  Dynamical supersymmetry breaking is an important issue for applications of
supersymmetry in particle physics. The functional renormalization group
equations allow for a nonperturbative approach that leaves supersymmetry
intact. Therefore they offer a promising tool to investigate dynamical
supersymmetry breaking. Here we will employ this method to derive the phase
diagram and a surprisingly rich RG fixed-point structure with corresponding
critical exponents for the $\mathcal N=1$ Wess-Zumino model in two dimensions.


  We study here the impact of priorities on conflict resolution in inconsistent
relational databases. We extend the framework of repairs and consistent query
answers. We propose a set of postulates that an extended framework should
satisfy and consider two instantiations of the framework: (locally preferred)
l-repairs and (globally preferred) g-repairs. We study the relationships
between them and the impact each notion of repair has on the computational
complexity of repair checking and consistent query answers.


  This work addresses the problems of (a) designing utilization measurements of
trained artificial intelligence (AI) models and (b) explaining how training
data are encoded in AI models based on those measurements. The problems are
motivated by the lack of explainability of AI models in security and safety
critical applications, such as the use of AI models for classification of
traffic signs in self-driving cars. We approach the problems by introducing
theoretical underpinnings of AI model utilization measurement and understanding
patterns in utilization-based class encodings of traffic signs at the level of
computation graphs (AI models), subgraphs, and graph nodes. Conceptually,
utilization is defined at each graph node (computation unit) of an AI model
based on the number and distribution of unique outputs in the space of all
possible outputs (tensor-states). In this work, utilization measurements are
extracted from AI models, which include poisoned and clean AI models. In
contrast to clean AI models, the poisoned AI models were trained with traffic
sign images containing systematic, physically realizable, traffic sign
modifications (i.e., triggers) to change a correct class label to another label
in a presence of such a trigger. We analyze class encodings of such clean and
poisoned AI models, and conclude with implications for trojan injection and
detection.


  We calculate the Ehrenfest-time dependence of the leading quantum correction
to the spectral form factor of a ballistic chaotic cavity using periodic orbit
theory. For the case of broken time-reversal symmetry, our result differs from
that previously obtained using field-theoretic methods [Tian and Larkin, Phys.
Rev. B 70, 035305 (2004)]. The discrepancy shows that short-time regularization
procedures dramatically affect physics near the Ehrenfest-time.


  We examine several assignments of spin and parity for the pentaquark Theta+
state (J^P=1/2^{+,-}, 3/2^{+,-}) in connection with known baryon resonances.
Assuming that the Theta+ belongs to an antidecuplet representation which mixes
with an octet, we calculate the mass spectra of the flavor partners of the
Theta+ based on the SU(3) symmetry. The decay widths of the Theta+ and nucleon
partners are analyzed for the consistency check of the mixing angle obtained
from the masses. It is found that a suitable choice of the mixing angle
successfully reproduces the observed masses of Theta(1540) and Xi_{3/2}(1860),
when their spin and parity are assigned to be J^P=3/2^-, together with other
J^P=3/2^- resonances. The decay widths of Theta -> KN, N(1520) -> pi N, and
N(1700) -> pi N are also reproduced simultaneously.


  We introduce cooperative sequential state space estimation in the domain of
augmented complex statistics, whereby nodes in a network collaborate locally to
estimate noncircular complex signals. For rigour, a distributed augmented
(widely linear) complex Kalman filter (D-ACKF) suited to the generality of
complex signals is introduced, allowing for unified treatment of both proper
(rotation invariant) and improper (rotation dependent) signal distributions.
Its duality with the bivariate real-valued distributed Kalman filter, along
with several issues of implementation are also illuminated. The analysis and
simulations show that unlike existing distributed Kalman filter solutions, the
D-ACKF caters for both the improper data and the correlations between nodal
observation noises, thus providing enhanced performance in real-world
scenarios.


  We show that generically the initial singularity is isotropic in spatially
homogeneous cosmological models in the brane-world scenario. We then argue that
it is plausible that the initial singularity is isotropic in typical brane
world cosmological models. Therefore, brane cosmology naturally gives rise to a
set of initial data that provide the conditions for inflation to subsequently
take place, thereby solving the initial conditions problem and leading to a
self--consistent and viable cosmology.


  Determining the number of common factors is an important and practical topic
in high dimensional factor models. The existing literatures are mainly based on
the eigenvalues of the covariance matrix. Due to the incomparability of the
eigenvalues of the covariance matrix caused by heterogeneous scales of observed
variables, it is very difficult to give an accurate relationship between these
eigenvalues and the number of common factors. To overcome this limitation, we
appeal to the correlation matrix and show surprisingly that the number of
eigenvalues greater than $1$ of population correlation matrix is the same as
the number of common factors under some mild conditions. To utilize such a
relationship, we study the random matrix theory based on the sample correlation
matrix in order to correct the biases in estimating the top eigenvalues and to
take into account of estimation errors in eigenvalue estimation. This leads us
to propose adjusted correlation thresholding (ACT) for determining the number
of common factors in high dimensional factor models, taking into account the
sampling variabilities and biases of top sample eigenvalues. We also establish
the optimality of the proposed methods in terms of minimal signal strength and
optimal threshold. Simulation studies lend further support to our proposed
method and show that our estimator outperforms other competing methods in most
of our testing cases.


  The architecture of the BlueGene/L massively parallel supercomputer is
described. Each computing node consists of a single compute ASIC plus 256 MB of
external memory. The compute ASIC integrates two 700 MHz PowerPC 440 integer
CPU cores, two 2.8 Gflops floating point units, 4 MB of embedded DRAM as cache,
a memory controller for external memory, six 1.4 Gbit/s bi-directional ports
for a 3-dimensional torus network connection, three 2.8 Gbit/s bi-directional
ports for connecting to a global tree network and a Gigabit Ethernet for I/O.
65,536 of such nodes are connected into a 3-d torus with a geometry of
32x32x64. The total peak performance of the system is 360 Teraflops and the
total amount of memory is 16 TeraBytes.


  We demonstrate a nanophotonic parametric light source with a record high
normalized conversion efficiency of $3\times 10^6\, W^{-2}$, owing to
resonantly enhanced four wave mixing in coupled high-Q photonic crystal
resonators. The rate of spontaneously emitted photons reaches 14 MHz.


  On-line privacy is of major public concern. Unfortunately, for the average
consumer, there is no simple mechanism to browse the Internet privately on
multiple devices. Most available Internet privacy mechanisms are either
expensive, not readily available, untrusted, or simply provide trivial
information masking. We propose that the simplest, most effective and
inexpensive way of gaining privacy, without sacrificing unnecessary amounts of
functionality and speed, is to mask the user's IP address while also encrypting
all data. We hypothesized that the Tor protocol is aptly suited to address
these needs. With this in mind we implemented a Tor router using a single board
computer and the open-source Tor protocol code. We found that our proposed
solution was able to meet five of our six goals soon after its implementation:
cost effectiveness, immediacy of privacy, simplicity of use, ease of execution,
and unimpaired functionality. Our final criterion of speed was sacrificed for
greater privacy but it did not fall so low as to impair day-to-day
functionality. With a total cost of roughly $100.00 USD and a speed cap of
around 2 Megabits per second we were able to meet our goal of an affordable,
convenient, and usable solution to increased on-line privacy for the average
consumer.


  The Internet of Things (IoT) is growing fast. In 2018, there was
approximately one connected device per person on earth and the number has been
growing ever since. The devices interact with the environment via different
modalities at the same time using sensors and actuators making the programs
parallel. Yet, writing this type of programs is difficult because the devices
have little computation power and memory, the platforms are heterogeneous and
the languages are low level. Task Oriented Programming (TOP) is a declarative
programming language paradigm that is used to express coordination of work,
collaboration of users and systems, the distribution of shared data and the
human-computer interaction. The mTask language is a specialized, yet
full-fledged, multi-backend TOP language for IoT devices. With the bytecode
interpretation backend and the integration with iTask, tasks can be executed on
the device dynamically. This means that -- according to the current state of
affairs -- tasks can be tailor-made at run time, compiled to device-agnostic
bytecode and shipped to the device for interpretation. Tasks sent to the device
are fully integrated in iTask to allow every form of interaction with the tasks
such as observation of the task value and interaction with Shared Data Sources
(SDSs). The entire IoT application -- both server and devices -- are programmed
in a single language, albeit using two embedded Domain Specific Languages
(EDSLs).


  Evidence suggests that different prompts lead large language models (LLMs) to
generate responses with varying quality. Yet, little is known about prompts'
effects on response quality in healthcare domains. In this exploratory study,
we address this gap, focusing on a specific healthcare domain: dementia
caregiving. We first developed an innovative prompt template with three
components: (1) system prompts (SPs) featuring 4 different roles; (2) an
initialization prompt; and (3) task prompts (TPs) specifying different levels
of details, totaling 12 prompt combinations. Next, we selected 3 social media
posts containing complicated, real-world questions about dementia caregivers'
challenges in 3 areas: memory loss and confusion, aggression, and driving. We
then entered these posts into GPT-4, with our 12 prompts, to generate 12
responses per post, totaling 36 responses. We compared the word count of the 36
responses to explore potential differences in response length. Two experienced
dementia care clinicians on our team assessed the response quality using a
rating scale with 5 quality indicators: factual, interpretation, application,
synthesis, and comprehensiveness (scoring range: 0-5; higher scores indicate
higher quality).


  DNA polymerase (DNAP) is a dual-purpose enzyme that plays two opposite roles
in two different situations during DNA replication. It plays its normal role as
a {\it polymerase} catalyzing the elongation of a new DNA molecule by adding a
monomer. However, it can switch to the role of an {\it exonuclease} and shorten
the same DNA by cleavage of the last incorporated monomer from the nascent DNA.
Just as misincorporated nucleotides can escape exonuclease causing replication
error, correct nucleotide may get sacrificed unnecessarily by erroneous
cleavage. The interplay of polymerase and exonuclease activities of a DNAP is
explored here by developing a minimal stochastic kinetic model of DNA
replication. Exact analytical expressions are derived for a few key statistical
distributions; these characterize the temporal patterns in the mechanical
stepping and the chemical (cleavage) reaction. The Michaelis-Menten-like
analytical expression derived for the average rates of these two processes not
only demonstrate the effects of their coupling, but are also utilized to
measure the extent of {\it replication error} and {\it erroneous cleavage}.


  We study the spherical gravitational collapse of a compact object under the
approximation that the radial pressure is identically zero, and the tangential
pressure is related to the density by a linear equation of state. It turns out
that the Einstein equations can be reduced to the solution of an integral for
the evolution of the area radius. We show that for positive pressure there is a
finite region near the center which necessarily expands outwards, if collapse
begins from rest. This region could be surrounded by an inward moving one which
could collapse to a singularity - any such singularity will necessarily be
covered by a horizon. For negative pressure the entire object collapses
inwards, but any singularities that could arise are not naked. Thus the nature
of the evolution is very different from that of dust, even when the ratio of
pressure to density is infinitesimally small.


  The classical scalar massive field satisfying the Klein-Gordon equation in a
finite one-dimensional space interval of periodically varying length with
Dirichlet boundary conditions is studied. For the sufficiently small mass, the
energy can exponentially grow with time under the same conditions as for the
massless case. The proofs are based on estimates of exactly given mass-induced
corrections to the massless case.


  We present measurements of the elliptic ($\mathrm{v}_2$), triangular
($\mathrm{v}_3$) and quadrangular ($\mathrm{v}_4$) anisotropic azimuthal flow
over a wide range of pseudorapidities ($-3.5< \eta < 5$). The measurements are
performed with Pb-Pb collisions at $\sqrt{s_{\text{NN}}} = 2.76$ TeV using the
ALICE detector at the Large Hadron Collider (LHC). The flow harmonics are
obtained using two- and four-particle correlations from nine different
centrality intervals covering central to peripheral collisions. We find that
the shape of $\mathrm{v}_n(\eta)$ is largely independent of centrality for the
flow harmonics $n=2-4$, however the higher harmonics fall off more steeply with
increasing $|\eta|$. We assess the validity of extended longitudinal scaling of
$\mathrm{v}_2$ by comparing to lower energy measurements, and find that the
higher harmonic flow coefficients are proportional to the charged particle
densities at larger pseudorapidities. Finally, we compare our measurements to
both hydrodynamical and transport models, and find they both have challenges
when it comes to describing our data.


  This paper has rather a pedagogical meaning. Surprising symmetries in the
$(j,0)\oplus (0,j)$ Lorentz group representation space are analyzed. The aim is
to draw reader's attention to the possibility of describing the particle world
on the ground of the Dirac "doubles". Several tune points of the variational
principle for this kind of equations are briefly discussed.


  In this paper, an evolutionary many-objective optimization algorithm based on
corner solution search (MaOEA-CS) was proposed. MaOEA-CS implicitly contains
two phases: the exploitative search for the most important boundary optimal
solutions - corner solutions, at the first phase, and the use of angle-based
selection [1] with the explorative search for the extension of PF approximation
at the second phase. Due to its high efficiency and robustness to the shapes of
PFs, it has won the CEC'2017 Competition on Evolutionary Many-Objective
Optimization. In addition, MaOEA-CS has also been applied on two real-world
engineering optimization problems with very irregular PFs. The experimental
results show that MaOEA-CS outperforms other six state-of-the-art compared
algorithms, which indicates it has the ability to handle real-world complex
optimization problems with irregular PFs.


  Supernova remnants (SNRs) are thought to be the most plausible sources of
Galactic cosmic rays. One of the principal questions is whether they are
accelerating particles up to the maximum energy of Galactic cosmic rays
($\sim$PeV). In this paper, we summarize our recent studies on
gamma-ray-emitting SNRs. We first evaluated the reliability of SNR age
estimates to quantitatively discuss time dependence of their acceleration
parameters. Then we systematically modeled their gamma-ray spectra to constrain
the acceleration parameters. The current maximum energy estimates were found to
be well below PeV for most sources. The basic time dependence of the maximum
energy assuming the Sedov evolution ($\approx t^{-0.8\pm0.2}$) cannot be
explained with the simplest acceleration condition (Bohm limit) and requires
shock-ISM (interstellar medium) interaction. The inferred maximum energies
during lifetime averaged over the sample can be expressed as $\lesssim 20$ TeV
($t_{{\rm M}}/\text{1 kyr})^{-0.8}$ with $t_{\rm M}$ being the age at the
maximum, which reaches $\sim$PeV only if $t_{\rm M} \lesssim 10$ yr. The
maximum energies during lifetime are suggested to have a variety of 1-2 orders
of magnitude from object to object on the other hand. This variety will reflect
the dependence on environments.


  A basic premise in scalable human-machine coding is that the base layer is
intended for automated machine analysis and is therefore more compressible than
the same content would be for human viewing. Use cases for such coding include
video surveillance and traffic monitoring, where the majority of the content
will never be seen by humans. Therefore, base layer efficiency is of paramount
importance because the system would most frequently operate at the base-layer
rate. In this paper, we analyze the coding efficiency of the base layer in a
state-of-the-art scalable human-machine image codec, and show that it can be
improved. In particular, we demonstrate that gains of 20-40% in BD-Rate
compared to the currently best results on object detection and instance
segmentation are possible.


  The predictive soft-wall AdS/QCD model with a modified 5D metric at the
infrared region is constructed to obtain a non-trivial dilaton solution for
three flavor quarks $u$, $d$ and $s$. Such a model is shown to incorporate both
the chiral symmetry breaking and linear confinement. After considering some
high-order terms including the $U(1)_L\times U(1)_R$ chiral symmetry breaking
term, we find that the resulting predictions for the SU(3) octet and singlet
resonance states of pseudoscalar, scalar, vector and axial-vector mesons agree
well with the experimentally confirmed resonance states. Contributions from the
instanton effects given by the determinant term are also discussed. It is
observed that the chiral symmetry breaking phenomena of $SU(3)_L\times SU(3)_R$
and $U(1)_L\times U(1)_R$ can be well described in this model, while the SU(3)
flavor symmetry breaking effect due to quark mass difference in the source term
is not enough to explain all of the current experimental data.


  We design three-dimensional (3D) metallic nanowire media with different
structures and numerically demonstrate that they can be homogeneous effective
indefinite anisotropic media by showing that their dispersion relations are
hyperbolic. For a finite slab, a nice fitting procedure is exploited to obtain
the dispersion relations from which we retrieve the effective permittivities.
The pseudo focusing for the real 3D wire medium agrees very well with the
homogeneous medium having the effective permittivity tensor of the wire medium.
Studies also show that in the long-wavelength limit, the hyperbolic dispersion
relation of the 3D wire medium can be valid even for evanescent modes.


  In the present work, we analyze the $hp$ version of Virtual Element methods
for the 2D Poisson problem. We prove exponential convergence of the energy
error employing sequences of polygonal meshes geometrically refined, thus
extending the classical choices for the decomposition in the $hp$ Finite
Element framework to very general decomposition of the domain. A new
stabilization for the discrete bilinear form with explicit bounds in $h$ and
$p$ is introduced. Numerical experiments validate the theoretical results. We
also exhibit a numerical comparison between $hp$ Virtual Elements and $hp$
Finite Elements.


  We present a phase-space representation of the hydrogen atom using the
Kirkwood-Rikaczek distribution function. This distribution allows us to obtain
analytical results, which is quite unique because an exact analytical form of
the Wigner functions corresponding to the atom states is not known. We show how
the Kirkwood-Rihaczek distribution reflects properties of the hydrogen atom
wave functions in position and momentum representations.


  The connections between Tarski's Q-relation algebras and Thompson's groups F,
T, V, and monoid M are reviewed here, along with Jonsson-Tarski algebras, fork
algebras, true pairing algebras, and tabular relation algebras. All of these
are related to the finitization problem and Tarski's formalization of set
theory without variables. Most of the technical details occur in the variety of
J-algebras, which is obtained from relation algebras by omitting union and
complementation and adopting a set of axioms created by Jonsson. Every relation
algebra or J-algebra that contains a pair of conjugated quasiprojections
satisfying the Domain and Unicity conditions, such as those that arise from
J\'onsson-Tarski algebras or fork algebras, will also contain homomorphic
images of F, T, V, and M. The representability of tabular relation algebras is
extended here to J-algebras, using a notion of tabularity equivalent among
relation algebras to the original definition.


  In this paper, we study the algebraic structure of Z_2[u]Z_2[u, v]-additive
codes which are Z_2[u, v]-submodules where u^2 = v^2 = 0 and uv = vu. In
particular, we determine a Gray map from Z_2[u]Z_2 [u, v] to
Z_2^{2{\alpha}+8\b{eta}} and study generator and parity check matrices for
these codes. Further we study the structure of Z_2[u]Z_2[u, v]-additive cyclic
codes and constacyclic codes.


  Synthesizing information from multiple data sources is critical to ensure
knowledge generalizability. Integrative analysis of multi-source data is
challenging due to the heterogeneity across sources and data-sharing
constraints due to privacy concerns. In this paper, we consider a general
robust inference framework for federated meta-learning of data from multiple
sites, enabling statistical inference for the prevailing model, defined as the
one matching the majority of the sites. Statistical inference for the
prevailing model is challenging since it requires a data-adaptive mechanism to
select eligible sites and subsequently account for the selection uncertainty.
We propose a novel sampling method to address the additional variation arising
from the selection. Our devised CI construction does not require sites to share
individual-level data and is shown to be valid without requiring the selection
of eligible sites to be error-free. The proposed robust inference for federated
meta-learning (RIFL) methodology is broadly applicable and illustrated with
three inference problems: aggregation of parametric models, high-dimensional
prediction models, and inference for average treatment effects. We use RIFL to
perform federated learning of mortality risk for patients hospitalized with
COVID-19 using real-world EHR data from 16 healthcare centers representing 275
hospitals across four countries.


  Starlink is a low-Earth orbit (LEO) satellite constellation operated by Space
Exploration Technologies Corp. (SpaceX) which aims to provide global satellite
internet access. Thus far, most photometric observations of Starlink satellites
have primarily been from citizen scientists' visual observations without using
quantitative detectors. This paper aims to characterize Starlink satellites and
investigate the impact of mega constellations on ground-based astronomy,
considering both the observed magnitude and two-line element (TLE) residuals.
We collected 353 observations of 61 different Starlink satellites over a
16-month period and we found an average GAIA G magnitude of 5.5 +/- 0.13 with a
standard deviation of 1.12. The average magnitude of V1.0 (pre-VisorSat)
Starlinks was 5.1 +/- 0.13 with a standard deviation of 1.13. SpaceX briefly
used a low-albedo coating on a Starlink satellite called DarkSat to test light
pollution mitigation technologies. The brightness of DarkSat was found to be
7.3 +/- 0.13 with a standard deviation of 0.78, or 7.6 times fainter than V1.0
Starlinks. This concept was later abandoned due to thermal control issues and
sun visors were used in future models called VisorSats. The brightness of
VisorSats was found to be 6.0 +/- 0.13 with a standard deviation of 0.79, or
2.3 times fainter than V1.0 Starlinks. Over the span of the observations, we
found that TLEs were accurate to within an average of 0.12 degrees in right
ascension and -0.08 degrees in declination. The error is predominantly
along-track, corresponding to a 0.3 second time error between the observed and
TLE trajectories. Our observations show that a time difference of 0.3 +/- 0.28
seconds is viable for a proposed 10 second shutter closure time to avoid
Starlinks in images.


  Timmes, Brown & Truran found that metallicity variations could theoretically
account for a 25% variation in the mass of 56Ni synthesized in Type Ia
supernovae (SNe Ia), and thus account for a large fraction of the scatter in
observed SN Ia luminosities. Higher-metallicity progenitors are more
neutron-rich, producing more stable burning products relative to radioactive
56Ni. We develop a new method for estimating bolometric luminosity and 56Ni
yield in SNe Ia and use it to test the theory with data from the Supernova
Legacy Survey. We find that the average 56Ni yield does drop in SNe Ia from
high metallicity environments, but the theory can only account for 7%--10% of
the dispersion in SN Ia 56Ni mass, and thus luminosity. This is because the
effect is dominant at metallicities significantly above solar, whereas we find
that SN hosts have predominantly subsolar or only moderately above-solar
metallicities. We also show that allowing for changes in O/Fe with the
metallicity [Fe/H] does not have a major effect on the theoretical prediction
of Timmes, Brown & Truran, so long as one is using the O/H as the independent
variable. Age may have a greater effect than metallicity -- we find that the
luminosity weighted age of the host galaxy is correlated with 56Ni yield, and
thus more massive progenitors give rise to more luminous explosions. This is
hard to understand if most SNe Ia explode when the primaries reach the
Chandrasekhar mass. Finally, we test the findings of Gallagher et al., that the
residuals of SNe Ia from the Hubble diagram are correlated with host galaxy
metallicity, and we find no such correlation.


  Betting strategies are often expressed formally as martingales. A martingale
is called integer-valued if each bet must be an integer value. Integer-valued
strategies correspond to the fact that in most betting situations, there is a
minimum amount that a player can bet. According to a well known paradigm,
algorithmic randomness can be founded on the notion of betting strategies. A
real X is called integer-valued random if no effective integer-valued
martingale succeeds on X. It turns out that this notion of randomness has
interesting interactions with genericity and the computably enumerable degrees.
We investigate the computational power of the integer-valued random reals in
terms of standard notions from computability theory.


  An expression for the spin-orbit interaction coupling between different
levels, which was shown to be aberrant more than thirty years ago persists in
the literature without clear indication of what is used. It leads to
expressions quite simpler than they should be. After an attempt to warn the
community of the nuclear physicists on this strange situation
(nucl-th/0312038), the authors of the publication in which the "aberrant"
interaction is described and used, try to justify their work (nucl-th/0401055),
by a very strange "symmetrization" of something already symmetric. They claim
also that their method allows to solve some problem related to the Pauli
principle and give some references, among which a book which reports the
solution of such problem almost forty years ago, with a very small effect. An
examination of their own results shows that their optimism is not completely
justified. Nevertheless, any user of ECIS, sensitive to their arguments, is
requested to ask their opinion to these five coauthors before publishing.


  The Pauli exclusion principle in quantum mechanics has a profound influence
on the structure of matter and on interactions between fermions. Almost 30
years ago it was predicted that the Pauli exclusion principle could lead to a
suppression of spontaneous emission, and only recently several experiments
confirmed this phenomenon. Here we report that this so-called Pauli blockade
not only affects incoherent processes but also, more generally, coherently
driven systems. It manifests itself as an intriguing sub-Doppler narrowing of a
doubly-forbidden transition profile in an optically trapped Fermi gas of
$^3\mathrm{He}$. By actively pumping atoms out of the excited state, we break
the coherence of the excitation and lift the narrowing effect, confirming the
influence of Pauli blockade on the transition profile. This new insight into
the interplay between quantum statistics and coherent driving is a promising
development for future applications involving fermionic systems.


  Let $F\in\mathbb{Z}[x,y]$ and $m\ge2$ be an integer. A set $A\subset
\mathbb{Z}$ is called an $(F,m)$-Diophantine set if $F(a,b)$ is a perfect
$m$-power for any $a,b\in A$ where $a\ne b$. If $F$ is a bivariate polynomial
for which there exist infinite $(F,m)$-Diophantine sets, then there is a
complete qualitative characterization of all such polynomials $F$. Otherwise,
various finiteness results are known. We prove that given a finite set of
distinct integers $ S$ of size $n$, there are infinitely many bivariate
polynomials $F$ such that $ S$ is an $(F,2)$-Diophantine set. In addition, we
show that the degree of $F$ can be as small as $\displaystyle 4\lfloor
n/3\rfloor$.


  Recent work has demonstrated that black hole thermodynamics and information
loss/restoration in AdS$_3$/CFT$_2$ can be derived almost entirely from the
behavior of the Virasoro conformal blocks at large central charge, with
relatively little dependence on the precise details of the CFT spectrum or OPE
coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro
blocks by classifying all `saddles' that can contribute for arbitrary values of
external and internal operator dimensions in the semiclassical large central
charge limit. The leading saddles, which determine the naive semiclassical
behavior of the Virasoro blocks, all decay exponentially at late times, and at
a rate that is independent of internal operator dimensions. Consequently, the
semiclassical contribution of high-energy states does not resolve a well-known
version of the information loss problem in AdS$_3$. However, we identify two
infinite classes of sub-leading saddles, and one of these classes does not
decay at late times.


  Embedding-based neural topic models could explicitly represent words and
topics by embedding them to a homogeneous feature space, which shows higher
interpretability. However, there are no explicit constraints for the training
of embeddings, leading to a larger optimization space. Also, a clear
description of the changes in embeddings and the impact on model performance is
still lacking. In this paper, we propose an embedding regularized neural topic
model, which applies the specially designed training constraints on word
embedding and topic embedding to reduce the optimization space of parameters.
To reveal the changes and roles of embeddings, we introduce \textbf{uniformity}
into the embedding-based neural topic model as the evaluation metric of
embedding space. On this basis, we describe how embeddings tend to change
during training via the changes in the uniformity of embeddings. Furthermore,
we demonstrate the impact of changes in embeddings in embedding-based neural
topic models through ablation studies. The results of experiments on two
mainstream datasets indicate that our model significantly outperforms baseline
models in terms of the harmony between topic quality and document modeling.
This work is the first attempt to exploit uniformity to explore changes in
embeddings of embedding-based neural topic models and their impact on model
performance to the best of our knowledge.


  A new type of effective atomic pseudopotential for passivation of
semiconductor surfaces is presented. It is shown that the spherical
approximation used in the effective and empirical pseudopotential methods is
not suitable for describing passivants and that, instead, they have to be
regarded as complex quantities. Since the new seudopotentials cannot be handled
as usual bulk ones, the way of implementing them in atomistic methods is
described here, together with a methodology for extracting them trough an
analytic connection to density functional theory, meaning that the new type of
surface potential keeps the {\it ab inito} identity. The effectiveness and high
transferability of this new approach is demonstrated by generating passivant
potentials for six different semiconductor compounds (GaAs, AlAs, Si, Ge, CdSe
and ZnO) and testing them on different kinds of surfaces, including a
passivated 68 atoms CdSe quantum wire in wurtzite structure, obtaining always
an excellent agreement to density functional theory calculations done on the
same systems.


  We report new measurements of the intergalactic medium (IGM) Ly$\alpha$ and
Ly$\beta$ effective optical depth at $5.3<z<6.5$, using a new sample of quasar
sightlines including 32 quasars at $6.308\le z\le7.00$. These quasars provide a
large statistical sample to measure the IGM evolution during the transition
phase of the reionization epoch. We construct a data set of deep optical
spectra of these quasars using VLT, Keck, Gemini, LBT, and MMT. We measure the
Ly$\alpha$ effective optical depth at $5.36<z<6.57$ using the Ly$\alpha$
forests of both individual spectra and the stacked spectrum. The large scatter
of individual measurements is consistent with previous work, suggesting an
inhomogeneous reionization process. Combining our new measurements and previous
results, we obtain a best-fit for the Ly$\alpha$ effective optical depth
evolution at $z>5.3$, $\tau\propto(1+z)^{8.6\pm1.0}$. We then estimate the
observed Ly$\beta$ effective optical depth using Ly$\beta$ forests and convert
them to Ly$\alpha$ optical depth for comparison, which provides additional
constraints on the evolution of the IGM optical depth. The Ly$\beta$-based
measurements are generally in agreement with the best-fit evolution obtained
from Ly$\alpha$ forests. Using this new sample, we identify 389 Ly$\alpha$ and
50 Ly$\beta$ transmission spikes at $5.5<z<6.3$. The upper limits of Ly$\alpha$
optical depth estimated using transmission spikes are well consistent with our
best-fit evolution. The evolution in number density of these high-redshift
transmission spikes suggests a rapid transition phase at the end of the
reionization. Comparison of our optical depth measurements with hydrodynamical
simulations indicates a IGM neutral hydrogen fraction $\langle f_{\rm
HI}\rangle\gtrsim10^{-4}$ at $z=6$.


  We present new magnetic heat capacity and neutron scattering results for two
magnetically frustrated molybdate pyrochlores: $S=1$ oxide Lu$_2$Mo$_2$O$_7$
and $S={\frac{1}{2}}$ oxynitride Lu$_2$Mo$_2$O$_5$N$_2$. Lu$_2$Mo$_2$O$_7$
undergoes a transition to an unconventional spin glass ground state at $T_f
{\sim} 16$ K. However, the preparation of the corresponding oxynitride tunes
the nature of the ground state from spin glass to quantum spin liquid. The
comparison of the static and dynamic spin correlations within the oxide and
oxynitride phases presented here reveals the crucial role played by quantum
fluctuations in the selection of a ground state. Furthermore, we estimate an
upper limit for a gap in the spin excitation spectrum of the quantum spin
liquid state of the oxynitride of ${\Delta} {\sim} 0.05$ meV or
${\frac{\Delta}{|\theta|}}\sim0.004$, in units of its antiferromagnetic Weiss
constant ${\theta} {\sim}-121$ K.


  The focus of this thesis is the construction and analysis of efficient
representations in nonlinear signal processing, and the applications of these
structures to inverse problems in a variety of fields. The work is composed of
three major sections, each associated with a different form of data:
  - Regression and Distance Estimation on Graphs and Riemannian Manifolds. -
Instantaneous Time-Frequency Analysis via Synchrosqueezing. - Multiscale
Dictionaries of Slepian Functions on the Sphere.


  Relations between parameter rigidity of locally free Lie group actions on
closed manifolds and the 1st leafwise cohomology of the orbit foliations are
discussed. Some computational results of the leafwise cohomology are included.


  We construct new supersymmetric multi-black ring solutions on the
Eguchi-Hanson base space as solutions of the five-dimensional minimal
supergravity. The space-time has an asymptotically locally Euclidean time
slice, i.e., it has the spatial infinity with the topology of the lens space
$L(2;1)=S^3/Z_2$. The configurations of black rings are restricted by the
requirement of the absence of a Dirac-Misner string everywhere outside
horizons. Especially, in the case of two black rings, the solutions have the
limit to a pair of rotating black holes with the horizon topology of S^3.


  This paper is a continuation of the work by the same authors on the Cartan
group equipped with the sub-Finsler $\ell_\infty$ norm. We start by giving a
detailed presentation of the structure of bang-bang extremal trajectories. Then
we prove upper bounds on the number of switchings on bang-bang minimizers. We
prove that any normal extremal is either bang-bang, or singular, or mixed.
Consequently, we study mixed extremals. In particular, we prove that every two
points can be connected by a piecewise smooth minimizer, and we give a uniform
bound on the number of such pieces.


  An $e$-star system of order $n$ is a decomposition of the complete graph
$K_n$ into copies of the complete bipartite graph $K_{1,e}$ (or $e$-star). Such
systems are known to exist if and only if $n\geq 2e$ and $e$ divides
$\binom{n}{2}$. We consider block colourings of such systems, where each
$e$-star is assigned a colour, and two $e$-stars which share a vertex receive
different colours. We present a computer analysis of block colourings of small
$3$-star systems. Furthermore, we prove that: (i) for $n\equiv 0,1$ mod $2e$
there exists either an $n$ or $(n-1)$-block colourable $e$-star system of order
$n$; and (ii) when $e=3$, the same result holds in the remaining congruence
classes mod $6$.


  We consider a Deligne-Mumford stack $X$ which is the quotient of an affine
scheme $\operatorname{Spec}A$ by the action of a finite group $G$ and show that
the Balmer spectrum of the tensor triangulated category of perfect complexes on
$X$ is homeomorphic to the space of homogeneous prime ideals in the group
cohomology ring $H^*(G,A)$.


  We present evidence that there is a 4D model that satisfies the conditions of
renormalizability and diffeomorphism invariance simultaneously at the 2-loop
level. The traceless mode is treated perturbatively, while the conformal mode
can be managed exactly. The two conditions constrain the theory strongly and
determine the measure of the gravitational field uniquely. Quantum corrections
of the cosmological constant are computed in part to 3-loop diagrams. The
method to remove the negative-metric states is also discussed from the
viewpoint of diffeomorphism invariance in analogy to the $R_{\xi}$ gauge in
spontaneously broken gauge theory. The model may be a candidate for a continuum
version of 4D simplicial quantum geometry realized in recent numerical
simulations.


  In this article we study functionals of the type considered in \cite{HS21},
i.e. $$ J(v):=\int_{B_1} A(x,u)|\nabla u|^2 +f(x,u)u+ Q(x)\lambda (u)\,dx $$
here $A(x,u)= A_+(x)\chi_{\{u>0\}}+A_-(x) \chi _{\{u<0\}}$, $f(x,u)=
f_+(x)\chi_{\{u>0\}}+f_-(x) \chi _{\{u<0\}}$ and $\lambda(x,u) = \lambda_+(x)
\chi_{\{u>0\}} + \lambda_-(x) \chi_{\{u\le 0\}}$. We prove the optimal
$C^{0,1^-}$ regularity of minimizers of the functional indicated above (with
precise H\"older estimates) when the coefficients $A_{\pm}$ are continuous
functions and $\mu \le A_{\pm}\le \frac{1}{\mu}$ for some $0<\mu<1$, with $f
\in L^N(B_1)$ and $Q$ bounded. We do this by presenting a new compactness
argument and approximation theory similar to the one developed by L. Caffarelli
in \cite{Ca89} to treat the regularity theory for solutions to fully nonlinear
PDEs. Moreover, we introduce the $\mathcal{T}_{a,b}$ operator that allows one
to transfer minimizers from the transmission problems to the
Alt-Caffarelli-Friedman type functionals, {in small scales,} allowing this way
the study of the regularity theory of minimizers of Bernoulli type free
transmission problems.


  We present SIMCO, the first agnostic multi-class object counting approach.
SIMCO starts by detecting foreground objects through a novel Mask RCNN-based
architecture trained beforehand (just once) on a brand-new synthetic 2D shape
dataset, InShape; the idea is to highlight every object resembling a primitive
2D shape (circle, square, rectangle, etc.). Each object detected is described
by a low-dimensional embedding, obtained from a novel similarity-based head
branch; this latter implements a triplet loss, encouraging similar objects
(same 2D shape + color and scale) to map close. Subsequently, SIMCO uses this
embedding for clustering, so that different types of objects can emerge and be
counted, making SIMCO the very first multi-class unsupervised counter.
Experiments show that SIMCO provides state-of-the-art scores on counting
benchmarks and that it can also help in many challenging image understanding
tasks.


  Reconfigurable intelligent surface (RIS) technology is a promising solution
to improve the performance of existing wireless communications. To achieve its
cost-effectiveness advantage, there inevitably exist certain hardware
impairments in the system. Therefore, it is more reasonable to design passive
beamforming in this scenario. Some existing research has considered such
problems under transceiver impairments. However, their performance still leaves
room for improvement, possibly due to their algorithms not properly handling
the fractional structure of the objective function. To address this, the
passive beamforming is redesigned in this correspondence paper, taking into
account both transceiver impairments and the practical phase-shift model. We
tackle the fractional structure of the problem by employing the quadratic
transform. The remaining sub-problems are addressed utilizing the penalty-based
method and the difference-of-convex programming. Since we provide closed-form
solutions for all sub-problems, our algorithm is highly efficient. The
simulation results demonstrate the superiority of our proposed algorithm.


  Spectral measurements in the infrared (IR) optical range provide unique
fingerprints of materials which are useful for material analysis, environmental
sensing, and health diagnostics. Current IR spectroscopy techniques require the
use of optical equipment suited for operation in the IR range, which faces
challenges of inferior performance and high cost. Here we develop a
spectroscopy technique, which allows spectral measurements in the IR range
using visible spectral range components. The technique is based on nonlinear
interference of infrared and visible photons, produced via Spontaneous
Parametric Down Conversion (SPDC). The intensity interference pattern for a
visible photon depends on the phase of an IR photon, which travels through the
media. This allows determining properties of the media in the IR range from the
measurements of visible photons. The technique can substitute and/or complement
conventional IR spectroscopy techniques, as it uses well-developed optical
components for the visible range.


  Recent testing and validation have found that the Geostationary Operational
Environmental Satellite (GOES) microburst products are effective in the
assessment and short-term forecasting of downburst potential and associated
wind gust magnitude. Two products, the GOES sounder Microburst Windspeed
Potential Index (MWPI) and a new two-channel GOES imager brightness temperature
difference (BTD) product have demonstrated capability in downburst potential
assessment. The MWPI, a diagnostic nowcasting product, is designed to infer
attributes of a favorable microburst environment: large CAPE and a convective
mixed layer with a steep temperature lapse rate and low relative humidity in
the surface layer. These conditions foster intense convective downdrafts due to
evaporational cooling as precipitation descends in the sub-cloud layer. More
recently, a new application of the brightness temperature difference (BTD)
between GOES imager channels 3 and 4 has been developed. It has been found that
the BTD between GOES infrared channel 3 (water vapor) and channel 4 (thermal
infrared) can highlight regions where severe outflow wind generation (i.e.
downbursts, microbursts) is likely due to the channeling of dry
mid-tropospheric air into the precipitation core of a deep, moist convective
storm. This paper provides an updated assessment of the MWPI and new GOES BTD
algorithm, presents case studies demonstrating effective operational use of the
microburst products, and presents validation results for the 2010 convective
season over the United States Great Plains and Atlantic Coast regions.


  Sample complexity and safety are major challenges when learning policies with
reinforcement learning for real-world tasks, especially when the policies are
represented using rich function approximators like deep neural networks.
Model-based methods where the real-world target domain is approximated using a
simulated source domain provide an avenue to tackle the above challenges by
augmenting real data with simulated data. However, discrepancies between the
simulated source domain and the target domain pose a challenge for simulated
training. We introduce the EPOpt algorithm, which uses an ensemble of simulated
source domains and a form of adversarial training to learn policies that are
robust and generalize to a broad range of possible target domains, including
unmodeled effects. Further, the probability distribution over source domains in
the ensemble can be adapted using data from target domain and approximate
Bayesian methods, to progressively make it a better approximation. Thus,
learning on a model ensemble, along with source domain adaptation, provides the
benefit of both robustness and learning/adaptation.


  We present Las Vegas algorithms for constructive recognition and constructive
membership testing of the Ree groups 2G_2(q) = Ree(q), where q = 3^{2m + 1} for
some m > 0, in their natural representations of degree 7. The input is a
generating set X.
  The constructive recognition algorithm is polynomial time given a discrete
logarithm oracle. The constructive membership testing consists of a
pre-processing step, that only needs to be executed once for a given X, and a
main step. The latter is polynomial time, and the former is polynomial time
given a discrete logarithm oracle.
  Implementations of the algorithms are available for the computer algebra
system MAGMA.


  Within the framework of the displacement-based Virtual Element Method (VEM)
for plane elasticity a significant problem is represented by an accurate
evaluation of the stress field. In particular, in the classical VEM
formulation, a suitable operator which maps to the strain field is introduced
in order to allow the calculation of the stiffness matrix. The stress field is
then computed using that strian field, by using the constitutive law.
Considering for example a first-order formulation for a homogeneous material,
strains are locally mapped onto constant functions, and stresses are
accordingly piecewise constant. However, the virtual displacements might
engender more complex strain fields for polygons which are not triangles. In
this paper, Recovery by Compatibility in Patches is used in order to mitigate
such an effect and, thus, enhance the accuracy of the recovered stress field.
The procedure is simple, efficient and can be readily implemented in existing
codes. Numerical tests confirm the soundness of the proposed approach.


  We present a new approach to discuss two dimensional chiral and non-chiral
hydrodynamics with gauge and gravitational anomalies. Exact constitutive
relations for the stress tensor and charge current are obtained. For the chiral
theory, the constitutive relations may be put in the ideal (chiral) fluid form
whereas the constitutive relations corresponding to non-chiral case do not take
the ideal fluid form. The constitutive relations in the presence of both
gravity and gauge sectors are new. These expressions, in the absence of the
gauge sector, reproduce the results obtained in the gradient expansion
approach.


  Let H^2(D) denote the classical Hardy space of the open unit disk D in the
complex plane. We obtain descriptions of both the spectrum and essential
spectrum of composition operators on H^2(D) whose symbols belong to the class
S(2) introduced by Kriete and Moorhouse [Trans. Amer. Math. Soc., 359, 2007].
Our work reveals new possibilities for the shapes of composition-operator
spectra, settling a conjecture of Cowen's [J. Operator Th. 9, 1983]. Our
results depend on a number of lemmas, perhaps of independent interest, that
provide spectral characterizations of sums of elements of a unital algebra over
a field when certain pairwise products of the summands are zero.


  We obtain a concentration inequality for the maximum degree of a vertex in a
uniformly random dissection of a polygon. This resolves a conjecture posed by
Curien and Kortchemski in 2012. Our approach is based on a bijection with dual
trees and the tools of analytic combinatorics.


  We analyze one particle, two-center quantum problems which admit separation
of variables in prolate spheroidal coordinates, a natural restriction satisfied
by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly.
We give the details of the Hamiltonian reduction of the 3D system to a 2D
system with modified potential that is separable in elliptic coordinates. The
potentials for which there is double-periodicity of the Schr\"odinger operator
in the space of prolate spheroidal coordinates, including one for the H$_2^+$
molecular ion, are indicated. We study possible potentials that admit
exact-solvability is as well as all models known to us with the
(quasi)-exact-solvability property for the separation equations. We find deep
connections between second-order superintegrable and conformally
superintegrable systems and these tractable problems. In particular we derive a
general 4-parameter expression for a model potential that is always integrable
and is conformally superintegrable for some parameter choices.


  Strong coupling between magnons and cavity photons was studied extensively
for quantum electrodynamics in the past few years. Recently, the strong
magnon-magnon coupling between adjacent layers in magnetic multilayers has been
reported. However, the strongly coupled magnons confined in a single nanomagnet
remains to be revealed. Here, we report the interaction between different
magnon modes in a single magnonic cavity. The intermodel coupling between edge
and center magnon modes in the strong coupling regime was approached with a
maximum coupling strength of 0.494 GHz and cooperativity of 60.1 with a damping
of 1X10-3. Furthermore, it is found that the coupling strength is highly
dependent on the geometric parameters of the magnonic cavity. Our findings
could greatly enrich the still evolving field of quantum magnonics.


  Long-range effects on the pyroelectric coefficient of a ferroelectric
superlattice consisting of two different ferroelectric materials are
investigated based on the Transverse Ising Model. The effects of the
interfacial coupling and the thickness of one period on the pyroelectric
coefficient of the ferroelectric superlattice are studied by taking into
account the long-range interaction. It is found that with the increase of the
strength of the long-range interaction, the pyroelectric coefficient decreases
when the temperature is lower than the phase transition temperature; the number
of the pyroelectric peaks decreases gradually and the phase transition
temperature increases. It is also found that with the decrease of the
interfacial coupling and the thickness of one period, the phase transition
temperature and the number of the pyroelectric peaks decrease.


  This article, based on a talk, treats some elementary, but not completely
simple examples from probability. They concern multiple birthday coincidences,
throwing dice, the combinatorics of the German card game "Doppelkopf", and the
properties of products of uniformly distributed random numbers. The material, a
lot of which was not taken from or found in other sources, should be of
interest to all those who lecture or plan to lecture on probability, especially
on an elementary or introductory level, and are looking for challenging
examples or problems.


  A short historical overview is given on the development of our knowledge of
complex dynamical systems with special emphasis on ergodicity and chaos, and on
the semiclassical quantization of integrable and chaotic systems. The general
trace formula is discussed as a sound mathematical basis for the semiclassical
quantization of chaos. Two conjectures are presented on the basis of which it
is argued that there are unique fluctuation properties in quantum mechanics
which are universal and, in a well defined sense, maximally random if the
corresponding classical system is strongly chaotic. These properties constitute
the quantum mechanical analogue of the phenomenon of chaos in classical
mechanics. Thus quantum chaos has been found.


  Autonomous driving and its widespread adoption have long held tremendous
promise. Nevertheless, without a trustworthy and thorough testing procedure,
not only does the industry struggle to mass-produce autonomous vehicles (AV),
but neither the general public nor policymakers are convinced to accept the
innovations. Generating safety-critical scenarios that present significant
challenges to AV is an essential first step in testing. Real-world datasets
include naturalistic but overly safe driving behaviors, whereas simulation
would allow for unrestricted exploration of diverse and aggressive traffic
scenarios. Conversely, higher-dimensional searching space in simulation
disables efficient scenario generation without real-world data distribution as
implicit constraints. In order to marry the benefits of both, it seems
appealing to learn to generate scenarios from both offline real-world and
online simulation data simultaneously. Therefore, we tailor a Reversely
Regularized Hybrid Offline-and-Online ((Re)$^2$H2O) Reinforcement Learning
recipe to additionally penalize Q-values on real-world data and reward Q-values
on simulated data, which ensures the generated scenarios are both varied and
adversarial. Through extensive experiments, our solution proves to produce more
risky scenarios than competitive baselines and it can generalize to work with
various autonomous driving models. In addition, these generated scenarios are
also corroborated to be capable of fine-tuning AV performance.


  Almost climate neutral buildings are one of the core goals in terms of
sustainability. Beside the support of the necessary design decisions for an
integrated, interoperable, ecological and economical operation of building
energy systems, innovative management solutions for scheduling the operation of
decentralized energy systems are of great importance. The challenge is optimal
interaction between energy system components in terms of own consumption,
energy efficiency and resource consumption as well as greenhouse gas emissions.
To achieve these goals a modular optimization approach based on Mixed Integer
Programming is proposed. In detail, and to our knowledge the first time, a MIP
model for the dynamic behavior of fuel cell Combined Heat and Power plants is
presented. Our approach is evaluated for the operation of heat pumps showing
that their energy efficiency can be increased significantly.


  We summarise basic properties of MHD turbulence. First, MHD turbulence is not
so messy as it is believed. In fact, the notion of strong non-linear coupling
of compressible and incompressible motions along MHD cascade is not tenable.
Alfven, slow and fast modes of MHD turbulence follow their own cascades and
exhibit degrees of anisotropy consistent with theoretical expectations. Second,
the fast decay of turbulence is not related to the compressibility of fluid.
Rates of decay of compressible and incompressible motions are very similar.
Third, the properties of Alfven and slow modes are similar to their
counterparts in the incompressible MHD. The properties of fast modes are
similar to accoustic turbulence, which does require more studies. Fourth, the
density at low Mach numbers and logarithm of density at higher Mach numbers
exhibit Kolmogorov-type spectrum.


  Changes in lattice structure across sub-regions of protein crystals are
challenging to assess when relying on whole crystal measurements. Because of
this difficulty, macromolecular structure determination from protein micro and
nano crystals requires assumptions of bulk crystallinity and domain block
substructure. To evaluate the fidelity of these assumptions in protein
nanocrystals we map lattice structure across micron size areas of cryogenically
preserved three-dimensional peptide crystals using a nano-focused electron
beam. This approach produces diffraction from as few as 1,500 molecules in a
crystal, is sensitive to crystal thickness and three-dimensional lattice
orientation. Real-space maps reconstructed from unsupervised classification of
diffraction patterns across a crystal reveal regions of crystal order/disorder
and three-dimensional lattice reorientation on a 20nm scale. The lattice
nano-ripples observed in micron-sized macromolecular crystals provide a direct
view of their plasticity. Knowledge of these features is a first step to
understanding crystalline macromolecular self-assembly and improving the
determination of structures from protein nano and microcrystals from single or
serial crystal diffraction.


  We point out that neutrinos can have enhanced couplings to photons, if light
(pseudo)scalar mediators are present, resulting in potentially measurable
neutrino polarizability. We show that the expected suppression from small
neutrino masses can be compensated by the light mediator mass, generating
dimension 7 Rayleigh operators at low scales. We explore the rich phenomenology
of such models, computing in details the constraints on the viable parameter
space, spanned by the couplings of the mediator to neutrinos and photons.
Finally, we build several explicit models that lead to enhanced neutrino
polarizability by modifying the inverse see-saw majoron, i.e., the
pseudo-Nambu-Goldstone boson of the $U(1)_L$ global lepton number responsible
for generating small neutrino masses.


  The graphs of Okamoto's functions, denoted by $K_q$, are self-affine fractal
curves contained in $[0,1]^2$, parameterised by $q \in (1,2)$. In this paper we
consider the cardinality and dimension of the intersection of these curves with
horizontal lines. Our first theorem proves that if $q$ is sufficiently close to
$2$, then $K_q$ admits a horizontal slice with exactly three elements. Our
second theorem proves that if a horizontal slice of $K_q$ contains an
uncountable number of elements then it has positive Hausdorff dimension
provided $q$ is in a certain subset of $(1,2)$. Finally, we prove that if $q$
is a $k$-Bonacci number for some $k \in \mathbb{N}_{\geq 3}$, then the set of
$y \in [0,1]$ such that the horizontal slice at height $y$ has $(2m+1)$
elements has positive Hausdorff dimension for any $m \in \mathbb{N}$. We also
show that, under the same assumption on $q$, there is some horizontal slice
whose cardinality is countably infinite.


  Kraichnan (1965) proposed that MHD turbulence occurs as a result of
collisions between oppositely directed Alfv\'en wave packets. Recent work has
generated some controversy over the nature of non linear couplings between
colliding Alfv\'en waves. We find that the resolution to much of the confusion
lies in the existence of a new type of turbulence, intermediate turbulence, in
which the cascade of energy in the inertial range exhibits properties
intermediate between those of weak and strong turbulent cascades. Some
properties of intermediate MHD turbulence are: (i) in common with weak
turbulent cascades, wave packets belonging to the inertial range are long
lived; (ii) however, components of the strain tensor are so large that, similar
to the situation in strong turbulence, perturbation theory is not applicable;
(iii) the breakdown of perturbation theory results from the divergence of
neighboring field lines due to wave packets whose perturbations in velocity and
magnetic fields are localized, but whose perturbations in displacement are not;
(iv) 3--wave interactions dominate individual collisions between wave packets,
but interactions of all orders $n\geq 3$ make comparable contributions to the
intermediate turbulent energy cascade; (v) successive collisions are correlated
since wave packets are distorted as they follow diverging field lines; (vi) in
common with the weak MHD cascade, there is no parallel cascade of energy, and
the cascade to small perpendicular scales strengthens as it reaches higher wave
numbers; (vii) For an appropriate weak excitation, there is a natural
progression from a weak, through an intermediate, to a strong cascade.


  In the present work, we have searched the existence of anisotropic and
non-singular compact star in the $f(R,T)$ gravity by taking into account the
non-exotic equation of state (EoS). In order to obtain the solutions of the
matter content of compact object, we assume the well known barotropic form of
EoS that yields the linear relation between pressures and energy density. We
propose the existence of non-exotic compact star which shows the validation of
energy conditions and stability with in the $f(R,T)$ extended theory of gravity
perspective. The linear material correction in the extended theory the matter
content of compact star remarkably able to satisfies energy condition. We
discuss various physical features of compact star and show that proposed model
of stellar object satisfies all regularity conditions and is stable as well as
singularity-free.


  Propagation of extremely short pulses of electromagnetic field
(electromagnetic spikes) is considered in the framework of the total
Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities
(Duffing model) represent the material medium and wave propagation is governed
by the 1-d bidirectional Maxwell equations. This system of equations has a one
parameter family of exact analytical solutions representing an electromagnetic
spike propagating on a zero or a nonzero background. We find that the total
Maxwell-Duffing equations can be written as a system in bilinear form and that
the one-soliton solution of this system coincides with the steady state
solution obtained previously.


  We investigate magnetization dynamics in a spin-Hall oscillator using a
direct current measurement as well as conventional microwave spectrum analysis.
When the current applies an anti-damping spin-transfer torque, we observe a
change in resistance which we ascribe to the excitation of incoherent exchange
magnons. A simple model is developed based on the reduction of the effective
saturation magnetization, quantitatively explaining the data. The observed
phenomena highlight the importance of exchange magnons on the operation of
spin-Hall oscillators.


  We studied the field dependencies of specific heat coefficient $\gamma(H) =
\lim_{T \rightarrow 0} C(T,H)/T $ and thermal conductivity coefficient $\lim_{T
\rightarrow 0} \kappa(T ,H)/T$ of the $\pm$s-wave state in the mixed state. We
found that it is a generic feature of the two band s-wave state with the
unequal sizes of gaps, small $\Delta_S$ and large $\Delta_L$, that Doppler
shift of the quasiparticle excitations (Volovik effect) creates a finite
density of states, on the extended states outside of vortex cores, proportional
to $H$ in contrast to the $\sqrt{H}$ dependence of the d-wave state. Impurity
scattering effect on the $\pm$s-wave state, however, makes this generic
$H$-linear dependence sublinear approaching to the $\sqrt{H}$ behavior. Our
calculations of $\lim_{T \rightarrow 0} \kappa(T ,H)/T$ successfully fit the
experimental data of Ba(Fe$_{1-x}$Co$_x )_2$ As$_2$ with different Co-doping
$x$ by systematically varying the gap size ratio $R= |\Delta_S | / |\Delta_L
|$. We also resolve the dilemma of a substantial value of $\gamma(H \rightarrow
0)$ but almost zero value of $\lim_{T \rightarrow 0} \kappa(T ,H \rightarrow
0)/T$, observed in experiments.


  In sandstorms and thunderclouds, turbulence-induced collisions between solid
particles and ice crystals lead to inevitable triboelectrification. The charge
segregation is usually size-dependent, with small particles charged negatively
and large particles charged positively. In this work, we perform numerical
simulations to study the influence of charge segregation on the dynamics of
bidispersed inertial particles in turbulence. Direct numerical simulations of
homogeneous isotropic turbulence are performed with the Taylor Reynolds number
$\mathrm{Re}_{\lambda}=147.5$, while particles are subjected to both
electrostatic interactions and fluid drag, with Stokes number of 1 and 10 for
small and large particles, respectively. Coulomb repulsion/attraction are shown
to effectively inhibit/enhance particle clustering within a short range.
Besides, the mean relative velocity between same-size particles is found to
rise as the particle charge increases because of the exclusion of low-velocity
pairs, while the relative velocity between different-size particles is almost
unaffected, emphasizing the dominant roles of differential inertia. The mean
Coulomb-turbulence parameter, $\mathrm{Ct}_0$, is then defined to characterize
the competition between the Coulomb potential energy and the mean relative
kinetic energy. In addition, a model is proposed to quantify the rate at which
charged particles approach each other and captures the transition of the
particle relative motion from the turbulence-dominated regime to the
electrostatic-dominated regime. Finally, the probability distribution function
of the approaching rate between particle pairs are examined, and its dependence
on the Coulomb force is further discussed using the extended Coulomb-turbulence
parameter.


  We report a new workflow for background-oriented schlieren (BOS), termed
"physics-informed BOS," to extract density, velocity, and pressure fields from
a pair of reference and distorted images. Our method uses a physics-informed
neural network (PINN) to produce flow fields that simultaneously satisfy the
measurement data and governing equations. For the high-speed flows of interest
in this work, we specify a physics loss based on the Euler and irrotationality
equations. BOS is a quantitative fluid visualization technique that is used to
characterize high-speed flows. Images of a background pattern, positioned
behind the target flow, are processed using computer vision and tomography
algorithms to determine the density field. Crucially, BOS features a series of
ill-posed inverse problems that require supplemental information (i.e., in
addition to the images) to accurately reconstruct the flow. Current BOS
workflows rely upon interpolation of the images or a penalty term to promote a
globally- or piecewise-smooth solution. However, these algorithms are
invariably incompatible with the flow physics, leading to errors in the density
field. Physics-informed BOS directly reconstructs all the flow fields using a
PINN that includes the BOS measurement model and governing equations. This
procedure improves the accuracy of density estimates and also yields velocity
and pressure data, which was not previously available. We demonstrate our
approach by reconstructing synthetic data that corresponds to analytical and
numerical phantoms as well as experimental measurements. Our physics-informed
reconstructions are significantly more accurate than conventional BOS
estimates. Further, to the best of our knowledge, this work represents the
first use of a PINN to reconstruct a supersonic flow from experimental data of
any kind.


  Previous works on Human Pose and Shape Estimation (HPSE) from RGB images can
be broadly categorized into two main groups: parametric and non-parametric
approaches. Parametric techniques leverage a low-dimensional statistical body
model for realistic results, whereas recent non-parametric methods achieve
higher precision by directly regressing the 3D coordinates of the human body
mesh. This work introduces a novel paradigm to address the HPSE problem,
involving a low-dimensional discrete latent representation of the human mesh
and framing HPSE as a classification task. Instead of predicting body model
parameters or 3D vertex coordinates, we focus on predicting the proposed
discrete latent representation, which can be decoded into a registered human
mesh. This innovative paradigm offers two key advantages. Firstly, predicting a
low-dimensional discrete representation confines our predictions to the space
of anthropomorphic poses and shapes even when little training data is
available. Secondly, by framing the problem as a classification task, we can
harness the discriminative power inherent in neural networks. The proposed
model, VQ-HPS, predicts the discrete latent representation of the mesh. The
experimental results demonstrate that VQ-HPS outperforms the current
state-of-the-art non-parametric approaches while yielding results as realistic
as those produced by parametric methods when trained with little data. VQ-HPS
also shows promising results when training on large-scale datasets,
highlighting the significant potential of the classification approach for HPSE.
See the project page at https://g-fiche.github.io/research-pages/vqhps/


  We propose a new mode of operation of an electron pump consisting of two
weakly coupled quantum dots connected to reservoirs. An electron can be
transferred within the device at zero bias voltage when it is subjected to
electromagnetic radiation, thereby exciting the double dot. The excited state
can decay by transferring charge from one lead and to the other lead in one
direction. Depending on the energies of the intermediate states in the pumping
cycle, which are controlled by the gate voltages, this transport is either
incoherent via well-known sequential tunneling processes, or coherent via a
inelastic co-tunneling process. The latter novel mode of operation is possible
only when interdot Coulomb charging is important. The D.C. transport through
the system can be controlled by the frequency of the applied radiation. We
concentrate on the resonant case, when the frequency matches the energy
difference for exciting an electron from one dot into the other. The resonant
peaks in the pumping current should be experimentally observable. We have
developed a density matrix approach which describes the dynamics of the system
on timescales much larger than the period of the applied irradiation. In
contrast to previous works we additionally consider the case of slow modulation
of the irradiation amplitude. Harmonic modulation produces additional sidepeaks
in the photoresponse, and pulsed modulation can be used to resolve the Rabi
frequency in the time-averaged current.


  In this paper, we propose a new self-supervised method, which is called
Denoising Masked AutoEncoders (DMAE), for learning certified robust classifiers
of images. In DMAE, we corrupt each image by adding Gaussian noises to each
pixel value and randomly masking several patches. A Transformer-based
encoder-decoder model is then trained to reconstruct the original image from
the corrupted one. In this learning paradigm, the encoder will learn to capture
relevant semantics for the downstream tasks, which is also robust to Gaussian
additive noises. We show that the pre-trained encoder can naturally be used as
the base classifier in Gaussian smoothed models, where we can analytically
compute the certified radius for any data point. Although the proposed method
is simple, it yields significant performance improvement in downstream
classification tasks. We show that the DMAE ViT-Base model, which just uses
1/10 parameters of the model developed in recent work arXiv:2206.10550,
achieves competitive or better certified accuracy in various settings. The DMAE
ViT-Large model significantly surpasses all previous results, establishing a
new state-of-the-art on ImageNet dataset. We further demonstrate that the
pre-trained model has good transferability to the CIFAR-10 dataset, suggesting
its wide adaptability. Models and code are available at
https://github.com/quanlin-wu/dmae.


  Optimization of resonances associated with 1-D wave equations in
inhomogeneous media is studied under the constraint $\| B \|_1 <= m$ on the
nonnegative function $B \in L^1 (0,\ell)$ that represents the medium's
structure. From the Physics and Optimization points of view, it convenient to
generalize the problem replacing $B$ by a nonnegative measure $d M$ and
imposing on $d M$ the condition that its total mass is $<= m$. The problem is
to design for a given frequency $\alpha \in R$ a medium that generates a
resonance $ \omega $ on the line $\alpha + i R$ with a minimal possible decay
rate $| Im \omega |$. Such resonances are said to be of minimal decay and form
a Pareto frontier. We show that corresponding optimal measures consist of
finite number of point masses, and that this result yields non-existence of
optimizers for the problem over the set of absolutely continuous measures $B(x)
dx$. Then we derive restrictions on optimal point masses and their positions.
These restrictions are strong enough to calculate optimal $d M$ if the optimal
resonance $ \omega $, the first point mass $m_1$, and one more geometric
parameter are known. This reduces the original infinitely-dimensional problem
to optimization over four real parameters. For small frequencies, we explicitly
find the Pareto set and the corresponding optimal measures $d M$. The technique
of the paper is based on the two-parameter perturbation method and the notion
of local boundary point. The latter is introduced as a generalization of local
extrema to vector optimization problems.


  In recent times machine learning methods have made significant advances in
becoming a useful tool for analyzing physical systems. A particularly active
area in this theme has been "physics-informed machine learning" which focuses
on using neural nets for numerically solving differential equations. In this
work, we aim to advance the theory of measuring out-of-sample error while
training DeepONets -- which is among the most versatile ways to solve PDE
systems in one-shot.
  Firstly, for a class of DeepONets, we prove a bound on their Rademacher
complexity which does not explicitly scale with the width of the nets involved.
Secondly, we use this to show how the Huber loss can be chosen so that for
these DeepONet classes generalization error bounds can be obtained that have no
explicit dependence on the size of the nets. We note that our theoretical
results apply to any PDE being targeted to be solved by DeepONets.


  The superconducting phase of the 2D one-band Hubbard model is studied within
the FLEX approximation and by using an Eliashberg theory. We investigate the
doping dependence of $T_c$, of the gap function $\Delta ({\bf k},\omega)$ and
of the effective pairing interaction. Thus we find that $T_c$ becomes maximal
for $13 \; \%$ doping. In {\it overdoped} systems $T_c$ decreases due to the
weakening of the antiferromagnetic correlations, while in the {\it underdoped}
systems due to the decreasing quasi particle lifetimes. Furthermore, we find
{\it shadow states} below $T_c$ which affect the electronic excitation spectrum
and lead to fine structure in photoemission experiments.


  Industrial sensor data provides significant insights into the failure risks
of microgrid generation assets. In traditional applications, these
sensor-driven risks are used to generate alerts that initiate maintenance
actions without considering their impact on operational aspects. The focus of
this paper is to propose a framework that i) builds a seamless integration
between sensor data and operational & maintenance drivers, and ii) demonstrates
the value of this integration for improving multiple aspects of microgrid
operations. The proposed framework offers an integrated stochastic optimization
model that jointly optimizes operations and maintenance in a multi-microgrid
setting. Maintenance decisions identify optimal crew routing, opportunistic
maintenance, and repair schedules as a function of dynamically evolving
sensor-driven predictions on asset life. Operational decisions identify
commitment and generation from a fleet of distributed energy resources,
storage, load management, as well as power transactions with the main grid and
neighboring microgrids. Operational uncertainty from renewable generation,
demand, and market prices are explicitly modeled through scenarios in the
optimization model. We use the structure of the model to develop a
decomposition-based solution algorithm to ensure computational scalability. The
proposed model provides significant improvements in reliability and enhances a
range of operational outcomes, including costs, renewables, generation
availability, and resilience.


  We study Vasiliev's system of higher spin gauge fields coupled to massive
scalars in AdS_3, and compute the tree level two and three point functions.
These are compared to the large N limit of the W_N minimal model, and
nontrivial agreements are found. We propose a modified version of the
conjecture of Gaberdiel and Gopakumar, under which the bulk theory is
perturbatively dual to a subsector of the CFT that closes on the sphere.


  The antiferromagnetic kagome lattice compound FeGe has been revealed to host
an emergent charge-density-wave (CDW) state which manifests complex interplay
between the spin, charge and lattice degrees of freedom. Here, we present a
comprehensive study of the de Haas-van Alphen effect by measuring torque
magnetometry under magnetic fields up to 45.2 T to map Fermi surfaces in this
unusual CDW state. For field along the $c$ direction, we resolve four cyclotron
orbits; the largest one roughly corresponding to the area of the 2$\times$2
folded Brillouin zone. Three smaller orbits are characterized by light
effective cyclotron masses range from (0.18-0.30) $m_e$. Angle-resolved
measurements identify one Fermi surface segment with weak anisotropy. Combined
with band structure calculations, our results suggest that features of unfolded
Fermi surfaces are robust against CDW reconstruction, corroborating the novel
effect of a short-ranged CDW on the electronic structure.


  Spin relaxation torque ${\cal T}$ in uniform metallic ferromagnets with the
spin-orbit interaction arising from random impurities is calculated
microscopically. ${\cal T}$ is shown to be written by spatial derivatives of
the electric field, but is not always given as a divergence of a torque dipole
density. The result is due to the fast dissipation of the orbital angular
momentum, and thus a conserving spin current cannot be defined. It is discussed
that the $\beta$ term in the spin transfer torque can also be asymmetric.


  We prove the following conjecture of Zeilberger. Denoting by $C_n$ the
Catalan number, define inductively $A_n$ by $(-1)^{n-1}A_n=C_n+\sum_{j=1}^{n-1}
(-1)^{j} \binom{2n-1}{2j-1} A_j \,C_{n-j}$ and $a_n=2A_n/C_n$. Then $a_n$
(hence $A_n$) is a positive integer.


  The parametric g-formula is an approach to estimating causal effects of
sustained treatment strategies from observational data. An often cited
limitation of the parametric g-formula is the g-null paradox: a phenomenon in
which model misspecification in the parametric g-formula is guaranteed under
the conditions that motivate its use (i.e., when identifiability conditions
hold and measured time-varying confounders are affected by past treatment).
Many users of the parametric g-formula know they must acknowledge the g-null
paradox as a limitation when reporting results but still require clarity on its
meaning and implications. Here we revisit the g-null paradox to clarify its
role in causal inference studies. In doing so, we present analytic examples and
a simulation-based illustration of the bias of parametric g-formula estimates
under the conditions associated with this paradox. Our results highlight the
importance of avoiding overly parsimonious models for the components of the
g-formula when using this method.


  The authors discuss the role of controversy in mathematics as a preface to
two opposing articles on computational complexity theory: "Some basic
information on information-based complexity theory" by Beresford Parlett
[math.NA/9201266] and "Perspectives on information-based complexity" by J. F.
Traub and Henryk Wo\'zniakowski [math.NA/9201269].


  We present theoretical analysis of the astrometric searches for extrasolar
planets with the Space Interferometry Mission (SIM). Particularly, we derive a
model for the future measurements with SIM and discuss the problem of reliable
estimation of orbital elements of planets. For this purpose we propose a new
method of data analysis and present a numerical test of its application on
simulated SIM astrometric measurements of $\upsilon$ Andromedae planetary
system. We demonstrate that our approach allows successfull determination of
its orbital elements.


  I summarize the current state of solar neutrino research and then give my
answer to the question: What should we do next?


  In this work, we propose the Haar wavelet method for the coupled degenerate
reaction-diffusion PDEs and the ODEs having non-linear a source with Neumann
boundary, applicable in various fields of the natural sciences, engineering,
and economics, for example in gas dynamics, certain biological models, assets
pricing in economics, composite media etc. Convergence analysis of the proposed
numerical scheme has been carried out. We use the GMRES solver to solve the
linear system of equations. Numerical solutions for the model problems of
medical significance have been successfully solved.


  The quay crane scheduling problem (QCSP) determines the handling sequence of
tasks at ship bays by a set of cranes assigned to a container vessel such that
the vessel's service time is minimized. A number of heuristics or
meta-heuristics have been proposed to obtain the near-optimal solutions to
overcome the NP-hardness of the problem. In this article, the idea of
generalized extremal optimization (GEO) is adapted to solve the QCSP with
respect to various interference constraints. The resulted GEO is termed as the
modified GEO. A randomized searching method for neighboring task-to-QC
assignments to an incumbent task-to-QC assignment is developed in executing the
modified GEO. In addition, a unidirectional search decoding scheme is employed
to transform a task-to-QC assignment to an active quay crane schedule. The
effectiveness of the developed GEO is tested on a suite of benchmark problems
introduced by \citet{KimPark2004}. Compared with other well known existing
approaches, the experiment results show that the proposed modified GEO is
capable of obtaining the optimal or near-optimal solution in reasonable time,
especially for large-sized problems.


  We consider a symmetric finite-range contact process on $\mathbb{Z}$ with two
types of particles (or infections), which propagate according to the same
supercritical rate and die (or heal) at rate $1$. Particles of type 1 can
occupy any site in $(-\infty, 0]$ that is empty or occupied by a particle of
type 2 and, analogously, particles of type 2 can occupy any site in
$[1,+\infty)$ that is empty or occupied by a particle of type 1. We consider
the model restricted to a finite interval $[-N + 1,N] \cap \mathbb{Z}$. If the
initial configuration is $\mathbf{1}_ {(-N,0]}+2\mathbf{1}_{[1,N)}$, we prove
that this system exhibits two metastable states: one with the two species and
the other one with the family that survives the competition.


  This paper is concerned with the dynamics of a binary mixture of rod--like,
repulsive colloidal particles driven out of equilibrium by means of a steady
shear flow (Couette geometry). To this end we first derive, starting from a
microscopic density functional in Parsons--Lee approximation, a mesoscopic free
energy functional whose main variables are the orientational order parameter
tensors. Based on this mesoscopic functional we then explore the stability of
isotropic and nematic equilibrium phases in terms of composition and rod
lengths. Second, by combining the equilibrium theory with the Doi--Hess
approach for the order parameter dynamics under shear, we investigate the
orientational dynamics of binary mixtures for a range of shear rates and
coupling parameters. We find a variety of dynamical states, including
synchronized oscillatory states of the two components, but also symmetry
breaking behavior where the components display different in--plane oscillatory
states.


  The formation of primordial black holes is studied using superconformal
inflationary $\alpha$-attractors. An inflaton potential is constructed with a
plateau-like region which brings about the onset of an ultra slow-roll region
where the required enhancement in the curvature power spectrum takes place.
This is accomplished by carefully fine-tuning the parameters in the potential.
For the parameter sets, the amount of observable inflation is such that the
curvature perturbation $\mathcal{P}_{\mathcal{R}}$ peaks at $\sim
10^{14}\text{Mpc}^{-1}$, producing PBHs in the mass window $10^{16}\text{g}\leq
M \leq 10^{18}\text{g}$. The reheating period after inflation is taken into
account to determine whether or not PBH formation takes place in such a phase.
Finally, the spectrum of second order gravitational waves, that can arise due
to the curvature perturbation enhancement, is calculated.


  We address the problem of estimating the relative 6D pose, i.e., position and
orientation, of a target spacecraft, from a monocular image, a key capability
for future autonomous Rendezvous and Proximity Operations. Due to the
difficulty of acquiring large sets of real images, spacecraft pose estimation
networks are exclusively trained on synthetic ones. However, because those
images do not capture the illumination conditions encountered in orbit, pose
estimation networks face a domain gap problem, i.e., they do not generalize to
real images. Our work introduces a method that bridges this domain gap. It
relies on a novel, end-to-end, neural-based architecture as well as a novel
learning strategy. This strategy improves the domain generalization abilities
of the network through multi-task learning and aggressive data augmentation
policies, thereby enforcing the network to learn domain-invariant features. We
demonstrate that our method effectively closes the domain gap, achieving
state-of-the-art accuracy on the widespread SPEED+ dataset. Finally, ablation
studies assess the impact of key components of our method on its generalization
abilities.


  Reconstructing perceived natural images from fMRI signals is one of the most
engaging topics of neural decoding research. Prior studies had success in
reconstructing either the low-level image features or the semantic/high-level
aspects, but rarely both. In this study, we utilized an Instance-Conditioned
GAN (IC-GAN) model to reconstruct images from fMRI patterns with both accurate
semantic attributes and preserved low-level details. The IC-GAN model takes as
input a 119-dim noise vector and a 2048-dim instance feature vector extracted
from a target image via a self-supervised learning model (SwAV ResNet-50);
these instance features act as a conditioning for IC-GAN image generation,
while the noise vector introduces variability between samples. We trained ridge
regression models to predict instance features, noise vectors, and dense
vectors (the output of the first dense layer of the IC-GAN generator) of
stimuli from corresponding fMRI patterns. Then, we used the IC-GAN generator to
reconstruct novel test images based on these fMRI-predicted variables. The
generated images presented state-of-the-art results in terms of capturing the
semantic attributes of the original test images while remaining relatively
faithful to low-level image details. Finally, we use the learned regression
model and the IC-GAN generator to systematically explore and visualize the
semantic features that maximally drive each of several regions-of-interest in
the human brain.


  Semi-competing risks data arise when both non-terminal and terminal events
are considered in a model. Such data with multiple events of interest are
frequently encountered in medical research and clinical trials. In this
framework, terminal event can censor the non-terminal event but not vice versa.
It is known that variable selection is practical in identifying significant
risk factors in high-dimensional data. While some recent works on penalized
variable selection deal with these competing risks separately without
incorporating possible correlation between them, we perform variable selection
in an illness-death model using shared frailty where semiparametric hazard
regression models are used to model the effect of covariates. We propose a
broken adaptive ridge (BAR) penalty to encourage sparsity and conduct extensive
simulation studies to compare its performance with other popular methods. We
perform variable selection in an event specific manner so that the potential
risk factors and covariates effects can be estimated and selected,
simultaneously corresponding to each event in the study. The grouping effect,
as well as the oracle property of the proposed BAR procedure are investigated
using simulation studies. The proposed method is then applied to real-life data
arising from a Colon Cancer study.


  We present multi-frequency VLBI observations of the Compact Steep-spectrum
Quasar 3C147 (0538+498) made with the VLBA at the four frequencies in the
available 5 GHz band and at 8.4 GHz (still under analysis), from which we
derived millarcsecond-resolution images of the total intensity, polarization,
and rotation measure distributions. The source shows a core-jet structure, with
a compact feature and a jet, extending about 200 mas to the South-West. We
detect polarized emission in two bright features in the inner jet; the rotation
measure of this features (aprox -1630 rad m(-2), aprox -540 rad m(-2)).


  The paper examines the performance of regression models (OLS linear
regression, Ridge regression, Random Forest, and Fully-connected Neural
Network) on the prediction of CMA (Conservative Minus Aggressive) factor
premium and the performance of factor timing investment with them.
Out-of-sample R-squared shows that more flexible models have better performance
in explaining the variance in factor premium of the unseen period, and the back
testing affirms that the factor timing based on more flexible models tends to
over perform the ones with linear models. However, for flexible models like
neural networks, the optimal weights based on their prediction tend to be
unstable, which can lead to high transaction costs and market impacts. We
verify that tilting down the rebalance frequency according to the historical
optimal rebalancing scheme can help reduce the transaction costs.


  With the support of the national program on measurements, standards, and
evaluation of quantum technologies MetriQs-France, a part of the French
national quantum strategy, the BACQ project is dedicated to
application-oriented benchmarks for quantum computing. The consortium gathering
THALES, EVIDEN, an Atos business, CEA, CNRS, TERATEC, and LNE aims at
establishing performance evaluation criteria of reference, meaningful for
industry users.


  We propose a scheme for realizing the continuously tunable spectrum based on
monatomic carbon chains. By hybrid density functional calculations, we first
show that the direct band gap of monatomic carbon chains change continuously
from 1.58 to 3.8 eV as strain is applied from -5 to 10% to the chain, with
separated Van Hove singularity peaks enhanced. To realize this tunability, a
realistic stretching device is proposed by contacting the chain with graphene
sheets, which can apply up to 9% elongation to the chain, yielding tunable
light-emitting wavelengths from 345 to 561 nm.


  Gravitational radiation from the Galactic population of close white dwarf
binaries (CWDBs) is expected to produce a confusion-limited signal at the lower
end of the sensitivity band of the Laser Interferometer Space Antenna (LISA).
The canonical scale height of the disk population has been taken to be 90 pc
for most studies of the nature of this confusion-limited signal. This estimate
is probably too low, and the consequences of a more realistic scale height are
investigated with a model of the LISA signal due to populations of close white
dwarf binaries with different scale heights. If the local space density of
CWDBs is held constant, increasing the scale height results in both an increase
in the overall strength of the confusion-limited signal as well as in increase
in the frequency at which the signals become individually resolvable. If the
total number of binaries is held constant, increasing the scale height results
in a reduction of the number of expected bright signals above the
confusion-limited signal at low frequencies. We introduce an estimator for
comparing this transition frequency that takes into account the signal
spreading at higher frequencies.


  In this poster we present a detailed chemical analysis of the RV Tauri star
of low intrinsic metallicity, V453 Oph ([Fe/H]=-2.2), which shows a mild but
clear s-process surface overabundance. This result is strengthened by a
relative analysis to the RV Tauri star DS Aqr of similar metal deficiency
([Fe/H]=-1.6), but without such s-process enrichment. A remarkable result is
that the s-process enrichment of V453 Oph is not accompanied by a measurable C
enhancement. To explain the surface abundances observed in V453 Oph, two
nucleosynthesis models are considered. The first model assumes the partial
mixing of protons during the radiative interpulse phase while the second
scenario is based on the possible production of s-process elements within the
flash-driven convective pulse only. Both models can give a satisfactory
explanation for the s-process enrichment of V453 Oph, but not the simultaneous
low C-abundance observed.


  We demonstrate that a Quark-Gluon Plasma (QGP) with a dilute admixture of
heavy quarks has, in general, a lower speed of sound than a "pure" QGP without
effects from heavy flavors. The change in the speed of sound is sensitive to
the details of the theory, making the hydrodynamic response to "flavoring" a
sensitive probe of the underlying microscopic dynamics. We suggest that this
effect may be measured in ultrarelativistic heavy ion collisions by relating
the event-by-event number of charm quarks to flow observables such as the
average transverse momentum.


  Astronomers use to derive MOdified Newtonian Dynamics (MOND) rotation curves
using the simple algebraic rule of calculating the acceleration as equal to the
Newtonian acceleration ($a$) divided by some factor $\mu (a)$. However, there
are velocity differences between this simple rule and the calculation derived
from more sophisticated MOND versions such as AQUAL or QMOND, created to expand
MOND heuristic law and preserve the conservation of momentum, angular momentum,
and energy, and follow the weak equivalence principle. Here we provide recipes
based on Milgrom's proposal to calculate semianalytically (without numerical
simulations) MOND rotation curves for any density distribution based on AQUAL,
applying it to different models of thin disks. The application of this
formalism is equivalent to the creation of a fictitious phantom mass whose
field may be used in a Newtonian way to calculate iteratively the MOND
accelerations. In most cases, the differences between the application of the
simple algebraic rule and the AQUAL-MOND calculations are small, $\lesssim 5$%.
However, the error of the algebraic solution is larger than 5% when more than
half of the mass is in the MONDian regime (where Newtonian and MOND rotation
speeds differ by more than 10%), reaching in some cases $>70$% discrepance,
such as in Maclaurin disks, representative of galaxies for which the rotational
velocity rises to the edge of the disk as is seen in irregular galaxies. The
slope of the rotation speed in the dependence with the radius or the vertical
distance of the plane is also significantly changed.