biodiversity, and look at the influence of the parameters on these
characteristics. With the first research topic we want to lay a foundation for
the understanding of non-monotonic gene regulation and take the first steps
toward synthetic biology in archaea. In the second part of the thesis, we
investigate experimental time series from complex ecosystems and seek
theoretical models reproducing all observed characteristics in view of building
predictive models.


Abstract:
  Materials with ultralow thermal conductivity are of great interest for
efficient energy conversion and thermal barrier coating. Copper-based
semiconductors such as copper chalcogenides and copper halides are known to
possess extreme low thermal conductivity, whereas the fundamental origin of the
low thermal conductivity observed in the copper-based materials remains
elusive. Here, we reveal that s-d coupling induced giant phonon anharmonicity
is the fundamental mechanism responsible for the ultralow thermal conductivity
of copper compounds. The symmetry controlled strong coupling of high-lying
occupied copper 3d orbital with the unoccupied 4s state under thermal vibration
remarkably lowers the lattice potential barrier, which enhances anharmonic
scattering between phonons. This understanding is confirmed by
temperature-dependent Raman spectra measurements. Our study offers an insight
at atomic level connecting electronic structures with phonon vibration modes,
and thus sheds light on materials properties that rely on electron-phonon
coupling, such as thermoelectricity and superconductivity.


Abstract:
  We investigate the propagator of 3d quantum gravity, formulated as a discrete
topological path integral. We define it as the Ponzano-Regge amplitude of the
solid cylinder swept by a 2d disk evolving in time. Quantum states for a 2d
disk live in the tensor products of N spins, where N is the number of holonomy
insertions connecting to the disk boundary. We formulate the cylindric
amplitude in terms of a transfer matrix and identify its eigen-modes in terms
of spin recoupling. We show that the propagator distinguishes the subspaces
with different total spin and may select the vanishing total spin sector at
late time depending on the chosen cylinder boundary data. We discuss
applications to quantum circuits and the possibility of experimental
simulations of this 3d quantum gravity propagator.


Abstract:
  We show that in electron-hole bilayers with excitonic order arising from
conduction and valence bands formed by atomic orbitals that have different
parities, nonzero interlayer tunneling leads to a second order Josephson
effect. This means the interlayer electrical current is related to the phase of
the excitonic order parameter as $J = J_c \sin2\theta$ instead of $J = J_c \sin
\theta$, and that the system has two degenerate ground states at $\theta=0,
\pi$ that can be switched by an interlayer voltage pulse. When generalized to a
three dimensional stack of alternating electron-hole planes or a two
dimensional stack of chains, AC Josephson effect implies that electric field
pulses perpendicular to the layers and chains can steer the order parameter
phase between the two degenerate ground states, making these devices ultrafast
memories. The order parameter steering also applies to the excitonic insulator
candidate Ta$_2$NiSe$_5$.


Abstract:
  We study the extremal Betti numbers of the class of $t$--spread strongly
stable ideals. More precisely, we determine the maximal number of admissible
extremal Betti numbers for such ideals, and thereby we generalize the known
results for $t\in \{1,2\}$.


Abstract:
  Multi-goal reinforcement learning is widely applied in planning and robot
manipulation. Two main challenges in multi-goal reinforcement learning are
sparse rewards and sample inefficiency. Hindsight Experience Replay (HER) aims
to tackle the two challenges via goal relabeling. However, HER-related works
still need millions of samples and a huge computation. In this paper, we
propose Multi-step Hindsight Experience Replay (MHER), incorporating multi-step
relabeled returns based on $n$-step relabeling to improve sample efficiency.
Despite the advantages of $n$-step relabeling, we theoretically and
experimentally prove the off-policy $n$-step bias introduced by $n$-step
relabeling may lead to poor performance in many environments. To address the
above issue, two bias-reduced MHER algorithms, MHER($\lambda$) and Model-based
MHER (MMHER) are presented. MHER($\lambda$) exploits the $\lambda$ return while
MMHER benefits from model-based value expansions. Experimental results on
numerous multi-goal robotic tasks show that our solutions can successfully
alleviate off-policy $n$-step bias and achieve significantly higher sample
efficiency than HER and Curriculum-guided HER with little additional
computation beyond HER.


Abstract:
  Projection-free conditional gradient (CG) methods are the algorithms of
choice for constrained optimization setups in which projections are often
computationally prohibitive but linear optimization over the constraint set
remains computationally feasible. Unlike in projection-based methods, globally
accelerated convergence rates are in general unattainable for CG. However, a
very recent work on Locally accelerated CG (LaCG) has demonstrated that local
acceleration for CG is possible for many settings of interest. The main
downside of LaCG is that it requires knowledge of the smoothness and strong
convexity parameters of the objective function. We remove this limitation by
introducing a novel, Parameter-Free Locally accelerated CG (PF-LaCG) algorithm,
for which we provide rigorous convergence guarantees. Our theoretical results
are complemented by numerical experiments, which demonstrate local acceleration
and showcase the practical improvements of PF-LaCG over non-accelerated
algorithms, both in terms of iteration count and wall-clock time.


Abstract:
  Let $M$ be the $6$-manifold $M$ as the total space of the sphere bundle of a
rank $3$ vector bundle over a simply connected closed $4$-manifold. We show
that after looping $M$ is homotopy equivalent to a product of loops on spheres
in general. This particularly implies the cohomology rigidity property of $M$
after looping. Furthermore, passing to the rational homotopy, we show that such
$M$ is Koszul in the sense of Berglund.