  We consider a simple network consisting of a source, a half-duplex DF relay
with a buffer, and a destination. We assume that the direct source-destination
link is not available and all links undergo fading. We propose two new
buffer-aided relaying schemes. In the first scheme, neither the source nor the
relay have CSIT, and consequently, both nodes are forced to transmit with fixed
rates. In contrast, in the second scheme, the source does not have CSIT and
transmits with fixed rate but the relay has CSIT and adapts its transmission
rate accordingly. In the absence of delay constraints, for both fixed rate and
mixed rate transmission, we derive the throughput-optimal buffer-aided relaying
protocols which select either the source or the relay for transmission based on
the instantaneous SNRs of the source-relay and the relay-destination links. In
addition, for the delay constrained case, we develop buffer-aided relaying
protocols that achieve a predefined average delay. Compared to conventional
relaying protocols, which select the transmitting node according to a
predefined schedule independent of the link instantaneous SNRs, the proposed
buffer-aided protocols with adaptive link selection achieve large performance
gains. In particular, for fixed rate transmission, we show that the proposed
protocol achieves a diversity gain of two as long as an average delay of more
than three time slots can be afforded. Furthermore, for mixed rate transmission
with an average delay of $E{T}$ time slots, a multiplexing gain of
$r=1-1/(2E{T})$ is achieved. Hence, for mixed rate transmission, for
sufficiently large average delays, buffer-aided half-duplex relaying with and
without adaptive link selection does not suffer from a multiplexing gain loss
compared to full-duplex relaying.


  In this paper, we prove via counterexamples that adding an advection term of
the form Shear flow (whose streamlines are parallel to the direction of
propagation) to a reaction-diffusion equation will be an enough heterogeneity
to spoil the increasing behavior of the KPP speed of propagation with respect
to diffusion. The non-monotonicity of the speed with respect to diffusion will
occur even when the reaction term and the diffusion matrices are considered
homogeneous (do not depend on space variables). For the sake of completeness,
we announce our results in a setting which allows domains with periodic
perforations that may or may not be equal to the whole space $\mathbb{R}^N.$


  We investigate the effect of helium enrichment on the evolution and
nucleosynthesis of low-mass asymptotic giant branch (AGB) stars of 1.7Msun and
2.36Msun with a metallicity of Z=0.0006 ([Fe/H] = -1.4). We calculate
evolutionary sequences with the primordial helium abundance (Y = 0.24) and with
helium-enriched compositions (Y = 0.30, 0.35, 0.40). For comparison we
calculate models of the same mass but at a lower metallicity Z=0.0003 ([Fe/H] =
-1.8) with Y=0.24. Post-processing nucleosynthesis calculations are performed
on each of the evolutionary sequences to determine the production of elements
from hydrogen through to bismuth. Elemental surface abundance predictions and
stellar yields are presented for each model. The models with enriched helium
have shorter main sequence and AGB lifetimes, and enter the AGB with a more
massive hydrogen exhausted core than the primordial helium model. The main
consequences are 1) low-mass AGB models with enhanced helium will evolve more
than twice as fast, giving them the chance to contribute sooner to the chemical
evolution of the forming globular clusters, and 2) the stellar yields will be
strongly reduced relative to their primordial helium counterparts. An increase
of Delta Y = 0.10 at a given mass decreases the yields of carbon by up to ~60%,
of fluorine by up to 80%, and decreases the yields of the s-process elements
barium and lanthanum by about 45%. While the yields of first s-process peak
elements strontium, yttrium and zirconium decrease by up to 50%, the yields of
rubidium either do not change or increase.


  We study the typical behavior of the least common multiple of the elements of
a random subset $A\subset \{1,\dots, n\}$. For example we prove that
$\text{lcm}\{a:\ a\in A\}=2^{n(1+o(1))}$ for almost all subsets
$A\subset\{1,\dots,n\}$.


  A Global Enhanced Vibrational Kinetic (GEVKM) model is presented for a new
High Current Negative Hydrogen Ion Source (HCNHIS) developed by Busek Co. Inc.
and Worcester Polytechnic Institute. The HCNHIS consists of a high-pressure
radio-frequency discharge (RFD) chamber where high-lying vibrational states of
the hydrogen molecules are produced, a bypass system, a nozzle, and a
low-pressure negative hydrogen ion production region where $\text{H}^-$ are
generated by the dissociative attachment of low energy electrons to
rovibrationally excited hydrogen molecules. The GEVKM is developed from moment
equations for multi-temperature chemically reacting plasmas derived from the
Wang Chang-Uhlenbeck equations for a cylindrical geometry of an inductively
coupled RFD chamber. The species included into the model are $\text{H}(n),
n=0-3, \text{H}_2(v), v=0-14, \text{H}^+, \text{H}_2^+, \text{H}_3^+,
\text{H}^-$, and $e$. The volume-averaged steady-state continuity equations
coupled with the electron energy equation, the total energy equation and heat
transfer to the chamber walls are solved simultaneously to obtain the
volume-averaged number densities of the plasma components, the electron,
heavy-particle and wall temperatures. The GEVKM is supplemented by a
comprehensive set of surface and volumetric chemical processes governing
vibrational and ionization kinetics of hydrogen plasmas. Analytic boundary
conditions developed for the flow in the bypass tubes and in the nozzle take
into account rarefaction effects and are validated by comparing pressures
predictions in the RFD chamber with the pressure measurements. The GEVKM is
verified and validated in the wide range of pressures and absorbed powers of
different plasma reactors and is used in a parametric investigation of the RFD
chamber of the HCNHIS with hydrogen inlet flow rates 5-1000 sccm and absorbed
powers 200-1000 W.


  The Multidimensional Assignment Problem (MAP or s-AP in the case of s
dimensions) is an extension of the well-known assignment problem. The most
studied case of MAP is 3-AP, though the problems with larger values of s have
also a number of applications. In this paper we propose a memetic algorithm for
MAP that is a combination of a genetic algorithm with a local search procedure.
The main contribution of the paper is an idea of dynamically adjusted
generation size, that yields an outstanding flexibility of the algorithm to
perform well for both small and large fixed running times. The results of
computational experiments for several instance families show that the proposed
algorithm produces solutions of very high quality in a reasonable time and
outperforms the state-of-the art 3-AP memetic algorithm.


  We consider the Bernstein--Sato polynomial of a polynomial $f \in R =
\mathbb{C}[x_{1}, x_{2}, x_{3}]$ that analytically locally everywhere admits a
positively weighted homogeneous defining equation. We construct, in the
analytic category, a complex of $\mathscr{D}_{X}[s]$-modules that can be used
to compute the $\mathscr{D}_{X}[s]$-dual of $\mathscr{D}_{X}[s] f^{s-1}$ as the
middle term of a short exact sequence where the outer terms are well
understood. This extends a result by Narv\'{a}ez Macarro where a freeness
assumption was required.
  We derive many results about the zeroes of the Bernstein--Sato polynomial.
First, we prove each nonvanishing degree of the zeroeth local cohomology of the
Milnor algebra $H_{\mathfrak{m}}^{0} (R / (\partial f))$ contributes a root to
the Bernstein--Sato polynomial, generalizing a result of Saito's (where the
argument cannot weaken homogeneity to positive homogeneity). Second, we prove
the zeroes of Bernstein--Sato polynomial admit a partial symmetry about $-1$,
extending a result of Narv\'{a}ez Macarro that again required freeness. We give
applications to very small roots, the twisted Logarithmic Comparison Theorem,
and more precise statements when $f$ is additionally assumed to be homogeneous.
  Finally, when $f$ defines a hyperplane arrangement in $\mathbb{C}^{3}$ we
give a complete formula for the zeroes of the Bernstein--Sato polynomial of
$f$. We show all zeroes except the candidate root $-2 + (2 / \text{deg}(f))$
are (easily) combinatorially given; we give many equivalent characterizations
of when the only non-combinatorial candidate root $-2 + (2/ \text{deg}(f))$ is
in fact a zero of the Bernstein--Sato polynomial. One equivalent condition is
the nonvanishing of $H_{\mathfrak{m}}^{0}( R / (\partial f))_{\text{deg}(f) -
1}$.


  We study thick subcategories defined by modules of complexity one in
$\underline{\md}R$, where $R$ is the exterior algebra in $n+1$ indeterminates.


  We consider the identifiability and stable numerical estimation of multiple
parameters in a Cahn-Hilliard model for phase separation. Spatially resolved
measurements of the phase fraction are assumed to be accessible, with which the
identifiability of single and multiple parameters up to certain scaling
invariances is established. A regularized equation error approach is proposed
for the stable numerical solution of the parameter identification problems, and
convergence of the regularized approximations is proven under reasonable
assumptions on the data noise. The viability of the theoretical results and the
proposed methods is demonstrated in numerical tests.


  If we pick $n$ random points uniformly in $[0,1]^d$ and connect each point to
its $k-$nearest neighbors, then it is well known that there exists a giant
connected component with high probability. We prove that in $[0,1]^d$ it
suffices to connect every point to $ c_{d,1} \log{\log{n}}$ points chosen
randomly among its $ c_{d,2} \log{n}-$nearest neighbors to ensure a giant
component of size $n - o(n)$ with high probability. This construction yields a
much sparser random graph with $\sim n \log\log{n}$ instead of $\sim n \log{n}$
edges that has comparable connectivity properties. This result has nontrivial
implications for problems in data science where an affinity matrix is
constructed: instead of picking the $k-$nearest neighbors, one can often pick
$k' \ll k$ random points out of the $k-$nearest neighbors without sacrificing
efficiency. This can massively simplify and accelerate computation, we
illustrate this with several numerical examples.


  This paper extends Bayesian mortality projection models for multiple
populations considering the stochastic structure and the effect of spatial
autocorrelation among the observations. We explain high levels of
overdispersion according to adjacent locations based on the conditional
autoregressive model. In an empirical study, we compare different hierarchical
projection models for the analysis of geographical diversity in mortality
between the Japanese counties in multiple years, according to age. By a Markov
chain Monte Carlo (MCMC) computation, results have demonstrated the flexibility
and predictive performance of our proposed model.


  We use resonant and non-resonant X-ray diffraction measurements in
combination with first-principles electronic structure calculations and Monte
Carlo simulations to study the relationship between crystal structure and
multiferroic orders in the orthorhombic perovskite manganites, o-$R$MnO$_3$
($R$ is a rare-earth cation or Y). In particular, we focus on how the internal
lattice parameters (Mn-O bond lengths and Mn-O-Mn bond angles) evolve under
chemical pressure and epitaxial strain, and the effect of these structural
variations on the microscopic exchange interactions and long-range magnetic
order. We show that chemical pressure and epitaxial strain are accommodated
differently by the crystal lattice of o-$R$MnO$_3$, which is key for
understanding the difference in magnetic properties between bulk samples and
strained films. Finally, we discuss the effects of these differences in the
magnetism on the electric polarization in o-$R$MnO$_3$.


  Linearity allows several versions of reality to simultaneously exist in the
state vector. But it implies that there is no interaction between versions, and
that there will never be perception of more than one version. It also implies,
in conjunction with group representation theory, that the particle-like
properties of mass, energy, momentum, spin and charge are attributes of the
state vectors. These results can be used to show there is no evidence for the
objective existence of particles. The properties of the wave function are
sufficient to explain all the particle-like properties of matter.
Representation theory is also extensively employed in the Standard Model, with
gauge fields transforming as representations of the internal symmetry group.
And when applied to the permutation group, it is essential for understanding
symmetric and antisymmetric states. In fact all of quantum mechanics is set up
exactly as if it were the representation of an underlying pre-representational
theory. A linear equation structure for the underlying theory is suggested, and
it is shown in outline how quantum field theory emerges as a representational
form of the pre-representational theory.


  Recent work of Scott and Wilmer and of Woodroofe extends the
Erd\H{o}s-Ko-Rado theorem from set systems to subspaces of k-forms in an
exterior algebra. We prove an extension of the Hilton-Milner theorem to the
exterior algebra setting, answering in a strong way a question asked by these
authors.


  We analyze the DAMA/Libra-phase2 modulation result using a basis of 16
effective operators describing the WIMP interaction with photons, gluons and
quarks up to mass dimension seven. For each operator we fix the effective
theory at the scale of 2 GeV and parametrize WIMP-quark interactions in terms
of two independent couplings for up-type and down-type quarks. We discuss the
connection with the non-relativistic limit of the effective theory in terms of
operators invariant by Galilean transformations, and the impact of the ensuing
momentum-dependent Wilson coefficients due to long-range interactions or light
meson poles. Most relativistic operators yield a good fit of the DAMA
modulation effect, although for parameters excluded by the constraints from
XENON1T and PICO60.


  We reconsider Hara's theorem in its relation to the well-known properties of
beta-decay. All assumptions necessary for the theorem to be true are explicitly
formulated. Further, we study the W-exchange contribution to weak radiative
decays and show that it does not violate Hara's theorem. However, this
contribution reveals the essential role of particle mixing in symmetry
considerations and some peculiar features of gauge-invariant amplitudes under
perturbative expansion. Together they explain an effect, which was treated as
contradicting Hara's theorem, without any violation. The properties of
W-exchange we describe here may have more general importance and should be
taken into account in further detailed calculations of weak processes.


  A ferromagnetic axion haloscope searches for Dark Matter in the form of
axions by exploiting their interaction with electronic spins. It is composed of
an axion-to-electromagnetic field transducer coupled to a sensitive rf
detector. The former is a photon-magnon hybrid system, and the latter is based
on a quantum-limited Josephson parametric amplifier. The hybrid system consists
of ten 2.1 mm diameter YIG spheres coupled to a single microwave cavity mode by
means of a static magnetic field. Our setup is the most sensitive rf
spin-magnetometer ever realized. The minimum detectable field is
$5.5\times10^{-19}\,$T with 9 h integration time, corresponding to a limit on
the axion-electron coupling constant $g_{aee}\le1.7\times10^{-11}$ at 95% CL.
The scientific run of our haloscope resulted in the best limit on DM-axions to
electron coupling constant in a frequency span of about 120 MHz, corresponding
to the axion mass range $42.4$-$43.1\,\mu$eV. This is also the first apparatus
to perform an axion mass scanning by changing the static magnetic field.


  We investigate black hole thermodynamics involving a scalar hair which is
dual to a momentum relaxation of the dual field theory. This black hole
geometry is able to be classified by two parameters. One is a momentum
relaxation and the other is a mass density of another matter localized at the
center. Even though all parameters are continuous, there exists a specific
point where its thermodynamic interpretation is not continuously connected to
the one defined in the other parameter regime. The similar feature also appears
in a topological AdS black hole. In this work, we show why such an unusual
thermodynamic feature happens and provide a unified way to understand such an
exotic black hole thermodynamically in the entire parameter range.


  We consider scalar tensor theories in D-dimensional spacetime, D \ge 4. They
consist of metric and a non minimally coupled scalar field, with its non
minimal coupling characterised by a function. The probes couple minimally to
the metric only. We obtain vacuum solutions - both cosmological and static
spherically symmetric ones - and study their properties. We find that, as seen
by the probes, there is no singularity in the cosmological solutions for a
class of functions which obey certain constraints. It turns out that for the
same class of functions, there are static spherically symmetric solutions which
exhibit novel properties: {\em e.g.} near the ``horizon'', the gravitational
force as seen by the probe becomes repulsive.


  Active learning is proposed for selection of the next operating points in the
design of experiments, for identifying linear parameter-varying systems. We
extend existing approaches found in literature to multiple-input
multiple-output systems with a multivariate scheduling parameter. Our approach
is based on exploiting the probabilistic features of Gaussian process
regression to quantify the overall model uncertainty across locally identified
models. This results in a flexible framework which accommodates for various
techniques to be applied for estimation of local linear models and their
corresponding uncertainty. We perform active learning in application to the
identification of a diesel engine air-path model, and demonstrate that measures
of model uncertainty can be successfully reduced using the proposed framework.


  We introduce a notion of smooth fields of operators following the notion of
smooth fields of Hilbert spaces recently defined by L. Lempert and R.
Sz\H{o}oke arXiv:1004.4863(2) . Formally, if $\nabla$ is the connection of a
smooth field of Hilbert spaces we show that $\hat\nabla=[\nabla,\cdot]$ defines
a connection on a suitable space of fields of operators. In order to provide
examples we prove that, if $u$ is a suitable constant of motion of
$h(q,p)=\|q\|^2$ (i.e.\ $\{u,h\}=0$), then $\mathfrak{Op}(u)$ is a smooth field
of operators over the open interval $(0,\infty)$, where $\mathfrak{Op}$ denotes
the canonical quantization (Weyl calculus). Moreover, in such case we show that
we can compute derivatives using the formula
$\hat\nabla_{X_0}(\mathfrak{Op}(u))=\mathfrak{Op}(\tilde\nabla_{X_0}(u))$,
where $\tilde\nabla$ is a Poisson connection on the Poisson algebra of
constants of motion and $X_0=2\lambda\frac{\partial}{\partial \lambda}$. We
also introduce a notion of smooth field of $C^*$-algebras and we give an
example using Hilbert modules theory.


  According to the dynamical quasiparticle model (DQPM) - matched to reproduce
lattice QCD results in thermodynamic limit, - the constituents of the strongly
interacting quark-gluon plasma (sQGP) are massive and off-shell quasi-particles
(quarks and gluons) with broad spectral functions. In order to address the
electromagnetic radiation of the sQGP, we derive off-shell cross sections of
q+qbar->gamma*, q+qbar->gamma*+glue and q+glue->gamma*+q(qbar+glue->gamma*qbar)
reactions taking into account the effective propagators for quarks and gluons
from the DQPM. Dilepton production in In+In collisions at 158 AGeV is studied
by implementing these processes into the parton-hadron-string dynamics (PHSD)
transport approach. The microscopic PHSD transport approach describes the full
evolution of the heavy-ion collision: from the dynamics of quasi-particles in
the sQGP phase (when the local energy density is above ~1 GeV/fm^3) through
hadronization and to the following hadron interactions and off-shell
propagation after the hadronization. A comparison to the data of the NA60
Collaboration shows that the low mass dilepton spectra are well described by
including a collisional broadening of vector mesons, while the spectra in the
intermediate mass range are dominated by off-shell quark-antiquark
annihilation, quark Bremsstrahlung and gluon-Compton scattering in the
nonperturbative QGP. In particular, the observed softening of the mT spectra at
intermediate masses (1 GeV < M < 3 GeV) is approximately reproduced.


  In hydrodynamics, Taylor's frozen-in hypothesis connects the wavenumber
spectrum to the frequency spectrum of a time series measured in real space. In
this paper, we generalize Taylor's hypothesis to magnetohydrodynamic
turbulence. We analytically derive one-point two-time correlation functions for
Els\"{a}sser variables whose Fourier transform yields the corresponding
frequency spectra, $ E^\pm(f) $. We show that $ E^\pm(f) \propto |{\bf U}_0 \mp
{\bf B}_0|^{2/3} $ in Kolmogorov-like model, and $ E^\pm(f) \propto (B_0 |{\bf
U}_0 \mp {\bf B}_0|)^{1/2} $ in Iroshnikov-Kraichnan model, where $ {\bf U}_0,
{\bf B}_0$ are the mean velocity and mean magnetic fields respectively.


  Radiative capture reaction rates for $^6$He, $^9$Be and $^{17}$Ne formation
at astrophysical conditions are studied within a three-body model using the
analytical transformed harmonic oscillator method to calculate their states. An
alternative procedure to estimate these rates from experimental data on
low-energy breakup is also discussed


  The JWST has ushered in a new era in atmospheric characterisations of
temperate low-mass exoplanets with recent detections of carbon-bearing
molecules in the candidate Hycean world K2-18 b. We investigated JWST
observations of the TOI-270 system, with two sub-Neptunes simultaneously
transiting the nearby M dwarf during the visit. We report our atmospheric
characterisation of the outer planet TOI-270 d, a candidate Hycean world, with
JWST transmission spectroscopy using the NIRSpec G395H instrument in the
2.7-5.2 $\mu$m range, combined with previous observations obtained with the HST
WFC3 spectrograph (1.1-1.6 $\mu$m). The spectrum reveals strong signatures of
CH4 and CO2 at 3.8-4.9$\sigma$ and 2.9-3.9$\sigma$ confidence, respectively,
and no evidence of NH3. The abundant CH4 and CO2, at ~0.1-1% mixing ratios, and
the non-detection of NH3 are similar to the findings reported for K2-18 b and
consistent with predictions for a Hycean world with a planet-wide ocean under a
H2-rich atmosphere. We also report evidence of CS2 at a 2.3-3.0$\sigma$
confidence and a potential inference of H2O at 1.6-4.4$\sigma$, depending on
the data analysis approach, and discuss possible interpretations of these
results. The spectrum does not provide strong constraints on the presence of
clouds or hazes in the observable atmosphere, nor any evidence for the effects
of stellar heterogeneities, which is consistent with previous studies. For the
smaller inner planet TOI-270 b, we find that the spectrum is inconsistent with
a featureless spectrum at ~3$\sigma$, showing some preference for an H2-rich
atmosphere in a super-Earth. We discuss the implications of our findings and
future prospects.


  Face morphing attacks seek to deceive a Face Recognition (FR) system by
presenting a morphed image consisting of the biometric qualities from two
different identities with the aim of triggering a false acceptance with one of
the two identities, thereby presenting a significant threat to biometric
systems. The success of a morphing attack is dependent on the ability of the
morphed image to represent the biometric characteristics of both identities
that were used to create the image. We present a novel morphing attack that
uses a Diffusion-based architecture to improve the visual fidelity of the image
and the ability of the morphing attack to represent characteristics from both
identities. We demonstrate the effectiveness of the proposed attack by
evaluating its visual fidelity via the Frechet Inception Distance (FID). Also,
extensive experiments are conducted to measure the vulnerability of FR systems
to the proposed attack. The ability of a morphing attack detector to detect the
proposed attack is measured and compared against two state-of-the-art GAN-based
morphing attacks along with two Landmark-based attacks. Additionally, a novel
metric to measure the relative strength between different morphing attacks is
introduced and evaluated.


  The use of supersymmetric localisation has recently led to modular covariant
expressions for certain integrated correlators of half-BPS operators in
$\mathcal{N} = 4$ supersymmetric Yang-Mills theory with a general classical
gauge group $G_N$. Here we determine generating functions that encode such
integrated correlators for any classical gauge group and provide a proof of
previous conjectured formulae. This gives a systematic understanding of the
relation between properties of these correlators at finite $N$ and their
expansions at large $N$. In particular, it determines a duality-invariant
non-perturbative completion of the large-$N$ expansion in terms of a sum of
novel non-holomorphic modular functions. These functions are exponentially
suppressed at large $N$ and have the form of a sum of contributions from
coincident $(p, q)$-string world-sheet instantons.


  Synthetic tabular data generation becomes crucial when real data is limited,
expensive to collect, or simply cannot be used due to privacy concerns.
However, producing good quality synthetic data is challenging. Several
probabilistic, statistical, generative adversarial networks (GANs), and
variational auto-encoder (VAEs) based approaches have been presented for
synthetic tabular data generation. Once generated, evaluating the quality of
the synthetic data is quite challenging. Some of the traditional metrics have
been used in the literature but there is lack of a common, robust, and single
metric. This makes it difficult to properly compare the effectiveness of
different synthetic tabular data generation methods. In this paper we propose a
new universal metric, TabSynDex, for robust evaluation of synthetic data. The
proposed metric assesses the similarity of synthetic data with real data
through different component scores which evaluate the characteristics that are
desirable for ``high quality'' synthetic data. Being a single score metric and
having an implicit bound, TabSynDex can also be used to observe and evaluate
the training of neural network based approaches. This would help in obtaining
insights that was not possible earlier. We present several baseline models for
comparative analysis of the proposed evaluation metric with existing generative
models. We also give a comparative analysis between TabSynDex and existing
synthetic tabular data evaluation metrics. This shows the effectiveness and
universality of our metric over the existing metrics. Source Code:
\url{https://github.com/vikram2000b/tabsyndex}


  The spectral characteristics of a fiber Bragg grating (FBG) with a
transversely inhomogeneous refractive index profile, differs con- siderably
from that of a transversely uniform one. Transmission spectra of inhomogeneous
and asymmetric FBGs that have been inscribed with focused ultrashort pulses
with the so-called point-by-point technique are investigated. The cladding mode
resonances of such FBGs can span a full octave in the spectrum and are very
pronounced (deeper than 20dB). Using a coupled-mode approach, we compute the
strength of resonant coupling and find that coupling into cladding modes of
higher azimuthal order is very sensitive to the position of the modification in
the core. Exploiting these properties allows precise control of such
reflections and may lead to many new sensing applications.


  Conversational recommendation systems (CRS) engage with users by inferring
user preferences from dialog history, providing accurate recommendations, and
generating appropriate responses. Previous CRSs use knowledge graph (KG) based
recommendation modules and integrate KG with language models for response
generation. Although KG-based approaches prove effective, two issues remain to
be solved. First, KG-based approaches ignore the information in the
conversational context but only rely on entity relations and bag of words to
recommend items. Second, it requires substantial engineering efforts to
maintain KGs that model domain-specific relations, thus leading to less
flexibility. In this paper, we propose a simple yet effective architecture
comprising a pre-trained language model (PLM) and an item metadata encoder. The
encoder learns to map item metadata to embeddings that can reflect the semantic
information in the dialog context. The PLM then consumes the semantic-aligned
item embeddings together with dialog context to generate high-quality
recommendations and responses. Instead of modeling entity relations with KGs,
our model reduces engineering complexity by directly converting each item to an
embedding. Experimental results on the benchmark dataset ReDial show that our
model obtains state-of-the-art results on both recommendation and response
generation tasks.


  Measuring an entangled state of two particles is crucial to many quantum
communication protocols. Yet Bell state distinguishability using a finite
apparatus obeying linear evolution and local measurement is theoretically
limited. We extend known bounds for Bell-state distinguishability in one and
two variables to the general case of entanglement in $n$ two-state variables.
We show that at most $2^{n+1}-1$ classes out of $4^n$ hyper-Bell states can be
distinguished with one copy of the input state. With two copies, complete
distinguishability is possible. We present optimal schemes in each case.


  The assumption of a static environment is common in many geometric computer
vision tasks like SLAM but limits their applicability in highly dynamic scenes.
Since these tasks rely on identifying point correspondences between input
images within the static part of the environment, we propose a graph neural
network-based sparse feature matching network designed to perform robust
matching under challenging conditions while excluding keypoints on moving
objects. We employ a similar scheme of attentional aggregation over graph edges
to enhance keypoint representations as state-of-the-art feature-matching
networks but augment the graph with epipolar and temporal information and
vastly reduce the number of graph edges. Furthermore, we introduce a
self-supervised training scheme to extract pseudo labels for image pairs in
dynamic environments from exclusively unprocessed visual-inertial data. A
series of experiments show the superior performance of our network as it
excludes keypoints on moving objects compared to state-of-the-art feature
matching networks while still achieving similar results regarding conventional
matching metrics. When integrated into a SLAM system, our network significantly
improves performance, especially in highly dynamic scenes.


  The properties of X-ray clusters of galaxies can be well understood in terms
of a competition between shock heating and adiabatic compression. Strong shocks
are expected to be important for massive clusters, while adiabatic compression
is dominant for small clusters and groups. The scale of the shock/adiabatic
transition is marked by a change of slope of the L-T relation and in the global
properties of the emitting plasma. This scale is connected to star formation
processes. Two quantities are crucial: the average energy injected in the IGM
from stars and SNe, and the epoch of the energy injection. We show how these
quantities can be synthesized in terms of specific entropy, which ultimately
determines the X-ray emission from groups and clusters.


  Euclidean geometry is among the earliest forms of mathematical thinking.
While the geometric primitives underlying its constructions, such as perfect
lines and circles, do not often occur in the natural world, humans rarely
struggle to perceive and reason with them. Will computer vision models trained
on natural images show the same sensitivity to Euclidean geometry? Here we
explore these questions by studying few-shot generalization in the universe of
Euclidean geometry constructions. We introduce Geoclidean, a domain-specific
language for Euclidean geometry, and use it to generate two datasets of
geometric concept learning tasks for benchmarking generalization judgements of
humans and machines. We find that humans are indeed sensitive to Euclidean
geometry and generalize strongly from a few visual examples of a geometric
concept. In contrast, low-level and high-level visual features from standard
computer vision models pretrained on natural images do not support correct
generalization. Thus Geoclidean represents a novel few-shot generalization
benchmark for geometric concept learning, where the performance of humans and
of AI models diverge. The Geoclidean framework and dataset are publicly
available for download.


  We theoretically study magnon-phonon hybrid excitations in a square lattice
ferromagnet subjected to a magnetic field by varying the field direction. The
bulk bands of hybrid excitations, which are referred to as magnon-polarons, are
investigated by considering all three phonon modes: vertical phonon, transverse
phonon, and longitudinal phonon. We show that the topological proprieties of
three hybridizations are different in terms of the Berry curvature and the
Chern numbers. We also find that the topological properties of the bands can be
controlled by changing the direction of the magnetic field, exhibiting one or
more topological phase transitions. The dependence of thermal Hall conductivity
as a function of magnetic field direction is proposed as an experiment probe of
our theoretical results.


  Using a model quantum clock, I evaluate an expression for the time of a
non-relativistic quantum particle to transit a piecewise geodesic path in a
background gravitational field with small spacetime curvature (gravity
gradient), in the case that the apparatus is in free fall. This calculation
complements and extends an earlier one (Davies 2004) in which the apparatus is
fixed to the surface of the Earth. The result confirms that, for particle
velocities not too low, the quantum and classical transit times coincide, in
conformity with the principle of equivalence. I also calculate the quantum
corrections to the transit time when the de Broglie wavelengths are long enough
to probe the spacetime curvature. The results are compared with the calculation
of Chaio and Speliotopoulos (2003), who propose an experiment to measure the
foregoing effects.


  We report on an experimental and theoretical study of the dynamic (ac) Stark
effect on a forbidden transition. A general framework for parameterizing and
describing off-resonant ac-Stark shifts is presented. A model is developed to
calculate spectral line shapes resulting from resonant excitation of atoms in
an intense standing light-wave in the presence of off-resonant ac-Stark shifts.
The model is used in the analysis and interpretation of a measurement of the
ac-Stark shifts of the static-electric-field-induced \mbox{${\rm 6s^2}~ ^1{\rm
S}_0~\to ~{\rm 5d6s}~ ^3{\rm D}_1\:$} transition at 408 nm in atomic Yb. The
results are in agreement with estimates of the ac-Stark shift of the transition
under the assumption that the shift is dominated by that of the ${\rm 6s^2 \:}
^1{\rm S}_0\:$ ground state. A detailed description of the experiment and
analysis is presented. A bi-product of this work is an independent
determination (from the saturation behavior of the 408-nm transition) of the
Stark transition polarizability, which is found to be in agreement with our
earlier measurement. This work is part of the ongoing effort aimed at a
precision measurement of atomic parity-violation effects in Yb.


  The kinematics of isolated brown dwarfs in the Galaxy, beyond the solar
neighborhood, is virtually unknown. Microlensing has the potential to probe
this hidden population, as it can measure both the mass and five of the six
phase-space coordinates (all except the radial velocity) even of a dark
isolated lens. However, the measurements of both the microlens parallax and
finite-source effects are needed in order to recover the full information.
Here, we combine $Spitzer$ satellite parallax measurement with the ground-based
light curve, which exhibits strong finite-source effects, of event
OGLE-2017-BLG-0896. We find two degenerate solutions for the lens (due to the
known satellite-parallax degeneracy), which are consistent with each other
except for their proper motion. The lens is an isolated brown dwarf with a mass
of either $18\pm1M_J$ or $20\pm1M_J$. This is the lowest isolated-object mass
measurement to date, only $\sim$45\% more massive than the theoretical
deuterium-fusion boundary at solar metallicity, which is the common definition
of a free-floating planet. The brown dwarf is located at either $3.9\pm0.1$ kpc
or $4.1\pm0.1$ kpc toward the Galactic bulge, but with proper motion in the
opposite direction of disk stars, with one solution suggesting it is moving
within the Galactic plane. While it is possibly a halo brown dwarf, it might
also represent a different, unknown population.


  For $S_g(x,y)=x-g(y), x,y\in\mathbb{R}^n, g\in O(n),$ we investigate the
Lebesgue measure and Hausdorff dimension of $S_g(A)$ given the dimension of
$A$, both for general Borel subsets of $\mathbb{R}^{2n}$ and for product sets.


  Cosmic microwave background (CMB) experiments generally infer a temperature
fluctuation from a measured intensity fluctuation through the first term in the
Taylor expansion of the Planck function, the relation between the intensity in
a given frequency and the temperature. However, with the forthcoming Planck
satellite, and perhaps even with the Microwave Anisotropy Probe, the CMB-dipole
amplitude will be large enough to warrant inclusion of the next higher order
term. To quadratic order in the dipole amplitude, there is an intensity
quadrupole induced by the dipole with a frequency dependence given by the
second derivative of the Planck function. The Planck satellite should be able
to detect this dipole-induced intensity quadrupole and distinguish it through
its frequency depdendence from the intrinsic CMB temperature and foreground
quadrupoles. This higher-order effect provides a robust pre-determined target
that may provide tests of Planck's and MAP's large-angle-fluctuation
measurements and of their techniques for multi-frequency foreground
subtraction.


  Let $r \ge 2$ be an integer. We adapt the Maynard-Tao sieve to produce the
asymptotically best-known bounded gaps between products of $r$ distinct primes.
Our result applies to positive-density subsets of the primes that satisfy
certain equidistribution conditions. This improves on the work of Thorne and
Sono.


  Recently, the joint learning framework (JOINT) integrates matching based
transductive reasoning and online inductive learning to achieve accurate and
robust semi-supervised video object segmentation (SVOS). However, using the
mask embedding as the label to guide the generation of target features in the
two branches may result in inadequate target representation and degrade the
performance. Besides, how to reasonably fuse the target features in the two
different branches rather than simply adding them together to avoid the adverse
effect of one dominant branch has not been investigated. In this paper, we
propose a novel framework that emphasizes Learning to Learn Better (LLB) target
features for SVOS, termed LLB, where we design the discriminative label
generation module (DLGM) and the adaptive fusion module to address these
issues. Technically, the DLGM takes the background-filtered frame instead of
the target mask as input and adopts a lightweight encoder to generate the
target features, which serves as the label of the online few-shot learner and
the value of the decoder in the transformer to guide the two branches to learn
more discriminative target representation. The adaptive fusion module maintains
a learnable gate for each branch, which reweighs the element-wise feature
representation and allows an adaptive amount of target information in each
branch flowing to the fused target feature, thus preventing one branch from
being dominant and making the target feature more robust to distractor.
Extensive experiments on public benchmarks show that our proposed LLB method
achieves state-of-the-art performance.


  For the paramagnetic insulating phase in the metal-ordered manganite
YBaMn2O6, the so-called CE-type of charge/orbital ordered state was observed
within the monoclinic ab-plane, which is most commonly observed for the
ordinary half doped manganites. However, TEM revealed a 4-fold periodicity
along the c-axis, suggesting a new stacking pattern, where planes of the
CE-type are built up according to the sequence [aabb...]. Interestingly, when
th system enters into the antiferromagnetic state, this stacking pattern
changes into [aaaa...] or [abab], suggesting close interplay between spins and
orbitals. These features are discusses in terms of inherent structural
alternation, i.e., the Y/Ba order along the c-axis.


  Many physiological phenomena involve directional cell migration. It is
usually attributed to chemical gradients in vivo. Recently, other cues have
been shown to guide cells in vitro, including stiffness/adhesion gradients or
micro-patterned adhesive motifs. However, the cellular mechanism leading to
these biased migrations remains unknown, and, often, even the direction of
motion is unpredictable. In this study, we show the key role of fluctuating
protrusions on ratchet-like structures in driving NIH3T3 cell migration. We
identified the concept of efficient protrusion and an associated direction
index. Our analysis of the protrusion statistics facilitated the quantitative
prediction of cell trajectories in all investigated conditions. We varied the
external cues by changing the adhesive patterns. We also modified the internal
cues using drug treatments, which modified the protrusion activity.
Stochasticity affects the short- and long-term steps. We developed a
theoretical model showing that an asymmetry in the protrusion fluctuations is
sufficient for predicting all measures associated with the long-term motion,
which can be described as a biased persistent random walk.


  The use of reduced models for investigating the self-assembly dynamics
underlying protein shell formation in spherical viruses is described. The
spontaneous self-assembly of these polyhedral, supramolecular structures, in
which icosahedral symmetry is a conspicuous feature, is a phenomenon whose
dynamics remain unexplored; studying the growth process by means of computer
simulation provides access to the mechanisms underlying assembly. In order to
capture the more universal aspects of self-assembly, namely the manner in which
component shapes influence structure and assembly pathway, in this exploratory
study low-resolution approximations are used to represent the basic protein
building blocks. Alternative approaches involving both irreversible and
reversible assembly are discussed, models based on both schemes are introduced,
and examples of the resulting behavior described.


  An inverse problem of elasticity of $n$ elastic inclusions embedded into an
elastic half-plane is analyzed. The boundary of the half-plane is free of
traction. The half-plane and the inclusions are subjected to antiplane shear,
and the conditions of ideal contact hold in the interfaces between the
inclusions and the half-plane. The shapes of the inclusions are not prescribed
and have to be determined by enforcing uniform stresses inside the inclusions.
The method of conformal mappings from a slit domain onto the $(n+1)$-connected
physical domain is worked out. It is shown that to recover the map and
therefore the inclusions shapes, one needs to solve a vector Riemann-Hilbert
problem on a genus-$n$ hyperelliptic surface. In a particular case of loading
of a single inclusion in a half-plane, the problem is equivalent to two scalar
Riemann-Hilbert problems on two slits on an elliptic surface. In addition to
three parameters of the model the conformal map possesses a free geometric
parameter. Results of numerical tests which show the impact of these parameters
on the inclusion shape are presented.


  An improved unified formulation based on the effective field theory is
introduced for a spin-1 Ising model with nearest neighbor interactions with
arbitrary coordination number z. Present formulation is capable of calculating
all the multi-spin correlations systematically in a representative manner, as
well as its single site counterparts in the system and gives much better
results for critical temperature, in comparison with the other works in the
literature. The formulation can be easily used to various kinds of spin-1 Ising
models, as long as the system contains only the nearest neighbor interactions
as spin-spin interactions.


  Future searches for biomarkers on habitable exoplanets will rely on telescope
instruments that achieve extremely high contrast at small planet-to-star
angular separations. Coronagraphy is a promising starlight suppression
technique, providing excellent contrast and throughput for off-axis sources on
clear apertures. However, the complexity of space- and ground-based telescope
apertures goes on increasing over time, owing to the combination of primary
mirror segmentation, secondary mirror, and support structures. These
discontinuities in the telescope aperture limit the coronagraph performance. In
this paper, we present ACAD-OSM, a novel active method to correct for the
diffractive effects of aperture discontinuities in the final image plane of a
coronagraph. Active methods use one or several deformable mirrors that are
controlled with an interaction matrix to correct for the aberrations in the
pupil. However, they are often limited by the amount of aberrations introduced
by aperture discontinuities. This algorithm relies on the recalibration of the
interaction matrix during the correction process to overcome this limitation.
We first describe the ACAD-OSM technique and compare it to the previous active
methods for the correction of aperture discontinuities. We then show its
performance in terms of contrast and off-axis throughput for static aperture
discontinuities (segmentation, struts) and for some aberrations evolving over
the life of the instrument (residual phase aberrations, artifacts in the
aperture, misalignments in the coronagraph design). This technique can now
obtain the earth-like planet detection threshold of 10^(-10) contrast on any
given aperture over at least a 10% spectral bandwidth, with several coronagraph
designs.


  Quantum codes are subspaces of the state space of a quantum system that are
used to protect quantum information. Some common classes of quantum codes are
stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained
from stabilizer codes, and Clifford codes. We analyze these in the framework of
the Fourier inversion formula on a group algebra, the group in question being a
subgroup of the error group considered. We study other possible code spaces
that may be obtained via such an approach, obtaining codes that are the direct
sums of translates of Clifford codes, and more general codes obtained from
idempotents in the transform domain. We derive necessary and sufficient
conditions for error detection by direct sums of translates of Clifford codes,
and provide an example using an error group with non-Abelian index group.


  We examine the general problem of inter-domain Gaussian Processes (GPs):
problems where the GP realization and the noisy observations of that
realization lie on different domains. When the mapping between those domains is
linear, such as integration or differentiation, inference is still closed form.
However, many of the scaling and approximation techniques that our community
has developed do not apply to this setting. In this work, we introduce the
hierarchical inducing point GP (HIP-GP), a scalable inter-domain GP inference
method that enables us to improve the approximation accuracy by increasing the
number of inducing points to the millions. HIP-GP, which relies on inducing
points with grid structure and a stationary kernel assumption, is suitable for
low-dimensional problems. In developing HIP-GP, we introduce (1) a fast
whitening strategy, and (2) a novel preconditioner for conjugate gradients
which can be helpful in general GP settings. Our code is available at https:
//github.com/cunningham-lab/hipgp.


  Robust performance of control schemes for open quantum systems is
investigated under classical uncertainties in the generators of the dynamics
and nonclassical uncertainties due to decoherence and initial state preparation
errors. A formalism is developed to measure performance based on the
transmission of a dynamic perturbation or initial state preparation error to
the quantum state error. This makes it possible to apply tools from classical
robust control such as structured singular value analysis. A difficulty arising
from the singularity of the closed-loop Bloch equations for the quantum state
is overcome by introducing the #-inversion lemma, a specialized version of the
matrix inversion lemma. Under some conditions, this guarantees continuity of
the structured singular value at s = 0. Additional difficulties occur when
symmetry gives rise to multiple open-loop poles, which under symmetry-breaking
unfold into single eigenvalues. The concepts are applied to systems subject to
pure decoherence and a general dissipative system example of two qubits in a
leaky cavity under laser driving fields and spontaneous emission. A
nonclassical performance index, steady-state entanglement quantified by the
concurrence, a nonlinear function of the system state, is introduced.
Simulations confirm a conflict between entanglement, its log-sensitivity and
stability margin under decoherence.


  Experimental results of the $p(^{13}{\rm B},d)^{12}{\rm B}$ transfer reaction
to the low-lying states in $^{12}$B are reported. The optical potential
parameters for the entrance channel are extracted from the elastic scattering
$p$($^{13}{\rm B}$, $p$) measured in the same experiment, while those for the
exit channel are global ones. Spectroscopic factors associated with the $p$-,
$s$-, and $d$-wave neutron transfer to the known $^{12}$B states, are extracted
by comparing the deuteron angular distributions with the calculation results.
The separated $s$- and $d$-wave intruder strengths in $^{13}{\rm B}_{\rm g.s.}$
were determined to be $10(2)\%$ and $6(1)\%$, respectively, which follow
roughly the systematics for the $N$ = 8 neutron-rich isotones. The measured
total intruder strength is in good agreement with the shell model calculation,
while the individual ones evolve quite differently. Particularly, the sudden
change of the $d$-wave intensity between $^{13}$B and $^{12}$Be needs further
theoretical interpretation.


  We report an in-plane thermal transport study of the honeycomb Kitaev
material Na$_2$Co$_2$TeO$_6$ at subKelvin temperatures. In zero field, the
$\kappa(T)$ displays a rather weak $T$-dependence but has a non-zero residual
term $\kappa_0/T$, indicating strong phonon scattering by magnetic excitation
and the possibility of itinerant spinon-like excitations coexisting with an
antiferromagnetic order below 27 K. We propose the zero-field ground state is a
novel fractionalized antiferromagnetic (AF*) state with both magnetic order and
fractionalized excitations. With both the heat current and external field along
the $a*$ (Co-Co bond) direction, the $\kappa_{a*}$ exhibits two sharp minima at
7.5 T and 10 T, and its value at 8.5 T is almost the same as the pure phononic
transport for the high-field polarized state. This confirms the phase
boundaries of the reported field-induced intermediate state and suggest its
gapless continuum excitations possibly transport heat. No such intermediate
phase was found in the $\kappa_a$ for the current and field along the $a$
(zigzag chain) direction. Finally, Na$_2$Co$_2$TeO$_6$ displays a strongly
anisotropic magneto-thermal conductivity since the in-plane (out-of-plane)
field strongly enhances (suppresses) the $\kappa_{a*}$ and $\kappa_a$.


  Using the reduced formulation of large-N Quantum Field Theories we study
strings in space-time dimensions higher than one. Some preliminary results
concerning the possible string susceptibilities and general properties of the
model are presented.


  The anisotropic optical absorption edge of $\beta$-Ga$_2$O$_3$ follows a
modified Beer-Lambert law having two effective absorption coefficients. The
absorption coefficient of linearly polarized light reduces to the least
absorbing direction beyond a critical penetration depth, which itself depends
on polarization and wavelength. To understand this behavior, a Stokes vector
analysis is performed to track the polarization state as a function of depth.
The weakening of the absorption coefficient is associated with a gradual shift
of linear polarization to the least absorbing crystallographic direction in the
plane, which is along the a-exciton within the (010) plane or along the
b-exciton in the (001) plane. We show that strong linear dichroism near the
optical absorption edge causes this shift in $\beta$-Ga$_2$O$_3$, which arises
from the anisotropy and spectral splitting of the physical absorbers i.e.,
excitons. The linear polarization shift is accompanied by a variation in the
ellipticity due to the birefringence of $\beta$-Ga$_2$O$_3$. Analysis of the
phase relationship between the incoming electric field to that at a certain
depth reveals the phase speed as an effective refractive index, which varies
along different crystallographic directions. The critical penetration depth is
shown to be correlated with the depth at which the ellipticity is maximal.
Thus, the anisotropic Beer-Lambert law arises from the interplay of both the
dichroic and birefringent properties of $\beta$-Ga$_2$O$_3$.


  We calculate the frequency dependent spin susceptibilities for a
two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit
interaction. The resonances of the susceptibilities depends on the relative
values of the Rashba and Dresselhaus spin-orbit constants, which could be
manipulated by gate voltages. We derive exact continuity equations, with source
terms, for the spin density and use those to connect the spin current to the
spin density. In the free electron model the susceptibilities play a central
role in the spin dynamics since both the spin density and the spin current are
proportional to them.


  Empirical studies of the first generation of stars and quasars will likely
become feasible within the next decade in several different wavelength bands.
Microwave anisotropy experiments, such as MAP or Planck, will set constraints
on the ionization history of the intergalactic medium due to these sources. In
the infrared, the Next Generation Space Telescope (NGST) will be able to
directly detect sub-galactic objects at redshifts z>10. In the optical, data
from the Hubble Deep Field already places a constraint on the abundance of
high-redshift quasars. However, the epoch of the first quasars might be first
probed in X-ray bands, by instruments such as the Chandra X-ray Observatory
(CXO) and the X-ray Multi-mirror Mission (XMM). In a 500 Ksec integration, CXO
reaches a sensitivity of 2x10-16 erg/s cm^2. Based on simple hierarchical CDM
models, we find that at this flux threshold approx. 100 quasars might be
detectable from redshifts z>5, and approx. 1 quasar at z=10, in each 17x17
arcmin field. Measurement of the power spectrum of the unresolved soft X-ray
background will further constrain models of faint, high-redshift quasars.


  We offer a novel view of AdaBoost in a statistical setting. We propose a
Bayesian model for binary classification in which label noise is modeled
hierarchically. Using variational inference to optimize a dynamic evidence
lower bound, we derive a new boosting-like algorithm called VIBoost. We show
its close connections to AdaBoost and give experimental results from four
datasets.


  Human gait is considered a unique biometric identifier which can be acquired
in a covert manner at a distance. However, models trained on existing public
domain gait datasets which are captured in controlled scenarios lead to drastic
performance decline when applied to real-world unconstrained gait data. On the
other hand, video person re-identification techniques have achieved promising
performance on large-scale publicly available datasets. Given the diversity of
clothing characteristics, clothing cue is not reliable for person recognition
in general. So, it is actually not clear why the state-of-the-art person
re-identification methods work as well as they do. In this paper, we construct
a new gait dataset by extracting silhouettes from an existing video person
re-identification challenge which consists of 1,404 persons walking in an
unconstrained manner. Based on this dataset, a consistent and comparative study
between gait recognition and person re-identification can be carried out. Given
that our experimental results show that current gait recognition approaches
designed under data collected in controlled scenarios are inappropriate for
real surveillance scenarios, we propose a novel gait recognition method, called
RealGait. Our results suggest that recognizing people by their gait in real
surveillance scenarios is feasible and the underlying gait pattern is probably
the true reason why video person re-idenfification works in practice.


  We report on the interplay between a van Hove singularity and a charge
density wave state in 2H-TaSe$_{2}$. We use angle-resolved photoemission
spectroscopy to investigate changes in the Fermi surface of this material under
surface doping with potassium. At high doping, we observe modifications which
imply the disappearance of the $(3\times 3)$ charge density wave and formation
of a different correlated state. Using a tight-binding-based approach as well
as an effective model, we explain our observations as a consequence of coupling
between the single-particle Lifshitz transition during which the Fermi level
passes a van Hove singularity and the charge density order. In this scenario,
the high electronic density of states associated with the van Hove singularity
induces a change in the periodicity of the charge density wave from the known
$(3\times 3)$ to a new $(2\times 2)$ superlattice.


  We test the merger-induced dual active galactic nuclei (dAGN) paradigm using
a sample of 35 radio galaxy pairs from the SDSS Stripe 82 field. Using Keck
optical spectroscopy, we confirm 21 pairs have consistent redshifts,
constituting kinematic pairs; the remaining 14 pairs are line-of-sight
projections. We classify the optical spectral signatures via emission line
ratios, equivalent widths, and excess of radio power above star-formation
predicted outputs. We find 6 galaxies are classified as LINERs and 7 are
AGN/starburst composites. Most of the LINERs are retired galaxies, while the
composites likely have AGN contribution. All of the kinematic pairs exhibit
radio power more than 10$\times$ above the level expected from just
star-formation, suggestive of a radio AGN contribution. We also analyze
high-resolution (0.3") imaging at 6 GHz from the NSF's Karl G. Jansky Very
Large Array for 17 of the kinematic pairs. We find 6 pairs (2 new, 4 previously
known) host two separate radio cores, confirming their status as dAGNs. The
remaining 11 pairs contain single AGNs, with most exhibiting prominent
jets/lobes overlapping their companion. Our final census indicates a dAGN duty
cycle slightly higher than predictions of purely stochastic fueling, although a
larger sample (potentially culled from VLASS) is needed to fully address the
dAGN fraction. We conclude that while dAGNs in the Stripe 82 field are rare,
the merger process plays some role in their triggering and it facilitates low
to moderate levels of accretion.


  IAs is well known, when D6 branes wrap a special lagrangian cycle on a non
compact CY 3-fold in such a way that the internal string frame metric is Kahler
there exists a dual description, which is given in terms of a purely
geometrical eleven dimensional background with an internal metric of $G_2$
holonomy. It is also known that when D6 branes wrap a coassociative cycle of a
non compact $G_2$ manifold in presence of a self-dual two form strength the
internal part of the string frame metric is conformal to the $G_2$ metric and
there exists a dual description, which is expressed in terms of a purely
geometrical eleven dimensional background with an internal non compact metric
of Spin(7) holonomy. In the present work it is shown that any $G_2$ metric
participating in the first of these dualities necessarily participates in one
of the second type. Additionally, several explicit Spin(7) holonomy metrics
admitting a $G_2$ holonomy reduction along one isometry are constructed. These
metrics can be described as $R$-fibrations over a 6-dimensional Kahler metric,
thus realizing the pattern Spin(7) $\to G_2\to$ (Kahler) mentioned above.
Several of these examples are further described as fibrations over the
Eguchi-Hanson gravitational instanton and, to the best of our knowledge, have
not been previously considered in the literature.


  In an effort to understand the glass transition, the kinetics of a spin model
with frustration but no quenched randomness has been analyzed. The
phenomenology of the spin model is remarkably similiar to that of structural
glasses. Analysis of the model suggests that defects play a major role in
dictating the dynamics as the glass transition is approached.


  We provide a geometric interpretation for a normalized version of the minimal
denominator function, $$q_{\min}(x,\delta)=\min\left\{q\in \mathbb{N}: \text{
there exists } p\in\mathbb{Z} \text{ such that } \frac{p}{q}\in
(x-\delta,x+\delta)\right\},$$ introduced by Chen and Haynes. We use this
interpretation to compute the limiting distribution of a suitably normalized
version of $q_{\min}(x,\delta)$ as a function of $x$, and give generalizations
of the idea of minimal denominators to higher-dimensional unimodular lattices,
linear forms, and translation surfaces. The key idea is to turn this circle of
problems into equidistribution problems for translates of unipotent orbits of a
Lie group action on an appropriate moduli space.


  Humans can learn a variety of concepts and skills incrementally over the
course of their lives while exhibiting many desirable properties, such as
continual learning without forgetting, forward transfer and backward transfer
of knowledge, and learning a new concept or task with only a few examples.
Several lines of machine learning research, such as lifelong learning, few-shot
learning, and transfer learning, attempt to capture these properties. However,
most previous approaches can only demonstrate subsets of these properties,
often by different complex mechanisms. In this work, we propose a simple yet
powerful unified framework that supports almost all of these properties and
approaches through one central mechanism. We also draw connections between many
peculiarities of human learning (such as memory loss and "rain man") and our
framework. While we do not present any state-of-the-art results, we hope that
this conceptual framework provides a novel perspective on existing work and
proposes many new research directions.


  Serendipitously, we have rediscovered radio emission from the binary system
Ross 867 (M4.5V) and Ross 868 (M3.5V) while inspecting archival Giant Metrewave
Radio Telescope (GMRT) observations. The binary system consists of two M-dwarf
stars that share common characteristics such as spectral type, astrometric
parameters, age and emission at infrared, optical and X-rays frequencies. The
GMRT data at 610 MHz taken on July 2011 shows that the radio emission from Ross
867 is polarized and highly variable on hour time scales with a peak flux of
10.4 $\pm$ 0.7 mJy/beam. Additionally, after reviewing archival data from
several observatories (VLA, GMRT, JVLA and LOFAR), we confirm that although
both stars are likely coeval, only Ross 867 has been detected, while Ross 868
remains undetected at radio wavelengths. As they have a a large orbital
separation, this binary stellar system provides a coeval laboratory to examine
and constrain the stellar properties linked to radio activity in M dwarfs. We
speculate that the observed difference in radio activity between the dwarfs
could be due to vastly different magnetic field topologies or that Ross 867 has
an intrinsically different dynamo.


  We explore the consequences of dynamical evolution of field binaries composed
of a primary black hole (BH) and a Wolf-Rayet (WR) star in the context of
gravitational wave (GW) source progenitors. We argue, from general
considerations, that the spin of the WR-descendent BH will be maximal in a
significant number of cases due to dynamical effects. In other cases, the spin
should reflect the natal spin of the primary BH which are currently
theoretically unconstrained. We argue that the three currently published LIGO
systems (GW150914, GW151226, LVT151012) suggest that this spin is small. The
resultant effective spin distribution of gravitational wave sources should thus
be bi-model if this classic GW progenitor channel is indeed dominant. While
this is consistent with the LIGO detections thus far, it is in contrast to the
three best-measured high-mass x-ray binary (HMXB) systems. A comparison of the
spin distribution of HMXBs and GW sources should ultimately reveal whether or
not these systems arise from similar astrophysical channels.


  In this paper, we propose a distributed second- order method for
reinforcement learning. Our approach is the fastest in literature so-far as it
outperforms state-of-the-art methods, including ADMM, by significant margins.
We achieve this by exploiting the sparsity pattern of the dual Hessian and
transforming the problem of computing the Newton direction to one of solving a
sequence of symmetric diagonally dominant system of equations. We validate the
above claim both theoretically and empirically. On the theoretical side, we
prove that similar to exact Newton, our algorithm exhibits super-linear
convergence within a neighborhood of the optimal solution. Empirically, we
demonstrate the superiority of this new method on a set of benchmark
reinforcement learning tasks.


  We study the dc Josephson effect in a diffusive multilayered SF'FF'S
structure, where S is a superconductor and F,F' are different ferromagnets. We
assume that the exchange energies in the F' and F layers are different ($% h $
and $H$, respectively) and the middle F layer consists of two layers with
parallel or antiparallel magnetization vectors $M$. The $M$ vectors in the left
and right F' layers are generally not collinear to those in the F layer. In the
limit of a weak proximity effect we use a linearized Usadel equation. Solving
this equation, we calculate the Josephson critical current for arbitrary
temperatures, arbitrary thicknesses of the F' and F layers ($% L_{h}$ and
$L_{H}$) in the case of parallel and antiparallel $M$ orientations in the F
layer. The part of the critical current $I_{cSR}$ formed by the short-range
(SRC) singlet and S=0 triplet condensate components decays on a short length
$\xi_{H}=\sqrt{D/H}$, whereas the part $% I_{cLR}$ due to the long-range
triplet $|S|=1$ component (LRTC) decreases with increasing $L_{H}$ on the
length $\xi_{N}=\sqrt{D/\pi T}$. Our results are in agreement with the
experiment \cite{Birge}.


  The theory of causal fermion systems is an approach to describe fundamental
physics. We here introduce the mathematical framework and give an overview of
the objectives and current results.


  This study proposes algorithms for building tilt grain boundary (GB) models
with a boundary plane-oriented approach that does not rely on existence of a
coincidence site lattice (CSL). As conventional GB model generation uses the
CSL of superimposed grains as the starting point, our totally different
approach allows systematic treatment of diverse grain boundary systems that was
previously not possible. Candidates of a pair of GB planes for a selected
rotation axis, constituting a symmetrical or asymmetrical tilt GB, are
thoroughly obtained by computational search that is applicable to any crystal
structure. A GB interface for feasible computational analysis would have
two-dimensional (2D) periodicity shared by the 2D lattices of the two GB
planes, hence surface-slab supercells (slab-and-vacuum models) with common
in-plane basis vectors of the shared 2D lattice are obtained. Finally, a
procedure to obtain a GB-model supercell with alternately stacking such slabs
is given. Symmetry operations of each slab may be considered such that the
iterated interfaces are symmetrically equivalent, which is beneficial in ab
initio calculations. The proposed algorithms allow streamlined generation of GB
models, both symmetric and asymmetric, with or without an exact 3D-CSL
relation.


  The study of dissipative systems has attracted great attention, as
dissipation engineering has become an important candidate towards manipulating
light in classical and quantum ways. Here,we investigate the behavior of a
topological system with purely dissipative couplings in a synthetic
time-frequency space. An imaginary bandstructure is shown, where eigen-modes
experience different eigen-dissipation rates during the evolution of the
system, resulting in mode competition between edge states and bulk modes. We
show that distributions associated with edge states can dominate over bulk
modes with stable amplification once the pump and saturation mechanisms are
taken into consideration, which therefore points to a laser-like behavior for
edge states robust against disorders. This work provides a scheme for
manipulating multiple degrees of freedom of light by dissipation engineering,
and also proposes a great candidate for topological lasers with dissipative
photonics.


  The recent Spectre attacks have demonstrated that modern microarchitectural
optimizations can make software insecure. These attacks use features like
pipelining, out-of-order and speculation to extract information about the
memory contents of a process via side-channels. In this paper we demonstrate
that Cortex-A53 is affected by speculative leakage even if the
microarchitecture does not support out-of-order execution. We named this new
class of vulnerabilities SiSCloak.


  The advent of high resolution imaging has made data on surface shape
widespread. Methods for the analysis of shape based on landmarks are well
established but high resolution data require a functional approach. The
starting point is a systematic and consistent description of each surface
shape. Three innovative forms of analysis are then introduced. The first uses
surface integration to address issues of registration, principal component
analysis and the measurement of asymmetry, all in functional form.
Computational issues are handled through discrete approximations to integrals,
based in this case on appropriate surface area weighted sums. The second
innovation is to focus on sub-spaces where interesting behaviour such as group
differences are exhibited, rather than on individual principal components. The
third innovation concerns the comparison of individual shapes with a relevant
control set, where the concept of a normal range is extended to the highly
multivariate setting of surface shape. This has particularly strong
applications to medical contexts where the assessment of individual patients is
very important. All of these ideas are developed and illustrated in the
important context of human facial shape, with a strong emphasis on the
effective visual communication of effects of interest.


  We consider the problem of filling an unknown area represented by an
arbitrary connected graph of $n$ vertices by mobile luminous robots. In this
problem, the robots enter the graph one-by-one through a specific vertex,
called the Door, and they eventually have to cover all vertices of the graph
while avoiding collisions. The robots are anonymous and make decisions driven
by the same local rule of behavior. They have limited persistent memory and
limited visibility range. We investigate the Filling problem in the
asynchronous model.
  We assume that the robots know an upper bound $\Delta$ on the maximum degree
of the graph before entering. We present an algorithm solving the asynchronous
Filling problem with robots having $1$ hop visibility range, $O(\log\Delta)$
bits of persistent storage, and $\Delta+4$ colors, including the color when the
light is off. We analyze the algorithm in terms of asynchronous rounds, where a
round means the smallest time interval in which each robot, which has not yet
finished the algorithm, has been activated at least once. We show that this
algorithm needs $O(n^2)$ asynchronous rounds. Our analysis provides the first
asymptotic upper bound on the running time in terms of asynchronous rounds.
  Then we show how the number of colors can be reduced to $O(1)$ at the cost of
the running time. The algorithm with $1$ hop visibility range, $O(\log \Delta)$
bits of persistent memory, and $O(1)$ colors needs $O(n^2\log \Delta)$ rounds.
We show how the running time can be improved by robots with a visibility range
of $2$ hops, $O(\log \Delta)$ bits of persistent memory, and $\Delta + 4$
colors (including the color when the light is off). We show that the algorithm
needs $O(n)$ asynchronous rounds. Finally, we show how to extend our solution
to the $k$-Door case, $k\geq 2$, by using $\Delta + k + 4$ colors, including
the color when the light is off.


  We introduce an agent-based model, in which agents set their prices to
maximize profit. At steady state the market self-organizes into three groups:
excess producers, consumers and balanced agents, with prices determined by
their own resource level and a couple of macroscopic parameters that emerge
naturally from the analysis, akin to mean-field parameters in statistical
mechanics. When resources are scarce prices rise sharply below a turning point
that marks the disappearance of excess producers. To compare the model with
real empirical data, we study the relations between commodity prices and
stock-to-use ratios of a range of commodities such as agricultural products and
metals. By introducing an elasticity parameter to mitigate noise and long-term
changes in commodities data, we confirm the trend of rising prices, provide
evidence for turning points, and indicate yield points for less essential
commodities.


  Motivated by medium access control for resource-challenged wireless Internet
of Things (IoT), we consider the problem of queue scheduling with reduced queue
state information. In particular, we consider a time-slotted scheduling model
with $N$ sensor nodes, with pair-wise dependence, such that Nodes $i$ and $i +
1,~0 < i < N$ cannot transmit together. We develop new throughput-optimal
scheduling policies requiring only the empty-nonempty state of each queue that
we term Queue Nonemptiness-Based (QNB) policies. We propose a Policy Splicing
technique to combine scheduling policies for small networks in order to
construct throughput-optimal policies for larger networks, some of which also
aim for low delay. For $N = 3,$ there exists a sum-queue length optimal QNB
scheduling policy. We show, however, that for $N > 4,$ there is no QNB policy
that is sum-queue length optimal over all arrival rate vectors in the capacity
region.
  We then extend our results to a more general class of interference
constraints that we call cluster-of-cliques (CoC) conflict graphs. We consider
two types of CoC networks, namely, Linear Arrays of Cliques (LAoC) and
Star-of-Cliques (SoC) networks. We develop QNB policies for these classes of
networks, study their stability and delay properties, and propose and analyze
techniques to reduce the amount of state information to be disseminated across
the network for scheduling. In the SoC setting, we propose a throughput-optimal
policy that only uses information that nodes in the network can glean by
sensing activity (or lack thereof) on the channel. Our throughput-optimality
results rely on two new arguments: a Lyapunov drift lemma specially adapted to
policies that are queue length-agnostic, and a priority queueing analysis for
showing strong stability.


  We re-examine the symmetry structure of massive momentum bispinors in four
dimensional Minkowski spacetime and apply the result to the geometry of a
two-qubit entanglement system. The geometry of entanglement is recovered by
restricting the momentum to unit-energy hyperplane inside the future
light-cone. On a more formal side, to understand Czachor's alternative
normalization of the bispinor and its projection property, we analyze the
geometry of momentum twistor space. An interesting correpondence between a
submanifold of the momentum twistor space and tachyonic particle is also
investigated.


  Broadband, coherent light carrying optical angular momentum is of potential
utility for a variety of classical and quantum communication applications, but
at present few such sources exist. We study the generation of supercontinua in
a ring array of coupled optical fibres. Short pulses carrying discrete angular
momentum undergo soliton fission, spontaneously breaking azimuthal symmetry.
This results in a train of pulses with a broadband frequency spectrum as well
as a non-trivial angular momentum distribution. These spatio-temporal solitary
waves, localised around a single fibre core, emit an unusual form of resonant
radiation which can be present even in the absence of intrinsic higher order
dispersion, being induced by the lattice dispersion of the ring array. We
explore how the coupling properties between fibre cores affect the resulting
supercontinuum, in particular how mildly twisting the array can effectively
manipulate its angular momentum content and resonant frequencies through the
induced Peierls phase.


  For many models in Biology and Physics, Liouville systems defined on Riemann
surfaces are used to describe the growth of species and movements of particles.
In this article we study one essential difficulty of singular Liouville
systems: Bubble interaction. Let $u=(u_1,...,u_n)$ be a solution of the
following singular Liouville system: \begin{equation*} \Delta_g
u_i+\sum_{j=1}^n a_{ij}\rho_j(\frac{h_je^{u_j}}{\int_M
h_je^{u_j}dV_g}-1)=\sum_{l=1}^{N}4\pi\gamma_l(\delta_{p_l}-1), \end{equation*}
where $h_i$ are positive smooth functions, $p_1,\cdots,p_N$ are distinct points
on $M$, $\delta_{p_l}$ are Dirac masses, $\rho=(\rho_1,,,,\rho_n)$ and
$(\gamma_1,\cdots,\gamma_N)(-1<\gamma_l<0)$ are constant vectors. The main
achievement of this article is that when blowup phenomenon happens, the profile
of bubbling solutions around different blowup points can be described with
upmost precision. As a result we know the precise heights of bubbling solutions
around each blowup point, the exact values of integration of each component and
the locations of blowup points. In addition, if the parameter $\rho$ is tending
to a critical hypersurface, we can identity a leading term that is crucial for
a number of applications.


  I discuss a solution to the dark energy problem, which arises when the
visible universe is approximated by a black hole, in a quasi-static
asymptotically-flat approximation. Using data, provided by WMAP7, I calculate
the Schwarzschild radius $r_S$ and compare to the measured physical radius of
the visible universe, bounded by the surface of last scatter. The ratio,
$\epsilon(t_0) = r/r_S$ is found to be comparable to $\epsilon = 1$, as allowed
by the holographic principle. The measurement of a shift parameter, $\sigma$,
introduced by Bond, Efstathiou and Tegmark in 1997, plays an important role in
the accuracy of the calculation. The approximation leads to a surprisingly
small discrepancy, presumably explicable by the de Sitter, and expanding,
nature of the actual universe.


  The purpose of this paper is to study the Hermite-Hadamard type inequality
for r-preinvex and ({\alpha}, m)-preinvex function which is based on Sugeno
integral.


  We consider a synchronized, circular-orbit binary consisting of a polytrope
with index n and a point-mass object, and use a self-consistent field method to
construct the equilibrium structure of the polytrope under rotational and tidal
perturbations. Our self-consistent field method is distinct from others in that
the equilibrium orbital angular velocity is calculated automatically rather
than being prescribed, which is crucial for obtaining apsidal motion rates
accurately. We find that the centrifugal and tidal forces make perturbed stars
more centrally condensed and larger in size. For n=1.5 polytopes with fixed
entropy, the enhancement factor in stellar radii is about 23% and 4-8% for mu=1
and sim0.1-0.9, respectively, where mu is the fractional mass of the polytrope
relative to the total. The centrifugal force dominates the tidal force in
determining the equilibrium structure provided mu > 0.13-0.14 for n > 1.5. The
shape and size of rotationally- and tidally-perturbed polytropes are well
described by the corresponding Roche models as long as n > 2. The apsidal
motion rates calculated for circular-orbit binaries under the equilibrium tide
condition agree well with the predictions of the classical formula only when
the rotational and tidal perturbations are weak. When the perturbations are
strong as in critical configurations, the classical theory underestimates the
real apsidal motion rates by as much as 50% for n=1.5 polytropes, although the
discrepancy becomes smaller as n increases. For practical uses, we provide
fitting formulae for various quantities including the density concentration,
volume radius, and effective internal structure constant, as functions of mu
and the perturbation parameters.


  The human thalamus is a highly connected subcortical grey-matter structure
within the brain. It comprises dozens of nuclei with different function and
connectivity, which are affected differently by disease. For this reason, there
is growing interest in studying the thalamic nuclei in vivo with MRI. Tools are
available to segment the thalamus from 1 mm T1 scans, but the contrast of the
lateral and internal boundaries is too faint to produce reliable segmentations.
Some tools have attempted to incorporate information from diffusion MRI in the
segmentation to refine these boundaries, but do not generalise well across
diffusion MRI acquisitions. Here we present the first CNN that can segment
thalamic nuclei from T1 and diffusion data of any resolution without retraining
or fine tuning. Our method builds on a public histological atlas of the
thalamic nuclei and silver standard segmentations on high-quality diffusion
data obtained with a recent Bayesian adaptive segmentation tool. We combine
these with an approximate degradation model for fast domain randomisation
during training. Our CNN produces a segmentation at 0.7 mm isotropic
resolution, irrespective of the resolution of the input. Moreover, it uses a
parsimonious model of the diffusion signal at each voxel (fractional anisotropy
and principal eigenvector) that is compatible with virtually any set of
directions and b-values, including huge amounts of legacy data. We show results
of our proposed method on three heterogeneous datasets acquired on dozens of
different scanners. An implementation of the method is publicly available at
https://freesurfer.net/fswiki/ThalamicNucleiDTI.


  We formulate the notion of the classical
Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) reaction diffusion equation
associated with a homogeneous conservative fragmentation process and study its
traveling waves. Specifically, we establish existence, uniqueness and
asymptotics. In the spirit of classical works such as McKean [Comm. Pure Appl.
Math. 28 (1975) 323-331] and [Comm. Pure Appl. Math. 29 (1976) 553-554], Neveu
[In Seminar on Stochastic Processes (1988) 223-242 Birkh\"{a}user] and Chauvin
[Ann. Probab. 19 (1991) 1195-1205], our analysis exposes the relation between
traveling waves and certain additive and multiplicative martingales via laws of
large numbers which have been previously studied in the context of
Crump-Mode-Jagers (CMJ) processes by Nerman [Z. Wahrsch. Verw. Gebiete 57
(1981) 365-395] and in the context of fragmentation processes by Bertoin and
Martinez [Adv. in Appl. Probab. 37 (2005) 553-570] and Harris, Knobloch and
Kyprianou [Ann. Inst. H. Poincar\'{e} Probab. Statist. 46 (2010) 119-134]. The
conclusions and methodology presented here appeal to a number of concepts
coming from the theory of branching random walks and branching Brownian motion
(cf. Harris [Proc. Roy. Soc. Edinburgh Sect. A 129 (1999) 503-517] and Biggins
and Kyprianou [Electr. J. Probab. 10 (2005) 609-631]) showing their
mathematical robustness even within the context of fragmentation theory.


  We systematically investigate the crystal structure of Ba-doped phenanthrene
with various Ba doping levels by the first principle calculation method
combining with the X-ray diffraction (XRD) spectra simulation. The optimized
lattice parameters and the simulated XRD spectra of Ba$_2$phenanthrene are in
good agreement with the experiment ones, and the strength difference of a few
of XRD peaks can be explained by the existence of undoped phenanthrene in the
experimental sample. Although the stoichiometry ratio of Ba atom and
phenanthrene molecule is 1.5:1, the simulated XRD spectra, space group symmetry
and the optimized lattice parameters of Ba$_{1.5}$phenanthrene are not
consistent to the measured values. The sample of Ba-doped phenanthrene is
deduced to be the mixture of Ba$_2$phenanthrene and some amount of undoped
phenanthrene, instead of uniform Ba$1.5$phenanthrene. Our calculations indicate
that Ba$_2$phenanthrene is a semiconductor with a small energy gap less than
0.05 eV. Our findings provide the fundamental information of crystal structure
and electronic properties of Ba-doped phenanthrene superconductor.


  We demonstrate paired generation of a single photo-electron in a quantum dot
and a single photon from a single polarization-entangled photon pair that is
generated by spontaneous parametric down conversion. The electron is reated in
a GaAs quantum dot via inter-band resonantexcitation by irradiating one of the
paired photons on the dot, while the remaining photon is detected by a single
photon counter. Because the paired photons are generated simultaneously, the
photo-electron and the remaining photon should be observed as a coincident
event if the traveling distance is equivalent between them. The coincidence is
probabilistic due to the probabilistic generation of the paired photon. We
observe the probability of finding the photon with the photo-electron detection
substantially higher then that without the photo-electron detection and derive
the coincident rate comparable to the emission rate of the original photon
pairs.


  A \emph{trace} of a sequence is generated by deleting each bit of the
sequence independently with a fixed probability. The well-studied \emph{trace
reconstruction} problem asks how many traces are required to reconstruct an
unknown binary sequence with high probability. In this paper, we study the
multivariate version of this problem for matrices and hypermatrices, where a
trace is generated by deleting each row/column of the matrix or each slice of
the hypermatrix independently with a constant probability. Previously,
Krishnamurthy et al. showed that $\exp(\widetilde{O}(n^{d/(d+2)}))$ traces
suffice to reconstruct any unknown $n\times n$ matrix (for $d=2$) and any
unknown $n^{\times d}$ hypermatrix. By developing a dimension reduction
procedure and establishing a multivariate version of the Littlewood-type
result, we improve this upper bound by showing that
$\exp(\widetilde{O}(n^{3/7}))$ traces suffice to reconstruct any unknown
$n\times n$ matrix, and $\exp(\widetilde{O}(n^{3/5}))$ traces suffice to
reconstruct any unknown $n^{\times d}$ hypermatrix. This breaks the tendency to
trivial $\exp(O(n))$ as the dimension $d$ grows.


  Due to popularization of internet and e-commerce, more and more people
getting involved in online shopping market. A large number of companies have
been transferred to the internet where online customers have been increased due
to easy access. The online business facilitates people to communicate without
knowing each other. The e-commerce systems are the combination of commerce
behavior and internet technologies. Therefore, trust aspects are positive
elements in buyer-seller transactions and a potential source of competitive
e-commerce industry. There are two different approaches to handle the trust.
The first approach has a solid authentication set of rules where decisions are
made on some digital or logical rules called policy based trust mechanism. The
second approach is a decentralized trust approach where reputation assembled
and shared in distributed environment called reputation based trust mechanism.
Objectives: In this thesis, the strengths and weaknesses of policy and
reputation based trust mechanisms have been identified through systematic
literature review and industrial interviews. Furthermore, the process of
integrated trust mechanism has been proposed. The integrated trust mechanism is
proposed through mapping process, weakness of one mechanism with the strength
of other. The proposed integrated trust mechanism was validated by conducting
experiment with buyer/seller scenario in auction system. The analysis of
collected results indicated that proposed integrated trust mechanism improved
the trust of buyer against eBay and Tradera. At the end, we have discussed some
key points that may affect trust relationship between seller and buyer.
Furthermore, there is a need for further validation of proposed trust mechanism
in auction system/e-commerce industry.


  We interpret steady linear statistical inverse problems as artificial dynamic
systems with white noise and introduce a stochastic differential equation (SDE)
system where the inverse of the ending time $T$ naturally plays the role of the
squared noise level. The time-continuous framework then allows us to apply
classical methods from data assimilation, namely the Kalman-Bucy filter and
3DVAR, and to analyze their behaviour as a regularization method for the
original problem. Such treatment offers some connections to the famous
asymptotical regularization method, which has not yet been analyzed in the
context of random noise. We derive error bounds for both methods in terms of
the mean-squared error under standard assumptions and discuss commonalities and
differences between both approaches. If an additional tuning parameter $\alpha$
for the initial covariance is chosen appropriately in terms of the ending time
$T$, one of the proposed methods gains order optimality. Our results extend
theoretical findings in the discrete setting given in the recent paper Iglesias
et al. (2017). Numerical examples confirm our theoretical results.


  We compute the electrical and thermal conductivities and Hall conductivities
of the $d$-density wave (DDW) state in the low-temperature
impurity-scattering-dominated regime for low-dopings, at which they are
dominated by nodal quasiparticles. We show that the longitudinal conductivity
in this limit in the DDW state is not Drude-like. However, the thermal
conductivty is Drude-like; this is a reflection of the discrepancy between
electrical and thermal transport at finite frequency in the DDW state. An
extreme example of this occurs in the $\mu=0$, $\tau\to\infty$ limit, where
there is a strong violation of the Wiedemann-Franz law:
${\kappa_{xx}}/{\sigma_{xx}} \propto {T^2}$ at $\omega=0$ and
${\kappa_{xx}}/{\sigma_{xx}}=0$ at finite frequency. The DDW electrical and
thermal Hall conductivities are linear in the magnetic field, $B$, for weak
fields. The formation of Landau levels at the nodes leads to the quantization
of these Hall conductivities at high fields. In all of these ways, the
quasiparticles of the DDW state differ from those of the $d_{{x^2}-{y^2}}$
superconducting (DSC) state.


  In this work, we experimentally demonstrate two key building blocks for
realizing Binary/Ternary Neural Networks (BNNs/TNNs): (i) 130 nm CMOS based
sigmoidal neurons and (ii) HfOx based multi-level (MLC) OxRAM-synaptic blocks.
An optimized vector matrix multiplication programming scheme that utilizes the
two building blocks is also presented. Compared to prior approaches that
utilize differential synaptic structures, a single device per synapse with two
sets of READ operations is used. Proposed hardware mapping strategy shows
performance change of <5% (decrease of 2-5% for TNN, increase of 0.2% for BNN)
compared to ideal quantized neural networks (QNN) with significant memory
savings in the order of 16-32x for classification problem on Fashion MNIST
(FMNIST) dataset. Impact of OxRAM device variability on the performance of
Hardware QNN (BNN/TNN) is also analyzed.


  We study the determinant $\det(I-K_{\textnormal{PII}})$ of an integrable
Fredholm operator $K_{\textnormal{PII}}$ acting on the interval $(-s,s)$ whose
kernel is constructed out of the $\Psi$-function associated with the
Hastings-McLeod solution of the second Painlev\'e equation. This Fredholm
determinant describes the critical behavior of the eigenvalue gap probabilities
of a random Hermitian matrix chosen from the Unitary Ensemble in the bulk
double scaling limit near a quadratic zero of the limiting mean eigenvalue
density. Using the Riemann-Hilbert method, we evaluate the large
$s$-asymptotics of $\det(I-K_{\textnormal{PII}})$.


  We carry out a detailed superspace analysis of the OPE of two N=2
stress-tensor multiplets. Knowledge of the multiplets appearing in the
expansion, together with the two-dimensional chiral algebra description of N=2
SCFTs, imply an analytic bound on the central charge c. This bound is valid for
any N=2 SCFT regardless of its matter content and flavor symmetries, and is
saturated by the simplest Argyres-Douglas fixed point. We also present a
partial conformal block analysis for the scalar superconformal primary of the
multiplet.


  In 1987 Brehm and K\"uhnel showed that any combinatorial $d$-manifold with
less than $3d/2+3$ vertices is PL homeomorphic to the sphere and any
combinatorial $d$-manifold with exactly $3d/2+3$ vertices is PL homeomorphic to
either the sphere or a manifold like a projective plane in the sense of Eells
and Kuiper. The latter possibility may occur for $d\in\{2,4,8,16\}$ only. There
exist a unique $6$-vertex triangulation of $\mathbb{RP}^2$, a unique $9$-vertex
triangulation of $\mathbb{CP}^2$, and at least three $15$-vertex triangulations
of $\mathbb{HP}^2$. However, until now, the question of whether there exists a
$27$-vertex triangulation of a manifold like the octonionic projective plane
has remained open. We solve this problem by constructing a lot of examples of
such triangulations. Namely, we construct $634$ vertex-transitive $27$-vertex
combinatorial $16$-manifolds like the octonionic projective plane. Four of them
have symmetry group $\mathrm{C}_3^3\rtimes \mathrm{C}_{13}$ of order $351$, and
the other $630$ have symmetry group $\mathrm{C}_3^3$ of order $27$. Further, we
construct more than $10^{103}$ non-vertex-transitive $27$-vertex combinatorial
$16$-manifolds like the octonionic projective plane. Most of them have trivial
symmetry group, but there are also symmetry groups $\mathrm{C}_3$,
$\mathrm{C}_3^2$, and $\mathrm{C}_{13}$. We conjecture that all the
triangulations constructed are PL homeomorphic to the octonionic projective
plane $\mathbb{OP}^2$. Nevertheless, we have no proof of this fact so far.


  We focus on the Clifford-algebra valued variable coefficients Riemann-Hilbert
boundary value problems $\big{(}$for short RHBVPs$\big{)}$ for axially
monogenic functions on Euclidean space $\mathbb{R}^{n+1},n\in \mathbb{N}$. With
the help of Vekua system, we first make one-to-one correspondence between the
RHBVPs considered in axial domains and the RHBVPs of generalized analytic
function on complex plane. Subsequently, we use it to solve the former
problems, by obtaining the solutions and solvable conditions of the latter
problems, so that we naturally get solutions to the corresponding Schwarz
problems. In addition, we also use the above method to extend the case to
RHBVPs for axially null-solutions to
$\big{(}\mathcal{D}-\alpha\big{)}\phi=0,\alpha\in\mathbb{R}$.


  For sufficiently strong in-plane magnetic field a $\nu_T=1$ bilayer quantum
Hall pseudo-ferromagnet is expected to exhibit a soliton lattice. For
sufficiently close layers and large in-plane field, we predict this
incommensurate ``planar'' phase $P_I$ to undergo a reentrant pseudo-spin
canting transition to an incommensurate state $C_I$, with a finite out-of-plane
pseudo-magnetization component, corresponding to an interlayer charge imbalance
in regions between solitons. At $T>0$ the transition is in the 2d compressible
Ising universality class, and at T=0, the quantum transition is in heretofore
unexplored universality class. The striking experimental signatures are the
universal nonlinear charge-voltage and in-plane field relations, and the
divergence of the differential bilayer capacitance at the transition, resulting
in a bilayer capacitor that spontaneously charges itself, even in the absence
of an applied interlayer voltage.