  The idea of modular invariance provides a novel explanation of flavour
mixing. Within the context of finite modular symmetries $\Gamma_N$ and for a
given element $\gamma \in \Gamma_N$, we present an algorithm for finding
stabilisers (specific values for moduli fields $\tau_\gamma$ which remain
unchanged under the action associated to $\gamma$). We then employ this
algorithm to find all stabilisers for each element of finite modular groups for
$N=2$ to $5$, namely, $\Gamma_2\simeq S_3$, $\Gamma_3\simeq A_4$,
$\Gamma_4\simeq S_4$ and $\Gamma_5\simeq A_5$. These stabilisers then leave
preserved a specific cyclic subgroup of $\Gamma_N$. This is of interest to
build models of fermionic mixing where each fermionic sector preserves a
separate residual symmetry.


  Hawking radiation can usefully be viewed as a semi-classical tunnelling
process that originates at the black hole horizon. The conservation of energy
implies the effect of self-gravitation. For a static black hole, a generalized
Painleve coordinate system is introduced, and Hawking radiation as tunnelling
under the effect of self-gravitation is investigated. The corrected radiation
is consistent with the underlying unitary theory.


  We present models that utilize smart contracts and interledger mechanisms to
provide decentralized authorization for constrained IoT devices. The models
involve different tradeoffs in terms of cost, delay, complexity, and privacy,
while exploiting key advantages of smart contracts and multiple blockchains
that communicate with interledger mechanisms. These include immutably recording
hashes of authorization information and policies in smart contracts, resilience
through the execution of smart contract code on all blockchain nodes, and
cryptographically linking transactions and IoT events recorded on different
blockchains using hash and time-lock mechanisms. The proposed models are
evaluated on the public Ethereum testnets Rinkeby and Ropsten, in terms of
execution cost (gas), delay, and reduction of data that needs to be sent to the
constrained IoT devices.


  We propose an all-optical implementation of quantum-information processing in
semiconductor quantum dots, where electron-hole excitations (excitons) serve as
the computational degrees of freedom (qubits). The strong dot confinement leads
to a strong renormalization of excitonic states, which, in analogy to NMR-based
implementations of quantum-information processing, can be exploited for
performing conditional and unconditional qubit operations.


  Through the utilization of smart materials and well-designed structures,
functional surfaces have been developed to enable small-scale liquid/solid
manipulation tasks, thereby facilitating crucial applications in the fields of
microfluidics, soft robotics, and biomedical engineering. However, the design
of functional systems with flexible, tunable, and multimodal liquid/solid
manipulation capabilities remains a challenging endeavor. Here, inspired by
asymmetric structural features in natural plants and metachrony in cross-scale
biological systems, I report a magnetic-responsive functional surface that can
achieve rich liquid operations under static magnetic fields, while also
enabling the transportation of solids with multiple degrees of freedom (DOFs)
under dynamic magnetic fields. The presence of curvature pillars on the
surface, combined with their magnetic-driven tilt/gradient arrangement, imparts
liquids with multi-directional spreading modes based on the asymmetry of
Laplace pressure. I elucidate the mechanisms governing these liquid spreading
modes and subsequently develop compelling liquid operations, such as adjustable
anti-gravity climbing, spontaneous modal shifts in liquid transport, and liquid
mixing. Furthermore, the dynamic metachronal motion of the magnetic pillars can
be harnessed for solid object transportation. I illustrate the
synchronous/asynchronous transport modes of the surface and propose a novel
strategy for achieving 3-DOF solid transportation by coordinating the
arrangement of objects and employing magnetic actuation strategies. This study
presents a new design concept for application-oriented manipulation surfaces,
which hold significant potential for extensive engineering applications.


  Identifying physical traits and emotions based on system-sensed physical
activities is a challenging problem in the realm of human-computer interaction.
Our work contributes in this context by investigating an underlying connection
between head movements and corresponding traits and emotions. To do so, we
utilize a head movement measuring device called eSense, which gives
acceleration and rotation of a head. Here, first, we conduct a thorough study
over head movement data collected from 46 persons using eSense while inducing
five different emotional states over them in isolation. Our analysis reveals
several new head movement based findings, which in turn, leads us to a novel
unified solution for identifying different human traits and emotions through
exploiting machine learning techniques over head movement data. Our analysis
confirms that the proposed solution can result in high accuracy over the
collected data. Accordingly, we develop an integrated unified solution for
real-time emotion and trait identification using head movement data leveraging
outcomes of our analysis.


  Neutral Fe lines are the most abundant in the spectrum of late stars. They
are used to obtain different basic stellar parameters such as relative
abundances, surface gravity, and effective temperature. However, the centers of
many of these lines are formed in the stellar chromosphere, being affected by
the changes produced by magnetic activity. Calculating non-local thermodynamic
equilibrium (NLTE) semi-empirical models of the stellar atmosphere, it is
possible to study the formation of these lines in detail. We present a new
updated model of the Fe i atom, which allows us to calculate 1715 lines of Fe i
between 3000 and 7000 A in stars with different levels of chromospheric
activity. Preliminary results show the presence of spectral ranges more
sensitive to chromospheric heating, suggesting that the lines with greater
variations must be taken into account, and should even be excluded, when be
used for the purposes described above.


  Consider a finite irreducible Markov chain with invariant probability $\pi$.
Define its inverse communication speed as the expectation to go from x to y,
when x, y are sampled independently according to $\pi$. In the discrete time
setting and when $\pi$ is the uniform distribution $\upsilon$, Litvak and Ejov
have shown that the permutation matrices associated to Hamiltonian cycles are
the fastest Markov chains. Here we prove (A) that the above optimality is with
respect to all processes compatible with a fixed graph of permitted transitions
(assuming that it does contain a Hamiltonian cycle), not only the Markov
chains, and, (B) that this result admits a natural extension in both discrete
and continuous time when $\pi$ is close to $\upsilon$: the fastest Markov
chains/processes are those moving successively on the points of a Hamiltonian
cycle, with transition probabilities/jump rates dictated by $\pi$.
Nevertheless, the claim is no longer true when $\pi$ is significantly different
from $\upsilon$.


  Since the release of LLM-based tools such as GitHub Copilot and ChatGPT the
media and popular scientific literature, but also journals such as the
Communications of the ACM, have been flooded with opinions how these tools will
change programming. The opinions range from ``machines will program
themselves'', to ``AI does not help programmers''. Of course, these statements
are meant to to stir up a discussion, and should be taken with a grain of salt,
but we argue that such unfounded statements are potentially harmful. Instead,
we propose to investigate which skills are required to develop software using
LLM-based tools.
  In this paper we report on an experiment in which we explore if Computational
Thinking (CT) skills predict the ability to develop software using LLM-based
tools. Our results show that the ability to develop software using LLM-based
tools can indeed be predicted by the score on a CT assessment. There are many
limitations to our experiment, and this paper is also a call to discuss how to
approach, preferably experimentally, the question of which skills are required
to develop software using LLM-based tools. We propose to rephrase this question
to include by what kind of people/programmers, to develop what kind of software
using what kind of LLM-based tools.


  Collaborative robots are becoming part of intelligent automation systems in
modern industry. Development and control of such systems differs from
traditional automation methods and consequently leads to new challenges.
Thankfully, Robot Operating System (ROS) provides a communication platform and
a vast variety of tools and utilities that can aid that development. However,
it is hard to use ROS in large-scale automation systems due to communication
issues in a distributed setup, hence the development of ROS2. In this paper, a
ROS2 based communication architecture is presented together with an industrial
use-case of a collaborative and intelligent automation system.


  We propose a model for the longitudinal polarization of Lambda baryons
produced in deep-inelastic lepton scattering at any xF, based on static SU(6)
quark-diquark wave functions and polarized intrinsic strangeness in the nucleon
associated with individual valence quarks. Free parameters of the model are
fixed by fitting NOMAD data on the longitudinal polarization of Lambda hyperons
in neutrino collisions. Our model correctly reproduces the observed dependences
of Lambda polarization on the kinematic variables. Within the context of our
model, the NOMAD data imply that the intrinsic strangeness associated with a
valence quark has anticorrelated polarization. We also compare our model
predictions with results from the HERMES and E665 experiments using charged
leptons. Predictions of our model for the COMPASS experiment are also
presented.


  A method of constructing an entire function with given zeros and estimates of
growth is suggested. It gives a possibility to describe zero sets of certain
classes of entire functions of one and several variables in terms of growth of
volume of these sets in certain polycylinders.


  In this work, we present a new characterization of symmetric $H^+$-tensors.
It is known that a symmetric tensor is an $H^+$-tensor if and only if it is a
generalized diagonally dominant tensor with nonnegative diagonal elements. By
exploring the diagonal dominance property, we derive new necessary and
sufficient conditions for a symmetric tensor to be an $H^+$-tensor. Based on
these conditions, we propose a novel method that allows to check if a tensor is
a symmetric $H^+$-tensor in polynomial time. Moreover, these results can be
applied to the closely related and important class of $M$-tensors. In
particular, this allows to efficiently compute the minimum $H$-eigenvalue of
symmetric $M$-tensors. Furthermore, we show how this latter result can be used
to provide tighter lower bounds for the minimum $H$-eigenvalue of the Fan
product of two symmetric $M$-tensors.


  We introduce a novel method to find exact density operators for a spin-1/2
particle in time-dependent magnetic fields by using the one-mode bosonic
representation of $su(2)$ and the connection with a time-dependent oscillator.
As illustrative examples, we apply the method to find the density operators for
constant and/or oscillating magnetic fields, which turn out to be
time-dependent in general.


  Disasters instances have been increasing both in frequency and intensity
causing the tragic loss of life and making life harder for the survivors.
Disaster relief management plays a crucial role in enhancing the lifestyle of
disaster victims by managing the disaster impacts. Disaster relief management
is a process with many collaborative sectors where different stakeholders
should operate in all major phases of the disaster management progression. In
the different phases of the disaster management process, many collaborative
government organisations along with nongovernment organisations, leadership,
community, and media at different levels need to share the responsibility with
disaster victims to achieve effective disaster relief management. Shared
responsibility enhances disaster relief management effectiveness and reduces
the disaster's impact on the victims. Considering the diverse roles of
different stakeholders, there has been a need for a framework that can bind
different stakeholders together during disaster management. this paper shows a
framework with major stakeholders of disaster relief management and how
different stakeholders can take part in an effective disaster relief management
process. The framework also highlights how each stakeholder can contribute to
relief management at different phases after a disaster. The paper also explores
some of the shared responsibility collaborative practices that have been
implemented around the world in response to the disaster as a disaster relief
management process. In addition, the paper highlights the knowledge obtained
from those disaster instances and how this knowledge can be transferred and can
be helpful in disaster mitigation and preparedness for future disaster
scenarios.


  We present an active learning algorithm for the problem of body schema
learning, i.e. estimating a kinematic model of a serial robot. The learning
process is done online using Recursive Least Squares (RLS) estimation, which
outperforms gradient methods usually applied in the literature. In addiction,
the method provides the required information to apply an active learning
algorithm to find the optimal set of robot configurations and observations to
improve the learning process. By selecting the most informative observations,
the proposed method minimizes the required amount of data. We have developed an
efficient version of the active learning algorithm to select the points in
real-time. The algorithms have been tested and compared using both simulated
environments and a real humanoid robot.


  The origin of short timescale (weeks/months) variability of AGN, whether due
to intrinsic disc variations or reprocessing of X-ray emission by a surrounding
accretion disc, has been a puzzle for many years. However recently a number of
observational programmes, particularly of NGC5548 with Swift, have shown that
the UV/optical variations lag behind the X-ray variations in a manner strongly
supportive of X-ray reprocessing. Somewhat surprisingly the implied size of the
accretion disc is ~3x greater than expected from a standard, smooth,
Shakura-Sunyaev thin disc model. Although the difference may be explained by a
clumpy accretion disc, it is not clear whether the difference will occur in all
AGN or whether it may change as, eg, a function of black hole mass, accretion
rate or disc temperature. Measurements of interband lags for most AGN require
long timescale monitoring, which is hard to arrange. However for low mass (<1
million solar mass) AGN, the combination of XMM-Newton EPIC (X-rays) with the
optical monitor in fast readout mode allows an X-ray/UV-optical lag to be
measured within a single long observation. Here we summarise previous related
observations and report on XMM-Newton observations of NGC4395 (mass ~100x lower
and accretion rate ~20x lower than for NGC5548). We find that the UVW1 lags the
X-rays by ~470s. Simultaneous observations at 6 different ground based
observatories also allowed the g-band lag (~800s) to be measured. These
observations are in agreement with X-ray reprocessing but initial analysis
suggests that, for NGC4395, they do not differ markedly from the predictions of
the standard thin disc model.


  This papers presents a detailed analysis of pseudocodewords of Tanner graphs.
Pseudocodewords arising on the iterative decoder's computation tree are
distinguished from pseudocodewords arising on finite degree lifts. Lower bounds
on the minimum pseudocodeword weight are presented for the BEC, BSC, and AWGN
channel. Some structural properties of pseudocodewords are examined, and
pseudocodewords and graph properties that are potentially problematic with
min-sum iterative decoding are identified. An upper bound on the minimum degree
lift needed to realize a particular irreducible lift-realizable pseudocodeword
is given in terms of its maximal component, and it is shown that all
irreducible lift-realizable pseudocodewords have components upper bounded by a
finite value $t$ that is dependent on the graph structure. Examples and
different Tanner graph representations of individual codes are examined and the
resulting pseudocodeword distributions and iterative decoding performances are
analyzed. The results obtained provide some insights in relating the structure
of the Tanner graph to the pseudocodeword distribution and suggest ways of
designing Tanner graphs with good minimum pseudocodeword weight.


  The thermal partition function of photons in any covariant gauge and
gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed
using a local $\zeta$-function regularization approach. The correct Planckian
leading order temperature dependence $T^4$ is obtained in both cases. For the
photons, the existence of a surface term giving a negative contribution to the
entropy is confirmed, as earlier obtained by Kabat, but this term is shown to
be gauge dependent in the four-dimensional case and, therefore is discarded. It
is argued that similar terms could appear dealing with any integer spin $s\geq
1$ in the massless case and in more general manifolds. Our conjecture is
checked in the case of a graviton in the harmonic gauge, where different
surface terms also appear, and physically consistent results arise dropping
these terms. The results are discussed in relation to the quantum corrections
to the black hole entropy.


  We consider uniformly elliptic operators with Dirichlet or Neumann
homogeneous boundary conditions on a domain $\Omega $ in ${\mathbb{R}}^N$. We
consider deformations $\phi (\Omega)$ of $\Omega $ obtained by means of a
locally Lipschitz homeomorphism $\phi $ and we estimate the variation of the
eigenfunctions and eigenvalues upon variation of $\phi $. We prove general
stability estimates without using uniform upper bounds for the gradients of the
maps $\phi$. As an application, we obtain estimates on the rate of convergence
for eigenvalues and eigenfunctions when a domain with an outward cusp is
approximated by a sequence of Lipschitz domains.


  Rust is an emerging programming language that aims to prevent memory-safety
bugs. However, the current design of Rust also brings side effects which may
increase the risk of memory-safety issues. In particular, it employs OBRM
(ownership-based resource management) and enforces automatic deallocation of
unused resources without the garbage collector. It may therefore falsely
deallocate reclaimed memory and lead to use-after-free or double-free issues.
In this paper, we study the problem of invalid memory deallocation and propose
SafeDrop, a static path-sensitive data-flow analysis approach to detect such
bugs. Our approach analyzes each API of a Rust crate iteratively by traversing
the control-flow graph and extracting all aliases of each data-flow. To
guarantee precision and scalability, we leverage a modified Tarjan algorithm to
achieve scalable path-sensitive analysis, and a cache-based strategy to achieve
efficient inter-procedural analysis. Our experiment results show that our
approach can successfully detect all existing CVEs of such issues with a
limited number of false positives. The analysis overhead ranges from 1.0% to
110.7% in comparison with the original compilation time. We further apply our
tool to several real-world Rust crates and find 8 Rust crates involved with
invalid memory deallocation issues.


  In the present paper, we investigate the Sahlqvist-type correspondence theory
for instantial neighbourhood logic (INL), which can talk about existential
information about the neighbourhoods of a given world and is a mixture between
relational semantics and neighbourhood semantics. We have two proofs of the
correspondence results, the first proof is obtained by using standard
translation and minimal valuation techniques directly, the second proof follows
[4] and [6], where we use bimodal translation method to reduce the
correspondence problem in instantial neighbourhood logic to normal bimodal
logics in classical Kripke semantics. We give some remarks and future
directions at the end of the paper.


  Dirac-Heisenberg-Wigner formalism is used to study chirp effects on the
vacuum pair creation under inhomogeneous electric fields. For rapidly
oscillating electric fields, the particle momentum spectrum is sensitive to
both of the spatial scale and the chirp parameter, and the external field width
has less significant effect for the maximally large chirp. For slowly
oscillating electric fields, chirp effects could be identified at large spatial
extents and the carrier phase plays a significant role reflecting chirp effects
even at small spatial scales. We also notice that, the local density
approximation holds for all external field profiles considered in this work at
the quasihomogeneous limit allowing one to use arguments from homogeneous
scenarios to analyze inhomogeneous results.


  We report a ferroelectric order at ~ 98 K for NiFe2O4, which carries an
inverse spinel structure with a centrosymmetric Fd3m structure at room
temperature. The value of spontaneous electric polarization is considerably
high as ~ 0.29 {\mu}C/cm2 for 5 kV/cm poling field. The electric polarization
decreases considerably (~ 17 %) around liquid nitrogen temperature upon
application of 50 kOe field, proposing a significant magnetoelectric coupling.
The synchrotron diffraction studies confirm a structural transition at ~ 98 K
to a noncentrosymmetric structure of P4122 space group. The occurrence of polar
order is associated with an ordered occupancy of Ni and Fe atoms at the
octahedral sites of the P4122 structure, instead of random occupancies at the
octahedral site of the inverse spinel structure. The results propose that
NiFe2O4 is a new type-II multiferroic material.


  Suppose that wirelessly communicating sensors are placed in a regular fashion
on the points of a lattice. Common communication protocols allow the sensors to
broadcast messages at arbitrary times, which can lead to problems should two
sensors broadcast at the same time. It is shown that one can exploit a tiling
of the lattice to derive a deterministic periodic schedule for the broadcast
communication of sensors that is guaranteed to be collision-free. The proposed
schedule is shown to be optimal in the number of time slots.


  A new generalized Statistical Complexity Measure (SCM) was proposed by Rosso
et al in 2010. It is a functional that captures the notions of order/disorder
and of distance to an equilibrium distribution. The former is computed by a
measure of entropy, while the latter depends on the definition of a stochastic
divergence. When the scene is illuminated by coherent radiation, image data is
corrupted by speckle noise, as is the case of ultrasound-B, sonar, laser and
Synthetic Aperture Radar (SAR) sensors. In the amplitude and intensity formats,
this noise is multiplicative and non-Gaussian requiring, thus, specialized
techniques for image processing and understanding. One of the most successful
family of models for describing these images is the Multiplicative Model which
leads, among other probability distributions, to the G0 law. This distribution
has been validated in the literature as an expressive and tractable model,
deserving the "universal" denomination for its ability to describe most types
of targets. In order to compute the statistical complexity of a site in an
image corrupted by speckle noise, we assume that the equilibrium distribution
is that of fully developed speckle, namely the Gamma law in intensity format,
which appears in areas with little or no texture. We use the Shannon entropy
along with the Hellinger distance to measure the statistical complexity of
intensity SAR images, and we show that it is an expressive feature capable of
identifying many types of targets.


  In Dirac materials, the low energy excitations behave like ultra-relativistic
massless particles with linear energy dispersion. A particularly intriguing
phenomenon arises with the intrinsic charge transport behavior at the Dirac
point where the charge density approaches zero. In graphene, a 2-D Dirac
fermion system, it was predicted that charge transport near the Dirac point is
carried by evanescent modes, resulting in unconventional pseudo-diffusive
charge transport even in the absence of disorder. In the past decade,
experimental observation of this phenomenon remained challenging due to the
presence of strong disorder in graphene devices which limits the accessibility
of the low carrier density regime close enough to the Dirac point. Here we
report transport measurements on ballistic suspended graphene-Niobium Josephson
weak links that demonstrate a transition from ballistic to pseudo-diffusive
like evanescent transport below a carrier density of $(10^{10}
cm^{-2})$.Approaching the Dirac point, the sub-harmonic gap structures due to
multiple Andreev reflections display a strong Fermi energy-dependence and
become increasingly pronounced, while the normalized excess current through the
superconductor-graphene interface decreases sharply. Our observations are in
qualitative agreement with the longstanding theoretical prediction for the
emergence of evanescent transport mediated pseudo-diffusive transport in
graphene.


  The automotive industry is experiencing a serious transformation due to a
digitalisation process and the transition to the new paradigm of
Mobility-as-a-Service. The next-generation vehicles are going to be very
complex cyber-physical systems, whose design must be reinvented to fulfil the
increasing demand of smart services, both for safety and entertainment
purposes, causing the manufacturers' model to converge towards that of IT
companies. Connected cars and autonomous driving are the preeminent factors
that drive along this route, and they cause the necessity of a new design to
address the emerging cybersecurity issues: the "old" automotive architecture
relied on a single closed network, with no external communications; modern
vehicles are going to be always connected indeed, which means the attack
surface will be much more extended. The result is the need for a paradigm shift
towards a secure-by-design approach.


  Let us consider the elliptic restricted three body problem (Elliptic RTBP)
for the Jupiter Sun system with eccentricity $e=0.048$ and $\mu=0.000953339$.
Let us denote by $T$ the period of their orbits. In this paper we provide
initial conditions for the position and velocity for a spacecraft such that
after one period $T$ the spacecraft comes back to the same place, with the same
velocity, within an error of 4 meters for the position and 0.2 meters per
second for the velocity. Taking this solution as periodic, we present numerical
evidence showing that this solution is stable. In order to compare this
periodic solution with the motion of celestial bodies in our solar system, we
end this paper by providing an ephemeris of the spacecraft motion from February
17, 2017 to December 28, 2028.


  Cascading failures in power systems normally occur as a result of initial
disturbance or faults on electrical elements, closely followed by errors of
human operators. It remains a great challenge to systematically trace the
source of cascading failures in power systems. In this paper, we develop a
mathematical model to describe the cascading dynamics of transmission lines in
power networks. In particular, the direct current (DC) power flow equation is
employed to calculate the transmission power on the branches. By regarding the
disturbances on the elements as the control inputs, we formulate the problem of
determining the initial disturbances causing the cascading blackout of power
grids in the framework of optimal control theory, and the magnitude of
disturbances or faults on the selected branch can be obtained by solving the
system of algebraic equations. Moreover, an iterative search algorithm is
proposed to look for the optimal solution leading to the worst case of
cascading failures. Theoretical analysis guarantees the asymptotic convergence
of the iterative search algorithm. Finally, numerical simulations are carried
out in IEEE 9 Bus System and IEEE 14 Bus System to validate the proposed
approach.


  Adverse Childhood Experiences (ACEs) are defined as a collection of highly
stressful, and potentially traumatic, events or circumstances that occur
throughout childhood and/or adolescence. They have been shown to be associated
with increased risks of mental health diseases or other abnormal behaviours in
later lives. However, the identification of ACEs from free-text Electronic
Health Records (EHRs) with Natural Language Processing (NLP) is challenging
because (a) there is no NLP ready ACE ontologies; (b) there are limited cases
available for machine learning, necessitating the data annotation from clinical
experts. We are currently developing a tool that would use NLP techniques to
assist us in surfacing ACEs from clinical notes. This will enable us further
research in identifying evidence of the relationship between ACEs and the
subsequent developments of mental illness (e.g., addictions) in large-scale and
longitudinal free-text EHRs, which has previously not been possible.


  A single-epoch low resolution GHRS spectrum of the eclipsing binary Epsilon
Aurigae was obtained while the secondary was orbiting towards eclipse by the
primary. The detected emission line profiles have the appearance of double-
peaked emission with a stronger red component at a radial velocity of +108
km/s, and a weaker blue emission bump at ca. -92 km/s. We compare these
observational results with known orbital properties of the epsilon Aur binary
system, and propose that the emission originates at the inner radius of the
disk surrounding the enigmatic secondary. We interpret the kinematic data as a
possible means to uncover the underlying stellar masses and we speculate about
the binary's relationship to other "high-mass" models.


  Differential privacy (DP) is the de facto standard for training machine
learning (ML) models, including neural networks, while ensuring the privacy of
individual examples in the training set. Despite a rich literature on how to
train ML models with differential privacy, it remains extremely challenging to
train real-life, large neural networks with both reasonable accuracy and
privacy.
  We set out to investigate how to do this, using ImageNet image classification
as a poster example of an ML task that is very challenging to resolve
accurately with DP right now. This paper shares initial lessons from our
effort, in the hope that it will inspire and inform other researchers to
explore DP training at scale. We show approaches that help make DP training
faster, as well as model types and settings of the training process that tend
to work better in the DP setting. Combined, the methods we discuss let us train
a Resnet-18 with DP to $47.9\%$ accuracy and privacy parameters $\epsilon = 10,
\delta = 10^{-6}$. This is a significant improvement over "naive" DP training
of ImageNet models, but a far cry from the $75\%$ accuracy that can be obtained
by the same network without privacy. The model we use was pretrained on the
Places365 data set as a starting point. We share our code at
https://github.com/google-research/dp-imagenet, calling for others to build
upon this new baseline to further improve DP at scale.


  Halo bias is the one of the key ingredients of the halo models. It was shown
at a given redshift to be only dependent, to the first order, on the halo mass.
In this study, four types of cosmic web environments: clusters, filaments,
sheets and voids are defined within a state of the art high resolution $N$-body
simulation. Within those environments, we use both halo-dark matter
cross-correlation and halo-halo auto correlation functions to probe the
clustering properties of halos. The nature of the halo bias differs strongly
among the four different cosmic web environments we describe. With respect to
the overall population, halos in clusters have significantly lower biases in
the {$10^{11.0}\sim 10^{13.5}h^{-1}\rm M_\odot$} mass range. In other
environments however, halos show extremely enhanced biases up to a factor 10 in
voids for halos of mass {$\sim 10^{12.0}h^{-1}\rm M_\odot$}. Such a strong
cosmic web environment dependence in the halo bias may play an important role
in future cosmological and galaxy formation studies. Within this cosmic web
framework, the age dependency of halo bias is found to be only significant in
clusters and filaments for relatively small halos $\la 10^{12.5}\msunh$.


  In this paper, we propose a method to solve a bi-objective variant of the
well-studied Traveling Thief Problem (TTP). The TTP is a multi-component
problem that combines two classic combinatorial problems: Traveling Salesman
Problem (TSP) and Knapsack Problem (KP). We address the BI-TTP, a bi-objective
version of the TTP, where the goal is to minimize the overall traveling time
and to maximize the profit of the collected items. Our proposed method is based
on a biased-random key genetic algorithm with customizations addressing
problem-specific characteristics. We incorporate domain knowledge through a
combination of near-optimal solutions of each subproblem in the initial
population and use a custom repair operator to avoid the evaluation of
infeasible solutions. The bi-objective aspect of the problem is addressed
through an elite population extracted based on the non-dominated rank and
crowding distance. Furthermore, we provide a comprehensive study showing the
influence of each parameter on the performance. Finally, we discuss the results
of the BI-TTP competitions at EMO-2019 and GECCO-2019 conferences where our
method has won first and second places, respectively, thus proving its ability
to find high-quality solutions consistently.


  Recent studies suggest that ultra-short period planets (USPs), Earth-sized
planets with sub-day periods, constitute a statistically distinct sub-sample of
{\it Kepler} planets: USPs have smaller radii ($1-1.4R_\oplus$) and larger
mutual inclinations with neighboring planets than nominal {\it Kepler} planets,
and their period distribution is steeper than longer-period planets. We study a
"low-eccentricity" migration scenario for the formation of USPs, in which a
low-mass planet with initial period of a few days maintains a small but finite
eccentricity due to secular forcings from exterior companion planets, and
experiences orbital decay due to tidal dissipation. USP formation in this
scenario requires that the initial multi-planet system have modest
eccentricities ($\gtrsim 0.1$) or angular momentum deficit. During the orbital
decay of the inner-most planet, the system can encounter several apsidal and
nodal precession resonances that significantly enhance eccentricity excitation
and increase the mutual inclination between the inner planets. We develop an
approximate method based on eccentricity and inclination eigenmodes to
efficiently evolve a large number of multi-planet systems over Gyr timescales
in the presence of rapid (as short as $\sim 100$~years) secular planet-planet
interactions and other short-range forces. Through a population synthesis
calculation, we demonstrate that the "low-$e$ migration" mechanism can
naturally produce USPs from the large population of {\it Kepler} multis under a
variety of conditions, with little fine tuning of parameters. This mechanism
favors smaller inner planets with more massive and eccentric companion planets,
and the resulting USPs have properties that are consistent with observations.


  We calculate, in a class of Gauge invariant functionals, by variational
methods, the difference of vacuum energy between two different backgrounds:
Schwarzschild and Flat Space. We perform this evaluation in an Hamiltonian
formulation of Quantum Gravity by standard ''$3+1$'' decomposition. After the
decomposition the scalar curvature is expanded to second order with respect to
the Schwarzschild metric. We evaluate this energy difference in momentum space,
in the lowest possible state (regardless of any negative mode). We find a
singular behaviour in the UV-limit, due to the presence of the horizon when
$r=2m.$ When $r>2m$ this singular behaviour disappears, which is in agreement
with various other models presented in the literature.


  We report the detection of new 12.178, 12.229, 20.347, and 23.121 GHz
methanol masers in the massive star-forming region G358.93-0.03, which are
flaring on similarly short timescales (days) as the 6.668 GHz methanol masers
also associated with this source. The brightest 12.178 GHz channel increased by
a factor of over 700 in just 50 d. The masers found in the 12.229 and 20.347
GHz methanol transitions are the first ever reported and this is only the
fourth object to exhibit associated 23.121 GHz methanol masers. The 12.178 GHz
methanol maser emission appears to have a higher flux density than that of the
6.668 GHz emission, which is unusual. No associated near-infrared flare
counterpart was found, suggesting that the energy source of the flare is deeply
embedded.


  We investigate the spatial extent and structure of the Pegasus dwarf
irregular galaxy using deep, wide-field, multicolour CCD photometry from the
Sloan Digital Sky Survey (SDSS) and new deep HI observations. We study an area
of ~0.6 square degrees centred on the Pegasus dwarf that was imaged by SDSS.
Using effective filtering in colour-magnitude space we reduce the contamination
by foreground Galactic field stars and increase significantly the contrast in
the outer regions of the Pegasus dwarf. Our extended surface photometry,
reaches down to a surface brightness magnitude mu_r~32 mag/sq.arcsec. It
reveals a stellar body with a diameter of ~8 kpc that follows a Sersic surface
brightness distribution law, which is composed of a significantly older stellar
population than that observed in the ~2 kpc main body. The galaxy is at least
five times more extended than listed in NED. The faint extensions of the galaxy
are not equally distributed around its circumference; the north-west end is
more jagged than the south-east end. We also identified a number of stellar
concentrations, possibly stellar associations, arranged in a ring around the
main luminous body. New HI observations were collected at the Arecibo
Observatory as part of the ALFALFA survey. They reveal an HI distribution
somewhat elongated in RA and about 0.3 deg. wide, with the region of highest
column density coincident with the luminous galaxy. The HI rotation curve shows
a solid-body rotation behaviour, with opposite ends differing by 15 km/s. There
is a stream to lower velocities about 5 arcmin from the centre of the galaxy.
We were able to measure ugriz colours in a number of apertures using the SDSS
data and compared these with predictions of evolutionary synthesis models.
(abridged)


  The transmission spectrum of two dipole-dipole coupled atoms interacting with
a single-mode optical cavity in strong coupling regime is investigated
theoretically for the lower and higher excitation cases, respectively. The
dressed states containing the dipole-dipole interaction (DDI) are obtained by
transforming the two-atom system into an effective single-atom one. We found
that the DDI can enhance the effects resulting from the positive atom-cavity
detunings but weaken them for the negative detunings cases for lower
excitation, which can promote the spectrum exhibiting two asymmetric peaks and
shift the heights and the positions of them. For the higher excitation cases,
DDI can augment the atomic saturation and lead to the deforming of the
spectrum. Furthermore, the large DDI can make the atom and the cavity decouple,
making a singlet of the normal-mode spectrum.


  In this paper we briefly present our works on the relic gravitational waves
(RGW) and the CMB polarization in the accelerating universe. The spectrum of
RGW has been obtained, showing the influence of the dark energy. Compared with
those from non-accelerating models, the shape of the spectrum is approximately
similar, nevertheless, the amplitude of RGW now acquires a suppressing factor
of the ratio of matter over dark energy $\propto \Omega_m/\Omega_{\Lambda}\sim
0.4$ over almost the whole range of frequencies. The RGW spectrum is then used
as the source to calculate the spectra of CMB polarization. By a two half
Gaussian function as an approximation to the visibility function during the
photon decoupling, both the "electric" and "magnetic" spectra have been
analytically derived, which are quite close to the numerical ones. Several
physical elements that affect the spectra have been examined, such as the
decoupling process, the inflation, the dark energy, the baryons, etc.


  We show that under a certain topological assumption on two compact hereditary
families $\F$ and $\G$ on some infinite cardinal $\kappa$, the corresponding
combinatorial spaces $X_\F$ and $X_\G$ are isometric if and only if there is a
permutation of $\kappa$ inducing a homeomorphism between $\F$ and $\G$. We also
prove that two different regular families $\F$ and $\G$ on $\omega$ cannot be
permuted one to the other. Both these results strengthen the main result of
\cite{BrechFerencziTcaciuc}.


  We consider the problem of existence of polynomials with small norm. This
range of problems has been extensively studied by many authors in the case of
the unit circle (or a compact Abelian group), i.e. when the characters are
bounded. In general, on compact homogeneous Riemannian manifolds, the
eigenfunctions of the Laplace-Beltrami operator are not uniformly bounded. This
creates difficulties of a fundamental nature in applications of known methods
and results. The method we develop is based on a geometric inequality between
norms induced by two convex bodies in Euclidean space.


  Recent observations suggest that long-duration gamma-ray bursts and their
afterglows are produced by highly relativistic jets emitted in core-collapse
explosions. As the jet makes its way out of the stellar mantle, a bow shock
runs ahead and a strong thermal precursor is produced as the shock breaks out.
Such erupting fireballs produce a very bright gamma-ray precursor as they
interact with the thermal break-out emission. The prompt gamma-ray emission
propagates ahead of the fireball before it becomes optically thin, leading to
electron-positron pair loading and radiative acceleration of the external
medium. The detection of such precursors would offer the possibility of
diagnosing not only the radius of the stellar progenitor and the initial
Lorentz factor of the collimated fireball, but also the density of the external
environment.


  Let $W_0(\mathbb R)$ be the Wiener Banach algebra of functions representable
by the Fourier integrals of Lebesgue integrable functions. It is proven in the
paper that, in particular, a trigonometric series
$\sum\limits_{k=-\infty}^\infty c_k e^{ikt}$ is the Fourier series of an
integrable function if and only if there exists a $\phi\in W_0(\mathbb R)$ such
that $\phi(k)=c_k$, $k\in\mathbb Z$. If $f\in W_0(\mathbb R)$, then the
piecewise linear continuous function $\ell_f$ defined by $\ell_f(k)=f(k)$,
$k\in\mathbb Z$, belongs to $W_0(\mathbb R)$ as well. Moreover,
$\|\ell_f\|_{W_0}\le \|f\|_{W_0}$. Similar relations are established for more
advanced Wiener algebras. These results are supplemented by numerous
applications. In particular, new necessary and sufficient conditions are proved
for a trigonometric series to be a Fourier series and new properties of $W_0$
are established.


  In this paper, we propose a digital twin (DT)-based user-centric approach for
processing sensing data in an integrated sensing and communication (ISAC)
system with high accuracy and efficient resource utilization. The considered
scenario involves an ISAC device with a lightweight deep neural network (DNN)
and a mobile edge computing (MEC) server with a large DNN. After collecting
sensing data, the ISAC device either processes the data locally or uploads them
to the server for higher-accuracy data processing. To cope with data drifts,
the server updates the lightweight DNN when necessary, referred to as continual
learning. Our objective is to minimize the long-term average computation cost
of the MEC server by optimizing two decisions, i.e., sensing data offloading
and sensing data selection for the DNN update. A DT of the ISAC device is
constructed to predict the impact of potential decisions on the long-term
computation cost of the server, based on which the decisions are made with
closed-form formulas. Experiments on executing DNN-based human motion
recognition tasks are conducted to demonstrate the outstanding performance of
the proposed DT-based approach in computation cost minimization.


  let $R$ be a regular local ring of a mixed characteristic $(0,p)$ where
$p\neq 2$ is a prime number. Suppose that the quotient ring $R/pR$ is also
regular. Fix a non-degenerate Pfister form $Q(T_{1},\ldots,T_{2^{m}})$ over $R$
and an invertible element $c$ in $R$. Then the equation
$Q(T_{1},\ldots,T_{2^{m}})=c$ has a solution over $R$ if and only if it has a
solution over the fraction field $K$.


  It was shown in \cite{GL} that the maximal surface area of a convex set in
$\mathbb{R}^n$ with respect to a rotation invariant log-concave probability
measure $\gamma$ is of order $\frac{\sqrt{n}}{\sqrt[4]{Var|X|}
\sqrt{\mathbb{E}|X|}}$, where $X$ is a random vector in $\mathbb{R}^n$
distributed with respect to $\gamma$. In the present paper we discuss surface
area of convex polytopes $P_K$ with $K$ facets. We find tight bounds on the
maximal surface area of $P_K$ in terms of $K$. We show that $\gamma(\partial
P_K)\lesssim \frac{\sqrt{n}}{\mathbb{E}|X|}\cdot\sqrt{\log K}\cdot\log n$ for
all $K$. This bound is better then the general bound for all $K\in
[2,e^{\frac{c}{{\sqrt{Var|X|}}}}]$. Moreover, for all $K$ in that range the
bound is exact up to a factor of $\log n$: for each $K\in
[2,e^{\frac{c}{{\sqrt{Var|X|}}}}]$ there exists a polytope $P_K$ with at most
$K$ facets such that $\gamma(\partial P_K)\gtrsim
\frac{\sqrt{n}}{\mathbb{E}|X|}\sqrt{\log K}.$ %For the measures $\gamma_p$ with
densities $C_{n,p} e^{-\frac{|y|^p}{p}}$ (where $p>0$) we obtain:
$\gamma_p(\partial P_K)\lesssim \frac{\sqrt{n}}{\mathbb{E}X}\sqrt{\log K},$
which was obtained for the standard Gaussian measure $\gamma_2$ by F. Nazarov.


  Extraction of Application Programming Interfaces (APIs) and their semantic
relations from unstructured text (e.g., Stack Overflow) is a fundamental work
for software engineering tasks (e.g., API recommendation). However, existing
approaches are rule-based and sequence-labeling based. They must manually
enumerate the rules or label data for a wide range of sentence patterns, which
involves a significant amount of labor overhead and is exacerbated by
morphological and common-word ambiguity. In contrast to matching or labeling
API entities and relations, this paper formulates heterogeneous API extraction
and API relation extraction task as a sequence-to-sequence generation task, and
proposes AERJE, an API entity-relation joint extraction model based on the
large pre-trained language model. After training on a small number of ambiguous
but correctly labeled data, AERJE builds a multi-task architecture that
extracts API entities and relations from unstructured text using dynamic
prompts. We systematically evaluate AERJE on a set of long and ambiguous
sentences from Stack Overflow. The experimental results show that AERJE
achieves high accuracy and discrimination ability in API entity-relation joint
extraction, even with zero or few-shot fine-tuning.


  Reconfigurable intelligent surfaces, with their large number of antennas,
offer an interesting opportunity for high spatial-resolution imaging. In this
paper, we propose a novel RIS-aided integrated imaging and communication system
that can reduce the RIS beam training overhead for communication by leveraging
the imaging of the surrounding environment. In particular, using the RIS as a
wireless imaging device, our system constructs the scene depth map of the
environment, including the mobile user. Then, we develop a user detection
algorithm that subtracts the background and extracts the mobile user attributes
from the depth map. These attributes are then utilized to design the RIS
interaction vector and the beam selection strategy with low overhead.
Simulation results show that the proposed approach can achieve comparable
beamforming gain to the optimal/exhaustive beam selection solution while
requiring 1000 times less beam training overhead.


  We give explicit expressions of a deformation quantization with separation of
variables for CP^N and CH^N. This quantization method is one of the ways to
perform a deformation quantization of Kahler manifolds, which is introduced by
Karabegov. Star products are obtained as explicit formulae in all order in the
noncommutative parameter. We also give the Fock representations of the
noncommutative CP^N and CH^N.


  A consolidated mathematical formulation of the spherically symmetric
mass-transfer problem is presented, with the quasi-stationary approximating
equations derived from a perturbation point of view for the leading-order
effect. For the diffusion-controlled quasi-stationary process, a mathematically
complete set of the exact analytical solutions is obtained in implicit forms to
cover the entire parameter range. Furthermore, accurate explicit formulas for
the particle radius as a function of time are also constructed semi-empirically
for convenience in engineering practice. Both dissolution of a particle in a
solvent and growth of it by precipitation in a supersaturated environment are
considered in the present work.


  When the light from a distant object passes very near to a foreground galaxy
or cluster, gravitational lensing can cause it to appear as multiple images on
the sky. If the source is variable, it can be used to constrain the cosmic
expansion rate and dark energy models. Achieving these cosmological goals
requires many lensed transients with precise time delay measurements. Lensed
supernovae (SN) are attractive for this purpose because they have relatively
simple photometric behavior, with well-understood light curve shapes and
colours $-$ in contrast to the stochastic variation of quasars. Here we report
the discovery of a multiply-imaged supernova, AT2016jka ("SN Requiem"). It
appeared in an evolved galaxy at $z=1.95$, gravitationally lensed by a
foreground galaxy cluster. It is likely a Type Ia supernova $-$ the explosion
of a low-mass stellar remnant, whose light curve can be used to measure cosmic
distances. In archival Hubble Space Telescope imaging, three lensed images of
the supernova are detected with relative time delays of $<$200 days. We predict
a fourth image will appear close to the cluster core in the year 2037$\pm$2.
Observation of the fourth image could provide a time delay precision of
$\approx$7 days, $<1\%$ of the extraordinary 20 year baseline. The SN
classification and the predicted reappearance time could be improved with
further lens modelling and a comprehensive analysis of systematic
uncertainties.


  By implementing a dynamic wind-tunnel model in a smoothed-particle
chemodynamic/hydrodynamic simulation suite, we have investigated the effects of
ram pressure and tidal forces on dwarf galaxies similar to the Magellanic
Clouds, within host galaxies with gas and dark matter halos that are varied, to
compare the relative effects of tides and ram pressure. We concentrate on how
the distributions of metals are affected by interactions. We find that while
ram pressure and tidal forces have some effect on dwarf galaxy outflows, these
effects do not produce large differences in the metal distributions of the
dwarf disks other than truncation in the outer regions in some cases, and that
confinement from the host galaxy gas halo appears to be more significant than
ram pressure stripping. We find that stochastic variations in the star
formation rate can explain the remaining variations in disk metal properties.
This raises questions on the cause of low metallicities in dwarf galaxies.


  Semantic Segmentation using deep convolutional neural network pose more
complex challenge for any GPU intensive task. As it has to compute million of
parameters, it results to huge memory consumption. Moreover, extracting finer
features and conducting supervised training tends to increase the complexity.
With the introduction of Fully Convolutional Neural Network, which uses finer
strides and utilizes deconvolutional layers for upsampling, it has been a go to
for any image segmentation task. In this paper, we propose two segmentation
architecture which not only needs one-third the parameters to compute but also
gives better accuracy than the similar architectures. The model weights were
transferred from the popular neural net like VGG19 and VGG16 which were trained
on Imagenet classification data-set. Then we transform all the fully connected
layers to convolutional layers and use dilated convolution for decreasing the
parameters. Lastly, we add finer strides and attach four skip architectures
which are element-wise summed with the deconvolutional layers in steps. We
train and test on different sparse and fine data-sets like Pascal VOC2012,
Pascal-Context and NYUDv2 and show how better our model performs in this tasks.
On the other hand our model has a faster inference time and consumes less
memory for training and testing on NVIDIA Pascal GPUs, making it more efficient
and less memory consuming architecture for pixel-wise segmentation.


  The Lewis Carroll Identity expresses the determinant of a matrix in terms of
subdeterminants obtained by deleting one row and column or a pair of rows and
columns. Using the matrix tree theorem, we can convert this into an equivalent
identity involving sums over pairs of forests. Unlike the Lewis Carroll
Identity, the Forest Identity involves no minus signs. In 2011, Vlasev and
Yeats suggested that such a Forest Identity could be proven using edge
transfers similar to Zeilberger's 1997 matrix proof. However, until now, such
an algorithm has not yet been developed. In this paper, we provide this edge
transfer algorithm and a bijective proof for both the Lewis Carroll Identity
and Forest Identity. This bijection is implemented by the Red Hot Potato
algorithm, so called because the way edges get tossed back and forth between
the two forests is reminiscent of the children's game of hot potato.


  Non-autoregressive approaches aim to improve the inference speed of
translation models, particularly those that generate output in a one-pass
forward manner. However, these approaches often suffer from a significant drop
in translation quality compared to autoregressive models. This paper introduces
a series of innovative techniques to enhance the translation quality of
Non-Autoregressive Translation (NAT) models while maintaining a substantial
acceleration in inference speed. We propose fine-tuning Pretrained Multilingual
Language Models (PMLMs) with the CTC loss to train NAT models effectively.
Furthermore, we adopt the MASK insertion scheme for up-sampling instead of
token duplication, and we present an embedding distillation method to further
enhance performance. In our experiments, our model outperforms the baseline
autoregressive model (Transformer \textit{base}) on multiple datasets,
including WMT'14 DE$\leftrightarrow$EN, WMT'16 RO$\leftrightarrow$EN, and
IWSLT'14 DE$\leftrightarrow$EN. Notably, our model achieves better performance
than the baseline autoregressive model on the IWSLT'14 En$\leftrightarrow$De
and WMT'16 En$\leftrightarrow$Ro datasets, even without using distillation data
during training. It is worth highlighting that on the IWSLT'14
DE$\rightarrow$EN dataset, our model achieves an impressive BLEU score of
39.59, setting a new state-of-the-art performance. Additionally, our model
exhibits a remarkable speed improvement of 16.35 times compared to the
autoregressive model.


  Multi-wavelength studies of solar analogs (G0-5 V stars) with ages from ~50
Myr to 9 Gyr have been carried out as part of the "Sun in Time" program for
nearly 20 yrs. From these studies it is inferred that the young (ZAMS) Sun was
rotating more than 10x faster than today. As a consequence, young solar-type
stars and the early Sun have vigorous magnetohydrodynamic (MHD) dynamos and
correspondingly strong coronal X-ray and transition region / chromospheric
FUV-UV emissions. To ensure continuity and homogeneity for this program, we use
a restricted sample of G0-5 V stars with masses, radii, T(eff), and internal
structure (i.e. outer convective zones) closely matching those of the Sun. From
these analogs we have determined reliable rotation-age-activity relations and
X-ray - UV (XUV) spectral irradiances for the Sun (or any solar-type star) over
time. These XUV irradiance measures serve as input data for investigating the
photo-ionization and photo-chemical effects of the young, active Sun on the
paleo-planetary atmospheres and environments of solar system planets. These
measures are also important to study the effects of these high energy emissions
on the numerous exoplanets hosted by solar-type stars of different ages.
Recently we have extended the study to include lower mass, main-sequence
(dwarf) dK and dM stars to determine relationships among their rotation
spin-down rates and coronal and chromospheric emissions as a function of mass
and age. From rotation-age-activity relations we can determine reliable ages
for main-sequence G, K, M field stars and, subsequently, their hosted planets.
Also inferred are the present and the past XUV irradiance and plasma flux
exposures that these planets have endured and the suitability of the hosted
planets to develop and sustain life.


  We consider the dynamics of semi-hyperbolic semigroups generated by finitely
many rational maps on the Riemann sphere. Assuming that the nice open set
condition holds it is proved that there exists a geometric measure on the Julia
set with exponent $h$ equal to the Hausdorff dimension of the Julia set. Both
$h$-dimensional Hausdorff and packing measures are finite and positive on the
Julia set and are mutually equivalent with Radon-Nikodym derivatives uniformly
separated from zero and infinity. All three fractal dimensions, Hausdorff,
packing and box counting are equal. It is also proved that for the canonically
associated skew-product map there exists a unique $h$-conformal measure.
Furthermore, it is shown that this conformal measure admits a unique Borel
probability absolutely continuous invariant (under the skew-product map)
measure. In fact these two measures are equivalent, and the invariant measure
is metrically exact, hence ergodic.


  We develop a group-theoretical approach to the formulation of generalized
abelian gauge theories, such as those appearing in string theory and M-theory.
We explore several applications of this approach. First, we show that there is
an uncertainty relation which obstructs simultaneous measurement of electric
and magnetic flux when torsion fluxes are included. Next we show how to define
the Hilbert space of a self-dual field. The Hilbert space is Z2-graded and we
show that, in general, self-dual theories (including the RR fields of string
theory) have fermionic sectors. We indicate how rational conformal field
theories associated to the two-dimensional Gaussian model generalize to
(4k+2)-dimensional conformal field theories. When our ideas are applied to the
RR fields of string theory we learn that it is impossible to measure the
K-theory class of a RR field. Only the reduction modulo torsion can be
measured.


  The effects of the symmetry energy softening of the relativistic mean field
(RMF) models on the properties of matter with neutrino trapping are
investigated. It is found that the effects are less significant than those in
the case without neutrino trapping. The weak dependence of the equation of
state on the symmetry energy is shown as the main reason of this finding. Using
different RMF models the dynamical instabilities of uniform matters, with and
without neutrino trapping, have been also studied. The interplay between the
dominant contribution of the variation of matter composition and the role of
effective masses of mesons and nucleons leads to higher critical densities for
matter with neutrino trapping. Furthermore, the predicted critical density is
insensitive to the number of trapped neutrinos as well as to the RMF model used
in the investigation. It is also found that additional nonlinear terms in the
Horowitz-Piekarewicz and Furnstahl-Serot-Tang models prevent another kind of
instability, which occurs at relatively high densities. The reason is that the
effective sigma meson mass in their models increases as a function of the
matter density.


  We construct a family of trees on which a lazy simple random walk exhibits
total variation cutoff. The main idea behind the construction is that hitting
times of large sets should be concentrated around their means. For this
sequence of trees we compute the mixing time, the relaxation time and the
cutoff window.


  We present high-sensitivity eMERLIN radio images of the Seyfert galaxy NGC
4151 at 1.5 GHz. We compare the new eMERLIN images to those from archival
MERLIN observations in 1993 to determine the change in jet morphology in the 22
years between observations. We report an increase by almost a factor of 2 in
the peak flux density of the central core component, C4, thought to host the
black hole, but a probable decrease in some other components, possibly due to
adiabatic expansion. The core flux increase indicates an AGN which is currently
active and feeding the jet. We detect no significant motion in 22 years between
C4 and the component C3, which is unresolved in the eMERLIN image. We present a
spectral index image made within the 512 MHz band of the 1.5 GHz observations.
The spectrum of the core, C4, is flatter than that of other components further
out in the jet. We use HST emission line images (H$\alpha$, [O III] and [O II])
to study the connection between the jet and the emission line region. Based on
the changing emission line ratios away from the core and comparison with the
eMERLIN radio jet, we conclude that photoionisation from the central AGN is
responsible for the observed emission line properties further than 4" (360 pc)
from the core, C4. Within this region, several evidences (radio-line
co-spatiality, low [O III]/H$\alpha$ and estimated fast shocks) suggest
additional ionisation from the jet.


  A general analytical framework for the determination of the mean field states
at arbitrary rational filling factors for the 2DEG in FQHE regime is given. Its
use allows to obtain analytic expressions for the solutions at filling factors
of the form $\nu=1/q$ for arbitrary odd $q$. The analysis can be performed for
two general classes of states characterized by $\gamma=1$ or $\gamma={1/2}$
particles per unit cell. Instead of the periodic peaks of the Wigner solid
solution, the new states show electron densities forming percolating ridges
that may favor an energy decrease through correlated ring of exchange
contributions. Therefore, we estimate that they can realize mean field versions
of the so called Hall Crystal (HC) states. The obtained analytic HC solution
shows the same crystalline symmetry that the corresponding WC state in its
class $\gamma=1$, but a qualitatively different charge density distribution.
The energy dependence of the corresponding HC and WC states on the filling
factor is also evaluated here for the class $\gamma=1/2$. The results show a
crossover between HC state and the Wigner crystal, close to filling 1/7.
Therefore, transitions may occur from one to the other as the electron density
is varied. This result is consistent with recent experimental findings.


  We consider a multi-armed bandit problem in which a set of arms is registered
by each agent, and the agent receives reward when its arm is selected. An agent
might strategically submit more arms with replications, which can bring more
reward by abusing the bandit algorithm's exploration-exploitation balance. Our
analysis reveals that a standard algorithm indeed fails at preventing
replication and suffers from linear regret in time $T$. We aim to design a
bandit algorithm which demotivates replications and also achieves a small
cumulative regret. We devise Hierarchical UCB (H-UCB) of replication-proof,
which has $O(\ln T)$-regret under any equilibrium. We further propose Robust
Hierarchical UCB (RH-UCB) which has a sublinear regret even in a realistic
scenario with irrational agents replicating careless. We verify our theoretical
findings through numerical experiments.


  We show that the presented in Phys.Rev.B, v.101, 214312 (2020) theoretical
expressions for longitudinal current spectral function $C^L(k,\omega)$ and
dispersion of collective excitations are not correct. Indeed, they are not
compatible with the continuum limit and $C^L(k,\omega\to 0)$ contradicts the
continuity equation.


  We use stellar mass functions to study the properties and the significance of
quenching through major galaxy mergers. In addition to SDSS DR7 and Galaxy Zoo
1 data, we use samples of visually selected major galaxy mergers and post
merger galaxies. We determine the stellar mass functions of the stages that we
would expect major merger quenched galaxies to pass through on their way from
the blue cloud to the red sequence: 1: major merger, 2: post merger, 3: blue
early type, 4: green early type and 5: red early type. Based on the similar
mass function shapes we conclude that major mergers are likely to form an
evolutionary sequence from star formation to quiescence via quenching. Relative
to all blue galaxies, the major merger fraction increases as a function of
stellar mass. Major merger quenching is inconsistent with the mass and
environment quenching model. At z~0 major merger quenched galaxies are unlikely
to constitute the majority of galaxies that transition the green valley.
Furthermore, between z~0-0.5 major merger quenched galaxies account for 1-5% of
all quenched galaxies at a given stellar mass. Major galaxy mergers are
therefore not a significant quenching pathway, neither at z~0 nor within the
last 5 Gyr. The majority of red galaxies must have been quenched through an
alternative quenching mechanism which causes a slow blue to red evolution.


  Due to the data imbalance and the diversity of defects, student-teacher
networks (S-T) are favored in unsupervised anomaly detection, which explores
the discrepancy in feature representation derived from the knowledge
distillation process to recognize anomalies. However, vanilla S-T network is
not stable. Employing identical structures to construct the S-T network may
weaken the representative discrepancy on anomalies. But using different
structures can increase the likelihood of divergent performance on normal data.
To address this problem, we propose a novel dual-student knowledge distillation
(DSKD) architecture. Different from other S-T networks, we use two student
networks a single pre-trained teacher network, where the students have the same
scale but inverted structures. This framework can enhance the distillation
effect to improve the consistency in recognition of normal data, and
simultaneously introduce diversity for anomaly representation. To explore
high-dimensional semantic information to capture anomaly clues, we employ two
strategies. First, a pyramid matching mode is used to perform knowledge
distillation on multi-scale feature maps in the intermediate layers of
networks. Second, an interaction is facilitated between the two student
networks through a deep feature embedding module, which is inspired by
real-world group discussions. In terms of classification, we obtain pixel-wise
anomaly segmentation maps by measuring the discrepancy between the output
feature maps of the teacher and student networks, from which an anomaly score
is computed for sample-wise determination. We evaluate DSKD on three benchmark
datasets and probe the effects of internal modules through ablation
experiments. The results demonstrate that DSKD can achieve exceptional
performance on small models like ResNet18 and effectively improve vanilla S-T
networks.


  We review the techniques of lattice QCD calculations for excited hadrons with
light quarks and outline the future challenges that are faced in calculations
with fully dynamical fermions.


  We discuss observational consequences of the curvaton scenario, which
naturally appears in the context of the simplest model of chaotic inflation in
supergravity. The non-gaussianity parameter f_NL in this scenario can take
values in the observationally interesting range from O(10) to O(100). These
values may be different in different parts of the universe. The regions where
f_NL is particularly large form a curvaton web resembling a net of thick domain
walls, strings, or global monopoles.


  In this paper, we investigate twist sequences for Kauffman finite-type
invariants and Goussarov-Polyak-Viro finite-type invariants. It is shown that
one obtains a Kauffman or GPV type of degree $\le n$ if and only if an
invariant is a polynomial of degree $\le n$ on every twist lattice of the right
form. The main result of this paper is an application of this technique to the
coefficients of the Jones-Kauffman polynomial. It is shown that the Kauffman
finite-type invariants obtained from these coefficients are not GPV finite-type
invariants of any degree by explicitly showing they can never be polynomials.
This generalizes a result of Kauffman, where it is known for degree $k=2$.


  A method is presented for constructing a class of Poincare invariant quantum
mechanical models of systems of a finite number of degrees of freedom that
satisfy cluster separability, the spectral condition, but do not conserve
particle number. The class of models includes the relativistic Lee model and
relativistic isobar models.


  Heterogeneous graph neural networks (HGNNs) have attracted increasing
research interest in recent three years. Most existing HGNNs fall into two
classes. One class is meta-path-based HGNNs which either require domain
knowledge to handcraft meta-paths or consume huge amount of time and memory to
automatically construct meta-paths. The other class does not rely on meta-path
construction. It takes homogeneous convolutional graph neural networks
(Conv-GNNs) as backbones and extend them to heterogeneous graphs by introducing
node-type- and edge-type-dependent parameters. Regardless of the meta-path
dependency, most existing HGNNs employ shallow Conv-GNNs such as GCN and GAT to
aggregate neighborhood information, and may have limited capability to capture
information from high-order neighborhood. In this work, we propose two
heterogeneous graph tree network models: Heterogeneous Graph Tree Convolutional
Network (HetGTCN) and Heterogeneous Graph Tree Attention Network (HetGTAN),
which do not rely on meta-paths to encode heterogeneity in both node features
and graph structure. Extensive experiments on three real-world heterogeneous
graph data demonstrate that the proposed HetGTCN and HetGTAN are efficient and
consistently outperform all state-of-the-art HGNN baselines on semi-supervised
node classification tasks, and can go deep without compromising performance.


  The spread of COVID-19 has been a major disruptive force in people's everyday
lives and mobility behavior. The demand for on-demand ride services, such as
taxis and ridehailing has been specifically impacted, given both restrictions
in service operations and user's concerns about virus transmission in shared
vehicles. During the pandemic, demand for these modes have decreased by as much
as 80%. This study examines intentions to use on-demand ride services in a
period of drastic changes in lifestyles and daily routines coupled with
unprecedented mobility reductions. Specifically, we examine the determinants
for the shift of intentions to use these on-demand modes of travel in the early
stages of the pandemic. Using data from a survey disseminated in June 2020 to
700 respondents from contiguous United States, ordinal regression modeling is
applied to analyze the shift in consideration. The results indicate that
political orientation and health-related experiences during the pandemic are
significant sources of variation for individual changes in intentions to use
ridehailing. Additionally, characteristics such as age and income result in
consideration shifts that contradict the typical ridership profiles found in
the ridehailing literature. Specifically, on-demand ride consideration
decreases as a function of age and income. Moreover, transit-users are more
willing to consider on-demand rides than private vehicle users, suggesting that
shared vehicle modes have a similar risk-profile. We discuss the role of
on-demand ride services in the pandemic era, and the need to investigate
political orientation and evolving pandemic experiences to pinpoint their role
in future mobility systems.


  We study the null-controllability of parabolic equations associated to a
general class of hypoelliptic quadratic differential operators. Quadratic
differential operators are operators defined in the Weyl quantization by
complex-valued quadratic symbols. We consider in this work the class of
accretive quadratic operators with zero singular spaces. These possibly
degenerate non-selfadjoint differential operators are known to be hypoelliptic
and to generate contraction semigroups which are smoothing in specific
Gelfand-Shilov spaces for any positive time. Thanks to this regularizing
effect, we prove by adapting the Lebeau-Robbiano method that parabolic
equations associated to these operators are null-controllable in any positive
time from control regions, for which null-controllability is classically known
to hold in the case of the heat equation on the whole space. Some applications
of this result are then given to the study of parabolic equations associated to
hypoelliptic Ornstein-Uhlenbeck operators acting on weighted $L^2$ spaces with
respect to invariant measures. By using the same strategy, we also establish
the null-controllability in any positive time from the same control regions for
parabolic equations associated to any hypoelliptic Ornstein-Uhlenbeck operator
acting on the flat $L^2$ space extending in particular the known results for
the heat equation or the Kolmogorov equation on the whole space.


  The bulk of cosmic matter resides in a dilute reservoir that fills the space
between galaxies, the intergalactic medium (IGM). The history of this reservoir
is intimately tied to the cosmic histories of structure formation, star
formation, and supermassive black hole accretion. Our models for the IGM at
intermediate redshifts (2<z<5) are a tremendous success, quantitatively
explaining the statistics of Lyman-alpha absorption of intergalactic hydrogen.
However, at both lower and higher redshifts (and around galaxies) much is still
unknown about the IGM. We review the theoretical models and measurements that
form the basis for the modern understanding of the IGM, and we discuss unsolved
puzzles (ranging from the largely unconstrained process of reionization at
high-z to the missing baryon problem at low-z), highlighting the efforts that
have the potential to solve them.


  Several intriguing aspects of neutrino oscillation phenomenology like the
origin of small neutrino masses, the absolute neutrino mass scale, the neutrino
mass hierarchy, i.e. normal or inverted and the nature of neutrinos, i.e. Dirac
or Majorana, etc. have been addressed from a general perspective. We show how
the fundamental considerations of unitary transformations, naturalness and
seesaw mechanism suffices to determine the texture structure of fermion Yukawa
couplings and discuss the significance of the effective mass in
0{\nu}{\beta}{\beta} decay for the texture structure of these couplings.


  Automated batch refactoring has become a de-facto mechanism to restructure
software that may have significant design flaws negatively impacting the code
quality and maintainability. Although automated batch refactoring techniques
are known to significantly improve overall software quality and
maintainability, their impact on resource utilization is not well studied. This
paper aims to bridge the gap between batch refactoring code smells and
consumption of resources. It determines the relationship between software code
smell batch refactoring, and resource consumption. Next, it aims to design
algorithms to predict the impact of code smell refactoring on resource
consumption. This paper investigates 16 code smell types and their joint effect
on resource utilization for 31 open source applications. It provides a detailed
empirical analysis of the change in application CPU and memory utilization
after refactoring specific code smells in isolation and in batches. This
analysis is then used to train regression algorithms to predict the impact of
batch refactoring on CPU and memory utilization before making any refactoring
decisions. Experimental results also show that our ANN-based regression model
provides highly accurate predictions for the impact of batch refactoring on
resource consumption. It allows the software developers to intelligently decide
which code smells they should refactor jointly to achieve high code quality and
maintainability without increasing the application resource utilization. This
paper responds to the important and urgent need of software engineers across a
broad range of software applications, who are looking to refactor code smells
and at the same time improve resource consumption. Finally, it brings forward
the concept of resource aware code smell refactoring to the most crucial
software applications.


  We extend Deuber's theorem on $(m,p,c)$-sets to hold over the
multidimensional positive integer lattices. This leads to a multidimensional
Rado theorem where we are guaranteed monochromatic multidimensional points in
all finite colorings of $\left(\mathbb{Z}^+\right)^d$ where the
$i^{\mathrm{th}}$ set of coordinates satisfies the $i^{\mathrm{th}}$ given
linear Rado system.


  The Bernoulli sieve is the infinite "balls-in-boxes" occupancy scheme with
random frequencies $P_k=W_1... W_{k-1}(1-W_k)$, where $(W_k)_{k\in\mn}$ are
independent copies of a random variable $W$ taking values in $(0,1)$. Assuming
that the number of balls equals $n$, let $L_n$ denote the number of empty boxes
within the occupancy range. In the paper we investigate convergence in
distribution of $L_n$ in the two cases which remained open after the previous
studies. In particular, provided that $\me |\log W|=\me |\log (1-W)|=\infty$
and that the law of $W$ assigns comparable masses to the neighborhoods of 0 and
1, it is shown that $L_n$ weakly converges to a geometric law. This result is
derived as a corollary to a more general assertion concerning the number of
zero decrements of nonincreasing Markov chains. In the case that $\me |\log
W|<\infty$ and $\me |\log (1-W)|=\infty$ we derive several further possible
modes of convergence in distribution of $L_n$. It turns out that the class of
possible limiting laws for, properly normalized and centered, $L_n$ includes
normal laws and spectrally negative stable laws with finite mean. While
investigating the second problem we develop some general results concerning the
weak convergence of renewal shot-noise processes. This allows us to answer a
question asked in Mikosch and Resnick (2006).


  Quantum neural networks (QNNs) require an efficient training algorithm to
achieve practical quantum advantages. A promising approach is the use of
gradient-based optimization algorithms, where gradients are estimated through
quantum measurements. However, it is generally difficult to efficiently measure
gradients in QNNs because the quantum state collapses upon measurement. In this
work, we prove a general trade-off between gradient measurement efficiency and
expressivity in a wide class of deep QNNs, elucidating the theoretical limits
and possibilities of efficient gradient estimation. This trade-off implies that
a more expressive QNN requires a higher measurement cost in gradient
estimation, whereas we can increase gradient measurement efficiency by reducing
the QNN expressivity to suit a given task. We further propose a general QNN
ansatz called the stabilizer-logical product ansatz (SLPA), which can reach the
upper limit of the trade-off inequality by leveraging the symmetric structure
of the quantum circuit. In learning an unknown symmetric function, the SLPA
drastically reduces the quantum resources required for training while
maintaining accuracy and trainability compared to a well-designed symmetric
circuit based on the parameter-shift method. Our results not only reveal a
theoretical understanding of efficient training in QNNs but also provide a
standard and broadly applicable efficient QNN design.


  In this paper, we propose methods for computing the Hilbert series of
multigraded right modules over the free associative algebra. In particular, we
compute such series for noncommutative multigraded algebras. Using results from
the theory of regular languages, we provide conditions when the methods are
effective and hence the sum of the Hilbert series is a rational function.
Moreover, a characterization of finite-dimensional algebras is obtained in
terms of the nilpotency of a key matrix involved in the computations. Using
this result, efficient variants of the methods are also developed for the
computation of Hilbert series of truncated infinite-dimensional algebras whose
(non-truncated) Hilbert series may not be rational functions. We consider some
applications of the computation of multigraded Hilbert series to algebras that
are invariant under the action of the general linear group. In fact, in this
case such series are symmetric functions which can be decomposed in terms of
Schur functions. Finally, we present an efficient and complete implementation
of (standard) graded and multigraded Hilbert series that has been developed in
the kernel of the computer algebra system Singular. A large set of tests
provides a comprehensive experimentation for the proposed algorithms and their
implementations.


  Proteins play a critical role in carrying out biological functions, and their
3D structures are essential in determining their functions. Accurately
predicting the conformation of protein side-chains given their backbones is
important for applications in protein structure prediction, design and
protein-protein interactions. Traditional methods are computationally intensive
and have limited accuracy, while existing machine learning methods treat the
problem as a regression task and overlook the restrictions imposed by the
constant covalent bond lengths and angles. In this work, we present DiffPack, a
torsional diffusion model that learns the joint distribution of side-chain
torsional angles, the only degrees of freedom in side-chain packing, by
diffusing and denoising on the torsional space. To avoid issues arising from
simultaneous perturbation of all four torsional angles, we propose
autoregressively generating the four torsional angles from $\chi_1$ to $\chi_4$
and training diffusion models for each torsional angle. We evaluate the method
on several benchmarks for protein side-chain packing and show that our method
achieves improvements of $11.9\%$ and $13.5\%$ in angle accuracy on CASP13 and
CASP14, respectively, with a significantly smaller model size ($60\times$ fewer
parameters). Additionally, we show the effectiveness of our method in enhancing
side-chain predictions in the AlphaFold2 model. Code is available at
https://github.com/DeepGraphLearning/DiffPack.


  For a curve of genus at least four which is either very general or very
general hyperelliptic, we classify all ways in which a power of its Jacobian
can be isogenous to a product of Jacobians of curves. As an application, we
show that, for a very general principally polarized abelian variety of
dimension at least four, or the intermediate Jacobian of a very general cubic
threefold, no power is isogenous to a product of Jacobians of curves. This
confirms some cases of the Coleman-Oort conjecture. We further deduce from our
results some progress on the question whether the integral Hodge conjecture
fails for such abelian varieties.


  Fuzzy controllers are efficient and interpretable system controllers for
continuous state and action spaces. To date, such controllers have been
constructed manually or trained automatically either using expert-generated
problem-specific cost functions or incorporating detailed knowledge about the
optimal control strategy. Both requirements for automatic training processes
are not found in most real-world reinforcement learning (RL) problems. In such
applications, online learning is often prohibited for safety reasons because
online learning requires exploration of the problem's dynamics during policy
training. We introduce a fuzzy particle swarm reinforcement learning (FPSRL)
approach that can construct fuzzy RL policies solely by training parameters on
world models that simulate real system dynamics. These world models are created
by employing an autonomous machine learning technique that uses previously
generated transition samples of a real system. To the best of our knowledge,
this approach is the first to relate self-organizing fuzzy controllers to
model-based batch RL. Therefore, FPSRL is intended to solve problems in domains
where online learning is prohibited, system dynamics are relatively easy to
model from previously generated default policy transition samples, and it is
expected that a relatively easily interpretable control policy exists. The
efficiency of the proposed approach with problems from such domains is
demonstrated using three standard RL benchmarks, i.e., mountain car, cart-pole
balancing, and cart-pole swing-up. Our experimental results demonstrate
high-performing, interpretable fuzzy policies.


  In order to explore how blind interference alignment (BIA) schemes may take
advantage of side-information in computation tasks, we study the degrees of
freedom (DoF) of a $K$ user wireless network setting that arises in full-duplex
wireless MapReduce applications. In this setting the receivers are assumed to
have reconfigurable antennas and channel knowledge, while the transmitters have
neither, i.e., the transmitters lack channel knowledge and are only equipped
with conventional antennas. The central ingredient of the problem formulation
is the message structure arising out of MapReduce, whereby each transmitter has
a subset of messages that need to be delivered to various receivers, and each
receiver has a subset of messages available to it in advance as
side-information. The challenge resides in both achievability and converse
arguments. Unlike conventional BIA where alignments occur only within the
symbols of the same message (intra-message) the new achievable scheme also
requires inter-message alignments, as well as an outer MDS (maximum distance
separable) code structure. The scheme emerges from two essential ideas: 1)
understanding the DoF of a $K$ user vector broadcast channel with groupcast
messages, and 2) a mapping of messages from the broadcast setting to the
MapReduce setting that makes use of inter-message alignment. On the converse
side, whereas prior BIA converse bounds relied only on a compound channel
argument, in the new setting our converse bounds also require a statistical
equivalence assumption.


  Many programmers, when they encounter an error, would like to have the
benefit of automatic fix suggestions---as long as they are, most of the time,
adequate. Initial research in this direction has generally limited itself to
specific areas, such as data structure classes with carefully designed
interfaces, and relied on simple approaches. To provide high-quality fix
suggestions in a broad area of applicability, the present work relies on the
presence of contracts in the code, and on the availability of dynamic analysis
to gather evidence on the values taken by expressions derived from the program
text. The ideas have been built into the AutoFix-E2 automatic fix generator.
Applications of AutoFix-E2 to general-purpose software, such as a library to
manipulate documents, show that the approach provides an improvement over
previous techniques, in particular purely model-based approaches.


  We report magnetotransport measurements of PrSb in high magnetic fields. Our
results show that PrSb exhibits extremely large magnetoresistance(XMR) at low
temperatures. Meanwhile angle-dependent magnetoresistance measurements were
used to probe the Fermi surface via Shubnikov-de Haas (SdH) oscillations. The
angular dependence of the frequencies of the $\alpha$-branch indicate a
two-dimensional character for this Fermi surface sheet, while the effective
mass of this branch as a function of angle shows a four-fold signature. The
evolution of the Fermi surface with field was also studied up to 32~T. An
enlargement of the Fermi surface up to 14~T is observed, before the oscillation
frequencies become constant at higher fields. Meanwhile our analysis of the
residual Landau index from the high field data reveals a zero Berry phase and
therefore trivial topology of the Fermi surface.


  With each semigroup one can associate a partial algebra, called the biordered
set, which captures important algebraic and geometric features of the structure
of idempotents of that semigroup. For a biordered set $\mathcal{E}$, one can
construct the free idempotent-generated semigroup over $\mathcal{E}$,
$\mathsf{IG}(\mathcal{E})$, which is the free-est semigroup (in a definite
categorical sense) whose biorder of idempotents is isomorphic to $\mathcal{E}$.
Studies of these intriguing objects have been recently focusing on their
particular aspects, such as maximal subgroups, the word problem, etc. In 2012,
Gray and Ru\v{s}kuc pointed out that a more detailed investigation into the
structure of the free idempotent-generated semigroup over the biorder of
$\mathcal{T}_n$, the full transformation monoid over an $n$-element set, might
be worth pursuing. In 2019, together with Gould and Yang, the present author
showed that the word problem for $\mathsf{IG}(\mathcal{E}_{\mathcal{T}_n})$ is
algorithmically soluble. In a recent work by the author, it was showed that,
for a wide class of biorders $\mathcal{E}$, the algorithmic solution of the
word problem revolves around the so-called vertex groups, which arise as
certain subgroups of direct products of pairs of maximal subgroups of
$\mathsf{IG}(\mathcal{E})$. In this paper we determine these vertex groups for
the case when $\mathcal{E}$ is the biorder of idempotents of $\mathcal{T}_n$.


  In this work, we explain in what sense the generic level set of the constants
of motion for the periodic nonlinear Schrodinger equation is an infinite
dimensional torus on which each generalized nonlinear Schrodinger flow is
reduced to straight line almost periodic motion, and describe how neighboring
generic infinite dimensional tori are connected.


  A revised global fit of electroweak $ep$ and $\nu p$ elastic scattering data
has been performed, with the goal of determining the strange quark contribution
to the vector and axial-vector form factors of the nucleon in the
momentum-transfer range $0<Q^2<1$ GeV$^2$. The two vector (electric and
magnetic) form factors $G_E^s(Q^2)$ and $G_M^s(Q^2)$ are strongly constrained
by $ep$ elastic scattering data, while the major source of information on the
axial-vector form factor $G_A^s(Q^2)$ is $\nu p$ scattering data. Combining the
two kinds of data into a single global fit makes possible additional precision
in the determination of these form factors, and provides a unique way to
determine the strange quark contribution to the nucleon spin, $\Delta S$,
independently of leptonic deep-inelastic scattering. The fit makes use of data
from the BNL-E734, SAMPLE, HAPPEx, G0, and PVA4 experiments; we will also
compare the result of the fit with recent data from MiniBooNE, and anticipate
how this fit can be improved when new data from MicroBooNE become available.


  We consider the problem of classifying irreducible Specht modules for the
Iwahori-Hecke algebra of type B with parameters Q,q. We solve this problem
completely in the case where q is not a root of unity, and in the case q=-1 we
reduce the problem to the corresponding problem in type A.


  Density functionals with a range-separated treatment of the exchange energy
are known to improve upon their semilocal forerunners and fixed-fraction
hybrids. The conversion of a given semilocal functional into its short-range
analog is not straightforward, however, and not even unique, because the latter
has a higher information content that has to be recovered in some way. Simple
models of the spherically-averaged exchange hole as an interpolation between
the uniform electron gas limit and a few-term Hermite function are developed
here for use with generalized-gradient approximations, so that the energy
density of the error-function-weighted Coulomb interaction is given by explicit
closed-form expressions in terms of elementary and error functions. For
comparison, some new non-oscillatory models in the spirit of earlier works are
also built and studied, their energy densities match rather closely (within
less than 5%) but do lack the exact uniform electron gas limit.


  By examining the deterministic limit of a general $\epsilon$-dependent
generator for Markovian dynamics, which includes the continuous Fokker-Planck
equations and discrete chemical master equations as two special cases, the
intrinsic connections among mesoscopic stochastic dynamics, deterministic ODEs
or PDEs, large deviations rate function, and macroscopic thermodynamic
potential are established. Our result not only solves the long-lasting question
on the origin of entropy function in classical irreversible thermodynamics, but
also reveals an emergent feature that arises automatically during the
deterministic limit, through its large deviations rate function, with both
time-reversible dynamics equipped with a Hamiltonian function and
time-irreversible dynamics equipped with an entropy function.


  We performed a series of direct N-body simulations with the aim to follow the
dynamical evolution of a galaxy cluster (GC) ($M_{clus}\simeq 10^{14}
M_{\odot}$) in different environment. The results show the formation of heavy
sub-structures in the cluster centre in consequence of multiple merging among
the innermost galaxies. Moreover we investigate the dynamics of super-massive
black holes (SMBHs) residing in the centre of galaxies that form the most
massive sub-structure.


  The article is devoted to the construction of explicit one-step numerical
methods with the strong orders of convergence 2.0, 2,5, and 3.0 for Ito
stochastic differential equations with multidimensional non-commutative noise.
We consider the numerical methods based on the unified Taylor-Ito and
Taylor-Stratonovich expansions. For numerical modeling of iterated Ito and
Stratonovich stochastic integrals of multiplicities 1 to 6 we appling the
method of multiple Fourier-Legendre series converging in the sense of norm in
Hilbert space $L_2([t, T]^k),$ $k=1,\ldots,6$. The article is addressed to
engineers who use numerical modeling in stochastic control and for solving the
non-linear filtering problem. The article can be interesting for the
mathematicians who working in the field of high-order strong numerical methods
for Ito stochastic differential equations.


  Fluorescence microscopy is a quintessential tool for observing cells and
understanding the underlying mechanisms of life-sustaining processes of all
living organisms. The problem of extracting 3D shape of mitochondria from
fluorescence microscopy images remains unsolved due to the complex and varied
shapes expressed by mitochondria and the poor resolving capacity of these
microscopes. We propose an approach to bridge this gap by learning a shape
prior for mitochondria termed as MiShape, by leveraging high-resolution
electron microscopy data. MiShape is a generative model learned using implicit
representations of mitochondrial shapes. It provides a shape distribution that
can be used to generate infinite realistic mitochondrial shapes. We demonstrate
the representation power of MiShape and its utility for 3D shape reconstruction
given a single 2D fluorescence image or a small 3D stack of 2D slices. We also
showcase applications of our method by deriving simulated fluorescence
microscope datasets that have realistic 3D ground truths for the problem of 2D
segmentation and microscope-to-microscope transformation.


  We define a functor $\rr^\ast$ from the category of positively determined
modules to the category of squarefree modules which plays the role of passing
from a monomial ideal to its radical. By using this functor, we generalize
several results on properties that are shared by a monomial ideal and its
radical. Moreover, we study the connection of $\rr^\ast$ to the Alexander
duality and Auslander-Reiten translate functor.


  A time-dependent emission model for blazar jets, taking acceleration due to
Fermi-I and Fermi-II processes for electrons and protons as well as all
relevant radiative processes self-consistently into account, is presented. The
presence of highly relativistic protons within the jet extends the simple
synchrotron self-Compton case not only in the very high energy radiation of
blazars, but also in the X-ray regime, introducing non-linear behaviour in the
emitting region of the model by photon-meson production and emerging electron
positron pair cascades. We are able to investigate the variability patterns of
blazars in terms of our model in all energy bands, thus narrowing down the
parameters used. The blazar 1 ES 1011+496 serves as an example of how this
model is applied to high frequency peaked BL Lac Objects in the presence of
non-thermal protons within the jet. Typical multiband patterns are derived,
which are experimentally accessible.