  In this paper we examine on a pair of adjoint functors $(\phi
^{\ast},\phi_{\ast})$ for a subcategory of the category of crossed modules over
commutative algebras where $\phi ^{\ast}:\mathbf{XMod}$\textbf{/}$%
Q\rightarrow $ $\mathbf{XMod/}P$, pullback, which enables us to move from
crossed $Q$-modules to crossed $P$-modules by an algebra morphism $\phi
:P\rightarrow Q$ and $\phi_{\ast}:\mathbf{XMod}$\textbf{/}$P\rightarrow $
$\mathbf{XMod/}Q$, induced. We note that this adjoint functor pair $(\phi
^{\ast},\phi_{\ast})$ makes $p:\mathbf{XMod}\rightarrow $ $k$\textbf{-Alg}into
a bifibred category over $k$\textbf{-Alg}, the category of commutative
algebras, where $p$ is given by $p(C,R,\partial)=R.$
  Also, some examples and results on induced crossed modules are given.


  We compute the Hodge numbers of the moduli space of semi-stable sheaves on
the complex projective plane supported on quintic curves and having Euler
characteristic 3. For this purpose we study the fixed-point set for a certain
torus action on the moduli space.


  Artificial Intelligence (AI) relies heavily on deep learning - a technology
that is becoming increasingly popular in real-life applications of AI, even in
the safety-critical and high-risk domains. However, it is recently discovered
that deep learning can be manipulated by embedding Trojans inside it.
Unfortunately, pragmatic solutions to circumvent the computational requirements
of deep learning, e.g. outsourcing model training or data annotation to third
parties, further add to model susceptibility to the Trojan attacks. Due to the
key importance of the topic in deep learning, recent literature has seen many
contributions in this direction. We conduct a comprehensive review of the
techniques that devise Trojan attacks for deep learning and explore their
defenses. Our informative survey systematically organizes the recent literature
and discusses the key concepts of the methods while assuming minimal knowledge
of the domain on the readers part. It provides a comprehensible gateway to the
broader community to understand the recent developments in Neural Trojans.


  Ordering by thermal fluctuations is studied for the classical XY
antiferromagnet on a checkerboard lattice in zero and finite magnetic fields by
means of analytical and Monte Carlo methods. The model exhibits a variety of
novel broken symmetries including states with nematic ordering in zero field
and with triatic order parameter at high fields.


  Resting State Networks (RSNs) of the brain extracted from Resting State
functional Magnetic Resonance Imaging (RS-fMRI) are used in the pre-surgical
planning to guide the neurosurgeon. This is difficult, though, as expert
knowledge is required to label each of the RSNs. There is a lack of efficient
and standardized methods to be used in clinical workflows. Additionally, these
methods need to be generalizable since the method needs to work well regardless
of the acquisition technique. We propose an accurate, fast, and lightweight
deep learning approach to label RSNs. Group Independent Component Analysis
(ICA) was used to extract large scale functional connectivity patterns in the
cohort and dual regression was used to back project them on individual subject
RSNs. We compare a Multi-Layer Perceptron (MLP) based method with 2D and 3D
Convolutional Neural Networks (CNNs) and find that the MLP is faster and more
accurate. The MLP method performs as good or better than other works despite
its compact size. We prove the generalizability of our method by showing that
the MLP performs at 100% accuracy in the holdout dataset and 98.3% accuracy in
three other sites' fMRI acquisitions.


  A generalization of coherent states has been developed in the context of
supersymmetric quan- tum mechanics. For many cases, no link has been made with
the corresponding classical system. In this work, we consider a very simple
superpotential and compare the classical and quantum trajectories. Keywords:
Coherent States, SUSYQM.


  We consider the problem of determining the relationship between two
representations knowing that some tensor or symmetric power of the original
represetations coincide. Combined with refinements of strong multiplicity one,
we show that if the characters of some tensor or symmetric powers of two
absolutely irreducible $l$-adic representation with the algebraic envelope of
the image being connected, agree at the Frobenius elements corresponding to a
set of places of positive upper density, then the representations are twists of
each other by a finite order character.


  Diagnosing epilepsy requires accurate seizure detection and classification,
but traditional manual EEG signal analysis is resource-intensive. Meanwhile,
automated algorithms often overlook EEG's geometric and semantic properties
critical for interpreting brain activity. This paper introduces NeuroGNN, a
dynamic Graph Neural Network (GNN) framework that captures the dynamic
interplay between the EEG electrode locations and the semantics of their
corresponding brain regions. The specific brain region where an electrode is
placed critically shapes the nature of captured EEG signals. Each brain region
governs distinct cognitive functions, emotions, and sensory processing,
influencing both the semantic and spatial relationships within the EEG data.
Understanding and modeling these intricate brain relationships are essential
for accurate and meaningful insights into brain activity. This is precisely
where the proposed NeuroGNN framework excels by dynamically constructing a
graph that encapsulates these evolving spatial, temporal, semantic, and
taxonomic correlations to improve precision in seizure detection and
classification. Our extensive experiments with real-world data demonstrate that
NeuroGNN significantly outperforms existing state-of-the-art models.


  We study the critical dynamics of the generalized Smoluchowski-Poisson system
(for self-gravitating Langevin particles) or generalized Keller-Segel model
(for the chemotaxis of bacterial populations). These models [Chavanis & Sire,
PRE, 69, 016116 (2004)] are based on generalized stochastic processes leading
to the Tsallis statistics. The equilibrium states correspond to polytropic
configurations with index $n$ similar to polytropic stars in astrophysics. At
the critical index $n_{3}=d/(d-2)$ (where $d\ge 2$ is the dimension of space),
there exists a critical temperature $\Theta_{c}$ (for a given mass) or a
critical mass $M_{c}$ (for a given temperature). For $\Theta>\Theta_{c}$ or
$M<M_{c}$ the system tends to an incomplete polytrope confined by the box (in a
bounded domain) or evaporates (in an unbounded domain). For $\Theta<\Theta_{c}$
or $M>M_{c}$ the system collapses and forms, in a finite time, a Dirac peak
containing a finite fraction $M_c$ of the total mass surrounded by a halo. This
study extends the critical dynamics of the ordinary Smoluchowski-Poisson system
and Keller-Segel model in $d=2$ corresponding to isothermal configurations with
$n_{3}\to +\infty$. We also stress the analogy between the limiting mass of
white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial
populations in the generalized Keller-Segel model of chemotaxis.


  Vacuum structure, one-particle excitations' spectra and bound states of these
excitations are studied in frame of non-relativistic quantum field model with
current $\times$ current type interaction. Hidden symmetry of the model is
found. It could be broken or exact depending on the coupling constant value.
The effect of "piercing" vacuum , generating the appearance of heavy fermionic
excitations, could occur in the spontaneously broken phase.


  In this paper, taking in to account Brans-Dick theory, we investigate
thermodynamic behavior of charged black hole solutions. We study the analogy of
the black hole solution with the Van der Waals liquid-gas system in the
extended phase space by considering the cosmological constant as dynamical
pressure. We obtain critical values of thermodynamic coordinates and plot
$P-r_{+}$ and $G-T$ diagrams to study the phase transition.


  We introduce a notion of formally \'etale $\mathbb{E}_{\infty}$-coalgebras
and show that they admit essentially unique, functorial lifts along square zero
extensions of $\mathbb{E}_{\infty}$-rings. Using this, we show that for a
perfect $\mathbb{F}_p$-algebra $k$, Weil restriction along the augmentation
$\mathbb{W}(k)\to k$ induces a fully faithful functor from formally \'etale,
connective $\mathbb{E}_{\infty}$-coalgebras in $k$-modules to connective
$\mathbb{E}_{\infty}$-coalgebras in $p$-complete modules over the spherical
Witt vectors $\mathbb{W}(k)$. Finally, we prove that for any connected space
$X$, the $k$-homology $k[X]$ is a formally \'etale
$\mathbb{E}_\infty$-coalgebra in $k$-modules. This shows that
$\mathbb{W}(k)[X]^{\wedge}_p$ can be recovered as the essentially unique lift
of $k[X]$ to a connective coalgebra in $p$-complete $\mathbb{W}(k)$-modules.


  We prove that the dynamical sine-Gordon equation on the two dimensional torus
introduced in [HS16] is locally well-posed for the entire subcritical regime.
At first glance this equation is far out of the scope of the local existence
theory available in the framework of regularity structures [Hai14, BHZ16, CH16,
BCCH17] since it involves a non-polynomial nonlinearity and the solution is
expected to be a distribution (without any additional small parameter as in
[FG17, HX18]). In [HS16] this was overcome by a change of variable, but the new
equation that arises has a multiplicative dependence on highly non-Gaussian
noises which makes stochastic estimates highly non-trivial - as a result [HS16]
was only able to treat part of the subcritical regime. Moreover, the cumulants
of these noises fall out of the scope of the later work [CH16]. In this work we
systematically leverage "charge" cancellations specific to this model and
obtain stochastic estimates that allow us to cover the entire subcritical
regime.


  The nonorientable 4-genus $\gamma_4(K)$ of a knot $K$ is the smallest first
Betti number of any nonorientable surface properly embedded in the 4-ball, and
bounding the knot $K$. We study a conjecture proposed by Batson about the value
of $\gamma_4$ for torus knots, which can be seen as a nonorientable analogue of
Milnor's Conjecture for the orientable 4-genus of torus knots. We prove the
conjecture for many infinite families of torus knots, by relying on a lower
bound for $\gamma_4$ formulated by Ozsv\'ath, Stipsicz, and Szab\'o. As a side
product we obtain new closed formulas for the signature of torus knots.


  We propose a time-of-arrival operator in quantum mechanics by conditioning on
a quantum clock. This allows us to bypass some of the problems of previous
proposals, and to obtain a Hermitian time of arrival operator whose probability
distribution arises from the Born rule and which has a clear physical
interpretation. The same procedure can be employed to measure the "time at
which some event happens" for arbitrary events (and not just specifically for
the arrival time of a particle).


  We search for the $\psi(4S)$ state in $B^\pm \ra \eta J/\psi K^\pm$ and
$e^+e^- \ra \eta J/\psi$ based on the Belle measurements with the assumed mass
$M=(4230\pm8)$ MeV/$c^2$ and width $\Gamma=(38\pm12)$ MeV. No significant
signal is observed in the $\eta J/\psi$ mass spectra. The 90\% confidence level
upper limit on the product branching fraction $\BR(B^\pm \ra
\psi(4S)K^\pm)\BR(\psi(4S) \ra \eta J/\psi)<6.8\times 10^{-6}$ is obtained in
$B^\pm \ra \eta J/\psi K^\pm$ decays. By assuming the partial width of
$\psi(4S) \to e^+e^-$ being 0.63 keV, the branching fraction limit
$\BR(\psi(4S) \ra \eta J/\psi) < 1.3\%$ is obtained at the 90\% confidence
level in $e^+e^- \ra \eta J/\psi$, which is consistent with the theoretical
prediction.


  In this article, we introduce a four-point analogue of Banach-type,
Kannan-type, and Chatterjea-type contractions, and examine their properties. We
establish sufficient conditions under which these mappings achieve fixed points
in a complete metric space. Notably, the classical Banach contraction principle
emerges as a special case of our results. To illustrate our theoretical
findings, we present several non-trivial examples.


  Starting from a phenomenological standard energy functional to describe the
condensation of a dilute gas of bosonic quasiparticles in magnetic insulators,
we find that the inclusion of a perturbation term that explicitly violates the
axial symmetry significantly modifies the details of the resulting Bose
Einstein condensation. Systems with an originally axial symmetry must show an
intrinsic tendency to spontaneously violate this symmetry as soon as the
condensation sets in, and the phase transition at the respective critical field
may even become of first order. We can explain a number of features in the
experimental data of various insulating spin systems, such as a slightly
nonlinear magnetization near the critical field as well as hysteresis effects
and peculiarities in the energy-level scheme of TlCuCl3. We also offer a
consistent explanation for certain anomalies in the magnetocaloric effect and
in the magnetization of BaCuSi2O6 by assuming a spontaneous violation of axial
symmetry at the magnetic phase transition on an energy scale of about 1
micro-eV. The resulting anisotropy gap in the magnetic excitation spectrum,
that inevitably forms at the critical field of all such systems, lifts the
linear Goldstone mode and is therefore seriously limiting the lifetime of
magnetic condensates to a few nanoseconds at most.


  We analyze a contrasting dynamical behavior of Gibbs-Shannon and conditional
Kullback-Leibler entropies, induced by time-evolution of continuous probability
distributions. The question of predominantly purpose-dependent entropy
definition for non-equilibrium model systems is addressed. The conditional
Kullback-Leibler entropy is often believed to properly capture physical
features of an asymptotic approach towards equilibrium. We give arguments in
favor of the usefulness of the standard Gibbs-type entropy and indicate that
its dynamics gives an insight into physically relevant, but generally ignored
in the literature, non-equilibrium phenomena. The role of physical units in the
Gibbs-Shannon entropy definition is iscussed.


  Interpenetrated polymer network microgels, composed of crosslinked networks
of poly(N-isopropylacrylamide) and polyacrylic acid (PAAc), have been
investigated through rheological measurements at four different amounts of
polyacrylic acid. Both PAAc content and crosslinking degree modify particle
dimensions, mass and softness, thereby strongly affecting the volume fraction
and the system viscosity. Here the volume fraction is derived from the flow
curves at low concentrations by fitting the zero-shear viscosity with the
Einstein-Batchelor equation which provides a parameter k to shift weight
concentration to volume fraction. We find that particles with higher PAAc
content and crosslinker are characterized by a greater value of k and therefore
by larger volume fractions when compared to softer particles. The packing
fractions obtained from rheological measurements are compared with those from
static light scattering for two PAAc contents revealing a good agreement.
Moreover, the behaviour of the viscosity as a function of packing fraction, at
room temperature, has highlighted an Arrhenius dependence for microgels
synthesized with low PAAc content and a Vogel-Fulcher-Tammann dependence for
the highest investigated PAAc concentration. A comparison with the hard spheres
behaviour indicates a steepest increase of the viscosity with decreasing
particles softness. Finally, the volume fraction dependence of the viscosity at
a fixed PAAc and at two different temperatures, below and above the volume
phase transition, shows a quantitative agreement with the structural relaxation
time measured through dynamic light scattering indicating that IPN microgels
softness can be tuned with PAAc and temperature and that, depending on particle
softness, two different routes are followed.


  The recently observed possible antimagnetic rotation band in $^{101}$Pd is
investigated by the cranked shell model with pairing correlations treated by a
particle-number conserving method, in which the blocking effects are taken into
account exactly. The experimental moments of inertia and reduced $B(E2)$
transition probabilities and their variations with the rotational frequency
$\omega$ are well reproduced. By analyzing the $\omega$-dependence of the
occupation probability of each cranked Nilsson orbital near the Fermi surface
and the contributions of valence orbitals in each major shell to the total
angular momentum alignment, the upbending mechanism of $\nu h_{11/2}$ in
$^{101}$Pd is understood clearly. The proton angular momentum alignment and its
influence on the two-shears-like mechanism are also discussed.


  To generate drug molecules of desired properties with computational methods
is the holy grail in pharmaceutical research. Here we describe an AI strategy,
retro drug design, or RDD, to generate novel small molecule drugs from scratch
to meet predefined requirements, including but not limited to biological
activity against a drug target, and optimal range of physicochemical and ADMET
properties. Traditional predictive models were first trained over experimental
data for the target properties, using an atom typing based molecular descriptor
system, ATP. Monte Carlo sampling algorithm was then utilized to find the
solutions in the ATP space defined by the target properties, and the deep
learning model of Seq2Seq was employed to decode molecular structures from the
solutions. To test feasibility of the algorithm, we challenged RDD to generate
novel drugs that can activate {\mu} opioid receptor (MOR) and penetrate blood
brain barrier (BBB). Starting from vectors of random numbers, RDD generated
180,000 chemical structures, of which 78% were chemically valid. About 42,000
(31%) of the valid structures fell into the property space defined by MOR
activity and BBB permeability. Out of the 42,000 structures, only 267 chemicals
were commercially available, indicating a high extent of novelty of the
AI-generated compounds. We purchased and assayed 96 compounds, and 25 of which
were found to be MOR agonists. These compounds also have excellent BBB scores.
The results presented in this paper illustrate that RDD has potential to
revolutionize the current drug discovery process and create novel structures
with multiple desired properties, including biological functions and ADMET
properties. Availability of an AI-enabled fast track in drug discovery is
essential to cope with emergent public health threat, such as pandemic of
COVID-19.


  First we make a brief review of coherent states and prove that the resolution
of unity can be obtained by the 1-st Chern character of some bundle. Next we
define a Grassmann manifold for a set of coherent states and construct the
pull-back bundle making use of a projector from the parameter space to this
Grassmann manifold. We study some geometric properties (Chern-characters
mainly) of these bundles. Although the calculations of Chern-characters are in
general not easy, we can perform them for the special cases. In this paper we
report our calculations and propose some interesting problems to be solved in
the near future.


  This preprint was split in two and became the first two parts of a four-part
series (arXiv:1405.1956, arXiv:1405:1955, and two in preparation). The
remaining relevance of this preprint is due to the series of videotaped
lectures (wClips) that are linked within.


  Magnetism is very important in science and technology, from magnetic
recording to energy generation to trapping cold atoms. Physicists have managed
to master magnetism - to create and manipulate magnetic fields- almost at will.
Surprisingly, there is at least one property which until now has been elusive:
how to 'switch off' the magnetic interaction of a magnetic material with
existing magnetic fields without modifying them. Here we introduce the
antimagnet, a design to conceal the magnetic response of a given volume from
its exterior, without altering the external magnetic fields, somehow analogous
to the recent theoretical proposals for cloaking electromagnetic waves with
metamaterials. However, different from these devices requiring extreme material
properties, our device is feasible and needs only two kinds of available
materials: superconductors and isotropic magnetic materials. Antimagnets may
have applications in magnetic-based medical techniques such as MRI or in
reducing the magnetic signature of vessels or planes.


  During the last few years, several studies have proposed the existence of a
threshold separating classical from quantum behavior of objects that is
dependent on the size and mass of an object as well as being dependent on
certain properties usually associated with the universe as a whole. Here, we
reexamine the results of these studies and recast the threshold criteria in
terms of a critical threshold value for the moments of inertia of physical
objects. Physical objects having moments of inertia above this critical
threshold value would be expected to behave necessarily in a classical manner
in terms of their center of mass motion as entire objects, while physical
objects having moments of inertia lower than this threshold value could exhibit
quantum behavior unless brought into classicality by other effects. A
comparison with observed values of moments of inertia is presented, and the
moment of inertia is suggested as a classifying parameter for examination of
the quantum versus classical behavior of objects in the mesoscale domain.


  Hybrid (exotic) mesons, which are important predictions of quantum
chromodynamics (QCD), are states of quarks and anti-quarks bound by excited
gluons. First principle lattice study of such states would help us understand
the role of ``dynamical'' color in low energy QCD and provide valuable
information for experimental search for these new particles. In this paper, we
apply both improved gluon and quark actions to the hybrid mesons, which might
be much more efficient than the previous works in reducing lattice spacing
error and finite volume effect. Quenched simulations were done at $\beta=2.6$
and on a $\xi=3$ anisotropic $12^3\times36$ lattice using our PC cluster. We
obtain $2013 \pm 26 \pm 71$ MeV for the mass of the $1^{-+}$ hybrid meson
${\bar q}qg$ in the light quark sector, and $4369 \pm 37 \pm 99$Mev in the
charm quark sector; the mass splitting between the $1^{-+}$ hybrid meson ${\bar
c}c g$ in the charm quark sector and the spin averaged S-wave charmonium mass
is estimated to be $1302 \pm 37 \pm 99$ MeV. As a byproduct, we obtain $1438
\pm 32 \pm 57$ MeV for the mass of a P-wave $1^{++}$ ${\bar u}u$ or ${\bar d}d$
meson and $1499 \pm 28 \pm 65$ MeV for the mass of a P-wave $1^{++}$ ${\bar
s}s$ meson, which are comparable to their experimental value 1426 MeV for the
$f_1(1420)$ meson. The first error is statistical, and the second one is
systematical. The mixing of the hybrid meson with a four quark state is also
discussed.


  We propose a new type of K\"ahler moduli stabilization mechanisms in type IIB
superstring theory on Calabi-Yau manifolds with the positive Euler number. The
overall K\"ahler modulus can be perturbatively stabilized by radiative
corrections due to sparticles. Its minimum is the anti-de Sitter vacuum, where
supersymmetry is broken. We can uplift it to the de Sitter vacuum by
introducing anti-D-branes, keeping the modulus stabilized. Although our
numerical results depend on the choice of the cutoff scale and degeneracies of
sparticles, at any rate there exist the parameter spaces where the masses of
Kaluza-Klein and stringy modes are larger than the cutoff scale. Furthermore,
this stabilization scenario predicts an ultralight axion.


  We study the early time dynamics of the 2d ferromagnetic Ising model
instantaneously quenched from the disordered to the ordered, low temperature,
phase. We evolve the system with kinetic Monte Carlo rules that do not conserve
the order parameter. We confirm the rapid approach to random critical
percolation in a time-scale that diverges with the system size but is much
shorter than the equilibration time. We study the scaling properties of the
evolution towards critical percolation and we identify an associated growing
length, different from the curvature driven one. By working with the model
defined on square, triangular and honeycomb microscopic geometries we establish
the dependence of this growing length on the lattice coordination. We discuss
the interplay with the usual coarsening mechanism and the eventual fall into
and escape from metastability.


  The subspace generated by the eigenvectors pertaining to the peripheral
spectrum of any stochastic matrix is naturally equipped with a structure of a
(finite dimensional abelian) $C^*$-algebra, and the restriction of such a
stochastic matrix to this subspace, indeed a $C^*$-algebra under this canonical
new product, generates a conservative $C^*$-dynamical system.


  We study codimension two determinantal varieties with isolated singularities.
These singularities admit a unique smoothing, thus we can define their Milnor
number as the middle Betti number of their generic fiber. For surfaces in C^4,
we obtain a L\^e-Greuel formula expressing the Milnor number of the surface in
terms of the second polar multiplicity and the Milnor number of a generic
section. We also relate the Milnor number with Ebeling and Gusein-Zade index of
the 1- form given by the differential of a generic linear projection defined on
the surface. To illustrate the results, in the last section we compute the
Milnor number of some normal forms from A. Fr\"uhbis-Kr\"uger and A. Neumer [2]
list of simple determinantal surface singularities.


  The exclusive two-photon production at the LHC of pairs of W and Z bosons
provides a novel and unique test-ground for the electroweak gauge boson sector.
In particular it offers, thanks to high gamma-gamma center-of-mass energies,
large and direct sensitivity to the anomalous quartic gauge couplings otherwise
very difficult to investigate at the LHC. An initial analysis has been
performed assuming leptonic decays and generic acceptance cuts. Simulation of a
simple counting experiment has shown for the integrated luminosity of 10 fb-1
at least four thousand times larger sensitivity to the genuine quartic
couplings, a_0^W, a_0^Z, a_C^W and a_C^Z, than those obtained at LEP. The
impact of the unitarity constraints on the estimated limits has been studied
using the dipole form-factors. Finally, differential distributions of the decay
leptons have been provided to illustrate the potential for further improvements
of the sensitivities.


  Skewness measures can be used to measure the level of asymmetry of a
distribution. Given the prevalence of statistical methods that assume
underlying symmetry, and also the desire for symmetry in order to make
meaningful judgements for common summary measures (e.g. the sample mean),
reliably quantifying asymmetry is an important problem. There are several
measures, among them generalizations of Bowley's well known skewness
coefficient, that use sample quartiles and other quantile-based measures. The
main drawbacks of many measures is that they are either limited to quartiles
and do not take into account more extreme tail behavior, or that they require
one to choose other quantiles (i.e. choose a value for $p$ different from 0.25)
in place of the quartiles. Our objective is to (i) average the skewness
measures over all $p$ and (ii) provide interval estimators for the new measure
with good coverage properties. Our simulation results show that the interval
estimators perform very well for all distributions considered.


  This paper studies the distributed L2-gain control problem for
continuous-time large-scale systems under Round-Robin communication protocol.
In this protocol, each sub-controller obtains its own subsystem's state
information continuously, while communicating with neighbors at discrete-time
instants periodically. Distributed controllers are designed such that the
closed-loop system is exponentially stable and that the prescribed L2-gain is
satisfied. The design condition is obtained based on a time-delay approach and
given in terms of linear matrix inequalities. Finally, three numerical examples
are presented to illustrate the efficiency of the proposed scheme.


  We prove a recent conjecture of Lassalle about positivity and integrality of
coefficients in some polynomial expansions. We also give a combinatorial
interpretation of those numbers. Finally, we show that this question is closely
related to the fundamental problem of calculating the linearization
coefficients for binomial coefficients.


  We present an alternative domain concerning mathematics to investigate
universal evolution mechanisms by focusing on large cycles theory (LCT) - a
simplified version of well-known hamiltonian graph theory. LCT joins together a
number of $NP$-complete cycle problems in graph theory. $NP$-completeness is
the kay factor insuring (by conjecture of Cook) the generation of endless
developments and great diversity around large cycles problems. Originated about
60 years ago, the individuals (claims, propositions, lemmas, conjectures,
theorems, and so on) in LCT continually evolve and adapt to their environment
by an iterative process from primitive beginnings to best possible theorems
based on inductive reasoning. LCT evolves much more rapidly than biosphere and
has a few thousand pronounced species (theorems). Recall that life on earth
with more than 2 million species was originated about 3.7 billion years ago and
evolves extremely slowly. We show that all theorems in LCT have descended from
some common primitive propositions such as "every complete graph is
hamiltonian" or "every graph contains a cycle of length at least one" via
improvements, modifications and three kinds of generalizations - closing,
associating and extending. It is reasonable to review Darwinian mechanisms in
light of LCT evolution mechanisms (especially inductive reasoning) including
the origin and macroevolution disputable phenomena in the biosphere.


  We have calculated relative elemental abundances for a sample of 43 symbiotic
stars. Helium abundances and the relative elemental abundances N/O, Ne/O, Ar/O
were derived from new spectra collected in the optical range through low
dispersion spectroscopy. The He ionic abundances were derived taking into
account self-absorption effects in Balmer lines. We found that the symbiotic
stars in the galactic bulge have heavy element abundances showing the same wide
distribution as other bulge objects. In the galactic disk, the symbiotic stars
follow the abundance gradient as derived from different kinds of objects.


  Symmetry is one of the most generic and useful concepts in physics and
chemistry, often leading to conservation laws and selection rules. For example,
symmetry considerations have been used to predict selection rules for
transitions in atoms, molecules, and solids. Floquet systems also demonstrate a
variety of symmetries which are spatiotemporal (i.e. dynamical symmetries
(DSs)). However, the derivation of selection rules from DSs has so far been
limited to several ad hoc cases. A general theory for deducing the impact of
DSs in physical systems has not been formulated yet. Here we explore symmetries
exhibited in Floquet systems using group theory, and discover novel DSs and
selection rules. We derive the constraints on a general system's temporal
evolution, and selection rules that are imposed by the DSs. As an example, we
apply the theory to harmonic generation, and derive tables linking (2+1)D and
(3+1)D DSs of the driving laser and medium to allowed harmonic emission and its
polarization. We identify several new symmetries and selection rules, including
an elliptical DS that leads to production of elliptically polarized harmonics
where all the harmonics have the same ellipticity, and selection rules that
have no explanation based on currently known conservation laws. We expect the
theory to be useful for manipulating the harmonic spectrum, and for ultrafast
spectroscopy. Furthermore, the presented Floquet group theory should be useful
in various other systems, e.g., Floquet topological insulators and photonic
lattices, possibly yielding formal and general classification of symmetry and
topological properties.


  The quest to develop intelligent visual analytics (VA) systems capable of
collaborating and naturally interacting with humans presents a multifaceted and
intriguing challenge. VA systems designed for collaboration must adeptly
navigate a complex landscape filled with the subtleties and unpredictabilities
that characterize human behavior. However, it is noteworthy that scenarios
exist where human behavior manifests predictably. These scenarios typically
involve routine actions or present a limited range of choices. This paper
delves into the predictability of user behavior in the context of visual
analytics tasks. It offers an evidence-based discussion on the circumstances
under which predicting user behavior is feasible and those where it proves
challenging. We conclude with a forward-looking discussion of the future work
necessary to cultivate more synergistic and efficient partnerships between
humans and the VA system. This exploration is not just about understanding our
current capabilities and limitations in mirroring human behavior but also about
envisioning and paving the way for a future where human-machine interaction is
more intuitive and productive.


  Since the quark-gluon plasma (QGP) reveals some obvious similarities to the
well-known electromagnetic plasma (EMP), an accumulated knowledge on EMP can be
used in the QGP studies. After discussing similarities and differences of the
two systems, we present theoretical tools which are used to describe the
plasmas. The tools include: kinetic theory, hydrodynamic approach and
diagrammatic perturbative methods. We consider collective phenomena in the
plasma with a particular emphasis on instabilities which crucially influence
temporal evolution of the system. Finally, properties of strongly coupled
plasma are discussed.


  Density-functional simulations are used to calculate structural properties
and high-symmetry phonons of the hypothetical cubic phase, the stable
orthorhombic phase and an intermediate tetragonal phase of magnesium silicate
perovskite. We show that the structure of the stable phase is well described by
freezing in a small number of unstable phonons into the cubic phase. We use the
frequencies of these unstable modes to estimate transition temperatures for
cubic--tetragonal and tetragonal--orthorhombic phase transitions. These are
investigated further to find that the coupling with the strain suggests that
phonons give a better representation than rigid unit modes. The phonons of an
intermediate tetragonal phase were found to be stable except for two rotational
modes. The eigenvectors of the most unstable mode of each of the cubic and
tetragonal phases account for all the positional parameters of the orthorhombic
phase. The phase boundary for the orthorhombic--tetragonal transition
intersects possible mantle geotherms, suggesting that the tetragonal phase may
be present in the lower mantle.


  We investigate the upper critical field in a stripe--phase and in the
presence of a phenomenological pseudogap. Our results indicate that the
formation of stripes affects the Landau orbits and results in an enhancement of
$H_{c2}$. On the other hand, phenomenologically introduced pseudogap leads to a
reduction of the upper critical field. This effect is of particular importance
when the magnitude of the gap is of the order of the superconducting transition
temperature. We have found that a suppression of the upper critical field takes
place also for the gap that originates from the charge--density waves.


  In this paper, we first get a criterion formula for whether a differential
form is holomorphic with respect to the generalized complex structure induced
by $\epsilon$. Next, we get the local extensions of $\overline\partial$-closed
forms on a smooth family of compact generalized Hermitian manifolds by using
this criterion. Finally, as an application, we use this extension to get the
invariance of the generalized Hodge number of the deformations of compact
generalized Hermitian manifolds with $\partial\overline\partial$-lemma holds.


  The wireless network places vital role in the present day communication
scenario. The ad hoc nature of wireless communication adds flavour to suit
various real world applications. This improves the performance of the network
tremendously while the clustering mechanism gets added to the ad hoc network.
It has been found out that the existing WCA lacks in forming efficient
clusters. Thus, this work proposes an Extended weighted partitioning around
cluster head mechanism by considering W-PAC as a base to form clusters. The
cluster members are configured with IPv6 address. This IPv6 clusters formed
through W-PAC will be taken further for validation to determine the perfectness
of clusters. The cluster formation and maintenance have been implemented in C++
as a programming language. The cluster validation has been carried out using
OMNET++ simulator.


  In solving scientific, engineering or pure mathematical problems one is often
faced with a need to approximate the function of a given class by the linear
combination of a preferably small number of functions that are localised one
way or another both in the time and frequency domain. Over the last seventy
years or so a range of systems of thus localised functions have been developed
to allow the decomposition and synthesis of functions of various classes. The
most prominent examples of such systems are Gabor functions, wavelets,
ridgelets, curvelets, shearlets and wave atoms. We recently introduced a family
of quasi-Banach spaces -- which we called wave packet spaces -- that
encompasses all those classes of functions whose elements have sparse
expansions in one of the above-mentioned systems, supplied them with Banach
frames and provided their atomic decompositions. Herein we prove that the
Banach frames and sets of atoms of the wave packet spaces are well localised
or, more specifically, that they are near orthogonal. We believe that good
localisation of the wave packet systems -- a property of paramount importance
that can't be taken for granted even for frames in Hilbert spaces, let alone
Banach spaces -- will pave the way, among other things, for their use for
representing Fourier integral operators on Banach spaces by sparse and well
structured matrices by the Galerkin method. This, in its turn, should allow one
to design efficient computer programmes for solving corresponding operator
equations on two-dimensional manifolds.


  Manifestations of quantum interference effects in macroscopic objects are
rare. Weak localization is one of the few examples of such effects showing up
in the electron transport through solid state. Here we show that weak
localization becomes prominent also in optical spectroscopy via detection of
the electron spin dynamics. In particular, we find that weak localization
controls the free electron spin relaxation in semiconductors at low
temperatures and weak magnetic fields by slowing it down by almost a factor of
two in $n$-doped GaAs in the metallic phase. The weak localization effect on
the spin relaxation is suppressed by moderate magnetic fields of about 1 T,
which destroy the interference of electron trajectories, and by increasing the
temperature. The weak localization suppression causes an anomalous decrease of
the longitudinal electron spin relaxation time $T_1$ with magnetic field, in
stark contrast with well-known magnetic field induced increase in $T_1$. This
is consistent with transport measurements which show the same variation of
resistivity with magnetic field. Our discovery opens a vast playground to
explore quantum magneto-transport effects optically in the spin dynamics.


  Deep learning offers promising new ways to accurately model aleatoric
uncertainty in robotic estimation systems, particularly when the uncertainty
distributions do not conform to traditional assumptions of being fixed and
Gaussian. In this study, we formulate and evaluate three fundamental deep
learning approaches for conditional probability density modeling to quantify
non-Gaussian aleatoric uncertainty: parametric, discretized, and generative
modeling. We systematically compare the respective strengths and weaknesses of
these three methods on simulated non-Gaussian densities as well as on
real-world terrain-relative navigation data. Our results show that these deep
learning methods can accurately capture complex uncertainty patterns,
highlighting their potential for improving the reliability and robustness of
estimation systems.


  We present the results of a computer simulation study of thermodynamical
properties of TIP4P water confined in a hydrophobic disordered matrix of soft
spheres upon supercooling. The hydrogen bond network of water appears preserved
in this hydrophobic confinement. Nonetheless a reduction in the average number
of hydrogen bonds due to the geometrical constraints is observed. The liquid
branch of the spinodal line is calculated from 350 K down to 210 K. The same
thermodynamic scenario of the bulk is found: the spinodal curve is
monotonically decreasing. The line of maximum density bends avoiding a crossing
of the spinodal. There is however a shift both of the line of maximum density
and of the spinodal toward higher pressures and lower temperatures with respect
to bulk.


  In this paper we study the extreme and the periodic $L_2$ discrepancy of
plane point sets. The extreme discrepancy is based on arbitrary rectangles as
test sets whereas the periodic discrepancy uses "periodic intervals", which can
be seen as intervals on the torus. The periodic $L_2$ discrepancy is, up to a
multiplicative factor, also known as diaphony. The main results are exact
formulas for these kinds of discrepancies for the Hammersley point set and for
rational lattices.
  In order to value the obtained results we also prove a general lower bound on
the extreme $L_2$ discrepancy for arbitrary point sets in dimension $d$, which
is of order of magnitude $(\log N)^{(d-1)/2}$, like the standard and periodic
$L_2$ discrepancies, respectively. Our results confirm that the extreme and
periodic $L_2$ discrepancies of the Hammersley point set are of best possible
asymptotic order of magnitude. This is in contrast to the standard $L_2$
discrepancy of the Hammersley point set. Furthermore our exact formulas show
that also the $L_2$ discrepancies of the Fibonacci lattice are of the optimal
order.
  We also prove that the extreme $L_2$ discrepancy is always dominated by the
standard $L_2$ discrepancy, a result that was already conjectured by Morokoff
and Caflisch when they introduced the notion of extreme $L_2$ discrepancy in
the year 1994.


  In this paper we consider the use of wide field of view radar sensors such as
the Murchison Widefield Array (MWA), a low frequency radio telescope designed
for astrophysics and cosmology, for rapid response observations of the debris
clouds produced by collisions between objects in Earth orbit. With an
increasing density of objects in Low Earth Orbit, including legacy assets used
by the astronomy community over decades, the risk of new debris clouds forming
is also increasing. The MWA constitutes a wide field, rapid response passive
radar system and we explore its likely performance in the detection and
characterisation of debris clouds. In general, astronomy facilities such as the
MWA can play a role in protecting the space environment for the future. In
order to undertake this work, we adapt the NASA EVOLVE 4.0 breakup model,
utilising the EVOLVE outputs to produce representative dynamic debris clouds.
We find that the MWA is likely to detect a large fraction (>70%) of modelled
debris cloud fragments for collision masses between 100 kg and 1000 kg for
orbits in the lower part of LEO, if the MWA can achieve close to optimal
detection sensitivity. Useful detection fractions are still achieved for more
conservative assumptions. The detection fraction of fragments decreases as a
function of altitude and inversely with collision mass. Encouragingly, we find
that the wide field nature of the MWA allows the full evolving debris clouds to
be observed in a single observation, with only $\sim2\%$ of the debris
fragments escaping the sensitive portion of the field of view after 100
seconds, for all collision masses and altitudes. These results show that the
MWA is an intrinsically useful facility for the rapid characterisation of
debris clouds, but that work is required to achieve the data processing within
an appropriate timeframe to provide rapid alerts.


  It is a simple consequence of the Cafarelli-Kohn-Nirenberg theory that every
possible singularity in a thin Haussdorff-measurable set of a Leray- Hopf
solution of the incompressible Navier Stokes equation is on the tip of a small
open cone, where the solution is smooth. Using global regularity results for
weak Hopf-Leray solutions this potential singularity can be analyzed by
investigation of the asymptotic behavior at infinite time of a solution of a
related initial-boundary value problem posed in transformed coordinates on a
cylinder. Next to some new consequences such as global regularity of the Leray
Hopf solution after finite time, many known results can be recovered with this
method succinctly, especially the result that H1-regularity implies global
existence and smoothness.


  We give the details of the construction of a map to restate a conjectural
expression about adjoint group action on generic representations in L-packets.
We give an application of the construction to give another proof of the
classification of the Knapp-Stein R-group associated to a unitary unramified
character of a torus. Finally we prove the conjecture for unramified L-packets.


  High quality strongly correlated two-dimensional (2D) electron systems at low
temperatures $T\rightarrow 0$ exhibits an apparent metal-to-insulator
transition (MIT) at a large $r_s$ value around 40. We have measured the
magnetoresistance of 2D holes in weak perpendicular magnetic field in the
vicinity of the transition for a series of carrier densities ranging from
$0.2-1.5\times10^{10}$ $cm^{-2}$. The sign of the magnetoresistance is found to
be charge density dependent: in the direction of decreasing density, the sign
changes from being positive to negative across a characteristic value that
coincides with the critical density of MIT.


  We show that the functor from curved differential graded algebras to
differential graded categories, defined by the second author in [B], sends
Cartesian diagrams to homotopy Cartesian diagrams, under certain reasonable
hypotheses. This is an extension to the arena of dg categories of a
construction of projective modules due to Milnor. As an example, we show that
the functor satisfies descent for certain partitions of a complex manifold.


  The paper is a continuation of our earlier article where we developed a
theory of active and non-active infinitesimals and intended to establish
quantifier elimination in quasianalytic structures. That article, however, did
not attain full generality, which refers to one of its results, namely the
theorem on an active infinitesimal, playing an essential role in our
non-standard analysis. The general case was covered in our subsequent preprint,
which constitutes a basis for the approach presented here. We also provide a
quasianalytic exposition of the results concerning rectilinearization of terms
and of definable functions from our earlier research. It will be used to
demonstrate a quasianalytic structure corresponding to a Denjoy-Carleman class
which, unlike the classical analytic structure, does not admit quantifier
elimination in the language of restricted quasianalytic functions augmented
merely by the reciprocal function. More precisely, we construct a plane
definable curve, which indicates both that the classical theorem by J. Denef
and L. van den Dries as well as \L{}ojasiewicz's theorem that every subanalytic
curve is semianalytic are no longer true for quasianalytic structures. Besides
rectilinearization of terms, our construction makes use of some theorems on
power substitution for Denjoy-Carleman classes and on non-extendability of
quasianalytic function germs. The last result relies on Grothendieck's
factorization and open mapping theorems for (LF)-spaces. Note finally that this
paper comprises our earlier preprints on the subject from May 2012.


  News diversity in the media has for a long time been a foundational and
uncontested basis for ensuring that the communicative needs of individuals and
society at large are met. Today, people increasingly rely on online content and
recommender systems to consume information challenging the traditional concept
of news diversity. In addition, the very concept of diversity, which differs
between disciplines, will need to be re-evaluated requiring a interdisciplinary
investigation, which requires a new level of mutual cooperation between
computer scientists, social scientists, and legal scholars. Based on the
outcome of a multidisciplinary workshop, we have the following recommendations,
directed at researchers, funders, legislators, regulators, and the media
industry: 1. Do more research on news recommenders and diversity. 2. Create a
safe harbor for academic research with industry data. 3. Optimize the role of
public values in news recommenders. 4. Create a meaningful governance
framework. 5. Fund a joint lab to spearhead the needed interdisciplinary
research, boost practical innovation, develop. reference solutions, and
transfer insights into practice.


  Using a combination of first-principles density functional theory (DFT)
calculations and exact diagonalization studies of a first-principles derived
model, we carry out a microscopic analysis of the magnetic properties of the
half-metallic double perovskite compound, Sr$_2$CrMoO$_6$, a sister compound of
the much discussed material Sr$_2$FeMoO$_6$. The electronic structure of
Sr$_2$CrMoO$_6$, though appears similar to Sr$_2$FeMoO$_6$ at first glance,
shows non trivial differences with that of Sr$_2$FeMoO$_6$ on closer
examination. In this context, our study highlights the importance of charge
transfer energy between the two transition metal sites. The change in charge
transfer energy due to shift of Cr $d$ states in Sr$_2$CrMoO$_6$ compared to Fe
$d$ in Sr$_2$FeMoO$_6$ suppresses the hybridization between Cr $t_{2g}$ and Mo
$t_{2g}$. This strongly weakens the hybridization-driven mechanism of magnetism
discussed for Sr$_2$FeMoO$_6$. Our study reveals that, nonetheless, the
magnetic transition temperature of Sr$_2$CrMoO$_6$ remains high since
additional superexchange contribution to magnetism arises with a finite
intrinsic moment developed at the Mo site. We further discuss the situation in
comparison to another related double perovskite compound, Sr$_2$CrWO$_6$. We
also examine the effect of correlation beyond DFT, using dynamical mean field
theory (DMFT).


  We explore how neural differential equations (NDEs) may be trained on highly
resolved fluid-dynamical models of unresolved scales providing an ideal
framework for data-driven parameterizations in climate models. NDEs overcome
some of the limitations of traditional neural networks (NNs) in fluid dynamical
applications in that they can readily incorporate conservation laws and
boundary conditions and are stable when integrated over time. We advocate a
method that employs a 'residual' approach, in which the NN is used to improve
upon an existing parameterization through the representation of residual fluxes
which are not captured by the base parameterization. This reduces the amount of
training required and providing a method for capturing up-gradient and nonlocal
fluxes. As an illustrative example, we consider the parameterization of free
convection of the oceanic boundary layer triggered by buoyancy loss at the
surface. We demonstrate that a simple parameterization of the process -
convective adjustment - can be improved upon by training a NDE against highly
resolved explicit models, to capture entrainment fluxes at the base of the
well-mixed layer, fluxes that convective adjustment itself cannot represent.
The augmented parameterization outperforms existing commonly used
parameterizations such as the K-Profile Parameterization (KPP). We showcase
that the NDE performs well independent of the time-stepper and that an online
training approach using differentiable simulation via the Julia scientific
machine learning software stack improves accuracy by an order-of-magnitude. We
conclude that NDEs provide an exciting route forward to the development of
representations of sub-grid-scale processes for climate science, opening up
myriad new opportunities.


  (Abridged). Stellar absorption lines in the optical have been extensively
studied and constitute an important stellar population diagnostic for galaxies
in the local universe and up to moderate redshifts. Proceeding towards higher
look-back times, galaxies are younger and the ultraviolet becomes the relevant
spectral region where the dominant stellar populations shine. A comprehensive
study of ultraviolet absorption lines of stellar population models is however
still lacking. We study absorption line indices in the far and mid-ultraviolet
in order to determine age and metallicity indicators for UV-bright stellar
populations in the local universe as well as at high redshift. We explore
empirical and theoretical spectral libraries and use evolutionary population
synthesis to compute synthetic line indices of stellar population models. From
the empirical side, we exploit the IUE-low resolution library of stellar
spectra and system of absorption lines. From the theoretical side we use a
high-resolution library of Kurucz synthetic spectra. In order to select indices
that can be used as age and/or metallicity indicators for distant galaxies and
globular clusters, we compare the models to data of template globular clusters
from the Magellanic Clouds. We provide synthetic line indices in the wavelength
range 1200 Angstrom to 3000 Angstrom for stellar populations of various ages
and metallicities. This adds several new indices to the well-studied CIV and
SiIV absorptions. Based on the comparison with globular cluster data, we select
a set of 11 indices blueward of the 2000 Angstrom rest-frame that allows to
recover well the ages and the metallicities of the clusters. These indices are
ideal to study young galaxies at high redshift. We also provide the synthetic
high-resolution stellar population SEDs.


  We try to establish a connection between the hadronic distributions, in
proton-proton collisions at very high transverse momentum $p_{\mathrm{T}}$,
obtained via perturbative QCD and the Tsallis non extensive statistics. Our
motivation is that while the former is expected to be valid at extremely high
momentum, due to asymptotic freedom, the latter has been very successful in
describing experimental spectra over a wide range of momentum. Matching the non
extensive statistics with the asymptotic $p_{\mathrm{T}}$ behaviour expected
from QCD leads to the value of $q=1.25$.


  We report transport and magnetic relaxation measurements in the mixed state
of strongly underdoped Y_{1-x}Pr_{x}Ba_{2}Cu_{3}O_{7} crystals. A transition
from thermally activated flux creep to temperature independent quantum flux
creep is observed in both transport and magnetic relaxation at temperatures T *
5 K. Flux transformer measurements indicate that the crossover to quantum creep
is preceded by a coupling transition. Based on these observations we argue that
below the coupling transition the current is confined within a very narrow
layer beneath the current contacts.


  We review, under a perspective which appears different from previous ones,
the so-called Hilbert Property (HP) for an algebraic variety (over a number
field); this is linked to Hilbert's Irreducibility Theorem and has important
implications, for instance towards the Inverse Galois Problem.
  We shall observe that the HP is in a sense `opposite' to the Chevalley-Weil
Theorem, which concerns unramified covers; this link shall immediately entail
the result that the HP can possibly hold only for simply connected varieties
(in the appropriate sense). In turn, this leads to new counterexamples to the
HP, involving Enriques surfaces. We also prove the HP for a K3 surface related
to the above Enriques surface, providing what appears to be the first example
of a non-rational variety for which the HP can be proved.
  We also formulate some general conjectures relating the HP with the topology
of algebraic varieties.


  Many machine learning tasks can be formulated in terms of predicting
structured outputs. In frameworks such as the structured support vector machine
(SVM-Struct) and the structured perceptron, discriminative functions are
learned by iteratively applying efficient maximum a posteriori (MAP) decoding.
However, maximum likelihood estimation (MLE) of probabilistic models over these
same structured spaces requires computing partition functions, which is
generally intractable. This paper presents a method for learning discrete
exponential family models using the Bethe approximation to the MLE. Remarkably,
this problem also reduces to iterative (MAP) decoding. This connection emerges
by combining the Bethe approximation with a Frank-Wolfe (FW) algorithm on a
convex dual objective which circumvents the intractable partition function. The
result is a new single loop algorithm MLE-Struct, which is substantially more
efficient than previous double-loop methods for approximate maximum likelihood
estimation. Our algorithm outperforms existing methods in experiments involving
image segmentation, matching problems from vision, and a new dataset of
university roommate assignments.


  $SU(N_c)$ gauge theories in the strong coupling limit can be described by
integer variables representing monomers, dimers and baryon loops. We
demonstrate how the D-wave quantum annealer can perform importance sampling on
$U(N_c)$ gauge theory in the strong coupling formulation of this theory. In
addition to causing a sign problem in importance sampling, baryon loops induce
a complex QUBO matrix which cannot be optimized by the D-Wave annealer. Instead
we show that simulating the sign-problem free quenched action on the D-Wave is
sufficient when combined with a sign reweighting method. As the first test on
$SU(3)$ gauge theory, we simulate on $2 \times 2$ lattice and compare the
results with its analytic solutions.


  In this paper, we consider a family of twists of a superelliptic curve over a
global field, and obtain results on the distribution of the Mordell-Weil rank
of these twists. Our results have applications to the distribution of the
number of rational points.


  It is pointed out that the apparent presence of the fusing rule for purely
elastic scattering theories in theories with dynamical Yangian invariance
implies beautiful and hitherto unseen structure in the finite-dimensional
representation theory of Yangians.


  The control of thermal decoherence via dynamical decoupling and via the
quantum Zeno effect (Zeno control) is investigated for a model of trapped ion,
where the dynamics of two low lying hyperfine states undergoes decoherence due
to the thermal interaction with an excited state. Dynamical decoupling is a
procedure that consists in periodically driving the excited state, while the
Zeno control consists in frequently measuring it. When the control frequency is
high enough, decoherence is shown to be suppressed. Otherwise, both controls
may accelerate decoherence.


  An exact Quantum Kinetic Monte Carlo method is proposed to calculate electron
transport for 1D Fermi Hubbard model. The method is directly formulated in real
time and can be applied to extract time dependent dynamics of general
interacting Fermion models in 1D. When coupled with Density Functional Theory
and Maximally Localized Wannier Functions, our method can be used to predict
electron transport in materials in presence of interfaces. The first
application of our method on case study of $\alpha$-quartz dielectric breakdown
seems promising.


  We report simulation studies of 33 single intrinsically disordered proteins
(IDPs) using coarse-grained (CG) bead-spring models where interactions among
different amino acids are introduced through a hydropathy matrix and additional
screened Coulomb interaction for the charged amino acid beads. Our simulation
studies of two different hydropathy scales (HPS1, HPS2) [Dignon et al., PLOS
Comp. Biology, 14, 2018, Tesei et al. PNAS, 118, 2021] and the comparison with
the existing experimental data indicates an optimal interaction parameter
$\epsilon = 0.1$ kcal/mol and $0.2$ kcal/mol for the HPS1 and HPS2 hydropathy
scales. We use these best-fit parameters to investigate both the universal
aspects as well as the fine structures of the individual IDPs by introducing
additional characteristics.(i) First, we investigate the polymer specific
scaling relations of the IDPs in comparison to the universal scaling relations
[Bair et al., J. Chem. Phys. 158, 204902 (2023)] for the homopolymers and we
demonstrate that IDPs are broadly characterized with a Flory exponent of 0.56
with the conclusion that conformations of the IDPs interpolate between Gaussian
and 3DSAW chains. (ii) Then we introduce Wilson charge index W that captures
the essential features of charge interactions and distribution in the sequence
space, and (iii) a skewness parameter S that captures the finer shape variation
of the gyration radii distribution related to the charge asymmetry. Finally,
our study of the variation of <$R_g$> as a function of salt concentration
provides another important metric to bring out finer characteristics of the
IDPs which may carry relevant information for the origin of life.


  We identify that both the dynamic core polarization and dynamic orbital
deformation are important in the orientation-dependent high-harmonic generation
of CO molecules subjected to intense few cycle laser fields. These polarization
dynamics allow for the observation of strong orientation effects and dynamic
minimum in the harmonic spectra. The generated attosecond pulses can be greatly
affected by these multielectron effects. This work sheds light on future
development of dynamic orbital imaging on attosecond time scale.


  In this work, two mathematical models for malaria under resistance are
presented. More precisely, the first model shows the interaction between humans
and mosquitoes inside a patch under infection of malaria when the human
population is resistant to antimalarial drug and mosquitoes population is
resistant to insecticides. For the second model, human-mosquitoes population
movements in two patches is analyzed under the same malaria transmission
dynamic established in one patch. For a single patch, existence and stability
conditions for the equilibrium solutions in terms of the local basic
reproductive number are developed. These results reveal the existence of a
forward bifurcation and the global stability of disease-free equilibrium. In
the case of two patches, a theoretical and numerical framework on sensitivity
analysis of parameters is presented. After that, the use of antimalarial drugs
and insecticides are incorporated as control strategies and an optimal control
problem is formulated. Numerical experiments are carried out in both models to
show the feasibility of our theoretical results.


  We contribute a scalable implementation of Ryoo et al's Pooled Time Series
algorithm from CVPR 2015. The updated algorithm has been evaluated on a large
and diverse dataset of approximately 6800 videos collected from a crawl of the
deep web related to human trafficking on DARPA's MEMEX effort. We describe the
properties of Pooled Time Series and the motivation for using it to relate
videos collected from the deep web. We highlight issues that we found while
running Pooled Time Series on larger datasets and discuss solutions for those
issues. Our solution centers are re-imagining Pooled Time Series as a
Hadoop-based algorithm in which we compute portions of the eventual solution in
parallel on large commodity clusters. We demonstrate that our new Hadoop-based
algorithm works well on the 6800 video dataset and shares all of the properties
described in the CVPR 2015 paper. We suggest avenues of future work in the
project.


  Hourglass dispersion is generally believed to be solely protected by
nonsymmorphic symmetries, because these symmetries can introduce
high-dimensional projective representations. Here, based on symmetry arguments,
we propose that the hourglass dispersion can be jointly protected by symmorphic
and nonsymmorphic symmetries, instead of the only conventional nonsymmorphic
symmetry. Moreover, using first-principles calculations, we realize our
proposal in phonon spectra of realistic materials that share an antiperovskite
structure with space group \emph{P}4/\emph{nmm}. Importantly, the neck points
of these hourglass dispersions trace out two nodal rings tangent to four nodal
lines, forming a unique hourglass nodal cage in the bulk Brillouin zone. The
Berry phase analysis reveal the nontrivial topology of these nodal rings and
nodal lines. Furthermore, the nontrivial surface states and isofrequency
surface arcs are visible, facilitating their experimental confirmation of such
exotic quasiparticles. Our work not only offers a new insight into the
hourglass dispersion, but also expands aspects for studying promising
topological quasiparticles in condensed-matter systems.


  We study the vacuum polarization of a massless minimally coupled scalar field
at the horizon of four-charge STU black holes. We compare the results for the
standard asymptotically flat black holes and for the black holes obtained in
the "subtracted limit", both in the general static case and at the horizon pole
for the general rotating case. The original and the subtracted results are
identical only in the BPS limit, and have opposite sign in the extremal Kerr
limit. We also compute the vacuum polarization on the static solutions that
interpolate between both the original and the subtracted case through a
solution-generating transformation and show that the vacuum polarization stays
positive throughout the interpolating solution. In the Appendix we provide a
closed-form solution for the Green's function on general (static or rotating)
subtracted black hole geometries.


  We report the results of our search for the progenitor candidate of SN
2013dk, a Type Ic supernova (SN) that exploded in the Antennae Galaxy system.
We compare pre-explosion Hubble Space Telescope (HST) archival images with SN
images obtained using adaptive optics at the ESO Very Large Telescope. We
isolate the SN position to within 3 sigma uncertainty radius of 0.02", and show
that there is no detectable point source in any of the HST filter images within
the error circle. We set an upper limit to the absolute magnitude of the
progenitor to be M_F555W > -5.7, which does not allow Wolf-Rayet (WR) star
progenitors to be ruled out. A bright source appears 0.17" away, which is
either a single bright supergiant or compact cluster, given its absolute
magnitude of M_F555W=-9.02 +- 0.28 extended wings and complex environment.
However, even if this is a cluster, the spatial displacement of SN 2013dk means
that its membership is not assured. The strongest statement we can make is that
in the immediate environment of SN 2013dk (within 10 pc or so) we find no clear
evidence of either a point source coincident with the SN or a young stellar
cluster that could host a massive WR progenitor.


  Schr\"odinger operators often display singularities at the origin, the
Coulomb problem in atomic physics or the various matter coupling terms in the
Friedmann-Robertson-Walker problem being prominent examples. For various
applications it would be desirable to have at one's disposal an explicit basis
spanning a dense and invariant domain for such types of Schr\"odinger
operators, for instance stationary perturbation theory or the Raleigh-Ritz
method.
  Here we make the observation, that not only a such basis can indeed be
provided but that in addition relevant matrix elements and inner products can
be computed analytically in closed form, thus providing the required data e.g.
for an analytical Gram-Schmid orthonormalisation.


  Future observations of terrestrial exoplanet atmospheres will occur for
planets at different stages of geological evolution. We expect to observe a
wide variety of atmospheres and planets with alternative evolutionary paths,
with some planets resembling Earth at different epochs. For an Earth-like
atmospheric time trajectory, we simulate planets from prebiotic to current
atmosphere based on geological data. We use a stellar grid F0V to M8V
($T_\mathrm{eff}$ = 7000$\mskip3mu$K to 2400$\mskip3mu$K) to model four
geological epochs of Earth's history corresponding to a prebiotic world
(3.9$\mskip3mu$Ga), the rise of oxygen at 2.0$\mskip3mu$Ga and at
0.8$\mskip3mu$Ga, and the modern Earth. We show the VIS - IR spectral features,
with a focus on biosignatures through geological time for this grid of Sun-like
host stars and the effect of clouds on their spectra.
  We find that the observability of biosignature gases reduces with increasing
cloud cover and increases with planetary age. The observability of the visible
O$_2$ feature for lower concentrations will partly depend on clouds, which
while slightly reducing the feature increase the overall reflectivity thus the
detectable flux of a planet. The depth of the IR ozone feature contributes
substantially to the opacity at lower oxygen concentrations especially for the
high near-UV stellar environments around F stars. Our results are a grid of
model spectra for atmospheres representative of Earth's geological history to
inform future observations and instrument design and are publicly available
online.


  We present CO(2-1), $^{13}$CO(2-1), CO(6-5), CO(7-6), and SO(6$_5-5_4$) line
observations made with the {\it IRAM 30 m} and {\it APEX} radiotelescopes and
the {\it Submillimeter Array} toward the highly collimated and extended
southwest lobe of the bipolar outflow {\it Ori-S6} located in the Orion South
region. We report, for all these lines, the detection of velocity asymmetries
about the flow axis, with velocity differences roughly on the order of 1 km
s$^{-1}$ over distances of about 5000 AU, 4 km s$^{-1}$ over distances of about
2000 AU, and close to the source of between 7 and 11 km s$^{-1}$ over smaller
scales of about 1000 AU. We interpret these velocity differences as a signature
of rotation but also discuss some alternatives which we recognize as unlikely
in view of the asymmetries' large downstream continuation. This rotation across
the {\it Ori-S6} outflow is observed out to (projected) distances beyond 2.5
$\times$ 10$^4$ AU from the flow's presumed origin. Comparison of our
large-scale and small-scale observations suggests the rotational velocity to
decline not faster than 1/R with distance R from the axis; in the innermost few
arcsecs an increase of rotational velocity with R is even indicated. The
magnetic field lines threading the inner rotating CO shell may well be anchored
in a disk of radius $\sim$ 50 AU; the field lines further out need a more
extended rotating base.


  We present a call-by-need $\lambda$-calculus that enables strong reduction
(that is, reduction inside the body of abstractions) and guarantees that
arguments are only evaluated if needed and at most once. This calculus uses
explicit substitutions and subsumes the existing strong-call-by-need strategy,
but allows for more reduction sequences, and often shorter ones, while
preserving the neededness. The calculus is shown to be normalizing in a strong
sense: Whenever a $\lambda$-term t admits a normal form n in the
$\lambda$-calculus, then any reduction sequence from t in the calculus
eventually reaches a representative of the normal form n. We also exhibit a
restriction of this calculus that has the diamond property and that only
performs reduction sequences of minimal length, which makes it systematically
better than the existing strategy. We have used the Abella proof assistant to
formalize part of this calculus, and discuss how this experiment affected its
design. In particular, it led us to derive a new description of call-by-need
reduction based on inductive rules.


  Continuing the previous work, we propose a further extension of the structure
equation for a truncated CMC hierarchy by the non-commuting, truncated Virasoro
algebra of non-local symmetries. Via a canonical dressing transformation, we
first define a wave function for the CMC hierarchy. This leads to a pair of
additional formal Killing fields, and the corresponding spectral Killing field
is defined by a purely algebraic formula up to an integrable extension. The
extended CMC hierarchy is obtained by packaging these data into the associated
affine Kac-Moody algebra valued Killing fields. The log of tau function of the
extended CMC hierarchy is defined as the central component of the affine
extension of the spectral Killing field. We give a closed formula for the tau
function in terms of the determinant of the spectral Killing field.


  In recent years, theoretical and experimental interest in dark matter (DM)
candidates have shifted focus from primarily Weakly-Interacting Massive
Particles (WIMPs) to an entire suite of candidates with masses from the
zeV-scale to the PeV-scale to 30 solar masses. One particular recent
development has been searches for light dark matter (LDM), which is typically
defined as candidates with masses in the range of keV to GeV. In searches for
LDM, eV-scale and below detector thresholds are needed to detect the small
amount of kinetic energy that is imparted to nuclei in a recoil. One such
detector technology that can be applied to LDM searches is that of
Transition-Edge Sensors (TESs). Operated at cryogenic temperatures, these
sensors can achieve the required thresholds, depending on the optimization of
the design.
  In this thesis, I will motivate the evidence for DM and the various DM
candidates beyond the WIMP. I will then detail the basics of TES
characterization, expand and apply the concepts to an athermal phonon
sensor--based Cryogenic PhotoDetector (CPD), and use this detector to carry out
a search for LDM at the surface. The resulting exclusion analysis provides the
most stringent limits in DM-nucleon scattering cross section (comparing to
contemporary searches) for a cryogenic detector for masses from 93 to 140 MeV,
showing the promise of athermal phonon sensors in future LDM searches.
Furthermore, unknown excess background signals are observed in this LDM search,
for which I rule out various possible sources and motivate stress-related
microfractures as an intriguing explanation. Finally, I will shortly discuss
the outlook of future searches for LDM for various detection channels beyond
nuclear recoils.


  We investigate the interplay between the Kondo effect and randomness in
MxTiSe2 (M = Co, Ni, and Fe) single crystals. Although the typical low-T upturn
of resistivity implies the Kondo effect around the single-ion Kondo temperature
\overline{T}_{K}, positive magnetoresistance linearly proportional to the
magnetic field and the power-law scaling of magnetization suggest the forbidden
coexistence between Kondo effect and time reversal symmetry breaking. This
puzzling result is resolved by the Griffiths scenario - disorder-induced
distribution of the Kondo temperature produces an effective Kondo temperature
(\overline{T}_{K}) much lower than \overline{T}_{K}, allowing unscreened local
moments above \overline{T}_{K} and resulting in non-Fermi liquid properties in
MxTiSe2 below the percolation threshold (x<xc).


  Methods for automatically flag poor performing-predictions are essential for
safely implementing machine learning workflows into clinical practice and for
identifying difficult cases during model training. We present a readily
adoptable method using sub-models trained on different dataset folds, where
their disagreement serves as a surrogate for model confidence. Thresholds
informed by human interobserver values were used to determine whether a final
ensemble model prediction would require manual review. In two different
datasets (abdominal CT and MR predicting kidney tumors), our framework
effectively identified low performing automated segmentations. Flagging images
with a minimum Interfold test Dice score below human interobserver variability
maximized the number of flagged images while ensuring maximum ensemble test
Dice. When our internally trained model was applied to an external publicly
available dataset (KiTS21), flagged images included smaller tumors than those
observed in our internally trained dataset, demonstrating the methods
robustness to flagging poor performing out-of-distribution input data.
Comparing interfold sub-model disagreement against human interobserver values
is an efficient way to approximate a model's epistemic uncertainty - its lack
of knowledge due to insufficient relevant training data - a key functionality
for adopting these applications in clinical practice.


  In this talk, we describe an effective theory for electroweak symmetry
breaking without a physical Higgs, based on a symmetry larger than the
electroweak gauge group. This symmetry forbids deviations from the Standard
Model at the leading order in the appropriate chiral expansion. Indeed, the
large symmetry allows for a consistent expansion of the effective theory in
powers of momenta and spurions. The latter are automatically present: they
define the covariant reduction from the large symmetry to the electroweak
group.


  In \cite{HigherGnk}, the author has constructed natural maps from fundamental
groups of topological spaces (restricted configuration spaces) to the groups
$G_{n}^{k}$. In the present paper, we show that in the case of $n=k+1$, the
group $G_{k+1}^{k}$ is isomorphic to the fundamental group of some (quotient
space of) some configuration space. In particular, this leads to the solution
of word and conjugacy problems in $G_{4}^{3}$ and sheds light on $G_{k+1}^{k}$
for higher $k$.


  We consider the efficient numerical solution of the three-dimensional wave
equation with Neumann boundary conditions via time-domain boundary integral
equations. A space-time Galerkin method with $C^\infty$-smooth, compactly
supported basis functions in time and piecewise polynomial basis functions in
space is employed. We discuss the structure of the system matrix and its
efficient parallel assembly. Different preconditioning strategies for the
solution of the arising systems with block Hessenberg matrices are proposed and
investigated numerically. Furthermore, a C++ implementation parallelized by
OpenMP and MPI in shared and distributed memory, respectively, is presented.
The code is part of the boundary element library BEM4I. Results of numerical
experiments including convergence and scalability tests up to a thousand cores
on a cluster are provided. The presented implementation shows good parallel
scalability of the system matrix assembly. Moreover, the proposed algebraic
preconditioner in combination with the FGMRES solver leads to a significant
reduction of the computational time.


  This study explores the impact of whole-body vibrations induced by external
vehicle perturbations, such as aircraft turbulence, on the perception of
electrovibration displayed on touchscreens. Electrovibration holds promise as a
technology for providing tactile feedback on future touchscreens, addressing
usability challenges in vehicle cockpits. However, its performance under
dynamic conditions, such as during whole-body vibrations induced by turbulence,
still needs to be explored. We measured the absolute detection thresholds of 15
human participants for short- and long-duration electrovibration stimuli
displayed on a touchscreen, both in the absence and presence of two types of
turbulence motion generated by a motion simulator. Concurrently, we measured
participants' applied contact force and finger scan speeds. Significantly
higher (38%) absolute detection thresholds were observed for short
electrovibration stimuli than for long stimuli. Finger scan speeds in the
direction of turbulence, applied forces, and force fluctuation rates increased
during whole-body vibrations due to biodynamic feedthrough. As a result,
turbulence also significantly increased the perception thresholds, but only for
short-duration electrovibration stimuli. The results reveal that whole-body
vibrations can impede the perception of short-duration electrovibration
stimuli, due to involuntary finger movements and increased normal force
fluctuations. Our findings offer valuable insights for the future design of
touchscreens with tactile feedback in vehicle cockpits.


  Based upon the unique and simple starting point of the continuous flow of
time a physical theory is derived through an analysis of the elementary
arithmetic composition and symmetries of this one-dimensional progression. We
describe how the explicit development of the theory leads to a prediction of
the unique and largest exceptional Lie group E8 as the full `symmetry of time',
and hence as the unification group for the physical theory. This proposal
results from the identification of a series of esoteric properties of the
Standard Model of particle physics from a series of intermediate augmentations
in the `multi-dimensional form of time'. These physical properties derive from
the breaking of the full symmetry of time through the necessary interposition
of an external 4-dimensional spacetime arena, itself constructed from a
4-dimensional form of time, as the background to all observations. The basic
conceptual picture is presented together with reviews of a number of references
regarding E8 structures which may provide a significant guide in pursuing the
goal of converging upon a complete unified theory.


  A general procedure for constructing coherent states, which are eigenstates
of annihilation operators, related to quantum mechanical potential problems, is
presented. These coherent states, by construction are not potential specific
and rely on the properties of the orthogonal polynomials, for their derivation.
The information about a given quantum mechanical potential enters into these
states, through the orthogonal polynomials associated with it and also through
its ground state wave function. The time evolution of some of these states
exhibit fractional revivals, having relevance to the factorization problem.


  In 2013 Andriy V. Bondarenko showed how to construct a two-distance
counterexample to Borsuk's conjecture from any strongly regular graph whose
vertex set is not the union of at most $f+1$ cliques (sets of pairwise adjacent
vertices) where $f$ is the multiplicity of the second-largest eigenvalue of its
adjacency matrix.
  He applied that construction to those two graphs that he had been able to
prove to fulfill the condition: From the $G_2(4)$ graph (on 416 vertices) he
got a 65-dimensional two-distance counterexample. From the $Fi_{23}$ graph (on
31671 vertices) he got a 782-dimensional one and, by considering certain
induced subgraphs, counterexamples in dimensions 781, 780 and 779.
  This article presents two other strongly regular graphs fulfilling the
condition, on 28431 and on 2401, resp., vertices. It gives dedicated
counterexamples in dimensions from 781 down to 764 derived from the bigger
graph (that turned out to be an induced subgraph of the $Fi_{23}$ graph) and a
240-dimensional counterexample derived from the smaller graph.
  Several contained propositions rely on the results of (often extensive)
computations, mainly within the computer algebra system GAP. The source package
contains (almost) all used source files.


  In the early days of quantum mechanics Kapitza and Dirac predicted that
matter waves would scatter off the optical intensity grating formed by two
counter-propagating light waves [1]. This interaction, driven by the
ponderomotive potential of the optical standing wave, was both studied
theoretically and demonstrated experimentally for atoms [2] and electrons
[3-5]. In the original version of the experiment [1,5], only the transverse
momentum of particles was varied, but their energy and longitudinal momentum
remained unchanged after the interaction. Here, we report on the generalization
of the Kapitza-Dirac effect. We demonstrate that the energy of sub-relativistic
electrons is strongly modulated on the few-femtosecond time scale via the
interaction with a travelling wave created in vacuum by two colliding laser
pulses at different frequencies. This effect extends the possibilities of
temporal control of freely propagating particles with coherent light and can
serve the attosecond ballistic bunching of electrons [6], or for the
acceleration of neutral atoms or molecules by light.


  We consider N=2 four dimensional field theories compactified on a two torus
in the presence of a U(1) magnetic field. We discuss the restrictions leading
to theories with (2,2) supersymmetry or (0,2) supersymmetry in two dimensions.
The field theories live on D5 branes wrapped on four cycles of Calabi-Yau
3-folds or 4-folds described as resolved ADE singularities or resolved conifold
fibered over a two torus.


  In this paper we study a new reinforcement learning setting where the
environment is non-rewarding, contains several possibly related objects of
various controllability, and where an apt agent Bob acts independently, with
non-observable intentions. We argue that this setting defines a realistic
scenario and we present a generic discrete-state discrete-action model of such
environments. To learn in this environment, we propose an unsupervised
reinforcement learning agent called CLIC for Curriculum Learning and Imitation
for Control. CLIC learns to control individual objects in its environment, and
imitates Bob's interactions with these objects. It selects objects to focus on
when training and imitating by maximizing its learning progress. We show that
CLIC is an effective baseline in our new setting. It can effectively observe
Bob to gain control of objects faster, even if Bob is not explicitly teaching.
It can also follow Bob when he acts as a mentor and provides ordered
demonstrations. Finally, when Bob controls objects that the agent cannot, or in
presence of a hierarchy between objects in the environment, we show that CLIC
ignores non-reproducible and already mastered interactions with objects,
resulting in a greater benefit from imitation.


  We consider Sturm-Liouville operators with measure-valued weight and
potential, and positive, bounded diffusion coefficient which is bounded away
from zero. By means of a local periodicity condition, which can be seen as a
quantitative Gordon condition, we prove a bound on eigenvalues for the
corresponding operator in $L_p$, for $1\leq p<\infty$. We also explain the
sharpness of our quantitative bound, and provide an example for quasiperiodic
operators.


  We analyze the single-particle spectra of a bi-layered electron system near a
stripe instability and compare the results with ARPES experiments on the Bi2212
cuprate superconductor near optimum doping, addressing also the issue of the
puzzling absence of bonding-antibonding splitting.


  readPTU is a python package designed to analyze time-correlated single-photon
counting data. The use of the library promotes the storage of the complete time
arrival information of the photons and full flexibility in post-processing data
for analysis. The library supports the computation of time resolved signal with
external triggers and second order autocorrelation function analysis can be
performed using multiple algorithms that provide the user with different
trade-offs with regards to speed and accuracy. Additionally, a thresholding
algorithm to perform time post-selection is also available. The library has
been designed with performance and extensibility in mind to allow future users
to implement support for additional file extensions and algorithms without
having to deal with low level details. We demonstrate the performance of
readPTU by analyzing the second-order autocorrelation function of the resonance
fluorescence from a single quantum dot in a two-dimensional semiconductor.


  We have developed the laser-diode-heated floating zone (LDFZ) method, in
order to improve the broad and inhomogeneous light focusing in the conventional
lamp-heated floating zone method, which often causes difficulties in the
crystal growth especially for the incongruently melting materials. We have
simulated the light focusing properties of the LDFZ method to make irradiated
light homogeneous and restricted mostly to the molten zone. We have designed
and assembled an LDFZ furnace, and have demonstrated how it works through
actual crystal growth. The method is applicable to various kinds of materials,
and enables stable and reproducible crystal growth even for the incongruently
melting materials. We have succeeded in the crystal growth of representative
incongruently melting materials such as BiFeO3 and (La,Ba)2CuO4, which are
difficult to grow by the conventional method. Tolerance to the decentering of
the sample and highly efficient heating are also established in the LDFZ
method.


  We study Yukawa unification in string models with moduli-dominant SUSY
breaking. This type of SUSY breaking in general leads to non-universal soft
masses, i.e., soft scalar masses and gaugino masses. Such non-universality is
important for phenomenological aspects of Yukawa unification, i.e., successful
electroweak breaking, SUSY corrections to the bottom mass and the branching
ratio of $b \to s \gamma$. We show three regions in the whole parameter space
which lead to successful electroweak breaking and allow small SUSY corrections
to the bottom mass. For these three regions we investigate the $b \to s \gamma$
decay and mass spectra.


  The application of large-scale models in medical image segmentation demands
substantial quantities of meticulously annotated data curated by experts along
with high computational resources, both of which are challenges in
resource-poor settings. In this study, we present the Medical Segment Anything
Model with Galore MedSAGa where we adopt the Segment Anything Model (SAM) to
achieve memory-efficient, few-shot medical image segmentation by applying
Gradient Low-Rank Projection GaLore to the parameters of the image encoder of
SAM. Meanwhile, the weights of the prompt encoder and mask decoder undergo full
parameter fine-tuning using standard optimizers. We further assess MedSAGa's
few-shot learning capabilities, reporting on its memory efficiency and
segmentation performance across multiple standard medical image segmentation
datasets. We compare it with several baseline models, including LoRA fine-tuned
SAM (SAMed) and DAE-Former. Experiments across multiple datasets and these
baseline models with different number of images for fine tuning demonstrated
that the GPU memory consumption of MedSAGa is significantly less than that of
the baseline models, achieving an average memory efficiency of 66% more than
current state-of-the-art (SOTA) models for medical image segmentation. The
combination of substantially lower memory requirements and comparable to SOTA
results in few-shot learning for medical image segmentation positions MedSAGa
as an optimal solution for deployment in resource-constrained settings.


  Humans are increasingly interacting with machines through language, sometimes
in contexts where the user may not know they are talking to a machine (like
over the phone or a text chatbot). We aim to understand how system designers
and researchers might allow their systems to confirm its non-human identity. We
collect over 2,500 phrasings related to the intent of ``Are you a robot?". This
is paired with over 2,500 adversarially selected utterances where only
confirming the system is non-human would be insufficient or disfluent. We
compare classifiers to recognize the intent and discuss the precision/recall
and model complexity tradeoffs. Such classifiers could be integrated into
dialog systems to avoid undesired deception. We then explore how both a
generative research model (Blender) as well as two deployed systems (Amazon
Alexa, Google Assistant) handle this intent, finding that systems often fail to
confirm their non-human identity. Finally, we try to understand what a good
response to the intent would be, and conduct a user study to compare the
important aspects when responding to this intent.


  We prove that the cyclicity of a quadratic slow-fast integrable system of
Darboux type with a double heteroclinic loop is finite and uniformly bounded.


  Heart failure (HF) is one of the leading causes of hospital admissions in the
US. Readmission within 30 days after a HF hospitalization is both a recognized
indicator for disease progression and a source of considerable financial burden
to the healthcare system. Consequently, the identification of patients at risk
for readmission is a key step in improving disease management and patient
outcome. In this work, we used a large administrative claims dataset to
(1)explore the systematic application of neural network-based models versus
logistic regression for predicting 30 days all-cause readmission after
discharge from a HF admission, and (2)to examine the additive value of
patients' hospitalization timelines on prediction performance. Based on data
from 272,778 (49% female) patients with a mean (SD) age of 73 years (14) and
343,328 HF admissions (67% of total admissions), we trained and tested our
predictive readmission models following a stratified 5-fold cross-validation
scheme. Among the deep learning approaches, a recurrent neural network (RNN)
combined with conditional random fields (CRF) model (RNNCRF) achieved the best
performance in readmission prediction with 0.642 AUC (95% CI, 0.640-0.645).
Other models, such as those based on RNN, convolutional neural networks and CRF
alone had lower performance, with a non-timeline based model (MLP) performing
worst. A competitive model based on logistic regression with LASSO achieved a
performance of 0.643 AUC (95%CI, 0.640-0.646). We conclude that data from
patient timelines improve 30 day readmission prediction for neural
network-based models, that a logistic regression with LASSO has equal
performance to the best neural network model and that the use of administrative
data result in competitive performance compared to published approaches based
on richer clinical datasets.


  We investigate the effects of cosmic ray (CR) dynamics on cold, dense clouds
embedded in a hot, tenuous galactic halo. If the magnetic field does not
increase too much inside the cloud, the local reduction in Alfv\'en speed
imposes a bottleneck on CRs streaming out from the star-forming galactic disk.
The bottleneck flattens the upstream CR gradient in the hot gas, implying that
multi-phase structure could have global effects on CR driven winds. A large CR
pressure gradient can also develop on the outward-facing edge of the cloud.
This pressure gradient has two independent effects. The CRs push the cloud
upward, imparting it with momentum. On smaller scales, the CRs pressurize cold
gas in the fronts, reducing its density, consistent with the low densities of
cold gas inferred in recent COS observations of local $L_{*}$ galaxies. They
also heat the material at the cloud edge, broadening the cloud-halo interface
and causing an observable change in interface ionic abundances. Due to the much
weaker temperature dependence of cosmic ray heating relative to thermal
conductive heating, CR mediated fronts have a higher ratio of low to high ions
compared to conduction fronts, in better agreement with observations. We
investigate these effects separately using 1D simulations and analytic
techniques.


  Effective-medium theory is applied to the percolation description of the
metal-insulator transition in two dimensions with emphasis on the continuous
connection between the zero-magnetic-field transition and the quantum Hall
transition. In this model the system consists of puddles connected via saddle
points, and there is loss of quantum coherence inside the puddles. The
effective conductance of the network is calculated using appropriate
integration over the distribution of conductances, leading to a determination
of the magnetic field dependence of the critical density. Excellent
quantitative agreement is obtained with the experimental data, which allows an
estimate of the puddle physical parameters.


  In any communication network, the maximum number of link-disjoint paths
between any pair of communicating nodes, S and T, is limited by the S-T minimum
link-cut. Multipath routing protocols have been proposed in the literature to
make use of these S-T paths in enhancing the survivability of the S-T
information flow. This is usually accomplished by using a subset of these paths
to forward redundant data units or combinations (if network coding is allowed)
from S to T. Therefore, this enhancement in survivability reduces the useful
S-T information rate. In this paper we present a new way to enhance the
survivability of the S-T information flow without compromising the maximum
achievable S-T information rate. To do this, bottleneck links (in the min-cut)
should only forward useful information, and not redundant data units. We
introduce the idea of extra source or destination connectivity with respect to
a certain S-T max-flow, and then we study two problems: namely, pre-cut
protection and post-cut protection. Although our objective in both problems is
the same, where we aim to maximize the number of protected paths, our analysis
shows that the nature of these two problems are very different, and that the
pre-cut protection problem is much harder. Specifically, we prove the hardness
of the pre-cut protection problem, formulate it as an integer linear program,
and propose a heuristic approach to solve it. Simulations show that the
performance of the heuristic is acceptable even on relatively large networks.
In the post-cut problem we show that all the data units, forwarded by the
min-cut edges not incident to T, can be post-cut-protected.