  We study the resonances of Schr\"odinger operators on the infinite product
$X=\mathbb{R}^d\times \mathbb{S}^1$, where $d$ is odd, $\mathbb{S}^1$ is the
unit circle, and the potential $V\in L^\infty_c(X)$. This paper shows that at
high energy, resonances of the Schr\"odinger operator $-\Delta +V$ on
$X=\mathbb{R}^d\times \mathbb{S}^1$ which are near the continuous spectrum are
approximated by the resonances of $-\Delta +V_0$ on $X$, where the potential
$V_0$ given by averaging $V$ over the unit circle. These resonances are, in
turn, given in terms of the resonances of a Schr\"odinger operator on
$\mathbb{R}^d$ which lie in a bounded set. If the potential is smooth, we
obtain improved localization of the resonances, particularly in the case of
simple, rank one poles of the corresponding scattering resolvent on
$\mathbb{R}^d$. In that case, we obtain the leading order correction for the
location of the corresponding high energy resonances. In addition to direct
results about the location of resonances, we show that at high energies away
from the resonances, the resolvent of the model operator $-\Delta+V_0$ on $X$
approximates that of $-\Delta+V$ on $X$. If $d=1$, in certain cases this
implies the existence of an asymptotic expansion of solutions of the wave
equation. Again for the special case of $d=1$, we obtain a resonant rigidity
type result for the zero potential among all real-valued potentials.


  In this work, we present a conceptually simple yet powerful baseline for the
multimodal dialog task, an S3 model, that achieves near state-of-the-art
results on two compelling leaderboards: MMMU and AI Journey Contest 2023. The
system is based on a pre-trained large language model, pre-trained modality
encoders for image and audio, and a trainable modality projector. The proposed
effective data mixture for training such an architecture demonstrates that a
multimodal model based on a strong language model and trained on a small amount
of multimodal data can perform efficiently in the task of multimodal dialog.


  A search is presented for CPT-violating effects in the mixing of $B^0_s$
mesons using the D0 detector at the Fermilab Tevatron Collider. The
CPT-violating asymmetry in the decay $B^0_s \rightarrow \mu^{\pm} D_s^{\mp} X$
as a function of sidereal phase is measured. No evidence for CPT-violating
effects is observed and limits are placed on CPT- and Lorentz-invariance
violating coupling coefficients.


  This paper proposes a Mixed-Integer Linear Programming approach for the Soft
Graph Clustering Problem. This is the first method that simultaneously
allocates membership proportion for vertices that lie in multiple clusters, and
that enforces an equal balance of the cluster memberships. Compared to ([Palla
et al., 2005], [Derenyi et al., 2005], [Adamcsek et al., 2006]), the clusters
found in our method are not limited to k-clique neighbourhoods. Compared to
([Hope and Keller, 2013]), our method can produce non-trivial clusters even for
a connected unweighted graph.


  In this paper, we will generalize the definition of partially random or
complex reals, and then show the duality of random and complex, i.e., a
generalized version of Levin-Schnorr's theorem. We also study randomness from
the view point of arithmetic using the relativization to a complete
$\Pi^0_1$-class.


  The current understanding of aging phenomena is mainly confined to the study
of systems with short-ranged interactions. Little is known about the aging of
long-ranged systems. Here, the aging in the phase-ordering kinetics of the
two-dimensional Ising model with power-law long-range interactions is studied
via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin
autocorrelator is well described by simple aging for all interaction ranges
studied. The autocorrelation exponents are consistent with $\lambda=1.25$ in
the effectively short-range regime, while for stronger long-range interactions
the data are consistent with $\lambda=d/2=1$. For very long-ranged
interactions, strong finite-size effects are observed. We discuss whether such
finite-size effects could be misinterpreted phenomenologically as sub-aging.


  The condition for double bicrosssum to be a braided Lie bialgebra is given.
The result generalizes quantum double, bicrosssum, bicrosscosum, bisum. The
quantum double of braided Lie bialgebras is constructed. The relation between
double crosssum of Lie algebras and double crossproduct of Hopf algebras is
given.


  Routing in wireless mesh networks (WMNs) has been an active area of research
for the last several years. In this paper, we address the problem of packet
routing for efficient data forwarding in wireless mesh networks (WMNs) with the
help of smart ants acting as intelligent agents. The aim of this paper is to
study the use of such biologically inspired agents to effectively route the
packets in WMNs. In particular, we propose AntMesh, a distributed
interference-aware data forwarding algorithm which enables the use of smart
ants to probabilistically and concurrently perform the routing and data
forwarding in order to stochastically solve a dynamic network routing problem.
AntMesh belongs to the class of routing algorithms inspired by the behaviour of
real ants which are known to find a shortest path between their nest and a food
source. In addition, AntMesh has the capability to effectively utilize the
space/channel diversity typically common in multi radio WMNs and to discover
high throughput paths with less inter-flow and intra-flow interference while
conventional wireless network routing protocols fail to do so. We implement our
smart ant-based routing algorithm in ns-2 and carry out extensive evaluation.
We demonstrate the stability of AntMesh in terms of how quickly it adapts
itself to the changing dynamics or load on the network. We tune the parameters
of AntMesh algorithm to study the effect on its performance in terms of the
routing load and end-to-end delay and have tested its performance under various
network scenarios particularly fixed nodes mesh networks and also on mobile WMN
scenarios. The results obtained show AntMesh's advantages that make it a
valuable candidate to operate in mesh networks.


  We consider theoretically ultracold interacting bosonic atoms confined to
quasi-one-dimensional ladder structures formed by optical lattices and coupled
to the field of an optical cavity. The atoms can collect a spatial phase
imprint during a cavity-assisted tunneling along a rung via Raman transitions
employing a cavity mode and a transverse running wave pump beam. By adiabatic
elimination of the cavity field we obtain an effective Hamiltonian for the
bosonic atoms, with a self-consistency condition. Using the numerical density
matrix renormalization group method, we obtain a rich steady state diagram of
self-organized steady states. Transitions between superfluid to Mott-insulating
states occur, on top of which we can have Meissner, vortex liquid, and vortex
lattice phases. Also a state that explicitly breaks the symmetry between the
two legs of the ladder, namely the biased-ladder phase is dynamically
stabilized.


  We study universal solutions to reflection equations with a spectral
parameter, so-called K-operators, within a general framework of universal
K-matrices - an extended version of the approach introduced by Appel-Vlaar.
Here, the input data is a quasi-triangular Hopf algebra $H$, its comodule
algebra $B$ and a pair of consistent twists. In our setting, the universal
K-matrix is an element of $B\otimes H$ satisfying certain axioms, and we mostly
consider the case $H$ is the quantum loop algebra for $sl_2$, and $B={\cal
A}_q$ is the alternating central extension of the $q$-Onsager algebra.
Considering tensor products of evaluation representations of $H$ in
"non-semisimple" cases, the new set of axioms allows us to introduce and study
fused K-operators of spin-$j$; in particular, to prove that for all
$j\in\frac{1}{2}\mathbb{N}$ they satisfy the spectral-parameter dependent
reflection equation. We provide their explicit expression in terms of elements
of the algebra ${\cal A}_q$ for small values of spin-$j$. The precise relation
between the fused K-operators of spin-$j$ and evaluations of a universal
K-matrix for ${\cal A}_q$ is conjectured based on supporting evidences.
Independently, we study K-operator solutions of the twisted intertwining
relations associated with the comodule algebra ${\cal A}_q$, and expand them in
the Poincar\'e-Birkhoff-Witt basis. With a reasonably general ansatz, we found
a unique solution for first few values of $j$ which agrees with the fused
K-operators, as expected. We conjecture that in general such solutions are
uniquely determined and match with the expressions of the fused K-operators.


  Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$
compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We
investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as
a measure of the fluctuation properties of the eigenvalues in the strong
coupling and the Coulomb phase. In both phases we find agreement with the
Wigner surmise of the unitary ensemble of random-matrix theory indicating
quantum chaos. Combining this with previous results on QCD, we conjecture that
quite generally the non-linear couplings of quantum field theories lead to a
chaotic behavior of the eigenvalues of the Dirac operator.


  The metapopulation network model is effectively used to study the spatial
spread of epidemics with individuals mobility. Considering the time-varying
nature of individual activity and the preferences for attractive destinations
in population mobility, this paper develops a time-varying network model in
which activity of a population is correlated with its attractiveness. Based on
the model, the spreading processes of the SIR disease on different correlated
networks are studied, and global migration thresholds are derived. It is
observed that increasing the correlation between activity and attractiveness
results in a reduced outbreak threshold but suppresses the disease outbreak
size and introduces greater heterogeneity in the spatial distribution of
infected individuals. We also investigate the impact of non-pharmacological
interventions (self-isolation and self-protection) on the spread of epidemics
in different correlation networks. The results show that the simultaneous
implementation of these measures is more effective in negatively correlated
networks than in positively correlated or non-correlated networks, and the
prevalence is reduced significantly. In addition, both self-isolation and
self-protection strategies increase the migration threshold of the spreading
and thus slow the spread of the epidemic. However, the effectiveness of each
strategy in reducing the density of infected populations varies depending on
different correlated networks. Self-protection is more effective in positively
correlated networks, whereas self-isolation is more effective in negatively
correlated networks. These findings contribute to a better understanding of
epidemic spreading in large-scale time-varying metapopulation networks and
provide insights for epidemic prevention and control.


  Event-by-event fluctuations of the initial transverse density profile result
in a collective flow pattern which also fluctuates event by event. We propose a
number of new correlation observables to characterize these fluctuations and
discuss how they should be analyzed experimentally. We argue that most of these
quantities can be measured at RHIC and LHC.


  We propose a new method for labeling the eigenstates of qubit-cavity systems
based on the continuity of the qubit occupancy. The labeled eigenstates give a
rough estimation of the evolution of a quantum state under cavity driving. The
photon-number dependence of the resonant cavity frequency can be estimated from
the labeled eigenenergies, and resonances to higher excited qubit states are
visible in the dependence. Our proposed method can be applied to a broader
parameter region compared to an existing method. With the proposed method, we
investigate the offset charge dependence of the resonances to higher excited
states that can induce leakage effects from the computational basis. The
results imply that the leakage can occur with only around ten photons.


  Graph Convolutional Networks (GCNs) have emerged as the state-of-the-art
graph learning model. However, it can be notoriously challenging to inference
GCNs over large graph datasets, limiting their application to large real-world
graphs and hindering the exploration of deeper and more sophisticated GCN
graphs. This is because real-world graphs can be extremely large and sparse.
Furthermore, the node degree of GCNs tends to follow the power-law distribution
and therefore have highly irregular adjacency matrices, resulting in
prohibitive inefficiencies in both data processing and movement and thus
substantially limiting the achievable GCN acceleration efficiency. To this end,
this paper proposes a GCN algorithm and accelerator Co-Design framework dubbed
GCoD which can largely alleviate the aforementioned GCN irregularity and boost
GCNs' inference efficiency. Specifically, on the algorithm level, GCoD
integrates a split and conquer GCN training strategy that polarizes the graphs
to be either denser or sparser in local neighborhoods without compromising the
model accuracy, resulting in graph adjacency matrices that (mostly) have merely
two levels of workload and enjoys largely enhanced regularity and thus ease of
acceleration. On the hardware level, we further develop a dedicated two-pronged
accelerator with a separated engine to process each of the aforementioned
denser and sparser workloads, further boosting the overall utilization and
acceleration efficiency. Extensive experiments and ablation studies validate
that our GCoD consistently reduces the number of off-chip accesses, leading to
speedups of 15286x, 294x, 7.8x, and 2.5x as compared to CPUs, GPUs, and
prior-art GCN accelerators including HyGCN and AWB-GCN, respectively, while
maintaining or even improving the task accuracy. Codes are available at
https://github.com/RICE-EIC/GCoD.


  We discuss rigid compact complex manifolds of Kodaira dimension 1, arising as
product-quotient varieties. First, we show that there is no free rigid action
on the product of $(n-1)$ elliptic curves and a curve of genus at least two.
Then, we describe the occurring groups, study the quotients and prove that
there is always a suitable resolution of singularities preserving rigidity.
Finally, we give a complete classification of the cases arising for minimal
group orders.


  Large-scale continuous variable (CV) cluster state is necessary in quantum
information processing based on measurement-based quantum computing (MBQC).
Specially, generating large-scale CV cluster state multiplexed in time domain
is easier to implement and has strong scalability in experiment. Here
one-dimensional (1D) large-scale dual-rail CV cluster states multiplexed both
in time and frequency domains are parallelly generated, which can be further
extended to three-dimensional (3D) CV cluster state by combining two time-delay
NOPA systems with beamsplitters. It is shown that the number of parallel arrays
depends on the corresponding frequency comb lines and the partite number of
each array can be very large (million), and scale of the 3D cluster state can
be ultra-large. This scheme provides some special-structured CV cluster states,
which will be valuable for quantum computing of hybrid domains.


  To shed light on the early phase of a low-mass protostar formation process,
we conducted interferometric observations towards a protostar GF9-2 using the
CARMA and SMA. The observations have been carried out in the CO J=3-2 line and
in the continuum emission at the wavelengths of 3 mm, 1 mm and 850 micron. All
the continuum images detected a single point-like source with a radius of
250+/-80 AU at the center of the previously known ~3 Msun molecular cloud core.
A compact emission is detected towards the object at the Spitzer MIPS and IRAC
bands as well as the four bands at the WISE. Our spectroscopic imaging of the
CO line revealed that the continuum source is driving a 1000 AU scale molecular
outflow, including a pair of lobes where a collimated "higher" velocity red
lobe exists inside a poorly collimated "lower" velocity red lobe. These lobes
are rather young and the least powerful ones so far detected. A protostellar
mass of M~<0.06 Msun was estimated using an upper limit of the protostellar age
of (4+/-1)x10^3 yrs and an inferred non-spherical steady mass accretion rate of
~10^{-5} Msun/yr. Together with results from an SED analysis, we discuss that
the outflow system is driven by a protostar whose surface temperature
of~3,000K, and that the natal cloud core is being dispersed by the outflow.


  Ever since the COVID-19 pandemic started, all the governments have been
trying to limit its effects on their citizens and countries. This pandemic was
harsh on different levels for almost all populations worldwide and this is what
drove researchers and scientists to get involved and work on several kinds of
simulations to get a better insight into this virus and be able to stop it the
earliest possible. In this study, we simulate the spread of COVID-19 in Lebanon
using an Agent-Based Model where people are modeled as agents that have
specific characteristics and behaviors determined from statistical
distributions using Monte Carlo Algorithm. These agents can go into the world,
interact with each other, and thus, infect each other. This is how the virus
spreads. During the simulation, we can introduce different Non-Pharmaceutical
Interventions - or more commonly NPIs - that aim to limit the spread of the
virus (wearing a mask, closing locations, etc). Our Simulator was first
validated on concepts (e.g. Flattening the Curve and Second Wave scenario), and
then it was applied on the case of Lebanon. We studied the effect of opening
schools and universities on the pandemic situation in the country since the
Lebanese Ministry of Education is planning to do so progressively, starting
from 21 April 2021. Based on the results we obtained, we conclude that it would
be better to delay the school openings while the vaccination campaign is still
slow in the country.


  We combine high redshift Type Ia supernovae from the first 3 years of the
Supernova Legacy Survey (SNLS) with other supernova (SN) samples, primarily at
lower redshifts, to form a high-quality joint sample of 472 SNe (123 low-$z$,
93 SDSS, 242 SNLS, and 14 {\it Hubble Space Telescope}). SN data alone require
cosmic acceleration at >99.9% confidence, including systematic effects. For the
dark energy equation of state parameter (assumed constant out to at least
$z=1.4$) in a flat universe, we find $w = -0.91^{+0.16}_{-0.20}(\mathrm{stat})
^{+0.07}_{-0.14} (\mathrm{sys})$ from SNe only, consistent with a cosmological
constant. Our fits include a correction for the recently discovered
relationship between host-galaxy mass and SN absolute brightness. We pay
particular attention to systematic uncertainties, characterizing them using a
systematics covariance matrix that incorporates the redshift dependence of
these effects, as well as the shape-luminosity and color-luminosity
relationships. Unlike previous work, we include the effects of systematic terms
on the empirical light-curve models. The total systematic uncertainty is
dominated by calibration terms. We describe how the systematic uncertainties
can be reduced with soon to be available improved nearby and
intermediate-redshift samples, particularly those calibrated onto
USNO/SDSS-like systems.


  Recently, Neural networks have seen a huge surge in its adoption due to their
ability to provide high accuracy on various tasks. On the other hand, the
existence of adversarial examples have raised suspicions regarding the
generalization capabilities of neural networks. In this work, we focus on the
weight matrix learnt by the neural networks and hypothesize that ill
conditioned weight matrix is one of the contributing factors in neural
network's susceptibility towards adversarial examples. For ensuring that the
learnt weight matrix's condition number remains sufficiently low, we suggest
using orthogonal regularizer. We show that this indeed helps in increasing the
adversarial accuracy on MNIST and F-MNIST datasets.


  We explore the subtle relationships between partial separability and
entanglement of subsystems in multiqubit quantum states and give experimentally
accessible conditions that distinguish between various classes and levels of
partial separability in a hierarchical order. These conditions take the form of
bounds on the correlations of locally orthogonal observables. Violations of
such inequalities give strong sufficient criteria for various forms of partial
inseparability and multiqubit entanglement. The strength of these criteria is
illustrated by showing that they are stronger than several other well-known
entanglement criteria (the fidelity criterion, violation of Mermin-type
separability inequalities, the Laskowski-\.Zukowski criterion and the
D\"ur-Cirac criterion), and also by showing their great noise robustness for a
variety of multiqubit states, including N-qubit GHZ states and Dicke states.
Furthermore, for N greater than or equal to 3 they can detect bound entangled
states. For all these states, the required number of measurement settings for
implementation of the entanglement criteria is shown to be only N+1. If one
chooses the familiar Pauli matrices as single-qubit observables, the
inequalities take the form of bounds on the anti-diagonal matrix elements of a
state in terms of its diagonal matrix elements.


  The fundamental equation of the thermodynamic system gives the relation
between internal energy, entropy and volume of two adjacent equilibrium states.
Taking higher dimensional charged Gauss-Bonnet black hole in de Sitter space as
a thermodynamic system, the state parameters have to meet the fundamental
equation of thermodynamics. We introduce the effective thermodynamic quantities
to describe the black hole in de Sitter space. Considering that in the lukewarm
case the temperature of the black hole horizon is equal to that of the
cosmological horizon, the effective temperature of spacetime is the same, we
conjecture that the effective temperature has the same value. In this way, we
can obtain the entropy formula of spacetime by solving the differential
equation. We find that the total entropy contain an extra terms besides the sum
of the entropies of the two horizons. The corrected terms of the entropy is a
function of horizon radius ratio, and is independent of the charge of the
spacetime.


  The recently introduced complex active optical network (LANER) generalizes
the concept of laser system to a collection of links, building a bridge with
random-laser physics and quantum-graphs theory. So far, LANERs have been
studied with a linear approach. Here, we develop a nonlinear formalism in the
perspective of describing realistic experimental devices. The propagation along
active links is treated via suitable rate equations, which require the
inclusion of an auxiliary variable: the population inversion. Altogether, the
resulting mathematical model can be viewed as an abstract network, its nodes
corresponding to the (directed) fields in the physical links. The dynamical
equations differ from standard network models in that, they are a mixture of
differential delay (for the active links) and algebraic equations (for the
passive links). The stationary states of a generic setup with a single active
medium are thoroughly discussed, showing that the role of the passive
components can be combined into a single transfer function that takes into
account the corresponding resonances.


  3D titanium carbonitrides TiCxNy possess excellent physical, chemical, and
mechanical properties, attractive for various industrial applications. Most
recently, the uncommon nano-sized layers of 2D-like titanium carbonitrides were
fabricated from MAX phases. Herein, the structural, electronic properties and
stability of these new compounds as well as their hydroxylated derivatives -
so-called MXenes Ti3C2-xNx and Ti3C2-xNx(OH)2 are probed by means of SSC-DFTB
calculations. The genesis of the properties is discussed in the sequence:
binary MXenes Ti3C2 (Ti3N2) -> their hydroxylated forms Ti3C2(OH)2 (Ti3N2(OH)2)
-> pristine MXene Ti3C2-xNx -> hydroxylated Ti3C2-xNx(OH)2. Our results show
that the examined materials are metallic-like. The most favorable type of
OH-covering is presented by the occupation of the hollow sites between three
neighboring carbon (nitrogen) atoms. The formation of 2D MXene carbonitrides
with random distribution of C and N atoms was found to be thermodynamically
more favorable.


  We consider the signal reconstruction problem under the case of the signals
sampled in the multichannel way and with the presence of noise. Observing that
if the samples are inexact, the rigorous enforcement of multichannel
interpolation is inappropriate. Thus the reasonable smoothing and regularized
corrections are indispensable. In this paper, we propose several alternative
methods for the signal reconstruction from the noisy multichannel samples under
different smoothing and regularization principles. We compare these signal
reconstruction methods theoretically and experimentally in the various
situations. To demonstrate the effectiveness of the proposed methods, the
probability interpretation and the error analysis for these methods are
provided. Additionally, the numerical simulations as well as some guidelines to
use the methods are also presented.


  We present a model of NLP in which ontology and context are directly included
in a grammar. The model is based on the concept of {\em construction},
consisting of a set of features of form, a set of semantic and pragmatic
conditions describing its application context, and a description of its
meaning. In this model ontology is embedded into the grammar; e.g. the
hierarchy of {\it np} constructions is based on the corresponding ontology.
Ontology is also used in defining contextual parameters; e.g. $\left[
current\_question \ time(\_) \right] $.
  A parser based on this model allowed us to build a set of dialog
understanding systems that include an on-line calendar, a banking machine, and
an insurance quote system. The proposed approach is an alternative to the
standard "pipeline" design of morphology-syntax-semantics-pragmatics; the
account of meaning conforms to our intuitions about compositionality, but there
is no homomorphism from syntax to semantics.


  While Gaia has observed the phase space coordinates of over a billion stars
in the Galaxy, in the overwhelming majority of cases it has only obtained five
of the six coordinates, the missing dimension being the radial (line-of-sight)
velocity. Using a realistic mock dataset, we show that Bayesian neural networks
are highly capable of 'learning' these radial velocities as a function of the
other five coordinates, and thus filling in the gaps. For a given star, the
network outputs are not merely point predictions, but full posterior
distributions encompassing the intrinsic scatter of the stellar phase space
distribution, the observational uncertainties on the network inputs, and any
'epistemic' uncertainty stemming from our ignorance about the stellar phase
space distribution. Applying this technique to the real Gaia data, we generate
and publish a catalogue of posteriors (median width: 25 km/s) for the radial
velocities of 16 million Gaia DR2/EDR3 stars in the magnitude range 6<G<14.5.
Many of these gaps will be filled in very soon by Gaia DR3, which will serve to
test our blind predictions. Thus, the primary use of our published catalogue
will be to validate our method, justifying its future use in generating an
updated catalogue of posteriors for radial velocities missing from Gaia DR3.


  We propose a simplified mathematical construction of the quantum Fourier
transform which is suited for systems described by Ising-type Hamiltonians. By
contrast to the standard Cooley-Tuckey scheme, which prescribes sequences of
CPHASE gates, our implementation is based on one-qubit gates and a free
evolution process. We also show how to obtain a quadratic speed-up by applying
the conditional interactions simultaneously. Thus rather than O($N^2$) our
implementation time scales as O($N$). Finally, we show a realization of our
method with homogeneous microwave driven ion traps in a magnetic field with
gradient.


  We propose an original method for determining suitable refracting profiles
between two media to solve two related problems: to produce a given wave front
from a single point source after refraction at the refracting profile, and to
focus a given wave front in a fixed point. These profiles are obtained as
envelopes of specific families of Cartesian ovals. We study the singularities
of these profiles and give a method to construct them from the data of the
associated caustic.


  We prove several consistency results concerning the notion of
$\omega$-strongly measurable cardinal in HOD. In particular, we show that is it
consistent, relative to a large cardinal hypothesis weaker than $o(\kappa) =
\kappa$, that every successor of a regular cardinal is $\omega$-strongly
measurable in HOD.


  Methanol masers at 6.7~GHz are well-known signposts of high-mass star-forming
regions. [...] We aim to understand the origin of the ring-like structures
outlined by methanol maser emission in a number of sources. This emission could
be, a priori, spatially associated with an outflow and/or disc around a
high-mass protostar. [...] Using sensitive, three-epoch observations spanning
over eight years with the European VLBI Network, we have started the most
direct investigations of maser rings using very accurate proper motion
measurements with uncertainties below 1\,km~s$^{-1}$. We present full results
for the five targets of our sample, G23.207-00.377, G23.389+00.185,
G28.817+00.365, G31.047+00.356, and G31.581+00.077, where proper motions show
similar characteristics; maser cloudlets do not move inwards towards the centre
of the rings but rather outwards. We also include the most circular source,
G23.657-00.127, in the discussion as a reference. The magnitude of maser proper
motions ranges from a maximum of about 13\,km~s$^{-1}$ to 0.5~km~s$^{-1}$. In
two of the five sources with a high number of maser spots (>100), namely
G23.207-00.377 and G23.389+00.185, we show that the size of the best elliptical
model, fitted to the distribution of persistent masers, increases in time in a
manner similar to the case of G23.657-00.127. Moreover, we checked the
separations between the pairs of spots from distinct regions, and we were able
to assess that G28.817+00.365 and G31.047+00.356 can be interpreted as showing
expanding motions. We analysed the profiles of single maser cloudlets and
studied their variability. Contrary to single-dish studies, the interferometric
data indicate variability of the emission of single-masing cloudlets. In five
of the six targets expansion motions prevail. Only in the case of
G31.581+00.077 can a scenario of disc-like rotation not be excluded. [...]


  The paper considers the level of the extremely low-frequency magnetic field,
which is produced by laptop computers. The magnetic field, which is
characterized by extremely low frequencies up to 300 Hz is measured due to its
hazardous effects to the laptop user's health. The experiment consists of
testing 13 different laptop computers in normal operation conditions. The
measuring of the magnetic field is performed in the adjacent neighborhood of
the laptop computers. The measured data are presented and then classified. The
classification is performed by the K-Medians method in order to determine the
critical positions of the laptop. At the end, the measured magnetic field
values are compared with the critical values suggested by different safety
standards. It is shown that some of the laptop computers emit a very strong
magnetic field. Hence, they must be used with extreme caution.


  Altenbernd, Thomas and W\"ohrle have considered in [ATW02] acceptance of
languages of infinite two-dimensional words (infinite pictures) by finite
tiling systems, with the usual acceptance conditions, such as the B\"uchi and
Muller ones, firstly used for infinite words. Many classical decision problems
are studied in formal language theory and in automata theory and arise now
naturally about recognizable languages of infinite pictures. We first review in
this paper some recent results of [Fin09b] where we gave the exact degree of
numerous undecidable problems for B\"uchi-recognizable languages of infinite
pictures, which are actually located at the first or at the second level of the
analytical hierarchy, and "highly undecidable". Then we prove here some more
(high) undecidability results. We first show that it is $\Pi_2^1$-complete to
determine whether a given B\"uchi-recognizable languages of infinite pictures
is unambiguous. Then we investigate cardinality problems. Using recent results
of [FL09], we prove that it is $D_2(\Sigma_1^1)$-complete to determine whether
a given B\"uchi-recognizable language of infinite pictures is countably
infinite, and that it is $\Sigma_1^1$-complete to determine whether a given
B\"uchi-recognizable language of infinite pictures is uncountable. Next we
consider complements of recognizable languages of infinite pictures. Using some
results of Set Theory, we show that the cardinality of the complement of a
B\"uchi-recognizable language of infinite pictures may depend on the model of
the axiomatic system ZFC. We prove that the problem to determine whether the
complement of a given B\"uchi-recognizable language of infinite pictures is
countable (respectively, uncountable) is in the class $\Sigma_3^1 \setminus
(\Pi_2^1 \cup \Sigma_2^1)$ (respectively, in the class $\Pi_3^1 \setminus
(\Pi_2^1 \cup \Sigma_2^1)$).


  Energetic correlations due to polymeric constraints and the locality of
interactions, in conjunction with the apriori specification of the existence of
a particularly low energy state, provides a method of introducing the aspect of
minimal frustration to the energy landscapes of random heteropolymers. The
resulting funnelled landscape exhibits both a phase transition from a molten
globule to a folded state, and the heteropolymeric glass transition in the
globular state. We model the folding transition in the self-averaging regime,
which together with a simple theory of collapse allows us to depict folding as
a double-well free energy surface in terms of suitable reaction coordinates.
Observed trends in barrier positions and heights with protein sequence length,
stability, and temperature are explained within the context of the model. We
also discuss the new physics which arises from the introduction of explicitly
cooperative many-body interactions, as might arise from side-chain packing and
non-additive hydrophobic forces. Denaturation curves similar to those seen in
simulations are predicted from the model.


  As the advances in quantum hardware bring us into the noisy
intermediate-scale quantum (NISQ) era, one possible task we can perform without
quantum error correction using NISQ machines is the variational quantum
eigensolver (VQE) due to its shallow depth. A specific problem that we can
tackle is the strongly interacting Fermi-Hubbard model, which is classically
intractable and has practical implications in areas like superconductivity. In
this Article, we outline the details about the gate sequence, the measurement
scheme and the relevant error mitigation techniques for the implementation of
the Hubbard VQE on a NISQ platform. We perform resource estimation for both
silicon spin qubits and superconducting qubits for a 50-qubit simulation, which
cannot be solved exactly via classical means, and find similar results. The
number of two-qubit gates required is on the order of 20000. Hence, to suppress
the mean circuit error count to a level such that we can obtain meaningful
results with the aid of error mitigation, we need to achieve a two-qubit gate
error rate of $\sim 10^{-4}$. When searching for the ground state, we need a
few days for one gradient-descent iteration, which is impractical. This can be
reduced to around $10$ minutes if we distribute our task among hundreds of
quantum processing units. Hence, implementing a 50-qubit Hubbard model VQE on a
NISQ machine can be on the brink of being feasible in near term, but further
optimisation of our simulation scheme, improvements in the gate fidelity,
improvements in the optimisation scheme and advances in the error mitigation
techniques are needed to overcome the remaining obstacles. The scalability of
the hardware platform is also essential to overcome the runtime issue via
parallelisation, which can be done on one single silicon multi-core processor
or across multiple superconducting processors.


  The rod and slit paradox, as first proposed by R. Shaw, is revisited. In this
paradox, a rod of rest length $l_0$ moves parallel to the horizontal x-axis.
Simultaneously, a thin sheet parallel to the horizontal xz-plane with a
rod-shaped slit of rest length $d < l_0$ moves along the vertical y-axis. The
rod passes through the slit due to relativistic effects. Earlier papers do not
link the thought experiment to the Silberstein/Thomas/Wigner-rotation
(STW-rotation), which is essential to its outcome. In this paper the role of
the STW-rotation is discussed, and additional clarifying figures are provided.
Some misleading aspects of earlier treatments are pointed out and corrected.


  This paper presents a novel efficient method for gridless line spectrum
estimation problem with single snapshot, namely the gradient descent least
squares (GDLS) method. Conventional single snapshot (a.k.a. single measure
vector or SMV) line spectrum estimation methods either rely on smoothing
techniques that sacrifice the array aperture, or adopt the sparsity constraint
and utilize compressed sensing (CS) method by defining prior grids and
resulting in the off-grid problem. Recently emerged atomic norm minimization
(ANM) methods achieved gridless SMV line spectrum estimation, but its
computational complexity is extremely high; thus it is practically infeasible
in real applications with large problem scales. Our proposed GDLS method
reformulates the line spectrum estimations problem into a least squares (LS)
estimation problem and solves the corresponding objective function via gradient
descent algorithm in an iterative fashion with efficiency. The convergence
guarantee, computational complexity, as well as performance analysis are
discussed in this paper. Numerical simulations and real data experiments show
that the proposed GDLS algorithm outperforms the state-of-the-art methods e.g.,
CS and ANM, in terms of estimation performances. It can completely avoid the
off-grid problem, and its computational complexity is significantly lower than
ANM. Our method has been tested in tomographic SAR (TomoSAR) imaging
applications via simulated and real experiment data. Results show great
potential of the proposed method in terms of better cloud point performance and
eliminating the gridding effect.


  The freestanding twisted bilayer graphene (TBG) is unstable, below a critical
twist angle {\theta}_c~3.7 degrees, against a moire (2 \times 1) buckling
distortion at T=0. Realistic simulations reveal the concurrent unexpected
collapse of the bending rigidity, an unrelated macroscopic mechanical
parameter. An analytical model connects bending and buckling anomalies at T=0,
but as temperature rises the former fades, while buckling persists further. The
(2 \times 1) electronic properties are also surprising. The magic twist angle
narrow bands, now eight in number, fail to show zone boundary splittings
despite the new periodicity. Symmetry shows how this is dictated by an
effective single valley physics. These structural, critical, and electronic
predictions promise to make the freestanding state of TBG especially
interesting.


  We use the Wilsonian functional Renormalisation Group (RG) to study quantum
corrections for the Higgs inflationary action including the effect of
gravitons, and analyse the leading-order quantum gravitational corrections to
the Higgs' quartic coupling, as well as its non-minimal coupling to gravity and
Newton's constant, at the inflationary regime and beyond. We explain how within
this framework the effect of Higgs and graviton loops can be sufficiently
suppressed during inflation, and we also place a bound on the corresponding
value of the infrared RG cut-off scale during inflation. Finally, we briefly
discuss the potential embedding of the model within the scenario of Asymptotic
Safety, while all main equations are explicitly presented.


  We present a novel scheme for the appearance of Stochastic Resonance when the
dynamics of a Brownian particle takes place in a confined medium. The presence
of uneven boundaries, giving rise to an entropic contribution to the potential,
may upon application of a periodic driving force result in an increase of the
spectral amplification at an optimum value of the ambient noise level. This
Entropic Stochastic Resonance (ESR), characteristic of small-scale systems, may
constitute a useful mechanism for the manipulation and control of
single-molecules and nano-devices.


  Between 1996 and 2003 we have obtained 226 high resolution spectra of 16
stars in the field of the young open cluster NGC 6913, to the aim of
constraining its main properties and study its internal kinematics. Twelve of
the program stars turned out to be members, one of them probably unbound. Nine
are binaries (one eclipsing and another double lined) and for seven of them the
observations allowed to derive the orbital elements. All but two of the nine
discovered binaries are cluster members. In spite of the young age (a few Myr),
the cluster already shows signs that could be interpreted as evidence of
dynamical relaxation and mass segregation. However, they may be also the result
of an unconventional formation scenario. The dynamical (virial) mass as
estimated from the radial velocity dispersion is larger than the cluster
luminous mass, which may be explained by a combination of the optically thick
interstellar cloud that occults part of the cluster, the unbound state or
undetected very wide binary orbit of some of the members that inflate the
velocity dispersion and a high inclination for the axis of a possible cluster
angular momentum. All discovered binaries are hard enough to survive average
close encounters within the cluster and do not yet show sign of relaxation of
the orbital elements to values typical of field binaries.


  Paper withdrawn; will be replaced by revised version containing application
to lattice models as well.
  We study hierarchical properties of Sturmian words. These properties are
similar to those of substitution dynamical systems. This approach allows one to
carry over to Sturmian dynamical systems methods developed in the context of
substitutions. For example, it allows for a very simple proof of a uniform
ergodic type theorem for additive functions taking values in a Banach space. We
then focus on establishing various versions of uniform subadditive ergodic type
theorems. The main result states that linear repetitivity of a Sturmian system
is equivalent to the validity of a uniform subadditive ergodic theorem which in
turn is equivalent to uniform positivity of certain weights. Thus, the results
of this paper completely cover the validity of uniform additive and subadditive
ergodic theorems on Sturmian systems.


  We study the problem of overcoming exponential sample complexity in
differential entropy estimation under Gaussian convolutions. Specifically, we
consider the estimation of the differential entropy $h(X+Z)$ via $n$
independently and identically distributed samples of $X$, where $X$ and $Z$ are
independent $D$-dimensional random variables with $X$ sub-Gaussian with bounded
second moment and $Z\sim\mathcal{N}(0,\sigma^2I_D)$. Under the absolute-error
loss, the above problem has a parametric estimation rate of
$\frac{c^D}{\sqrt{n}}$, which is exponential in data dimension $D$ and often
problematic for applications. We overcome this exponential sample complexity by
projecting $X$ to a low-dimensional space via principal component analysis
(PCA) before the entropy estimation, and show that the asymptotic error
overhead vanishes as the unexplained variance of the PCA vanishes. This implies
near-optimal performance for inherently low-dimensional structures embedded in
high-dimensional spaces, including hidden-layer outputs of deep neural networks
(DNN), which can be used to estimate mutual information (MI) in DNNs. We
provide numerical results verifying the performance of our PCA approach on
Gaussian and spiral data. We also apply our method to analysis of information
flow through neural network layers (c.f. information bottleneck), with results
measuring mutual information in a noisy fully connected network and a noisy
convolutional neural network (CNN) for MNIST classification.


  The cluster category is a triangulated category introduced for its
combinatorial similarities with cluster algebras. We prove that a cluster
algebra A of finite type can be realized as a Hall algebra, called the
exceptional Hall algebra, of the cluster category. This realization provides a
natural basis for A. We prove new results and formulate conjectures on `good
basis' properties, positivity, denominator theorems and toric degenerations.


  Subset sum is a very old and fundamental problem in theoretical computer
science. In this problem, $n$ items with weights $w_1, w_2, w_3, \ldots, w_n$
are given as input and the goal is to find out if there is a subset of them
whose weights sum up to a given value $t$. While the problem is NP-hard in
general, when the values are non-negative integer, subset sum can be solved in
pseudo-polynomial time $~\widetilde O(n+t)$.
  In this work, we consider the dynamic variant of subset sum. In this setting,
an upper bound $\tmax$ is provided in advance to the algorithm and in each
operation, either a new item is added to the problem or for a given integer
value $t \leq \tmax$, the algorithm is required to output whether there is a
subset of items whose sum of weights is equal to $t$. Unfortunately, none of
the existing subset sum algorithms is able to process these operations in truly
sublinear time\footnote{Truly sublinear means $n^{1-\Omega(1)}$.} in terms of
$\tmax$.
  Our main contribution is an algorithm whose amortized processing
time\footnote{Since the runtimes are amortized, we do not use separate terms
update time and query time for different operations and use processing time for
all types of operations.} for each operation is truly sublinear in $\tmax$ when
the number of operations is at least $\tmax^{2/3+\Omega(1)}$. We also show that
when both element addition and element removal are allowed, there is no
algorithm that can process each operation in time $\tmax^{1-\Omega(1)}$ on
average unless \textsf{SETH}\footnote{The \textit{strong exponential time
hypothesis} states that no algorithm can solve the satisfiability problem in
time $2^{n(1-\Omega(1))}$.} fails.


  We study two Heisenberg-Kitaev t-J-like models on a honeycomb lattice,
focusing on the zigzag magnetic phase of Na$_2$IrO$_3$, and investigate hole
motion by exact diagonalization and variational methods. The spectral functions
are quite distinct from those of cuprates and are dominated by large incoherent
spectral weight at high energy, almost independent of the microscopic
parameters --- a universal and generic feature for zigzag magnetic
correlations. We explain why quasiparticles at low energy are strongly
suppressed in the photoemission spectra and determine an analog of a pseudogap.
We point out that the qualitative features of the predominantly incoherent
spectra obtained within the two different models for the zigzag phase are
similar, and they have remarkable similarity to recently reported angular
resolved photoemission spectra for Na$_2$IrO$_3$.


  Aims: We search new T Tauri star (TTS) candidates with the mid-infrared (MIR)
part of the AKARI All-Sky Survey at 9 and 18 um wavelengths. Methods: We used
the point source catalogue (PSC), obtained by the Infrared Camera (IRC) on
board AKARI. We combined the 2MASS PSC and the 3rd version of the USNO CCD
Astrograph Catalogue (UCAC) with the AKARI IRC-PSC, and surveyed 517 known TTSs
over a 1800-square-degree part of the Taurus-Auriga region to find criteria to
extract TTSs. We considered asymptotic giant branch (AGB) stars, post-AGB
stars, Planetary Nebulae (PNe), and galaxies, which have similar MIR colours,
to separate TTSs from these sources. Results: Of the 517 known TTSs, we
detected 133 sources with AKARI. Based on the colour-colour and
colour-magnitude diagrams made from the AKARI, 2MASS, and UCAC surveys, we
propose the criteria to extract TTS candidates from the AKARI All-Sky data. On
the basis of our criteria, we selected 176/14725 AKARI sources as TTS
candidates which are located around the Taurus-Auriga region. Comparing these
sources with SIMBAD, there are 148 previously identified sources including 115
Young Stellar Objects (YSOs), and 28 unidentified sources. Conclusions: Based
on SIMBAD identifications, we take the TTS-identification probability using our
criteria to be ~75 %. We find 28 TTS candidates, of which we expect 21 to be
confirmed once follow-up observations can be obtained. Although the probability
of ~75 % is not so high, it is affected by the completeness of the SIMBAD
database, and we can search for TTSs over the whole sky, over all star forming
regions.


  The quantum eigenvalue problem arises in the study of the geometric measure
of the quantum entanglement. In this paper, we convert the quantum eigenvalue
problem to the Z-eigenvalue problem of a real symmetric tensor. In this way,
the theory and algorithms for Z-eigenvalues can be applied to the quantum
eigenvalue problem. In particular, this gives an upper bound for the number of
quantum eigenvalues. We show that the quantum eigenvalues appear in pairs,
i.e., if a real number $\lambda$ is a quantum eigenvalue of a square symmetric
tensor $\Psi$, then $-\lambda$ is also a quantum eigenvalue of $\Psi$. When
$\Psi$ is real, we show that the entanglement eigenvalue of $\Psi$ is always
greater than or equal to the Z-spectral radius of $\Psi$, and that in several
cases the equality holds. We also show that the ratio between the entanglement
eigenvalue and the Z-spectral radius of a real symmetric tensor is bounded
above in a real symmetric tensor space of fixed order and dimension.


  In this work, we propose, fabricate and characterize a full duplex
communication system using visible light on a single chip. Both the suspended
p-n junction InGaN/GaN multiple quantum well (MQW) devices and the suspended
waveguides are obtained on a GaN-on-silicon platform by wafer-level processing.
Two suspended p-n junction InGaN/GaN MQW devices that can both emit and detect
light simultaneously are connected using suspended waveguides to form an
in-plane visible light communication (VLC) system. The light that is emitted
from one suspended p-n junction InGaN/GaN MQW device can induce a current in
the device located at the other end of the waveguide via in-plane light
coupling, thus leading to full duplex communication using visible light. This
proof-of-concept in-plane VLC system paves the way towards the implementation
of a full duplex communications system operating at the same frequency using
visible light on a single chip.


  Using the definition of a Finsler--Laplacian given by the first author, we
show that two bi-Lipschitz Finsler metrics have a controlled spectrum. We
deduce from that several generalizations of Riemannian results. In particular,
we show that the spectrum on Finsler surfaces is controlled above by a constant
depending on the topology of the surface and on the quasireversibility constant
of the metric. In contrast to Riemannian geometry, we then give examples of
highly non-reversible metrics on surfaces with arbitrarily large first
eigenvalue.


  In this paper we study factorization formulae for the Lax matrices of the
classical Ruijsenaars-Schneider and Calogero-Moser models. We review the
already known results and discuss their possible origins. The first origin
comes from the IRF-Vertex relations and the properties of the intertwining
matrices. The second origin is based on the Schlesinger transformations
generated by modifications of underlying vector bundles. We show that both
approaches provide explicit formulae for $M$-matrices of the integrable systems
in terms of the intertwining matrices (and/or modification matrices). In the
end we discuss the Calogero-Moser models related to classical root systems. The
factorization formulae are proposed for a number of special cases.


  Two new nontrivial U(1) gauge symmetries are proposed, one based on the
particle content of the standard model and the other on that of its
supersymmetric generalization. Each is an unexpected first example of its kind.
A third new proposal is the successful derivation of a realistic Majorana
neutrino mass matrix, based on the underlying symmetry A_4 and its radiative
corrections.


  There are $n$ queues, each with a single server. Customers arrive in a
Poisson process at rate $\lambda n$, where $0<\lambda<1$. Upon arrival each
customer selects $d\geq2$ servers uniformly at random, and joins the queue at a
least-loaded server among those chosen. Service times are independent
exponentially distributed random variables with mean 1. We show that the system
is rapidly mixing, and then investigate the maximum length of a queue in the
equilibrium distribution. We prove that with probability tending to 1 as
$n\to\infty$ the maximum queue length takes at most two values, which are
$\ln\ln n/\ln d+O(1)$.


  Preferential attachment models of network growth are bivariate heavy tailed
models for in- and out-degree with limit measures which either concentrate on a
ray of positive slope from the origin or on all of the positive quadrant
depending on whether the model includes reciprocity or not. Concentration on
the ray is called full dependence. If there were a reliable way to distinguish
full dependence from not-full, we would have guidance about which model to
choose. This motivates investigating tests that distinguish between (i) full
dependence; (ii) strong dependence (support of the limit measure is a proper
subcone of the positive quadrant); (iii) weak dependence (limit measure
concentrates on positive quadrant). We give two test statistics, analyze their
asymptotically normal behavior under full and not-full dependence, and discuss
applicability using bootstrap methods applied to simulated and real data.


  We consider the problem of developing an efficient multi-threaded
implementation of the matrix-vector multiplication algorithm for sparse
matrices with structural symmetry. Matrices are stored using the compressed
sparse row-column format (CSRC), designed for profiting from the symmetric
non-zero pattern observed in global finite element matrices. Unlike classical
compressed storage formats, performing the sparse matrix-vector product using
the CSRC requires thread-safe access to the destination vector. To avoid race
conditions, we have implemented two partitioning strategies. In the first one,
each thread allocates an array for storing its contributions, which are later
combined in an accumulation step. We analyze how to perform this accumulation
in four different ways. The second strategy employs a coloring algorithm for
grouping rows that can be concurrently processed by threads. Our results
indicate that, although incurring an increase in the working set size, the
former approach leads to the best performance improvements for most matrices.


  We have investigated, in the framework of proximity effect theory, the
interface transparency T of superconducting/normal metal layered systems which
consist of Nb and high paramagnetic Pd deposited by dc magnetron sputtering.
The obtained T value is relatively high, as expected by theoretical arguments.
This leads to a large value of the ratio $d_{s}^{cr}/ \xi_{s}$ although Pd does
not exhibit any magnetic ordering.


  Within the Hamiltonian approach to Yang-Mills theory in Coulomb gauge the
ghost and gluon propagators are determined from a variational solution of the
Yang-Mills Schroedinger equation showing both gluon and heavy quark
confinement. The continuum results are in good agreement with lattice data. The
ghost form factor is identified as the dielectric function of the Yang--Mills
vacuum and the Gribov-Zwanziger confinement scenario is shown to imply the dual
Meissner effect. The topological susceptibility is calculated.


  Generally speaking, for a fractional quantum Hall (FQH) state, the electronic
occupation number for each Landau orbit could be obtained from numerical
methods such as exact diagonalization, density matrix renormalization group or
algebraic recursive schemes (Jack polynomial). In this work, we apply a
Metroplis Monte Carlo method to calculate the occupation numbers of several FQH
states in cylinder geometry. The convergent occupation numbers for more than 40
particles are used to verify the chiral bosonic edge theory and determine the
topological quantities via momentum polarization or dipole moment. The guiding
center spin, central charge and topological spin of different topological
sectors are consistent with theoretical values and other numerical studies.
Especially, we obtain the topological spin of $e/4$ quasihole in Moore-Read and
331 states. At last, we calculate the electron edge Green's functions and
analysis position dependence of the non-Fermi liquid behavior.


  We present an optical investigation of surface plasmon polaritons propagating
along nanoscale Au-wires, lithographically defined on GaAs substrates. A
two-axis confocal microscope was used to perform spatially and polarization
resolved measurements in order to confirm the guiding of surface plasmon
polaritons over lengths ranging from $5-20 \mu m$ along nanowires with a
lateral dimension of only $\approx 100 nm$. Finite difference time domain
simulations are used to corroborate our experimental observations and highlight
the potential to couple proximal quantum dot emitters to propagating plasmon
modes in such extreme sub-wavelength devices. Our findings are of strong
relevance for the development of semiconductor based integrated plasmonic and
active quantum plasmonic nanosystems that merge quantum emitters with nanoscale
plasmonic elements.


  For the Legendre-Stirling numbers of the second kind asymptotic formulae are
derived in terms of a local central limit theorem. Thereby, supplements of the
recently published asymptotic analysis of the Chebyshev-Stirling numbers are
established. Moreover, we provide results on the asymptotic normality and
unimodality for modified Legendre-Stirling numbers.


  We classify Jordan $G$-tori, where $G$ is any torsion-free abelian group.
Using the Zelmanov prime structure theorem, such a class divides into three
types, namely, {the Hermitian type, the Clifford type and the Albert type.} We
concretely describe Jordan $G$-tori of each type.


  We present a computational study of a simple finite-dimensional feedback
control algorithm for stabilizing solutions of infinite-dimensional dissipative
evolution equations such as reaction-diffusion systems, the Navier-Stokes
equations and the Kuramoto-Sivashinsky equation. This feedback control scheme
takes advantage of the fact that such systems possess finite number of
determining parameters or degrees of freedom, namely, finite number of
determining Fourier modes, determining nodes, and determining interpolants and
projections. In particular, the feedback control scheme uses finitely many of
such observables and controllers that are acting on the coarse spatial scales.
We demonstrate our numerical results for the stabilization of the unstable zero
solution of the 1D Chafee-Infante equation and 1D Kuramoto-Sivashinksky
equation. We give rigorous stability analysis for the feedback control
algorithm and derive sufficient conditions relating the control parameters and
model parameter values to attune to the control objective.


  We analyze the ergodic properties of quantum channels that are covariant with
respect to diagonal orthogonal transformations. We prove that the ergodic
behaviour of a channel in this class is essentially governed by a classical
stochastic matrix. This allows us to exploit tools from classical ergodic
theory to study quantum ergodicity of such channels. As an application of our
analysis, we study dual unitary brickwork circuits which have recently been
proposed as minimal models of quantum chaos in many-body systems. Upon imposing
a local diagonal orthogonal invariance symmetry on these circuits, the
long-term behaviour of spatio-temporal correlations between local observables
in such circuits is completely determined by the ergodic properties of a
channel that is covariant under diagonal orthogonal transformations. We utilize
this fact to show that such symmetric dual unitary circuits exhibit a rich
variety of ergodic behaviours, thus emphasizing their importance.


  The set of triangulations of a cyclic polytope possesses two a priori
different partial orders, known as the higher Stasheff-Tamari orders. The first
of these orders was introduced by Kapranov and Voevodsky, while the second
order was introduced by Edelman and Reiner, who also conjectured the two to
coincide in 1996. In this paper we prove their conjecture, thereby
substantially increasing our understanding of these orders. This result also
has ramifications in the representation theory of algebras, as established in
previous work of the author. Indeed, it means that the two corresponding orders
on tilting modules, cluster-tilting objects and their maximal chains are equal
for the higher Auslander algebras of type $A$.


  For describing the first-order isostructural valence phase transition in
mixed valence compounds we develop a new approach based on the lattice Anderson
model. We take into account the Coulomb interaction between localized f and
conduction band electrons and two mechanisms of electron-lattice coupling. One
is related to the volume dependence of the hybridization. The other is related
to local deformations produced by f- shell size fluctuations accompanying
valence fluctuations. The large f -state degeneracy allows us to use the 1/N
expansion method. Within the model we develop a mean-field theory for the
first-order valence phase transition in YbInCu_{4}. It is shown that the
Coulomb interaction enhances the exchange interaction between f and conduction
band electron spins and is the driving force of the phase transition. A
comparison between the theoretical calculations and experimental measurements
of the valence change, susceptibility, specific heat, entropy, elastic
constants and volume change in YbInCu_{4} and YbAgCu_{4} are presented, and a
good quantitative agreement is found. On the basis of the model we describe the
evolution from the first-order valence phase transition to the continuous
transition into the heavy-fermion ground state in the series of compounds
YbIn_{1-x}Ag_{x}Cu_{4}. The effect of pressure on physical properties of
YbInCu_{4} is studied and the H-T phase diagram is found.


  The molecular dynamics simulations were used to obtain the radius of gyration
of real ring polymer chains with different topological structures consisting of
360 monomers. We focus on the entropic force which is exerted by a dilute
solution of ring polymer chains of different topological structures with the
excluded volume interaction (EVI) in a good solvent on the confining parallel
walls of a slit geometry. We consider mixed boundary conditions of one
repulsive wall and the other one at the adsorption threshold. The obtained
molecular dynamics simulation results for a wide slit region demonstrate a
qualitative agreement with previous analytical results for ideal ring polymers.
These results could lead to interesting potential applications in materials
engineering and improve understanding of some biological processes suggested in
the paper. Additionally, they could be applied in micro- and
nano-electromechanical devices (MEMS and NEMS) in order to reduce the static
friction.


  In this paper we obtain some new refinements and reverses of Young's operator
inequality. Extensions for convex functions of operators are also provided.


  It is well-known that the Artin-Mazur dynamical zeta function of a hyperbolic
or quasi-hyperbolic toral automorphism is a rational function, which can be
calculated in terms of the eigenvalues of the corresponding integer matrix. We
give an elementary proof of this fact that extends to the case of general toral
endomorphisms without change. The result is a closed formula that can be
calculated by integer arithmetic only. We also address the functional equation
and the relation between the Artin-Mazur and Lefschetz zeta functions.


  At one loop, we provide an explicit formula for the ground state of the
one-soliton sector in the Sine-Gordon theory. The state is given in the basis
of eigenstates of the field operator, or equivalently as a Schrodinger wave
functional. The formula readily generalizes to other solitons in other models
and as an example we also provide the ground state of the kink in the
(1+1)-dimensional $\phi^4$ double well.


  We present a modified scenario of gamma-ray emission from pulsars within the
framework of polar cap models. Our model incorporates possible acceleration of
electron-positron pairs created in magnetospheres, and their subsequent
contribution to gamma-ray luminosity L_\gamma. It also reproduces the empirical
trend in L_\gamma for seven pulsars detected with Compton Gamma Ray Observatory
(CGRO) experiments. At the same time it avoids basic difficulties (Nel et al.
1996, Arons 1996) faced by theoretical models when confronted with
observational constraints.
  We show that the classical and millisecond pulsars form two distinct branches
in the L_gamma - L_sd diagram (where L_sd is the spin-down luminosity). In
particular, we explain why the millisecond pulsar J0437-4715 has not been
detected with any of the CGRO instruments despite its very high position in the
ranking list of spin-down fluxes (i.e. L_sd/D^2, where D is a distance). The
gamma-ray luminosity predicted for this particular object is about one order of
magnitude below the upper limit set by EGRET.


  The separation of micron-sized bacterial spores (Bacillus cereus) from a
steady flow of water through the use of ultrasonic standing waves is
demonstrated. An ultrasonic resonator with cross-section of 0.0254 m x 0.0254 m
has been designed with a flow inlet and outlet for a water stream that ensures
laminar flow conditions into and out of the resonator section of the flow tube.
A 0.01905-m diameter PZT-4, nominal 2-MHz transducer is used to generate
ultrasonic standing waves in the resonator. The acoustic resonator is 0.0356 m
from transducer face to the opposite reflector wall with the acoustic field in
a direction orthogonal to the water flow direction. At fixed frequency
excitation, spores are concentrated at the stable locations of the acoustic
radiation force and trapped in the resonator region. The effect of the
transducer voltage and frequency on the efficiency of spore capture in the
resonator has been investigated. Successful separation of B. cereus spores from
water with typical volume flow rates of 40-250 ml/min has been achieved with
15% efficiency in a single pass at 40 ml/min.


  In this paper, we unearth symmetries of different types of a nonlinear
non-polynomial oscillator. The symmetries which we report here are
adjoint-symmetries, contact symmetries and telescopic vector fields. We also
obtain Jacobi last multipliers and Darboux polynomials as a by-product of our
procedure. All the aforementioned quantities are derived from a Theorem proved
by Muriel and Romero. The procedure which we present here is applicable to a
class of nonlinear oscillator equations.


  The quantization of the gravitational Chern-Simons coefficient is
investigated in the framework of $ISO(2,1)$ gauge gravity. Some paradoxes
involved are cured. The resolution is largely based on the inequivalence of
$ISO(2,1)$ gauge gravity and the metric formulation. Both the Lorentzian scheme
and the Euclidean scheme lead to the coefficient quantization, which means that
the induced spin is not quite exotic in this context.


  In this paper, we consider the distributive queue-aware power and subband
allocation design for a delay-optimal OFDMA uplink system with one base
station, $K$ users and $N_F$ independent subbands. Each mobile has an uplink
queue with heterogeneous packet arrivals and delay requirements. We model the
problem as an infinite horizon average reward Markov Decision Problem (MDP)
where the control actions are functions of the instantaneous Channel State
Information (CSI) as well as the joint Queue State Information (QSI). To
address the distributive requirement and the issue of exponential memory
requirement and computational complexity, we approximate the subband allocation
Q-factor by the sum of the per-user subband allocation Q-factor and derive a
distributive online stochastic learning algorithm to estimate the per-user
Q-factor and the Lagrange multipliers (LM) simultaneously and determine the
control actions using an auction mechanism. We show that under the proposed
auction mechanism, the distributive online learning converges almost surely
(with probability 1). For illustration, we apply the proposed distributive
stochastic learning framework to an application example with exponential packet
size distribution. We show that the delay-optimal power control has the {\em
multi-level water-filling} structure where the CSI determines the instantaneous
power allocation and the QSI determines the water-level. The proposed algorithm
has linear signaling overhead and computational complexity $\mathcal O(KN)$,
which is desirable from an implementation perspective.


  Large language models (LLMs) have already revolutionized code generation,
after being pretrained on publicly available code data. However, while various
methods have been proposed to augment LLMs with retrieved knowledge and enhance
the quality of code generation, the performance of these retrieval-based
methods is limited by the strength of the retrievers used. In addition, while
LLMs show great emergent ability, they still struggle to produce the correct
code in one turn. To address these challenges, we propose a novel two-step
pipeline, called \autoknow, that leverages LLMs as both knowledge providers and
self-reflective programmers. Unlike retrieval-based methods, \autoknow~obtains
the knowledge from input prompts and generates intermediate code based on the
generated knowledge. After that, \autoknow~asks LLM to act as an expert
programmer to perform debugging for the generated code. This is achieved by
receiving the error message from the interpreter, without requiring special
test cases for correctness verification. We evaluate \autoknow~on three code
generation datasets, including DS-1000 for data science code, HumanEval for
software engineering code, and TransCoder for C++-to-Python translation. Our
empirical experiments show that \autoknow~outperforms strong baselines by a
significant margin on all datasets. We also conduct exhaustive analytical
experiments to validate the effectiveness of the two stages of \autoknow, and
find that both are superior to other prompting-based methods. Further
scalability analysis demonstrates that \autoknow~can be adapted to other more
advanced models, such as GPT-4, and bring consistent efficacy improvement.


  The doubly nonnegative (DNN) cone, being the set of all positive semidefinite
matrices whose elements are nonnegative, is a popular approximation of the
computationally intractable completely positive cone. The major difficulty for
implementing a Newton-type method to compute the projection of a given large
scale matrix onto the DNN cone lies in the possible failure of the constraint
nondegeneracy, a generalization of the linear independence constraint
qualification for nonlinear programming. Such a failure results in the
singularity of the Jacobian of the nonsmooth equation representing the
Karush-Kuhn-Tucker optimality condition that prevents the semismooth Newton-CG
method from solving it with a desirable convergence rate. In this paper, we
overcome the aforementioned difficulty by solving a sequence of better
conditioned nonsmooth equations generated by the augmented Lagrangian method
(ALM) instead of solving one above mentioned singular equation. By leveraging
on the metric subregularity of the normal cone associated with the positive
semidefinite cone, we derive sufficient conditions to ensure the dual quadratic
growth condition of the underlying problem, which further leads to the
asymptotically superlinear convergence of the proposed ALM. Numerical results
on difficult randomly generated instances and from the semidefinite programming
library are presented to demonstrate the efficiency of the algorithm for
computing the DNN projection to a very high accuracy.


  This note is an attempt to give an answer for the following old I.M.
Gelfand's question: why some important problems of integral geometry (e.g., the
Radon transform and others) are related to harmonic analysis on groups, but for
other quite similar problems such relations are not clear? In the note we
examine standard problems of integral geometry generating harmonic analysis
(the Plancherel theorem etc.) on pairs of commutative hypergroups that are in a
duality of Pontryagin's type. As a result new meaningful examples of
hypergroups are constructed.


  We present a study of the shape of the Large Magellanic Cloud disk. We use
the brightnesses of core helium-burning red clump stars identified in V-I,I
color-magnitude diagrams of 50 randomly selected LMC fields, observed with the
CTIO 0.9-m telescope, to measure relative distances to the fields. Random
photometric errors and errors in the calibration are controlled to <1%.
Following correction for reddening measured through the color of the red clump,
we solve for the inclination and position angle of the line of nodes of the
tilted plane of the LMC, finding i=35.8 +/- 2.4 degrees and theta=145 +/- 4
degrees. Our solution requires that we exclude 15 fields in the southwest of
the LMC which have red clump magnitudes ~0.1 magnitudes brighter than the
fitted plane. On the basis of these fields, we argue that the LMC disk is
warped and twisted, containing features that extend up to 2.5 kpc out of the
plane. We argue that alternative ways of producing red clump stars brighter
than expected, such as variations in age and metallicity of the stars, are
unlikely to explain our observations.


  We continue our study of the thermodynamic geometry of the spin one model
from paper I by probing the state space geometry of the Blume Emery Griffiths
(BEG) model, and its limiting case of the Blume Capel model, in their mean
field approximation. By accounting for the stochastic variables involved we
construct from the thermodynamic state space two complimentary two-dimensional
geometries with curvatures $R_m$ and $R_q$ which are shown to encode
correlations in the model's two order parameters, namely, the magnetization $m$
and the quadrupole moment $q$. The geometry is investigated in the zero as well
as the non zero magnetic field region. We find that the relevant scalar
curvatures diverge to negative infinity along the critical lines with the
correct scaling and amplitude. We then probe the geometry of phase coexistence
and find that the relevant curvatures predict the coexistence curve remarkably
well via their respective $R$-crossing diagrams. We also briefly comment on the
effectiveness of the geometric correlation length compared to the commonly used
Ornstein-Zernicke type correlation length vis-a-vis their scaling properties.


  Melting of N=20 shell and development of N = 16 and N = 34 shells for
neutron-rich nuclei have been studied extensively through inclusion of tensor
interaction in Skyrme Hartree Fock theory optimized to reproduce the splitting
neutron 1f states of 40, 48Ca and 56Ni nuclei. Evolution of gap generated by
the energy difference of single particle levels neutron 2s1/2 and neutron 1d3/2
state has been found to be responsible for the development of a shell closure
at N = 16. The splitting pattern of spin-orbit partners 2p shell model state in
Ca, Ti, Cr, Fe and Ni isotopes indicates formation of a new shell at N = 34
region.


  In this paper, we study closed embedded minimal hypersurfaces in a Riemannian
$(n+1)$-manifold ($2\le n\le 6$) that minimize area among such hypersurfaces.
We show they exist and arise either by minimization techniques or by min-max
methods: they have index at most $1$. We apply this to obtain a lower area
bound for such minimal surfaces in some hyperbolic $3$-manifolds.


  Problem of finding an optimal upper bound for {\chi} of (3 Times K1)-free
graphs is still open and pretty hard. It was proved by Choudum et al that upper
bound on the {\chi} of {3 Times K1, {2 Times K1 + (K2 UNION K1)}-free graphs is
2{\omega}. We improve this by proving that if G is {3 Times K1, {2 Times K1 +
(K2 UNION K1)}-free, then {\chi} less than or equal to 3{\omega} divided by 2
for {\omega} not equal to 5, and {\chi} less than or equal to 8 for {\omega} =
5 where {\omega} is the size of a maximum clique in G. We also give examples of
extremal graphs.


  The space-time of the Universe has been perturbed under a scalar field $\phi$
considering the minimum coupling between {\phi} and the background metric. The
solutions of Einstein field equations have been obtained under perturbed
geometry and the corresponding conservation equation shows the non-equilibrium
thermodynamic prescription of the cosmic fluid. Following the stability
criteria of the cosmic fluid along with the laws of thermodynamics, some
constraints have been imposed on the choice of $\phi$.


  I obtain the exact ground state of $N$-fermions in $D$-dimensions $(D \geq
2)$ in case the $N$ particles are interacting via long-ranged two-body and
three-body interactions and further they are also interacting via the harmonic
oscillator potential. I also obtain the $N$-fermion ground state in case the
oscillator potential is replaced by an $N$-body Coulomb-like interaction.


  Single photon emitters are a key component for enabling the practical use of
quantum key distribution protocols for secure communications. For long-haul
optical networks it is imperative to use photons at wavelengths that are
compatible with standard single mode fibers: 1.31 {\mu}m and 1.55 {\mu}m. We
demonstrate high purity single photon emission at 1.31 {\mu}m using
deterministically positioned InP photonic waveguide nanowires containing single
InAsP quantum dot-in-a-rod structures. At 4 K the detected count rate in fiber
was 1.9 Mcps under above-band pulsed laser excitation at 80 MHz corresponding
to a single photon collection efficiency at the first lens of 25%. At this
count rate, the probability of multiphoton emission is g(2)(0) = 0.021. We have
also evaluated the performance of the source as a function of temperature.
Multiphoton emission probability increases with temperature with values of
0.11, 0.34 and 0.57 at 77 K, 220 K and 300 K, respectively, which is attributed
to an overlap of temperature-broadened excitonic emission lines. These results
are a promising step towards scalably fabricating telecom single photon
emitters that operate under relaxed cooling requirements.


  We compute an asymptotic formula for the twisted moment of GL(3)xGL(2)
L-functions and their derivatives. As an application we prove that
symmetric-square lifts of GL(2) Maass forms are uniquely determined by the
central values of the derivatives of GL(3)xGL(2) L-functions.


  We present an investigation of the statistics of velocity gradient related
quantities, in particluar energy dissipation rate and enstrophy, along the
trajectories of fluid tracers and of heavy/light particles advected by a
homogeneous and isotropic turbulent flow. The Refined Similarity Hypothesis
(RSH) proposed by Kolmogorov and Oboukhov in 1962 is rephrased in the
Lagrangian context and then tested along the particle trajectories. The study
is performed on state-of-the-art numerical data resulting from numerical
simulations up to Re~400 with 2048^3 collocation points. When particles have
small inertia, we show that the Lagrangian formulation of the RSH is well
verified for time lags larger than the typical response time of the particle.
In contrast, in the large inertia limit when the particle response time
approaches the integral-time-scale of the flow, particles behave nearly
ballistic, and the Eulerian formulation of RSH holds in the inertial-range.


  So far, many of the deep learning approaches for voice conversion produce
good quality speech by using a large amount of training data. This paper
presents a Deep Bidirectional Long Short-Term Memory (DBLSTM) based voice
conversion framework that can work with a limited amount of training data. We
propose to implement a DBLSTM based average model that is trained with data
from many speakers. Then, we propose to perform adaptation with a limited
amount of target data. Last but not least, we propose an error reduction
network that can improve the voice conversion quality even further. The
proposed framework is motivated by three observations. Firstly, DBLSTM can
achieve a remarkable voice conversion by considering the long-term dependencies
of the speech utterance. Secondly, DBLSTM based average model can be easily
adapted with a small amount of data, to achieve a speech that sounds closer to
the target. Thirdly, an error reduction network can be trained with a small
amount of training data, and can improve the conversion quality effectively.
The experiments show that the proposed voice conversion framework is flexible
to work with limited training data and outperforms the traditional frameworks
in both objective and subjective evaluations.


  Even though plenty of symbiotic stars (SySts) have been found in the Galactic
field and nearby galaxies, not a single one has ever been confirmed in a
Galactic globular cluster (GC). We investigate the lack of such systems in GCs
for the first time by analysing 144 GC models evolved with the MOCCA code,
which have different initial properties and are roughly representative of the
Galactic GC population. We focus here on SySts formed through the
wind-accretion channel, which can be consistently modelled in binary population
synthesis codes. We found that the orbital periods of the majority of such
SySts are sufficiently long (${\gtrsim10^3}$ d) so that, for very dense GC
models, dynamical interactions play an important role in destroying their
progenitors before the present day (${\sim11-12}$ Gyr). In less dense GC
models, some SySts are still predicted to exist. However, these systems tend to
be located far from the central parts (${\gtrsim70}$ per cent are far beyond
the half-light radius) and are sufficiently rare (${\lesssim1}$ per GC per
Myr), which makes their identification rather difficult in observational
campaigns. We propose that future searches for SySts in GCs should be performed
in the outskirts of nearby low-density GCs with sufficiently long half-mass
relaxation times and relatively large Galactocentric distances. Finally, we
obtained spectra of the candidate proposed in $\omega$ Cen (SOPS IV e-94) and
showed that this object is most likely not a SySt.


  Structures in the solar corona are the main drivers of space weather
processes that might directly or indirectly affect the Earth. Thanks to the
most recent space-based solar observatories, with capabilities to acquire
high-resolution images continuously, the structures in the solar corona can be
monitored over the years with a time resolution of minutes. For this purpose,
we have developed a method for automatic segmentation of solar corona
structures observed in EUV spectrum that is based on a deep learning approach
utilizing Convolutional Neural Networks. The available input datasets have been
examined together with our own dataset based on the manual annotation of the
target structures. Indeed, the input dataset is the main limitation of the
developed model's performance. Our \textit{SCSS-Net} model provides results for
coronal holes and active regions that could be compared with other generally
used methods for automatic segmentation. Even more, it provides a universal
procedure to identify structures in the solar corona with the help of the
transfer learning technique. The outputs of the model can be then used for
further statistical studies of connections between solar activity and the
influence of space weather on Earth.


  Paper is devoted to the construction of averaging procedure of Hamiltonian
structures in discrete Whitham method. The procedure is analogous to
Dubrovin-Novikov procedure of averaging of local field-theoretical Poisson
brackets and gives the Poisson bracket of Hydrodynamic Type starting from
Poisson bracket for a discrete chain.


  The reassembling of a simple connected graph G = (V,E) is an abstraction of a
problem arising in earlier studies of network analysis. Its simplest
formulation is in two steps: (1) We cut every edge of G into two halves, thus
obtaining a collection of n=|V| one-vertex components. (2) We splice the two
halves of every edge together, not of all the edges at once, but in some
ordering \Theta of the edges that minimizes two measures that depend on the
edge-boundary degrees of assembled components.
  The edge-boundary degree of a component A (subset of V) is the number of
edges in G with one endpoint in A and one endpoint in V-A. We call the maximum
edge-boundary degree encountered during the reassembling process the
alpha-measure of the reassembling, and the sum of all edge-boundary degrees is
its beta-measure. The alpha-optimization (resp. beta-optimization) of the
reassembling of G is to determine an order \Theta for splicing the edges that
minimizes its alpha-measure (resp. beta-measure).
  There are different forms of reassembling. We consider only cases satisfying
the condition that if the an edge between disjoint components A and B is
spliced, then all the edges between A and B are spliced at the same time. In
this report, we examine the particular case of linear reassembling, which
requires that the next edge to be spliced must be adjacent to an already
spliced edge. We delay other forms of reassembling to follow-up reports.
  We prove that alpha-optimization of linear reassembling and minimum-cutwidth
linear arrangment (CutWidth) are polynomially reducible to each other, and that
beta-optimization of linear reassembling and minimum-cost linear arrangement
(MinArr) are polynomially reducible to each other.


  Although adequate models of human language for syntactic analysis and
semantic interpretation are of at least context-free complexity, for
applications such as speech processing in which speed is important finite-state
models are often preferred. These requirements may be reconciled by using the
more complex grammar to automatically derive a finite-state approximation which
can then be used as a filter to guide speech recognition or to reject many
hypotheses at an early stage of processing. A method is presented here for
calculating such finite-state approximations from context-free grammars. It is
essentially different from the algorithm introduced by Pereira and Wright
(1991; 1996), is faster in some cases, and has the advantage of being
open-ended and adaptable.


  We compare the perturbatively calculated QCD potential to that obtained from
lattice calculations in the theory without light quark flavours. We examine
E_tot(r) = 2 m_pole + V_QCD(r) by re-expressing it in the MSbar mass m =
m^MSbar(m^MSbar) and by choosing specific prescriptions for fixing the scale mu
(dependent on r and m). By adjusting m so as to maximise the range of
convergence, we show that perturbative and lattice calculations agree up to
3*r_0 ~ 7.5 GeV^-1 (r_0 is the Sommer scale) within the uncertainty of order
Lambda^3 r^2.


  We construct a 1-parameter family of $\mathrm{SL}_2(\mathbf{R})$
representations of the pretzel knot $P(-2,3,7)$. As a consequence, we conclude
that Dehn surgeries on this knot are left-orderable for all rational surgery
slopes less than 6. Furthermore, we discuss a family of knots and exhibit
similar orderability results for a few other examples.


  Solving the wave equation is one of the most (if not the most) fundamental
problems we face as we try to illuminate the Earth using recorded seismic data.
The Helmholtz equation provides wavefield solutions that are dimensionally
reduced, per frequency, compared to the time domain, which is useful for many
applications, like full waveform inversion (FWI). However, our ability to
attain such wavefield solutions depends often on the size of the model and the
complexity of the wave equation. Thus, we use here a recently introduced
framework based on neural networks to predict functional solutions through
setting the underlying physical equation as a loss function to optimize the
neural network parameters. For an input given by a location in the model space,
the network learns to predict the wavefield value at that location, and its
partial derivatives using a concept referred to as automatic differentiation,
to fit, in our case, a form of the Helmholtz equation. We specifically seek the
solution of the scattered wavefield considering a simple homogeneous background
model that allows for analytical solutions of the background wavefield.
Providing the neural network (NN) a reasonable number of random points from the
model space will ultimately train a fully connected deep NN to predict the
scattered wavefield function. The size of the network depends mainly on the
complexity of the desired wavefield, with such complexity increasing with
increasing frequency and increasing model complexity. However, smaller networks
can provide smoother wavefields that might be useful for inversion
applications. Preliminary tests on a two-box-shaped scatterer model with a
source in the middle, as well as, the Marmousi model with a source on the
surface demonstrate the potential of the NN for this application. Additional
tests on a 3D model demonstrate the potential versatility of the approach.


  Superconductivity in alkali-intercalated iron selenide, with T_c's of 30K and
above, may have a different origin than that of the other Fe-based
superconductors, since it appears that the Fermi surface does not have any
holelike sheets centered around the Gamma point. Here we investigate the
symmetry of the superconducting gap in the framework of spin-fluctuation
pairing calculations using density functional theory bands downfolded onto a
three-dimensional (3D), ten-orbital tight-binding model, treating the
interactions in the random-phase approximation (RPA). We find a leading
instability towards a state with d-wave symmetry, but show that the details of
the gap function depend sensitively on electronic structure. As required by
crystal symmetry, quasi-nodes on electron pockets always occur, but are shown
to be either horizontal, looplike or vertical depending on details. A variety
of other 3D gap structures, including bonding-antibonding s-symmetry states
which change sign between inner and outer electron pockets are found to be
subdominant. We then investigate the possibility that spin-orbit coupling
effects on the one-electron band structure, which lead to enhanced splitting of
the two M-centered electron pockets in the 2-Fe zone, may stabilize the
bonding-antibonding s_+/- wave states. Finally, we discuss our results in the
context of current phenomenological theories and experiments.


  In the resource theory of thermodynamics, the decrease of the free energy
based on von Neumann entropy is not a sufficient condition to determine free
evolution. Rather, a whole family of generalised free energies $F_{\alpha}$
must be monotonically decreasing. We study the resilience of this result to
relaxations of the framework. We use a toy collisional model, in which the
deviations from the ideal situation can be described as arising from
inhomogeneities of local fields or temperatures. For any small amount of
perturbation, we find that there exist initial states such that both
single-shot and averaged values of $F_{\alpha}$ do not decrease monotonically
for all $\alpha>0$. A geometric representation accounts for the observed
behavior in a graphic way.


  In this talk I review the recent progress on the numerical evaluation of the
Hadronic Light-by-Light contribution to the anomalous magnetic moment of the
muon and I discuss the role of experimental data on the accuracy of its
determination.


  Let $B^{H}$ be a $d$-dimensional fractional Brownian motion with Hurst index
$H\in(0,1)$, $f:[0,1]\longrightarrow\mathbb{R}^{d}$ a Borel function, and
$E\subset[0,1]$, $F\subset\mathbb{R}^{d}$ are given Borel sets. The focus of
this paper is on hitting probabilities of the fractional Brownian motion
$B^{H}$ with the deterministic drift $f$. It aims to highlight the role of the
regularity properties of the drift $f$ as well as that of the dimension of $E$
in determining the upper and lower bounds of $\mathbb{P}\{(B^H+f)(E)\cap F\neq
\emptyset \}$ for $F$ a subset of $\mathbb{R}^{d}$ and also for $F$ a
singleton.


  Physically Unclonable Function (PUF) circuits are finding widespread use due
to increasing adoption of IoT devices. However, the existing strong PUFs such
as Arbiter PUFs (APUF) and its compositions are susceptible to machine learning
(ML) attacks because the challenge-response pairs have a linear relationship.
In this paper, we present a Recurrent-Neural-Network PUF (RNN-PUF) which uses a
combination of feedback and XOR function to significantly improve resistance to
ML attack, without significant reduction in the reliability. ML attack is also
partly reduced by using a shared comparator with offset-cancellation to remove
bias and save power. From simulation results, we obtain ML attack accuracy of
62% for different ML algorithms, while reliability stays above 93%. This
represents a 33.5% improvement in our Figure-of-Merit. Power consumption is
estimated to be 12.3uW with energy/bit of ~ 0.16pJ.


  We investigate the gluon transverse momentum dependent correlators as Fourier
transform of matrix elements of nonlocal operator combinations. At the operator
level these correlators include both field strength operators and gauge links
bridging the nonlocality. In contrast to the collinear PDFs, the gauge links
are no longer unique for transverse momentum dependent PDFs (TMDs) and also
Wilson loops lead to nontrivial effects. We look at gluon TMDs for unpolarized,
vector and tensor polarized targets. In particular a single Wilson loop
operators become important when one considers the small-x limit of gluon TMDs.


  In this work, we study metrics which are both homogeneous and Ricci soliton.
If there exists a transitive solvable group of isometries on a Ricci soliton,
we show that it is isometric to a solvsoliton. Moreover, unless the manifold is
flat, it is necessarily simply-connected and diffeomorphic to $\mathbb R^n$.
  In the general case, we prove that homogeneous Ricci solitons must be
semi-algebraic Ricci solitons in the sense that they evolve under the Ricci
flow by dilation and pullback by automorphisms of the isometry group. In the
special case that there exists a transitive semi-simple group of isometries on
a Ricci soliton, we show that such a space is in fact Einstein. In the compact
case, we produce new proof that Ricci solitons are necessarily Einstein.
  Lastly, we characterize solvable Lie groups which admit Ricci soliton
metrics.


  We study the ratio of harmonic functions $u,v$, which have the same zero set
$Z$ in the unit ball $B\subset \mathbb{R}^n$. The ratio $f=u/v$ can be extended
to a real analytic nowhere vanishing function in $B$. We prove the Harnack
inequality and the gradient estimate for such ratios in any dimension: for a
given compact set $K\subset B$ we show that $\sup_K|f|\le C_1\inf_K|f|$ and
$\sup_K\left|\nabla f\right|\le C_2 \inf_K|f|$, where $C_1$ and $C_2$ depend on
$K$ and $Z$ only. In dimension two we specify the dependence of the constants
on $Z$ in these inequalities by showing that only the number of nodal domains
of $u$, i.e. the number of connected components of $B\setminus Z$, plays a
role.


  A simple breaking of the subnuclear democracy of the quarks leads to a mixing
between the second and the third family, in agrement with observation.
Introducing the mixing between the first and the second family, one finds an
interesting pattern of maximal CP--violation as well as a complete
determination of the elements of the CKM matrix and of the unitarity triangle.


  A theoretical description of scanning tunneling potentoimetry (STP)
measurement is presented to address the increasing need for a basis to
interpret experiments on macrscopic samples. Based on a heuristic understanding
of STP provided to facilitate theoretical understanding, the total tunneling
current related to the density matrix of the sample is derived within the
general framework of quantum transport. The measured potentiometric voltage is
determined implicitly as the voltage necessary to null the tunneling current.
Explicit expressions of measured voltages are presented under certain
assumptions, and limiting cases are discussed to connect to previous results.
The need to go forward and formulate the theory in terms of a local density
matrix is also discussed.


  Many scientific and technological problems are related to optimization. Among
them, black-box optimization in high-dimensional space is particularly
challenging. Recent neural network-based black-box optimization studies have
shown noteworthy achievements. However, their capability in high-dimensional
search space is still limited. This study proposes a black-box optimization
method based on the evolution strategy (ES) and the generative neural network
(GNN) model. We designed the algorithm so that the ES and the GNN model work
cooperatively. This hybrid model enables reliable training of surrogate
networks; it optimizes multi-objective, high-dimensional, and stochastic
black-box functions. Our method outperforms baseline optimization methods in
this experiment, including ES, and Bayesian optimization.