  Consider a finite l-group acting on the affine space of dimension n over a
field k, whose characteristic differs from l. We prove the existence of a fixed
point, rational over k, in the following cases:
  --- The field k is p-special for some prime p different from its
characteristic.
  --- The field k is perfect and fertile, and n = 3.


  Large-scale language-vision pre-training models, such as CLIP, have achieved
remarkable text-guided image morphing results by leveraging several
unconditional generative models. However, existing CLIP-guided image morphing
methods encounter difficulties when morphing photorealistic images.
Specifically, existing guidance fails to provide detailed explanations of the
morphing regions within the image, leading to misguidance. In this paper, we
observed that such misguidance could be effectively mitigated by simply using a
proper regularization loss. Our approach comprises two key components: 1) a
geodesic cosine similarity loss that minimizes inter-modality features (i.e.,
image and text) on a projected subspace of CLIP space, and 2) a latent
regularization loss that minimizes intra-modality features (i.e., image and
image) on the image manifold. By replacing the na\"ive directional CLIP loss in
a drop-in replacement manner, our method achieves superior morphing results on
both images and videos for various benchmarks, including CLIP-inversion.


  In this Letter, we introduce a notion of local fraction for experiments
taking place against arbitrary static causal backgrounds -- greatly
generalising previous results on no-signalling scenarios -- and we explicitly
formulate a linear program to compute this quantity. We derive a free
characterisation of causal functions which allows us to efficiently construct
the matrices required to perform concrete calculations. We demonstrate our
techniques by analysing the local fraction of a novel example involving two
Bell tests in interleaved causal order.


  Production of electroweak bosons in e+e- annihilation into quarks and into
leptons at energies much greater than 100 Gev is considered. We account for
double-logarithmic contributions to all orders in electroweak couplings. It is
assumed that the bosons are emitted in the multi-Regge kinematics. The explicit
expressions for the scattering amplitudes of the process are obtained. It is
shown that the cross sections of the photon and Z production have the identical
energy dependence and asymptotically their ratio depends only on the Weinberg
angle whereas the energy dependence of the cross section of the W production is
suppressed by factor s^{-0.4} compared to them.


  The use of multilingual language models for tasks in low and high-resource
languages has been a success story in deep learning. In recent times, Arabic
has been receiving widespread attention on account of its dialectal variance.
While prior research studies have tried to adapt these multilingual models for
dialectal variants of Arabic, it still remains a challenging problem owing to
the lack of sufficient monolingual dialectal data and parallel translation data
of such dialectal variants. It remains an open problem on whether the limited
dialectical data can be used to improve the models trained in Arabic on its
dialectal variants. First, we show that multilingual-BERT (mBERT) incrementally
pretrained on Arabic monolingual data takes less training time and yields
comparable accuracy when compared to our custom monolingual Arabic model and
beat existing models (by an avg metric of +$6.41$). We then explore two
continual pre-training methods -- (1) using small amounts of dialectical data
for continual finetuning and (2) parallel Arabic to English data and a
Translation Language Modeling loss function. We show that both approaches help
improve performance on dialectal classification tasks ($+4.64$ avg. gain) when
used on monolingual models.


  In this article, we study the well-posedness of the energy-critical half-wave
maps equation (HWM) in dimension $1$. The half-wave maps equation emerges from
the continuum limit of the Haldane Shastry spin chains and has been shown to
arise as the continuum limit of Calogero-Moser classical spin systems. In
higher dimension $d\geq 5$, it has been shown that (HWM) is well-posed by
Krieger and Sire. This result has been improved by Krieger and Kiesenhofer to
$d = 4$ but the Strichartz estimate on which the argument is built no longer
holds for smaller dimensions. A Lax-pair structure has been revealed for this
equation by Lenzmann and G\'erard, indicating complete integrability and the
fact that rational solutions stay rational for all time. The well-posedness of
the (HWM) equation in lower dimensions remains an open problem. Here, we show
the well-posedness of (HWM) in the rational case for finite times with
separated poles, and for large and infinite times with distinct speeds of
propagation.


  The hidden metric space behind complex network topologies is a fervid topic
in current network science and the hyperbolic space is one of the most studied,
because it seems associated to the structural organization of many real complex
systems. The Popularity-Similarity-Optimization (PSO) model simulates how
random geometric graphs grow in the hyperbolic space, reproducing strong
clustering and scale-free degree distribution, however it misses to reproduce
an important feature of real complex networks, which is the community
organization. The Geometrical-Preferential-Attachment (GPA) model was recently
developed to confer to the PSO also a community structure, which is obtained by
forcing different angular regions of the hyperbolic disk to have variable level
of attractiveness. However, the number and size of the communities cannot be
explicitly controlled in the GPA, which is a clear limitation for real
applications. Here, we introduce the nonuniform PSO (nPSO) model that,
differently from GPA, forces heterogeneous angular node attractiveness by
sampling the angular coordinates from a tailored nonuniform probability
distribution, for instance a mixture of Gaussians. The nPSO differs from GPA in
other three aspects: it allows to explicitly fix the number and size of
communities; it allows to tune their mixing property through the network
temperature; it is efficient to generate networks with high clustering. After
several tests we propose the nPSO as a valid and efficient model to generate
networks with communities in the hyperbolic space, which can be adopted as a
realistic benchmark for different tasks such as community detection and link
prediction.


  We report on a measurement of the absorption length of scintillation light in
liquid argon due to dissolved nitrogen at the part-per-million (ppm) level. We
inject controlled quantities of nitrogen into a high purity volume of liquid
argon and monitor the light yield from an alpha source. The source is placed at
different distances from a cryogenic photomultiplier tube assembly. By
comparing the light yield from each position we extract the absorption cross
section of nitrogen. We find that nitrogen absorbs argon scintillation light
with strength of $(1.51\pm 0.15)\times10^{-4} \;\mathrm{cm^{-1} ppm^{-1}}$,
corresponding to an absorption cross section of $(7.14 \pm
0.74)\times10^{-21}\;\mathrm{cm^{2} molecule^{-1}}$. We obtain the relationship
between absorption length and nitrogen concentration over the 0 to 50 ppm range
and discuss the implications for the design and data analysis of future large
liquid argon time projection chamber (LArTPC) detectors. Our results indicate
that for a current-generation LArTPC, where a concentration of 2 parts per
million of nitrogen is expected, the attenuation length due to nitrogen will be
$30 \pm 3$ meters.


  Quantum field theory is assumed to be gauge invariant. It is shown that for a
Dirac field the assumption of gauge invariance impacts on the way the vacuum
state is defined. It is shown that the conventional definition of the vacuum
state must be modified to take into account the requirements of gauge
invariance.


  I present a detailed derivation of wideband optical pulses interacting with a
Raman transition in the kind of scheme currently used to generate the ultra
broadband light fields needed to create ultrashort pulses. In contrast to the
usual approach using separate field envelopes for the pump, Stokes, and
anti-Stokes spectral lines, I use a single field envelope. This requires the
inclusion of few-cycle corrections to the pulse propagation. The single-field
model makes fewer approximations and is mathematically (and hence
computationally) simpler, although it does require greater computational
resources to implement. The single-field theory reduces to the traditional
multi-field one using appropriate approximations.


  We study two classes of operator algebras associated with a unital
subsemigroup $P$ of a discrete group $G$: one related to universal structures,
and one related to co-universal structures. First we provide connections
between universal C*-algebras that arise variously from isometric
representations of $P$ that reflect the space $\mathcal{J}$ of constructible
right ideals, from associated Fell bundles, and from induced partial actions.
This includes connections of appropriate quotients with the strong covariance
relations in the sense of Sehnem. We then pass to the reduced representation
$\mathrm{C}^*_\lambda(P)$ and we consider the boundary quotient $\partial
\mathrm{C}^*_\lambda(P)$ related to the minimal boundary space. We show that
$\partial \mathrm{C}^*_\lambda(P)$ is co-universal in two different classes:
(a) with respect to the equivariant constructible isometric representations of
$P$; and (b) with respect to the equivariant C*-covers of the reduced
nonselfadjoint semigroup algebra $\mathcal{A}(P)$. If $P$ is an Ore semigroup,
or if $G$ acts topologically freely on the minimal boundary space, then
$\partial \mathrm{C}^*_\lambda(P)$ coincides with the usual C*-envelope
$\mathrm{C}^*_{\text{env}}(\mathcal{A}(P))$ in the sense of Arveson. This
covers total orders, finite type and right-angled Artin monoids, the Thompson
monoid, multiplicative semigroups of nonzero algebraic integers, and the
$ax+b$-semigroups over integral domains that are not a field. In particular, we
show that $P$ is an Ore semigroup if and only if there exists a canonical
$*$-isomorphism from $\partial \mathrm{C}^*_\lambda(P)$, or from
$\mathrm{C}^*_{\text{env}}(\mathcal{A}(P))$, onto $\mathrm{C}^*_\lambda(G)$. If
any of the above holds, then $\mathcal{A}(P)$ is shown to be hyperrigid.


  We present an analytical method of calculating the mean first-passage times
(MFPTs) for the magnetic moment of a uniaxial nanoparticle which is driven by a
rapidly rotating, circularly polarized magnetic field and interacts with a heat
bath. The method is based on the solution of the equation for the MFPT derived
from the two-dimensional backward Fokker-Planck equation in the rotating frame.
We solve these equations in the high-frequency limit and perform precise,
numerical simulations which verify the analytical findings. The results are
used for the description of the rates of escape from the metastable domains
which in turn determine the magnetic relaxation dynamics. A main finding is
that the presence of a rotating field can cause a drastic decrease of the
relaxation time and a strong magnetization of the nanoparticle system. The
resulting stationary magnetization along the direction of the easy axis is
compared with the mean magnetization following from the stationary solution of
the Fokker-Planck equation.


  Let $G$ be a finite group and $M,N$ be two normal subgroups of $G$. Let
$Aut_N^M(G)$ denote the group of all automorphisms of $G$ which fix $N$ element
wise and act trivially on $G/M$. Let $n$ be a positive integer. In this article
we have shown that if $G$ and $H$ are two $n$-isoclinic groups, then there
exists an isomorphism from $Aut_{Z_n(G)}^{\gamma_{n+1}(G)}(G)$ to
$Aut_{Z_n(H)}^{\gamma_{n+1}(H)}(H)$, which maps the group of $n^{th}$ class
preserving automorphisms of $G$ to the group of $n^{th}$ class preserving
automorphisms of $H$. Also, for a nilpotent group of class at most $(n+1)$,
with some suitable conditions on $\gamma_{n+1}(G)$, we prove that
$Aut_{Z_n(G)}^{\gamma_{n+1}(G)}(G)$ is isomorphic to the group of inner
automorphisms of a quotient group of $G$.


  We study the phenomenological implications of the recent neutrino data for
class B of two texture zeros and two vanishing cofactors for Majorana neutrinos
in the flavor basis. We find that classes $B_{1}$($B_2$) of two texture zeros
and classes $B_5$($B_6$) of two vanishing cofactors have similar predictions
for neutrino oscillation parameters for the same mass hierarchy. Similar
predictions for classes $B_3$($B_4$) of two texture zeros and classes
$B_3$($B_4$) of two vanishing cofactors are expected. However, a preference for
a shift in the quadrant of the Dirac-type CP violating phase($\delta$) in
contrast to the earlier analysis has been predicted for a relatively large
value of the reactor neutrino mixing angle($\theta_{13}$) for class B of two
texture zeros and two vanishing cofactors for an inverted mass spectrum. No
such shift in the quadrant of $\delta$ has been found for the normal mass
spectrum.


  Analysis of quantum error correcting codes is typically done using a
stochastic, Pauli channel error model for describing the noise on physical
qubits. However, it was recently found that coherent errors (systematic
rotations) on physical data qubits result in both physical and logical error
rates that differ significantly from those predicted by a Pauli model. Here we
examine the accuracy of the Pauli approximation for coherent errors on data
qubits under the repetition code. We analytically evaluate the logical error as
a function of concatenation level and code distance. We find that coherent
errors result in logical errors that are partially coherent and therefore
non-Pauli. However, the coherent part of the error is negligible after two or
more concatenation levels or at fewer than $\epsilon^{-(d-1)}$ error correction
cycles, where $\epsilon \ll 1$ is the rotation angle error per cycle for a
single physical qubit and $d$ is the code distance. These results lend support
to the validity of modeling coherent errors using a Pauli channel under some
minimum requirements for code distance and/or concatenation.


  Measurement-device-independent quantum key distribution (MDI-QKD), based on
two-photon interference, is immune to all attacks against the detection system
and allows a QKD network with untrusted relays. Since the MDI-QKD protocol was
proposed, fibre-based implementations have been rapidly developed towards
longer distance, higher key rates, and network verification. However, owing to
the effect of atmospheric turbulence, MDI-QKD over free-space channel remains
experimentally challenging. Here, by developing the robust adaptive optics
system, high precision time synchronization and frequency locking between
independent photon sources located far apart, we realised the first free-space
MDI-QKD over a 19.2-km urban atmospheric channel, which well exceeds the
effective atmospheric thickness. Our experiment takes the first step towards
satellite-based MDI-QKD. Moreover, the technology developed here opens the way
to quantum experiments in free space involving long-distance interference of
independent single photons.


  In this paper, we present an unsupervised learning approach to identify the
user points of interest (POI) by exploiting WiFi measurements from smartphone
application data. Due to the lack of GPS positioning accuracy in indoor,
sheltered, and high rise building environments, we rely on widely available
WiFi access points (AP) in contemporary urban areas to accurately identify POI
and mobility patterns, by comparing the similarity in the WiFi measurements. We
propose a system architecture to scan the surrounding WiFi AP, and perform
unsupervised learning to demonstrate that it is possible to identify three
major insights, namely the indoor POI within a building, neighbourhood
activity, and micro-mobility of the users. Our results show that it is possible
to identify the aforementioned insights, with the fusion of WiFi and GPS, which
are not possible to identify by only using GPS.


  We have redone a recent two-loop computation of the critical mass for Wilson
fermions in lattice QCD by evaluating Feynman integrals with the
coordinate-space method. We present the results for different types of infrared
regularization. We confirm both the previous numerical estimates and the power
of the coordinate-space method whenever high accuracy is needed.


  Sessions are a fundamental notion in message-passing systems. A session is an
abstract notion of communication between parties where each one owns an
endpoint. Session types are types that are assigned to the endpoints and that
are used to statically and dynamically enforce some desired properties of the
communications, such as the absence of deadlocks. Properties of concurrent
systems are usually divided in safety and liveness ones and depending on the
class it belongs to, a property is defined using different (dual) techniques.
However, there exist some properties that require to mix both techniques and
the challenges in defining them are exacerbated in proof assistants (e.g. Agda,
Coq, . . . ), that is, tools that allow users to formally characterize and
prove theorems. In particular, we mechanize the meta-theory of inference
systems in Agda. Among the interesting properties that can be studied in the
session-based context, we study fair termination which is the property of those
sessions that can always eventually reach successful termination under a
fairness assumption. Fair termination implies many desirable and well known
properties, such as lock freedom. Moreover, a lock free session does not imply
that other sessions are lock free as well. On the other hand, if we consider a
session and we assume that all the other ones are fairly terminating, we can
conclude that the one under analysis is fairly terminating as well.


  Let $\bigl\{X_k\bigr\}_{k \in \mathbb{Z}} \in \mathbb{L}^2(\mathcal{T})$ be a
stationary process with associated lag operators ${\boldsymbol{\cal C}}_h$.
Uniform asymptotic expansions of the corresponding empirical eigenvalues and
eigenfunctions are established under almost optimal conditions on the lag
operators in terms of the eigenvalues (spectral gap). In addition, the
underlying dependence assumptions are optimal, including both short and long
memory processes. This allows us to study the relative maximum deviation of the
empirical eigenvalues under very general conditions. Among other things, we
show convergence to an extreme value distribution, giving rise to the
construction of simultaneous confidence sets. We also discuss how the
asymptotic expansions transfer to the long-run covariance operator
${\boldsymbol{\cal G}}$ in a general framework.


  The bias-variance trade-off is a well-known problem in machine learning that
only gets more pronounced the less available data there is. In active learning,
where labeled data is scarce or difficult to obtain, neglecting this trade-off
can cause inefficient and non-optimal querying, leading to unnecessary data
labeling. In this paper, we focus on active learning with Gaussian Processes
(GPs). For the GP, the bias-variance trade-off is made by optimization of the
two hyperparameters: the length scale and noise-term. Considering that the
optimal mode of the joint posterior of the hyperparameters is equivalent to the
optimal bias-variance trade-off, we approximate this joint posterior and
utilize it to design two new acquisition functions. The first one is a Bayesian
variant of Query-by-Committee (B-QBC), and the second is an extension that
explicitly minimizes the predictive variance through a Query by Mixture of
Gaussian Processes (QB-MGP) formulation. Across six simulators, we empirically
show that B-QBC, on average, achieves the best marginal likelihood, whereas
QB-MGP achieves the best predictive performance. We show that incorporating the
bias-variance trade-off in the acquisition functions mitigates unnecessary and
expensive data labeling.


  In the last years there has been a growing interest for nonlinear speech
models. Several works have been published revealing the better performance of
nonlinear techniques, but little attention has been dedicated to the
implementation of the nonlinear model into real applications. This work is
focused on the study of the behaviour of a nonlinear predictive model based on
neural nets, in a speech waveform coder. Our novel scheme obtains an
improvement in SEGSNR between 1 and 2 dB for an adaptive quantization ranging
from 2 to 5 bits.


  We study the effect of external driving on the two level systems (TLSs)
assumed to be a major obstacle in increasing the coherence time of solid state
Josephson-junction qubits. We find, by use of a Bloch-Redfield approach, that
external driving has two major effects on the TLS. The first is increased
fluctuations between the two states of the TLS, the significance of this effect
compared to thermal fluctuations depend on the energy splitting of the TLS
compared to temperature. The second effect is a reduction in the intensity of
the noise spectrum at low frequencies, and at the same time an increase in
intensity around the renormalized Rabi frequency of the TLS, the driving
frequency and at beatings between these two frequencies. Finally we study the
ensemble averaged noise spectrum for a typical distribution of TLSs known to
give origin to $\propto 1/f$ noise. We find that strong driving leads to
reduced noise at low frequencies, and therefore to an increased dephasing time
$T_2^Q$ of the qubit. However this effect is exponentially suppressed when the
driving frequency is large compared to temperature, as we typically find for
Josephson qubits. We suggest that external driving at frequencies much lower
than the qubit frequency might be used in order to enhance the the qubit
coherence time.


  We present a simple, perturbative approach for calculating spectral densities
for random matrix ensembles in the thermodynamic limit we call the Perturbative
Resolvent Method (PRM). The PRM is based on constructing a linear system of
equations and calculating how the solutions to these equation change in
response to a small perturbation using the zero-temperature cavity method. We
illustrate the power of the method by providing simple analytic derivations of
the Wigner Semi-circle Law for symmetric matrices, the Marchenko-Pastur Law for
Wishart matrices, the spectral density for a product Wishart matrix composed of
two square matrices, and the Circle and elliptic laws for real random matrices.


  The world of empirical machine learning (ML) strongly relies on benchmarks in
order to determine the relative effectiveness of different algorithms and
methods. This paper proposes the notion of "a benchmark lottery" that describes
the overall fragility of the ML benchmarking process. The benchmark lottery
postulates that many factors, other than fundamental algorithmic superiority,
may lead to a method being perceived as superior. On multiple benchmark setups
that are prevalent in the ML community, we show that the relative performance
of algorithms may be altered significantly simply by choosing different
benchmark tasks, highlighting the fragility of the current paradigms and
potential fallacious interpretation derived from benchmarking ML methods. Given
that every benchmark makes a statement about what it perceives to be important,
we argue that this might lead to biased progress in the community. We discuss
the implications of the observed phenomena and provide recommendations on
mitigating them using multiple machine learning domains and communities as use
cases, including natural language processing, computer vision, information
retrieval, recommender systems, and reinforcement learning.


  Fitting the momentum distribution photoemission spectra to the Voigt profile
appears to be a robust procedure to purify the interaction effects from the
experimental resolution. In application to Bi-2212 high-Tc cuprates, the
procedure reveals the true scattering rate at low binding energies and
temperatures, and, consequently, the true value of the elastic scattering.
Reaching the minimal value ~ 16 meV, the elastic scattering does not reveal a
systematic dependence on doping level, but is rather sensitive to impurity
concentration, and can be explained by the forward scattering on out-of-plane
impurities. The inelastic scattering is found to form well-defined
quasiparticles with the quadratic and cubic energy dependence of the scattering
rate above and below Tc, respectively. The observed energy-temperature
asymmetry of the scattering rate is also discussed.


  We consider a multiscale Boolean percolation on $\mathbb R^d$ with radius
distribution $\mu$ on $[1,+\infty)$, $d\ge 2$. The model is defined by
superposing the original Boolean percolation model with radius distribution
$\mu$ with a countable number of scaled independent copies. The $n$-th copy is
a Boolean percolation with radius distribution $\mu|_{[1,\kappa]}$ rescaled by
$\kappa^{n}$. We prove that under some regularity assumption on $\mu$, the
subcritical phase of the multiscale model is sharp for $\kappa $ large enough.
Moreover, we prove that the existence of an unbounded connected component
depends only on the fractal part (and not of the balls with radius larger than
$1$).


  The search for continuous gravitational-wave signals requires the development
of techniques that can effectively explore the low-significance regions of the
candidate set. In this paper we present the methods that were developed for a
search for continuous gravitational-wave signals from the Galactic Center [1].
First, we present a data-selection method that increases the sensitivity of the
chosen data set by 20%-30% compared to the selection methods used in previous
directed searches. Second, we introduce postprocessing methods that reliably
rule out candidates that stem from random fluctuations or disturbances in the
data. In the context of [J. Aasi et al., Phys. Rev. D 88, 102002 (2013)] their
use enabled the investigation of candidates three standard deviations below the
loudest expected candidate in Gaussian noise from the entire search. Such
low-significance regions had not been explored in continuous gravitational-wave
searches before. We finally present a new procedure for deriving upper limits
on the gravitational-wave amplitude, which is several times faster with respect
to the standard injection-and-search approach commonly used.


  This paper addresses a challenging problem -- how to generate multi-view
cloth images from only a single view input. To generate realistic-looking
images with different views from the input, we propose a new image generation
model termed VariGANs that combines the strengths of the variational inference
and the Generative Adversarial Networks (GANs). Our proposed VariGANs model
generates the target image in a coarse-to-fine manner instead of a single pass
which suffers from severe artifacts. It first performs variational inference to
model global appearance of the object (e.g., shape and color) and produce a
coarse image with a different view. Conditioned on the generated low resolution
images, it then proceeds to perform adversarial learning to fill details and
generate images of consistent details with the input. Extensive experiments
conducted on two clothing datasets, MVC and DeepFashion, have demonstrated that
images of a novel view generated by our model are more plausible than those
generated by existing approaches, in terms of more consistent global appearance
as well as richer and sharper details.


  Effective modeling and numerical spectral-based propagation schemes are
proposed for addressing the challenges in time-dependent quantum simulations of
systems ranging from atoms, molecules, and nanostructures to emerging
nanoelectronic devices. While time-dependent Hamiltonian problems can be
formally solved by propagating the solutions along tiny simulation time steps,
a direct numerical treatment is often considered too computationally demanding.
In this paper, however, we propose to go beyond these limitations by
introducing high-performance numerical propagation schemes to compute the
solution of the time-ordered evolution operator. In addition to the direct
Hamiltonian diagonalizations that can be efficiently performed using the new
eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a
basis transformed propagation scheme (BTPS) which allow to reduce considerably
the simulation times needed by time intervals. It is outlined that BTPS offers
the best computational efficiency allowing new perspectives in time-dependent
simulations. Finally, these numerical schemes are applied to study the AC
response of a (5,5) carbon nanotube within a 3D real-space mesh framework.


  The C library \texttt{libkww} provides functions to compute the
Kohlrausch-Williams-Watts function, i.e.\ the Laplace-Fourier transform of the
stretched (or compressed) exponential function $\exp(-t^\beta)$ for exponents
$\beta$ between 0.1 and 1.9 with sixteen-digits accuracy. Analytic error bounds
are derived for the low and high frequency series expansions. For intermediate
frequencies the numeric integration is enormously accelerated by using the
Ooura-Mori double exponential transformation. The source code is available from
the project home page \url{http://apps.jcns.fz-juelich.de/doku/sc/kww}.


  We present a novel self-referenced method for the complete temporal
characterization (phase and amplitude) of ultrashort optical laser pulses. The
technique, called TIme-Gated Electric field Reconstruction (TIGER), measures a
second-order nonlinear signal (namely, second harmonic generation or two-photon
absorption) produced by four time-delayed replicas of the input pulse. The
delays are spatially encoded in the beam profile using a four-faced
pyramid-like optical element. The presented technique enables single shot
measurement and does not require any spectral measurements, in contrast with
well-known self-referenced characterization methods. Depending on the chosen
geometry, the recorded TIGER signal can be either interferometric (i.e.,
carrier frequency resolved) or intensimetric. This paper describes the
principle operation of the device together with a detailed theoretical
analysis. TIGER measurements of various laser pulse shapes with their
reconstructions are then presented demonstrating the relevance of this original
approach.


  Although many research vehicle platforms for autonomous driving have been
built in the past, hardware design, source code and lessons learned have not
been made available for the next generation of demonstrators. This raises the
efforts for the research community to contribute results based on real-world
evaluations as engineering knowledge of building and maintaining a research
vehicle is lost. In this paper, we deliver an analysis of our approach to
transferring an open source driving stack to a research vehicle.
  We put the hardware and software setup in context to other demonstrators and
explain the criteria that led to our chosen hardware and software design.
Specifically, we discuss the mapping of the Apollo driving stack to the system
layout of our research vehicle, fortuna, including communication with the
actuators by a controller running on a real-time hardware platform and the
integration of the sensor setup. With our collection of the lessons learned, we
encourage a faster setup of such systems by other research groups in the
future.


  Numerous empirical evidences have corroborated the importance of noise in
nonconvex optimization problems. The theory behind such empirical observations,
however, is still largely unknown. This paper studies this fundamental problem
through investigating the nonconvex rectangular matrix factorization problem,
which has infinitely many global minima due to rotation and scaling invariance.
Hence, gradient descent (GD) can converge to any optimum, depending on the
initialization. In contrast, we show that a perturbed form of GD with an
arbitrary initialization converges to a global optimum that is uniquely
determined by the injected noise. Our result implies that the noise imposes
implicit bias towards certain optima. Numerical experiments are provided to
support our theory.


  A new algorithm for calculating the stransverse mass, $M_{T2}$, in either
symmetric or asymmetric situations has been developed which exhibits good
stability, high precision and quadratic convergence for the majority of the
$M_{T2}$ parameter space, leading to up to a factor of ten increase in speed
compared to other $M_{T2}$ calculators of comparable precision. This document
describes and validates the methodology used by the algorithm, and provides
comparisons both in terms of accuracy and speed with other existing
implementations.


  Recent studies have demonstrated that noise in stochastic gradient descent
(SGD) is closely related to generalization: A larger SGD noise, if not too
large, results in better generalization. Since the covariance of the SGD noise
is proportional to $\eta^2/B$, where $\eta$ is the learning rate and $B$ is the
minibatch size of SGD, the SGD noise has so far been controlled by changing
$\eta$ and/or $B$. However, too large $\eta$ results in instability in the
training dynamics and a small $B$ prevents scalable parallel computation. It is
thus desirable to develop a method of controlling the SGD noise without
changing $\eta$ and $B$. In this paper, we propose a method that achieves this
goal using ``noise enhancement'', which is easily implemented in practice. We
expound the underlying theoretical idea and demonstrate that the noise
enhancement actually improves generalization for real datasets. It turns out
that large-batch training with the noise enhancement even shows better
generalization compared with small-batch training.


  Cyber threat intelligence (CTI) is being used to search for indicators of
attacks that might have compromised an enterprise network for a long time
without being discovered. To have a more effective analysis, CTI open standards
have incorporated descriptive relationships showing how the indicators or
observables are related to each other. However, these relationships are either
completely overlooked in information gathering or not used for threat hunting.
In this paper, we propose a system, called POIROT, which uses these
correlations to uncover the steps of a successful attack campaign. We use
kernel audits as a reliable source that covers all causal relations and
information flows among system entities and model threat hunting as an inexact
graph pattern matching problem. Our technical approach is based on a novel
similarity metric which assesses an alignment between a query graph constructed
out of CTI correlations and a provenance graph constructed out of kernel audit
log records. We evaluate POIROT on publicly released real-world incident
reports as well as reports of an adversarial engagement designed by DARPA,
including ten distinct attack campaigns against different OS platforms such as
Linux, FreeBSD, and Windows. Our evaluation results show that POIROT is capable
of searching inside graphs containing millions of nodes and pinpoint the
attacks in a few minutes, and the results serve to illustrate that CTI
correlations could be used as robust and reliable artifacts for threat hunting.


  This paper presents an overview of close parallels that exist between the
theory of positive operator-valued measures (POVMs) associated with a separable
Hilbert space and the theory of frames on that space, including its most
important generalizations. The concept of a framed POVM is introduced, and
classical frames, fusion frames, generalized frames, and other variants of
frames are all shown to to arise as framed POVMs. This observation allows
drawing on a rich existing theory of POVMs to provide new perspectives in the
study of frames.


  Automatic Defect Analysis and Qualification (ADAQ) is a collection of
automatic workflows developed for high-throughput simulations of
magneto-optical properties of point defect in semiconductors. These workflows
handle the vast number of defects by automating the processes to relax the unit
cell of the host material, construct supercells, create point defect clusters,
and execute calculations in both the electronic ground and excited states. The
main outputs are the magneto-optical properties which include zero-phonon
lines, zero-field splitting, and hyperfine coupling parameters. In addition,
the formation energies are calculated. We demonstrate the capability of ADAQ by
performing a complete characterization of the silicon vacancy in silicon
carbide in the polytype 4H (4H-SiC).


  Pathfinding in hospitals is challenging for patients, visitors, and even
employees. Many people have experienced getting lost due to lack of clear
guidance, large footprint of hospitals, and confusing array of hospital wings.
In this paper, we propose Halo; An indoor navigation application based on
voice-user interaction to help provide directions for users without assistance
of a localization system. The main challenge is accurate detection of origin
and destination search terms. A custom convolutional neural network (CNN) is
proposed to detect origin and destination search terms from transcription of a
submitted speech query. The CNN is trained based on a set of queries tailored
specifically for hospital and clinic environments. Performance of the proposed
model is studied and compared with Levenshtein distance-based word matching.


  We consider the optimal design of a scheduling policy for adaptive video
streaming in a wireless network formed by several users and helpers. A feature
of such networks is that any user is typically in the range of multiple
helpers. Hence, in order to cope with user-helper association, load balancing
and inter-cell interference, an efficient streaming policy should allow the
users to dynamically select the helper node to download from, and determine
adaptively the video quality level of the download. In order to obtain a
tractable formulation, we follow a "divide and conquer" approach: i) Assuming
that each video packet (chunk) is delivered within its playback delay ("smooth
streaming regime"), the problem is formulated as a network utility maximization
(NUM), subject to queue stability, where the network utility function is a
concave and componentwise non-decreasing function of the users' video quality
measure. ii) We solve the NUM problem by using a Lyapunov Drift Plus Penalty
approach, obtaining a scheme that naturally decomposes into two sub-policies
referred to as "congestion control" (adaptive video quality and helper station
selection) and "transmission scheduling" (dynamic allocation of the helper-user
physical layer transmission rates).Our solution is provably optimal with
respect to the proposed NUM problem, in a strong per-sample path sense. iii)
Finally, we propose a method to adaptively estimate the maximum queuing delays,
such that each user can calculate its pre-buffering and re-buffering time in
order to cope with the fluctuations of the queuing delays. Through simulations,
we evaluate the performance of the proposed algorithm under realistic
assumptions of a network with densely deployed helper nodes, and demonstrate
the per-sample path optimality of the proposed solution by considering a
non-stationary non-ergodic scenario with user mobility, VBR video coding.


  New HI observations are presented for a complete sample of 109 low luminosity
star-forming galaxies taken from the KPNO International Spectroscopic Survey
(KISS), the first CCD-based wide-field objective-prism survey for emission-line
galaxies. This sample consists of all star-forming galaxies with M_B > -18.0
and cz < 11,000 km/s from the first Halpha-selected survey list. Overall, 97
out of 109 galaxies have been detected in HI. We confirm the weak trend of
increasing gas richness with decreasing luminosity found by previous authors.
Gas richness is also shown to be weakly anti-correlated with metallicity. The
dependence of star formation rates (SFRs) and HI gas depletion timescales on
metallicity is examined. The median solar metallicity based SFR and gas
depletion timescale are 0.1639 M_sun/yr and 5 Gyrs, respectively. Corrections
for variations in metallicity decreases SFRs by about 0.5 dex and increases gas
depletion timescales by an average of about 8 Gyrs. The majority of galaxies in
this sample still have large reservoirs of HI gas, and despite their large
current star formation rates, could have formed stars in a quasi-continuous
manner for a Hubble time. Finally, we present the first HI mass function for
low luminosity star-forming galaxies and show that this subpopulation
contributes 10-15% of the overall HI density in the local universe. We conclude
that if the HI mass function of the Universe does indeed have a steeply rising
low-mass slope as suggested by previous authors, it is not due to the
population of low luminosity star-forming galaxies.


  In a recent paper "Probing gravitational wave polarizations with signals from
compact binary coalescences" (arXiv:1710.03794 [gr-qc]) the authors argue that
a single detection of gravitational wave by the LIGO-Virgo network is capable
to distinguish between pure tensor and pure vector polarizations of
gravitational waves. Here we point out a mistake in the author's analysis and
show that such differentiation is possible only in the unlikely event when
gravitational wave propagates in the direction of interferometer zero response
for the tensor or vector polarizations. Nevertheless, the LIGO-Virgo network
can distinguish between pure tensor and pure vector polarizations by collecting
statistics, as we showed in Phys. Scr. 92, 125001 (2017).


  We investigate the possible molecules composed of two heavy flavor baryons
such as "$A_QB_Q$"(Q=b, c) within the one-pion-exchange model (OPE). Our
results indicate that the long-range $\pi$ exchange force is strong enough to
form molecules such as $[\Sigma_Q\Xi_Q^{'}]^{I=1/2}_{S=1}$(Q=b, c),
$[\Sigma_Q\Lambda_Q]^{I=1}_{S=1}$(Q=b, c), $[\Sigma_b\Xi_b^{'}]^{I=3/2}_{S=1}$
and $[\Xi_b\Xi^{'}_b]^{I=0}_{S=1}$ where the S-D mixing plays an important
role. In contrast, the $\pi$ exchange does not form the spin-singlet $A_QB_Q$
bound states. If we consider the heavier scalar and vector meson exchanges as
well as the pion exchange, some loosely bound spin-singlet S-wave states appear
while results of the spin-triplet $A_QB_Q$ system does not change
significantly, which implies the pion exchange plays an dominant role in
forming the spin-triplet molecules. Moreover, we perform an extensive coupled
channel analysis of the $\Lambda_Q\Lambda_Q$ system within the OPE and
one-boson-exchange (OBE) framework and find that there exist loosely bound
states of $\Lambda_Q\Lambda_Q$(Q=b,c) with quantum numbers $I(J^P)=0(0^+)$,
$0(0^-)$ and $0(1^-)$. The binding solutions of $\Lambda_Q\Lambda_Q$ system
mainly come from the coupled-channel effect in the flavor space. Besides the
OPE force, the medium- and short-range attractive force also plays a
significant role in the formation of the loosely bound $\Lambda_c\Lambda_c$ and
$\Lambda_b\Lambda_b$ states. Once produced, they will be very stable because
such a system decays via weak interaction with a very long lifetime around
$10^{-13}\sim10^{-12}$s.


  In this paper, a superlattice VO2/SiO2 metamaterial on a lossy substrate is
designed to create a near perfect absorber with tunability across the infrared
spectrum. We selected VO2 as it presents a dielectric to metal-like phase
change slightly above room temperature. Additionally, the slightly lossy nature
of high-temperature VO2 presents comparable and small components (real and
imaginary) of the complex refractive index across portions of the visible and
infrared. Coupled with a limited conductivity substrate, VO2 has been employed
to create highly absorbing/emitting structures where the thickness of the VO2
is ultra-thin (t << lambda/4n). Nevertheless, metal-like VO2 does not possess
comparable and small components of the complex refractive index across the
entire infrared spectrum, which limits the universality of this ultra-thin VO2
absorber design. Here we employ an ultra-thin superlattice of VO2/SiO2 to
create a composite metamaterial that is readily designed for high absorbance
across the infrared spectrum.


  Recently a framework has been introduced within which a large number of
classical and modern adaptive filter algorithms can be viewed as special cases.
Variable Step-Size (VSS) normalized least mean square (VSSNLMS) and VSS Affine
Projection Algorithms (VSSAPA) are two particular examples of the adaptive
algorithms that can be covered by this generic adaptive filter. In this paper,
we introduce a new VSS Partial Rank (VSSPR) adaptive algorithm based on the
generic VSS adaptive filter and use it for channel equalization. The proposed
algorithm performs very well in attenuating noise and inter-symbol interference
(ISI) in comparison with the standard NLMS and the recently introduced AP
algorithms.


  The system of particles interacting via multibody interatomic potential of
general form is considered. Possible variants of partition of the total force
acting on a single particle into pair contributions are discussed. Two
definitions for the force acting between a pair of particles are compared. The
forces coincide only if the particles interact via pair or embedded-atom
potentials. However in literature both definitions are used in order to
determine Cauchy stress tensor. A simplest example of the linear pure shear of
perfect square lattice is analyzed. It is shown that, Hardy's definition for
the stress tensor gives different results depending on the radius of
localization function. The differences strongly depend on the way of the force
definition.


  The spin-Peierls instability in spin 1/2 XY chain coupled to dispersionless
phonons of frequency $\omega$ has been studied in the nonadiabatic limit. We
have chosen the Lang-Firsov variational wave function for the phonon subsystem
to obtain an effective spin Hamiltonian. The effective spin Hamiltonian is then
solved in the framework of mean-field approximation. We observed a dimerized
phase when g is less than a critical value and an anti-ferromagnetic phase when
it is greater than a critical value . The variation of lattice distortion,
dimerized order parameter and energy gap with spin phonon coupling parameter
has also been investigated here.


  For complete graphs and n-cubes bounds are found for the possible number of
colours in an interval edge colourings.


  We consider bilinear restriction estimates for wave-Schr\"odinger
interactions and provided a sharp condition to ensure that the product belongs
to $L^q_t L^r_x$ in the full bilinear range $\frac{2}{q} + \frac{d+1}{r} <
d+1$, $1 \leqslant q, r \leqslant 2$. Moreover, we give a counter-example which
shows that the bilinear restriction estimate can fail, even in the transverse
setting. This failure is closely related to the lack of curvature of the cone.
Finally we mention extensions of these estimates to adapted function spaces. In
particular we give a general transference type principle for $U^2$ type spaces
that roughly implies that if an estimate holds for homogeneous solutions, then
it also holds in $U^2$. This transference argument can be used to obtain
bilinear and multilinear estimates in $U^2$ from the corresponding bounds for
homogeneous solutions.


  We analyze theoretically the effect of technical fluctuations on laser
lineshape in terms of statistics of amplitude and phase noise and their
respective bandwidths. While the phase noise tends to broaden the linewidth as
the magnitude of the noise increases, the amplitude noise brings out an
additional structure with its spectral density reflecting the magnitude of the
noise. The effect of possible coupling between those two noises is also
discussed.


  On the basis of solutions of the master equation for networks with a small
number of neurons it is shown that the conditional entropy and integrated
information of neural networks depend on their average activity and
inter-cluster correlations.


  We consider the problem of detecting edges in piecewise smooth functions from
their N-degree spectral content, which is assumed to be corrupted by noise.
There are three scales involved: the "smoothness" scale of order 1/N, the noise
scale of order $\eta$ and the O(1) scale of the jump discontinuities. We use
concentration factors which are adjusted to the noise variance, $\eta$ >> 1/N,
in order to detect the underlying O(1)-edges, which are separated from the
noise scale, $\eta$ << 1.


  One can define the notion of primitive length spectrum for a simple regular
periodic graph via counting the orbits of closed reduced primitive cycles under
an action of a discrete group of automorphisms. We prove that this primitive
length spectrum satisfies an analogue of the `Multiplicity one' property. We
show that if all but finitely many primitive cycles in two simple regular
periodic graphs have equal lengths, then all the primitive cycles have equal
lengths. This is a graph-theoretic analogue of a similar theorem in the context
of geodesics on hyperbolic spaces. We also prove, in the context of actions of
finitely generated abelian groups on a graph, that if the adjacency operators
for two actions of such a group on a graph are similar, then corresponding
periodic graphs are length isospectral.


  In this paper, we present a simple strategy to identify Non-Terrestrial
artefacts \citep[NTAs;][]{Kopparapu} in or near geosynchronous Earth orbits
(GEOs). We show that even the small pieces of reflective debris in orbit around
the Earth can be identified through searches for multiple transients in old
photographic plate material exposed before the launch of first human satellite
in 1957. In order to separate between possible false point-like sources on
photographic plates from real reflections, we present calculations to quantify
the associated probabilities of alignments. We show that in an image with nine
"simultaneous transients" at least four or five point sources along a line
within a $10 \ast 10$ arcmin$^{2}$ image box are a strong indicator of NTAs,
corresponding to significance levels of $2.5$ to $3.9 \sigma$. This given
methodology can then be applied to set an upper limit to the prevalence of NTAs
with reflective surfaces in geosynchronous orbits.


  Let T_n denote the set of log canonical thresholds of pairs (X,Y), with X a
nonsingular variety of dimension n, and Y a nonempty closed subscheme of X.
Using non-standard methods, we show that every limit of a decreasing sequence
in T_n lies in T_{n-1}, proving in this setting a conjecture of Koll\'{a}r. We
also show that T_n is a closed subset in the set of real numbers; in
particular, every limit of log canonical thresholds on smooth varieties of
fixed dimension is a rational number. As a consequence of this property, we see
that in order to check Shokurov's ACC Conjecture for all T_n, it is enough to
show that 1 is not a point of accumulation from below of any T_n. In a
different direction, we interpret the ACC Conjecture as a semi-continuity
property for log canonical thresholds of formal power series.


  A terrain is an $x$-monotone polygon whose lower boundary is a single line
segment. We present an algorithm to find in a terrain a triangle of largest
area in $O(n \log n)$ time, where $n$ is the number of vertices defining the
terrain. The best previous algorithm for this problem has a running time of
$O(n^2)$.


  In this paper we construct some "pathological" volume preserving partially
hyperbolic diffeomorphisms on $\toro{3}$ such that their behaviour in small
scales in the central direction (Lyapunov exponent) is opposite to the behavior
of their linearization. These examples are isotopic to Anosov. We also get
partially hyperbolic diffeomorphisms isotopic to Anosov (consequently with
non-compact central leaves) with zero central Lyapunov exponent at almost every
point.


  I present a calculation of structure functions at leading order which
includes an unambiguous inclusion of the leading ln(1/x) terms for each power
of alpha_s, and also the correct effects due to the mass of the charm and
bottom quarks. I compare the results of fits to data to those obtained using
conventional NLO in alpha_s calculations, noting a clear preference for my
approach, especially at small x. The predictions for both the charm structure
function and F_L(x,Q^2) using the two approaches are compared, the latter being
much more discriminating.


  Gravitational wave echoes, if they exist, could encode important information
of new physics from the strong gravity regime. Current echo searches usually
assume constant interval echoes (CIEs) a priori, although unequal interval
echoes (UIEs) are also possible. Despite of its simplicity, the using of CIE
templates need to be properly justified, especially given the high sensitivity
of future gravitational wave detectors. In this paper, we assess the necessity
of UIE templates in echo searches. By reconstructing injected UIE signals with
both CIE and UIE templates, we show that the CIE template may significantly
misinterpret the echo signals if the variation of the interval is greater than
the statistical errors of the interval, which is further confirmed by a
Bayesian analysis on model stelection. We also forecast the constraints on the
echo intervals given by future GW detectors such as Advanced LIGO and Einstein
Telescope.


  We theoretically study a Josephson junction based on a semiconducting
nanowire subject to a time-dependent flux bias. We establish a general density
matrix approach for the dynamical response of the Majorana junction and
calculate the resulting flux-dependent susceptibility using both microscopic
and effective low-energy descriptions for the nanowire. We find that the
diagonal component of the susceptibility, associated with the dynamics of the
Majorana states populations, dominates over the standard Kubo contribution for
a wide range of experimentally relevant parameters. The diagonal term, thus far
unexplored in the context of Majorana physics, allows to probe accurately the
presence of Majorana bound states in the junction.


  Two new X-ray timing observations of the 44.7 ms pulsar in G12.82-0.02/HESS
J1813-178 were obtained with Chandra and XMM-Newton to determine its precise
spin-down rate. With a period derivative of dP/dt = 1.265E-13, PSR J1813-1749
is the third most energetic pulsar in the Galaxy, having spin-down luminosity
dE/dt = 5.6E37 erg/s. Lack of pulsed detection in a deep radio search from the
Green Bank Telescope, and in gamma-rays from Fermi, are reported. We reconsider
the distance to PSR J1813-1749/G12.82-0.02 in view of its large X-ray measured
column density, N(H) = 10.E22 cm^-2, which exceeds the visual extinction A(V) =
9.1 to a young stellar cluster at d = 4.8 kpc that has been associated with it.
Although the distance may well be larger, existing data do not constrain it
further. The small radiative output of PSR J1813-1749/G12.82-0.02 in all bands
would not exceed its spin-down power at any distance in the Galactic disk.


  Encouraged by a recent observation of the B_c^+ -> B_s^0 + pi^+ decay by the
LHCb collaboration we present the meson dominance predictions for other weak
decays of the B_c^+ into B_s^0 or B^0 in the form of branching ratios to the
observed decay.


  We demonstrate lasing in arrays of microring resonators with underlying
para-Fermi symmetry. The properties of the algebra allow the analytic
prediction of propagation constants and normal modes of an array of passive
resonators that show the optical analogue of a zero-energy mode that is its own
chiral pair. The rest of the normal modes in the linear model form chiral pairs
that are evenly distributed around the pseudo zero-energy mode. We use this
information to construct a class-B laser model where even and odd sites are
driven with different strength in a pattern following para-Fermi algebra
chirality to demonstrate lasing with enhancement or suppression of the
zero-energy mode. Zero-energy mode lasing is stable to initial conditions for a
large set of driving ratios. Lasing with zero-energy mode suppression is
unstable and more susceptible to initial field configurations.


  Let $2.O_{m+1}$ denote the doubled Odd graph with vertex set $X$ on a set of
cardinality $2m+1$, where $m\geq 1$. Fix a vertex $x_0\in X$. Let
$\mathcal{A}:=\mathcal{A}(x_0)$ denote the centralizer algebra of the
stabilizer of $x_0$ in the automorphism group of $2.O_{m+1}$, and $T:=T(x_0)$
the Terwilliger algebra of $2.O_{m+1}$. In this paper, we first give a basis of
$\mathcal{A}$ by considering the action of the stabilizer of $x_0$ on $X\times
X$ and determine the dimension of $\mathcal{A}$. Furthermore, we give three
subalgebras of $\mathcal{A}$ such that their direct sum is $\mathcal{A}$ as
vector space. Next, for $m\geq 3$ we find all isomorphism classes of
irreducible $T$-modules to display the decomposition of $T$ in a
block-diagonalization form. Finally, we show that the two algebras
$\mathcal{A}$ and $T$ coincide. This result tells us that the graph $2.O_{m+1}$
may be the first example of bipartite but not $Q$-polynomial
distance-transitive graph for which the corresponding centralizer algebra and
Terwilliger algebra are equal.


  Establishing and approaching the fundamental limit of orbital angular
momentum (OAM) multiplexing are necessary and increasingly urgent for current
multiple-input multiple-output research. In this work, we elaborate the
fundamental limit in terms of independent scattering channels (or degrees of
freedom of scattered fields) through angular-spectral analysis, in conjunction
with a rigorous Green function method. The scattering channel limit is
universal for arbitrary spatial mode multiplexing, which is launched by a
planar electromagnetic device, such as antenna, metasurface, etc, with a
predefined physical size. As a proof of concept, we demonstrate both
theoretically and experimentally the limit by a metasurface hologram that
transforms orthogonal OAM modes to plane-wave modes scattered at critically
separated angular-spectral regions. Particularly, a minimax optimization
algorithm is applied to suppress angular spectrum aliasing, achieving good
performances in both full-wave simulation and experimental measurement at
microwave frequencies. This work offers a theoretical upper bound and
corresponding approach route for engineering designs of OAM multiplexing.


  We find rotating black hole solutions in the Randall-Sundrum II (RSII) model,
by numerically solving a three-dimensional PDE problem using pseudospectral
collocation methods. We compute the area and equatorial inner-most stable
orbits of these solutions. For large black holes compared with the AdS length
scale, $\ell$, the black hole exhibits four-dimensional behaviour, approaching
the Kerr metric on the brane, whilst for small black holes, the solution tends
instead towards a five-dimensional Myers-Perry black hole with a single
non-zero rotation parameter aligned with the brane. This departure from exact
four-dimensional gravity may lead to different phenomenological predictions for
rotating black holes in the RSII model to those in standard four-dimensional
general relativity. This letter provides a stepping stone for studying such
modifications.


  The physical nature of compressible turbulence is of fundamental importance
in a variety of astrophysical settings. We present the first direct evidence
that mean kinetic energy cascades conservatively beyond a transitional
"conversion" scale-range despite not being an invariant of the compressible
flow dynamics. We use high-resolution three-dimensional simulations of
compressible hydrodynamic turbulence on $512^3$ and $1024^3$ grids. We probe
regimes of forced steady-state isothermal flows and of unforced decaying ideal
gas flows. The key quantity we measure is pressure dilatation cospectrum,
$E^{PD}(k)$, where we provide the first numerical evidence that it decays at a
rate faster than $k^{-1}$ as a function of wavenumber. This is sufficient to
imply that mean pressure dilatation acts primarily at large-scales and that
kinetic and internal energy budgets statistically decouple beyond a
transitional scale-range. Our results suggest that an extension of Kolmogorov's
inertial-range theory to compressible turbulence is possible.


  The Perona-Malik model has been very successful at restoring images from
noisy input. In this paper, we reinterpret the Perona-Malik model in the
language of Gaussian scale mixtures and derive some extensions of the model.
Specifically, we show that the expectation-maximization (EM) algorithm applied
to Gaussian scale mixtures leads to the lagged-diffusivity algorithm for
computing stationary points of the Perona-Malik diffusion equations. Moreover,
we show how mean field approximations to these Gaussian scale mixtures lead to
a modification of the lagged-diffusivity algorithm that better captures the
uncertainties in the restoration. Since this modification can be hard to
compute in practice we propose relaxations to the mean field objective to make
the algorithm computationally feasible. Our numerical experiments show that
this modified lagged-diffusivity algorithm often performs better at restoring
textured areas and fuzzy edges than the unmodified algorithm. As a second
application of the Gaussian scale mixture framework, we show how an efficient
sampling procedure can be obtained for the probabilistic model, making the
computation of the conditional mean and other expectations algorithmically
feasible. Again, the resulting algorithm has a strong resemblance to the
lagged-diffusivity algorithm. Finally, we show that a probabilistic version of
the Mumford-Shah segementation model can be obtained in the same framework with
a discrete edge-prior.


  Exploiting photonic high-dimensional entanglement allows one to expand the
bandwidth of quantum communication and information processing protocols through
increased photon information capacity. However, the characterization of
entanglement in higher dimensions is experimentally challenging because the
number of measurements required scales unfavourably with dimension. While
bounds can be used to certify high-dimensional entanglement, they do not
quantify the degree to which quantum states are entangled. Here, we propose a
quantitative measure that is both an entanglement measure and a dimension
witness, which we coin the P-concurrence. We derive this measure by requiring
entanglement to extend to qubit subspaces that constitute the high-dimensional
state. The computation of the P-concurrence is not contingent on reconstructing
the full density matrix, and requires less measurements compared to standard
quantum state tomography by orders of magnitude. This allows for faster and
more efficient characterization of high-dimensional quantum states.


  Forensic application of automatically matching skull with face images is an
important research area linking biometrics with practical applications in
forensics. It is an opportunity for biometrics and face recognition researchers
to help the law enforcement and forensic experts in giving an identity to
unidentified human skulls. It is an extremely challenging problem which is
further exacerbated due to lack of any publicly available database related to
this problem. This is the first research in this direction with a two-fold
contribution: (i) introducing the first of its kind skull-face image pair
database, IdentifyMe, and (ii) presenting a preliminary approach using the
proposed semi-supervised formulation of transform learning. The experimental
results and comparison with existing algorithms showcase the challenging nature
of the problem. We assert that the availability of the database will inspire
researchers to build sophisticated skull-to-face matching algorithms.


  We show that an invariant an universal length scale can be consistently
introduced in a generally covariant theory through the gravitational sector
using the Palatini approach. The resulting theory is able to capture different
aspects of quantum gravity phenomenology in a single framework. In particular,
it is found that in this theory field excitations propagating with different
energy-densities perceive different background metrics, which is a fundamental
characteristic of the DSR and Rainbow Gravity approaches. We illustrate these
properties with a particular gravitational model and explicitly show how the
{\it soccer ball problem} is avoided in this framework. The isotropic and
anisotropic cosmologies of this model also avoid the big bang singularity by
means of a big bounce.


  Feshbach's projector technique is employed to quantize the electromagnetic
field in optical resonators with an arbitray number of escape channels. We find
spectrally overlapping resonator modes coupled due to the damping and noise
inflicted by the external radiation field. For wave chaotic resonators the mode
dynamics is determined by a non--Hermitean random matrix. Upon including an
amplifying medium, our dynamics of open-resonator modes may serve as a starting
point for a quantum theory of random lasing.


  This paper describes our attempt to understand the recent success of Na Wang
in constructing the 3-Schur polynomials, associated with the plane partitions.
We provide a rather detailed review and try to figure out the new insights,
which allowed to overcome the problems of the previous efforts. In result we
provide a very simple definition of time-variables ${\bf P}_{i\geqslant j}$ and
the cut-and-join operator $\hat W_2$, which generates the set of $3$-Schur
functions. Some coefficients in $\hat W_2$ remain undefined and require more
effort to be fixed.


  The groupoids description of Schwinger's picture of quantum mechanics is
continued by discussing the closely related notions of composition of systems,
subsystems, and their independence. Physical subsystems have a neat algebraic
description as subgroupoids of the Schwinger's groupoid of the system. The
groupoids picture offers two natural notions of composition of systems: Direct
and free products of groupoids, that will be analyzed in depth as well as their
universal character. Finally, the notion of independence of subsystems will be
reviewed, finding that the usual notion of independence, as well as the notion
of free independence, find a natural realm in the groupoids formalism. The
ideas described in this paper will be illustrated by using the EPRB experiment.
It will be observed that, in addition to the notion of the non-separability
provided by the entangled state of the system, there is an intrinsic
`non-separability' associated to the impossibility of identifying the entangled
particles as subsystems of the total system.


  Neural network based approximate computing is a universal architecture
promising to gain tremendous energy-efficiency for many error resilient
applications. To guarantee the approximation quality, existing works deploy two
neural networks (NNs), e.g., an approximator and a predictor. The approximator
provides the approximate results, while the predictor predicts whether the
input data is safe to approximate with the given quality requirement. However,
it is non-trivial and time-consuming to make these two neural network
coordinate---they have different optimization objectives---by training them
separately. This paper proposes a novel neural network structure---AXNet---to
fuse two NNs to a holistic end-to-end trainable NN. Leveraging the philosophy
of multi-task learning, AXNet can tremendously improve the invocation
(proportion of safe-to-approximate samples) and reduce the approximation error.
The training effort also decrease significantly. Experiment results show 50.7%
more invocation and substantial cuts of training time when compared to existing
neural network based approximate computing framework.


  A method for moving least squares interpolation and differentiation is
presented in the framework of orthogonal polynomials on discrete points. This
yields a robust and efficient method which can avoid singularities and
breakdowns in the moving least squares method caused by particular
configurations of nodes in the system. The method is tested by applying it to
the estimation of first and second derivatives of test functions on random
point distributions in two and three dimensions and by examining in detail the
evaluation of second derivatives on one selected configuration. The accuracy
and convergence of the method are examined with respect to length scale (point
separation) and the number of points used. The method is found to be robust,
accurate and convergent.


  We study the variation of the electronic properties at the surface of a high
temperature superconductor as a function of vacuum conditions in angle resolved
photoemission spectroscopy (ARPES) experiments. Normally, under less than ideal
vacuum conditions the carrier concentration of Bi2Sr2CaCu2O{8+x} (Bi2212)
increases with time due to the absorption of oxygen from CO2 and CO molecules
that are prime contaminants present in ultra high vacuum (UHV) systems. We find
that in a high quality vacuum environment at low temperatures, the surface of
Bi2212 is quite stable (the carrier concentration remains constant), however at
elevated temperatures the carrier concentration decreases due to the loss of
oxygen atoms from the Bi-O layer. These two effects can be used to control the
carrier concentration in-situ. Our finding opens the possibility of studying
the electronic properties of the cuprates as a function of doping across the
phase diagram on the same piece of sample (i.e. with the same impurities and
defects). We envision that this method could be utilized in other surface
sensitive techniques such as scanning tunneling microscopy/spectroscopy.


  This paper aims at giving a novel approach to investigate the behavior of the
renormalization group flow for tensorial group field theories to all orders of
the perturbation theory. From an appropriate choice of the kinetic kernel, we
build an infinite family of just-renormalizable models, for tensor fields with
arbitrary rank $d$. Investigating the large $ d$ limit, we show that the
self-energy melonic amplitude is decomposed as a product of loop-vertex
functions, depending only on dimensionless mass. The corresponding melonic
amplitudes may be mapped as trees in the so-called Hubbard-Stratonivich
representation, and we show that only trees with edges of different colors
survive in the large $d$-limit. These two key features allow us to resum the
perturbative expansion for self-energy, providing an explicit expression for
arbitrary external momenta in terms of Lambert function. Finally, inserting
this resumed solution into the Callan-Symanzik equations, and taking into
account the strong relation between two and four-point functions arising from
melonic Ward-Takahashi identities, we then deduce an explicit expression for
relevant and marginal $\beta$-functions, valid to all orders of the
perturbative expansion. By investigating the solutions of the resulting flow,
we conclude about the non-existence of any fixed point in the investigated
region of the full phase space.


  We investigate submicron ferromagnetic PdNi thin-film strips intended as
contact electrodes for carbon nanotube-based spintronic devices. The magnetic
anisotropy and micromagnetic structure are measured as function of temperature
and aspect ratio. Contrary to the expectation from shape anisotropy, magnetic
hysteresis measurements of Pd0.3Ni0.7 on arrays containing strips of various
width point towards a magnetically easy axis in the sample plane, but
transversal to the strip direction. Anisotropic magnetoresistance measured on
individual Pd0.3Ni0.7 contact strips and magnetic force microscopy images
substantiate that conclusion.


  The curse of dimensionality is commonly encountered in numerical partial
differential equations (PDE), especially when uncertainties have to be modeled
into the equations as random coefficients. However, very often the variability
of physical quantities derived from a PDE can be captured by a few features on
the space of the coefficient fields. Based on such an observation, we propose
using a neural-network (NN) based method to parameterize the physical quantity
of interest as a function of input coefficients. The representability of such
quantity using a neural-network can be justified by viewing the neural-network
as performing time evolution to find the solutions to the PDE. We further
demonstrate the simplicity and accuracy of the approach through notable
examples of PDEs in engineering and physics.


  The goal of this paper is to share our experience in designing and organizing
educational competitions with anonymous and (near) real-time leaderboards in
both academic and industrial settings. While such competitions serve as a great
educational tool and provide participants with hands-on experience, they
require significant planning, technical setup, and administration from
organizers. In this paper, we first outline several important areas including
team registration, data access, submission systems, rules and conditions that
organizers should consider when planning such events. We then present a
high-level system design that can support (near) real-time evaluation of
submissions to power anonymous leaderboards and provide immediate feedback for
participants. Finally, we share our experience applying this abstract system in
academic and industrial settings. We hope the set of guidelines and the
high-level system design proposed here help others in their organization of
similar educational events.


  A typical linear projection of the Grassmannian in its Plucker embedding is
injective, unless its image is a projective space. A notable exception are
self-adjoint linear projections, which have even degree. We consider linear
projections of Gr_3(C^6) with low-dimensional centers of projection. When the
center has dimension less than five, we show that the projection has degree 1.
When the center has dimension five and the projection has degree greater than
1, we show that it is self-adjoint.


  This paper presents the different models submitted by the LT@Helsinki team
for the SemEval 2020 Shared Task 12. Our team participated in sub-tasks A and
C; titled offensive language identification and offense target identification,
respectively. In both cases we used the so-called Bidirectional Encoder
Representation from Transformer (BERT), a model pre-trained by Google and
fine-tuned by us on the OLID and SOLID datasets. The results show that
offensive tweet classification is one of several language-based tasks where
BERT can achieve state-of-the-art results.


  Question Generation (QG) is fundamentally a simple syntactic transformation;
however, many aspects of semantics influence what questions are good to form.
We implement this observation by developing SynQG, a set of transparent
syntactic rules leveraging universal dependencies, shallow semantic parsing,
lexical resources, and custom rules which transform declarative sentences into
question-answer pairs. We utilize PropBank argument descriptions and VerbNet
state predicates to incorporate shallow semantic content, which helps generate
questions of a descriptive nature and produce inferential and semantically
richer questions than existing systems. In order to improve syntactic fluency
and eliminate grammatically incorrect questions, we employ back-translation
over the output of these syntactic rules. A set of crowd-sourced evaluations
shows that our system can generate a larger number of highly grammatical and
relevant questions than previous QG systems and that back-translation
drastically improves grammaticality at a slight cost of generating irrelevant
questions.


  We assess proposals for entangling two distant atoms by measurement of
emitted photons, analyzing how their performance depends on the photon
detection efficiency. We consider schemes based on measurement of one or two
photons and compare them in terms of the probability to obtain the detection
event and of the conditional fidelity with which the desired entangled state is
created. Based on an unravelling of the master equation, we quantify the
parameter regimes in which one or the other scheme is more efficient, including
the possible combination of the one-photon scheme with state purification. In
general, protocols based on one-photon detection are more efficient in set-ups
characterized by low photon detection efficiency, while at larger values
two-photon protocols are preferable. We give numerical examples based on
current experiments.


  Statistical matching is a technique for integrating two or more data sets
when information available for matching records for individual participants
across data sets is incomplete. Statistical matching can be viewed as a missing
data problem where a researcher wants to perform a joint analysis of variables
that are never jointly observed. A conditional independence assumption is often
used to create imputed data for statistical matching.
  We consider an alternative approach to statistical matching without using the
conditional independence assumption. We apply parametric fractional imputation
of Kim (2011) to create imputed data using an instrumental variable assumption
to identify the joint distribution. We also present variance estimators
appropriate for the imputation procedure. We explain how the method applies
directly to the analysis of data from split questionnaire designs and
measurement error models.


  We establish our recently proposed holographic entanglement negativity
conjecture for mixed states of adjacent subsystems in conformal field theories
with concrete higher dimensional examples. In this context we compute the
holographic entanglement negativity for mixed states of adjacent subsystems in
$d$-dimensional conformal field theories dual to bulk $AdS_{d+1}$ vacuum and
$AdS_{d+1}$-Schwarzschild black holes. These representative examples provide
strong indication for the universality of our conjecture which affirms
significant implications for diverse applications.


  We report detailed inelastic neutron scattering measurements on single
crystals of the frustrated two-leg ladder BiCu2PO6, whose ground state is
described as a spin liquid phase with no long-range order down to 6 K. Two
branches of steeply dispersing long-lived spin excitations are observed with
excitation gaps of \Delta_1 = 1.90(9) meV and \Delta_2 = 3.95(8) meV.
Significant frustrating next-nearest neighbour interactions along the ladder
leg drive the minimum of each excitation branch to incommensurate wavevectors
\zeta_1 = 0.574\pi and \zeta_2 = 0.553\pi for the lower and upper energy
branches respectively. The temperature dependence of the excitation spectrum
near the gap energy is consistent with thermal activation into singly and
doubly degenerate excited states. The observed magnetic excitation spectrum as
well as earlier thermodynamic data could be consistently explained by the
presence of strong anisotropic interactions in the ground state Hamiltonian.


  The work is devoted to the investigation of the surface plasmon polaritons in
the metal - dielectric heterostructures containing materials with
magnetoelectric properties. The analysis of various possible configurations
shows that the magnetoelectric effect influences the plasmonic surface wave
polarization, localization and dispersion. The essential case of chromium (III)
oxide as a magnetoelectric dielectric is described in detail, revealing the
switching between different regimes of magnetoelectric impact on
plasmon-polaritons. Plasmonic heterostructures with magnetoelectric
constituents can be used as a polarization- and dispersion-sensitive instrument
to reveal the magnetoelectric coupling and besides might act as an optical tool
for control of the surface plasmon-polariton dispersion and dynamics via
external electric and magnetic fields. Apart from that, the described effects
can be applied to the manipulation of the far-field optical response of
plasmonic structures. Composite magnetoelectric materials like
$\mathrm{BaTiO_3/BiFeO_3}$ that exhibit giant magnetoelectric effect are very
promising for these purposes.


  Two main mechanisms dictate the tunneling process in a double quantum dot:
overlap of excited wave functions, effectively described as a tunneling rate,
and phonon-assisted tunneling. In this paper, we study different regimes of
tunneling that arise from the competition between these two mechanisms in a
double quantum dot molecule immersed in a unimodal optical cavity. We show how
such regimes affect the mean number of excitations in each quantum dot and in
the cavity, the spectroscopic resolution and emission peaks of the
photoluminescence spectrum, and the second-order coherence function which is an
indicator of the quantumness of emitted light from the cavity.


  Manner of articulation detection using deep neural networks require a priori
knowledge of the attribute discriminative features or the decent phoneme
alignments. However generating an appropriate phoneme alignment is complex and
its performance depends on the choice of optimal number of senones, Gaussians,
etc. In the first part of our work, we exploit the manner of articulation
detection using connectionist temporal classification (CTC) which doesn't need
any phoneme alignment. Later we modify the state-of-the-art character based
posteriors generated by CTC using the manner of articulation CTC detector. Beam
search decoding is performed on the modified posteriors and it's impact on open
source datasets such as AN4 and LibriSpeech is observed.


  Employing a new approach toward thermodynamic phase space, we investigate the
phase transition, critical behavior and microscopic structure of higher
dimensional black holes in an Anti-de Sitter (AdS) background and in the
presence of Power-Maxwell field. In contrast to the usual extended $P-V$ phase
space where the cosmological constant (pressure) is treated as a thermodynamic
variable, we fix the cosmological constant and treat the charge of the black
hole (or more precisely $Q^s$) as a thermodynamic variable. Based on this new
standpoint, we develop the resemblance between higher dimensional nonlinear
black hole and Van der Waals liquid-gas system. We write down the equation of
state as $% Q^s=Q^s(T,\psi)$, where $\psi$ is the conjugate of $Q^s$, and
construct a Smarr relation based on this new phase space as $M=M(S,P,Q^s)$,
while $% s=2p/(2p-1)$ and $p$ is the power parameter of the Power-Maxwell
Lagrangian. We obtain the Gibbs free energy of the system and find a
swallowtail behaviour in Gibbs diagrams, which is a characteristic of
first-order phase transition and express the analogy between our system and van
der Waals fluid-gas system. Moreover, we calculate the critical exponents and
show that they are independent of the model parameters and are the same as
those of Van der Waals system which is predicted by the mean field theory.
Finally , we successfully explain the microscopic behavior of the black hole by
using thermodynamic geometry. We observe a gap in the scalar curvature $R$
occurs between small and large black hole. The maximum amount of the gap
increases as the number of dimensions increases. We finally find that character
of the interaction among the internal constituents of the black hole
thermodynamic system is intrinsically a strong repulsive interaction.


  We present a simple algorithm for identifying and correcting real-valued
noisy labels from a mixture of clean and corrupted sample points using Gaussian
process regression. A heteroscedastic noise model is employed, in which
additive Gaussian noise terms with independent variances are associated with
each and all of the observed labels. Optimizing the noise model using maximum
likelihood estimation leads to the containment of the GPR model's predictive
error by the posterior standard deviation in leave-one-out cross-validation. A
multiplicative update scheme is proposed for solving the maximum likelihood
estimation problem under non-negative constraints. While we provide proof of
convergence for certain special cases, the multiplicative scheme has
empirically demonstrated monotonic convergence behavior in virtually all our
numerical experiments. We show that the presented method can pinpoint corrupted
sample points and lead to better regression models when trained on synthetic
and real-world scientific data sets.


  A butterfly-based direct combined-field integral equation (CFIE) solver for
analyzing scattering from electrically large, perfect electrically conducting
objects is presented. The proposed solver leverages the butterfly scheme to
compress blocks of the hierarchical LU-factorized discretized CFIE operator and
uses randomized butterfly reconstruction schemes to expedite the factorization.
The memory requirements and computational cost of the direct butterfly-CFIE
solver scale as $O(N\mathrm{log}^2N)$ and $O(N^{1.5}\mathrm{log}N)$,
respectively. These scaling estimates permit significant memory and CPU savings
when compared to those realized by low-rank (LR) decomposition-based solvers.
The efficacy and accuracy of the proposed solver are demonstrated through its
application to the analysis of scattering from canonical and realistic objects
involving up to 14 million unknowns.


  Studying the kinematics and mass modelling of galaxies from HI 21 cm data
provides valuable insights into the properties of both the baryonic components
and the dark matter halo in nearby galaxies. Despite many observational
studies, mass modelling of galaxies remains challenging due to different
limitations. For example, most of the previous studies involving mass modelling
are based on rotation curves derived from two-dimensional velocity fields from
HI or H$\alpha$ spectroscopic observation which are often affected by beam
smearing and projection effect. However, kinematic modelling done by fitting
the "Tilted ring model" to three-dimensional data cube is not affected by these
issues. In this study, we present and compare 3D kinematic modelling of a pilot
sample of eleven galaxies from the GMRT archive atomic gas survey (GARCIA)
using two different publicly available pipelines. We model the observed HI
rotation curve using 3.6 $\mu$m infrared data and SDSS r-band data for stellar
contribution, HI surface density profile for gas, and Navarro-Frenk-White (NFW)
profile for dark matter halo; and employ the Markov Chain Monte Carlo (MCMC)
optimization method for parameter estimation. Further, to validate our
analysis, we revisit important scaling relations, e.g., the
M$_{gas}$-M$_{star}$ relation, M$_{star}$-M$_{halo}$ relation,
M$_{gas}$-M$_{halo}$ relation and Baryonic Tully-Fisher relation (BTFR). The
scaling relations from our analysis are broadly consistent with that reported
in the literature. A larger sample of galaxies from GARCIA in the near future
will allow studying these scaling relations in greater details.


  It is shown that a germ of a holomorphic mapping sending a real-analytic
generic submanifold of finite type into another is determined by its projection
on the Segre variety of the target manifold. A necessary and sufficient
condition is given for a germ of a mapping into the Segre variety of the target
manifold to be the projection of a holomorphic mapping sending the source
manifold into the target. An application to the biholomorphic equivalence
problem is also given.


  We consider a resonantly perturbed system of coupled nonlinear oscillators
with small dissipation and outer periodic perturbation. We show that for the
large time $t \sim \epsilon^{-2}$ one component of the system is described in
the main by the inhomogeneous Mathieu equation while the other component
represents pulsation of large amplitude. A Hamiltonian system is obtained which
describes the behaviour of the envelope in the main. The analytic results agree
to numerical simulations.


  The so-called phaseless quantum Monte-Carlo method currently offers one of
the best performing theoretical framework to investigate interacting Fermi
systems. It allows to extract an approximate ground-state wavefunction by
averaging independent-particle states undergoing a Brownian motion in
imaginary-time. Here, we extend the approach to a random walk in the space of
Hartree-Fock-Bogoliubov (HFB) vacua that are better suited for superconducting
or superfluid systems. Well-controlled statistical errors are ensured by
constraining stochastic paths with the help of a trial wavefunction, also
guiding the dynamics and in the form of a linear combination of HFB ans\"atze.
Estimates for the observables are reconstructed through an extension of Wick's
theorem to matrix elements between HFB product states. The usual combinatory
complexity associated to the application of this theorem for four- and more-
body operators is bypassed with a compact expression in terms of Pfaffians. The
limiting case of a stochastic motion within Slater determinants but guided with
HFB trial wavefunctions is also considered. Finally, exploratory results for
the spin polarized Hubbard model in the attractive regime are presented.


  Evacuation assistants and their guiding strategies play an important role in
the multi-exits pedestrian evacuation. To investigate the effect of guiding
strategies on evacuation efficiency, we propose a force-driven cellular
automaton model with adjustable guiding attractions imposed by the evacuation
assistants located in the exits. In this model, each of the evacuation
assistants tries to attract the pedestrians in the evacuation space towards its
own exit by sending a quantifiable guiding signal, which may be adjusted
according to the values of pedestrian density near the exit. The effects of
guiding strategies pursuing balanced pedestrian densities are studied. It is
observed that the unbalanced pedestrian distribution is mainly yielded by a
snowballing effect generated from the mutual attractions among the pedestrians,
and can be suppressed by controlling the pedestrian densities around the exits.
We also reveal an interesting fact that given a moderate target density value,
the density control for the partial regions (near the exits) could yield a
global effect for balancing the pedestrians in the rest of the regions and
hence improve the evacuation efficiency. Our findings may contribute to give
new insight into designing effective guiding strategies in the realistic
evacuation process.


  I introduce a concave function of allocations and prices -- the economy's
potential -- which measures the difference between utilitarian social welfare
and its dual. I show that Walrasian equilibria correspond to roots of the
potential: allocations maximize weighted utility and prices minimize weighted
indirect utility. Walrasian prices are "utility clearing" in the sense that the
utilities consumers expect at Walrasian prices are just feasible. I discuss the
implications of this simple duality for equilibrium existence, the welfare
theorems, and the interpretation of Walrasian prices.


  Ancient history relies on the study of ancient characters. However,
real-world scanned oracle characters are difficult to collect and annotate,
posing a major obstacle for oracle character recognition (OrCR). Besides,
serious abrasion and inter-class similarity also make OrCR more challenging. In
this paper, we propose a novel unsupervised domain adaptation method for OrCR,
which enables to transfer knowledge from labeled handprinted oracle characters
to unlabeled scanned data. We leverage pseudo-labeling to incorporate the
semantic information into adaptation and constrain augmentation consistency to
make the predictions of scanned samples consistent under different
perturbations, leading to the model robustness to abrasion, stain and
distortion. Simultaneously, an unsupervised transition loss is proposed to
learn more discriminative features on the scanned domain by optimizing both
between-class and within-class transition probability. Extensive experiments
show that our approach achieves state-of-the-art result on Oracle-241 dataset
and substantially outperforms the recently proposed structure-texture
separation network by 15.1%.


  We report on re-calculation of the next-to-leading order DGLAP evolution
kernels performed in a scheme suited for Monte Carlo simulations of parton
cascades (parton showers).


  In this article, we study the cell-structure of simple arrangements of
pairwise intersecting pseudocircles. The focus will be on two problems from
Gr\"unbaum's monograph from the 1970's.
  First, we discuss the maximum number of digons or touching points. Gr\"unbaum
conjectured that there are at most $2n-2$ digon cells or equivalently at most
$2n-2$ touchings. Agarwal et al. (2004) verified the conjecture for cylindrical
arrangements. We show that the conjecture holds for any arrangement which
contains three pseudocircles that pairwise form a touching. The proof makes use
of the result for cylindrical arrangements. Moreover, we construct
non-cylindrical arrangements which attain the maximum of $2n-2$ touchings and
have no triple of pairwise touching pseudocircles.
  Second, we discuss the minimum number of triangular cells (triangles) in
arrangements without digons and touchings. Felsner and Scheucher (2017) showed
that there exist arrangements with only $\lceil \frac{16}{11}n \rceil$
triangles, which disproved a conjecture of Gr\"unbaum. Here we provide a
construction with only $\lceil \frac{4}{3}n \rceil$ triangles. A corresponding
lower bound was obtained by Snoeyink and Hershberger (1991).


  A central object in the computational studies of rare events is the committor
function. Though costly to compute, the committor function encodes complete
mechanistic information of the processes involving rare events, including
reaction rates and transition-state ensembles. Under the framework of
transition path theory (TPT), recent work [1] proposes an algorithm where a
feedback loop couples a neural network that models the committor function with
importance sampling, mainly umbrella sampling, which collects data needed for
adaptive training. In this work, we show additional modifications are needed to
improve the accuracy of the algorithm. The first modification adds elements of
supervised learning, which allows the neural network to improve its prediction
by fitting to sample-mean estimates of committor values obtained from short
molecular dynamics trajectories. The second modification replaces the
committor-based umbrella sampling with the finite-temperature string (FTS)
method, which enables homogeneous sampling in regions where transition pathways
are located. We test our modifications on low-dimensional systems with
non-convex potential energy where reference solutions can be found via
analytical or the finite element methods, and show how combining supervised
learning and the FTS method yields accurate computation of committor functions
and reaction rates. We also provide an error analysis for algorithms that use
the FTS method, using which reaction rates can be accurately estimated during
training with a small number of samples. The methods are then applied to a
molecular system in which no reference solution is known, where accurate
computations of committor functions and reaction rates can still be obtained.


  It was shown that two distant particles can be entangled by sending a third
particle never entangled with the other two [T. S. Cubitt et al., Phys. Rev.
Lett. 91, 037902 (2003)]. In this paper, we investigate a class of three-qubit
separable states to distribute entanglement by the same way, and calculate the
maximal amount of entanglement which two particles of separable states in the
class can have after applying the way.


  We investigate how elimination of variables can affect the asymptotic
dynamics and phenotype control of Boolean networks. In particular, we look at
the impact on minimal trap spaces, and identify a structural condition that
guarantees their preservation. We examine the possible effects of variable
elimination under three of the most popular approaches to control
(attractor-based control, value propagation and control of minimal trap
spaces), and under different update schemes (synchronous, asynchronous,
generalized asynchronous). We provide some insights on the application of
reduction, and an ample inventory of examples and counterexamples.


  Text-driven diffusion-based video editing presents a unique challenge not
encountered in image editing literature: establishing real-world motion. Unlike
existing video editing approaches, here we focus on score distillation sampling
to circumvent the standard reverse diffusion process and initiate optimization
from videos that already exhibit natural motion. Our analysis reveals that
while video score distillation can effectively introduce new content indicated
by target text, it can also cause significant structure and motion deviation.
To counteract this, we propose to match space-time self-similarities of the
original video and the edited video during the score distillation. Thanks to
the use of score distillation, our approach is model-agnostic, which can be
applied for both cascaded and non-cascaded video diffusion frameworks. Through
extensive comparisons with leading methods, our approach demonstrates its
superiority in altering appearances while accurately preserving the original
structure and motion.


  We study the construction of quasimorphisms on groups acting on trees
introduced by Monod and Shalom, that we call median quasimorphisms, and in
particular we fully characterise actions on trees that give rise to non-trivial
median quasimorphisms. Roughly speaking, either the action is highly transitive
on geodesics, it fixes a point in the boundary, or there exists an infinite
family of non-trivial median quasimorphisms. In particular, in the last case
the second bounded cohomology of the group is infinite dimensional as a vector
space. As an application, we show that a cocompact lattice in a product of
trees only has trivial quasimorphisms if and only if both closures of the
projections on the two factors are locally $\infty$-transitive.


  We describe the planned near-term and potential longer-term upgrades of the
Belle II detector at the SuperKEKB electron-positron collider in Tsukuba,
Japan. These upgrades will allow increasingly sensitive searches for possible
new physics beyond the Standard Model in flavor, tau, electroweak and dark
sector physics that are both complementary to and competitive with the LHC and
other experiments. We encourage the instrumentation-frontier community to
contribute and study upgrade ideas as part of the Snowmass process.