  We theoretically and numerically investigate the transport of active colloids
to target regions, delimited by asymmetric energy barriers. We show that it is
possible to introduce a generalized effective temperature that is related to
the local variance of particle velocities. The stationary probability
distributions can be derived from a simple diffusion equation in the presence
of an inhomogeneous effective temperature resulting from the action of external
force fields. In particular, transitions rates over asymmetric energy barriers
can be unbalanced by having different effective temperatures over the two
slopes of the barrier. By varying the type of active noise, we find that equal
values of diffusivity and persistence time may produce strongly varied
effective temperatures and thus stationary distributions.


  Phenotypic heterogeneity in an isogenic, microbial population enables a
subset of the population to persist under stress. In mycobacteria, stresses
like nutrient and oxygen deprivation activate the stress response pathway
involving the two-component system MprAB and the sigma factor, SigE. SigE in
turn activates the expression of the stringent response regulator, rel. The
enzyme polyphosphate kinase 1 (PPK1) regulates this pathway by synthesizing
polyphosphate required for the activation of MprB. The precise manner in which
only a subpopulation of bacterial cells develops persistence, remains unknown.
Rel is required for mycobacterial persistence. Here we show that the
distribution of rel expression levels in a growing population of mycobacteria
is bimodal with two distinct peaks corresponding to low (L) and high (H)
expression states, and further establish that a positive feedback loop
involving the mprAB operon along with stochastic gene expression are
responsible for the phenotypic heterogeneity. Combining single cell analysis by
flow cytometry with theoretical modeling, we observe that during growth,
noise-driven transitions take a subpopulation of cells from the L to the H
state within a "window of opportunity" in time preceding the stationary phase.
We find evidence of hysteresis in the expression of rel in response to changing
concentrations of PPK1. Our results provide, for the first time, evidence that
bistability and stochastic gene expression could be important for the
development of "heterogeneity with an advantage" in mycobacteria.


  Cohomology and deformation theories are developed for Poisson algebras
starting with the more general concept of a Leibniz pair, namely of an
associative algebra $A$ together with a Lie algebra $L$ mapped into the
derivations of $A$. A bicomplex (with both Hochschild and Chevalley-Eilenberg
cohomologies) is essential.


  We generalize the Weisskopf-Wigner theory for the line shape and transition
rates of decaying states to the case of the energy-driven stochastic
Schr\"odinger equation that has been used as a phenomenology for state vector
reduction. Within the standard approximations used in the Weisskopf-Wigner
analysis, and assuming that the perturbing potential inducing the decay has
vanishing matrix elements within the degenerate manifold containing the
decaying state, the stochastic Schr\"odinger equation linearizes. Solving the
linearized equations, we find no change from the standard analysis in the line
shape or the transition rate per unit time. The only effect of the stochastic
terms is to alter the early time transient behavior of the decay, in a way that
eliminates the quantum Zeno effect. We apply our results to estimate
experimental bounds on the parameter governing the stochastic effects.


  Somos 4 sequences are a family of sequences defined by a fourth-order
quadratic recurrence relation with constant coefficients.For particular choices
of the coefficients and the four initial data, such recurrences can yield
sequences of integers. Fomin and Zelevinsky have used the theory of cluster
algebras to prove that these recurrences also provide one of the simplest
examples of the Laurent phenomenon: all the terms of a Somos 4 sequence are
Laurent polynomials in the initial data. The integrality of certain Somos 4
sequences has previously been understood in terms of the Laurent phenomenon.
However, each of the authors of this paper has independently established the
precise correspondence between Somos 4 sequences and sequences of points on
elliptic curves. Here we show that these sequences satisfy a stronger condition
than the Laurent property, and hence establish a broad set of sufficient
conditions for integrality. As a by-product, non-periodic sequences provide
infinitely many solutions of an associated quartic Diophantine equation in four
variables. The analogous results for Somos 5 sequences are also presented, as
well as various examples, including parameter families of Somos 4 integer
sequences.


  We give a very short proof that determinantal point processes have a trivial
tail $\sigma$-field. This conjecture of the author has been proved by Osada and
Osada as well as by Bufetov, Qiu, and Shamov. The former set of authors relied
on the earlier result of the present author that the conjecture held in the
discrete case, as does the present short proof.


  These are lecture notes for a course to be held. They provide a full
discussion of certain analytic aspects of the uniformisation theory of
(singular) holomorphic foliations by curves on compact Kaehler manifolds, with
emphasis on their consequences on positivity properties of the corresponding
canonical bundles.


  Exclusive J/Psi electroproduction is studied in the framework of the analytic
S-matrix theory. The differential and integrated elastic cross sections are
calculated using the Modified Dual Amplitude with Mandelstam Analyticity
(M-DAMA) model. The model is applied to the description of the available
experimantal data and proves to be valid in a wide region of the kinematical
variables s, t and Q^2. Our amplitude can be used also as a universal
background parametrization for the extraction of tiny resonance signals.


  An optimization algorithm for nonsmooth nonconvex constrained optimization
problems with upper-C2 objective functions is proposed and analyzed. Upper-C2
is a weakly concave property that exists in difference of convex (DC) functions
and arises naturally in many applications, particularly certain classes of
solutions to parametric optimization problems [34, 4], e.g., recourse of
stochastic programming [36] and projection into closed sets [34]. The algorithm
can be viewed as a bundle method specialized for upper-C2 problems and is
globally convergent with bounded algorithm parameters. Compared to conventional
bundle methods, the proposed method is both simpler and computationally more
efficient. The algorithm handles general smooth constraints similarly to
sequential quadratic programming (SQP) methods and uses a line search to ensure
progress. The potential inconsistencies from the linearization of the
constraints are addressed through a penalty method. The capabilities of the
algorithm are demonstrated by solving both simple upper-C2 problems and
real-world optimal power flow problems used in current power grid industry
practices.


  Although it has a history that goes back about three decades, Metaverse has
grown to be one of the most talked-about subjects today. Metaverse gradually
increased its influence in the realm of business discourse after initially
being restricted to discussions about entertainment. Before getting deep into
the Metaverse, it should be noted that failure and deviating from the business
path are highly likely for an enterprise that relies heavily on information
technology (IT) because of improper use and thinking about IT. The idea of
enterprise architecture (EA) emerged as a management strategy to address this
issue. As the first school of thought of EA, it sought to transform IT from an
unnecessary burden in an enterprise to a guiding and supporting force. Then an
extended EA model is suggested as a result of the attempt made in this paper to
use the idea of EA to steer virtual enterprises on Metaverse-based platforms.
Finally, to evaluate the conceptual model and demonstrate that the Metaverse
can support businesses, three case studies Decentraland, Battle Infinity, and
Rooom were utilized.


  Grid cells in the entorhinal cortex of mammalian brains exhibit striking
hexagon grid firing patterns in their response maps as the animal (e.g., a rat)
navigates in a 2D open environment. In this paper, we study the emergence of
the hexagon grid patterns of grid cells based on a general recurrent neural
network (RNN) model that captures the navigation process. The responses of grid
cells collectively form a high dimensional vector, representing the 2D
self-position of the agent. As the agent moves, the vector is transformed by an
RNN that takes the velocity of the agent as input. We propose a simple yet
general conformal normalization of the input velocity of the RNN, so that the
local displacement of the position vector in the high-dimensional neural space
is proportional to the local displacement of the agent in the 2D physical
space, regardless of the direction of the input velocity. We apply this
mechanism to both a linear RNN and nonlinear RNNs. Theoretically, we provide an
understanding that explains the connection between conformal normalization and
the emergence of hexagon grid patterns. Empirically, we conduct extensive
experiments to verify that conformal normalization is crucial for the emergence
of hexagon grid patterns, across various types of RNNs. The learned patterns
share similar profiles to biological grid cells, and the topological properties
of the patterns also align with our theoretical understanding.


  We have used catalogues from several Galactic plane surveys and dedicated
observations to investigate the relationship between various maser species and
Galactic star forming clumps, as identified by the ATLASGAL survey. The maser
transitions of interest are the 6.7 & 12.2 GHz methanol masers, 22.2 GHz water
masers, and the masers emitting in the four ground-state hyperfine structure
transitions of hydroxyl. We find clump association rates for the water,
hydroxyl and methanol masers to be 56, 39 and 82 per cent respectively, within
the Galactic longitude range of 60{\deg} > $l$ > -60{\deg}. We investigate the
differences in physical parameters between maser associated clumps and the full
ATLASGAL sample, and find that clumps coincident with maser emission are more
compact with increased densities and luminosities. However, we find the
physical conditions within the clumps are similar for the different maser
species. A volume density threshold of $n$(H$_{2}$) > 10$^{4.1}$ cm$^{-3}$ for
the 6.7 GHz methanol maser found in our previous study is shown to be
consistent across for all maser species investigated. We find limits that are
required for the production of maser emission to be 500 L$_{\odot}$ and 6
M$_{\odot}$ respectively. The evolutionary phase of maser associated clumps is
investigated using the L/M ratio of clumps coincident with maser emission, and
these have similar L/M ranges (~10$^{0.2}$ - 10$^{2.7}$
L$_{\odot}$/M$_{\odot}$) regardless of the associated transitions. This implies
that the conditions required for the production of maser emission only occur
during a relatively narrow period during a star's evolution. Lower limits of
the statistical lifetimes for each maser species are derived, ranging from ~0.4
- 2 x 10$^{4}$ yrs and are in good agreement with the "straw man" evolutionary
model previously presented.


  The size of non-perturbative corrections to event shape observables is
predicted to fall like a power of the inverse centre of mass energy. These
power corrections are investigated for different observables from
e+e-annihilation and compared to the theoretical predictions. Using the latest
DELPHI high energy data advantages of determining \alpha_s from these
predictions are discussed and compared to conventional methods.


  The largest known reset thresholds for DFAs are equal to $(n-1)^2$, where $n$
is the number of states. This is conjectured to be the maximum possible. PFAs
(with partial transition function) can have exponentially large reset
thresholds. This is still true if we restrict to binary PFAs. However,
asymptotics do not give conclusions for fixed $n$. We prove that the maximal
reset threshold for binary PFAs is strictly greater than $(n-1)^2$ if and only
if $n\geq 6$.
  These results are mostly based on the analysis of synchronizing word lengths
for a certain family of binary PFAs. This family has the following properties:
it contains the well-known \v{C}ern\'y automata; for $n\leq 10$ it contains a
binary PFA with maximal possible reset threshold; for all $n\geq 6$ it contains
a PFA with reset threshold larger than the maximum known for DFAs.
  Analysis of this family reveals remarkable patterns involving the Fibonacci
numbers and related sequences such as the Padovan sequence. We derive explicit
formulas for the reset thresholds in terms of these recurrent sequences.
  Asymptotically the \v{C}ern\'y family gives reset thresholds of polynomial
order. We prove that PFAs in the family are not extremal for $n\geq 41$. For
that purpose, we present an improvement of Martyugin's prime number
construction of binary PFAs.


  Statistical mechanics provides a framework for describing the physics of
large, complex many-body systems using only a few macroscopic parameters to
determine the state of the system. For isolated quantum many-body systems, such
a description is achieved via the eigenstate thermalization hypothesis (ETH),
which links thermalization, ergodicity and quantum chaotic behavior. However,
tendency towards thermalization is not observed at finite system sizes and
evolution times in a robust many-body localization (MBL) regime found
numerically and experimentally in the dynamics of interacting many-body systems
at strong disorder. Although the phenomenology of the MBL regime is
well-established, the central question remains unanswered: under what
conditions does the MBL regime give rise to an MBL phase in which the
thermalization does not occur even in the asymptotic limit of infinite system
size and evolution time?
  This review focuses on recent numerical investigations aiming to clarify the
status of the MBL phase, and it establishes the critical open questions about
the dynamics of disordered many-body systems. Persistent finite size drifts
towards ergodicity consistently emerge in spectral properties of disordered
many-body systems, excluding naive single-parameter scaling hypothesis and
preventing comprehension of the status of the MBL phase. The drifts are related
to tendencies towards thermalization and non-vanishing transport observed in
the dynamics of many-body systems, even at strong disorder. These phenomena
impede understanding of microscopic processes at the ETH-MBL crossover.
Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength
suggests the proximity of the MBL phase. This review concludes that the
questions about thermalization and its failure in disordered many-body systems
remain a captivating area open for further explorations.


  We show that the Tate conjecture for divisors over a finite field $\mathbb F$
is equivalent to an explicit algebraic problem about the third Milnor K-group
of the function field $\bar {\mathbb F}(x,y,z)$ in three variables over $\bar
{\mathbb F}$.


  Empirical evidence questions fundamental concepts of the human population
dynamics. One of the key conclusions of this study is that positive checks
activate the efficient Malthusian regeneration mechanism, suggesting that the
Epoch of Malthusian Stagnation, the first stage of growth claimed by the
Demographic Transition Theory, did not exist.


  Ideal subarrangements of a Weyl arrangement are proved to be free by the
multiple addition theorem (MAT) due to Abe-Barakat-Cuntz-Hoge-Terao (2016).
They form a significant class among Weyl subarrangements that are known to be
free so far. The concept of MAT-free arrangements was introduced recently by
Cuntz-M{\"u}cksch (2020) to capture a core of the MAT, which enlarges the ideal
subarrangements from the perspective of freeness. The aim of this paper is to
give a precise characterization of the MAT-freeness in the case of type $A$
Weyl subarrangements (or graphic arrangements). It is known that the ideal and
free graphic arrangements correspond to the unit interval and chordal graphs
respectively. We prove that a graphic arrangement is MAT-free if and only if
the underlying graph is strongly chordal. In particular, it affirmatively
answers a question of Cuntz-M{\"u}cksch that MAT-freeness is closed under
taking localization in the case of graphic arrangements.


  In this work, exact mathematical expansions for the intrinsic electromagnetic
(EM) or optical cross-sections (i.e., extinction, scattering and absorption)
for a pair of perfectly conducting circular cylinders in a homogeneous medium
are derived. The incident illuminating field is an axially-polarized electric
field composed of plane travelling waves with an arbitrary angle of incidence
in the polar plane. The formalism is based on the multipole modal expansion
method in cylindrical coordinates and the translational addition theorem
applicable to any range of frequencies. An effective EM field, incident on the
probed cylinder, is defined first, which includes the initial and re-scattered
field from the second cylinder. Subsequently, it is used jointly with the
scattered field to derive the mathematical expressions for the intrinsic/local
cross-sections based on integrating their corresponding time-averaged
intensities over the surface of the probed object by applying the Poynting
theorem. Numerical computations for the intrinsic extinction (or scattering)
energy efficiencies for a pair of conducting circular cylinders with different
radii in a homogeneous medium are considered. Emphasis is given on varying the
interparticle distance, the angle of incidence, and the dimensionless sizes of
the cylinders. The results computed a priori can be useful in the full
characterization of a multiple scattering system of many particles, in
conjunction with experimental data for the extrinsic cross-sections.


  In this communication we have shown that Schwarzschild solution is possible
in brane world for some specific choices of brane matter and the non local
effects from the bulk. A conformally flat bulk space time with fine-tuned
vacuum energy (brane tension) shows that, Schwarzschild solution may also be
the vacuum solution for brane world scenario.


  Structural re-parameterization (Rep) methods achieve noticeable improvements
on simple VGG-style networks. Despite the prevalence, current Rep methods
simply re-parameterize all operations into an augmented network, including
those that rarely contribute to the model's performance. As such, the price to
pay is an expensive computational overhead to manipulate these unnecessary
behaviors. To eliminate the above caveats, we aim to bootstrap the training
with minimal cost by devising a dynamic re-parameterization (DyRep) method,
which encodes Rep technique into the training process that dynamically evolves
the network structures. Concretely, our proposal adaptively finds the
operations which contribute most to the loss in the network, and applies Rep to
enhance their representational capacity. Besides, to suppress the noisy and
redundant operations introduced by Rep, we devise a de-parameterization
technique for a more compact re-parameterization. With this regard, DyRep is
more efficient than Rep since it smoothly evolves the given network instead of
constructing an over-parameterized network. Experimental results demonstrate
our effectiveness, e.g., DyRep improves the accuracy of ResNet-18 by $2.04\%$
on ImageNet and reduces $22\%$ runtime over the baseline. Code is available at:
https://github.com/hunto/DyRep.


  Let p be an odd prime. Let K_p = Q(zeta) be the p-cyclotomic field. Let pi be
the prime ideal of K_p lying over p. Let G be the Galois group of K_p. Let v be
a primitive root mod p. Let sigma be a Q-isomorphism of K_p. Let P(sigma) =
sigma^{p-2}v^{-(p-2)}+ ... + sigma v^{-1} +1 in Z[G], where v^n is understood
(mod p). We apply Stickelberger relation to odd prime numbers q different of p
and to some singular integers A of K_p connected with the p-class group C_p of
K_p and prove the pi-adic congruences:
  1) pi^{2p-1} | A^{P(\sigma)} if q = 1 (mod p),
  2) pi^{2p-1} || A^{P(\sigma)} if q = 1 (mod p) and p^{(q-1)/p} = 1 (mod q).
  3) pi^{2p} | A^{P(\sigma)} if q not = 1 (mod p).
  These results allow us to connect the structure of the p-class group C_p with
pi-adic expression of singular numbers A and with solutions of some explicit
congruences mod p in Z[X].
  The last secion applies Stickelberger relation to describe the structure of
the complete class group of K_p.


  Photon-dominated regions (PDRs) are powerful molecular line emitters in
external galaxies. They are expected in galaxies with high rates of massive
star formation due to either starburst (SB) events or starburst coupled with
active galactic nuclei (AGN) events. We have explored the PDR chemistry for a
range of physical conditions representing a variety of galaxy types. Our main
result is a demonstration of the sensitivity of the chemistry to changes in the
physical conditions. We adopt crude estimates of relevant physical parameters
for several galaxy types and use our models to predict suitable molecular
tracers of those conditions. The set of recommended molecular tracers differs
from that which we recommended for use in galaxies with embedded massive stars.
Thus, molecular observations can in principle be used to distinguish between
excitation by starburst and by SB+AGN in distant galaxies. Our recommendations
are intended to be useful in preparing Herschel and ALMA proposals to identify
sources of excitation in galaxies.


  Word Sense Disambiguation (WSD) is one of the hardest tasks in natural
language understanding and knowledge engineering. The glass ceiling of 80% F1
score is recently achieved through supervised deep-learning, enriched by a
variety of knowledge graphs. Here, we propose a novel neurosymbolic methodology
that is able to push the F1 score above 90%. The core of our methodology is a
neurosymbolic sense embedding, in terms of a configuration of nested balls in
n-dimensional space. The centre point of a ball well-preserves word embedding,
which partially fix the locations of balls. Inclusion relations among balls
precisely encode symbolic hypernym relations among senses, and enable simple
logic deduction among sense embeddings, which cannot be realised before. We
trained a Transformer to learn the mapping from a contextualized word embedding
to its sense ball embedding, just like playing the game of darts (a game of
shooting darts into a dartboard). A series of experiments are conducted by
utilizing pre-training n-ball embeddings, which have the coverage of around 70%
training data and 75% testing data in the benchmark WSD corpus. The F1 scores
in experiments range from 90.1% to 100.0% in all six groups of test data-sets
(each group has 4 testing data with different sizes of n-ball embeddings). Our
novel neurosymbolic methodology has the potential to break the ceiling of
deep-learning approaches for WSD. Limitations and extensions of our current
works are listed.


  If n points B_1,---,B_n$ in the standard simplex \Delta_n are affinely
independent, then they can span an (n-1)-simplex denoted by
\Lambda=Con(B_1,---,B_n). Here \Lambda corresponds to an n*n matrix [\Lambda]
whose columns are B_1,---,B_n. In this paper, we firstly proved that if \Lambda
of diameter sufficiently small contains a point $P$, and f(P)>0 (<0) for a form
f in R[X], then the coefficients of f([\Lambda] X) are all positive (negative).
Next, as an application of this result, a necessary and sufficient condition
for determining the real zeros on \Delta_n of a system of homogeneous algebraic
equations with integral coefficients is established.


  In this paper we relate dynamics associated to zero-sum games (Fictitious
play) to Hamiltonian dynamics. It turns out that the Hamiltonian dynamics which
is induced from fictitious play, has properties which are rather different from
those found in more classically defined Hamiltonian dynamics. Although the
vectorfield is piecewise constant (and so the flow $\phi_t$ piecewise a
translation), the dynamics is rather rich. For example, there exists a Hamilton
$H$ so that for each $t>0$ the level set $H^{-1}(t)$ is homeomorphic to $S^3$
(the level sets consist of pieces of hyperplanes in $\R^4$) and with the
following property. There exists a periodic orbit $\Gamma$ of the Hamiltonian
flow in $H^{-1}(1)$ so that the first return map $F$ to a section $Z\subset
H^{-1}(1)$ transversal to $\Gamma$ at $x\in \Gamma$ acts as a random-walk:
there exist a nested sequence of annuli $A_n$ in $Z$ (around $x$ so that $\cup
A_n\cup \{x\}$ is a neighbourhood of $x$ in $Z$) shrinking geometrically to $x$
so that for each sequence $n(i)\ge 0$ with $|n(i+1)-n(i)|\le 1$ there exists a
point $z\in Z$ so that $F^i(z)\in A_{n(i)}$ for all $i\ge 0$.


  Three unit spheres were used to represent the two-qubit pure states. The
three spheres are named the base sphere, entanglement sphere, and fiber sphere.
The base sphere and entanglement sphere represent the reduced density matrix of
the base qubit and the non-local entanglement measure, concurrence, while the
fiber sphere represents the fiber qubit via a simple rotation under a local
single-qubit unitary operation; however, in an entangled bipartite state, the
fiber sphere has no information on the reduced density matrix of the fiber
qubit. When the bipartite state becomes separable, the base and fiber spheres
seamlessly become the single-qubit Bloch spheres of each qubit. Since either
qubit can be chosen as the base qubit, two alternative sets of these three
spheres are available, where each set fully represents the bipartite pure
state, and each set has information of the reduced density matrix of its base
qubit. Comparing this model to the two Bloch balls representing the reduced
density matrices of the two qubits, each Bloch ball corresponds to two unit
spheres in our model, namely, the base and entanglement spheres. The
concurrence-coherence complementarity is explicitly shown on the entanglement
sphere via a single angle.


  We initiate the investigation of the zero temperature holographic superfluids
with two competing orders, where besides the vacuum phase, two one band
superfluid phases, the coexistent superfluid phase has also been found in the
AdS soliton background for the first time. We construct the complete phase
diagram in the $e-\mu$ plane by numerics, which is consistent with our
qualitative analysis. Furthermore, we calculate the corresponding optical
conductivity and sound speed by the linear response theory. The onset of pole
of optical conductivity at $\omega=0$ indicates that the spontaneous breaking
phase always represents the superfluid phase, and the residue of pole is
increased with the chemical potential, which is consistent with the fact that
the particle density is essentially the superfluid density for zero temperature
superfluids. In addition, the resulting sound speed demonstrates the
non-smoothness at the critical points as the order parameter of condensate,
which indicates that the phase transitions can also be identified by the
behavior of sound speed. Moreover, as expected from the boundary conformal
field theory, the sound speed saturates to $\frac{1}{\sqrt{2}}$ at the large
chemical potential limit for our two band holographic superfluid model.


  Accurate vegetation models can produce further insights into the complex
interaction between vegetation activity and ecosystem processes. Previous
research has established that long-term trends and short-term variability of
temperature and precipitation affect vegetation activity. Motivated by the
recent success of Transformer-based Deep Learning models for medium-range
weather forecasting, we adapt the publicly available pre-trained FourCastNet to
model vegetation activity while accounting for the short-term dynamics of
climate variability. We investigate how the learned global representation of
the atmosphere's state can be transferred to model the normalized difference
vegetation index (NDVI). Our model globally estimates vegetation activity at a
resolution of \SI{0.25}{\degree} while relying only on meteorological data. We
demonstrate that leveraging pre-trained weather models improves the NDVI
estimates compared to learning an NDVI model from scratch. Additionally, we
compare our results to other recent data-driven NDVI modeling approaches from
machine learning and ecology literature. We further provide experimental
evidence on how much data and training time is necessary to turn FourCastNet
into an effective vegetation model. Code and models will be made available upon
publication.


  The long-range entanglement dynamics of an one-dimensional spin-1/2
anisotropic XXZ model are studied using the method of the adaptive
time-dependent density-matrix renormalization-group. The long-range
entanglement can be generated when a local quench on one of boundary bonds is
performed in the system. The anisotropic interaction has a strong influence
both on the maximal value of long-range entanglement and the time of reaching
the maximum long-range entanglement. The local coupling has a notable impact on
the long-range entanglement, but it can be neglected in the time of reaching
the maximal long-range entanglement.


  In the developing field of magnonics,it is very important to achieve
tailoring of spin wave propagation by both a proper combination of materials
with different magnetic properties and their nanostructuring on the
submicrometric scale. We have exploited deep ultra-violet lithography, in
combination with tilted shadow deposition technique, to fabricate arrays of
closely spaced bi-layer nanowires (NWs), with separation d=100 nm and
periodicity a=440 nm, having bottom and top layers made of Permalloy and Iron,
respectively. The NWs have either rectangular cross section (bottom and upper
layers of equal width) or L-shaped cross section (upper layer of half width).
The frequency dispersion of collective spin wave excitations in the above
bi-layered NWs arrays has been measured by the Brillouin light scattering
technique while sweeping the wave vector perpendicularly to the wire length
over three Brillouin zones of the reciprocal space. For the rectangular NWs,
the lowest frequency fundamental mode, characterized by a quasi- uniform
profile of the amplitude of the dynamic magnetization across the NW width,
exhibits a sizeable and periodic frequency dispersion. A similar dispersive
mode is also present in L-shaped NWs, but the mode amplitude is concentrated in
the thin side of the NWs. The width and the center frequency of the magnonic
band associated with the above fundamental modes has been analyzed, showing
that both can be tuned by varying the external applied field. Moreover, for the
L-shaped NWs it is shown that there is also a second dispersive mode,at higher
frequency,characterized by an amplitude concentrated in the thick side of the
NW. These experimental results have been quantitatively reproduced by an
original numerical model that includes two-dimensional Green's function of the
dipole field of the dynamic magnetization and interlayer exchange coupling
between the layers.


  Within a Supersymmetric Quantum Mechanics (SUSY-QM) framework, the (3+1)
Dirac equation describing a Dirac material in the presence of external parallel
electric and magnetic fields is solved. Considering static but non-uniform
electric and magnetic profiles with translational symmetry along the
y-direction, the Dirac equation is transformed into two decoupled pairs of
Schr\"odinger equations, one for each chirality of the fermion fields. Taking
trigonometric and hyperbolic profiles for the vector and scalar potentials,
respectively, we arrive at SUSY partner P\"oschl-Teller-like quantum
potentials. Restricting to the conditions of the potentials that support an
analytic zero-mode solution, we obtain a nontrivial current density in the same
plane where the electric and magnetic fields lie, but perpendicular to both of
them, indicating the possibility of realizing the Planar Hall Effect.
Furthermore, this non-vanishing current density is the sum of current densities
for the left- and right-chiralities, suggesting that the net current is a
consequence of chiral symmetry.


  We show that every 2-degenerate graph with maximum degree $\Delta$ has a
strong edge-coloring with at most $8\Delta-4$ colors.


  Knowledge Distillation (KD) methods are capable of transferring the knowledge
encoded in a large and complex teacher into a smaller and faster student. Early
methods were usually limited to transferring the knowledge only between the
last layers of the networks, while latter approaches were capable of performing
multi-layer KD, further increasing the accuracy of the student. However,
despite their improved performance, these methods still suffer from several
limitations that restrict both their efficiency and flexibility. First,
existing KD methods typically ignore that neural networks undergo through
different learning phases during the training process, which often requires
different types of supervision for each one. Furthermore, existing multi-layer
KD methods are usually unable to effectively handle networks with significantly
different architectures (heterogeneous KD). In this paper we propose a novel KD
method that works by modeling the information flow through the various layers
of the teacher model and then train a student model to mimic this information
flow. The proposed method is capable of overcoming the aforementioned
limitations by using an appropriate supervision scheme during the different
phases of the training process, as well as by designing and training an
appropriate auxiliary teacher model that acts as a proxy model capable of
"explaining" the way the teacher works to the student. The effectiveness of the
proposed method is demonstrated using four image datasets and several different
evaluation setups.


  Motivated by high interest in the close relation between string theory and
black hole solutions, in this paper, we take into account the
Einstein-Gauss-Bonnet Lagrangian in the context of massive gravity. We examine
the possibility of black hole in this regard, and discuss the types of
horizons. Next, we calculate conserved and thermodynamic quantities and check
the validity of the first law of thermodynamics. In addition, we investigate
the stability of these black holes in context of canonical ensemble. We show
that number, type and place of phase transition points may be significantly
affected by different parameters. Next, by considering cosmological constant as
thermodynamical pressure, we will extend phase space and calculate critical
values. Then, we construct thermodynamical spacetime by considering mass as
thermodynamical potential. We study geometrical thermodynamics of these black
holes in context of heat capacity and extended phase space. We show that
studying heat capacity, geometrical thermodynamics and critical behavior in
extended phase space lead to consistent results. Finally, we will employ a new
method for obtaining critical values and show that the results of this method
are consistent with those of other methods.


  The electronic response of a composite consisting of aligned metallic
cylinders in vacuum is investigated, on the basis of photonic band structure
calculations. The effective long-wavelength dielectric response function is
computed, as a function of the filling fraction. A spectral representation of
the effective response is considered, and the surface mode strengths and
positions are analyzed. The range of validity of a Maxwell-Garnett-like
approach is discussed, and the impact of our results on absorption spectra and
electron energy-loss phenomena is addressed.


  A strong version of the Orlicz maximal operator is introduced and a natural
$B_p$ condition for the rectangle case is defined to characterize its
boundedness. This fact let us to describe a sufficient condition for the two
weight inequalities of the strong maximal function in terms of power and
logarithmic bumps. Results for the multilinear version of this operator and for
others multi(sub)linear maximal functions associated with bases of open sets
are also studied.


  Real-world events exhibit a high degree of interdependence and connections,
and hence data points generated also inherit the linkages. However, the
majority of AI/ML techniques leave out the linkages among data points. The
recent surge of interest in graph-based AI/ML techniques is aimed to leverage
the linkages. Graph-based learning algorithms utilize the data and related
information effectively to build superior models. Neural Graph Learning (NGL)
is one such technique that utilizes a traditional machine learning algorithm
with a modified loss function to leverage the edges in the graph structure. In
this paper, we propose a model using NGL - NodeNet, to solve node
classification task for citation graphs. We discuss our modifications and their
relevance to the task. We further compare our results with the current state of
the art and investigate reasons for the superior performance of NodeNet.


  Good quality video services always require higher bandwidth. Hence, to
provide the video services e.g., multicast/broadcast services (MBS) and unicast
services along with the existing voice, internet, and other background traffic
services over the wireless cellular networks, it is required to efficiently
manage the wireless resources in order to reduce the overall forced call
termination probability, to maximize the overall service quality, and to
maximize the revenue. Fixed bandwidth allocation for the MBS sessions either
reduces the quality of the MBS videos and bandwidth utilization or increases
the overall forced call termination probability and of course the handover call
dropping probability as well. Scalable Video Coding (SVC) technique allows the
variable bit rate allocation for the video services. In this paper, we propose
a bandwidth allocation scheme that efficiently allocates bandwidth among the
MBS sessions and the non-MBS traffic calls (e.g., voice, unicast, internet, and
other background traffic). The proposed scheme reduces the bandwidth allocation
for the MBS sessions during the congested traffic condition only to accommodate
more calls in the system. Instead of allocating fixed bandwidths for the BMS
sessions and the non-MBS traffic, our scheme allocates variable bandwidths for
them. However, the minimum quality of the videos is guaranteed by allocating
minimum bandwidth for them. Using the mathematical and numerical analyses, we
show that the proposed scheme maximizes the bandwidth utilization and
significantly reduces the overall forced call termination probability as well
as the handover call dropping probability.


  In this paper, we have developed a general-purpose architecture, Vit-Gan,
capable of performing most of the image-to-image translation tasks from
semantic image segmentation to single image depth perception. This paper is a
follow-up paper, an extension of generator-based model [1] in which the
obtained results were very promising. This opened the possibility of further
improvements with adversarial architecture. We used a unique vision
transformers-based generator architecture and Conditional GANs(cGANs) with a
Markovian Discriminator (PatchGAN) (https://github.com/YigitGunduc/vit-gan). In
the present work, we use images as conditioning arguments. It is observed that
the obtained results are more realistic than the commonly used architectures.


  A large number of autonomous driving tasks need high-definition stereo
images, which requires a large amount of storage space. Efficiently executing
lossless compression has become a practical problem. Commonly, it is hard to
make accurate probability estimates for each pixel. To tackle this, we propose
L3C-Stereo, a multi-scale lossless compression model consisting of two main
modules: the warping module and the probability estimation module. The warping
module takes advantage of two view feature maps from the same domain to
generate a disparity map, which is used to reconstruct the right view so as to
improve the confidence of the probability estimate of the right view. The
probability estimation module provides pixel-wise logistic mixture
distributions for adaptive arithmetic coding. In the experiments, our method
outperforms the hand-crafted compression methods and the learning-based method
on all three datasets used. Then, we show that a better maximum disparity can
lead to a better compression effect. Furthermore, thanks to a compression
property of our model, it naturally generates a disparity map of an acceptable
quality for the subsequent stereo tasks.


  The hydrogen-based route could be a valuable way to produce steel considering
its low carbon dioxide emissions. In ULCOS, it is regarded as a long-term
option, largely dependent on the emergence of a hydrogen economy. To anticipate
its possible development, it was decided to check the feasibility of using 100%
H2 in a Direct Reduction shaft furnace and to determine the best operating
conditions, through appropriate experimental and modelling work. We developed
from scratch a new model, called REDUCTOR, for simulating this process and
predicting its performance. This sophisticated numerical model is based on the
mathematical description of the detailed physical, chemical and thermal
phenomena occurring. In particular, kinetics were derived from experi-ments.
The current version is suited to the reduction with pure hydrogen, but an
extension of the model to CO is planned so that it will also be adapted to the
simulation and optimisation of the current DR processes. First re-sults have
confirmed that the reduction with hydrogen is much faster than that with CO,
making it possible to design a hydrogen-operated shaft reactor quite smaller
than current MIDREX and HYL.


  We measure the intensity correlation function of two interfering spatially
displaced copies of a phase fluctuating Bose-Einstein Condensate (BEC). It is
shown that this corresponds to a measurement of the phase correlation
properties of the initial condensate. Analogous to the method used in the
stellar interferometer experiment of Hanbury Brown and Twiss, we use spatial
intensity correlations to determine the phase coherence lengths of elongated
BECs. We find good agreement with our prediction of the correlation function
and confirm the expected coherence length.


  We prove complete reducibility for an integrable module for an affine Lie
algebra where the canonical central element acts non-trivially. We further
prove that integrable modules does not exists for most of the super affine Lie
algebras where the center acts non-trivially.


  Quantum frequency combs from chip-scale integrated sources are promising
candidates for scalable and robust quantum information processing (QIP).
However, to use these quantum combs for frequency domain QIP, demonstration of
entanglement in the frequency basis, showing that the entangled photons are in
a coherent superposition of multiple frequency bins, is required. We present a
verification of qubit and qutrit frequency-bin entanglement using an on-chip
quantum frequency comb with 40 mode pairs, through a two-photon interference
measurement that is based on electro-optic phase modulation. Our demonstrations
provide an important contribution in establishing integrated optical
microresonators as a source for high-dimensional frequency-bin encoded quantum
computing, as well as dense quantum key distribution.


  The quality of electricity system modelling heavily depends on the input data
used. Although a lot of data is publicly available, it is often dispersed,
tedious to process and partly contains errors. We argue that a central
provision of input data for modelling has the character of a public good: it
reduces overall societal costs for quantitative energy research as redundant
work is avoided, and it improves transparency and reproducibility in
electricity system modelling. This paper describes the Open Power System Data
platform that aims at realising the efficiency and quality gains of centralised
data provision by collecting, checking, processing, aggregating, documenting
and publishing data required by most modellers. We conclude that the platform
can provide substantial benefits to energy system analysis by raising
efficiency of data pre-processing, providing a method for making data
pre-processing for energy system modelling traceable, flexible and reproducible
and improving the quality of original data published by data providers.


  An increasing number of publications present the joint application of Design
of Experiments (DOE) and machine learning (ML) as a methodology to collect and
analyze data on a specific industrial phenomenon. However, the literature shows
that the choice of the design for data collection and model for data analysis
is often not driven by statistical or algorithmic advantages, thus there is a
lack of studies which provide guidelines on what designs and ML models to
jointly use for data collection and analysis. This article discusses the choice
of design in relation to the ML model performances. A study is conducted that
considers 12 experimental designs, 7 families of predictive models, 7 test
functions that emulate physical processes, and 8 noise settings, both
homoscedastic and heteroscedastic. The results of the research can have an
immediate impact on the work of practitioners, providing guidelines for
practical applications of DOE and ML.


  The Rossby mode (r-mode) perturbation in pulsars as a steady gravitational
wave (GW) source has been explored. The effect of a rigid crust on viscous
damping and dissipation rate in the boundary layer between fluid core and crust
has been studied. The time evolution and intensity of the emitted GWs in terms
of the strain tensor amplitude have been estimated with the approximation of
slow rotation using equation of state derived from the APR and Skyrme effective
interactions with Brussels-Montreal parameter sets. The core of the neutron
star has been considered to be $\beta$-equilibrated nuclear matter containing
neutrons, protons, electrons and muons, surrounded by a solid crust.
Calculations have been made for critical frequencies, their time evolution and
rate of change of frequencies across a broad spectrum of pulsar masses.


  We perform numerical simulations for photoionization of the argon atom when
exposed to a combined field of an infrared laser (abbreviated IR) and its 13th
harmonic (H13) by solving the Time-Dependent Schr\"odinger Equation (TDSE)],
noting that the associated energy spectrum displays a harmonic peak dressed by
the IR and other peaks called side-bands SB+-n corresponds to the absorption
(+n) and the emission (-n) of the n-infrared photons above the ionization
threshold. In two-color H13+IR photoionization of argon, the analysis of the
angular distribution of the ejected electron in the continuum, and our
calculation approach is based on the method of projection of the electronic
wave function on the states of the continuum, the latter was found in using the
Runge-Kutta 4 method and the Schutting method. Our simulation results
demonstrate that either for the harmonic peak or the sideband, the shape of the
angular distribution exhibits a good agreement with the interpretation based on
the generalized Fano rule for the absorption and emission of photons.


  Power series distributions form a useful subclass of one-parameter discrete
exponential families suitable for modeling count data. A zero-inflated power
series distribution is a mixture of a power series distribution and a
degenerate distribution at zero, with a mixing probability $p$ for the
degenerate distribution. This distribution is useful for modeling count data
that may have extra zeros. One question is whether the mixture model can be
reduced to the power series portion, corresponding to $p=0$, or whether there
are so many zeros in the data that zero inflation relative to the pure power
series distribution must be included in the model i.e., $p\geq0$. The problem
is difficult partially because $p=0$ is a boundary point. Here, we present a
Bayesian test for this problem based on recognizing that the parameter space
can be expanded to allow $p$ to be negative. Negative values of $p$ are
inconsistent with the interpretation of $p$ as a mixing probability, however,
they index distributions that are physically and probabilistically meaningful.
We compare our Bayesian solution to two standard frequentist testing procedures
and find that using a posterior probability as a test statistic has slightly
higher power on the most important ranges of the sample size $n$ and parameter
values than the score test and likelihood ratio test in simulations. Our method
also performs well on three real data sets.


  Perturbations of Kerr spacetime are typically studied with the Teukolsky
formalism, in which a pair of invariant components of the perturbed Weyl tensor
are expressed in terms of separable modes that satisfy ordinary differential
equations. However, for certain applications it is desirable to construct the
full metric perturbation in the Lorenz gauge, in which the linearized Einstein
field equations take a manifestly hyperbolic form. Here we obtain a set of
Lorenz-gauge solutions to the vacuum field equations in terms of homogeneous
solutions to the spin-2, spin-1 and spin-0 Teukolsky equations; and completion
pieces that represent perturbations to the mass and angular momentum of the
spacetime. The solutions are valid in vacuum Petrov type-D spacetimes that
admit a conformal Killing-Yano tensor.


  A grand unified model based on SO(10) and supersymmetry is presented to
account for the masses and mixing of the neutrinos observed in experiments.


  We derive new cases of conjectures of Rubin and of Burns--Kurihara--Sano
concerning derivatives of Dirichlet $L$-series at $s = 0$ in $p$-elementary
extensions of number fields for arbitrary prime numbers $p$. In naturally
arising examples of such extensions one therefore obtains annihilators of class
groups from $S$-truncated Dirichlet $L$-series for `large-enough' sets of
places $S$.


  The main goal of this article is to study how an auxiliary information can be
used to improve the efficiency of two famous statistical tests: the $ Z$-test
and the chi-square test. Many definitions of auxiliary information can be found
in the statistical literature. In this article, the notion of auxiliary
information is discussed from a very general point of view and depends on the
relevant test. These two statistical tests are modified so that this
information is taken into account. It is shown in particular that the
efficiency of these new tests is improved in the sense of Pitman's ARE. Some
statistical examples illustrate the use of this method.


  We demonstrate that AA-stacked bilayer graphene (AA-BLG) encapsulated by
dielectric materials can possess an energy gap due to the induced mass term.
Using the four-band continuum model, we evaluate transmission and reflection
probabilities along with the respective conductance. Considering interlayer
mass-term difference opens a gap in the energy spectrum and also couples the
two Dirac cones. This cone coupling induces an inter-cone transport that is
asymmetric with respect to the normal incidence in the presence of asymmetric
mass-term. The energy spectrum of the gapped AA-BLG exhibits electron-hole
asymmetry that is reflected in the associated intra- and inter-cone channels.
We also find that even though Klein tunneling exists in gated and biased
AA-BLG, it is precluded by the interlayer mass-term difference and instead
Febry-P\'erot resonances appear.


  We study the supersymmetric GUT models where the supersymmetry and GUT gauge
symmetry can be broken by the discrete symmetry. First, with the ansatz that
there exist discrete symmetries in the branes' neighborhoods, we discuss the
general reflection $Z_2$ symmetries and GUT breaking on $M^4\times M^1$ and
$M^4\times M^1\times M^1$. In those models, the extra dimensions can be large
and the KK states can be set arbitrarily heavy. Second, considering the extra
space manifold is the annulus $A^2$ or disc $D^2$, we can define any $Z_n$
symmetry and break any 6-dimensional N=2 supersymmetric SU(M) models down to
the 4-dimensional N=1 supersymmetric $SU(3)\times SU(2)\times U(1)^{M-4}$
models for the zero modes. In particular, there might exist the interesting
scenario on $M^4\times A^2$ where just a few KK states are light, while the
others are relatively heavy. Third, we discuss the complete global discrete
symmetries on $M^4\times T^2$ and study the GUT breaking.


  A density-functional formalism for superconductivity {\em and} magnetism is
presented. The resulting relations unify previously derived Kohn-Sham equations
for superconductors and for non-collinear magnetism. The formalism, which
discriminates Cooper pair singlets from triplets, is applied to two quantum
liquids coupled by tunneling through a barrier. An exact expression is derived,
relating the eigenstates and eigenvalues of the Kohn-Sham equations,
unperturbed by tunneling, on one side of the barrier to the proximity-induced
ordering potential on the other.


  This paper is a discussion of relations between some free-boundary problems
and infinite dimensional Lie groups; particularly a version of Nahm's equations
for the group of Hamiltonian diffeomorphisms in two dimensions.


  Any N=2 superconformal field theory (SCFT) in four dimensions has a sector of
operators related to a two-dimensional chiral algebra containing a Virasoro
sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose
chiral algebra is a Virasoro algebra. In this note, we consider the chiral
algebras associated with interacting N=2 SCFTs possessing an exactly marginal
deformation that can be interpreted as a gauge coupling (i.e., at special
points on the resulting conformal manifolds, free gauge fields appear that
decouple from isolated SCFT building blocks). At any point on these conformal
manifolds, we argue that the associated chiral algebras possess at least three
generators. In addition, we show that there are examples of SCFTs realizing
such a minimal chiral algebra: they are certain points on the conformal
manifold obtained by considering the low-energy limit of type IIB string theory
on the three complex-dimensional hypersurface singularity x_1^3+x_2^3+x_3^3+A
x_1x_2x_3+w^2=0. The associated chiral algebra is the A(6) theory of Feigin,
Feigin, and Tipunin. As byproducts of our work, we argue that (i) a collection
of isolated theories can be conformally gauged only if there is a SUSY moduli
space associated with the corresponding symmetry current moment maps in each
sector, and (ii) N=2 SCFTs with a>=c have hidden fermionic symmetries (in the
sense of fermionic chiral algebra generators).


  We introduce a mini-batch stochastic variance-reduced algorithm to solve
finite-sum scale invariant problems which cover several examples in machine
learning and statistics such as principal component analysis (PCA) and
estimation of mixture proportions. The algorithm is a stochastic generalization
of scale invariant power iteration, specializing to power iteration when
full-batch is used for the PCA problem. In convergence analysis, we show the
expectation of the optimality gap decreases at a linear rate under some
conditions on the step size, epoch length, batch size and initial iterate.
Numerical experiments on the non-negative factorization problem with the
Kullback-Leibler divergence using real and synthetic datasets demonstrate that
the proposed stochastic approach not only converges faster than
state-of-the-art deterministic algorithms but also produces excellent quality
robust solutions.


  We develop stellar population models to predict the number of binaries with a
single luminous member is Gaia and Hipparcos. Our models yield dozens of
detections of black hole - luminous companion binaries (BHLC) and hundreds to
thousands of neutron star - luminous companion binaries (NSLC) with Gaia.
Interestingly, our models also yield a single detection of BHLC binary with
Hipparcos, and a few NSLC binaries. We also show how the statistical
distribution of detected binaries with a single luminous companion can be used
to constrain the formation process of neutron stars and black holes.


  The heavy quark propagation behavior inside the quark-gluon plasma (QGP), is
usually described in terms of the Boltzmann dynamics, which can be reduced to
the Langevin approach by assuming a small momentum transfer for the scattering
processes between heavy quarks and the QGP constituents. In this work, the
temperature and energy dependence of the transport coefficients are calculated
in the framework of both Boltzmann and Langevin dynamics. The derived transport
coefficients are found to be systematically larger in the Boltzmann approach as
compared with the Langevin, in particular in the high temperature and high
energy region. Within each of the two theoretical frameworks, we simulate the
charm quark production and the subsequent evolution processes in relativistic
heavy-ion collisions. We find that the total in-medium energy loss is larger
from the Langevin dynamics, resulting in a smaller (larger) $R_{\rm AA}$ at
high (low) $p_{\rm T}$, for both the charm quark and heavy-flavor mesons.
Meanwhile, the Boltzmann model is found to induce larger $v_{\rm 2}$, in
particular at moderate $p_{\rm T}$, as well as stronger broadening behavior for
the azimuthal distributions. By comparing the model calculations with available
experimental measurements for D-mesons, we find that the Langevin approach is
more favored by the $R_{\rm AA}$ data while the Boltzmann approach is more
favored favor by the $v_{\rm 2}$ data. A simultaneous description of both
observables appear challenging for both models.


  Gamma-spectrometric methods suitable for the characterization of highly
enriched uranium samples encountered in illicit trafficking of nuclear
materials are presented. In particular, procedures for determining the 234U,
235U, 238U, 232U and 236U contents and the age of highly enriched uranium are
described. Consequently, the total uranium content and isotopic composition can
be calculated. For determining the 238U and 232U contents a low background
chamber was used. In addition, age dating of uranium was also performed using
low-background spectrometry.


  We have developed and implemented a compact transparent nozzle for use in
laser vaporization sources. This nozzle eliminates the need for an ablation
aperture, allowing for a more intense molecular beam. We use this nozzle to
prepare a molecular beam of aluminum monohydride (AlH) suitable for ion trap
loading of AlH$^+$ via photoionization in ultra-high vacuum. We demonstrate
stable AlH production over hour time scales using a liquid ablation target. The
long-term stability, low heat load and fast ion production rate of this source
are well-suited to molecular ion experiments employing destructive state
readout schemes requiring frequent trap reloading.


  The signatures of the formation and evolution of a galaxy are imprinted in
its stars. Their velocities, ages, and chemical compositions present major
constraints on models of galaxy formation, and on various processes such as the
gas inflows and outflows, the accretion of cold gas, radial migration, and the
variability of star formation activity. Understanding the evolution of the
Milky Way requires large observational datasets of stars via which these
quantities can be determined accurately. This is the science driver of the
4MOST MIlky way Disc And BuLgE High-Resolution (4MIDABLE-HR) survey: to obtain
high-resolution spectra at $R \sim 20\,000$ and to provide detailed elemental
abundances for large samples of stars in the Galactic disc and bulge. High data
quality will allow us to provide accurate spectroscopic diagnostics of two
million stellar spectra: precise radial velocities; rotation; abundances of
many elements, including those that are currently only accessible in the
optical, such as Li, s-, and r-process; and multi-epoch spectra for a
sub-sample of stars. Synergies with complementary missions like Gaia and TESS
will provide masses, stellar ages and multiplicity, forming a multi-dimensional
dataset that will allow us to explore and constrain the origin and structure of
the Milky Way.


  Large language models (LLMs) showcase impressive reasoning capabilities when
coupled with Chain-of-Thought (CoT) prompting. However, the robustness of this
approach warrants further investigation. In this paper, we introduce a novel
scenario termed preemptive answers, where the LLM obtains an answer before
engaging in reasoning. This situation can arise inadvertently or induced by
malicious users by prompt injection attacks. Experiments reveal that preemptive
answers significantly impair the model's reasoning capability across various
CoT methods and a broad spectrum of datasets. To bolster the robustness of
reasoning, we propose two measures aimed at mitigating this issue to some
extent.


  A chart for the quantum mechanics of a particle of mass $m$ in a
one-dimensional potential well of width $w$ and depth $V_0$ is derived. The
chart is obtained by normalizing energy and potential through multiplication by
${8 m}{w^2} / h^2$, and gives directly the allowed couples (potential, energy),
providing insights on the relation between the parameters and the number of
allowed energy levels.


  Can we ask computers to recognize what we see from brain signals alone? Our
paper seeks to utilize the knowledge learnt in the visual domain by popular
pre-trained vision models and use it to teach a recurrent model being trained
on brain signals to learn a discriminative manifold of the human brain's
cognition of different visual object categories in response to perceived visual
cues. For this we make use of brain EEG signals triggered from visual stimuli
like images and leverage the natural synchronization between images and their
corresponding brain signals to learn a novel representation of the cognitive
feature space. The concept of knowledge distillation has been used here for
training the deep cognition model, CogniNet\footnote{The source code of the
proposed system is publicly available at
{https://www.github.com/53X/CogniNET}}, by employing a student-teacher learning
technique in order to bridge the process of inter-modal knowledge transfer. The
proposed novel architecture obtains state-of-the-art results, significantly
surpassing other existing models. The experiments performed by us also suggest
that if visual stimuli information like brain EEG signals can be gathered on a
large scale, then that would help to obtain a better understanding of the
largely unexplored domain of human brain cognition.


  Selective Rips complexes corresponding to a sequence of parameters are a
generalization of Vietoris-Rips complexes utilizing the idea of thin simplices.
We prove that if a metric space $Y$ is close (in Gromov-Hausdorff distance) to
a closed Riemannian manifold $X$, then selective Rips complexes of $Y$ for
certain parameters attain the homotopy type of $X$. This result is a
generalization of Latchev's reconstruction result from Vietoris-Rips complexes
to selective Rips complexes. In particular, we present a novel proof for the
Latschev's theorem as a special case. We also present a functorial setting,
which is new even in the case of Vietoris-Rips complexes.


  The muon intensity attenuation method to detect heterogeneities in large
matter volumes is analyzed. Approximate analytical expressions to estimate the
collection time and the signal to noise ratio, are proposed and validated by
Monte Carlo simulations. Important parameters, including point spread function
and coordinate reconstruction uncertainty are also estimated using Monte Carlo
simulations.


  Absolute confinement of its color charges is a natural property of gauge
theories such as quantum chromodynamics. On the one hand, it can be attributed
to the existence of color-magnetic monopoles, a topological feature of the
theory, but one can also maintain that all non-Abelian gauge theories confine.
It is illustrated how ``confinement'' works in the SU(2) sector of the Standard
Model, and why for example the electron and its neutrino can be viewed as
SU(2)-hadronic bound states rather than a gauge doublet.
  The mechanism called `Abelian projection' then puts the Abelian sector of any
gauge theory on a separate footing.


  Recent observations have shown that coronal shocks driven by coronal mass
ejections can develop and accelerate particles within several solar radii in
large solar energetic particle (SEP) events. Motivated by this, we present an
SEP acceleration study including the process that a fast shock propagates
through a streamer-like magnetic field with both closed and open field lines in
the low corona region. The acceleration of protons is modeled by numerically
solving the Parker transport equation with spatial diffusion both along and
across the magnetic field. We show that particles can be sufficiently
accelerated to up to several hundred MeV within 2-3 solar radii. When the shock
propagates through a streamer-like magnetic field, particles are more
efficiently accelerated compared to the case with a simple radial magnetic
field, mainly due to perpendicular shock geometry and the natural trapping
effect of closed magnetic fields. Our results suggest that the coronal magnetic
field configuration is an important factor for producing large SEP events. We
further show that the coronal magnetic field configuration strongly influences
the distribution of energetic particles, leading to different locations of
source regions along the shock front where most of high energy particles are
concentrated. This work may have strong implications to SEP observations. The
upcoming Parker Solar Probe will provide in situ observations for the
distribution of energetic particles in the coronal shock region, and test the
results of the study.


  In this paper we are dealing with quantitative Rellich inequalities on
Finsler-Hadamard manifolds where the remainder terms are expressed by means of
the flag curvature. By exploring various arguments from Finsler geometry and
PDEs on manifolds we show that more weighty curvature implies more powerful
improvements in Rellich inequalities. The sharpness of the involved constants
are also studied. Our results complement those of Yang, Su and Kong [Commun.
Contemp. Math., 2014].


  We implement a three-body potential to model associative bond swaps, and
release it as part of the HOOMD-blue software. The use of a three-body
potential to model swaps has been proven to be effective and has recently
provided useful insights into the mechanics and dynamics of adaptive network
materials such as vitrimers. It is elegant because it can be used in plain
molecular dynamics simulations without the need for topology-altering Monte
Carlo steps, and naturally represents typical physical features such as
slip-bond behavior. It is easily tunable with a single parameter to control the
average swap rate. Here, we show how associative bond swaps can be used to
speed up the equilibration of systems that self-assemble by avoiding traps and
pitfalls, corresponding to long-lived metastable configurations. Our results
demonstrate the possibilities of these swaps not only for modeling systems that
are associative by nature, but also for increasing simulation efficiency in
other systems that are modellable in HOOMD-blue.


  We have applied the recently developed theory of topological Uhlmann numbers
to a representative model of a topological insulator in two dimensions, the
Qi-Wu-Zhang model. We have found a stable symmetry-protected topological (SPT)
phase under external thermal fluctuations in two-dimensions. A complete phase
diagram for this model is computed as a function of temperature and coupling
constants in the original Hamiltonian. It shows the appearance of large stable
phases of matter with topological properties compatible with thermal
fluctuations or external noise and the existence of critical lines separating
abruptly trivial phases from topological phases. These novel critical
temperatures represent thermal topological phase transitions. The initial part
of the paper comprises a self-contained explanation of the Uhlmann geometric
phase needed to understand the topological properties that it may acquire when
applied to topological insulators and superconductors.


  Based on exact integration of the Schr\"odinger equation, we numerically
study microscopic contributions to the entropy production for the single
electron transistor, a paradigmatic model describing a single Fermi level
tunnel coupled to two baths of free fermions. To this end, we decompose the
entropy production into a sum of information theoretic terms and study them
across all relevant time scales, including the nonequilibrium steady state
regime and the final stage of global thermalization. We find that the entropy
production is dominated for most times by microscopic deviations from
thermality in the baths and the correlation between (but not inside) the baths.
Despite these microscopic deviations from thermality, the temperatures and
chemical potentials of the baths thermalize as expected, even though our model
is integrable. Importantly, this observation is confirmed for both initially
mixed and pure states. We further observe that the bath-bath correlations are
quite insensitive to the system-bath coupling strength contrary to intuition.
Finally, the system-bath correlation, small in an absolute sense, dominates in
a relative sense and displays pure quantum correlations for all studied
parameter regimes.


  The quantum approximate optimization algorithm (QAOA) is one of the most
promising candidates for achieving quantum advantage through quantum-enhanced
combinatorial optimization. Optimal QAOA parameter concentration effects for
special MaxCut problem instances have been observed, but a rigorous study of
the subject is still lacking. Due to clustering of optimal QAOA parameters for
MaxCut, successful parameter transferability between different MaxCut instances
can be explained and predicted based on local properties of the graphs,
including the type of subgraphs (lightcones) from which graphs are composed as
well as the overall degree of nodes in the graph (parity). In this work, we
apply five different graph embedding techniques to determine good donor
candidates for parameter transferability, including parameter transferability
between different classes of MaxCut instances. Using this technique, we
effectively reduce the number of iterations required for parameter
optimization, obtaining an approximate solution to the target problem with an
order of magnitude speedup. This procedure also effectively removes the problem
of encountering barren plateaus during the variational optimization of
parameters. Additionally, our findings demonstrate that the transferred
parameters maintain effectiveness when subjected to noise, supporting their use
in real-world quantum applications. This work presents a framework for
identifying classes of combinatorial optimization instances for which optimal
donor candidates can be predicted such that QAOA can be substantially
accelerated under both ideal and noisy conditions.


  An application security has two primary goals: first, it is intended to
prevent unauthorised personnel from accessing information at higher
classification than their authorisation. Second, it is intended to prevent
personnel from declassifying information. Using an object oriented approach to
implementing application security results not only with the problem of code
scattering and code tangling, but also results in weaker enforcement of
security. This weaker enforcement of security could be due to the inherent
design of the system or due to a programming error. Aspect Oriented Programming
(AOP) complements Object-Oriented Programming (OOP) by providing another way of
thinking about program structure. The key unit of modularity in OOP is the
class, whereas in AOP the unit of modularity is the aspect. The goal of the
paper is to present that Aspect Oriented Programming AspectJ integrated with
Spring AOP provides very powerful mechanisms for stronger enforcement of
security.Aspect-oriented programming (AOP) allows weaving a security aspect
into an application providing additional security functionality or introducing
completely new security mechanisms.Implementation of security with AOP is a
flexible method to develop separated, extensible and reusable pieces of code
called aspects.In this comparative study paper, we argue that Spring AOP
provides stronger enforcement of security than AspectJ.We have shown both
Spring AOP and AspectJ strive to provide a comprehensive AOP solutions and
complements each other.


  We present the first calculation of the electron-energy loss spectrum of
infinite one-dimensional undoped CuO_3 chains within a multi-band Hubbard
model. The results show good agreement with experimental spectra of Sr_2CuO_3.
The main feature in the spectra is found to be due to the formation of
Zhang-Rice singlet-like excitations. The q-dependence of these excitations is a
consequence of the inner structure of the Zhang-Rice singlet. This makes the
inclusion of the oxygen degrees of freedom essential for the description of the
relevant excitations. We observe that no enhanced intersite Coulomb repulsion
is necessary to explain the experimental data.


  Photon number resolving detectors play a central role in quantum optics. A
key challenge in resolving the number of absorbed photons in the microwave
frequency range is finding a suitable material that provides not only an
appropriate band structure for absorbing low-energy photons but also a means of
detecting a discrete photoelectron excitation. To this end, we propose to
measure the temperature gain after absorbing a photon using superconducting
cadmium arsenide (Cd3As2) with a topological semimetallic surface state as the
detector. The surface electrons absorb the incoming photons and then transfer
the excess energy via heat to the superconducting bulk's phonon modes. The
temperature gain can be determined by measuring the change in the zero-bias
bulk resistivity, which does not significantly affect the lattice dynamics.
Moreover, the obtained temperature gain scales discretely with the number of
absorbed photons, enabling a photon-number resolving function. Here, we will
calculate the temperature increase as a function of the number and frequency of
photons absorbed. We will also derive the timescale for the heat transfer
process from the surface electrons to the bulk phonons. We will specifically
show that the transfer processes are fast enough to ignore heat dissipation
loss.


  We construct a qubit algebra from field creation and annihilation operators
acting on a global vacuum state. Particles to be used as qubits are created
from the vacuum by a near-deterministic single particle source. Our formulation
makes the space-time dependence of the qubits explicit, preparing the way for
quantum computation within a field framework. The method can be generalized to
deal with interacting qubits whose wavepackets are not perfectly matched to
each other. We give an example of how to calculate the Heisenberg evolution of
a simple two-qubit circuit, taking expectation values in the field vacuum
state.


  We prove a general asymptotic decay lemma which is applicable in various
contexts. As an example, the general theorem is shown to give lower growth
estimates for entire and exterior solutions of the minimal surface equation.


  Once considered essential to the explanation of electromagnetic phenomena,
the ether was eventually discarded after the advent of special relativity. The
lack of empirical signature of realist interpretative schemes of quantum
mechanics, like Bohmian trajectories, has led some to conclude that, just like
the ether, they can be dispensed with, replaced by the corresponding emergence
of the concept of information. Although devices like Bohmian trajectories and
the ether do present important analogies, I argue that there is also a crucial
difference, related to distinct explanatory functions of quantum mechanics.


  In lattice gauge theory, there exist field transformations that map the
theory to the trivial one, where the basic field variables are completely
decoupled from one another. Such maps can be constructed systematically by
integrating certain flow equations in field space. The construction is worked
out in some detail and it is proposed to combine the Wilson flow (which
generates approximately trivializing maps for the Wilson gauge action) with the
HMC simulation algorithm in order to improve the efficiency of lattice QCD
simulations.


  The emission of electromagnetic waves from a source within or near a
non-trivial medium (with or without boundaries, crystalline or amorphous, with
inhomogeneities, absorption and so on) is sometimes studied using the
reciprocity principle. This is a variation of the method of Green's functions.
If one is only interested in the asymptotic radiation fields the generality of
these methods may actually be a shortcoming: obtaining expressions valid for
the uninteresting near fields is not just a wasted effort but may be
prohibitively difficult. In this work we obtain a modified form the reciprocity
principle which gives the asymptotic radiation field directly. The method may
be used to obtain the radiation from a prescribed source, and also to study
scattering problems. To illustrate the power of the method we study a few
pedagogical examples and then, as a more challenging application we tackle two
related problems. We calculate the specular reflection of x rays by a rough
surface and by a smoothly graded surface taking polarization effects into
account. In conventional treatments of reflection x rays are treated as scalar
waves, polarization effects are neglected. This is a good approximation at
grazing incidence but becomes increasingly questionable for soft x rays and UV
at higher incidence angles.
  PACs: 61.10.Dp, 61.10.Kw, 03.50.De


  In this paper we develop linear transfer Perron Frobenius operator-based
approach for optimal stabilization of stochastic nonlinear system. One of the
main highlight of the proposed transfer operator based approach is that both
the theory and computational framework developed for the optimal stabilization
of deterministic dynamical system in [1] carries over to the stochastic case
with little change. The optimal stabilization problem is formulated as an
infinite dimensional linear program. Set oriented numerical methods are
proposed for the finite dimensional approximation of the transfer operator and
the controller. Simulation results are presented to verify the developed
framework.


  Multi-Objective Optimization Problems (MOPs) have attracted growing attention
during the last decades. Multi-Objective Evolutionary Algorithms (MOEAs) have
been extensively used to address MOPs because are able to approximate a set of
non-dominated high-quality solutions. The Multi-Objective Quadratic Assignment
Problem (mQAP) is a MOP. The mQAP is a generalization of the classical QAP
which has been extensively studied, and used in several real-life applications.
The mQAP is defined as having as input several flows between the facilities
which generate multiple cost functions that must be optimized simultaneously.
In this study, we propose PasMoQAP, a parallel asynchronous memetic algorithm
to solve the Multi-Objective Quadratic Assignment Problem. PasMoQAP is based on
an island model that structures the population by creating sub-populations. The
memetic algorithm on each island individually evolve a reduced population of
solutions, and they asynchronously cooperate by sending selected solutions to
the neighboring islands. The experimental results show that our approach
significatively outperforms all the island-based variants of the
multi-objective evolutionary algorithm NSGA-II. We show that PasMoQAP is a
suitable alternative to solve the Multi-Objective Quadratic Assignment Problem.


  We consider a parabolic problem with Robin boundary condition which arises
when the edge of a micro-electro-mechanical-system (MEMS) device is connected
with a flexible nonideal support. Then via a rigorous analysis we investigate
the structure of the solution set of the corresponding steady-state problem. We
show that a critical value (the pull-in voltage) exists so that the system has
exactly two stationary solutions when the applied voltage is lower than this
critical value, one stationary solution for applying this critical voltage, and
no stationary solution above the critical voltage.


  Cyber-physical systems (CPS) incorporate the complex and large-scale
engineered systems behind critical infrastructure operations, such as water
distribution networks, energy delivery systems, healthcare services,
manufacturing systems, and transportation networks. Industrial CPS in
particular need to simultaneously satisfy requirements of available, secure,
safe and reliable system operation against diverse threats, in an adaptive and
sustainable way. These adverse events can be of accidental or malicious nature
and may include natural disasters, hardware or software faults, cyberattacks,
or even infrastructure design and implementation faults. They may drastically
affect the results of CPS algorithms and mechanisms, and subsequently the
operations of industrial control systems (ICS) deployed in those critical
infrastructures. Such a demanding combination of properties and threats calls
for resilience-enhancement methodologies and techniques, working in real-time
operation. However, the analysis of CPS resilience is a difficult task as it
involves evaluation of various interdependent layers with heterogeneous
computing equipment, physical components, network technologies, and data
analytics. In this paper, we apply the principles of chaos engineering (CE) to
industrial CPS, in order to demonstrate the benefits of such practices on
system resilience. The systemic uncertainty of adverse events can be tamed by
applying runtime CE-based analyses to CPS in production, in order to predict
environment changes and thus apply mitigation measures limiting the range and
severity of the event, and minimizing its blast radius.


  In the superconducting regime of FeTe$_{(1-x)}$Se$_x$, there exist two types
of vortices which are distinct by the presence or absence of zero energy states
in their core. To understand their origin, we examine the interplay of Zeeman
coupling and superconducting pairings in three-dimensional metals with band
inversion. Weak Zeeman fields are found to suppress the intra-orbital
spin-singlet pairing, known to localize the states at the ends of the vortices
on the surface. On the other hand, an orbital-triplet pairing is shown to be
stable against Zeeman interactions, but leads to delocalized zero-energy
Majorana modes which extend through the vortex. In contrast, the finite-energy
vortex modes remain localized at the vortex ends even when the pairing is of
orbital-triplet form. Phenomenologically, this manifests as an observed
disappearance of zero-bias peaks within the cores of topological vortices upon
increase of the applied magnetic field. The presence of magnetic impurities in
FeTe$_{(1-x)}$Se$_x$, which are attracted to the vortices, would lead to such
Zeeman-induced delocalization of Majorana modes in a fraction of vortices that
capture a large enough number of magnetic impurities. Our results provide an
explanation to the dichotomy between topological and non-topological vortices
recently observed in FeTe$_{(1-x)}$Se$_x$.


  The extension of the Wagner hierarchy to blind counter automata accepting
infinite words with a Muller acceptance condition is effective. We determine
precisely this hierarchy.


  In this paper second order elliptic boundary value problems on bounded
domains $\Omega\subset\dR^n$ with boundary conditions on $\partial\Omega$
depending nonlinearly on the spectral parameter are investigated in an operator
theoretic framework. For a general class of locally meromorphic functions in
the boundary condition a solution operator of the boundary value problem is
constructed with the help of a linearization procedure. In the special case of
rational Nevanlinna or Riesz-Herglotz functions on the boundary the solution
operator is obtained in an explicit form in the product Hilbert space
$L^2(\Omega)\oplus (L^2(\partial\Omega))^m$, which is a natural generalization
of known results on $\lambda$-linear elliptic boundary value problems and
$\lambda$-rational boundary value problems for ordinary second order
differential equations.


  The local Tamagawa number conjecure, first formulated by Fontaine and
Perrin-Riou, expresses the compatibility of the (global) Tamagawa number
conjecture on motivic $L$-functions with the functional equation. The local
conjecture was proven for Tate motives over finite unramified extensions
$K/\mathbb{Q}_p$ by Bloch and Kato. We use the theory of $(\phi,
\Gamma_K)$-modules and a reciprocity law due to Cherbonnier and Colmez to
provide a new proof in the case of unramified extensions, and to prove the
conjecture for the motive $\mathbb{Q}_p(2)$ over certain tamely ramified
extensions.


  This paper extends approach of our joint paper with K\"{a}hler and recent
paper of the author, published in 2021, on problems of the static Maxwell
system in three dimensional inhomogeneous media. Applied pseudoanalytic
function theory developed by Kravchenko et al. allows to characterize, in
particular, meridional and transverse fields in cylindrically layered media.
Geometric properties of the electric field gradient ($EFG$) tensor within a
wide range of meridional fields allows us to introduce the concept of
$\alpha$-meridional mappings of the first and second kind depending on the
values of a real parameter $\alpha$. In case $\alpha =1$ tools of the radially
holomorphic potential provide essentially new meridional models in the context
of generalized axially symmetric potential theory (GASPT). Integral
representations of Bessel functions of the first kind of integer order and the
reduced quaternionic argument are first established. In case $\alpha =0$
geometric properties of harmonic meridional mappings of the second kind are
described. Some open problems in three dimensional inhomogeneous anisotropic
media are discussed using a generalized Riemannian modification of the system
$(R)$.


  Motivated by the close correlation between transition temperature ($T_c$) and
the tetrahedral bond angle of the As-Fe-As layer observed in the iron-based
superconductors, we study the interplay between spin and orbital physics of an
isolated iron-arsenide tetrahedron embedded in a metallic environment. Whereas
the spin Kondo effect is suppressed to low temperatures by Hund's coupling, the
orbital degrees of freedom are expected to quantum mechanically quench at high
temperatures, giving rise to an overscreened, non-Fermi liquid ground-state.
Translated into a dense environment, this critical state may play an important
role in the superconductivity of these materials.


  We report the first mid-IR detection of highly disturbed ionized gas in the
ultraluminous infrared galaxy IRAS F00183-7111. The gas, traced by the 12.81um
[NeII] and 15.56um [NeIII] lines, spans a velocity range of-3500 to 3000 km/s
with respect to systemic velocity. Optical and near-IR spectroscopic studies
show no evidence for similarly high velocity gas components in forbidden lines
at shorter wavelengths. We interpret this as the result of strong extinction
(Av=10-50) on the high-velocity gas, which identifies the base of the outflow
traced in 5007A [OIII] as a plausible origin. Unusual excitation conditions are
implied by a comparison of the mid-infrared low-excitation neon line emission
and the PAH emission for a sample of 56 ULIRGs. For IRAS F00183, the neon/PAH
ratio is 8 times higher than the average ratio. Similar mid-infrared kinematic
and excitation characteristics are found for only 2 other ULIRGs in our sample:
IRAS 12127-1412NE and IRAS 13451+1232. Both sources have an elevated neon/PAH
ratio and exhibit pronounced blue wings in their 15.56um [NeIII] line profiles.
IRAS 13451 even shows a strongly blue shifted and broad 14.32um [NeV] line.
While for IRAS 13451 the observed [NeIII]/[NeII] and [NeV]/[NeII] line ratios
indicate exposure of the blue shifted gas to direct radiation from the AGN, for
IRAS F00183 and 12127 the neon line ratios are consistent with an origin in
fast shocks in a high-density environment, and with an evolutionary scenario in
which strongly blue shifted [Ne II] and [Ne III] emission trace the (partial)
disruption of the obscuring medium around a buried AGN. The detection of
strongly blue shifted [Ne V] emission in IRAS 13451 would then indicate this
process to be much further advanced in this ULIRG than in IRAS F00183 and
12127, where this line is undetected.


  Cassiopeia A the youngest supernova remnant known in the Milky Way is one of
the brightest radio sources in the sky and a unique laboratory for supernova
physics. Although its compact remnant was discovered in 1999 by the Chandra
X-Ray Observatory, nowadays it is widely accepted that a neutron star lies in
the center of this supernova remnant. In addition, new observations suggest
that such neutron star with a low magnetic field and evidence of a carbon
atmosphere could have suffered a hypercritical accretion phase seconds after
the explosion. Considering this hypercritical accretion episode, we compute the
neutrino cooling effect, the number of events and neutrino flavor ratios
expected on Hyper-Kamiokande Experiment. The neutrino cooling effect (the
emissivity and luminosity of neutrinos) is obtained through numerical
simulations performed in a customized version of the FLASH code. Based on these
simulations, we forecast that the number of events expected on the
Hyper-Kamiokande Experiment is around 3195. Similarly, we estimate the neutrino
flavor ratios to be detected considering the neutrino effective potential due
to the thermal and magnetized plasma and thanks to the envelope of the star. It
is worth noting that our estimates correspond to the only trustworthy method
for verifying the hypercritical phase and although this episode took place 330
years ago, at present supernova remnants with these similarities might occur
thus confirming our predictions for this phase.


  By comparison of the quenched and full formulations of compact QED with
Wilson fermions we single out the effects of dynamical fermions on the `chiral
transition line' within the confinement phase. It is shown that this line
cannot correspond to the chiral limit of the theory for all values of the gauge
coupling. This seems to imply the existence of tri-critical points in this
theory, the phase structure of which has a close similarity to QCD at finite
temperature.


  In this article we present a characterization of elliptic curves defined over
a finite field Fq which possess a rational subgroup of order three. There are
two posible cases depending on the rationality of the points in these groups.
We show that for finite fields Fq, q= -1 mod 3, all elliptic curves with a
point of order 3, they have another rational subgroup whose points are not
defined over the finite field. If q = 1 mod 3, this is no true; but there exits
a one to one correspondence between curves with points of order 3 and curves
with rational subgroups whose points are not rational.


  This paper presents a hydrodynamical view of the Aharonov-Bohm effect, using
Nelson's formulation of quantum mechanics. Our aim is to compare our results
with other systems and gain a better understanding of the mysteries behind this
effect, such as why the motion of a particle is affected in a region where
there is no magnetic field. Some theories suggest that this effect is due to
the non-local action of the magnetic field on the particle, or even the
physical significance of vector potentials over magnetic fields. Our main
purpose is to use Nelson's formulation to describe the effect and demonstrate
that it can be explained by the direct action of the current surrounding the
magnetic field region (i.e. a cylinder) on the particle outside of it. In this
context, magnetic fields and vector potentials serve as tools for finding other
fundamental quantities that arise from the interaction between two fields: the
quantum background fields described by Nelson's quantum theory. Finally, we
investigate the relationship between hidden variables and quantum fluctuations
and their role in this phenomenon.


  Precision medicine is an emerging scientific topic for disease treatment and
prevention that takes into account individual patient characteristics. It is an
important direction for clinical research, and many statistical methods have
been recently proposed. One of the primary goals of precision medicine is to
obtain an optimal individual treatment rule (ITR), which can help make
decisions on treatment selection according to each patient's specific
characteristics. Recently, outcome weighted learning (OWL) has been proposed to
estimate such an optimal ITR in a binary treatment setting by maximizing the
expected clinical outcome. However, for ordinal treatment settings, such as
individualized dose finding, it is unclear how to use OWL. In this paper, we
propose a new technique for estimating ITR with ordinal treatments. In
particular, we propose a data duplication technique with a piecewise convex
loss function. We establish Fisher consistency for the resulting estimated ITR
under certain conditions, and obtain the convergence and risk bound properties.
Simulated examples and two applications to datasets from an irritable bowel
problem and a type 2 diabetes mellitus observational study demonstrate the
highly competitive performance of the proposed method compared to existing
alternatives.


  As an interpretation of the 750 GeV diphoton excesses recently reported by
both ATLAS and CMS collaborations, we consider a simple extension of the
Standard Model with a Dirac fermion dark matter where a singlet complex scalar
field mediates between dark matter and SM particles via effective couplings to
SM gauge bosons and/or Higgs-portal. In this model, we can accommodate the
diphoton events through the direct and/or cascade decays of pseudo-scalar and
real scalar partners of the complex scalar field. We show that mono-jet
searches and gamma-ray observations are complementary in constraining the
region where the width of the diphoton resonance can be enhanced due to the
couplings of the resonance to dark matter and the correct relic density is
obtained. In the case of cascade decay of the resonance, the effective
couplings of singlet scalars can be smaller, but the model is still testable by
the future discrimination between single photon and photon-jet at the LHC as
well as the gamma-ray searches for the cascade annihilation of dark matter.


  In the present work, we consider a prototypical example of a PT-symmetric
Dirac model. We discuss the underlying linear limit of the model and identify
the threshold of the PT-phase transition in an analytical form. We then focus
on the examination of the nonlinear model. We consider the continuation in the
PT-symmetric model of the solutions of the corresponding Hamiltonian model and
find that the solutions can be continued robustly as stable ones all the way up
to the PT-transition threshold. In the latter, they degenerate into linear
waves. We also examine the dynamics of the model. Given the stability of the
waveforms in the PT-exact phase we consider them as initial conditions for
parameters outside of that phase. We find that both oscillatory dynamics and
exponential growth may arise, depending on the size of the corresponding
"quench". The former can be characterized by an interesting form of
bi-frequency solutions that have been predicted on the basis of the SU(1,1)
symmetry. Finally, we explore some special, analytically tractable, but not
PT-symmetric solutions in the massless limit of the model.


  Geological maps are an extremely valuable source of information for the Earth
sciences. They provide insights into mineral exploration, vulnerability to
natural hazards, and many other applications. These maps are created using
numerical or conceptual models that use geological observations to extrapolate
data. Geostatistical techniques have traditionally been used to generate
reliable predictions that take into account the spatial patterns inherent in
the data. However, as the number of auxiliary variables increases, these
methods become more labor-intensive. Additionally, traditional machine learning
methods often struggle with spatially correlated data and extracting valuable
non-linear information from geoscientific datasets. To address these
limitations, a new architecture called the Spatially Constrained Bayesian
Network (SCB-Net) has been developed. The SCB-Net aims to effectively exploit
the information from auxiliary variables while producing spatially constrained
predictions. It is made up of two parts, the first part focuses on learning
underlying patterns in the auxiliary variables while the second part integrates
ground-truth data and the learned embeddings from the first part. Moreover, to
assess model uncertainty, a technique called Monte Carlo dropout is used as a
Bayesian approximation. The SCB-Net has been applied to two selected areas in
northern Quebec, Canada, and has demonstrated its potential in generating
field-data-constrained lithological maps while allowing assessment of
prediction uncertainty for decision-making. This study highlights the promising
advancements of deep neural networks in geostatistics, particularly in handling
complex spatial feature learning tasks, leading to improved spatial information
techniques.


  We study the effects of the wavevector-dependent losses on polariton
condensates. We demonstrate that because of these losses, a single vortex
becomes a center of a convergent flow, which allows describing it by an
analogue Kerr black hole metric with a dynamically evolving origin. For a pair
of vortices, we find an analogue of the 3rd Kepler's law and estimate the
emission rate of the gravitational waves. We simulate an analogue of the
inspiral phase of a black hole merger. Our work therefore suggests that
polariton condensates with quantum vortices represent a setting with a fully
self-consistent dynamical metric for broad analogue studies.