  In this paper we propose a possible explanation of the active neutrino
Majorana masses with the TeV scale new physics which also provide a dark matter
candidate. We extend the Standard Model (SM) with a local U(1)' symmetry and
introduce a seesaw relation for the vacuum expectation values (VEVs) of the
exotic scalar singlets, which break the U(1)' spontaneously. The larger VEV is
responsible for generating the Dirac mass term of the heavy neutrinos, while
the smaller for the Majorana mass term. As a result active neutrino masses are
generated via the modified inverse seesaw mechanism. The lightest of the new
fermion singlets, which are introduced to cancel the U(1)' anomalies, can be a
stable particle with ultra flavor symmetry and thus a plausible dark matter
candidate. We explore the parameter space with constraints from the dark matter
relic abundance and dark matter direct detection.


  Ulf Rehmann and Jun Morita, in their 1989 paper "A Matsumoto-type theorem for
Kac-Moody groups", gave a presentation of $K_2(A,F)$ for any generalised Cartan
matrix $A$ and field $F$. The purpose of this paper is to use this presentation
to compute $K_2(A,F)$ more explicitly in the case when $A$ is hyperbolic. In
particular, we shall show that these $K_2(A,F)$ can always be expressed as a
product of quotients of $K_2(F)$ and $K_2(2,F)$. Along the way, we shall also
prove a similar result in the case when $A$ has an odd entry in each column.


  In this paper we consider the overdetermined boundary problem for a general
second order semilinear elliptic equation on bounded domains of $\mathbf{R}^n$,
where one prescribes both the Dirichlet and Neumann data of the solution. We
are interested in the case where the data are not necessarily constant and
where the coefficients of the equation can depend on the position, so that the
overdetermined problem does not generally admit a radial solution. Our main
result is that, nevertheless, under minor technical hypotheses nontrivial
solutions to the overdetermined boundary problem always exist.


  A two-phase beamforming solution for secure communication using untrusted
relay nodes is presented. To thwart eavesdropping attempts of relay nodes, we
deliberately introduce artificial noise in the source message. After pointing
out the incongruity in evaluating secrecy rate in our model for certain
scenarios, we provide an SNR based frame work for secure communication. We
intend to bring down the SNR at each of the untrusted relay nodes below a
certain predefined threshold, whereas, using beamforming we want to boost the
SNR at the destination. With this motive optimal scaling vector is evaluated
for beamforming phase which not only nullifies the artificial noise transmitted
initially, but also maximizes the SNR at the destination. We discuss both the
total and individual power constraint scenarios and provide analytical solution
for both of them.


  Gamma-ray bursts (GRB) are short and intense bursts of $\sim$100 keV$-$1MeV
photons, usually followed by long-lasting decaying afterglow emission in a wide
range of electromagnetic wavelengths from radio to X-ray and, sometimes, even
to GeV gamma-rays. These emissions are believed to originate from a
relativistic jet, which is driven due to the collapse of special massive stars
and the mergers of compact binaries (i.e., double neutron stars or a neutron
star and a black hole). This chapter first briefly introduces the basic
observational facts of the GRB phenomena, including the prompt emission,
afterglow emission, and host galaxies. Secondly, a general theoretical
understanding of the GRB phenomena is described based on a relativistic jet's
overall dynamical evolution, including the acceleration, propagation, internal
dissipation, and deceleration phases. Here a long-lasting central engine of the
GRBs can substantially influence the dynamical evolution of the jet. In
addition, a supernova/kilonova emission can appear in the optical afterglow of
some nearby GRBs, which can provide an important probe to the nature of the GRB
progenitors. Finally, as luminous cosmological phenomena, it is expected to use
GRBs to probe the early universe and to constrain the cosmological parameters.


  Normalized exponential sums are entire functions of the form
  $$
  f(z)=1+H_1e^{w_1z}+\cdots+H_ne^{w_nz},
  $$ where $H_1,\ldots, H_n\in\C$ and $0<w_1<\ldots<w_n$. It is known that the
zeros of such functions are in finitely many vertical strips $S$. The
asymptotic number of the zeros in the union of all these strips was found by R.
E. Langer already in 1931. In 1973, C. J. Moreno proved that there are zeros
arbitrarily close to any vertical line in any strip $S$, provided that
$1,w_1,\ldots,w_n$ are linearly independent over the rational numbers. In this
study the asymptotic number of zeros in each individual vertical strip is found
by relying on R. J. Backlund's lemma, which was originally used to study the
zeros of the Riemann $\zeta$-function. As a counterpart to Moreno's result, it
is shown that almost every vertical line meets at most finitely many small
discs around the zeros of $f$.


  In the present review we discuss the past and present status of the
interacting OB-type binary frequency. We critically examine the popular idea
that Be-stars and supergiant sgB[e] stars are binary evolutionary products. The
effects of rotation on stellar evolution in general, stellar population studies
in particular, and the link with binaries will be evaluated. Finally a
discussion is presented of massive double compact star binary mergers as
possible major sites of chemical enrichment of r-process elements and as the
origin of recent aLIGO GW events.


  Forecast constraints for a Symmetric Teleparallel Gravity model with a
$\Lambda$CDM background are made using forthcoming ground and space based
gravitational waves observatories. A Bayesian analysis resorting to generated
mock catalogs shows that LIGO is not expected to be able to distinguish this
model from $\Lambda$CDM, while both LISA and the ET will, with the ET
outperforming LISA. We also show that low redshift events are favored in order
to improve the quality of the constrains.


  State-of-the-art large language models (LLMs) are commonly deployed as online
services, necessitating users to transmit informative prompts to cloud servers,
thus engendering substantial privacy concerns. In response, we present
ConfusionPrompt, a novel private LLM inference framework designed to obfuscate
the server by: (i) decomposing the prompt into sub-prompts, and (ii) generating
pseudo prompts along with the genuine sub-prompts as input to the online LLM.
Eventually, the returned responses can be recomposed by the user to obtain the
final whole response. Such designs endows our framework with advantages over
previous protocols that (i) it can be seamlessly integrated with existing
black-box LLMs, and (ii) it achieves significantly better privacy-utility
trade-off than existing text perturbation-based methods. We develop a
$(\lambda, \mu, \rho)$-privacy model to formulate the requirement for a
privacy-preserving group of prompts, and provide a complexity analysis,
affirming ConfusionPrompt's efficiency. Our empirical evaluation reveals that
our method offers significantly higher utility compared to local inference
methods using open-source models and perturbation-based techniques, while also
requiring much less memory than open-source LLMs.


  We study a one-dimensional system that consists of an electron gas coupled to
a spin-1/2 chain by Kondo interaction away from half-filling. We show that
zero-temperature transitions between phases with "small" and "large" Fermi
momenta can be continuous. Such a continuous but Fermi-momentum-changing
transition arises in the presence of spin anisotropy, from a Luttinger liquid
with a small Fermi momentum to a Kondo-dimer phase with a large Fermi momentum.
We have also added a frustrating next-nearest-neighbor interaction in the spin
chain to show the possibility of a similar Fermi-momentum-changing transition,
between the Kondo phase and a spin-Peierls phase, in the spin isotropic case.
This transition, however, appears to involve a region in which the two phases
coexist.


  Basic-block throughput models such as uiCA, IACA, GRANITE, Ithemal, llvm-mca,
OSACA, or CQA guide optimizing compilers and help performance engineers
identify and eliminate bottlenecks. For this purpose, basic-block throughput
models should ideally be fast, accurate, and interpretable.
  Recent advances have significantly improved accuracy: uiCA, the
state-of-the-art model, achieves an error of about 1% relative to measurements
across a wide range of microarchitectures. The computational efficiency of
throughput models, which is equally important for widespread adoption,
especially in compilers, has so far received little attention.
  In this paper, we introduce Facile, an analytical throughput model that is
fast, accurate, and interpretable. Facile analyzes different potential
bottlenecks independently and analytically. Due to its compositional nature,
Facile's predictions directly pinpoint the bottlenecks. We evaluate Facile on a
wide range of microarchitectures and show that it is almost two orders of
magnitude faster than existing models while achieving state-of-the-art
accuracy.


  The original Ando-Hiai and Golden-Thompson inequalities present comparisons
for the operator geometric mean $\sharp_v$ when $0\leq v\leq 1.$ Our main
target in this article is to study these celebrated inequalities for means
other than the geometric mean and for the geometric mean when $v\not\in [0,1].$


  In this paper we provide a solvability criterion for the monomial equation
$x^q=a$ over $Q_p$ for any natural number $q$.


  We present the results of a calculation of recombination coefficients for
O^{2+} + e^- using an intermediate coupling treatment that fully accounts for
the dependence of the distribution of population among the ground levels of
O^{2+} on electron density and temperature. The calculation is extended down to
low electron temperatures where dielectronic recombination arising from Rydberg
states converging on the O^{2+} ground levels is an important process. The
data, which consist of emission coefficients for 8889 recombination lines and
recombination coefficients for the ground and metastable states of O^+ are in
Cases A, B and C, and are organised as a function of the electron temperature
and number density, as well as wavelength. An interactive fortran 77 data
server is also provided as an accessory for mining the line emission
coefficients and obtaining Lagrange interpolated values for any choice of the
two variables between the explicitly provided values for any set of
wavelengths. Some illustrations of the application of the new data to nebular
observations are also provided.


  We investigate adaptive single-trial error/erasure decoding of binary codes
whose decoder is able to correct e errors and t erasures if le+t<=d-1. Thereby,
d is the minimum Hamming distance of the code and 1<l<=2 is the tradeoff
parameter between errors and erasures. The error/erasure decoder allows to
exploit soft information by treating a set of most unreliable received symbols
as erasures. The obvious question here is, how this erasing should be
performed, i.e. how the unreliable symbols which must be erased to obtain the
smallest possible residual codeword error probability are determined. In a
previous paper, we answer this question for the case of fixed erasing, where
only the channel state and not the individual symbol reliabilities are taken
into consideration. In this paper, we address the adaptive case, where the
optimal erasing strategy is determined for every given received vector.


  A selection of ultracool dwarfs are known to be radio active, with both
gyrosynchrotron emission and the electron cyclotron maser instability being
given as likely emission mechanisms. To explore whether ultracool dwarfs
previously undetected at 8.5 GHz may be detectable at a lower frequency. We
select a sample of fast rotating ultracool dwarfs with no detectable radio
activity at 8.5 GHz, observing each of them at 4.9 GHz. From the 8 dwarfs in
our sample, we detect emission from 2MASS J07464256+2000321, with a mean flux
level of 286 $\pm$ 24 $\mu Jy$. The light-curve of 2MASS J07464256+2000321, is
dominated towards the end of the observation by a very bright, $\approx $100 %
left circularly polarized burst during which the flux reached 2.4 mJy. The
burst was preceded by a raise in the level of activity, with the average flux
being $\approx$ 160 $\mu Jy$ in the first hour of observation rising to
$\approx$ 400 $\mu Jy$ in the 40 minutes before the burst. During both periods,
there is significant variability. The detection of 100% circular polarization
in the emission at 4.9 GHz points towards the electron cyclotron maser as the
emission mechanism. However, the observations at 4.9 GHz and 8.5 GHz were not
simultaneous, thus the actual fraction of dwarfs capable of producing radio
emission, as well as the fraction of those that show periodic pulsations is
still unclear, as indeed are the relative roles played by the electron
cyclotron maser instability versus gyrosynchrotron emission, therefore we
cannot assert if the previous non-detection at 8.5 GHz was due to a cut-off in
emission between 4.9 and 8.4 GHz, or due to long term variability.


  Based on the geometric-optics correspondence between the parameters of a
quasinormal mode and the conserved quantities along geodesics, we propose an
equation to calculate the typical shadow radius for asymptotically flat and
rotating black holes when viewed from the equatorial plane given by
\begin{equation}\notag \bar{R}_s=\frac{\sqrt{2}}{2}\left(\sqrt{\frac{
r_0^{+}}{f'(r)|_{r_0^{+}}}}+\sqrt{\frac{ r_0^{-}}{f'(r)|_{r_0^{-}}}}\right),
\end{equation} with $r_0^{\pm}$ being the radius of circular null geodesics for
the corresponding mode. Furthermore we have explicitly related the shadow
radius to the real part of QNMs in the eikonal regime corresponding to the
prograde and retrograde mode, respectively. As a particular example, we have
computed the typical black hole shadow radius for some well known black hole
solutions including the Kerr black hole, Kerr-Newman black hole and higher
dimensional black hole solutions described by the Myers-Perry black hole.


  Gate instability/hysteresis in modulation-doped p-type AlGaAs/GaAs
heterostructures impedes the development of nanoscale hole devices, which are
of interest for topics from quantum computing to novel spin physics. We present
an extended study conducted using custom-grown, matched modulation-doped n-type
and p-type heterostructures, with/without insulated gates, aimed at
understanding the origin of the hysteresis. We show the hysteresis is not due
to the inherent `leakiness' of gates on p-type heterostructures, as commonly
believed. Instead, hysteresis arises from a combination of GaAs surface-state
trapping and charge migration in the doping layer. Our results provide insights
into the physics of Si acceptors in AlGaAs/GaAs heterostructures, including
widely-debated acceptor complexes such as Si-X. We propose methods for
mitigating the gate hysteresis, including poisoning the modulation-doping layer
with deep-trapping centers (e.g., by co-doping with transition metal species),
and replacing the Schottky gates with degenerately-doped semiconductor gates to
screen the conducting channel from GaAs surface-states.


  In crowdsourcing when there is a lack of verification for contributed
answers, output agreement mechanisms are often used to incentivize participants
to provide truthful answers when the correct answer is hold by the majority. In
this paper, we focus on using output agreement mechanisms to elicit effort, in
addition to eliciting truthful answers, from a population of workers. We
consider a setting where workers have heterogeneous cost of effort exertion and
examine the data requester's problem of deciding the reward level in output
agreement for optimal elicitation. In particular, when the requester knows the
cost distribution, we derive the optimal reward level for output agreement
mechanisms. This is achieved by first characterizing Bayesian Nash equilibria
of output agreement mechanisms for a given reward level. When the requester
does not know the cost distribution, we develop sequential mechanisms that
combine learning the cost distribution with incentivizing effort exertion to
approximately determine the optimal reward level.


  We prove a number of results involving categories enriched over
\textsc{CMet}, the category of complete metric spaces with possibly infinite
distances. The category \textsc{CPMet} of intrinsic complete metric spaces is
locally $\aleph_1$-presentable, closed monoidal, and comonadic over
\textsc{CMet}. We also prove that the category \textsc{CCMet} of convex
complete metric spaces is not closed monoidal and characterize the
isometry-$\aleph_0$-generated objects in \textsc{CMet}, \textsc{CPMet} and
\textsc{CCMet}, answering questions by Di Liberti and Rosick\'{y}. Other
results include the automatic completeness of a colimit of bi-Lipschitz
morphisms of complete metric spaces and a characterization of those pairs
(metric space, unital $C^*$-algebra) that have a tensor product in the
\textsc{CMet}-enriched category of unital $C^*$-algebras.


  Hyperspectral images (HSIs) often suffer from noise arising from both
intra-imaging mechanisms and environmental factors. Leveraging domain knowledge
specific to HSIs, such as global spectral correlation (GSC) and non-local
spatial self-similarity (NSS), is crucial for effective denoising. Existing
methods tend to independently utilize each of these knowledge components with
multiple blocks, overlooking the inherent 3D nature of HSIs where domain
knowledge is strongly interlinked, resulting in suboptimal performance. To
address this challenge, this paper introduces a spatial-spectral recurrent
transformer U-Net (SSRT-UNet) for HSI denoising. The proposed SSRT-UNet
integrates NSS and GSC properties within a single SSRT block. This block
consists of a spatial branch and a spectral branch. The spectral branch employs
a combination of transformer and recurrent neural network to perform recurrent
computations across bands, allowing for GSC exploitation beyond a fixed number
of bands. Concurrently, the spatial branch encodes NSS for each band by sharing
keys and values with the spectral branch under the guidance of GSC. This
interaction between the two branches enables the joint utilization of NSS and
GSC, avoiding their independent treatment. Experimental results demonstrate
that our method outperforms several alternative approaches. The source code
will be available at https://github.com/lronkitty/SSRT.


  Although the roles of data centers and computing centers are becoming more
and more important, and on-line research is becoming the mainstream for
astronomy, individual research based on locally hosted data is still very
common. With the increase of personal storage capacity, it is easy to find
hundreds to thousands of FITS files in the personal computer of an
astrophysicist. Because Flexible Image Transport System (FITS) is a
professional data format initiated by astronomers and used mainly in the small
community, data management toolkits for FITS files are very few. Astronomers
need a powerful tool to help them manage their local astronomical data.
Although Virtual Observatory (VO) is a network oriented astronomical research
environment, its applications and related technologies provide useful solutions
to enhance the management and utilization of astronomical data hosted in an
astronomer's personal computer. FITSManager is such a tool to provide
astronomers an efficient management and utilization of their local data,
bringing VO to astronomers in a seamless and transparent way. FITSManager
provides fruitful functions for FITS file management, like thumbnail, preview,
type dependent icons, header keyword indexing and search, collaborated working
with other tools and online services, and so on. The development of the
FITSManager is an effort to fill the gap between management and analysis of
astronomical data.


  We introduce a class of time-inhomogeneous transition operators of
Feynman-Kac type that can be considered as a generalization of symmetric Markov
semigroups to the case of a time-dependent reference measure. Applying weighted
Poincar\'e and logarithmic Sobolev inequalities, we derive L^p-L^p and L^p-L^q
estimates for the transition operators. Since the operators are not Markovian,
the estimates depend crucially on the value of p. Our studies are motivated by
applications to sequential Markov Chain Monte Carlo methods.


  A significant hurdle in developing high-performance semiconductor quantum
technologies utilizing deep defects is related to charge dynamics.
Unfortunately, progress in modeling their charge dynamics has been hindered
over recent decades due to the absence of appropriate multiscale models capable
of accurately representing the atomic properties of these defects and their
impact on device performance. Here, we present a semi-\textit{ab initio} method
for modeling the bound states of deep defects in semiconductor quantum
technologies, applied to the negatively charged nitrogen vacancy (NV$^-$)
center in diamond. We employ density functional theory calculations to
construct accurate potentials for an effective mass model, which allow us to
unveil the structure of the bound hole states. We develop a model to calculate
the nonradiative capture cross sections, which agrees with experiment within
one order of magnitude. Finally, we present our attempt at constructing the
photoionization spectrum of NV$^0\rightarrow$ NV$^-$ + bound hole, showing that
the electronic transitions of the bound holes can be distinguished from phonon
sidebands. This paper offers a practical and efficient solution to a
long-standing challenge in understanding the charge dynamics of deep defects.


  The principles of creation of the mechanics of structured particles in the
frame of the Newton's laws are considered. The explanation how this mechanics
leads to the account of dissipative forces is offered. Why the motions of the
system determine by two type of symmetry: symmetry of the system and symmetry
of space and how it leads to two types of energy and forces accordingly are
discussed. How the mechanics of the structured particles leads to
thermodynamics, statistical physics and kinetics are explained.


  Integrating the reconfigurable intelligent surface (RIS) into a cell-free
massive multiple-input multiple-output (CF-mMIMO) system is an effective
solution to achieve high system capacity with low cost and power consumption.
However, existing works of RIS-assisted systems mostly assumed perfect
hardware, while the impact of hardware impairments (HWIs) is generally ignored.
In this paper, we consider the general Rician fading channel and uplink
transmission of the RIS-assisted CF-mMIMO system under transceiver impairments
and RIS phase noise. To reduce the feedback overhead and power consumption, we
propose a two-timescale transmission scheme to optimize the passive beamformers
at RISs with statistical channel state information (CSI), while transmit
beamformers at access points (APs) are designed based on instantaneous CSI.
Also, the maximum ratio combining (MRC) detection is applied to the central
processing unit (CPU). On this basis, we derive the closed-form approximate
expression of the achievable rate, based on which the impact of HWIs and the
power scaling laws are analyzed to draw useful theoretical insights. To
maximize the users' sum rate or minimum rate, we first transform our rate
expression into a tractable form, and then optimize the phase shifts of RISs
based on an accelerated gradient ascent method. Finally, numerical results are
presented to demonstrate the correctness of our derived expressions and
validate the previous analysis, which provide some guidelines for the practical
application of the imperfect RISs in the CF-mMIMO with transceiver HWIs.


  We develop a model for the weak pion production off the nucleon, which
besides the Delta pole mechanism (weak excitation of the $\Delta(1232)$
resonance and its subsequent decay into $N\pi$), includes also some background
terms required by chiral symmetry. We re-fit the $C_5^A(q^2)$ form factor to
the flux averaged $\nu_\mu p \to \mu^-p\pi^+$ ANL $q^2-$differential cross
section data, finding a substantially smaller contribution of the Delta pole
mechanism than traditionally assumed in the literature. Within this scheme, we
calculate several differential and integrated cross sections, including pion
angular distributions, induced by neutrinos and antineutrinos and driven both
by charged and neutral currents. In all cases we find that the background terms
produce quite significant effects and that they lead to an overall improved
description of the data, as compared to the case where only the Delta pole
mechanism is considered. We also show that the interference between the Delta
pole and the background terms produces parity-violating contributions to the
pion angular differential cross section, which are intimately linked to $T-$odd
correlations in the contraction between the leptonic and hadronic tensors.
However, these latter correlations do not imply a genuine violation of time
reversal invariance because of the existence of strong final state interaction
effects.


  Phase estimation is a major mission in quantum metrology. In the
finite-dimensional Fock space the NOON state ceases to be optimal when the
particle number is fixed yet not equal to the space dimension minus one, and
what is the true optimal state in this case is still undiscovered. Hereby we
present three theorems to answer this question and provide a complete optimal
scheme to realize the ultimate precision limit in practice. These optimal
states reveal an important fact that the space dimension could be treated as a
metrological resource, and the given scheme is particularly useful in scenarios
where weak light or limited particle number is demanded.


  We report on time-resolved optical and terahertz ultrafast spectroscopy of
charge-carrier dynamics in the room-temperature antiferromagnetic semiconductor
$\alpha $-MnTe. By optically pumping the system with 1.55 eV photons at room
temperature, we excite charge carriers in the conduction band through the
indirect band gap and investigate the dynamical response of nonequilibrium
states using optical as well as terahertz transmission probes. Three relaxation
processes are revealed by their characteristic relaxation times of the order of
1, 10, and 100~ps, whose exact values are functions of the pump fluence. For
high pump fluences nonlinear dependence on the pump fluence is observed both in
the optical and terahertz probes.


  A three-dimensional, steady, laminar shear-layer flow spatially developing
under a boundary-layer approximation with mixing, chemical reaction, and
imposed normal strain is analyzed. The imposed strain creates a counterflow
that stretches the vorticity in the spanwise direction. The equations are
reduced to a two-dimensional form for three velocity components. The
non-reactive and reactive cases of the two-dimensional form of the governing
equations are solved numerically, with consideration of the several of
parameter inputs such as Damk\"ohler number, Prandtl number, chemical
composition, and free-stream velocity ratios. The analysis of the non-reactive
case focuses on the mixing between hotter gaseous oxygen and cooler gaseous
propane. The free-stream strain rate \kappa is predicted by ordinary
differential equations based upon the imposed spanwise pressure variation.
One-step chemical kinetics are used to describe diffusion flames and
multi-flame structures. The imposed normal strain rate has a significant effect
on the width of downstream mixing layers as well as the burning rate.
Asymptotically in the downstream direction, a constant width of the shear layer
is obtained if imposed normal strain rate is constant. A similar solution with
layer width growing with the square root of downstream distance is found when
imposed strain rate decreases as the reciprocal of downstream distance.


  We report a technique which allows self-assembly of conducting nanoparticles
into long continuous chains. Transport properties of such chains have been
studied at low temperatures. At low bias voltages, the charges are pinned and
the chain resistance is exponentially high. Above a certain threshold
($V_{T}$), the system enters a conducting state. The threshold voltage is much
bigger than the Coulomb gap voltage for a single particle and decreases
linearly with increasing temperature. A sharp threshold was observed up to
about 77 K. Such chains may be used as switchable links in Coulomb charge
memories.


  We consider the problem of efficiently constructing polar codes over binary
memoryless symmetric (BMS) channels. The complexity of designing polar codes
via an exact evaluation of the polarized channels to find which ones are "good"
appears to be exponential in the block length. In \cite{TV11}, Tal and Vardy
show that if instead the evaluation if performed approximately, the
construction has only linear complexity. In this paper, we follow this approach
and present a framework where the algorithms of \cite{TV11} and new related
algorithms can be analyzed for complexity and accuracy. We provide numerical
and analytical results on the efficiency of such algorithms, in particular we
show that one can find all the "good" channels (except a vanishing fraction)
with almost linear complexity in block-length (except a polylogarithmic
factor).


  Let ${\bf A}={\bf A}_{n,m,k}$ be a random $n\times m$ matrix over
$\mathbf{GF}_2$ wher each column consists of $k$ randomly chosen ones. Let $M$
be an arbirary fixed binary matroid. We show that if $m/n$ and $k$ are
sufficiently large then as $n\to\infty$ the binary matroid induced by {\bf A}
contains $M$ as a minor.


  Higher-order non-holomorphic Eisenstein series associated to a Fuchsian group
$\Gamma$ are defined by twisting the series expansion for classical
non-holomorphic Eisenstein series by powers of modular symbols. Their
functional identities include multiplicative and additive factors, making them
distinct from classical Eisenstein series. Here we prove the meromorphic
continuation of these series and establish their functional equations. In
addition, we construct high rank vector bundles $\cal V$ from certain unipotent
representations $\pi$ of $\Gamma$ and show that higher-order non-holomorphic
Eisenstein series can be viewed as components of certain eigensections,
$\mathbb E$, of $\cal V$. With this viewpoint the functional identities of
these higher-order series are formally identical to the classical case. Going
further, we prove bounds for the Fourier coefficients of the higher-order
non-holomorphic Eisenstein series.


  We review some of the significant generalizations and applications of the
celebrated Douglas theorem on the equivalence of factorization, range
inclusion, and majorization of operators. We then apply it to find a
characterization of the positivity of $2\times 2$ block matrices of operators
in Hilbert spaces and finally describe the nature of such block matrices and
provide several ways for showing their positivity.


  We initiate the study of property testing of submodularity on the boolean
hypercube. Submodular functions come up in a variety of applications in
combinatorial optimization. For a vast range of algorithms, the existence of an
oracle to a submodular function is assumed. But how does one check if this
oracle indeed represents a submodular function?
  Consider a function f:{0,1}^n \rightarrow R. The distance to submodularity is
the minimum fraction of values of $f$ that need to be modified to make f
submodular. If this distance is more than epsilon > 0, then we say that f is
epsilon-far from being submodular. The aim is to have an efficient procedure
that, given input f that is epsilon-far from being submodular, certifies that f
is not submodular. We analyze a very natural tester for this problem, and prove
that it runs in subexponential time. This gives the first non-trivial tester
for submodularity. On the other hand, we prove an interesting lower bound (that
is, unfortunately, quite far from the upper bound) suggesting that this tester
cannot be very efficient in terms of epsilon. This involves non-trivial
examples of functions which are far from submodular and yet do not exhibit too
many local violations.
  We also provide some constructions indicating the difficulty in designing a
tester for submodularity. We construct a partial function defined on
exponentially many points that cannot be extended to a submodular function, but
any strict subset of these values can be extended to a submodular function.


  The Quantum Null Energy Condition (QNEC) is a new local energy condition that
a general Quantum Field Theory (QFT) is believed to satisfy, relating the
classical null energy condition (NEC) to the second functional derivative of
the entanglement entropy in the corresponding null direction. We present the
first series of explicit computations of QNEC in a strongly coupled QFT, using
holography. We consider the vacuum, thermal equilibrium, a homogeneous
far-from-equilibrium quench as well as a colliding system that violates NEC.
For vacuum and the thermal phase QNEC is always weaker than NEC. While for the
homogeneous quench QNEC is satisfied with a finite gap, we find the interesting
result that the colliding system can saturate QNEC, depending on the null
direction.


  We analyze the effect of the barrier motion on the Bose-Hubbard Hamiltonian
of a ring-shaped Bose-Einstein condensate interrupted by a pair of Josephson
junctions, a configuration which is the cold atom analog of the well-known dc
superconducting quantum interference device (SQUID). Such an effect is also
shown to modify the Heisenberg equation of motion of the boson field operator
in the two-mode approximation, where a hysteretic contribution that could
affect the dynamics for accelerated or overlapping barriers is identified. By
studying the energy landscape as a function of order and control parameters, we
determine the diagram with the location of the dc and ac Josephson regimes,
along with the critical points that are shown to depend on the junctions
position. We analyze the dc to ac Josephson transition for adiabatic barrier
trajectories that lead to a final uniform velocity, or which perform symmetric
velocity paths. We show that such symmetric trajectories may induce, when
reaching the critical point, highly hysteretic oscillating return paths within
the dc regime, similar to the underdamped hysteresis loops arising from the
action of a resistive flow in the ac regime. We also consider nonequilibrium
initial conditions resulting from a finite phase difference on either side of
the junctions, along with the critical features of such a parameter. An
excellent agreement between the Gross-Pitaevskii simulations and the two-mode
results is found in all cases.


  We study the thermal effects on the nuclear matter (NM) properties such as
binding energy, incompressibility, free symmetry energy and its coefficients
using NL3, G3 and IU-FSU parameter sets of relativistic mean-field models.
These models being consistent with the properties of cold NM, have also been
used to study the effect of temperature by incorporating the Fermi function.
The critical temperature for the liquid-gas phase transition in the symmetric
NM is found to be 14.60, 15.37 and 14.50 MeV for NL3, G3 and IU-FSU parameter
sets respectively, which is in excellent agreement with previous theoretical
and experimental studies. We inspect that the properties related to second
differential coefficient of the binding energy and free symmetry energy at
saturation density ( i.e. K 0 (n, T ) and Q sym,0) exhibit the contrary effects
for NL3 and G3 parameters as the temperature increases. We find that the
prediction of saturated curvature parameter ( K sym,0 ) for G3 equation of
state at finite temperature favour the combined analysis of K sym,0 for the
existence of massive pulsars, gravitational waves from GW170817 and NICER
observations of PSR J0030+0451. Further, we investigate the cooling mechanism
of newly born stars through neutrino emissivity controlled by direct Urca
process and instate some interesting remarks about neutrino emissivity. We also
deliberate the effect of temperature on the M-R profile of Proto-Neutron star.


  The Roper resonance is considered as a mixed state of a three-quark core
configuration and a hadron molecular component N+sigma. Based on this ansatz we
study electroproduction of the Roper resonance. The strong and electromagnetic
couplings induced by the quark core are calculated in the 3P0 model. The
contribution of the vector meson cloud to the electromagnetic transition is
given in the framework of the VMD model. Results are compared with the recent
JLab electroproduction data.


  The importance of radiomics features for predicting patient outcome is now
well-established. Early study of prognostic features can lead to a more
efficient treatment personalisation. For this reason new radiomics features
obtained through mathematical morphology-based operations are proposed. Their
study is conducted on an open database of patients suffering from Nonsmall
Cells Lung Carcinoma (NSCLC). The tumor features are extracted from the CT
images and analyzed via PCA and a Kaplan-Meier survival analysis in order to
select the most relevant ones. Among the 1,589 studied features, 32 are found
relevant to predict patient survival: 27 classical radiomics features and five
MM features (including both granularity and morphological covariance features).
These features will contribute towards the prognostic models, and eventually to
clinical decision making and the course of treatment for patients.


  In this paper we define cumulants for finite free convolution. We give a
moment-cumulant formula and show that these cumulants satisfy desired
properties: they are additive with respect to finite free convolution and they
approach free cumulants as the dimension goes to infinity.


  The model strongly correlated electron system Ho0.8Lu0.2B12 which
demonstrates a cooperative Jahn-Teller instability of the boron sub-lattice in
combination with rattling modes of Ho(Lu) ions, dynamic charge stripes and
unusual antiferromagnetic (AF) ground state has been studied in detail at low
temperatures by magnetoresistance, magnetization and heat capacity
measurements. Based on received results it turns out that the angular H-fi-T
magnetic phase diagrams of this non-equilibrium AF metal can be reconstructed
in the form of a Maltese cross. The dramatic AF ground state symmetry lowering
of this dodecaboride with fcc crystal structure can be attributed to the
redistribution of conduction electrons which leave the RKKY oscillations of the
electron spin density to participate in the dynamic charge stripes providing
with extraordinary changes in the indirect exchange interaction between
magnetic moments of Ho3+ ions and resulting in the emergence of a number of
various magnetic phases. It is also shown that the two main contributions to
magnetoresistance in the complex AF phase, the (i) positive linear on magnetic
field and the (ii) negative quadratic component can be separated and analyzed
quantitatively, correspondingly, in terms of charge carrier scattering on spin
density wave (5d) component of the magnetic structure and on local 4f-5d spin
fluctuations of holmium sites.


  Finding and designing ferromagnets that operate above room temperature is
crucial in advancing high-performance spintronic devices. The pioneering van
der Waals (vdW) ferromagnet Fe$_3$GaTe$_2$ has extended the way for spintronic
applications by achieving a record-high Curie temperature among its analogues.
However, the physical mechanism of increasing Cuire temperature still needs to
be explored. Here, we propose a practical approach to discovering
high-temperature ferromagnetic materials for spintronic applications through
flat band engineering. We simulate the magnetic transition directly from
strongly correlated calculations, reconciling the dual nature of $d$-electrons
with both localization and itinerant characters. Significantly, our systematic
studies unveil the emergence of quasi-particle flat bands arising from
collective many-body excitations preceding the ferromagnetic phase transition,
reinforcing magnetic stability through a positive feedback mechanism. This
research provides a promising pathway for exploring next-generation spintronic
devices utilizing low-dimensional vdW flat band systems.


  The idea of using measure theoretic concepts to investigate the size of
number theoretic sets, originating with E. Borel, has been used for nearly a
century. It has led to the development of the theory of metrical Diophantine
approximation, a branch of Number Theory which draws on a rich and broad
variety of mathematics. We discuss some recent progress and open problems
concerning this classical theory. In particular, generalisations of the
Duffin-Schaeffer and Catlin conjectures are formulated and explored.


  As gravitational-wave detectors become more sensitive, we will access a
greater variety of signals emitted by compact binary systems, shedding light on
their astrophysical origin and environment. A key physical effect that can
distinguish among formation scenarios is the misalignment of the spins with the
orbital angular momentum, causing the spins and the binary's orbital plane to
precess. To accurately model such systems, it is crucial to include multipoles
beyond the dominant quadrupole. Here, we develop the first multipolar
precessing waveform model in the effective-one-body (EOB) formalism for the
inspiral, merger and ringdown (IMR) of binary black holes: SEOBNRv4PHM. In the
nonprecessing limit, the model reduces to SEOBNRv4HM, which was calibrated to
numerical-relativity (NR) simulations, and waveforms from perturbation theory.
We validate SEOBNRv4PHM by comparing it to the public catalog of 1405
precessing NR waveforms of the Simulating eXtreme Spacetimes (SXS)
collaboration, and also to new 118 precessing NR waveforms, which span mass
ratios 1-4 and spins up to 0.9. We stress that SEOBNRv4PHM is not calibrated to
NR simulations in the precessing sector. We compute the unfaithfulness against
the 1523 SXS precessing NR waveforms, and find that, for $94\%$ ($57\%$) of the
cases, the maximum value, in the total mass range $20-200 M_\odot$, is below
$3\%$ ($1\%$). Those numbers become $83\%$ ($20\%$) when using the IMR,
multipolar, precessing phenomenological model IMRPhenomPv3HM. We investigate
the impact of such unfaithfulness values with two parameter-estimation studies
on synthetic signals. We also compute the unfaithfulness between those waveform
models and identify in which part of the parameter space they differ the most.
We validate them also against the multipolar, precessing NR surrogate model
NRSur7dq4, and find that the SEOBNRv4PHM model outperforms IMRPhenomPv3HM.


  We present the fifth release of the UMIST Database for Astrochemistry (UDfA).
The new reaction network contains 6173 gas-phase reactions, involving 467
species, 47 of which are new to this release. We have updated rate coefficients
across all reaction types. We have included 1171 new anion reactions and
updated and reviewed all photorates. In addition to the usual reaction network,
we also now include, for download, state-specific deuterated rate coefficients,
deuterium exchange reactions and a list of surface binding energies for many
neutral species. Where possible, we have referenced the original source of all
new and existing data. We have tested the main reaction network using a dark
cloud model and a carbon-rich circumstellar envelope model. We present and
briefly discuss the results of these models.


  We analyze the cross-over of a homogeneous one-dimensional Bose gas from the
ideal gas into the dense quasi-condensate phase. We review a number of
mean-field theories, perturbative or self-consistent, and provide accurate
evaluations of equation of state, density fluctuations, and correlation
functions. A smooth crossover is reproduced by classical-field simulations
based on the stochastic Gross-Pitaevskii equation, and the Yang-Yang solution
to the one-dimensional Bose gas.


  In this paper, we give an example of an autoequivalence with positive
categorical entropy (in the sense of Dimitrov, Haiden, Katzarkov and
Kontsevich) for any surface containing a (-2)-curve. Then we show that this
equivalence gives another counter-example to a conjecture proposed by Kikuta
and Takahashi. In a second part, we study the action on cohomology induced by
spherical twists composed with standard autoequivalences on a surface S and
show that their spectral radii correspond to the topological entropy of the
corresponding automorphisms of S.


  Addressing the ongoing examination of high-frequency trading practices in
financial markets, we report the results of an extensive empirical study
estimating the maximum possible profitability of the most aggressive such
practices, and arrive at figures that are surprisingly modest. By "aggressive"
we mean any trading strategy exclusively employing market orders and relatively
short holding periods. Our findings highlight the tension between execution
costs and trading horizon confronted by high-frequency traders, and provide a
controlled and large-scale empirical perspective on the high-frequency debate
that has heretofore been absent. Our study employs a number of novel empirical
methods, including the simulation of an "omniscient" high-frequency trader who
can see the future and act accordingly.


  A boson two--leg ladder in the presence of a synthetic magnetic flux is
investigated by means of bosonization techniques and Density Matrix
Renormalization Group (DMRG). We follow the quantum phase transition from the
commensurate Meissner to the incommensurate vortex phase with increasing flux
at different fillings. When the applied flux is $\rho \pi$ and close to it,
where $\rho$ is the filling per rung, we find a second incommensuration in the
vortex state that affects physical observables such as the momentum
distribution, the rung-rung correlation function and the spin-spin and
charge-charge static structure factors.


  A $\textit{regular polygon surface}$ $M$ is a surface graph $(\Sigma,
\Gamma)$ together with a continuous map $\psi$ from $\Sigma$ into Euclidean
3-space which maps faces to regular Euclidean polygons. When $\Sigma$ is
homeomorphic to the sphere and the degree of every face of $\Gamma$ is five, we
prove that $M$ can be realized as the boundary of a union of dodecahedra glued
together along common facets. Under the same assumptions but when the faces of
$\Gamma$ have degree four or eight, we prove that $M$ can be realized as the
boundary of a union of cubes and octagonal prisms glued together along common
facets. We exhibit counterexamples showing the failure of both theorems for
higher genus surfaces.


  Rydberg atom arrays have emerged as a novel platform exhibiting rich quantum
many-body physics and offering promise for universal quantum computation. The
Rydberg blockade effect plays an essential role in establishing many-body
correlations in this system. In this review, we will highlight that the lattice
gauge theory is an efficient description of the Rydberg blockade effect and
overview recent exciting developments in this system from equilibrium phases to
quantum dynamics. These developments include realizing exotic ground states
such as spin liquids, discovering quantum many-body scar states violating
quantum thermalization, and observing confinement-deconfinement transition
through quantum dynamics. We emphasize that the gauge theory description offers
a universal theoretical framework to capture all these phenomena. This
perspective of Rydberg atom arrays will inspire further the future development
of quantum simulation and quantum computation in this platform.


  We calculate the spectrum of elementary excitations in a two-dimensional
exciton superfluid in the vicinity of a two-dimensional electron gas. We show
that attraction of excitons due to their scattering with free electrons may
lead to formation of a roton minimum. The energy of this minimum may go below
the ground state energy which manifests breaking of the superfluidity. The
Berezinsky-Kosterlitz-Thouless phase transition temperature decreases due to
the exciton-exciton attraction mediated by electrons.


  We propose a novel approach to parameter estimation for simulator-based
statistical models with intractable likelihood. Our proposed method involves
recursive application of kernel ABC and kernel herding to the same observed
data. We provide a theoretical explanation regarding why the approach works,
showing (for the population setting) that, under a certain assumption, point
estimates obtained with this method converge to the true parameter, as
recursion proceeds. We have conducted a variety of numerical experiments,
including parameter estimation for a real-world pedestrian flow simulator, and
show that in most cases our method outperforms existing approaches.


  SMT-based program analysis and verification often involve reasoning about
program features that have been specified using quantifiers; incorporating
quantifiers into SMT-based reasoning is, however, known to be challenging. If
quantifier instantiation is not carefully controlled, then runtime and outcomes
can be brittle and hard to predict. In particular, uncontrolled quantifier
instantiation can lead to unexpected incompleteness and even non-termination.
E-matching is the most widely-used approach for controlling quantifier
instantiation, but when axiomatisations are complex, even experts cannot tell
if their use of E-matching guarantees completeness or termination.
  This paper presents a new formal model that facilitates the proof, once and
for all, that giving a complex E-matching-based axiomatisation to an SMT
solver, such as Z3 or cvc5, will not cause non-termination. Key to our
technique is an operational semantics for solver behaviour that models how the
E-matching rules common to most solvers are used to determine when quantifier
instantiations are enabled, but abstracts over irrelevant details of individual
solvers. We demonstrate the effectiveness of our technique by presenting a
termination proof for a set theory axiomatisation adapted from those used in
the Dafny and Viper verifiers.


  Equilibrium sequences were developed for rotating NS in the relativistic
mean-field interaction framework using four density-dependent equations of
state for the NS matter. These sequences were constructed for the observed
rotation frequencies of 25, 317, 346, 716, and 1122 Hz. The bounds of sequences
were calculated in each model to determine the stability region. The
gravitational mass, quadrupole moment, polar, forward and backward redshifts,
and Kerr parameter were calculated. DDF and DD-ME$\delta$ were unable to
properly describe the low-frequency neutron stars, PSR J0348+432, PSR
J1614-2230 , and PSR J0740+6620 rotate at a frequency of 25, 317, and 346 Hz,
respectively. All the selected EOSs properly described the rotation of PSR
J1748-244ad, and PSR J1739-285 at a frequency of 716 and 1122 Hz, respectively.
The mass of these stars was in the range of [0.68, 2.14]M$_{\odot}$ and [1.67,
2.24]M$_{\odot}$, respectively. The polar, forward and backward redshifts, and
the quadrupole moment were calculated in all selected rotating frequencies and
the Keplerian sequence. The results were consistent with observations.
Confirming the mass of $1.5^{+0.4}_{-1.0}M_{\odot}$ for EXO 0748-676, our
result will be close to the observed value, and the EOSs used in this study
properly describe this star. The extremum of Kerr parameter, polar, forward and
backward redshifts in all models reached constant values of, a/M$\approx$ 0.7,
Z$_{p}\approx$ 0.8, Z$_{eq}^{f}\approx$ -0.3 and Z$_{eq}^{b}\approx$ 2.2. These
behaviors of redshifts and Kerr parameter are approximately independent of EOS.
The observed behaviors must evaluate by other EOSs to find universal relations
for these quantities. Also, a limit value was found for each of these
parameters. In this case where these parameters are greater than the limit
value, the star can rotate at a frequency equal to or greater than $\nu$= 1122
Hz.


  We show how the coupling of gravitinos and gauginos to fluxes modifies
anomaly cancellation in M-theory on a manifold with boundary. Anomaly
cancellation continues to hold, after a shift of the definition of the gauge
currents by a local gauge invariant expression in the curvatures and E8
fieldstrengths. We compute the first nontrivial correction of this kind.
Warning: Ian Moss has called into question several of the numerical
coefficients in the extended Dirac operators in this paper. We have not
confirmed this but the reader is warned not to trust the precise coefficients
in the formulae for the Dirac operators and heat kernel expansions. We believe
these possible errors do not change our qualitative conclusions. One of us
intends to return to the issue and recheck the formulae. We thank Ian Moss for
pointing out these problems.


  While various deep learning methods have been proposed for low-dose computed
tomography (CT) denoising, most of them leverage the normal-dose CT images as
the ground-truth to supervise the denoising process. These methods typically
ignore the inherent correlation within a single CT image, especially the
anatomical semantics of human tissues, and lack the interpretability on the
denoising process. In this paper, we propose a novel Anatomy-aware Supervised
CONtrastive learning framework, termed ASCON, which can explore the anatomical
semantics for low-dose CT denoising while providing anatomical
interpretability. The proposed ASCON consists of two novel designs: an
efficient self-attention-based U-Net (ESAU-Net) and a multi-scale anatomical
contrastive network (MAC-Net). First, to better capture global-local
interactions and adapt to the high-resolution input, an efficient ESAU-Net is
introduced by using a channel-wise self-attention mechanism. Second, MAC-Net
incorporates a patch-wise non-contrastive module to capture inherent anatomical
information and a pixel-wise contrastive module to maintain intrinsic
anatomical consistency. Extensive experimental results on two public low-dose
CT denoising datasets demonstrate superior performance of ASCON over
state-of-the-art models. Remarkably, our ASCON provides anatomical
interpretability for low-dose CT denoising for the first time. Source code is
available at https://github.com/hao1635/ASCON.


  Instead of developing a customized typed lambda-calculus for each theory, we
attempt to design a general parametric calculus that permits to express the
proofs of any theory. This way, the problem of expressing proofs in the
lambda-calculus is separated from that of choosing a theory.


  The nonmodal linear stability of the Schwarzschild black hole established in
Phys. Rev. Lett. 112 (2014) 191101 is generalized to the case of a nonnegative
cosmological constant $\Lambda$. Two gauge invariant combinations $G_{\pm}$ of
perturbed scalars made out of the Weyl tensor and its first covariant
derivative are found such that the map $[h_{\alpha \beta}] \to \left( G_-
\left([h_{\alpha \beta}] \right), G_+ \left([h_{\alpha \beta}] \right) \right)$
with domain the set of equivalent classes $[h_{\alpha \beta}]$ under gauge
transformations of solutions of the linearized Einstein's equation, is
invertible. The way to reconstruct a representative of $[h_{\alpha \beta}]$ in
terms of $(G_-,G_+)$ is given. It is proved that, for an arbitrary perturbation
consistent with the background asymptote, $G_+$ and $G_-$ are bounded in the
the outer static region. At large times, the perturbation decays leaving a
linearized Kerr black hole around the Schwarzschild or Schwarschild de Sitter
background solution. For negative cosmological constant it is shown that there
is a choice of boundary conditions at the time-like boundary under which the
Schwarzschild anti de Sitter black hole is unstable. The root of
Chandrasekhar's duality relating odd and even modes is exhibited, and some
technicalities related to this duality and omitted in the original proof of the
$\Lambda=0$ case are explained in detail.


  Electromagnetic Star-Planet Interaction (SPI) describes the phenomenon, when
a planet couples to its host star via electromagnetic forces. Alfv\'en waves
can establish such a coupling by forming Alfv\'en wings. SPI allows phenomena
that we do not know from the Solar System. Wing-wing interaction is such an
example, where the Alfv\'en wings of two planets merge and interact
non-linearly. In this paper we focus on the effects that SPI has on other
planets and the stellar wind. First, we analyse the different wave structures
connected to SPI. The second part then investigates wing-wing interaction. Our
study applies a magnetohydrodynamic model to describe a stellar system with
multiple possible planets. As an example, we chose TRAPPIST-1 and its two
innermost planets. We extended the PLUTO code to simulate collisions between
atmospheric neutral particles and plasma ions. Neutral gas clouds imitate the
planets and move through the simulation domain. That allows the simulation of
fully time-dependent stellar systems. We analysed the wave structures, which
result from the interaction between stellar wind and TRAPPIST-1 b. The inward
going wave structure is an Alfv\'en wing. The outward going part of the
interaction consists of an Alfv\'en wing, slow mode waves, the planetary wake
and a slow shock. We quantified the strength of the respective wave
perturbations at the outer planets to be on the order of 10\% to 40\% of the
local background values of thermal, magnetic and dynamic pressure. Wing-wing
interaction occurs due to the relative position of two planets during their
conjunction and shows three phases. First there is an initial, non-linear
intensification of the Poynting flux by $20\%$, an intermediate phase with
reduced Poynting flux and a third phase when the Alfv\'en wing of planet c goes
through planet b's wave structures with another intensification of the Poynting
flux.


  Bright Ar K-shell x-ray with very little background has been generated using
an Ar clustering gas jet target irradiated with an 800 mJ, 30 fs ultra-high
contrast laser, with the measured flux of 1.1 x 10^4 photons/mrad^2/pulse. This
intense x-ray source critically depends on the laser contrast and the laser
energy and the optimization of this source with interaction is addressed.
Electron driven by laser electric field directly via nonlinear resonant is
proved in simulation, resulting in effective electron heating and the
enhancement of x-ray emission. The x-ray pulse duration is demonstrated to be
only 10 fs, as well as a source size of 20 um, posing great potential
application for single-shot ultrafast x-ray imaging.


  An analysis of radiative decays of the neutrinos $\nu_j\to \nu_l \gamma$ is
discussed in MSSM extensions with a vector like lepton generation. Specifically
we compute neutrino decays arising from the exchange of charginos and charged
sleptons where the photon is emitted by the charged particle in the loop. It is
shown that while the lifetime of the neutrino decay in the Standard Model is
$\sim 10^{43}$ yrs for a neutrino mass of 50 meV, the current lower limit from
experiment from the analysis of the Cosmic Infrared Background is $\sim
10^{12}$ yrs and thus beyond the reach of experiment in the foreseeable future.
However, in the extensions with a vector like lepton generation the lifetime
for the decays can be as low as $\sim 10^{12}- 10^{14}$ yrs and thus within
reach of future improved experiments. The effect of CP phases on the neutrino
lifetime is also analyzed. It is shown that while both the magnetic and the
electric transition dipole moments contribute to the neutrino lifetime, often
the electric dipole moment dominates even for moderate size CP phases.


  Based on the Veneziano ghost theory of QCD, we estimate the cosmological
constant $\Lambda$, which is related to the vacuum energy density,
$\rho_{\Lambda}$, by $\Lambda = 8\pi G \rho_{\Lambda}$. In the recent Veneziano
ghost theory $\rho_{\Lambda}$ is given by the absolute value of the product of
the local quark condensate and quark current mass:$\rho_{\Lambda} =
\frac{2N_{f}H}{m_{\eta'}}c |m_{q}<0|:\bar{q}q:|0>|$. By solving Dyson-Schwinger
Equations for a dressed quark propagator, we found the local quark condensate
$<0|:\bar{q}q:|0> \simeq -(235 MeV)^{3}$, the generally accepted value. The
quark current mass is $m_{q} \simeq$ 4.0 Mev. This gives the same result for
$\rho_{\Lambda}$ as found by previous authors, which is somewhat larger than
the observed value. However, when we make use of the nonlocal quark condensate,
$<0|:\bar{q}(x)q(0):|0>= g(x)<0|:\bar{q}q:|0>$, with g(x) estimated from our
previous work, we find $\Lambda$ is in a good agreement with the observations.


  We propose a simple rule of thumb for countries which have embarked on a
vaccination campaign while still facing the need to keep non-pharmaceutical
interventions (NPI) in place because of the ongoing spread of SARS-CoV-2. If
the aim is to keep the death rate from increasing, NPIs can be loosened when it
is possible to vaccinate more than twice the growth rate of new cases. If the
aim is to keep the pressure on hospitals under control, the vaccination rate
has to be about four times higher. These simple rules can be derived from the
observation that the risk of death or a severe course requiring hospitalization
from a COVID-19 infection increases exponentially with age and that the sizes
of age cohorts decrease linearly at the top of the population pyramid.
Protecting the over 60-year-olds, which constitute approximately one-quarter of
the population in Europe (and most OECD countries), reduces the potential loss
of life by 95 percent.


  The COVID-19 pandemic has significantly transformed the healthcare sector,
with telehealth services being among the most prominent changes. The adoption
of telehealth services, however, has raised new challenges, particularly in the
areas of security and privacy. To better comprehend the telehealth needs and
concerns of medical professionals, particularly those in private practice, we
conducted a study comprised of 20 semi-structured interviews with telehealth
practitioners in audiology and speech therapy. Our findings indicate that
private telehealth practitioners encounter difficult choices when it comes to
balancing security, privacy, usability, and accessibility, particularly while
caring for vulnerable populations. Additionally, the study revealed that
practitioners face challenges in ensuring HIPAA compliance due to inadequate
resources and a lack of technological comprehension. Policymakers and
healthcare providers should take proactive measures to address these
challenges, including offering resources and training to ensure HIPAA
compliance and enhancing technology infrastructure to support secure and
accessible telehealth.


  In the context of 6th generation (6G) networks, vehicular edge computing
(VEC) is emerging as a promising solution to let battery-powered ground
vehicles with limited computing and storage resources offload processing tasks
to more powerful devices. Given the dynamic vehicular environment, VEC systems
need to be as flexible, intelligent, and adaptive as possible. To this aim, in
this paper we study the opportunity to realize VEC via non-terrestrial networks
(NTNs), where ground vehicles offload resource-hungry tasks to Unmanned Aerial
Vehicles (UAVs), High Altitude Platforms (HAPs), or a combination of the two.
We define an optimization problem in which tasks are modeled as a Poisson
arrival process, and apply queuing theory to find the optimal offloading factor
in the system. Numerical results show that aerial-assisted VEC is feasible even
in dense networks, provided that high-capacity HAP/UAV platforms are available.


  With the advent of Network Function Virtualization (NFV), Physical Network
Functions (PNFs) are gradually being replaced by Virtual Network Functions
(VNFs) that are hosted on general purpose servers. Depending on the call flows
for specific services, the packets need to pass through an ordered set of
network functions (physical or virtual) called Service Function Chains (SFC)
before reaching the destination. Conceivably for the next few years during this
transition, these networks would have a mix of PNFs and VNFs, which brings an
interesting mix of network problems that are studied in this paper: (1) How to
find an SFC-constrained shortest path between any pair of nodes? (2) What is
the achievable SFC-constrained maximum flow? (3) How to place the VNFs such
that the cost (the number of nodes to be virtualized) is minimized, while the
maximum flow of the original network can still be achieved even under the SFC
constraint? In this work, we will try to address such emerging questions.
First, for the SFC-constrained shortest path problem, we propose a
transformation of the network graph to minimize the computational complexity of
subsequent applications of any shortest path algorithm. Second, we formulate
the SFC-constrained maximum flow problem as a fractional multicommodity flow
problem, and develop a combinatorial algorithm for a special case of practical
interest. Third, we prove that the VNFs placement problem is NP-hard and
present an alternative Integer Linear Programming (ILP) formulation. Finally,
we conduct simulations to elucidate our theoretical results.


  Multiwavelength identification of AGN is crucial not only to obtain a more
complete census, but also to learn about the physical state of the nuclear
activity (obscuration, efficiency, etc.). A panchromatic strategy plays an
especially important role when the host galaxies are star-forming. Selecting
far-Infrared galaxies at 0.3<z<1, and using AGN tracers in the X-ray, optical
spectra, mid-infrared, and radio regimes, we found a twice higher AGN fraction
than previous studies, thanks to the combined AGN identification methods and in
particular the recent Mass-Excitation (MEx) diagnostic diagram. We furthermore
find an intriguing relation between AGN X-ray absorption and the specific star
formation rate (sSFR) of the host galaxies, indicating a physical link between
X-ray absorption and either the gas fraction or the gas geometry in the hosts.
These findings have implications for our current understanding of both the AGN
unification model and the nature of the black hole-galaxy connection.
  These proceedings review selected results by Juneau et al. (2013, ApJ 764,
176), and their implications. The original work involved several members from
the GOODS and AEGIS teams.


  This paper describes a generalization of previous methods for constructing
tree-structured belief network with hidden variables. The major new feature of
the described method is the ability to produce a tree decomposition even when
there are errors in the correlation data among the input variables. This is an
important extension of existing methods since the correlational coefficients
usually cannot be measured with precision. The technique involves using a
greedy search algorithm that locally minimizes an error function.


  In order to understand the interactions between active galactic nuclei (AGN)
and star formation during the evolution of galaxies, we investigate 142
galaxies detected in both X-ray and 70{\mu}m observations in the COSMOS (Cosmic
Evolution Survey) field. All of our data are obtained from the archive, X-ray
point source catalogs from Chandra and XMM-Newton observations; far-infrared
70{\mu}m point source catalog from Spitzer-MIPS observations. Although the IRAC
[3.6{\mu}m]-[4.5{\mu}m] vs. [5.8{\mu}m]-[8.0{\mu}m] colours of our sample
indicate that only ~63% of our sources would be classified as AGN, the ratio of
the rest-frame 2-10 keV luminosity to the total infrared luminosity
(8-1000{\mu}m) shows that all of the sample has comparatively higher X-ray
luminosity than that expected from pure star-forming galaxies, suggesting the
presence of an AGN in all of our sources. From the analysis of the X-ray
hardness ratio, we find that sources with both 70{\mu}m and X-ray detection
tend to have a higher hardness ratio relative to the whole X-ray selected
source population, suggesting the presence of more X-ray absorption in the
70{\mu}m detected sources. In addition, we find that the observed far-infrared
colours of 70{\mu}m detected sources with and without X-ray emission are
similar, suggesting the far-infrared emission could be mainly powered by star
formation.


  The role of Israel-Hartle-Hawking vacuum is discussed for anomalous fluid in
presence of both the gauge and gravitational anomalies in ($1+3$) dimensions. I
show that imposition of this vacuum condition leads to the relation
$\tilde{c}_{4d}=-8\pi^2c_m$ between the response parameter ($\tilde{c}_{4d}$)
and the anomaly coefficient ($c_m$). This establishes a connection between the
coefficients appearing in a first order and a third order derivative terms in
the constitutive relation.


  Quantum mechanics predicts an exponentially small probability that a particle
with energy greater than the height of a potential barrier will nevertheless
reflect from the barrier in violation of classical expectations. This process
can be regarded as tunneling in momentum space, leading to a simple derivation
of the reflection probability.


  The present Fermilab proton Booster is an early example of a rapidly-cycling
synchrotron (RCS). Built in the 1960s, it features a design in which the
combined-function dipole magnets serve as vacuum chambers. Such a design is
quite cost-effective, and it does not have the limitations associated with the
eddy currents in a metallic vacuum chamber. However, an important drawback of
that design is a high impedance, as seen by a beam, because of the magnet
laminations. More recent RCS designs (e.g. J-PARC) employ large and complex
ceramic vacuum chambers in order to mitigate the eddy current effects and to
shield the beam from the magnet laminations. Such a design, albeit very
successful, is quite costly because it requires large-bore magnets and
large-bore RF cavities. In this article, we will consider an RCS concept with a
thin-wall metallic vacuum chamber as a compromise between the chamber-less
Fermilab Booster design and the large-bore design with ceramic chambers.


  This paper studies the configuration spaces of linkages whose underlying
graph is a single cycle. Assume that the edge lengths are such that there are
no configurations in which all the edges lie along a line. The main results are
that, modulo translations and rotations, each component of the space of convex
configurations is homeomorphic to a closed Euclidean ball and each component of
the space of embedded configurations is homeomorphic to a Euclidean space. This
represents an elaboration on the topological information that follows from the
convexification theorem of Connelly, Demaine, and Rote.


  We used ROS2 as a platform to conduct AI research for developing a Follow-Me
capability as a proof-of-concept on a wheeled robot, demonstrating that AI
research is possible in the ROS2 framework. We developed a complete system that
uses perception and navigation components based on a sensor suite of fisheye
cameras, lidar, and IMU running on an ARM64 Embedded Linux platform that runs
ROS2 natively. The perception package detects AR markers and/or IR beacons to
track a person. The tracker uses AI algorithms such as particle filters and
nonlinear optimization to extract the SE(3) information of the 2D feature.


  To realize novel topological phases and to pursue potential applications in
low-energy consumption spintronics, the study of magnetic topological materials
is of great interest. Starting from the theory of nonmagnetic topological
quantum chemistry [Bradlyn et al., Nature 547, 298 (2017)], we have obtained
irreducible (co)representations and compatibility relations (CRs) in momentum
space, and we constructed a complete list of magnetic band (co)representations
(MBRs) in real space for other MSGs with anti-unitary symmetries (i.e. type-III
and type-IV MSGs). The results are consistent with the magnetic topological
quantum chemistry [Elcoro et al., Nat. Comm. 12, 5965 (2021)]. Using the CRs
and MBRs, we reproduce the symmetry-based classifications for MSGs, and we
obtain a set of Fu-Kane-like formulas of symmetry indicators (SIs) in both
spinless (bosonic) and spinful (fermionic) systems, which are implemented in an
automatic code - TopMat - to diagnose topological magnetic materials. The
magnetic topological materials, whose occupied states can not be decomposed
into a sum of MBRs, are consistent with nonzero SIs. Lastly, using our online
code, we have performed spin-polarized calculations for magnetic compounds in
the materials database and find many magnetic topological candidates.


  We present a systematic investigation of rotation curves (RCs) of fully
hydrodynamically simulated galaxies, including cooling, star formation with
associated feedback and galactic winds. Applying two commonly used fitting
formulae to characterize the RCs, we investigate systematic effects on the
shape of RCs both by observational constraints and internal properties of the
galaxies. We mainly focus on effects that occur in measurements of intermediate
and high redshift galaxies. We find that RC parameters are affected by the
observational setup, like slit misalignment or the spatial resolution and also
depend on the evolution of a galaxy. Therefore, a direct comparison of
quantities derived from measured RCs with predictions of semi-analytic models
is difficult. The virial velocity V_c, which is usually calculated and used by
semi-analytic models can differ significantly from fit parameters like V_max or
V_opt inferred from RCs. We find that V_c is usually lower than typical
characteristic velocities derived from RCs. V_max alone is in general not a
robust estimator for the virial mass.


  Practical adaptive control implementations where human pilots coexist in the
loop are still uncommon, despite their success in handling uncertain dynamical
systems. This is owing to their special nonlinear characteristics which lead to
unfavorable interactions between pilots and adaptive controllers. To pave the
way for the implementation of adaptive controllers in piloted applications, we
propose an adaptive human pilot model that takes into account the time delay in
the pilot's response while operating on an adaptive control system. The model
can be utilized in the evaluation of adaptive controllers through the
simulation environment and guide in their design.


  In AdS/CFT, there can exist local 2-to-2 bulk scattering processes even when
local scattering is not possible on the boundary; these have previously been
studied in connection with boundary correlation functions. We show that
boundary regions associated with these scattering configurations must have
$O(1/G_N)$ mutual information, and hence a connected entanglement wedge. One of
us previously argued for this statement from the boundary theory using
operational tools in quantum information theory. We improve that argument to
make it robust to small errors and provide a proof in the bulk using focusing
arguments in general relativity. We also provide a direct link to entanglement
wedge reconstruction by showing that the bulk scattering region must lie inside
the connected entanglement wedge. Our construction implies the existence of
nonlocal quantum computation protocols that are exponentially more efficient
than the optimal protocols currently known.


  We investigate how the gap equations are obtained in the light-front
formalism within the four-Fermi theories. Instead of the zero-mode constraint,
we find that the "fermionic constraints" on nondynamical spinor components are
responsible for symmetry breaking. Careful treatment of the infrared divergence
is indispensable for obtaining the gap equation.


  We describe here in detail the recently introduced methodology for simulation
of structural transitions in crystals. The applications of the new scheme are
illustrated on various kinds of crystals and the advantages with respect to
previous schemes are emphasized. The relevance of the new method for the
problem of crystal structure prediction is also discussed.


  There are two classes of viable progenitors for normal Type Ia supernovae
(SNe Ia): systems in which a white dwarf explodes at the Chandrasekhar mass
($M_{ch}$), and systems in which a white dwarf explodes below the Chandrasekhar
mass (sub-$M_{ch}$). It is not clear which of these channels is dominant;
observations and light curve modeling have provided evidence for both. Here we
use an extensive grid of 4500 time-dependent, multiwavelength radiation
transport simulations to show that the sub-$M_{ch}$ model can reproduce the
entirety of the width-luminosity relation (WLR), while the $M_{ch}$ model can
only produce the brighter events $(0.8 < \Delta M_{15}(B) < 1.55)$, implying
that fast-declining SNe Ia come from sub-$M_{ch}$ explosions. We do not assume
a particular theoretical paradigm for the progenitor or explosion mechanism,
but instead construct parameterized models that vary the mass, kinetic energy,
and compositional structure of the ejecta, thereby realizing a broad range of
possible outcomes of white dwarf explosions. We provide fitting functions based
on our large grid of detailed simulations that map observable properties of SNe
Ia such as peak brightness and light curve width to physical parameters such as
$^{56}\mathrm{Ni}$ and total ejected mass. These can be used to estimate the
physical properties of observed SNe Ia.


  The Earth itself is not stationary but keeps revolving, and its motion
further satisfies the law of equal area according to the heliocentric doctrine.
That satisfaction can be used to construct the mathematical relationships
between the planet_Sun and Earth_Sun distances. The law of equal area for
planets can hence be reestablished naturally from the moving Earth using the
observed angular speed of a planet over the Sun. Furthermore, for the
periodicity of a planet to the Sun, the distance from each planet to the Sun
may be expressed as an angular periodic function. By coordinating with the
observed data, this periodic distance function depicts an exact elliptical
path. Here, we apply relatively simple mathematical skills to illustrate the
invariant forms of planetary motions and indicate the key factors used to
analyze the motions in complicated planetary systems.


  This study explores the impact of Large Language Models (LLMs) in higher
education, focusing on an automated oral examination simulation using a
prototype. The design considerations of the prototype are described, and the
system is evaluated with a select group of educators and students. Technical
and pedagogical observations are discussed. The prototype proved to be
effective in simulating oral exams, providing personalized feedback, and
streamlining educators' workloads. The promising results of the prototype show
the potential for LLMs in democratizing education, inclusion of diverse student
populations, and improvement of teaching quality and efficiency.


  We review recent developments on the thermodynamics of black holes in
extended phase space, where the cosmological constant is interpreted as
thermodynamic pressure and treated as a thermodynamic variable in its own
right. In this approach, the mass of the black hole is no longer regarded as
internal energy, rather it is identified with the chemical enthalpy. This leads
to an extended dictionary for black hole thermodynamic quantities, in
particular a notion of thermodynamic volume emerges for a given black hole
spacetime. This volume is conjectured to satisfy the reverse isoperimetric
inequality - an inequality imposing a bound on the amount of entropy black hole
can carry for a fixed thermodynamic volume. New thermodynamic phase transitions
naturally emerge from these identifications. Namely, we show that black holes
can be understood from the viewpoint of chemistry, in terms of concepts such as
Van der Waals fluids, reentrant phase transitions, and triple points. We also
review the recent attempts at extending the AdS/CFT dictionary in this setting,
discuss the connections with horizon thermodynamics, applications to Lifshitz
spacetimes, and outline possible future directions in this field.


  The effect of the nebula optical depth on the determination of the
temperature (T*) of the central stars in planetary nebulae is discussed. Based
on photoionization models for planetary nebulae with different optical depths,
we show, quantitatively, that the details of the distribution of the H and He
II Zanstra temperatures are mainly explained by an optical depth effect; in
particular, that the discrepancy is larger for low stellar temperatures. The
results also show that for high stellar temperatures the He II Zanstra
temperature underestimates the stellar temperature, even for high optical
depths. The stellar temperature, as well as the optical depth, can be obtained
from a Zanstra temperature ratio (ZR) plot ZR = Tz(He II)/Tz(H) versus Tz(He
II). The effects of departures from a blackbody spectrum, as well as of the He
abundance in the nebulae, are also discussed. For nebulae of very low optical
depth and/or high stellar temperature the distribution ZR versus Tz(He II) only
provides lower limits for T*. In order to obtain better values for the optical
depth and T*, we propose the use of the line intensity ratio He II/He I versus
Tz(He II) diagram.


  Scientific datasets present unique challenges for machine learning-driven
compression methods, including more stringent requirements on accuracy and
mitigation of potential invalidating artifacts. Drawing on results from
compressed sensing and rate-distortion theory, we introduce effective data
compression methods by developing autoencoders using high dimensional latent
spaces that are $L^1$-regularized to obtain sparse low dimensional
representations. We show how these information-rich latent spaces can be used
to mitigate blurring and other artifacts to obtain highly effective data
compression methods for scientific data. We demonstrate our methods for short
angle scattering (SAS) datasets showing they can achieve compression ratios
around two orders of magnitude and in some cases better. Our compression
methods show promise for use in addressing current bottlenecks in transmission,
storage, and analysis in high-performance distributed computing environments.
This is central to processing the large volume of SAS data being generated at
shared experimental facilities around the world to support scientific
investigations. Our approaches provide general ways for obtaining specialized
compression methods for targeted scientific datasets.


  Recent experiments for linear magnetoelectric (ME) response in honeycomb
antiferromagnet Co$_4$Nb$_2$O$_9$ revealed that the electric polarization can
be manipulated by the in-plane rotating magnetic field in a systematic way. We
propose the minimal model by extracting essential ingredients of
Co$_4$Nb$_2$O$_9$ to exhibit such ME response. It is the three-orbital model
with $xy$-type atomic spin-orbit coupling (SOC) on the single-layer honeycomb
structure, and it is shown to reproduce qualitatively the observed field-angle
dependence of the electric polarization. The obtained results can be understood
by the perturbative calculation with respect to the atomic SOC. These findings
could be useful to explore further ME materials having similar manipulability
of the electric polarization.


  We use Bryant Representation to construct constant mean curvature one
surfaces in hyperbolic space that desingularize a horosphere packing.


  A proof of G\"odel's incompleteness theorem is given. With this new proof a
transfinite extension of G\"odel's theorem is considered. It is shown that if
one assumes the set theory ZFC on the meta level as well as on the object
level, a contradiction arises. The cause is shown to be the implicit
identification of the meta level and the object level hidden behind the G\"odel
numbering. An implication of these considerations is stated.


  This study introduces a novel approach for solving the cosmological field
equations within scalar field theory by employing the Eisenhart lift. The field
equations are reformulated as a system of geodesic equations for the Eisenhart
metric. In the case of an exponential potential, the Eisenhart metric is shown
to be conformally flat. By applying basic geometric principles, a new set of
dynamical variables is identified, allowing for the linearization of the field
equations and the derivation of classical cosmological solutions. However, the
quantization of the Eisenhart system reveals a distinct set of solutions for
the wavefunction, particularly in the presence of symmetry breaking at the
quantum level.


  We study those finite dimensional quotients of the rational Cherednik algebra
at t=0 that are supported at a point of the centre. It is shown that each such
quotient is Morita equivalent to a certain cuspidal quotient of a rational
Cherednik algebra associated to a parabolic subgroup of W.


  Heterogeneous quantum key distribution chain orchestration over optical
networks is demonstrated with software-defined networking (SDN), achieving the
control-layer interoperability for BB84 (Bennett-Brassard-1984) and TF
(Twin-Field) based quantum key distribution devices.


  Unpredictable functions (UPFs) play essential roles in classical
cryptography, including message authentication codes (MACs) and digital
signatures. In this paper, we introduce a quantum analog of UPFs, which we call
unpredictable state generators (UPSGs). UPSGs are implied by pseudorandom
function-like states generators (PRFSs), which are a quantum analog of
pseudorandom functions (PRFs), and therefore UPSGs could exist even if one-way
functions do not exist, similar to other recently introduced primitives like
pseudorandom state generators (PRSGs), one-way state generators (OWSGs), and
EFIs. In classical cryptography, UPFs are equivalent to PRFs, but in the
quantum case, the equivalence is not clear, and UPSGs could be weaker than
PRFSs. Despite this, we demonstrate that all known applications of PRFSs are
also achievable with UPSGs. They include IND-CPA-secure secret-key encryption
and EUF-CMA-secure MACs with unclonable tags. Our findings suggest that, for
many applications, quantum unpredictability, rather than quantum
pseudorandomness, is sufficient.


  The growing interest in fair AI development is evident. The ''Leave No One
Behind'' initiative urges us to address multiple and intersecting forms of
inequality in accessing services, resources, and opportunities, emphasising the
significance of fairness in AI. This is particularly relevant as an increasing
number of AI tools are applied to decision-making processes, such as resource
allocation and service scheme development, across various sectors such as
health, energy, and housing. Therefore, exploring joint inequalities in these
sectors is significant and valuable for thoroughly understanding overall
inequality and unfairness. This research introduces an innovative approach to
quantify cross-sectoral intersecting discrepancies among user-defined groups
using latent class analysis. These discrepancies can be used to approximate
inequality and provide valuable insights to fairness issues. We validate our
approach using both proprietary and public datasets, including EVENS and Census
2021 (England & Wales) datasets, to examine cross-sectoral intersecting
discrepancies among different ethnic groups. We also verify the reliability of
the quantified discrepancy by conducting a correlation analysis with a
government public metric. Our findings reveal significant discrepancies between
minority ethnic groups, highlighting the need for targeted interventions in
real-world AI applications. Additionally, we demonstrate how the proposed
approach can be used to provide insights into the fairness of machine learning.


  We report on a numerical experiment in which we use time-dependent potentials
to braid non-abelian quasiparticles. We consider lattice bosons in a uniform
magnetic field within the fractional quantum Hall regime, where $\nu$, the
ratio of particles to flux quanta, is near 1/2, 1 or 3/2. We introduce
time-dependent potentials which move quasiparticle excitations around one
another, explicitly simulating a braiding operation which could implement part
of a gate in a quantum computation. We find that different braids do not
commute for $\nu$ near $1$ and $3/2$, with Berry matrices respectively
consistent with Ising and Fibonacci anyons. Near $\nu=1/2$, the braids commute.


  We investigate the effect of surface anisotropy in a spherical many-spin
magnetic nanoparticle. By computing minor loops, two-dimensional (2D) and 3D
energyscape, and by investigating the behavior of the net magnetization, we
show that in the case of not too strong surface anisotropy the behavior of the
many-spin particle may be modeled by that of a macrospin with an effective
energy containing uniaxial and cubic anisotropy terms. This holds for both the
transverse and N\'eel's surface anisotropy models.


  Like humans, deep networks have been shown to learn better when samples are
organized and introduced in a meaningful order or curriculum. Conventional
curriculum learning schemes introduce samples in their order of difficulty.
This forces models to begin learning from a subset of the available data while
adding the external overhead of evaluating the difficulty of samples. In this
work, we propose Learning with Incremental Labels and Adaptive Compensation
(LILAC), a two-phase method that incrementally increases the number of unique
output labels rather than the difficulty of samples while consistently using
the entire dataset throughout training. In the first phase, Incremental Label
Introduction, we partition data into mutually exclusive subsets, one that
contains a subset of the ground-truth labels and another that contains the
remaining data attached to a pseudo-label. Throughout the training process, we
recursively reveal unseen ground-truth labels in fixed increments until all the
labels are known to the model. In the second phase, Adaptive Compensation, we
optimize the loss function using altered target vectors of previously
misclassified samples. The target vectors of such samples are modified to a
smoother distribution to help models learn better. On evaluating across three
standard image benchmarks, CIFAR-10, CIFAR-100, and STL-10, we show that LILAC
outperforms all comparable baselines. Further, we detail the importance of
pacing the introduction of new labels to a model as well as the impact of using
a smooth target vector.


  Recently there has been a renewed interest in the spectra and role in
dynamical properties of excited states of the spin-1/2 Heisenberg
antiferromagnetic chain in longitudinal magnetic fields associated with Bethe
strings. The latter are bound states of elementary magnetic excitations
described by Bethe-ansatz complex non-real rapidities. Previous studies on this
problem referred to finite-size systems. Here we consider the thermodynamic
limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a
longitudinal magnetic field. We confirm that also in that limit the most
significant spectral weight contribution from Bethe strings leads to gapped
continua in the spectra of the spin +- and xx dynamical structure factors. The
contribution of Bethe strings to the zz dynamical structure factor is found to
be small at low spin densities and to become negligible upon increasing that
density above 0.317. For the -+ dynamical structure factor, that contribution
is found to be negligible at finite magnetic field. We derive analytical
expressions for the line shapes of the +-, xx, and zz dynamical structure
factors valid in the vicinity of singularities located at and just above the
gapped lower thresholds of the Bethe-string states's spectra. As a side result
and in order to provide an overall physical picture that includes the relative
location of all spectra with a significant amount of spectral weight, we
revisit the general problem of the line-shape of the transverse and
longitudinal spin dynamical structure factors at finite magnetic field and
excitation energies in the vicinity of other singularities. This includes those
located at and just above the lower thresholds of the spectra that stem from
excited states described by only real Bethe-ansatz rapidities.


  We use the knot filtration on the Heegaard Floer complex to define an integer
invariant tau(K) for knots. Like the classical signature, this invariant gives
a homomorphism from the knot concordance group to Z. As such, it gives lower
bounds for the slice genus (and hence also the unknotting number) of a knot;
but unlike the signature, tau gives sharp bounds on the four-ball genera of
torus knots. As another illustration, we calculate the invariant for several
ten-crossing knots.


  Emerging agile software development methods are people oriented development
approaches to be used by the software industry. The personal software process
(PSP) is an accepted method for improving the capabilities of a single software
engineer. Five original hypotheses regarding the impact of the PSP to
individual performance are tested. Data is obtained from 58 computer science
students in three university courses on the master level, which were held in
two different educational institutions in Finland and Denmark. Statistical data
treatment shows that the use of PSP did not improve size and time estimation
skills but that the productivity did not decrease and the resulting product
quality was improved. The implications of these findings are briefly addressed.


  We have carried out a thorough optical study of the closest star formation
jet. The inner arcminute surrounding the class 0/I binary protostar L1551 IRS5
and its associated jet (HH154) have been observed using the Hubble Space
Telescope with the WFPC2 camera, the ESO New Technology Telescope with the EMMI
spectrograph and the Nordic Optical Telescope with the ALFOSC spectrograph.
This data set is compared to earlier ground based imaging with the aim to study
the evolution of this particular jet, and its possible interaction with the
molecular material in the bipolar molecular outflow associated with this
source. The velocity field of the jet is mapped out. The highest velocities are
found in the vicinity of the recently discovered X-ray source emanating from a
shock in this jet. The energy radiated by the X-ray source is compatible with
these velocities. The \halpha and \hbeta emission from the jet is used to
determine the extinction, which is found to increase inwards in the jet towards
the protostar. The extinction towards the X-ray source is consistent with the
one determined from the X-ray spectrum.


  Supermassive black hole binaries (BHBs) are expected to be one of the most
powerful sources of low-frequency gravitational waves (GWs) for future
space-borne detectors. Prior to the GW emission stage, BHBs evolving in
gas-poor nuclei shrink primarily through the slingshot ejection of stars
approaching the BHB from sufficiently close distances. Here we address the
possibility that the BHB shrinking rate is enhanced through the infall of a
star cluster (SC) onto the BHB. We present the results of direct summation
N-body simulations exploring different orbits for the SC infall, and we show
that SCs reaching the BHB on non-zero angular momentum orbits (with
eccentricity 0.75) fail to enhance the BHB hardening, while SCs approaching the
BHB on radial orbits reduce the BHB separation by ~10% in less than 10 Myr,
effectively shortening the BHB path towards GWs.


  In this paper, we consider deformations of singular complex curves on complex
surfaces. Despite the fundamental nature of the problem, little seems to be
known for curves on general surfaces. Let $C\subset S$ be a complete integral
curve on a smooth surface. Let $\tilde C$ be a partial normalization of $C$,
and $\varphi\colon \tilde C\to S$ be the induced map. In this paper, we
consider deformations of $\varphi$. The problem of the existence of
deformations will be reduced to solving a certain explicit system of polynomial
equations. This system is universal in the sense that it is determined solely
by simple local data of the singularity of $C$, and does not depend on the
global geometry of $C$ or $S$. Under a relatively mild assumption on the
properties of these equations, we will show that the map $\varphi$ has
virtually optimal deformation property.


  Even though quantum systems in energy eigenstates do not evolve in time, they
can exhibit correlations between internal degrees of freedom in such a way that
one of the internal degrees of freedom behaves like a clock variable, and
thereby defines an internal time, that parametrises the evolution of the other
degrees of freedom. This situation is of great interest in quantum cosmology
where the invariance under reparametrisation of time implies that the temporal
coordinate dissapears and is replaced by the Wheeler-DeWitt constraint. Here we
show that this paradox can be investigated experimentally using the exquisite
control now available on moderate size quantum systems. We describe in detail
how to implement such an experimental demonstration using the spin and motional
degrees of freedom of a single trapped ion.


  The noninvariance of Lyapunov exponents in general relativity has led to the
conclusion that chaos depends on the choice of the space-time coordinates.
Strikingly, we uncover the transformation laws of Lyapunov exponents under
general space-time transformations and we find that chaos, as characterized by
positive Lyapunov exponents, is coordinate invariant. As a result, the previous
conclusion regarding the noninvariance of chaos in cosmology, a major claim
about chaos in general relativity, necessarily involves the violation of
hypotheses required for a proper definition of the Lyapunov exponents.