title:
Cuprates phase diagram deduced from magnetic susceptibility: what is the
  `true' pseudogap line?

abstract:
  Two contradictory phase diagrams have dominated the literature of high-$T_c$
cuprate superconductors. Does the pseudogap line cross the superconducting
$T_c$-dome or not? To answer, we have revisited the experimental magnetic
susceptibility and knight shift of four different compounds,
La$_{1-x}$Sr$_x$CuO$_4$, Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_8$,
Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$, and YBa$_2$Cu$_3$O$_{6+y}$, as a function of
temperature and doping. The susceptibility can be described by the same
function for all materials, having a magnetic and an electronic contributions.
The former is the 2D antiferromagnetic (AF) square lattice response, with a
characteristic temperature of magnetic correlations $T_{max}$. The latter is
the `Pauli' term, revealing the gap opening in the electronic density of states
at the pseudogap temperature $T^*$.
  From precise fits of the data, we find that $T_{max}(p)$ decreases linearly
as a function of doping ($p$) over a wide range, but saturates abruptly in the
overdoped regime. Concomitantly, $T^*(p)$ is {\it linear and tangent} to the
dome, either crossing or approaching $T_{max}(p)$ at the top of the dome,
indicating a qualitative change of behavior from underdoped to overdoped
regimes.
  Contrary to the idea that the pseudogap terminates just above optimal doping,
our analysis suggests that the gap exists throughout the phase diagram. It is
consistent with a pseudogap due to hole pairs, or `pairons', above $T_c$. We
conclude that $T_{max}$, reflecting the AF magnetic correlations, has often
been misinterpreted as the pseudogap temperature $T^*$.


title: Volumetric and structural connectivity abnormalities co-localise in TLE

abstract:
  Patients with temporal lobe epilepsy (TLE) exhibit both volumetric and
structural connectivity abnormalities relative to healthy controls. How these
abnormalities inter-relate and their mechanisms are unclear. We computed grey
matter volumetric changes and white matter structural connectivity
abnormalities in 144 patients with unilateral TLE and 96 healthy controls.
Regional volumes were calculated using T1-weighted MRI, while structural
connectivity was derived using white matter fibre tractography from
diffusion-weighted MRI. For each regional volume and each connection strength,
we calculated the effect size between patient and control groups in a
group-level analysis. We then applied hierarchical regression to investigate
the relationship between volumetric and structural connectivity abnormalities
in individuals. Additionally, we quantified whether abnormalities co-localised
within individual patients by computing Dice similarity scores. In TLE, white
matter connectivity abnormalities were greater when joining two grey matter
regions with abnormal volumes. Similarly, grey matter volumetric abnormalities
were greater when joined by abnormal white matter connections. The extent of
volumetric and connectivity abnormalities related to epilepsy duration, but
co-localisation did not. Co-localisation was primarily driven by neighbouring
abnormalities in the ipsilateral hemisphere. Overall, volumetric and structural
connectivity abnormalities were related in TLE. Our results suggest that shared
mechanisms may underlie changes in both volume and connectivity alterations in
patients with TLE.


title: Parametrised Noncommutative Motives and Equivariant Algebraic K-theory

abstract:
  We construct the parametrised symmetric monoidal category of noncommutative
motives associated to the algebraic K-theory of parametrised perfect-stable
categories. In the equivariant case for a finite group G, we will see that this
in particular means that algebraic K-theories of group actions attain a
refinement to the structure of G-ring spectra equipped with multiplicative
norms in the sense of Hill-Hopkins-Ravenel.


title:
PharmaChain: A Blockchain to Ensure Counterfeit Free Pharmaceutical
  Supply Chain

abstract:
  Access to essential medication is a primary right of every individual in all
developed, developing and underdeveloped countries. This can be fulfilled by
pharmaceutical supply chains (PSC) in place which will eliminate the boundaries
between different organizations and will equip them to work collectively to
make medicines reach even the remote corners of the globe. Due to multiple
entities, which are geographically widespread, being involved and very complex
goods and economic flows, PSC is very difficult to audit and resolve any issues
involved. This has given rise to many issues, including increased threats of
counterfeiting, inaccurate information propagation throughout the network
because of data fragmentation, lack of customer confidence and delays in
distribution of medication to the place in need. Hence, there is a strong need
for robust PSC which is transparent to all parties involved and in which the
whole journey of medicine from manufacturer to consumer can be tracked and
traced easily. This will not only build safety for the consumers, but will also
help manufacturers to build confidence among consumers and increase sales. In
this article, a novel Distributed Ledger Technology (DLT) based transparent
supply chain architecture is proposed and a proof-of-concept is implemented.
Efficiency and scalability of the proposed architecture is evaluated and
compared with existing solutions.


title: Energy fluctuation relations and repeated quantum measurements

abstract:
  In this review paper, we discuss the statistical description in
non-equilibrium regimes of energy fluctuations originated by the interaction
between a quantum system and a measurement apparatus applying a sequence of
repeated quantum measurements. To properly quantify the information about
energy fluctuations, both the exchanged heat probability density function and
the corresponding characteristic function are derived and interpreted. Then, we
discuss the conditions allowing for the validity of the fluctuation theorem in
Jarzynski form $\langle e^{-\beta Q}\rangle = 1$, thus showing that the
fluctuation relation is robust against the presence of randomness in the time
intervals between measurements. Moreover, also the late-time, asymptotic
properties of the heat characteristic function are analyzed, in the
thermodynamic limit of many intermediate quantum measurements. In such a limit,
the quantum system tends to the maximally mixed state (thus corresponding to a
thermal state with infinite temperature) unless the system's Hamiltonian and
the intermediate measurement observable share a common invariant subspace.
Then, in this context, we also discuss how energy fluctuation relations change
when the system operates in the quantum Zeno regime. Finally, the theoretical
results are illustrated for the special cases of two- and three-levels quantum
systems, now ubiquitous for quantum applications and technologies.


title: Parametrised Presentability over Orbital Categories

abstract:
  In this paper, we develop the notion of presentability in the parametrised
homotopy theory framework of Barwick-Dotto-Glasman-Nardin-Shah over orbital
categories. We formulate and prove a characterisation of parametrised
presentable categories in terms of its associated straightening. From this we
deduce the parametrised adjoint functor theorem from the unparametrised version
and prove various localisation results. Such a theory is of interest for
example in equivariant homotopy theory, and we will apply it in a companion
paper to construct the category of parametrised noncommutative motives for
equivariant algebraic K-theory.


title:
Memory Defense: More Robust Classification via a Memory-Masking
  Autoencoder

abstract:
  Many deep neural networks are susceptible to minute perturbations of images
that have been carefully crafted to cause misclassification. Ideally, a robust
classifier would be immune to small variations in input images, and a number of
defensive approaches have been created as a result. One method would be to
discern a latent representation which could ignore small changes to the input.
However, typical autoencoders easily mingle inter-class latent representations
when there are strong similarities between classes, making it harder for a
decoder to accurately project the image back to the original high-dimensional
space. We propose a novel framework, Memory Defense, an augmented classifier
with a memory-masking autoencoder to counter this challenge. By masking other
classes, the autoencoder learns class-specific independent latent
representations. We test the model's robustness against four widely used
attacks. Experiments on the Fashion-MNIST & CIFAR-10 datasets demonstrate the
superiority of our model. We make available our source code at GitHub
repository: https://github.com/eashanadhikarla/MemDefense


title: Does elastic stress modify the equilibrium corner angle?

abstract:
  We consider the influence of elasticity and anisotropic surface energy on the
energy-minimizing shape of a two-dimensional void under biaxial loading. In
particular, we consider void shapes with corners for which the strain energy
density is singular at the corner. The elasticity problem is formulated as a
boundary integral equation using complex potentials. By incorporating the
asymptotic behavior of the singular elastic fields at corners of the void, we
develop a numerical spectral method for determining the stress for a class of
arbitrary void shapes and corner angles. We minimize the total energy of
surface energy and elastic potential energy using calculus of variations to
obtain an Euler-Lagrange equation on the boundary that is coupled to the
elastic field. The shape of the void boundary is determined using a numerical
spectral method that simultaneously determines the equilibrium void shape and
singular elastic fields. Our results show that the precise corner angles that
minimize the total energy are not affected by the presence of the singular
elastic fields. However, the stress singularity on the void surface at the
corner must be balanced by a singularity in the curvature at the corner that
effectively changes the macroscopic geometry of the shape and effectively
changes the apparent corner angle. These results reconcile the apparent
contradiction regarding the effect of elasticity on equilibrium corner angles
in the results of Srolovitz and Davis (2001) and Siegel, Miksis and Voorhees
(2004), and identify an important nontrivial singular behavior associated with
corners on free-boundary elasticity problems.

categories: math.AP cond-mat.mtrl-sci cond-mat.soft cs.NA math.NA


title: K-2 rotated goodness-of-fit for multivariate data

abstract:
  Consider a set of multivariate distributions, $F_1,\dots,F_M$, aiming to
explain the same phenomenon. For instance, each $F_m$ may correspond to a
different candidate background model for calibration data, or to one of many
possible signal models we aim to validate on experimental data. In this
article, we show that tests for a wide class of apparently different models
$F_{m}$ can be mapped into a single test for a reference distribution $Q$. As a
result, valid inference for each $F_m$ can be obtained by simulating
\underline{only} the distribution of the test statistic under $Q$. Furthermore,
$Q$ can be chosen conveniently simple to substantially reduce the computational
time.

categories: stat.ME astro-ph.HE astro-ph.IM physics.data-an stat.CO


title:
Noncrystallographic tail-triangle C-groups of rank 4 and interlacing
  number 2

abstract:
  This work applies the modular reduction technique to the Coxeter group of
rank 4 having a star diagram with labels 5, 3, and $k = 3, 4, 5, \text{ or }
6$. As moduli, we use the odd primes in the quadratic integer ring
$\mathbb{Z}[\tau]$, where $\tau = \frac{1 + \sqrt{5}}{2}$, the golden ratio. We
classify each reduced group as a reflection group over a finite field, and
prove that it is a C-group, regardless of the prime used in the reduction.


title: Path eccentricity of graphs

abstract:
  Let $G$ be a connected graph. The eccentricity of a path $P$, denoted by
ecc$_G(P)$, is the maximum distance from $P$ to any vertex in $G$. In the
\textsc{Central path} (CP) problem our aim is to find a path of minimum
eccentricity. This problem was introduced by Cockayne et al., in 1981, in the
study of different centrality measures on graphs. They showed that CP can be
solved in linear time in trees, but it is known to be NP-hard in many classes
of graphs such as chordal bipartite graphs, planar 3-connected graphs, split
graphs, etc.
  We investigate the path eccentricity of a connected graph~$G$ as a parameter.
Let pe$(G)$ denote the value of ecc$_G(P)$ for a central path $P$ of $G$. We
obtain tight upper bounds for pe$(G)$ in some graph classes. We show that
pe$(G) \leq 1$ on biconvex graphs and that pe$(G) \leq 2$ on bipartite convex
graphs. Moreover, we design algorithms that find such a path in linear time. On
the other hand, by investigating the longest paths of a graph, we obtain tight
upper bounds for pe$(G)$ on general graphs and $k$-connected graphs.
  Finally, we study the relation between a central path and a longest path in a
graph. We show that on trees, and bipartite permutation graphs, a longest path
is also a central path. Furthermore, for superclasses of these graphs, we
exhibit counterexamples for this property.


title:
Investigating the blazar TXS 0506+056 through sharp multi-wavelength
  eyes during 2017-2019

abstract:
  The blazar TXS 0506+056 got into the spotlight of the astrophysical community
in September 2017, when a high-energy neutrino detected by IceCube
(IceCube-170922A) was associated at the 3 $\sigma$ level to a $\gamma$-ray
flare from this source. This multi-messenger photon-neutrino association
remains, as per today, the most significant one ever observed. TXS 0506+056 was
a poorly studied object before the IceCube-170922A event. To better
characterize its broad-band emission, we organized a multi-wavelength campaign
lasting 16 months (November 2017 to February 2019), covering the radio-band
(Mets\"ahovi, OVRO), the optical/UV (ASAS-SN, KVA, REM, Swift/UVOT), the X-rays
(Swift/XRT, NuSTAR), the high-energy $\gamma$ rays (Fermi/LAT) and the
very-high-energy (VHE) $\gamma$ rays (MAGIC). In $\gamma$ rays, the behaviour
of the source was significantly different from the 2017 one: MAGIC observations
show the presence of flaring activity during December 2018, while the source
only shows an excess at the 4$\sigma$ level during the rest of the campaign (74
hours of accumulated exposure); Fermi/LAT observations show several short
(days-to-week timescale) flares, different from the long-term brightening of
2017. No significant flares are detected at lower energies. The radio light
curve shows an increasing flux trend, not seen in other wavelengths. We model
the multi-wavelength spectral energy distributions in a lepto-hadronic
scenario, in which the hadronic emission emerges as Bethe-Heitler and
pion-decay cascade in the X-rays and VHE $\gamma$ rays. According to the model
presented here, the December 2018 $\gamma$-ray flare was connected to a
neutrino emission that was too brief and not bright enough to be detected by
current neutrino instruments.


title:
Exemplar-Based Contrastive Self-Supervised Learning with Few-Shot Class
  Incremental Learning

abstract:
  Humans are capable of learning new concepts from only a few (labeled)
exemplars, incrementally and continually. This happens within the context that
we can differentiate among the exemplars, and between the exemplars and large
amounts of other data (unlabeled and labeled). This suggests, in human
learning, supervised learning of concepts based on exemplars takes place within
the larger context of contrastive self-supervised learning (CSSL) based on
unlabeled and labeled data. We discuss extending CSSL (1) to be based mainly on
exemplars and only secondly on data augmentation, and (2) to apply to both
unlabeled data (a large amount is available in general) and labeled data (a few
exemplars can be obtained with valuable supervised knowledge). A major benefit
of the extensions is that exemplar-based CSSL, with supervised finetuning,
supports few-shot class incremental learning (CIL). Specifically, we discuss
exemplar-based CSSL including: nearest-neighbor CSSL, neighborhood CSSL with
supervised pretraining, and exemplar CSSL with supervised finetuning. We
further discuss using exemplar-based CSSL to facilitate few-shot learning and,
in particular, few-shot CIL.


title:
Connected and Automated Vehicle Platoon Formation Control via
  Differential Games

abstract:
  In this study, the connected and automated vehicles (CAVs) platooning problem
is resolved under a differential game framework. Three information topologies
are considered here. Firstly, Predecessor-following (PF) topology is utilized
where the vehicles control the distance with respect to the merely nearest
predecessor via a sensor link-based information flow. Secondly,
Two-predecessor-following topology (TPF) is exploited where each vehicle
controls the distance with respect to the two nearest predecessors. In this
topology, the second predecessor is communicated via a Vehicle-to-vehicle (V2V)
link. The individual trajectories of CAVs under the Nash equilibrium are
derived in closed-form for these two information topologies. Finally, general
information topology is examined and the differential game is formulated in
this context. In all these options, Pontryagin's principle is employed to
investigate the existence and uniqueness of the Nash equilibrium and obtain its
corresponding trajectories. In the general topology, we suppose numerical
computation of eigenvalues and eigenvectors. All these approaches represent
promising and powerful analytical representations of the CAV platoons under the
differential games. Simulation experiments have verified the efficiency of the
proposed models and their solutions.


title:
Target space diffeomorphisms in Poisson sigma models and asymptotic
  symmetries in 2D dilaton gravities

abstract:
  The dilaton gravity models in two dimensions, including the
Jackiw--Teitelboim model and its deformations, are particular cases of Poisson
sigma models. Target space diffeomorphisms map one Poisson sigma model to
another. We propose to use these diffsomorphisms to identify asymptotic
conditions, boundary actions, and asymptotic symmetries in distinct dilaton
gravity models. As an example, we use the asymptotic conditions in
Jackiw--Teitelboim gravity to construct an asymptotic problem with Virasoro
symmetry in a class of asymptotically Rindler models. We show, that the method
can be applied to a wide class of pairs of dilaton gravities and discuss
possible generalizations.


title:
$\it COD:$ An Algorithm for Shape Reconstruction of Transiting Celestial
  Bodies through Topological Optimization

abstract:
  We introduce a novel algorithm, $\textit{COD}$ -- Compact Opacity
Distribution, for shape reconstruction of a celestial body that has been
observed to occult a star, using the photometric time-series observations of
the occultation. $\textit{COD}$ finds a solution to the light-curve inversion
problem for an optically thick occulter having an approximately convex shape,
together with an estimate of its size, impact parameter and velocity, relative
to the occulted star. The algorithm is based on an optimization scheme that
uses topological constraints and an objective function for the geometry of the
occulter. The constraints of the problem follow linear relations, which enable
the use of linear programming optimization as the mathematical framework.
Multiple tests of the algorithm were performed, all of which resulted in high
correlations between the simulated and obtained shapes of the occulting
objects, with errors within $5\%$ in their projected velocities and horizontal
sizes, and within $0.1$ in their impact parameters. These tests include a video
of a solar eclipse by Phobos, as seen by NASA's Curiosity rover, which was
collapsed into its corresponding light curve and reconstructed afterwards. We
applied $\textit{COD}$ to the mysterious case of VVV-WIT-08 -- a single deep
occultation ($\sim 96 \%$) of a giant star lasting for over 200 days. The
analysis, which did not assume any specific shape of the occulter, suggested an
object with a projected opacity distribution resembling an ellipse with an
eccentricity of $\sim 0.5$, tilted at $\sim 30$ degrees relative to the
direction of motion, with a semi-minor axis similar to the stellar radius.


title:
Many body density of states in the edge of the spectrum: non-interacting
  limit

abstract:
  In noninteracting limit, the density of states of a many body system can be
expressed as the convolution of single body density of states of its subunits.
Here we use the formulation to derive the ensemble averaged many body density
of states for the cases in which subunits can be modelled by Gaussian or
Wishart random matrix ensembles.


title: ROMNet: Renovate the Old Memories

abstract:
  Renovating the memories in old photos is an intriguing research topic in
computer vision fields. These legacy images often suffer from severe and
commingled degradations such as cracks, noise, and color-fading, while lack of
large-scale paired old photo datasets makes this restoration task very
challenging. In this work, we present a novel reference-based end-to-end
learning framework that can jointly repair and colorize the degraded legacy
pictures. Specifically, the proposed framework consists of three modules: a
restoration sub-network for degradation restoration, a similarity sub-network
for color histogram matching and transfer, and a colorization subnet that
learns to predict the chroma elements of the images conditioned on chromatic
reference signals. The whole system takes advantage of the color histogram
priors in a given reference image, which vastly reduces the dependency on
large-scale training data. Apart from the proposed method, we also create, to
our knowledge, the first public and real-world old photo dataset with paired
ground truth for evaluating old photo restoration models, wherein each old
photo is paired with a manually restored pristine image by PhotoShop experts.
Our extensive experiments conducted on both synthetic and real-world datasets
demonstrate that our method significantly outperforms state-of-the-arts both
quantitatively and qualitatively.


title: Lazy Risk-Limiting Ballot Comparison Audits

abstract:
  Risk-limiting audits or RLAs are rigorous statistical procedures meant to
detect invalid election results. In general, they call for an examination of
paper ballots cast during the election to statistically assess potential
disagreements between the winner determined by the ballots and the winner
reported by tabulation. The design of an RLA must balance risk, the chance that
the audit fails to detect such a disagreement when one occurs, with efficiency,
the total effort to prepare and conduct the audit. The most efficient
approaches-when measured in terms of the number of ballots that must be
inspected-proceed by ballot comparison. This technique, however, requires an
untrusted declaration of the contents of each cast ballot, rather than a simple
tabulation of vote totals. This cast-vote record (CVR) is then spot-checked
against ballots for consistency. The cost of generating such a CVR dominates
the cost to conduct the audit in many practical settings which precludes
adoption. We introduce a new RLA procedure: a lazy ballot comparison audit. In
this audit, a global CVR is never produced; instead, when a ballot is selected
for audit a three-stage procedure is followed: 1) the batch containing the
ballot is announced, 2) a CVR is produced for that batch, and 3) the ballot is
announced and compared with the CVR. The analysis of such an audit is
complicated by the fact that the details of each CVR may depend-perhaps
adversarially-on the prior history of the audit. We present three main
contributions: (1) A formal adversarial model for RLAs; (2) Definition and
analysis of a lazy audit procedure with rigorous risk limits and an associated
correctness analysis accounting for the incidental errors arising in typical
audits; and (3) An analysis of the relative time savings of these techniques.


title:
Partial compensation of thermal noise in the fundamental mode of an
  optical cavity

abstract:
  Thermal noise of optical cavities limits the accuracy of many experiments on
precision laser spectroscopy and interferometry. The study of the physical
properties of this noise opens opportunities for the creation of more stable
cavities, reduction of phase noise of optical radiation, and performance of
accurate optical studies. The paper proposes a method of partial recording of
TEM00 mode thermal noise of a Fabry-Perot cavity using two "probe" modes of
higher order. The method allows partial compensation of noise in the
fundamental mode. Mathematical modeling is performed, which confirms the
efficiency of the method.


title: Logarithmic equal-letter runs for BWT of purely morphic words

abstract:
  In this paper we study the number $r_{bwt}$ of equal-letter runs produced by
the Burrows-Wheeler transform ($BWT$) when it is applied to purely morphic
finite words, which are words generated by iterating prolongable morphisms.
Such a parameter $r_{bwt}$ is very significant since it provides a measure of
the performances of the $BWT$, in terms of both compressibility and indexing.
In particular, we prove that, when $BWT$ is applied to any purely morphic
finite word on a binary alphabet, $r_{bwt}$ is $\mathcal{O}(\log n)$, where $n$
is the length of the word. Moreover, we prove that $r_{bwt}$ is $\Theta(\log
n)$ for the binary words generated by a large class of prolongable binary
morphisms. These bounds are proved by providing some new structural properties
of the \emph{bispecial circular factors} of such words.


title:
Structure and dynamics of HD$^+$ in the vicinity of the H$^+$ + D and
  D$^+$ + H dissociation thresholds: Feshbach resonances and the role of
  g/u-symmetry breaking

abstract:
  We report on the measurement and analysis of photoionisation,
mass-analysed-threshold-ionisation and pulsed-field-ionisation
zero-kinetic-energy photoelectron spectra of HD in the vicinity of the
dissociative-ionisation thresholds H$^+$ + D(1s) + e$^-$ and H(1s) + D$^+$ +
e$^-$. The spectra were recorded via the $v=11$-13 vibrational levels of the
$\bar{\rm H}$ and $\bar{\rm B}$ outer wells of the H$\bar{\rm
H}$~$^1\Sigma_g^+$ and B$^{\prime\prime}\bar{\rm B}$~$^1\Sigma_u^+$ states and
provide information on the weakly bound levels of the X$^+$ $^2\Sigma_g^+$
ground state of HD$^+$ with vibrational quantum numbers $v^+=16$-21 and
rotational angular-momentum quantum numbers $N^+=0$-10. The spectra also reveal
for the first time shape and Feshbach resonances of HD$^+$ located
energetically above the H$^+$ + D(1s) dissociation limit. The structure and
dissociation dynamics of the $\bar{\rm H}$ and $\bar{\rm B}$ states of HD and
of the X$^+$ $^2\Sigma_g^+$ and A$^+$ $^2\Sigma_u^+$ states of HD$^+$ near the
dissociation thresholds are strongly influenced by the g/u-symmetry breaking
caused by the nuclear-mass asymmetry.


title:
Privacy-preserving Speech Emotion Recognition through Semi-Supervised
  Federated Learning

abstract:
  Speech Emotion Recognition (SER) refers to the recognition of human emotions
from natural speech. If done accurately, it can offer a number of benefits in
building human-centered context-aware intelligent systems. Existing SER
approaches are largely centralized, without considering users' privacy.
Federated Learning (FL) is a distributed machine learning paradigm dealing with
decentralization of privacy-sensitive personal data. In this paper, we present
a privacy-preserving and data-efficient SER approach by utilizing the concept
of FL. To the best of our knowledge, this is the first federated SER approach,
which utilizes self-training learning in conjunction with federated learning to
exploit both labeled and unlabeled on-device data. Our experimental evaluations
on the IEMOCAP dataset shows that our federated approach can learn
generalizable SER models even under low availability of data labels and highly
non-i.i.d. distributions. We show that our approach with as few as 10% labeled
data, on average, can improve the recognition rate by 8.67% compared to the
fully-supervised federated counterparts.


title:
Entanglement entropy and flow in two dimensional QCD:parton and string
  duality

abstract:
  We discuss quantum entanglement between fast and slow degrees of freedom, in
a two dimensional (2D) large $N_c$ gauge theory with Dirac quarks, quantized on
the light front. Using the 't Hooft wave functions, we construct the reduced
density matrix for an interval in the momentum fraction $x$-space, and
calculate its von Neumann entropy in terms of structure functions, that are
measured by DIS on mesons (hadrons in general). We found that the entropy is
bounded by an area law with logarithmic divergences, proportional to the
rapidity of the meson. The evolution of the entanglement entropy with rapidity,
is fixed by the cumulative singlet PDF, and bounded from above by a
Kolmogorov-Sinai entropy of 1. At low-$x$, the entanglement exhibits an
asymptotic expansion, similar to the forward meson-meson scattering amplitude
in the Regge limit. The evolution of the entanglement entropy in parton-$x$ per
unit rapidity, measures the meson singlet PDF. The re-summed entanglement
entropy along the single meson Regge trajectory, is string-like. We suggest
that its extension to multi-meson states, models DIS scattering on a large 2D
$^\prime$nucleus$^\prime$. The result, is a large rate of change of the
entanglement entropy with rapidity, that matches the current
Bekenstein-Bremermann bound for maximum quantum information flow. This
mechanism may be at the origin of the large entropy deposition and rapid
thermalization, reported in current heavy ion colliders, and may extend to
future electron-ion colliders.


title: On the Complexity of Coordinated Table Selective Substitution Systems

abstract:
  We investigate computational resources used by Turing machines (TMs) and
alternating Turing machines (ATMs) to accept languages generated by coordinated
table selective substitution systems with two components. We prove that the
class of languages generated by real-time (RL; 0S)-systems, an alternative
device to generate lambda-free labeled marked Petri nets languages, can be
accepted by nondeterministic TMs in O(log n) space and O(nlog n) time.
Consequently, this proper sub-class of Petri nets languages (known also as
L-languages) is included in NSPACE(log n). The class of languages generated by
(RL; RB)-systems for which the nonterminal alphabet of the RL-grammar is
composed of only one symbol and the nonterminal alphabet of the RB-grammar is
composed of two symbols, can be accepted by ATMs in O(log n) time and space.
Consequently, this proper subclass of one-counter languages generated by
one-counter machines with only one control state is included in U_E*-uniform
NC1, hence in SPACE(log n).


title: Neutral Bremsstrahlung emission in xenon unveiled

abstract:
  We present evidence of non-excimer-based secondary scintillation in gaseous
xenon, obtained using both the NEXT-White TPC and a dedicated setup. Detailed
comparison with first-principle calculations allows us to assign this
scintillation mechanism to neutral bremsstrahlung (NBrS), a process that has
been postulated to exist in xenon that has been largely overlooked. For photon
emission below 1000 nm, the NBrS yield increases from about 10$^{-2}$
photon/e$^{-}$ cm$^{-1}$ bar$^{-1}$ at pressure-reduced electric field values
of 50 V cm$^{-1}$ bar$^{-1}$ to above 3$\times$10$^{-1}$ photon/e$^{-}$
cm$^{-1}$ bar$^{-1}$ at 500 V cm$^{-1}$ bar$^{-1}$. Above 1.5 kV cm$^{-1}$
bar$^{-1}$, values that are typically employed for electroluminescence, it is
estimated that NBrS is present with an intensity around 1 photon/e$^{-}$
cm$^{-1}$ bar$^{-1}$, which is about two orders of magnitude lower than
conventional, excimer-based electroluminescence. Despite being fainter than its
excimeric counterpart, our calculations reveal that NBrS causes luminous
backgrounds that can interfere, in either gas or liquid phase, with the ability
to distinguish and/or to precisely measure low primary-scintillation signals
(S1). In particular, we show this to be the case in the "buffer" and "veto"
regions, where keeping the electric field below the electroluminescence (EL)
threshold will not suffice to extinguish secondary scintillation. The electric
field in these regions should be chosen carefully to avoid intolerable levels
of NBrS emission. Furthermore, we show that this new source of light emission
opens up a viable path towards obtaining S2 signals for discrimination purposes
in future single-phase liquid TPCs for neutrino and dark matter physics, with
estimated yields up to 20-50 photons/e$^{-}$ cm$^{-1}$.


title:
In defense of Relational Quantum Mechanics: A note on `Qubits are not
  observers'

abstract:
  This is a short note to answer Brukner's objection [see arXiv:2107.03513] to
Rovelli's theory and concerning the preferred basis problem.


title: DSSIM: a structural similarity index for floating-point data

abstract:
  Data visualization is a critical component in terms of interacting with
floating-point output data from large model simulation codes. Indeed,
postprocessing analysis workflows on simulation data often generate a large
number of images from the raw data, many of which are then compared to each
other or to specified reference images. In this image-comparison scenario,
image quality assessment (IQA) measures are quite useful, and the Structural
Similarity Index (SSIM) continues to be a popular choice. However, generating
large numbers of images can be costly, and plot-specific (but data independent)
choices can affect the SSIM value. A natural question is whether we can apply
the SSIM directly to the floating-point simulation data and obtain an
indication of whether differences in the data are likely to impact a visual
assessment, effectively bypassing the creation of a specific set of images from
the data. To this end, we propose an alternative to the popular SSIM that can
be applied directly to the floating point data, which we refer to as the Data
SSIM (DSSIM). While we demonstrate the usefulness of the DSSIM in the context
of evaluating differences due to lossy compression on large volumes of
simulation data from a popular climate model, the DSSIM may prove useful for
many other applications involving simulation or image data.


title:
Adaptive Fine-Tuning of Transformer-Based Language Models for Named
  Entity Recognition

abstract:
  The current standard approach for fine-tuning transformer-based language
models includes a fixed number of training epochs and a linear learning rate
schedule. In order to obtain a near-optimal model for the given downstream
task, a search in optimization hyperparameter space is usually required. In
particular, the number of training epochs needs to be adjusted to the dataset
size. In this paper, we introduce adaptive fine-tuning, which is an alternative
approach that uses early stopping and a custom learning rate schedule to
dynamically adjust the number of training epochs to the dataset size. For the
example use case of named entity recognition, we show that our approach not
only makes hyperparameter search with respect to the number of training epochs
redundant, but also leads to improved results in terms of performance,
stability and efficiency. This holds true especially for small datasets, where
we outperform the state-of-the-art fine-tuning method by a large margin.


title:
Solving matrix nearness problems via Hamiltonian systems, matrix
  factorization, and optimization

abstract:
  In these lectures notes, we review our recent works addressing various
problems of finding the nearest stable system to an unstable one. After the
introduction, we provide some preliminary background, namely, defining
Port-Hamiltonian systems and dissipative Hamiltonian systems and their
properties, briefly discussing matrix factorizations, and describing the
optimization methods that we will use in these notes. In the third chapter, we
present our approach to tackle the distance to stability for standard
continuous linear time invariant (LTI) systems. The main idea is to rely on the
characterization of stable systems as dissipative Hamiltonian systems. We show
how this idea can be generalized to compute the nearest $\Omega$-stable matrix,
where the eigenvalues of the sought system matrix $A$ are required to belong a
rather general set $\Omega$. We also show how these ideas can be used to
compute minimal-norm static feedbacks, that is, stabilize a system by choosing
a proper input $u(t)$ that linearly depends on $x(t)$ (static-state feedback),
or on $y(t)$ (static-output feedback). In the fourth chapter, we present our
approach to tackle the distance to passivity. The main idea is to rely on the
characterization of stable systems as port-Hamiltonian systems. We also discuss
in more details the special case of computing the nearest stable matrix pairs.
In the last chapter, we focus on discrete-time LTI systems. Similarly as for
the continuous case, we propose a parametrization that allows efficiently
compute the nearest stable system (for matrices and matrix pairs), allowing to
compute the distance to stability. We show how this idea can be used in
data-driven system identification, that is, given a set of input-output pairs,
identify the system $A$.


title:
A bird's eye view on Multi-Objective Optimization techniques in
  Relational Databases

abstract:
  Multi-objective optimization is the problem of optimizing simultaneously
multiple objective functions and several techniques exist to deal with this
problem. This paper aims to present the main methods that can be used to solve
this issue in the context of relational databases. In particular, this work
examines Top-k query to get the k best result from a dataset and Skyline query
that provides a more general overview of the best results. We also discuss
Flexible-skyline, a new method designed to improve upon the previous
techniques, mitigating their shortcomings. For each method, we describe the
main characteristics and present an overview of the algorithms implementing
such thecniques, while comparing advantages and disadvantages.


title: Graphical parameters for classes of tumbling block graphs

abstract:
  The infinite tumbling block graph is a bipartite graph, where each vertex in
one partite set is of degree 3 and each vertex in the other partite set is of
degree 6. It is a 2-dimensional array of blocks of seven vertices and nine
edges, a planar graph that has 3-D looks. This paper introduces tumbling block
graphs and considers various graphical parameters for different classes of
infinite and finite tumbling blocks.


title:
COVID-19 and Influenza Joint Forecasts Using Internet Search Information
  in the United States

abstract:
  As COVID-19 pandemic progresses, severe flu seasons may happen alongside an
increase in cases in cases and death of COVID-19, causing severe burdens on
health care resources and public safety. A consequence of a twindemic may be a
mixture of two different infections in the same person at the same time,
"flurona". Admist the raising trend of "flurona", forecasting both influenza
outbreaks and COVID-19 waves in a timely manner is more urgent than ever, as
accurate joint real-time tracking of the twindemic aids health organizations
and policymakers in adequate preparation and decision making. Under the current
pandemic, state-of-art influenza and COVID-19 forecasting models carry valuable
domain information but face shortcomings under current complex disease
dynamics, such as similarities in symptoms and public healthcare seeking
patterns of the two diseases. Inspired by the inner-connection between
influenza and COVID-19 activities, we propose ARGOX-Joint-Ensemble which allows
us to combine historical influenza and COVID-19 disease forecasting models to a
new ensemble framework that handles scenarios where flu and COVID co-exist. Our
framework is able to emphasize learning from COVID-related or influenza
signals, through a winner-takes-all ensemble fashion. Moreover, our experiments
demonstrate that our approach is successful in adapting past influenza
forecasting models to the current pandemic, while improving upon previous
COVID-19 forecasting models, by steadily outperforming alternative benchmark
methods, and remaining competitive with publicly available models.


title: Killing forms on Riemannian Poisson warped product space

abstract:
  A formal treatment of Killing 1-form and 2-Killing 1-form on Riemannian
Poisson manifold, Riemannian Poisson warped product space are presented. In
this way, we obtain Bochner type result on compact Riemannian Poisson manifold,
compact Riemannian Poisson warped product space for Killing 1-form and
2-Killing 1-form. Finally, we give the characterization of a 2-Killing 1-form
on $(\mathbb{R}^2,g,\Pi)$.


title: The case for Zero Trust Digital Forensics

abstract:
  It is imperative for all stakeholders that digital forensics investigations
produce reliable results to ensure the field delivers a positive contribution
to the pursuit of justice across the globe. Some aspects of these
investigations are inevitably contingent on trust, however this is not always
explicitly considered or critically evaluated. Erroneously treating features of
the investigation as trusted can be enormously damaging to the overall
reliability of an investigations findings as well as the confidence that
external stakeholders can have in it. As an example, digital crime scenes can
be manipulated by tampering with the digital artefacts left on devices, yet
recent studies have shown that efforts to detect occurrences of this are rare
and argue that this leaves digital forensics investigations vulnerable to
accusations of inaccuracy. In this paper a new approach to digital forensics is
considered based on the concept of Zero Trust, an increasingly popular design
in network security. Zero Trust describes the practitioner mindset and
principles upon which the reliance on trust in network components is eliminated
in favour of dynamic verification of network interactions. An initial
definition of Zero Trust Digital Forensics will be proposed and then a specific
example considered showing how this strategy can be applied to digital forensic
investigations to mitigate against the specific risk of evidence tampering. A
definition of Zero Trust Digital Forensics is proposed, specifically that it is
a strategy adopted by investigators whereby each aspect of an investigation is
assumed to be unreliable until verified. A new principle will be introduced,
namely the multifaceted verification of digital artefacts that can be used by
practitioners who wish to adopt a Zero Trust Digital Forensics strategy during
their investigations...


title: Curvatures in contravariant warped product space

abstract:
  In this article, we introduce the sectional curvature in contravariant warped
product space $(M= M_{1}\times_{f_{1}}M_{2},\Pi,g^{f_{1}})$, where
$\Pi=\Pi_1+\nu_{1}\Pi_2$). After that we find the sectional curvature of $M$
for which $M_{1}$ and $M_{2}$ are Poisson manifolds of positive sectional
curvatures. In dual space of $M$, we introduce the notion of null, spacelike,
timelike $1 -$ forms and then by using these forms, qualar curvature is
defined. Finally, as an examples we obtain the sectional curvatures for $M_{1}
= H_{1}^2$, $M_{2} = S_{0}^2 , E_{2}^2$ and qualar curvature for $M$.


title:
Training Differentially Private Models with Secure Multiparty
  Computation

abstract:
  We address the problem of learning a machine learning model from training
data that originates at multiple data owners while providing formal privacy
guarantees regarding the protection of each owner's data. Existing solutions
based on Differential Privacy (DP) achieve this at the cost of a drop in
accuracy. Solutions based on Secure Multiparty Computation (MPC) do not incur
such accuracy loss but leak information when the trained model is made publicly
available. We propose an MPC solution for training DP models. Our solution
relies on an MPC protocol for model training, and an MPC protocol for
perturbing the trained model coefficients with Laplace noise in a
privacy-preserving manner. The resulting MPC+DP approach achieves higher
accuracy than a pure DP approach while providing the same formal privacy
guarantees. Our work obtained first place in the iDASH2021 Track III
competition on confidential computing for secure genome analysis.


title:
Layer-wise Regularized Adversarial Training using Layers Sustainability
  Analysis (LSA) framework

abstract:
  Deep neural network models are used today in various applications of
artificial intelligence, the strengthening of which, in the face of adversarial
attacks is of particular importance. An appropriate solution to adversarial
attacks is adversarial training, which reaches a trade-off between robustness
and generalization. This paper introduces a novel framework (Layer
Sustainability Analysis (LSA)) for the analysis of layer vulnerability in an
arbitrary neural network in the scenario of adversarial attacks. LSA can be a
helpful toolkit to assess deep neural networks and to extend the adversarial
training approaches towards improving the sustainability of model layers via
layer monitoring and analysis. The LSA framework identifies a list of Most
Vulnerable Layers (MVL list) of the given network. The relative error, as a
comparison measure, is used to evaluate representation sustainability of each
layer against adversarial inputs. The proposed approach for obtaining robust
neural networks to fend off adversarial attacks is based on a layer-wise
regularization (LR) over LSA proposal(s) for adversarial training (AT); i.e.
the AT-LR procedure. AT-LR could be used with any benchmark adversarial attack
to reduce the vulnerability of network layers and to improve conventional
adversarial training approaches. The proposed idea performs well theoretically
and experimentally for state-of-the-art multilayer perceptron and convolutional
neural network architectures. Compared with the AT-LR and its corresponding
base adversarial training, the classification accuracy of more significant
perturbations increased by 16.35%, 21.79%, and 10.730% on Moon, MNIST, and
CIFAR-10 benchmark datasets, respectively. The LSA framework is available and
published at https://github.com/khalooei/LSA.


title: Spatio-Temporal Failure Propagation in Cyber-Physical Power Systems

abstract:
  Cascading failure in power systems is triggered by a small perturbation that
leads to a sequence of failures spread through the system. The interconnection
between different components in a power system causes failures to easily
propagate across the system. The situation gets worse by considering the
interconnection between cyber and physical layers in power systems. A plethora
of work has studied the cascading failure in power systems to calculate its
impact on the system. Understanding how failures propagate into the system in
time and space can help the system operator to take preventive actions and
upgrade the system accordingly. Due to the nonlinearity of the power flow
equation as well as the engineering constraints in the power system, it is
essential to understand the spatio-temporal failure propagation in
cyber-physical power systems (CPPS). This paper proposes an asynchronous
algorithm for investigating failure propagation in CPPS. The physics of the
power system is addressed by the full AC power flow equations. Various
practical constraints including load shedding, load-generation balance, and
island operation are considered to address practical constraints in power
system operation. The propagation of various random initial attacks of
different sizes is analyzed and visualized to elaborate on the applicability of
the proposed approach. Our findings shed light on the cascading failure
evolution in CPPS.


title:
Improved Certified Defenses against Data Poisoning with (Deterministic)
  Finite Aggregation

abstract:
  Data poisoning attacks aim at manipulating model behaviors through distorting
training data. Previously, an aggregation-based certified defense, Deep
Partition Aggregation (DPA), was proposed to mitigate this threat. DPA predicts
through an aggregation of base classifiers trained on disjoint subsets of data,
thus restricting its sensitivity to dataset distortions. In this work, we
propose an improved certified defense against general poisoning attacks, namely
Finite Aggregation. In contrast to DPA, which directly splits the training set
into disjoint subsets, our method first splits the training set into smaller
disjoint subsets and then combines duplicates of them to build larger (but not
disjoint) subsets for training base classifiers. This reduces the worst-case
impacts of poison samples and thus improves certified robustness bounds. In
addition, we offer an alternative view of our method, bridging the designs of
deterministic and stochastic aggregation-based certified defenses. Empirically,
our proposed Finite Aggregation consistently improves certificates on MNIST,
CIFAR-10, and GTSRB, boosting certified fractions by up to 3.05%, 3.87% and
4.77%, respectively, while keeping the same clean accuracies as DPA's,
effectively establishing a new state of the art in (pointwise) certified
robustness against data poisoning.


title:
Improving Probabilistic Models in Text Classification via Active
  Learning

abstract:
  When using text data, social scientists often classify documents in order to
use the resulting document labels as an outcome or predictor. Since it is
prohibitively costly to label a large number of documents manually, automated
text classification has become a standard tool. However, current approaches for
text classification do not take advantage of all the data at one's disposal. We
propose a fast new model for text classification that combines information from
both labeled and unlabeled data with an active learning component, where a
human iteratively labels documents that the algorithm is least certain about.
Using text data from Wikipedia discussion pages, BBC News articles, historical
US Supreme Court opinions, and human rights abuse allegations, we show that by
introducing information about the structure of unlabeled data and iteratively
labeling uncertain documents, our model improves performance relative to
classifiers that (a) only use information from labeled data and (b) randomly
decide which documents to label at the cost of manually labelling a small
number of documents.


title: Non-equilibrium thermodynamics of diffusion in fluctuating potentials

abstract:
  A positive rate of entropy production at steady state is a distinctive
feature of truly non-equilibrium processes. Exact results, while being often
limited to simple models, offer a unique opportunity to explore the
thermodynamic features of these processes in full details. Here we derive
analytical results for the steady-state rate of entropy production in single
particle systems driven away from equilibrium by the fluctuations of an
external potential of arbitrary shapes. Subsequently, we provide exact results
for a diffusive particle in a harmonic trap whose potential stiffness varies in
time according to both discrete and continuous Markov processes. In particular,
studying the case of a fully intermittent potential allows us to introduce an
effective model of stochastic resetting for which it is possible to obtain
finite non-negative entropy production. Altogether, this work lays the
foundation for a non-equilibrium thermodynamic theory of fluctuating
potentials, with immediate applications to stochastic resetting processes,
fluctuations in optical traps and fluctuating interactions in living systems.


title: Study on Einstein Warped Product space with Quarter Symmetric Connection

abstract:
  We study Einstein warped space with a quarter symmetric connection. As a
result, first, we find basic results on curvature, Ricci and scalar tensors
with respect to the quarter symmetric connection. Moreover, we prove some
results corresponding to second order quarter symmetric connection. Finally, we
prove that if $M$ is an Einstein warped space with nonpositive scalar curvature
and compact base with respect to quarter symmetric connection and the warping
function satisfy some condition then $M$ is simply a Riemannian product space.


title:
Robust Routing, Entanglement Generation, and Phase Sensing as emergent
  behaviour in quantum spin networks

abstract:
  Spin chains can be used to describe a wide range of platforms for quantum
computation and quantum information. They enable the understanding,
demonstration and modelling of numerous useful phenomena, such as: high
fidelity transfer of quantum states; creation and distribution of entanglement;
creation of resources for measurement-based quantum processing. In this paper,
we study a more complex spin system, a two dimensional Spin Network (SN)
engineered by applying suitable unitaries to two uncoupled spin chains.
Considering only the single-excitation subspace of the SN, we demonstrate that
the system can be operated as a router, directing information through the SN.
We also show that it can serve to generate maximally entangled states between
two sites. Furthermore, we illustrate that our SN system can be used as a
sensor device able to determine an unknown phase applied to a system spin. A
detailed modelling investigation of the effects of static disorder in the
system shows that our system is robust against different types of disorder.


title:
Inverse eigenvalue and related problems for hollow matrices described by
  graphs

abstract:
  A hollow matrix described by a graph $G$ is a real symmetric matrix having
all diagonal entries equal to zero and with the off-diagonal entries governed
by the adjacencies in $G$. For a given graph $G$, the determination of all
possible spectra of matrices associated with $G$ is the hollow inverse
eigenvalue problem for $G$. Solutions to the hollow inverse eigenvalue problems
for paths and complete bipartite graphs are presented. Results for related
subproblems such as possible ordered multiplicity lists, maximum multiplicity
of an eigenvalue, and minimum number of distinct eigenvalues are presented for
additional families of graphs.


title:
A bibliometric investigation into the literature of semantic reasoning
  in Internet of Things

abstract:
  Nowadays, semantic interoperability is a new keyword in the Internet of
Things (IoT) for the exchange of information between sources. The constant need
for interaction and cooperation has resulted in the creation of the Semantic
Web with the help of tools and reasoners which manage personal information.
Given the significance of the IoT and the increasing use of semantic techniques
in this field, the present bibliometric investigation was conducted in the
domain of semantic reasoning in the IoT. Bibliometrics involves analyzing
bibliographic data of scientific sources, and it can be employed to arrive at
an analysis of the status quo in a scientific field. In this study, through the
analysis of 799 articles retrieved from the Web of Science database,
distribution of topic categories, prolific and influential authors, language of
articles, publishers of articles and their geographical distribution, the most
debated/researched and the most frequently cited articles, and keyword trends
were studied. The results of this study indicate that the number of articles
published in the domain of semantic reasoning in the IoT has increased
considerably in recent years. Of the articles analyzed, it was revealed that 10
countries produced 84% of the total documents, with China being in the lead.
Moreover, as a result of keyword analysis, it can be maintained that the words
fog computing, edge computing, Semantic Web, and wireless sensor network are
among the most important keywords in this domain. As well, ontology has the
highest average number of citations among the specialized keywords.


title:
Multilingual Hate Speech and Offensive Content Detection using Modified
  Cross-entropy Loss

abstract:
  The number of increased social media users has led to a lot of people
misusing these platforms to spread offensive content and use hate speech.
Manual tracking the vast amount of posts is impractical so it is necessary to
devise automated methods to identify them quickly. Large language models are
trained on a lot of data and they also make use of contextual embeddings. We
fine-tune the large language models to help in our task. The data is also quite
unbalanced; so we used a modified cross-entropy loss to tackle the issue. We
observed that using a model which is fine-tuned in hindi corpora performs
better. Our team (HNLP) achieved the macro F1-scores of 0.808, 0.639 in English
Subtask A and English Subtask B respectively. For Hindi Subtask A, Hindi
Subtask B our team achieved macro F1-scores of 0.737, 0.443 respectively in
HASOC 2021.


title:
Optimizing achromaticity in metalenses, and development of a layered
  thin-film metalens

abstract:
  Metalenses are ultrathin optical devices designed to replicate behavior of
conventional refractive lenses, or lens arrays, utilizing nanoscale resonant
structures to redirect incident light. These are often comprised of discrete
meta-atoms such as nanoscale dielectric pillars. Achromatic focusing -
associated with traditional multi-element refractive counterparts - is
frequently attempted with single-layer metalens designs, which has proven
difficult to achieve with bounded refractive indices and total lens thickness.
A recent study (F.Presutti and F.Monticone, 2020) formalized this, applying
optical delay-line limitations to metalenses, resulting in a generalized
trade-off in achromaticity for focusing systems. In this work, we (1)
theoretically explore achromaticity in metalens design, and (2) propose a
thin-film multilayer design as an alternative to the discrete meta-atom
approach for large numerical aperture (NA) achromatic metalenses. It is shown
that wavefront modulation can also be achieved with spectrally-varying
transmission magnitudes, rather than purely matching a phase profile. In fact,
even with a bounded refractive index, perfect achromatic operation over a given
spectral range can be offset by imperfect operation elsewhere, resulting in a
NA limited by the smallest general spectral feature controlled. These
considerations lead to a generalized phase-matching optimization routine, and a
thin-film metalens is simulated, utilizing layered TiO2/MgF2 with total
thicknesses under 1 {\mu}m (20 layers), focusing across 6 simultaneous
wavelengths (350-740 nm, {\Delta}{\lambda}~65 nm). A significant proportion
(>40% spectral average) of the reflected light is focused for moderate NA
(~0.35). With the maturity of the optical coating industry, the conformal
thin-film approach reduces manufacturing complexity from its discrete nanoscale
meta-atom equivalents.


title: Proof of two conjectures on Askey-Wilson polynomials

abstract:
  We give positive answer to two conjectures posed by M. E. H Ismail in his
monograph [Classical and quantum orthogonal polynomials in one variable,
Cambridge University Press, 2005].


title: A Zero-One Law for Virtual Markov Chains

abstract:
  A virtual Markov chain (VMC) is a sequence $\{X_N\}_{N=0}^{\infty}$ of Markov
chains (MCs) coupled together on the same probability space such that $X_N$ has
state space $\{0,1,\ldots, N\}$ and such that removing all instances of $N~+~1$
from the sample path of $X_{N+1}$ results in the sample path of $X_N$ almost
surely. In this paper, we prove an exact characterization of the triviality of
the $\sigma$-algebra $\bigcap_{N=0}^{\infty}\sigma(X_N,X_{N+1},\ldots)$. The
main tool for doing this is a decomposition theorem that the $\sigma$-algebra
generated by a VMC is equal to the $\sigma$-algebra generated by a certain
countably infinite collection of independent constituent MCs. These
constituents are so-called staircase MCs (SMCs), which are defined to be
inhomoheneous Markov chains on the non-negative integers which transition only
by holding or by jumping to a value equal to the current index. We also develop
some general aspects of the theory of SMCs, including a connection with some
classical but very much under-appreciated aspects of convex analysis.


title: Classification on Sentence Embeddings for Legal Assistance

abstract:
  Legal proceedings take plenty of time and also cost a lot. The lawyers have
to do a lot of work in order to identify the different sections of prior cases
and statutes. The paper tries to solve the first tasks in AILA2021 (Artificial
Intelligence for Legal Assistance) that will be held in FIRE2021 (Forum for
Information Retrieval Evaluation). The task is to semantically segment the
document into different assigned one of the 7 predefined labels or "rhetorical
roles." The paper uses BERT to obtain the sentence embeddings from a sentence,
and then a linear classifier is used to output the final prediction. The
experiments show that when more weightage is assigned to the class with the
highest frequency, the results are better than those when more weightage is
given to the class with a lower frequency. In task 1, the team legalNLP
obtained a F1 score of 0.22.


title: Non-resonant Diagrams for Single Production of Top and Bottom Partners

abstract:
  The search for Top and Bottom Partners is a major focus of analyses at both
the ATLAS and CMS experiments. When singly produced, these vector-like partners
of the Standard Model third generation quarks retain a sizeable cross-section
that makes them attractive search candidates in their respective topologies.
While most efforts have concentrated on the resonant mode for single production
of these hypothetical particles, the most dominant mode at narrow widths,
recent studies have revealed a wide and rich phenomenology involving the
non-resonant diagrams. In this letter we categorically investigate the impact
of the non-resonant diagrams on different Top and Bottom partner single
production topologies and their impact on the inclusive cross-section
estimation. We also propose a parameterization for calculating the the
correction factor to the single vector-like quark production cross-section when
such diagrams are included.


title:
Emblaze: Illuminating Machine Learning Representations through
  Interactive Comparison of Embedding Spaces

abstract:
  Modern machine learning techniques commonly rely on complex, high-dimensional
embedding representations to capture underlying structure in the data and
improve performance. In order to characterize model flaws and choose a
desirable representation, model builders often need to compare across multiple
embedding spaces, a challenging analytical task supported by few existing
tools. We first interviewed nine embedding experts in a variety of fields to
characterize the diverse challenges they face and techniques they use when
analyzing embedding spaces. Informed by these perspectives, we developed a
novel system called Emblaze that integrates embedding space comparison within a
computational notebook environment. Emblaze uses an animated, interactive
scatter plot with a novel Star Trail augmentation to enable visual comparison.
It also employs novel neighborhood analysis and clustering procedures to
dynamically suggest groups of points with interesting changes between spaces.
Through a series of case studies with ML experts, we demonstrate how
interactive comparison with Emblaze can help gain new insights into embedding
space structure.


title: Computation of generating symmetries

abstract:
  In this article we continue to develop the theory of generating symmetries
for integrable equations. The technique for computations of generating
symmetries using the Maple program is presented. The technique is based on the
standard symmetry method. By using it we find generating symmetries for KdV,
Camassa-Holm, mKdV, sine-Gordon, Boussinesq, associated Degasperis-Procesi and
associated Novikov equations.


title:
The Unreasonable Effectiveness of Random Pruning: Return of the Most
  Naive Baseline for Sparse Training

abstract:
  Random pruning is arguably the most naive way to attain sparsity in neural
networks, but has been deemed uncompetitive by either post-training pruning or
sparse training. In this paper, we focus on sparse training and highlight a
perhaps counter-intuitive finding, that random pruning at initialization can be
quite powerful for the sparse training of modern neural networks. Without any
delicate pruning criteria or carefully pursued sparsity structures, we
empirically demonstrate that sparsely training a randomly pruned network from
scratch can match the performance of its dense equivalent. There are two key
factors that contribute to this revival: (i) the network sizes matter: as the
original dense networks grow wider and deeper, the performance of training a
randomly pruned sparse network will quickly grow to matching that of its dense
equivalent, even at high sparsity ratios; (ii) appropriate layer-wise sparsity
ratios can be pre-chosen for sparse training, which shows to be another
important performance booster. Simple as it looks, a randomly pruned subnetwork
of Wide ResNet-50 can be sparsely trained to outperforming a dense Wide
ResNet-50, on ImageNet. We also observed such randomly pruned networks
outperform dense counterparts in other favorable aspects, such as
out-of-distribution detection, uncertainty estimation, and adversarial
robustness. Overall, our results strongly suggest there is larger-than-expected
room for sparse training at scale, and the benefits of sparsity might be more
universal beyond carefully designed pruning. Our source code can be found at
https://github.com/VITA-Group/Random_Pruning.


title: How a leak can stop itself

abstract:
  Small fluid leaks are common and frequently troublesome. We often consider
how to stop a leak, but here we ask a different question: how might a leak stop
itself? We experimentally study leaking flow transitions from continuous
drainage to spontaneous arrest. High-speed imaging reveals that fluid breakup
events generate droplets whose Laplace pressures oppose the leak. Early
droplets grow unstably, but a final droplet equilibrates to a stable spherical
cap via lightly damped harmonic oscillations. A total energetic theory shows
that inertia plays a key role in the leak-stop mechanism.


title: Intensity interferometry for ultralight bosonic dark matter detection

abstract:
  Ultralight bosonic dark matter (UBDM) can be described by a classical
wave-like field oscillating at the Compton frequency of the bosons. If a
measurement scheme for the direct detection of UBDM interactions is sensitive
to a signature quadratic in the field, then there is a near-zero-frequency (dc)
component of the signal. Thus, a detector with a given finite bandwidth can be
used to search for bosons with Compton frequencies many orders of magnitude
larger than its bandwidth. This opens the possibility of a detection scheme
analogous to Hanbury Brown and Twiss interferometry. Assuming that the UBDM is
virialized in the gravitational potential, for example of the Milky Way, the
random velocities produce slight deviations from the Compton frequency. These
result in stochastic fluctuations of the intensity on a time scale determined
by the spread in velocities. In order to mitigate ubiquitous local
low-frequency noise, a network of sensors can be used to search for the
stochastic intensity fluctuations by measuring cross-correlation between the
sensors. This method is inherently broadband, since a large range of Compton
frequencies will have a near-zero-frequency component within the sensor
bandwidth that can be searched for simultaneously. Experiments with existing
clock and magnetometer networks have sufficient sensitivity to search a broad
range of unexplored parameter space.

categories: hep-ph astro-ph.CO hep-ex physics.atom-ph


title:
RerrFact: Reduced Evidence Retrieval Representations for Scientific
  Claim Verification

abstract:
  Exponential growth in digital information outlets and the race to publish has
made scientific misinformation more prevalent than ever. However, the task to
fact-verify a given scientific claim is not straightforward even for
researchers. Scientific claim verification requires in-depth knowledge and
great labor from domain experts to substantiate supporting and refuting
evidence from credible scientific sources. The SciFact dataset and
corresponding task provide a benchmarking leaderboard to the community to
develop automatic scientific claim verification systems via extracting and
assimilating relevant evidence rationales from source abstracts. In this work,
we propose a modular approach that sequentially carries out binary
classification for every prediction subtask as in the SciFact leaderboard. Our
simple classifier-based approach uses reduced abstract representations to
retrieve relevant abstracts. These are further used to train the relevant
rationale-selection model. Finally, we carry out two-step stance predictions
that first differentiate non-relevant rationales and then identify supporting
or refuting rationales for a given claim. Experimentally, our system RerrFact
with no fine-tuning, simple design, and a fraction of model parameters fairs
competitively on the leaderboard against large-scale, modular, and joint
modeling approaches. We make our codebase available at
https://github.com/ashishrana160796/RerrFact.


title:
Ethics, Rules of Engagement, and AI: Neural Narrative Mapping Using
  Large Transformer Language Models

abstract:
  The problem of determining if a military unit has correctly understood an
order and is properly executing on it is one that has bedeviled military
planners throughout history. The advent of advanced language models such as
OpenAI's GPT-series offers new possibilities for addressing this problem. This
paper presents a mechanism to harness the narrative output of large language
models and produce diagrams or "maps" of the relationships that are latent in
the weights of such models as the GPT-3. The resulting "Neural Narrative Maps"
(NNMs), are intended to provide insight into the organization of information,
opinion, and belief in the model, which in turn provide means to understand
intent and response in the context of physical distance. This paper discusses
the problem of mapping information spaces in general, and then presents a
concrete implementation of this concept in the context of OpenAI's GPT-3
language model for determining if a subordinate is following a commander's
intent in a high-risk situation. The subordinate's locations within the NNM
allow a novel capability to evaluate the intent of the subordinate with respect
to the commander. We show that is is possible not only to determine if they are
nearby in narrative space, but also how they are oriented, and what
"trajectory" they are on. Our results show that our method is able to produce
high-quality maps, and demonstrate new ways of evaluating intent more
generally.


title: Transitions in Entanglement Complexity in Random Circuits

abstract:
  Entanglement is the defining characteristic of quantum mechanics. Bipartite
entanglement is characterized by the von Neumann entropy. Entanglement is not
just described by a number, however; it is also characterized by its level of
complexity. The complexity of entanglement is at the root of the onset of
quantum chaos, universal distribution of entanglement spectrum statistics,
hardness of a disentangling algorithm and of the quantum machine learning of an
unknown random circuit, and universal temporal entanglement fluctuations. In
this paper, we numerically show how a crossover from a simple pattern of
entanglement to a universal, complex pattern can be driven by doping a random
Clifford circuit with $T$ gates. This work shows that quantum complexity and
complex entanglement stem from the conjunction of entanglement and
non-stabilizer resources, also known as magic.


title:
The Implicit Bias of Gradient Descent on Generalized Gated Linear
  Networks

abstract:
  Understanding the asymptotic behavior of gradient-descent training of deep
neural networks is essential for revealing inductive biases and improving
network performance. We derive the infinite-time training limit of a
mathematically tractable class of deep nonlinear neural networks, gated linear
networks (GLNs), and generalize these results to gated networks described by
general homogeneous polynomials. We study the implications of our results,
focusing first on two-layer GLNs. We then apply our theoretical predictions to
GLNs trained on MNIST and show how architectural constraints and the implicit
bias of gradient descent affect performance. Finally, we show that our theory
captures a substantial portion of the inductive bias of ReLU networks. By
making the inductive bias explicit, our framework is poised to inform the
development of more efficient, biologically plausible, and robust learning
algorithms.


title: Efficient Logistic Regression with Local Differential Privacy

abstract:
  Internet of Things devices are expanding rapidly and generating huge amount
of data. There is an increasing need to explore data collected from these
devices. Collaborative learning provides a strategic solution for the Internet
of Things settings but also raises public concern over data privacy. In recent
years, large amount of privacy preserving techniques have been developed based
on differential privacy and secure multi-party computation. A major challenge
of collaborative learning is to balance disclosure risk and data utility while
maintaining high computation efficiency. In this paper, we proposed privacy
preserving logistic regression model using matrix encryption approach. The
secure scheme achieves local differential privacy and can be implemented for
both vertical and horizontal partitioning scenarios. Moreover, cross validation
is investigated to generate robust model results without increasing the
communication cost. Simulation illustrates the high efficiency of proposed
scheme to analyze dataset with millions of records. Experimental evaluations
further demonstrate high model accuracy while achieving privacy protection.


title:
Beyond Black Box Densities: Parameter Learning for the Deviated
  Components

abstract:
  As we collect additional samples from a data population for which a known
density function estimate may have been previously obtained by a black box
method, the increased complexity of the data set may result in the true density
being deviated from the known estimate by a mixture distribution. To model this
phenomenon, we consider the \emph{deviating mixture model} $(1-\lambda^{*})h_0
+ \lambda^{*} (\sum_{i = 1}^{k} p_{i}^{*} f(x|\theta_{i}^{*}))$, where $h_0$ is
a known density function, while the deviated proportion $\lambda^{*}$ and
latent mixing measure $G_{*} = \sum_{i = 1}^{k} p_{i}^{*}
\delta_{\theta_i^{*}}$ associated with the mixture distribution are unknown.
Via a novel notion of distinguishability between the known density $h_{0}$ and
the deviated mixture distribution, we establish rates of convergence for the
maximum likelihood estimates of $\lambda^{*}$ and $G^{*}$ under Wasserstein
metric. Simulation studies are carried out to illustrate the theory.


title: A Graph Neural Network Framework for Grid-Based Simulation

abstract:
  Reservoir simulations are computationally expensive in the well control and
well placement optimization. Generally, numerous simulation runs (realizations)
are needed in order to achieve the optimal well locations. In this paper, we
propose a graph neural network (GNN) framework to build a surrogate
feed-forward model which replaces simulation runs to accelerate the
optimization process. Our GNN framework includes an encoder, a process, and a
decoder which takes input from the processed graph data designed and generated
from the simulation raw data. We train the GNN model with 6000 samples
(equivalent to 40 well configurations) with each containing the previous step
state variable and the next step state variable. We test the GNN model with
another 6000 samples and after model tuning, both one-step prediction and
rollout prediction achieve a close match with the simulation results. Our GNN
framework shows great potential in the application of well-related subsurface
optimization including oil and gas as well as carbon capture sequestration
(CCS).


title:
Millisecond speed deep learning based proton dose calculation with Monte
  Carlo accuracy

abstract:
  Next generation online and real-time adaptive radiotherapy workflows require
precise particle transport simulations in sub-second times, which is unfeasible
with current analytical pencil beam algorithms (PBA) or stochastic Monte Carlo
(MC) methods. We present a data-driven millisecond speed dose calculation
algorithm (DoTA) accurately predicting the dose deposited by mono-energetic
proton pencil beams for arbitrary energies and patient geometries. Given the
forward-scattering nature of protons, we frame 3D particle transport as
modeling a sequence of 2D geometries in the beam's eye view. DoTA combines
convolutional neural networks extracting spatial features (e.g., tissue and
density contrasts) with a transformer self-attention backbone that routes
information between the sequence of geometry slices and a vector representing
the beam's energy, and is trained to predict low noise MC simulations of proton
beamlets using 80,000 different head and neck, lung, and prostate geometries.
Predicting beamlet doses in 5 ms with a very high gamma pass rate of 99.37%
(1%, 3 mm) compared to the ground truth MC calculations, DoTA significantly
improves upon analytical pencil beam algorithms both in precision and speed.
Offering MC accuracy 100 times faster than PBAs for pencil beams, our model
calculates full treatment plan doses in 10 to 15 s depending on the number of
beamlets, achieving a 99.70% (2%, 2 mm) gamma pass rate across 9 test patients.
Outperforming all previous analytical pencil beam and deep learning based
approaches, DoTA represents a new state of the art in data-driven dose
calculation and can directly compete with the speed of even commercial GPU MC
approaches. Providing the sub-second speed required for adaptive treatments,
straightforward implementations could offer similar benefits to other steps of
the radiotherapy workflow or other modalities such as helium or carbon
treatments.


title: Doing Right by Not Doing Wrong in Human-Robot Collaboration

abstract:
  As robotic systems become more and more capable of assisting humans in their
everyday lives, we must consider the opportunities for these artificial agents
to make their human collaborators feel unsafe or to treat them unfairly. Robots
can exhibit antisocial behavior causing physical harm to people or reproduce
unfair behavior replicating and even amplifying historical and societal biases
which are detrimental to humans they interact with. In this paper, we discuss
these issues considering sociable robotic manipulation and fair robotic
decision making. We propose a novel approach to learning fair and sociable
behavior, not by reproducing positive behavior, but rather by avoiding negative
behavior. In this study, we highlight the importance of incorporating
sociability in robot manipulation, as well as the need to consider fairness in
human-robot interactions.


title:
Surface passivation and oxide encapsulation to improve optical
  properties of a single GaAs quantum dot close to the surface

abstract:
  Epitaxial GaAs quantum dots grown by droplet etching have recently shown
excellent properties as sources of single photons as well as entangled photon
pairs. Integration in some nanophotonic structures requires surface-to-dot
distances of less than 100 nm. This demands a surface passivation scheme, which
could be useful to lower the density of surface states. To address this issue,
sulphur passivation with dielectric overlayer as an encapsulation is used for
surface to QD distances of 40 nm, which results in the partial recovery of
emission linewidths to bulk values as well as in the increase of the
photoluminescence intensity.


title: A survey of top-down approaches for human pose estimation

abstract:
  Human pose estimation in two-dimensional images videos has been a hot topic
in the computer vision problem recently due to its vast benefits and potential
applications for improving human life, such as behaviors recognition, motion
capture and augmented reality, training robots, and movement tracking. Many
state-of-the-art methods implemented with Deep Learning have addressed several
challenges and brought tremendous remarkable results in the field of human pose
estimation. Approaches are classified into two kinds: the two-step framework
(top-down approach) and the part-based framework (bottom-up approach). While
the two-step framework first incorporates a person detector and then estimates
the pose within each box independently, detecting all body parts in the image
and associating parts belonging to distinct persons is conducted in the
part-based framework. This paper aims to provide newcomers with an extensive
review of deep learning methods-based 2D images for recognizing the pose of
people, which only focuses on top-down approaches since 2016. The discussion
through this paper presents significant detectors and estimators depending on
mathematical background, the challenges and limitations, benchmark datasets,
evaluation metrics, and comparison between methods.


title: Notes on the Twistor $\mathbf P^1$

abstract:
  Remarkably, the twistor $\mathbf P^1$ occurs as a fundamental object in both
four-dimensional space-time geometry and in number theory. In Euclidean
signature twistor theory it is how one describes space-time points. In recent
work by Fargues and Scholze on the local Langlands conjecture using geometric
Langlands on the Fargues-Fontaine curve, the twistor $\mathbf P^1$ appears as
the analog of this curve at the infinite prime.
  These notes are purely expository, written with the goal of explaining, in a
form accessible to both mathematicians and physicists, various different ways
in which the twistor $\mathbf P^1$ makes an appearance, often as a geometric
avatar of the quaternions.


title:
Deep-HyROMnet: A deep learning-based operator approximation for
  hyper-reduction of nonlinear parametrized PDEs

abstract:
  To speed-up the solution to parametrized differential problems, reduced order
models (ROMs) have been developed over the years, including projection-based
ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well
as surrogate models obtained via a machine learning approach. Thanks to its
physics-based structure, ensured by the use of a Galerkin projection of the
full order model (FOM) onto a linear low-dimensional subspace, RB methods yield
approximations that fulfill the physical problem at hand. However, to make the
assembling of a ROM independent of the FOM dimension, intrusive and expensive
hyper-reduction stages are usually required, such as the discrete empirical
interpolation method (DEIM), thus making this strategy less feasible for
problems characterized by (high-order polynomial or nonpolynomial)
nonlinearities. To overcome this bottleneck, we propose a novel strategy for
learning nonlinear ROM operators using deep neural networks (DNNs). The
resulting hyper-reduced order model enhanced by deep neural networks, to which
we refer to as Deep-HyROMnet, is then a physics-based model, still relying on
the RB method approach, however employing a DNN architecture to approximate
reduced residual vectors and Jacobian matrices once a Galerkin projection has
been performed. Numerical results dealing with fast simulations in nonlinear
structural mechanics show that Deep-HyROMnets are orders of magnitude faster
than POD-Galerkin-DEIM ROMs, keeping the same level of accuracy.


title: A Game-theoretic Understanding of Repeated Explanations in ML Models

abstract:
  This paper formally models the strategic repeated interactions between a
system, comprising of a machine learning (ML) model and associated explanation
method, and an end-user who is seeking a prediction/label and its explanation
for a query/input, by means of game theory. In this game, a malicious end-user
must strategically decide when to stop querying and attempt to compromise the
system, while the system must strategically decide how much information (in the
form of noisy explanations) it should share with the end-user and when to stop
sharing, all without knowing the type (honest/malicious) of the end-user. This
paper formally models this trade-off using a continuous-time stochastic
Signaling game framework and characterizes the Markov perfect equilibrium state
within such a framework.


title:
Leveraging the Power of Graph Algorithms: Efficient Algorithms for
  Computer-Aided Verification

abstract:
  The goal of the thesis is to leverage fast graph algorithms and modern
algorithmic techniques for problems in model checking and synthesis on graphs,
MDPs, and game graphs. The results include symbolic algorithms, a well-known
class of algorithms in model checking that trades limited access to the input
model for an efficient representation. In particular, we present the following
results: Algorithms for game graphs with mean-payoff B\"uchi objectives and
mean-payoff coB\"uchi objectives which match one of the best running time
bounds for mean-payoff objectives. A near-linear time randomized algorithm for
Streett objectives in graphs and MDPs. A sub-cubic time algorithm for bounded
B\"uchi objectives in graphs and a cubic time algorithm for game graphs.
Conditional lower bounds for queries of reachability objectives in game graphs
and MDPs. Linear and near-linear time algorithms for sequential reachability
objectives in graphs and MDPs respectively. The first quasi-polynomial time
symbolic algorithm for parity objectives in game graphs. We break a
long-standing running time bound for MEC decomposition from the '90s by
providing a sub-quadratic time symbolic algorithm.


title:
LiDAR dataset distillation within bayesian active learning framework:
  Understanding the effect of data augmentation

abstract:
  Autonomous driving (AD) datasets have progressively grown in size in the past
few years to enable better deep representation learning. Active learning (AL)
has re-gained attention recently to address reduction of annotation costs and
dataset size. AL has remained relatively unexplored for AD datasets, especially
on point cloud data from LiDARs. This paper performs a principled evaluation of
AL based dataset distillation on (1/4th) of the large Semantic-KITTI dataset.
Further on, the gains in model performance due to data augmentation (DA) are
demonstrated across different subsets of the AL loop. We also demonstrate how
DA improves the selection of informative samples to annotate. We observe that
data augmentation achieves full dataset accuracy using only 60\% of samples
from the selected dataset configuration. This provides faster training time and
subsequent gains in annotation costs.


title: Destruction of CPE-normality along deterministic sequences

abstract:
  Let $\mu$ be a shift-invariant measure on $\Lambda^{\mathbb N}$, where
$\Lambda$ is a finite or countable alphabet. We say that an increasing sequence
of natural numbers $S=\{s_1,s_2,\dots\}$ preserves (destroys) $\mu$-normality
if, for any $x=(x_1,x_2,...)\in\Lambda^{\mathbb N}$ generic for $\mu$, the
sequence $x|_S=(x_{s_1},x_{s_2},...)$ is (is not) generic for $\mu$. It is
known from Kamae and Weiss that if $\mu$ is i.i.d. then any deterministic
sequence of positive lower density preserves $\mu$-normality. We show that
deterministic sequencess of positive upper density and lower density less than
one destroy $\mu$-normality for any non-i.i.d. measure $\mu$ with completely
positive entropy (CPE). This generalizes Heersink and Vandehey's result for
arithmetic progressions and the Gauss measure (associated to the continued
fraction transformation). We give several examples showing that, outside the
class of measures with CPE, $\mu$-normality preservation can coexist with
nearly any combination of three parameters: determinism of $S$ (or its lack),
entropy of $\mu$ (zero or positive), and disjointness (or its lack) between
$\mu$ and the measures derived from $S$.


title:
Compressible Navier--Stokes system with the hard sphere pressure law in
  an exterior domain

abstract:
  We consider the motion of compressible Navier-Stokes fluids with the hard
sphere pressure law around a rigid obstacle when the velocity and the density
at infinity are non zero. This kind of pressure model is largely employed in
various physical and industrial applications. We prove the existence of weak
solution to the system in the exterior domain.


title:
No Parameters Left Behind: Sensitivity Guided Adaptive Learning Rate for
  Training Large Transformer Models

abstract:
  Recent research has shown the existence of significant redundancy in large
Transformer models. One can prune the redundant parameters without
significantly sacrificing the generalization performance. However, we question
whether the redundant parameters could have contributed more if they were
properly trained. To answer this question, we propose a novel training strategy
that encourages all parameters to be trained sufficiently. Specifically, we
adaptively adjust the learning rate for each parameter according to its
sensitivity, a robust gradient-based measure reflecting this parameter's
contribution to the model performance. A parameter with low sensitivity is
redundant, and we improve its fitting by increasing its learning rate. In
contrast, a parameter with high sensitivity is well-trained, and we regularize
it by decreasing its learning rate to prevent further overfitting. We conduct
extensive experiments on natural language understanding, neural machine
translation, and image classification to demonstrate the effectiveness of the
proposed schedule. Analysis shows that the proposed schedule indeed reduces the
redundancy and improves generalization performance.


title: Conformal Embeddings via Heat Kernel

abstract:
  For any n-dimensional compact Riemannian Manifold $M$ with smooth metric $g$,
by using the heat kernel embedding introduced in [BBG], we construct a
canonical family of conformal embeddings $C_{t,k}$:
$M\rightarrow\mathbb{R}^{q(t)}$, with $t>0$ sufficiently small, $q(t)\gg
t^{-\frac{n}{2}}$, and $k$ as a function of $O(t^l)$ in proper sense. This is
done by finding all the conformal embeddings to overcome the differences from
the isometric embeddings introduced in [WZ].


title:
Simulation-to-Reality domain adaptation for offline 3D object annotation
  on pointclouds with correlation alignment

abstract:
  Annotating objects with 3D bounding boxes in LiDAR pointclouds is a costly
human driven process in an autonomous driving perception system. In this paper,
we present a method to semi-automatically annotate real-world pointclouds
collected by deployment vehicles using simulated data. We train a 3D object
detector model on labeled simulated data from CARLA jointly with real world
pointclouds from our target vehicle. The supervised object detection loss is
augmented with a CORAL loss term to reduce the distance between labeled
simulated and unlabeled real pointcloud feature representations. The goal here
is to learn representations that are invariant to simulated (labeled) and
real-world (unlabeled) target domains. We also provide an updated survey on
domain adaptation methods for pointclouds.


title:
Coexistence of coupling-induced transparency and absorption of
  transmission signals in magnon-mediated photon-photon coupling

abstract:
  Coexistence of coupling-induced transparency (CIT) and absorption (CIA) of
signals in magnon-mediated photon-photon coupling was experimentally determined
in a planar hybrid structure consisting of a yttrium iron garnet (YIG) film and
three concentric inverted-split-ring resonators (ISRRs). The experimental
observation of simultaneous CIT and CIA phenomena was ascribed to
magnon-mediated photon-photon coupling between the individually decoupled
ISRRs. In order to capture the generic physics of the observed interactions, we
constructed an appropriate analytical model based on the balance between the
coherent and dissipative multiple-paths interactions, which model precisely
reproduced both the CIT and CIA experimentally observed from a single hybrid
system. This work, promisingly, can provide guidance for design of efficient,
flexible, and well-controllable photon-magnonic devices that are highly in
demand for applications to quantum technologies currently under development.


title: Unnormalized Measures in Information Theory

abstract:
  Information theory is built on probability measures and by definition a
probability measure has total mass 1. Probability measures are used to model
uncertainty, and one may ask how important it is that the total mass is one. We
claim that the main reason to normalize measures is that probability measures
are related to codes via Kraft's inequality. Using a minimum description length
approach to statistics we will demonstrate with that measures that are not
normalized require a new interpretation that we will call the Poisson
interpretation. With the Poisson interpretation many problems can be
simplified. The focus will shift from from probabilities to mean values. We
give examples of improvements of test procedures, improved inequalities,
simplified algorithms, new projection results, and improvements in our
description of quantum systems.


title: SRPCN: Structure Retrieval based Point Completion Network

abstract:
  Given partial objects and some complete ones as references, point cloud
completion aims to recover authentic shapes. However, existing methods pay
little attention to general shapes, which leads to the poor authenticity of
completion results. Besides, the missing patterns are diverse in reality, but
existing methods can only handle fixed ones, which means a poor generalization
ability. Considering that a partial point cloud is a subset of the
corresponding complete one, we regard them as different samples of the same
distribution and propose Structure Retrieval based Point Completion Network
(SRPCN). It first uses k-means clustering to extract structure points and
disperses them into distributions, and then KL Divergence is used as a metric
to find the complete structure point cloud that best matches the input in a
database. Finally, a PCN-like decoder network is adopted to generate the final
results based on the retrieved structure point clouds. As structure plays an
important role in describing the general shape of an object and the proposed
structure retrieval method is robust to missing patterns, experiments show that
our method can generate more authentic results and has a stronger
generalization ability.


title: Pole recovery from noisy data on imaginary axis

abstract:
  This note proposes an algorithm for identifying the poles and residues of a
meromorphic function from its noisy values on the imaginary axis. The algorithm
uses M\"{o}bius transform and Prony's method in the frequency domain. Numerical
results are provided to demonstrate the performance of the algorithm.


title: Stable factorization for phase factors of quantum signal processing

abstract:
  This note proposes a new factorization algorithm for computing the phase
factors of quantum signal processing. The proposed algorithm avoids root
finding of high degree polynomials and is numerical stable in the double
precision arithmetics. Experimental results are reported for Hamiltonian
simulation, eigenstate filtering, matrix inversion, and Fermi-Dirac operator.


title:
(Almost) Envy-Free, Proportional and Efficient Allocations of an
  Indivisible Mixed Manna

abstract:
  We study the problem of finding fair and efficient allocations of a set of
indivisible items to a set of agents, where each item may be a good (positively
valued) for some agents and a bad (negatively valued) for others, i.e., a mixed
manna. As fairness notions, we consider arguably the strongest possible
relaxations of envy-freeness and proportionality, namely envy-free up to any
item (EFX and EFX$_0$), and proportional up to the maximin good or any bad
(PropMX and PropMX$_0$). Our efficiency notion is Pareto-optimality (PO).
  We study two types of instances:
  (i) Separable, where the item set can be partitioned into goods and bads, and
(ii) Restricted mixed goods (RMG), where for each item $j$, every agent has
either a non-positive value for $j$, or values $j$ at the same $v_j>0$. We
obtain polynomial-time algorithms for the following:
  (i) Separable instances: PropMX$_0$ allocation.
  (ii) RMG instances: Let pure bads be the set of items that everyone values
negatively.
  - PropMX allocation for general pure bads.
  - EFX+PropMX allocation for identically-ordered pure bads.
  - EFX+PropMX+PO allocation for identical pure bads.
  Finally, if the RMG instances are further restricted to binary mixed goods
where all the $v_j$'s are the same, we strengthen the results to guarantee
EFX$_0$ and PropMX$_0$ respectively.


title:
PhysFad: Physics-Based End-to-End Channel Modeling of RIS-Parametrized
  Environments with Adjustable Fading

abstract:
  Programmable radio environments parametrized by reconfigurable intelligent
surfaces (RISs) are emerging as a new wireless communications paradigm, but
currently used channel models for the design and analysis of signal-processing
algorithms cannot include fading in a manner that is faithful to the underlying
wave physics. To overcome this roadblock, we introduce a physics-based
end-to-end model of RIS-parametrized wireless channels with adjustable fading
(coined PhysFad) which is based on a first-principles coupled-dipole formalism.
PhysFad naturally incorporates the notions of space and causality, dispersion
(i.e., frequency selectivity) and the intertwinement of each RIS element's
phase and amplitude response, as well as any arising mutual coupling effects
including long-range mesoscopic correlations. PhysFad offers the to-date
missing tuning knob for adjustable fading. We thoroughly characterize PhysFad
and demonstrate its capabilities for a prototypical problem of RIS-enabled
over-the-air channel equalization in rich-scattering wireless communications.
We also share a user-friendly version of our code to help the community
transition towards physics-based models with adjustable fading.