  Presented here is a study of jets produced in association with vector bosons
production in pp collisions at \surds = 7 TeV using the full CMS 2010 data set,
corresponding to an integrated luminosity of 36 \pm 1.4 pb-1. The transverse
energy distribution of the reconstructed leading jets is measured and compared
to theoretical expectations. The jet multiplicity distributions are corrected
for efficiency and unfolded. The ratios of multiplicities, {\sigma}(V+ \geq n
jets)/{\sigma}(V+ \geq (n - 1) jets) and {\sigma}(V+ \geq n jets)/{\sigma}(V)
where n stands for number of jets, are also presented along with the first test
of the Berends-Giele scaling at \surds = 7 TeV.


  In the assembly process of printed circuit boards (PCB), most of the errors
are caused by solder joints in Surface Mount Devices (SMD). In the literature,
traditional feature extraction based methods require designing hand-crafted
features and rely on the tiered RGB illumination to detect solder joint errors,
whereas the supervised Convolutional Neural Network (CNN) based approaches
require a lot of labelled abnormal samples (defective solder joints) to achieve
high accuracy. To solve the optical inspection problem in unrestricted
environments with no special lighting and without the existence of error-free
reference boards, we propose a new beta-Variational Autoencoders (beta-VAE)
architecture for anomaly detection that can work on both IC and non-IC
components. We show that the proposed model learns disentangled representation
of data, leading to more independent features and improved latent space
representations. We compare the activation and gradient-based representations
that are used to characterize anomalies; and observe the effect of different
beta parameters on accuracy and on untwining the feature representations in
beta-VAE. Finally, we show that anomalies on solder joints can be detected with
high accuracy via a model trained on directly normal samples without designated
hardware or feature engineering.


  In this paper, we focus our attention on the large capacities unsplittable
flow problem in a game theoretic setting. In this setting, there are selfish
agents, which control some of the requests characteristics, and may be
dishonest about them. It is worth noting that in game theoretic settings many
standard techniques, such as randomized rounding, violate certain monotonicity
properties, which are imperative for truthfulness, and therefore cannot be
employed. In light of this state of affairs, we design a monotone deterministic
algorithm, which is based on a primal-dual machinery, which attains an
approximation ratio of $\frac{e}{e-1}$, up to a disparity of $\epsilon$ away.
This implies an improvement on the current best truthful mechanism, as well as
an improvement on the current best combinatorial algorithm for the problem
under consideration. Surprisingly, we demonstrate that any algorithm in the
family of reasonable iterative path minimizing algorithms, cannot yield a
better approximation ratio. Consequently, it follows that in order to achieve a
monotone PTAS, if exists, one would have to exert different techniques. We also
consider the large capacities \textit{single-minded multi-unit combinatorial
auction problem}. This problem is closely related to the unsplittable flow
problem since one can formulate it as a special case of the integer linear
program of the unsplittable flow problem. Accordingly, we obtain a comparable
performance guarantee by refining the algorithm suggested for the unsplittable
flow problem.


  The short range ordered magnetic correlations have been studied in half doped
La0.5Ca0.5-xSrxMnO3 (x = 0.1, 0.3 and 0.4) compounds by polarized neutron
scattering technique. On doping Sr2+ for Ca2+ ion, these compounds with x =
0.1, 0.3, and 0.4 exhibit CE-type, mixture of CE-type and A-type, and A-type
antiferromagnetic ordering, respectively. Magnetic diffuse scattering is
observed in all the compounds above and below their respective magnetic
ordering temperatures and is attributed to magnetic polarons. The correlations
are primarily ferromagnetic in nature above T\_N, although a small
antiferromagnetic contribution is also evident. Additionally, in samples x =
0.1 and 0.3 with CE-type antiferromagnetic ordering, superlattice diffuse
reflections are observed indicating correlations between magnetic polarons. On
lowering temperature below T\_N the diffuse scattering corresponding to
ferromagnetic correlations is suppressed and the long range ordered
antiferromagnetic state is established. However, the short range ordered
correlations indicated by enhanced spin flip scattering at low Q coexist with
long range ordered state down to 3K. In x = 0.4 sample with A-type
antiferromagnetic ordering, superlattice diffuse reflections are absent.
Additionally, in comparison to x = 0.1 and 0.3 sample, the enhanced spin flip
scattering at low Q is reduced at 310K, and as temperature is reduced below
200K, it becomes negligibly low. The variation of radial correlation function,
g(r) with temperature indicates rapid suppression of ferromagnetic correlations
at the first nearest neighbor on approaching TN. Sample x = 0.4 exhibits growth
of ferromagnetic phase at intermediate temperatures (~ 200K). This has been
further explored using SANS and neutron depolarization techniques.


  Cosmological models typically neglect the complicated nature of the spacetime
manifold at small scales in order to hypothesize idealized general relativistic
solutions for describing the average dynamics of the Universe. Although these
solutions are remarkably successful in accounting for data, they introduce a
number of puzzles in cosmology, and their foundational assumptions are
therefore important to test. In this paper, we go beyond the usual assumptions
in cosmology and propose a formalism for averaging the local general
relativistic spacetime on an observer's past null cone: we formulate average
properties of light fronts as they propagate from a cosmological emitter to an
observer. The energy-momentum tensor is composed of an irrotational dust source
and a cosmological constant -- the same components as in the $\Lambda$CDM model
for late cosmic times -- but the metric solution is not \emph{a
priori}constrained to be locally homogeneous or isotropic. This generally makes
the large-scale dynamics depart from that of a simple Friedmann--Lema\^\i
tre--Robertson--Walker solution through \emph{backreaction} effects. Our
formalism quantifies such departures through a fully covariant system of
area-averaged equations on the light fronts propagating towards an observer,
which can be directly applied to analytical and numerical investigations of
cosmic observables. For this purpose, we formulate light front averages of
observable quantities, including the effective angular diameter distance and
the cosmological redshift drift and we also discuss the backreaction effects
for these observables.


  This manuscript was originally submitted to Nature for consideration as a
"Brief Communication" in response to a "Corrigendum" that appeared in 2006 (1)
to an earlier paper in Nature. That corrigendum was the subject of a Nature
editorial (2) stating that "key data were misrepresented by the authors, both
during the review process and in the final published version of the paper" and
it claimed to provide an explanation for alterations in their data that had the
effect of changing their priority claim from a result no better than previous
work by Isaacson and Scheinfein that was 1 Angstrom shy of atomic resolution to
what appeared to be atomic resolution. In this manuscript we show that this
explanation is physically inconsistent with the evolution of their data. When
originally submitted to Nature, the manuscript was peer-reviewed, deemed
"carefully and properly argued" and recommended for publication with
appropriate responses from the corrigendum authors. Subsequent exchanges with
those authors did not reach a satisfactory state and publication did not occur.
We now have learnt that an article is likely to appear in Nature concerning the
circumstances surrounding the concerns expressed in this initial document and
we consider it important and relevant that this document and the supplementary
material be made available in the public domain. As to the question of proper
attribution of priority, we would suggest instead citing the concurrent work of
Batson (3).
  1. Browning, N.D., Chisholm, M.F., and Pennycook, S.J.
Corrigendum:Atomic-resolution chemical analysis using a scanning transmission
electron microscope, Nature 444, 235 (2006). 2. Editorial. Correction or
retraction? Nature 444, 123-124 (2006). 3. Batson, P.E. (1993). Simultaneous
STEM imaging and electron energy-loss spectroscopy with atomic-column
sensitivity. Nature 366, 727-728.


  A joint communication and channel state estimation problem is investigated,
in which reliable information transmission over a noisy channel, and
high-fidelity estimation of the channel state, are simultaneously sought. The
tradeoff between the achievable information rate and the estimation distortion
is quantified by formulating the problem as a constrained channel coding
problem, and the resulting capacity-distortion function characterizes the
fundamental limit of the joint communication and channel estimation problem.
The analytical results are illustrated through case studies, and further issues
such as multiple cost constraints, channel uncertainty, and capacity per unit
distortion are also briefly discussed.


  Future projection of climate is typically obtained by combining outputs from
multiple Earth System Models (ESMs) for several climate variables such as
temperature and precipitation. While IPCC has traditionally used a simple model
output average, recent work has illustrated potential advantages of using a
multitask learning (MTL) framework for projections of individual climate
variables. In this paper we introduce a framework for hierarchical multitask
learning (HMTL) with two levels of tasks such that each super-task, i.e., task
at the top level, is itself a multitask learning problem over sub-tasks. For
climate projections, each super-task focuses on projections of specific climate
variables spatially using an MTL formulation. For the proposed HMTL approach, a
group lasso regularization is added to couple parameters across the
super-tasks, which in the climate context helps exploit relationships among the
behavior of different climate variables at a given spatial location. We show
that some recent works on MTL based on learning task dependency structures can
be viewed as special cases of HMTL. Experiments on synthetic and real climate
data show that HMTL produces better results than decoupled MTL methods applied
separately on the super-tasks and HMTL significantly outperforms baselines for
climate projection.


  The topology of social networks can be understood as being inherently
dynamic, with edges having a distinct position in time. Most characterizations
of dynamic networks discretize time by converting temporal information into a
sequence of network "snapshots" for further analysis. Here we study a highly
resolved data set of a dynamic proximity network of 66 individuals. We show
that the topology of this network evolves over a very broad distribution of
time scales, that its behavior is characterized by strong periodicities driven
by external calendar cycles, and that the conversion of inherently
continuous-time data into a sequence of snapshots can produce highly biased
estimates of network structure. We suggest that dynamic social networks exhibit
a natural time scale \Delta_{nat}, and that the best conversion of such dynamic
data to a discrete sequence of networks is done at this natural rate.


  We discuss the internal structure of radially excited charmonium mesons based
on the equal-time and Coulomb gauge Bethe-Salpeter (BS) amplitudes, which are
obtained in lattice QCD. Our simulations are performed with a relativistic
heavy-quark action for the charm quark on the 2+1 flavor PACS-CS gauge
configurations at the lightest pion mass, $M_{\pi}=156(7)$ MeV. The variational
method is applied to the study of optimal charmonium operator for ground and
first excited states of $S$-wave charmonia. We successfully calculate the BS
wave functions of $\eta_c(2S)$ and $\psi(2S)$ states, as well as $\eta_c(1S)$
and $J/\psi$ states, and then estimate the root-mean-square radii of both the
$1S$ and $2S$ charmonium states. We also examine whether a series of the BS
wave functions from the ground state to excited states can be described by a
single set of the spin-independent and spin-dependent interquark potentials
with a unique quark mass. It is found that the quark kinetic mass and, both the
central and spin-spin charmonium potentials, determined from the $2S$ wave
functions, fairly agree with the ones from the $1S$ wave functions. This
strongly supports the validity of the potential description for the charmonium
system, at least, below open-charm threshold.


  We present two alternative complete sets of static modes of a homogeneous
dielectric sphere, for their use in the resonant-state expansion (RSE), a
rigorous perturbative method in electrodynamics. Physically, these modes are
needed to correctly describe the static electric field of a charge
redistribution within the optical system due to a perturbation of the
permittivity. We demonstrate the convergence of the RSE towards the exact
result for a perturbation describing a size reduction of the basis sphere. We
then revisit the quarter-sphere perturbation treated in [Doost {\it et al.},
Phys. Rev. A {\bf 90}, 013834 (2014)], where only a single static mode per each
angular momentum was introduced, and show that using a complete set of static
modes leads to a small, though non-negligible correction of the RSE result,
improving the agreement with finite-element simulations. As another example of
applying the RSE with a complete set of static modes, we calculate the resonant
states of a dielectric cylinder, also comparing the result with a
finite-element simulation.


  Linear transformation of the inputs alters the training performance of
feed-forward networks that are otherwise equivalent. However, most linear
transforms are viewed as a pre-processing operation separate from the actual
training. Starting from equivalent networks, it is shown that pre-processing
inputs using linear transformation are equivalent to multiplying the negative
gradient matrix with an autocorrelation matrix per training iteration. Second
order method is proposed to find the autocorrelation matrix that maximizes
learning in a given iteration. When the autocorrelation matrix is diagonal, the
method optimizes input gains. This optimal input gain (OIG) approach is used to
improve two first-order two-stage training algorithms, namely back-propagation
(BP) and hidden weight optimization (HWO), which alternately update the input
weights and solve linear equations for output weights. Results show that the
proposed OIG approach greatly enhances the performance of the first-order
algorithms, often allowing them to rival the popular Levenberg-Marquardt
approach with far less computation. It is shown that HWO is equivalent to BP
with Whitening transformation applied to the inputs. HWO effectively combines
Whitening transformation with learning. Thus, OIG improved HWO could be a
significant building block to more complex deep learning architectures.


  In this work we consider basic principles and problems of the standard
quantum mechanical formalism. Especially we consider final detection procedure
(collapse) as a quantum-classical continuous phase transition with spontaneous
(non-dynamical) unitary symmetry (superposition) breaking (effective hiding).
Practically, collapse as an effective (non-absolute) phenomena can be
considered as an especial case of the general formalism of spontaneous symmetry
breaking (with applications in many different domains of the physics, e.g. in
elasticity of rigid bodies, quantum theory of ferromagnetism, quantum theory of
electro-weak interactions as well as in chaotic inflation cosmology). General
theory of the detection procedure (collapse) we consider in real experiment of
single photon interference at beam splitter with final detection of the photon
coordinate by usual photographic plate.


  Real-time scene understanding has become crucial in many applications such as
autonomous driving. In this paper, we propose a deep architecture, called
BlitzNet, that jointly performs object detection and semantic segmentation in
one forward pass, allowing real-time computations. Besides the computational
gain of having a single network to perform several tasks, we show that object
detection and semantic segmentation benefit from each other in terms of
accuracy. Experimental results for VOC and COCO datasets show state-of-the-art
performance for object detection and segmentation among real time systems.


  In this note, we study the integrodifferential operator $(I-\Delta)^{\log}$
corresponding to the logarithmic symbol $\log(1+|\xi|^2)$, which is a singular
integral operator given by $$
  (I-\Delta)^{\log}
u(x)=d_{N}\int_{\mathbb{R}^N}\frac{u(x)-u(x+y)}{|y|^{N}}\omega(|y|)\, dy, $$
where $d_N=\pi^{-\frac{N}{2}}$,
$\omega(r)=2^{1-\frac{N}{2}}r^{\frac{N}{2}}K_{\frac{N}{2}}(r)$ and $K_{\nu}$ is
the modified Bessel function of second kind with index $\nu$. This operator is
the L\'evy generator of the variance gamma process and arises as derivative
$\partial_s\Big|_{s=0}(I-\Delta)^s$ of fractional relativistic Schr\"{o}dinger
operators at $s=0$. In order to study associated Dirichlet problems in bounded
domains, we first introduce the functional analytic framework and some
properties related to $(I-\Delta)^{\log}$, which allow to characterize the
induced eigenvalue problem and Faber-Krahn type inequality. We also derive a
decay estimate in $\mathbb{R}^N$ of the Poisson problem and investigate small
order asymptotics $s\to 0^+$ of Dirichlet eigenvalues and eigenfunctions of
$(I-\Delta)^s$ in a bounded open Lipschitz set.


  In mathematics information is a number that measures uncertainty (entropy)
based on a probabilistic distribution, often of an obscure origin. In real life
language information is a datum, a statement, more precisely, a formula. But
such a formula should be justified by a proof. I try to formalize this
perception of information. The measure of informativeness of a proof is based
on the set of proofs related to the formulas under consideration. This set of
possible proofs (`a knowledge base') defines a probabilistic measure, and
entropic weight is defined using this measure. The paper is mainly conceptual,
it is not clear where and how this approach can be applied.


  Given an action of the one-dimensional torus on a projective variety, the
associated Chow quotient arises as a natural parameter space of invariant
$1$-cycles, which dominates the GIT quotients of the variety. In this paper we
explore the relation between the Chow and the GIT quotients of a variety,
showing how to construct explicitly the former upon the latter via successive
blowups under suitable assumptions. We also discuss conditions for the
smoothness of the Chow quotient, and present some examples in which it is
singular.


  The displacement of conventional generation in favor of stochastic renewable
requires increasing regulation duties from the remaining dispatchable
resources. In high- and medium-head hydropower plants (HPPs), providing
regulation services to the grid and frequently changing the plant's set-point
causes water hammer, which engenders pressure and stress transients within the
pressurized conduits, especially the penstock, damaging it in the long run.
This paper proposes a model predictive control (MPC) that explicitly models the
hydraulic transients within the penstock. It achieves to reduce the mechanical
loads on the penstock wall, and, consequently, fatigue effectively. Thanks to a
suitable linearization of the plant model, the optimization problem underlying
the MPC scheme is convex and can be solved with off-the-shelf optimization
libraries. The performance of the proposed controller is tested with numerical
simulations on a 230MW medium-head HPP with Francis turbine providing primary
frequency control. Simulation results show substantially reduced penstock
fatigue, existing approaches outperformed, and problem resolution times
compatible with real-time control requirements.


  Band Structures and optical matrix elements of quantum wires(QWR's) made of
short-period superlattices(SPS) with strain-induced lateral ordering(SILO) are
investigated theoretically via an effective bond-orbital model(EBOM) combined
with a valence-force field(VFF) model. Valence-band anistropy, band mixing, and
effects due to local strain distribution at the atomistic level are all taken
into account. In particular, Ga(1-x)In(x)As QWR's grown by SILO process are
considered. A VFF model is used to find the equilibrium atomic positions in the
SILO QWR structure by minimizing the lattice energy. The strain tensor at each
atomic(In or GA) site is then obtained and included in the calculations of
electronic states and optical peroperties. It is found that different local
arrangement of atoms leads to very different strain distribution, which in term
alters the optical properties. In particular, we found that the optical
anisotropy can be reversed due to the change in shear strain caused by the
inter-change of atomic positions. Good agreement with the existing experimental
data on band gap and optical anisotropy can be obtained when a 2D alloy
structure with lateral composition modulation in the InAs/GaAs interface planes
of the SPS is used. Our studies revealed the possibility of "shear-strain
engineering" in SILO QWR light-emitting devices to achieve desired optical
anisotropy.


  We are interested in measures of central tendency for a population on a
network, which is modeled by a metric tree. The location parameters that we
study are generalized Fr\'echet means obtained by minimizing the objective
function $\alpha \mapsto E[\ell(d(\alpha,X))]$ where $\ell$ is a generic convex
nondecreasing loss.
  We leverage the geometry of the tree and the geodesic convexity of the
objective to develop a notion of directional derivative in the tree, which
helps up locate and characterize the minimizers.
  Estimation is performed using a sample analog. We extend to a metric tree the
notion of stickiness defined by Hotz et al. (2013), we show that this
phenomenon has a non-asymptotic component and we obtain a sticky law of large
numbers. For the particular case of the Fr\'echet median, we develop
non-asymptotic concentration bounds and sticky central limit theorems.


  The spin structure of the matrix element for the reactions $\gamma+ N\to Y_c
+{D}^*$, where $Y_c=\Lambda_c^+(2285)$, $\Sigma_c(2455)$ are charmed baryons
with spin 1/2, and $D^*(2010)$ is the vector charmed meson, can be
parametrized, in collinear regime, in terms of three independent scalar
amplitudes, which are functions of the photon energy $E_{\gamma}$, only. In
framework of an effective Lagrangian approach generalized to charm
photoproduction, we calculate the energy dependence of the differential cross
section, the density matrix element of $\bar{D}^*$, $\rho_{11}$, the asymmetry
$A_z$ in the collision of circularly polarized photons with polarized nucleons,
and the polarization of the produced $Y_c$-hyperon, $P_z$, in the collision of
circularly polarized photons with unpolarized target. All these polarization
observables either vanish or are large, in absolute value, with a smooth
$E_{\gamma}$-dependence, and differ for $\Lambda_c^+$ and $\Sigma_c$
--production.


  The ellipticity function of cosmic voids exhibits strong dependence on the
amplitude of the linear matter power spectrum. Analyzing the most recent void
catalogs constructed by Foster and Nelson from the fifth data release of the
Sloan Digital Sky Survey, we measure observationally the ellipticity function
of giant galaxy voids. Then, we incorporate the redshift distortion and galaxy
bias effect into the analytic model of the void ellipticity function and fit it
to the observational result by adjusting the value of the power-spectrum
normalization with the help of the generalized chi^{2}-minimization method. The
best-fit normalization of the linear power spectrum is found to be
sigma_{8}=0.90+/-0.04. Our result is higher than the WMAP sigma_{8}-value but
consistent with that from the recent work of Liu and Li who have constructed a
new improved CMB map independently.


  High-magnetic-field pulsars represent an important class of objects for
studying the relationship between magnetars and radio pulsars. Here we report
on four Chandra observations of the high-magnetic-field pulsar J1718-3718
($B=7.4\times10^{13}$\,G) taken in 2009 as well as on a re-analysis of 2002
Chandra observations of the region. We also report an improved radio position
for this pulsar based on ATCA observations. We detect X-ray pulsations at the
pulsar's period in the 2009 data, with pulsed fraction 52%$\pm$13% in the
0.8--2.0 keV band. We find that the X-ray pulse is aligned with the radio
pulse. The data from 2002 and 2009 show consistent spectra and fluxes; a merged
overall spectrum is well fit by a blackbody of temperature
$186^{+19}_{-18}$\,eV, slightly higher than predicted by standard cooling
models, however, the best-fit neutron star atmosphere model is consistent with
standard cooling. We find the bolometric luminosity $L^{\infty}_{\rm
bb}=4^{+5}_{-2} \times10^{32}$\,erg\,s$^{-1}\sim0.3\dot{E}$, for a distance of
4.5 kpc. We compile measurements of the temperatures of all X-ray detected
high-$B$ pulsars as well as those of low-$B$ radio pulsars and find evidence
for the former being on average hotter than the latter.


  We introduce a contextual quantum system comprising mutually complementary
observables organized into two or more collections of pseudocontexts with the
same probability sums of outcomes. These pseudocontexts constitute
non-orthogonal bases within the Hilbert space, featuring a state-independent
sum of probabilities. In other words, regardless of the initial state
preparation, the total probability remains constant but may be distinct from
unity. The measurement contextuality in this setup arises from the quantum
realizations of the hypergraph, which adhere to a specific bound on the linear
combination of probabilities. In contrast, classical realizations can surpass
this bound. The violation of quantum bounds stems from the inability of
classical ontological models, specifically the set-theoretic representation of
the hypergraph corresponding to the quantum observables' collections, to adhere
to and explain the observed statistics.


  The nonlocal behavior of quantum mechanics can be used to generate guaranteed
fresh randomness from an untrusted device that consists of two nonsignalling
components; since the generation process requires some initial fresh randomness
to act as a catalyst, one also speaks of randomness expansion. Colbeck and Kent
proposed the first method for generating randomness from untrusted devices,
however, without providing a rigorous analysis. This was addressed subsequently
by Pironio et al. [Nature 464 (2010)], who aimed at deriving a lower bound on
the min-entropy of the data extracted from an untrusted device, based only on
the observed non-local behavior of the device. Although that article succeeded
in developing important tools towards the acquired goal, it failed in putting
the tools together in a rigorous and correct way, and the given formal claim on
the guaranteed amount of min-entropy needs to be revisited. In this paper we
show how to combine the tools provided by Pironio et al., as to obtain a
meaningful and correct lower bound on the min-entropy of the data produced by
an untrusted device, based on the observed non-local behavior of the device.
Our main result confirms the essence of the improperly formulated claims of
Pironio et al., and puts them on solid ground. We also address the question of
composability and show that different untrusted devices can be composed in an
alternating manner under the assumption that they are not entangled. This
enables for superpolynomial randomness expansion based on two untrusted yet
unentangled devices.


  Although many studies have successfully applied transfer learning to medical
image segmentation, very few of them have investigated the selection strategy
when multiple source tasks are available for transfer. In this paper, we
propose a prior knowledge guided and transferability based framework to select
the best source tasks among a collection of brain image segmentation tasks, to
improve the transfer learning performance on the given target task. The
framework consists of modality analysis, RoI (region of interest) analysis, and
transferability estimation, such that the source task selection can be refined
step by step. Specifically, we adapt the state-of-the-art analytical
transferability estimation metrics to medical image segmentation tasks and
further show that their performance can be significantly boosted by filtering
candidate source tasks based on modality and RoI characteristics. Our
experiments on brain matter, brain tumor, and white matter hyperintensities
segmentation datasets reveal that transferring from different tasks under the
same modality is often more successful than transferring from the same task
under different modalities. Furthermore, within the same modality, transferring
from the source task that has stronger RoI shape similarity with the target
task can significantly improve the final transfer performance. And such
similarity can be captured using the Structural Similarity index in the label
space.


  We present a randomized, inverse-free algorithm for producing an approximate
diagonalization of any $n \times n$ matrix pencil $(A,B)$. The bulk of the
algorithm rests on a randomized divide-and-conquer eigensolver for the
generalized eigenvalue problem originally proposed by Ballard, Demmel, and
Dumitriu [Technical Report 2010]. We demonstrate that this divide-and-conquer
approach can be formulated to succeed with high probability provided the input
pencil is sufficiently well-behaved, which is accomplished by generalizing the
recent pseudospectral shattering work of Banks, Garza-Vargas, Kulkarni, and
Srivastava [Foundations of Computational Mathematics 2022]. In particular, we
show that perturbing and scaling $(A,B)$ regularizes its pseudospectra,
allowing divide-and-conquer to run over a simple random grid and in turn
producing an accurate diagonalization of $(A,B)$ in the backward error sense.
The main result of the paper states the existence of a randomized algorithm
that with high probability (and in exact arithmetic) produces invertible $S,T$
and diagonal $D$ such that $||A - SDT^{-1}||_2 \leq \varepsilon$ and $||B -
ST^{-1}||_2 \leq \varepsilon$ in at most $O \left(\log^2 \left(
\frac{n}{\varepsilon} \right) T_{\text{MM}}(n) \right)$ operations, where
$T_{\text{MM}}(n)$ is the asymptotic complexity of matrix multiplication. This
not only provides a new set of guarantees for highly parallel generalized
eigenvalue solvers but also establishes nearly matrix multiplication time as an
upper bound on the complexity of inverse-free, exact arithmetic matrix pencil
diagonalization.


  We present a first-order symmetric hyperbolic system in the Ashtekar
formulation of general relativity for vacuum spacetime. We add terms from
constraint equations to the evolution equations with appropriate combinations,
which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev.
Lett. 79, 4732 (1997)]. However our system is different from theirs in the
points that we primarily use Hermiticity of a characteristic matrix of the
system to characterize our system "symmetric", discuss the consistency of this
system with reality condition, and show the characteristic speeds of the
system.


Paper has been withdrawn for major repairs.


  We calculate the phonons in a graphene nanoconstriction(GNC) in the presence
of a high current density. The Joule-heating, current-induced forces, and
coupling to electrode phonons is evaluated using first principles
nonequilibrium DFT-NEGF calculations. Close to a resonance in the electronic
structure we observe a strongly nonlinear heating with bias and breakdown of
the harmonic approximation. This behavior results from negatively damped
phonons driven by the current. The effect may limit the stability and capacity
of graphene nanoconstrictions to carry high currents.


  We investigate the current-phase relations of Al/InAs-quantum well planar
Josephson junctions fabricated using nanowire shadowing technique. Based on
several experiments, we conclude that the junctions exhibit an unusually large
second-order Josephson harmonic, the $\sin(2\varphi)$ term. First,
superconducting quantum interference devices (dc-SQUIDs) show half-periodic
oscillations, tunable by gate voltages as well as magnetic flux. Second,
Josephson junction devices exhibit kinks near half-flux quantum in supercurrent
diffraction patterns. Third, half-integer Shapiro steps are present in the
junctions. Similar phenomena are observed in Sn/InAs quantum well devices. We
perform data fitting to a numerical model with a two-component current phase
relation. Analysis including a loop inductance suggests that the sign of the
second harmonic term is negative. The microscopic origins of the observed
effect remain to be understood. We consider alternative explanations which can
account for some but not all of the evidence.


  In this article, we illustrate an algorithm for the computation of the weight
distribution of CRC codes. The recursive structure of CRC codes will give us an
iterative way to compute the weight distribution of their dual codes starting
from just some ``representative'' words. Thanks to MacWilliams Theorem, the
computation of the weight distribution of dual codes can be easily brought back
to that of CRC codes. This algorithm is a good alternative to the standard
algorithm that involves listing every word of the code.


  Given a map $f: X\rightarrow Y$ of simply connected spaces of finite type
such. The space of based loops at $f$ of the space of maps between $X$ and $Y$
is denoted by $\Omega_{f} Map(X,Y)$. For $n> 0$, we give a model categorical
interpretation of the existence (in functorial way) of an injective map of
$\mathbb{Q}$-vector spaces $\pi_{n} \Omega_{f}Map(X,Y_{\mathbb{Q}}) \rightarrow
HH^{-n}(C^{\ast}(Y),C^{\ast}(X)_{f})$, where $HH^{\ast}$ is the (negative)
Hochschild cohomology and $C^{\ast}(X)_{f}$ is the rational cochain complex
associated to $X$ equipped with a structure of $C^{\ast}(Y)$-differential
graded bimodule via the induced map of differential graded algebras $f^{\ast}:
C^{\ast}(Y)\rightarrow C^{\ast}(X)$. Moreover, we identifiy the image in
presice way by using the Hodge filtration on Hochschild cohomology. In
particular, when $X=Y$, we describe the fundamental group of the identity
component of the monoid of self equivalence of a (rationalization of) space $X$
i.e., $\pi_{1} Aut(X_{\mathbb{Q}})_{id}$.


  In this paper, we generalize Colding and Minicozzi's work \cite{CM} on the
stability of self-shrinkers in the hypersurface case to higher co-dimensional
cases. The first and second variation formulae of the $F$-functional are
derived and an equivalent condition to the stability in general codimension is
found. Moreover, we show that the closed Lagrangian self-shrinkers given by
Anciaux in \cite{An} are unstable.


  We generalize the approach of Brodsky {\it et al.} for the intrinsic charm
quark distribution in the nucleons to the light-quark sector involving
intrinsic $\bar u, \bar d, s$ and $\bar s$ sea quarks. We compare the
calculations with the existing $\bar d - \bar u$, $s + \bar s$, and $\bar u +
\bar d - s -\bar s$ data. The good agreement between the theory and the data is
interpreted as evidence for the existence of the intrinsic light-quark sea in
the nucleons. The probabilities for the $|uudu\bar{u}>$, $|uudd\bar{d}>$ and
$|uuds\bar{s}>$ Fock states are also extracted.


  A strongly-driven ($\Omega >> \gamma$) two level atom relaxes towards an
equilibrium state rho which is almost completely mixed. One interpretation of
this state is that it represents an ensemble average, and that an individual
atom is at any time in one of the eigenstates of $\rho$. The theory of Teich
and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete,
with an individual atom jumping stochastically between the two eigenstates when
a photon is emitted. The dressed atom theory is also supposed to describe the
quantum jumps of an individual atom due to photo-emissions. But the two
pictures are contradictory because the dressed states of the atom are almost
orthogonal to the eigenstates of $\rho$. In this paper we investigate three
ways of measuring the field radiated by the atom, which attempt to reproduce
the simple quantum jump dynamics of the dressed state or Teich and Mahler
models. These are: spectral detection (using optical filters), two-state jumps
(using adaptive homodyne detection) and orthogonal jumps (another adaptive
homodyne scheme). We find that the three schemes closely mimic the jumps of the
dressed state model, with errors of order $(3/4) (\gamma/\Omega)^{2/3}$, $(1/4)
(\gamma/\Omega)^{2}$, and $(3/4) (\gamma/\Omega)^{2}$ respectively. The
significance of this result to the program of environmentally-induced
superselection is discussed.


  Fairness AI aims to detect and alleviate bias across the entire AI
development life cycle, encompassing data curation, modeling, evaluation, and
deployment-a pivotal aspect of ethical AI implementation. Addressing data bias,
particularly concerning sensitive attributes like gender and race, reweighting
samples proves efficient for fairness AI. This paper contributes a systematic
examination of reweighting samples for traditional machine learning (ML)
models, employing five models for binary classification on the Adult Income and
COMPUS datasets with various protected attributes. The study evaluates
prediction results using five fairness metrics, uncovering the nuanced and
model-specific nature of reweighting sample effectiveness in achieving fairness
in traditional ML models, as well as revealing the complexity of bias dynamics.


  One strategy to obtain user location information in a wireless network
operating at millimeter wave (mmWave) is based on the exploitation of the
geometric relationships between the channel parameters and the user position.
These relationships can be easily built from the LoS path and/or first order
reflections, but high resolution channel estimates are required for high
accuracy. In this paper, we consider a mmWave MIMO system based on a hybrid
architecture, and develop first a low complexity channel estimation strategy
based on MOMP suitable for high dimensional channels, as those associated to
operating with large planar arrays. Then, a deep neural network (DNN) called
PathNet is designed to classify the order of the estimated channel paths, so
that only the line-of-sight (LOS) path and first order reflections are selected
for localization purposes. Next, a 3D localization strategy exploiting the
geometry of the environment is developed to operate in both LOS and
non-line-of-sight (NLOS) conditions, while considering the unknown clock offset
between the transmitter (TX) and the receiver (RX). Finally, a Transformer
based network exploiting attention mechanisms called ChanFormer is proposed to
refine the initial position estimate obtained from the geometric system of
equations that connects user position and channel parameters. Simulation
results obtained with realistic vehicular channels generated by ray tracing
indicate that sub-meter accuracy (<= 0.45 m) can be achieved for 95% of the
users in LOS channels, and for 50% of the users in NLOS conditions.


  The non isotropic and non central elliptical shape distributions via the Le
and Kendall SVD decomposition approach are derived in this paper in the context
of invariant polynomials and zonal polynomials. The so termed cone and disk
densities here obtained generalise some results of the literature. Finally,
some particular densities are applied in a classical data of Biology, and the
inference is performed after choosing the best model by using a modified BIC
criterion.


  Cognitive Radio (CR) promises an efficient utilization of radio spectrum
resources by enabling dynamic spectrum access to overcome the spectrum scarcity
problem. Cognitive Radio Sensor Networks (CRSNs) are one type of Wireless
Sensor Networks (WSNs) equipped with CR capabilities. CRSN nodes need to
operate energy-efficiently to extend network lifetime due to their limited
battery capacity. In this paper, for the first time in literature, we formulate
the problem of finding a common energy-efficient transmission range and
transmission duration for all CRSN nodes and network deployment that would
minimize the energy consumed per goodput per meter toward the sink in a greedy
forwarding scenario. Results reveal non-trivial relations for energy-efficient
CRSN transmission range and duration as a function of nine critical network
parameters such as primary user activity levels. These relations provide
valuable insights for detailed CRSN designs prior to deployment.


  Univariate polynomial root-finding has been studied for four millennia and
very intensively in the last decades. Our new near-optimal root-finders
approximate all zeros of a polynomial p almost as fast as one accesses its
coefficients with the precision required for the solution within a prescribed
error bound. Furthermore, our root-finders can be applied to a black box
polynomial, defined by an oracle (black box subroutine) for its evaluation
rather than by its coefficients. Due to this feature our root-finders support
approximation of the eigenvalues of a matrix in a record Las Vegas expected bit
operation time and are particularly fast for a polynomial that can be evaluated
fast such as the sum of a few shifted monomials or a Mandelbrot-like polynomial
defined by a recurrence. Our divide and conquer algorithm of ACM STOC 1995 is
the only other known near-optimal polynomial root-finder, but it extensively
uses the coefficients, is quite involved, and has never been implemented, while
according to extensive numerical experiments with standard test polynomials,
already a slower initial implementation of our new root-finders competes with
user's choice package of root-finding subroutines MPSolve and supersedes it
more and more significantly as the degree of a polynomial grows large. We
elaborate upon the design and analysis of our algorithms, comment on their
potential heuristic acceleration, and briefly cover polynomial root-finding by
means of functional iterations. Our techniques can be of independent interest.


  We present a new approach to constructing inflationary models in closed
universes. Conformal embedding of closed-universe models in a de Sitter
background suggests a quantisation condition on the available conformal time.
This condition implies that the universe is closed at no greater than the 10%
level. When a massive scalar field is introduced to drive an inflationary phase
this figure is reduced to closure at nearer the 1% level. In order to enforce
the constraint on the available conformal time we need to consider conditions
in the universe before the onset of inflation. A formal series around the
initial singularity is constructed, which rests on a pair of dimensionless,
scale-invariant parameters. For physically-acceptable models we find that both
parameters are of order unity, so no fine tuning is required, except in the
mass of the scalar field. For typical values of the input parameters we predict
the observed values of the cosmological parameters, including the magnitude of
the cosmological constant. The model produces a very good fit to the most
recent CMBR data. The primordial curvature spectrum predicts the low-l fall-off
in the CMB power spectrum observed by WMAP. The spectrum also predicts a
fall-off in the matter spectrum at high k, relative to a power law. A further
prediction of our model is a large tensor mode component, with r~0.2.


  We investigate the bosonic Klein-Gordon (KG) oscillators in a global monopole
(GM) spacetime in Eddington-inspired Born-Infeld (EiBI) gravity and a Wu-Yang
magnetic monopole (WYMM). We discuss the gravitational effects in the presence
of Ricci scalar curvature $R=R_{\upsilon }^{\upsilon }$. It is observed that
the presence of the Ricci scalar curvature, effectively and manifestly,
introduces a force field that makes the corresponding quantum mechanical
repulsive core more repulsive. Similar effect is also observed for the
EiBI-gravitational field. We reiterate and report that the corresponding
bosonic KG-oscillator quantum mechanical system admits a solution in the form
of confluent Heun functions, the truncation of which into a physically
admissible polynomial is shown to be associated with some parametric
correlations/conditions. The use of such conditions/correlations is mandatory
and yields a set of allowed/restricted quantum mechanical orbital $\ell
$-excitations, for all radial quantum numbers $n_{r}\geq 0$. Our procedure is
shown to be quite handy, in the since that it allows one to retrieve results
for KG-oscillators in GM-spacetime in different EiBI-gravity and Ricci scalar
curvature settings.


  Some tails of ram-pressure stripped galaxies are detected in HI, some in
Halpha, and some in X-ray (but never all three so far). We use numerical
simulations to probe the conditions for the production of X-ray bright tails,
demonstrating that the primary requirement is a high pressure intracluster
medium (ICM). This is because the stripped tail is mostly in pressure
equilibrium with the ICM, but mixing leaves it with densities and temperatures
intermediate between the cold gas in the disk and the hot ICM. Given a high
enough ICM pressure, this mixed gas lies in the X-ray bright region of the
phase diagram. We compare the simulations to observations of the ram pressure
stripped tail of ESO 137-001, showing excellent agreement in the total measured
X-ray and Halpha emission and non-flaring morphology of the tail, and
consistent HI measurements. Using these comparisons we constrain the level of
mixing and efficiency of heat conduction in the intracluster medium (ICM)


  There appears to be a longtime, very slowly evolving state in dense simple
fluids which, for high enough density, approaches a glassy nonergodic state.
The nature of the nonergodic state can be characterized by the associated
static equilibrium state. In particular, systems driven by Smoluchowski or
Newtonian dynamics share the same static equilibrium and nonergodic states.
That these systems share the same nonergodic states is a highly nontrivial
statement and requires establishing a number of results. In the high-density
regime one finds that an equilibrating system decays via a three-step process
identified in mode-coupling theory (MCT). For densities greater than a critical
density one has time-power-law decay with exponents a and b. There are sets of
linear fluctuation dissipation relations (FDRs) which connect the cumulants of
these two fields. The form of the FDRs is the same for both Smoluchowski or
Newtonian dynamics. While we show this universality of nonergodic states within
perturbation theory, we expect it to be true more generally.
  The nature of the approach to the nonergodic state has been suggested by MCT.
It has been a point of contention that MCT is a phenomenological theory and not
a systematic theory with prospects for improvement. Recently a systematic
theory has been developed. It naturally allows one to calculate
self-consistently density cumulants in a perturbation expansion in a
pseudo-potential. At leading order one obtains a kinetic kernel quadratic in
the density. This is a "one-loop" theory like MCT. At this one-loop level one
finds vertex corrections which depend on the three-point equilibrium cumulants.
Here we assume these vertex-corrections can be ignored and focus on the
higher-order loops. We show that one can sum up all of the loop contributions.
The higher-order loops do not change the nonergodic state parameters
substantially.


  We introduce coroICA, confounding-robust independent component analysis, a
novel ICA algorithm which decomposes linearly mixed multivariate observations
into independent components that are corrupted (and rendered dependent) by
hidden group-wise stationary confounding. It extends the ordinary ICA model in
a theoretically sound and explicit way to incorporate group-wise (or
environment-wise) confounding. We show that our proposed general noise model
allows to perform ICA in settings where other noisy ICA procedures fail.
Additionally, it can be used for applications with grouped data by adjusting
for different stationary noise within each group. Our proposed noise model has
a natural relation to causality and we explain how it can be applied in the
context of causal inference. In addition to our theoretical framework, we
provide an efficient estimation procedure and prove identifiability of the
unmixing matrix under mild assumptions. Finally, we illustrate the performance
and robustness of our method on simulated data, provide audible and visual
examples, and demonstrate the applicability to real-world scenarios by
experiments on publicly available Antarctic ice core data as well as two EEG
data sets. We provide a scikit-learn compatible pip-installable Python package
coroICA as well as R and Matlab implementations accompanied by a documentation
at https://sweichwald.de/coroICA/


  We produce a complete list of group presentations for singly-cusped Bianchi
groups, $PSL_2 (\mathcal{O}_d)$ where $\mathcal{O}_d$ is the ring of integers
for $\mathbb{Q}(\sqrt{d})$ and $d$ is -1, -2, -3, -7, -11, -19, -43, -67, or
-163. To do this, we apply a theorem due to Macbeath to a sufficiently large
horoball, treating the Bianchi groups as discrete subgroups of isometries for
$\mathbf{H}^3$. As far as we know, explicit presentations were not previously
known when $d$ is -43, -67, or -163.


  In modern fundamental theories there is consideration of higher dimensions,
often in the context of what can be written as a Schr\"odinger equation. Thus,
the energetics of bound states in different dimensions is of interest. By
considering the quantum square well in continuous $D$ dimensions, it is shown
that there is always a bound state for $0<D \le 2$. This binding is complete
for D \to 0 and exponentially small for D \to 2_-. For D>2, a finite-sized well
is always needed for there to be a bound state. This size grows like D^2 as D
gets large. By adding the proper angular momentum tail a volcano, zero-energy,
bound state can be obtained.


  We provide a detailed overview of various approaches to word segmentation of
Asian Languages, specifically Chinese, Korean, and Japanese languages. For each
language, approaches to deal with word segmentation differs. We also include
our analysis about certain advantages and disadvantages to each method. In
addition, there is room for future work in this field.


  We numerically examine divergences of the total energy in metallic systems of
approximate many-body theories using Hartree--Fock as a reference, including
perturbative (M\oller-Plesset, MP), coupled cluster (CC) and configuration
interaction (CI) approaches. Controlling for finite size effects and basis set
incompleteness error by comparison with energies from the random phase
approximation (RPA), we suggest convincingly that non-perturbative coupled
cluster theories are acceptable for modelling electronic interactions in metals
whilst perturbative coupled cluster theories are not. Data are provided from
the RPA with which it is possible to test other approximate finite-basis
methods for divergences with only modest computational cost.


  We prove that every $(3+1)$-dimensional flat GHMC Minkowski spacetime which
is not a translation spacetime or a Misner spacetime carries a unique foliation
by spacelike hypersurfaces of constant scalar curvature. In otherwords, we
prove that every such spacetime carries a unique time function with isochrones
of constant scalar curvature. Furthermore, this time function is a smooth
submersion.


  This paper is concerned with a numerical method for a 3D coefficient inverse
problem with phaseless scattering data. These are multi-frequency data
generated by a single direction of the incident plane wave. Our numerical
procedure consists of two stages. The first stage aims to reconstruct the
(approximate) scattered field at the plane of measurements from its intensity.
We present an algorithm for the reconstruction process and prove a uniqueness
result of this reconstruction. After obtaining the approximate scattered field,
we exploit a newly developed globally convergent numerical method to solve the
coefficient inverse problem with the phased scattering data. The latter is the
second stage of our algorithm. Numerical examples are presented to demonstrate
the performance of our method. Finally, we present a numerical study which aims
to show that, under a certain assumption, the solution of the scattering
problem for the 3D scalar Helmholtz equation can be used to approximate the
component of the electric field which was originally incident upon the medium.


  The present contribution summarizes the content and slightly updates the
discussion of a recently proposed theoretical analysis of the halo phenomenon
in many-fermion systems. We focus here on applications to potential neutron
halos in mid-mass nuclei.


  The contra-directional coupling between a left-handed monomode waveguide and
a right-handed monomode waveguide is rigorously studied using a complex plane
analysis. Light is shown to rotate in this lamellar structure forming a very
exotic mode which we have called a light wheel. The light wheel can be excited
using evanescent coupling or by placing sources in one of the waveguides. This
structure can thus be seen as a new type of cavity. It is a way to suppress the
guided mode of a dielectric slab.


  We evaluate exclusive semileptonic decays of ground-state spin-1/2 and
spin-3/2 doubly heavy $cb$ baryons driven by a $c\to s,d$ transition at the
quark level. We check our results for the form factors against heavy quark spin
symmetry constraints obtained in the limit of very large heavy quark masses and
near zero recoil. Based on those constraints we make model independent, though
approximate, predictions for ratios of decay widths.


  We have measured the optical linear polarization of quasars belonging to
Gpc-scale quasar groups at redshift z ~ 1.3. Out of 93 quasars observed, 19 are
significantly polarized. We found that quasar polarization vectors are either
parallel or perpendicular to the directions of the large-scale structures to
which they belong. Statistical tests indicate that the probability that this
effect can be attributed to randomly oriented polarization vectors is of the
order of 1%. We also found that quasars with polarization perpendicular to the
host structure preferentially have large emission line widths while objects
with polarization parallel to the host structure preferentially have small
emission line widths. Considering that quasar polarization is usually either
parallel or perpendicular to the accretion disk axis depending on the
inclination with respect to the line of sight, and that broader emission lines
originate from quasars seen at higher inclinations, we conclude that quasar
spin axes are likely parallel to their host large-scale structures.


  We establish the global-in-time existence and uniqueness of classical
solutions to the "one and one-half" dimensional relativistic Vlasov--Maxwell
systems in a bounded interval, subject to an external magnetic field which is
infinitely large at the spatial boundary. We prove that the large external
magnetic field confines the particles to a compact set away from the boundary.
This excludes the known singularities that typically occur due to particles
that repeatedly bounce off the boundary. In addition to the confinement, we
follow the techniques introduced by Glassey and Schaeffer, who studied the
Cauchy problem without boundaries.


  In this work, we consider some relationships between a closed range operator
$T$ and a fusion frame $\mathcal{W}=(W_i,w_i)_{i\in I}$ for a Hilbert space
$\mathcal{H}$ that provides that the sequence $(\overline{T(W_i)},v_i)_{i\in
I}$ is a fusion frame sequence for $\mathcal{H}$, if we consider a suitable
family of weights $\{v_i\}_{i\in I}$. This (sufficient) condition generalizes
some previous work in the subject.


  The classical human-robot interface in uncalibrated image-based visual
servoing (UIBVS) relies on either human annotations or semantic segmentation
with categorical labels. Both methods fail to match natural human communication
and convey rich semantics in manipulation tasks as effectively as natural
language expressions. In this paper, we tackle this problem by using referring
expression segmentation, which is a prompt-based approach, to provide more
in-depth information for robot perception. To generate high-quality
segmentation predictions from referring expressions, we propose CLIPUNetr - a
new CLIP-driven referring expression segmentation network. CLIPUNetr leverages
CLIP's strong vision-language representations to segment regions from referring
expressions, while utilizing its ``U-shaped'' encoder-decoder architecture to
generate predictions with sharper boundaries and finer structures. Furthermore,
we propose a new pipeline to integrate CLIPUNetr into UIBVS and apply it to
control robots in real-world environments. In experiments, our method improves
boundary and structure measurements by an average of 120% and can successfully
assist real-world UIBVS control in an unstructured manipulation environment.


  Matter-wave interferometers reveal some of the most fascinating phenomena of
the quantum world. Phase shifts due to rotation (the Sagnac effect) for
neutrons, free atoms and superfluid 3He reveal the connection of matter waves
to a non-rotating inertial frame. In addition, phase shifts in electron waves
due to magnetic vector potentials (the Aharonov-Bohm effect) show that physical
states can be modified in the absence of classical forces. We report here the
observation of interference induced by the Earth's rotation in superfluid 4He
at 2 K, a temperature 2000 times higher than previously achieved with 3He. This
interferometer, an analog of a dc-SQUID, employs a recently reported phenomenon
wherein superfluid 4He exhibits quantum oscillations in an array of sub-micron
apertures. We find that the interference pattern persists not only when the
aperture array current-phase relation is a sinusoidal function characteristic
of the Josephson effect, but also at lower temperatures where it is linear and
oscillations occur by phase slips. The modest requirements for the
interferometer (2 K cryogenics and fabrication of apertures at the level of
100nm) and its potential resolution suggest that, when engineering challenges
such as vibration isolation are met, superfluid 4He interferometers could
become important scientific probes.


  Recent advances unveiled physical neural networks as promising machine
learning platforms, offering faster and more energy-efficient information
processing. Compared with extensively-studied optical neural networks, the
development of mechanical neural networks (MNNs) remains nascent and faces
significant challenges, including heavy computational demands and learning with
approximate gradients. Here, we introduce the mechanical analogue of in situ
backpropagation to enable highly efficient training of MNNs. We demonstrate
that the exact gradient can be obtained locally in MNNs, enabling learning
through their immediate vicinity. With the gradient information, we showcase
the successful training of MNNs for behavior learning and machine learning
tasks, achieving high accuracy in regression and classification. Furthermore,
we present the retrainability of MNNs involving task-switching and damage,
demonstrating the resilience. Our findings, which integrate the theory for
training MNNs and experimental and numerical validations, pave the way for
mechanical machine learning hardware and autonomous self-learning material
systems.


  We prove a Fredholm determinant and short-distance series representation of
the Painlev\'e V tau function $\tau(t)$ associated to generic monodromy data.
Using a relation of $\tau(t)$ to two different types of irregular $c=1$
Virasoro conformal blocks and the confluence from Painlev\'e VI equation,
connection formulas between the parameters of asymptotic expansions at $0$ and
$i\infty$ are conjectured. Explicit evaluations of the connection constants
relating the tau function asymptotics as $t\to 0,+\infty,i\infty$ are obtained.
We also show that irregular conformal blocks of rank 1, for arbitrary central
charge, are obtained as confluent limits of the regular conformal blocks.


  The BMO martingale theory is extensively used to study nonlinear
multi-dimensional stochastic equations (SEs) in $\cR^p$ ($p\in [1, \infty)$)
and backward stochastic differential equations (BSDEs) in $\cR^p\times \cH^p$
($p\in (1, \infty)$) and in $\cR^\infty\times \bar{\cH^\infty}^{BMO}$, with the
coefficients being allowed to be unbounded. In particular, the probabilistic
version of Fefferman's inequality plays a crucial role in the development of
our theory, which seems to be new. Several new results are consequently
obtained. The particular multi-dimensional linear case for SDEs and BSDEs are
separately investigated, and the existence and uniqueness of a solution is
connected to the property that the elementary solutions-matrix for the
associated homogeneous SDE satisfies the reverse H\"older inequality for some
suitable exponent $p\ge 1$. Finally, we establish some relations between
Kazamaki's quadratic critical exponent $b(M)$ of a BMO martingale $M$ and the
spectral radius of the solution operator for the $M$-driven SDE, which lead to
a characterization of Kazamaki's quadratic critical exponent of BMO martingales
being infinite.


  This research will examine the computational methods to calculate the
nonlinear optical process of second harmonic generation (SHG) that will be
hypothesized to be present during lithium ion insertion into silicon nanowires.
First it will be determined whether the medium in which SHG is conveyed is
non-centrosymmetric or whether the medium is inversion symmetric where SHG as a
part of the second-order nonlinear optical phenomenon does not exist. It will
be demonstrated that the main interaction that determines SHG is multiphoton
absorption on lithium ions. The quantum harmonic oscillator (QHO) is used as
the background that generates coherent states for electrons and photons that
transverse the length of the silicon nanowire. The matrix elements of the
Hamiltonian which represents the energy of the system will be used to calculate
the probability density of second-order nonlinear optical interactions which
includes collectively SHG, sum-frequency generation (SFG) and
difference-frequency generation (DFG). As a result it will be seen that at
varies concentrations of lithium ions (Li+) within the crystallized silicon
(c-Si) matrix the second-order nonlinear optical process has probabilities
substantial enough to create second harmonic generation that could possibly be
used for such applications as second harmonic imaging microscopy.


  The collective excitations in the Bose-Hubbard model in a trap are studied by
means of numerical diagonalization in one dimension. The strength function is
calculated for monopole and dipole perturbations, and moments of the strength
function are utilized in order to obtain information about the collective
behavior under external forces. In the superfluid regime, the spectrum is found
to be exhausted by one single frequency, while in systems that contain a Mott
insulating plateau several frequencies are excited. An explanation of recent
experimental findings in terms of a Mott plateau is suggested.


  Constraint based methods, such as the Flux Balance Analysis, are widely used
to model cellular growth processes without relying on extensive information on
the regulatory features. The regulation is instead substituted by an
optimization problem usually aiming at maximal biomass accumulation. A recent
extension to these methods called the dynamic enzyme-cost Flux Balance Analysis
(deFBA) is a fully dynamic modeling method allowing for the prediction of
necessary enzyme levels under changing environmental conditions. However, this
method was designed for deterministic settings in which all dynamics,
parameters, etc. are exactly known. In this work, we present a theoretical
framework extending the deFBA to handle uncertainties and provide a robust
solution. We use the ideas from multi-stage nonlinear Model Predictive Control
(MPC) and its feature to represent the evolution of uncertainties by an
exponentially growing scenario tree. While this representation is able to
construct a deterministic optimization problem in the presence of
uncertainties, the computational cost also increases exponentially. We counter
this by using a receding prediction horizon and reshape the standard deFBA to
the short-time deFBA (sdeFBA). This leads us, along with further simplification
of the scenario tree, to the robust deFBA (rdeFBA). This framework is capable
of handling the uncertainties in the model itself as well as uncertainties
experienced by the modeled system. We applied these algorithms to two
case-studies: a minimal enzymatic nutrient uptake network, and the abstraction
of the core metabolic process in bacteria.


  The Gaussian process (GP) model, which has been extensively applied as priors
of functions, has demonstrated excellent performance. The specification of a
large number of parameters affects the computational efficiency and the
feasibility of implementation of a control strategy. We propose a linear model
to approximate GPs; this model expands the GP model by a series of basis
functions. Several examples and simulation studies are presented to demonstrate
the advantages of the proposed method. A control strategy is provided with the
proposed linear model.


  Binary code summarization, while invaluable for understanding code semantics,
is challenging due to its labor-intensive nature. This study delves into the
potential of large language models (LLMs) for binary code comprehension. To
this end, we present BinSum, a comprehensive benchmark and dataset of over 557K
binary functions and introduce a novel method for prompt synthesis and
optimization. To more accurately gauge LLM performance, we also propose a new
semantic similarity metric that surpasses traditional exact-match approaches.
Our extensive evaluation of prominent LLMs, including ChatGPT, GPT-4, Llama 2,
and Code Llama, reveals 10 pivotal insights. This evaluation generates 4
billion inference tokens, incurred a total expense of 11,418 US dollars and 873
NVIDIA A100 GPU hours. Our findings highlight both the transformative potential
of LLMs in this field and the challenges yet to be overcome.


  The aim of this paper is to present the case that stellar mass primordial
black holes make up the dark matter component of the Universe. A near critical
density of compact bodies implies that most lines of sight will be
gravitationally microlensed, and the paper focuses on looking for the predicted
effects on quasar brightness and spectral variations. These signatures of
microlensing include the shape of the Fourier power spectrum of the light
curves, near achromatic and statistically symmetric variations, and the absence
of time dilation in the timescale of variability. For spectral changes, as the
continuum varies there should be little corresponding change in the strength of
the broad lines. In all these cases, the observations are found to be
consistent with the predictions for microlensing by a population of stellar
mass compact bodies. For multiply lensed quasars where the images vary
independently it is shown that stellar populations are too small to produce the
observed microlensing effects, implying a population of compact dark matter
bodies of around a stellar mass along the line of sight. The most serious
objection to dark matter in the form of compact bodies has come from
observations of microlensing of stars in the Magellanic Clouds. In this paper
the expected event rate is re-analysed using more recent values for the
structure and dynamics of the Galactic halo, and it is shown that there is then
no conflict with the observations. Finally, the possible identity of a near
critical density of dark matter in the form of stellar mass compact bodies is
reviewed, with the conclusion that by far the most plausible candidates are
primordial black holes formed during the QCD epoch. The overall conclusion of
the paper is that primordial black holes should be seen alongside elementary
particles as viable dark matter candidates.


  In this paper, using the structures of cone and bicone fields on vector
bundles, the author introduces a ILB (inverse limit of
  Banach)- manifold structure on $\mathcal M$ the space of
  Riemannian metrics on a noncompact manifold $M$. In the last section, it is
proven that, this way, on the open submanifold $\mathcal{M}_{finite}$ of finite
volume metrics, the canonical Riemannian metric is defined.


  Identifying collisionless shock crossings in data sent from spacecraft has so
far been done manually. It is a tedious job that shock physicists have to go
through if they want to conduct case studies or perform statistical studies. We
use a machine learning approach to automatically identify shock crossings from
the Magnetospheric Multiscale (MMS) spacecraft. We compile a database of those
crossings including various spacecraft related and shock related parameters for
each event. Furthermore, we show that the shocks in the database have
properties that are spread out both in real space and parameter space. We also
present a possible science application of the database by looking for
correlations between ion acceleration efficiency at shocks and different shock
parameters such as $\theta_{Bn}$ and $M_A$. Furthermore, we investigate
statistically the ion acceleration efficiency. We find no clear correlation
between the acceleration efficiency and $M_A$ and we find that quasi-parallel
shocks are more efficient at accelerating ions.


  Design and control of autonomous systems that operate in uncertain or
adversarial environments can be facilitated by formal modelling and analysis.
Probabilistic model checking is a technique to automatically verify, for a
given temporal logic specification, that a system model satisfies the
specification, as well as to synthesise an optimal strategy for its control.
This method has recently been extended to multi-agent systems that exhibit
competitive or cooperative behaviour modelled via stochastic games and
synthesis of equilibria strategies. In this paper, we provide an overview of
probabilistic model checking, focusing on models supported by the PRISM and
PRISM-games model checkers. This includes fully observable and partially
observable Markov decision processes, as well as turn-based and concurrent
stochastic games, together with associated probabilistic temporal logics. We
demonstrate the applicability of the framework through illustrative examples
from autonomous systems. Finally, we highlight research challenges and suggest
directions for future work in this area.


  The vast majority of extragalactic compact continuum radio sources are
associated with star formation or jets from (super)massive black holes and, as
such, are more likely to be found in association with starburst galaxies or
early-type galaxies. Two new populations of radio sources were recently
identified: (a) compact and persistent sources (PRSs) associated with fast
radio bursts (FRBs) in dwarf galaxies and (b) compact sources in dwarf galaxies
that could belong to the long-sought population of intermediate-mass black
holes. Despite the interesting aspects of these newly found sources, the
current sample size is small, limiting scrutiny of the underlying population.
Here, we present a search for compact radio sources coincident with dwarf
galaxies. We search the LOFAR Two-meter Sky Survey (LoTSS), the most sensitive
low-frequency (144 MHz central frequency) large-area survey for optically thin
synchrotron emission to date. Exploiting the high spatial resolution (6 arcsec)
and low astrometric uncertainty (~0.2 arcsec) of the LoTSS, we match its
compact sources to the compiled sample of dwarf galaxies in the Census of the
Local Universe, an H alpha survey with the Palomar Observatory 48 inch Samuel
Oschin Telescope. We identify 29 over-luminous compact radio sources, evaluate
the probability of chance alignment within the sample, investigate the
potential nature of these sources, and evaluate their volumetric density and
volumetric rate. While optical line-ratio diagnostics on the nebular lines from
the host galaxies support a star-formation origin rather than an AGN origin,
future high-angular-resolution radio data are necessary to ascertain the origin
of the radio sources. We discuss planned strategies to differentiate between
candidate FRB hosts and intermediate-mass black holes.


  SRAM-based FPGAs are popular in the aerospace industry for their field
programmability and low cost. However, they suffer from cosmic
radiation-induced Single Event Upsets (SEUs). Triple Modular Redundancy (TMR)
is a well-known technique to mitigate SEUs in FPGAs that is often used with
another SEU mitigation technique known as configuration scrubbing. Traditional
TMR provides protection against a single fault at a time, while partitioned TMR
provides improved reliability and availability. In this paper, we present a
methodology to analyze TMR partitioning at early design stage using
probabilistic model checking. The proposed formal model can capture both single
and multiple-cell upset scenarios, regardless of any assumption of equal
partition sizes. Starting with a high-level description of a design, a Markov
model is constructed from the Data Flow Graph (DFG) using a specified number of
partitions, a component characterization library and a user defined scrub rate.
Such a model and exhaustive analysis captures all the considered failures and
repairs possible in the system within the radiation environment. Various
reliability and availability properties are then verified automatically using
the PRISM model checker exploring the relationship between the scrub frequency
and the number of TMR partitions required to meet the design requirements.
Also, the reported results show that based on a known voter failure rate, it is
possible to find an optimal number of partitions at early design stages using
our proposed method.


  In 2003 we have measured the absolute frequency of the $(1S, F=1, m_F=\pm 1)
\leftrightarrow (2S, F'=1, m_F'=\pm 1)$ two-photon transition in atomic
hydrogen. We observed a variation of $(-29\pm 57)$ Hz over a 44 months interval
separating this measurement from the previous one performed in 1999. We have
combined this result with recently published results of optical transition
frequency measurement in the $^{199}$Hg$^+$ ion and and comparison between
clocks based on $^{87}$Rb and $^{133}$Cs. From this combination we deduce the
stringent limits for fractional time variation of the fine structure constant
$\partial/{\partial t}(\ln \alpha)=(-0.9\pm 4.2)\times 10^{-15}$ yr$^{-1}$ and
for the ratio of $^{87}$Rb and $^{133}$Cs spin magnetic moments
$\partial/{\partial t}(\ln[\mu_{\rm {Rb}}/\mu_{\rm {Cs}}])=(0.5\pm 2.1)\times
10^{-15}$ yr$^{-1}$. This is the first precise restriction for the fractional
time variation of $\alpha$ made without assumptions about the relative drifts
of the constants of electromagnetic, strong and weak interactions.


  Face verification remains a challenging problem in very complex conditions
with large variations such as pose, illumination, expression, and occlusions.
This problem is exacerbated when we rely unrealistically on a single training
data source, which is often insufficient to cover the intrinsically complex
face variations. This paper proposes a principled multi-task learning approach
based on Discriminative Gaussian Process Latent Variable Model, named
GaussianFace, to enrich the diversity of training data. In comparison to
existing methods, our model exploits additional data from multiple
source-domains to improve the generalization performance of face verification
in an unknown target-domain. Importantly, our model can adapt automatically to
complex data distributions, and therefore can well capture complex face
variations inherent in multiple sources. Extensive experiments demonstrate the
effectiveness of the proposed model in learning from diverse data sources and
generalize to unseen domain. Specifically, the accuracy of our algorithm
achieves an impressive accuracy rate of 98.52% on the well-known and
challenging Labeled Faces in the Wild (LFW) benchmark. For the first time, the
human-level performance in face verification (97.53%) on LFW is surpassed.


  The dynamical susceptibility of strongly correlated electronic systems can be
calculated within the framework of the dynamical mean-field theory (DMFT). The
required measurement of the four-point vertex of the auxiliary impurity model
is however costly and restricted to a finite grid of Matsubara frequencies,
leading to a cutoff error. It is shown that the propagation of this error to
the lattice response function can be minimized by virtue of an exact
decomposition of the DMFT polarization function into local and nonlocal parts.
The former is measured directly by the impurity solver, while the latter is
given in terms of a ladder equation for the Hedin vertex that features an
unprecedentedly fast decay of frequency summations compared to previous
calculation schemes, such as the one of the dual boson approach. At strong
coupling the local approximation of the TRILEX approach is viable, but vertex
corrections to the polarization should be dropped on equal footing to recover
the correct prefactor of the effective exchange. In finite dimensions the DMFT
susceptibility exhibits spurious mean-field criticality, therefore, a
two-particle self-consistent and frequency-dependent correction term is
introduced, similar to the Moriya-$\lambda$ correction of the dynamical vertex
approximation. Applications to the two- and three-dimensional Hubbard models on
the square and cubic lattices show that the expected critical behavior near an
antiferromagnetic instability is recovered.


  We dendrogram the Leike et al. 2020 3D dust map, leveraging its $\sim 1$ pc
spatial resolution to produce a uniform catalog of molecular clouds in the
solar neighborhood. Using accurate distances, we measure the properties of 65
clouds in true 3D space, eliminating much of the uncertainty in mass, size, and
density. Clouds in the catalog contain a total of $1.1 \times 10^5 \; \rm
M_{\odot}$, span distances of $116-440$ pc, and include a dozen well-studied
clouds in the literature. In addition to deriving cloud properties in 3D volume
density space, we create 2D dust extinction maps from the 3D data by projecting
the 3D clouds onto a 2D "Sky" view. We measure the properties of the 2D clouds
separately from the 3D clouds. We compare the scaling relation between the
masses and sizes of clouds following Larson 1981. We find that our 2D projected
mass-size relation, $M \propto r^{2.1}$, agrees with Larson's Third Relation,
but our 3D derived properties lead to a scaling relation of about one order
larger: $M \propto r^{2.9}$. Validating predictions from theory and numerical
simulations, our results indicate that the mass-size relation is sensitive to
whether column or volume density is used to define clouds, since mass scales
with area in 2D ($M \propto r^{2}$) and with volume in 3D ($M \propto r^{3}$).
Our results imply a roughly constant column and volume density in 2D and 3D,
respectively, for molecular clouds, as would be expected for clouds where the
lower density, larger volume-filling gas dominates the cloud mass budget.


  Pair collisions in atomic gases lead to decoherence and decay. Assuming that
all the atoms in the gas are equally likely to collide one is led to consider
Lindbladian of mean field type where the evolution in the limit of many atoms
reduces to a single qudit Lindbladian with quadratic non-linearity. We describe
three smoking guns for non-linear evolutions: Power law decay and dephasing
rates; Dephasing rates that take a continuous range of values depending on the
initial data and finally, anomalous flow of the Bloch ball towards a
hemisphere.


  Positron creation probabilities as well as energy and angular distributions
of outgoing positrons in slow collisions of two identical heavy nuclei are
obtained within the two-center approach beyond the monopole approximation. The
time-dependent Dirac equation for positron wave functions is solved with the
help of the generalized pseudospectral method in modified prolate spheroidal
coordinates adapted for variable internuclear separation. Depending on the
nuclear charge, the results are obtained for both subcritical and supercritical
regimes of the positron creation. The signatures of transition to the
supercritical regime in the total positron creation probabilities and energy
spectra are discussed. The angular distributions of emitted positrons
demonstrate a high degree of isotropy.


  Retrieving information from EHR systems is essential for answering specific
questions about patient journeys and improving the delivery of clinical care.
Despite this fact, most EHR systems still rely on keyword-based searches. With
the advent of generative large language models (LLMs), retrieving information
can lead to better search and summarization capabilities. Such retrievers can
also feed Retrieval-augmented generation (RAG) pipelines to answer any query.
However, the task of retrieving information from EHR real-world clinical data
contained within EHR systems in order to solve several downstream use cases is
challenging due to the difficulty in creating query-document support pairs. We
provide a blueprint for creating such datasets in an affordable manner using
large language models. Our method results in a retriever that is 30-50 F-1
points better than propriety counterparts such as Ada and Mistral for oncology
data elements. We further compare our model, called Onco-Retriever, against
fine-tuned PubMedBERT model as well. We conduct an extensive manual evaluation
on real-world EHR data along with latency analysis of the different models and
provide a path forward for healthcare organizations to build domain-specific
retrievers.


  We consider the disordered monomer-dimer model on general finite graphs with
bounded degrees. Under the finite fourth moment assumption on the weight
distributions, we prove a Gaussian central limit theorem for the free energy of
the associated Gibbs measure with a rate of convergence. The central limit
theorem continues to hold under a nearly optimal finite $(2+\epsilon)$-moment
assumption on the weight distributions if the underlying graphs are further
assumed to have a uniformly subexponential volume growth. This generalizes a
recent result by Dey and Krishnan (arXiv:2109.12716) who showed a Gaussian
central limit theorem in the disordered monomer-dimer model on cylinder graphs.
Our proof relies on the idea that the disordered monomer-dimer model exhibits a
decay of correlation with high probability. We also establish a central limit
theorem for the Gibbs average of the number of dimers where the underlying
graph has subexponential volume growth and the edge weights are Gaussians.


  We present evidence for entangled solid vortex matter in a glassy state in a
layered superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$ containing randomly
splayed linear defects. The interlayer phase coherence--probed by the Josephson
plasma resonance--is enhanced at high temperatures, reflecting the recoupling
of vortex liquid by the defects. At low temperatures in the vortex solid state,
the interlayer coherence follows a boomerang-shaped reentrant temperature path
with an unusual low field decrease in coherence, indicative of meandering
vortices. We uncover a distinct temperature scaling between in-plane and
out-of-plane critical currents with opposing dependencies on field and time,
consistent with the theoretically proposed "splayed-glass" state.


  The hidden symmetry of certain nano-magnets leads to many of the levels being
doubly degenerate for periodic values of the Zeeman energy. Corresponding to
such a symmetry is an operator, $K_{n}$, related to the time reversal operator,
and which commutes with the Hamiltonian. The degeneracies for whole integer
spin values are often similar to the Kramer's degeneracy for half-integer spin.
An all algebraic method for constructing Hamiltonians with such hidden
symmetries and different crystal symmetries is described.


  The current paper presents an experimental study of the energy budget of a
two-dimensional internal wave attractor in a trapezoidal domain filled with
uniformly stratified fluid. The injected energy flux and the dissipation rate
are simultaneously measured from a \ch{two-dimensional, two components,}
experimental velocity field. The pressure perturbation field needed to quantify
the injected energy is determined from the linear inviscid theory. The
dissipation rate in the bulk of the domain is directly computed from the
measurements, while the energy sink occurring in the boundary layers are
estimated using the theoretical expression of the velocity field in the
boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech. 841, 614
(2018)). In the linear regime, we show that the energy budget is closed, in the
steady-state and also in the transient regime, by taking into account the bulk
dissipation and, more important, the dissipation in the boundary layers without
any adjustable parameters. The dependence of the different sources on the
thickness of the experimental set-up is also discussed. In the nonlinear
regime, the analysis is extended by estimating the dissipation due to the
secondary waves generated by triadic resonant instabilities showing the
importance of the energy transfer from large scales to small scales. The method
tested here on internal wave attractors can be generalized straightforwardly to
any quasi two-dimensional stratified flow.


  Statistical relational AI and probabilistic logic programming have so far
mostly focused on discrete probabilistic models. The reasons for this is that
one needs to provide constructs to succinctly model the independencies in such
models, and also provide efficient inference.
  Three types of independencies are important to represent and exploit for
scalable inference in hybrid models: conditional independencies elegantly
modeled in Bayesian networks, context-specific independencies naturally
represented by logical rules, and independencies amongst attributes of related
objects in relational models succinctly expressed by combining rules.
  This paper introduces a hybrid probabilistic logic programming language, DC#,
which integrates distributional clauses' syntax and semantics principles of
Bayesian logic programs. It represents the three types of independencies
qualitatively. More importantly, we also introduce the scalable inference
algorithm FO-CS-LW for DC#. FO-CS-LW is a first-order extension of the
context-specific likelihood weighting algorithm (CS-LW), a novel sampling
method that exploits conditional independencies and context-specific
independencies in ground models. The FO-CS-LW algorithm upgrades CS-LW with
unification and combining rules to the first-order case.


  Graph-based Semi-Supervised Learning (GSSL) is a practical solution to learn
from a limited amount of labelled data together with a vast amount of
unlabelled data. However, due to their reliance on the known labels to infer
the unknown labels, these algorithms are sensitive to data quality. It is
therefore essential to study the potential threats related to the labelled
data, more specifically, label poisoning. In this paper, we propose a novel
data poisoning method which efficiently approximates the result of label
inference to identify the inputs which, if poisoned, would produce the highest
number of incorrectly inferred labels. We extensively evaluate our approach on
three classification problems under 24 different experimental settings each.
Compared to the state of the art, our influence-driven attack produces an
average increase of error rate 50\% higher, while being faster by multiple
orders of magnitude. Moreover, our method can inform engineers of inputs that
deserve investigation (relabelling them) before training the learning model. We
show that relabelling one-third of the poisoned inputs (selected based on their
influence) reduces the poisoning effect by 50\%.


  High energy photons from blazars interact within tens of kpc with the
extragalactic photon background, initiating electromagnetic pair cascades. The
charged component of such cascades is deflected by extragalactic magnetic
fields (EGMF), leading to halos even around initially point-like sources. We
calculate the intensity profile of the resulting secondary high-energy photons
for different assumptions on the initial source spectrum and the strength of
the EGMF, employing also fields found earlier in a constrained simulation of
structure formation including MHD processes. We find that the observation of
halos around blazars like Mrk~180 probes an interesting range of EGMF strengths
and acceleration models: In particular, blazar halos test if the photon energy
spectrum at the source extends beyond \sim 100 TeV and how anisotropic this
high energy component is emitted.


  We investigate the Ruderman-Kittel-Kasuya-Yosida oscillations of the
itinerant carrier spin density in a system where those oscillations appear only
due to a finite distribution of a localized spin. The system represents a
half-infinite one-dimensional quantum wire with a magnetic impurity located at
its edge. In contrast to the conventional model of a point-like exchange
interaction the itinerant carrier spin density oscillations in this system
exist. We {\it analytically} demonstrate that when the radius of the exchange
interaction is less than the wave length of the itinerant carriers living on
the Fermi surface, the long range behavior of the oscillations is identical to
the one taking place in the zero radius limit of the same exchange interaction
but for an infinite one-dimensional quantum wire where, in comparison with the
original half-infinite system, the mass of the itinerant carriers is {\it
strongly} modified by the exchange interaction radius. On the basis of our
analysis we make a suggestion on directionality of surface
Ruderman-Kittel-Kasuya-Yosida interaction shown in recent experiments: we
believe that in general the anisotropy of the Ruderman-Kittel-Kasuya-Yosida
interaction could result not only from the anisotropy of the {\it Fermi
surface} of itinerant carriers but also from the anisotropy of the {\it spin
carrying atomic orbitals} of magnetic impurities.


  The quantum torus algebra plays an important role in a special class of
solutions of the Toda hierarchy. Typical examples are the solutions related to
the melting crystal model of topological strings and 5D SUSY gauge theories.
The quantum torus algebra is realized by a 2D complex free fermion system that
underlies the Toda hierarchy, and exhibits mysterious "shift symmetries". This
article is based on collaboration with Toshio Nakatsu.


  We demonstrate that spin-charge separation can occur in two dimensions and
note its confluence with superconductivity, topology, gauge theory, and
fault-tolerant quantum computation. We construct a microscopic Ising-like model
and, at a special coupling constant value, find its exact ground state as well
as neutral spin 1/2 (spinon), spinless charge e (holon), and $Z_2$ vortex
(vison) states and energies. The fractionalized excitations reflect the
topological order of the ground state which is evinced by its fourfold
degeneracy on the torus -- a degeneracy which is unrelated to translational or
rotational symmetry -- and is described by a $Z_2$ gauge theory. Our model is
related to the quantum dimer model and is a member of a family of
topologically-ordered models, one of which is integrable and realizes the toric
quantum error correction code.


  We show that every Mori dream space of globally $F$-regular type is of Fano
type. As an application, we give a characterization of varieties of Fano type
in terms of the singularities of their Cox rings.


  Sparse training is one of the promising techniques to reduce the
computational cost of DNNs while retaining high accuracy. In particular, N:M
fine-grained structured sparsity, where only N out of consecutive M elements
can be nonzero, has attracted attention due to its hardware-friendly pattern
and capability of achieving a high sparse ratio. However, the potential to
accelerate N:M sparse DNN training has not been fully exploited, and there is a
lack of efficient hardware supporting N:M sparse training. To tackle these
challenges, this paper presents a computation-efficient training scheme for N:M
sparse DNNs using algorithm, architecture, and dataflow co-design. At the
algorithm level, a bidirectional weight pruning method, dubbed BDWP, is
proposed to leverage the N:M sparsity of weights during both forward and
backward passes of DNN training, which can significantly reduce the
computational cost while maintaining model accuracy. At the architecture level,
a sparse accelerator for DNN training, namely SAT, is developed to neatly
support both the regular dense operations and the computation-efficient N:M
sparse operations. At the dataflow level, multiple optimization methods ranging
from interleave mapping, pre-generation of N:M sparse weights, and offline
scheduling, are proposed to boost the computational efficiency of SAT. Finally,
the effectiveness of our training scheme is evaluated on a Xilinx VCU1525 FPGA
card using various DNN models and datasets. Experimental results show the SAT
accelerator with the BDWP sparse training method under 2:8 sparse ratio
achieves an average speedup of 1.75x over that with the dense training,
accompanied by a negligible accuracy loss of 0.56% on average. Furthermore, our
proposed training scheme significantly improves the training throughput by
2.97~25.22x and the energy efficiency by 1.36~3.58x over prior FPGA-based
accelerators.


  In this paper, we consider a Hamiltonian system combining a nonlinear Schr\"
odinger equation (NLS) and an ordinary differential equation (ODE). This system
is a simplified model of the NLS around soliton solutions. Following Nakanishi
\cite{NakanishiJMSJ}, we show scattering of $L^2$ small $H^1$ radial solutions.
The proof is based on Nakanishi's framework and Fermi Golden Rule estimates on
$L^4$ in time norms.


  This letter addresses basic questions concerning ferroelectric order in
positionally disordered dipolar materials. Three models distinguished by dipole
vectors which have one, two or three components are studied by computer
simulation. Randomly frozen and dynamically disordered media are considered. It
is shown that ferroelectric order is possible in spatially random systems, but
that its existence is very sensitive to the dipole vector dimensionality and
the motion of the medium. A physical analysis of our results provides
significant insight into the nature of ferroelectric transitions.


  Receptors of bacterial chemotaxis form clusters at the cell poles, where
clusters act as "antennas" to amplify small changes in ligand concentration.
Interestingly, chemoreceptors cluster at multiple length scales. At the
smallest scale, receptors form dimers, which assemble into stable timers of
dimers. At a large scale, trimers form large polar clusters composed of
thousands of receptors. Although much is known about the signaling properties
emerging from receptor clusters, it is unknown how receptors localize at the
cell poles and what the cluster-size determining factors are. Here, we present
a model of polar receptor clustering based on coupled trimers of dimers, where
cluster size is determined as a minimum of the cluster-membrane free energy.
This energy has contributions from the cluster-membrane elastic energy,
penalizing large clusters due to their high intrinsic curvature, and
receptor-receptor coupling favoring large clusters. We find that the reduced
cluster-membrane curvature mismatch at the curved cell poles leads to large and
robust polar clusters in line with experimental observation, while lateral
clusters are efficiently suppressed.


  A class of proposed coherent precipitate structures (Guinier-Preston zones)
in the Al-Mg-Si alloy are investigated using first-principles density
functional theory methods. The cluster expansion method is used to extract
effective interaction parameters, providing the means for large scale energy
calculations of alloy structures. The Mg$_1$Si$_1$ L$1_0$ structure and
structures related to the Mg$_5$Si$_6$ $\beta''$ phase are studied in more
detail, and e.g., precipitate/matrix interface energies are presented. Using
direct first-principles calculations we show that the former phase is
dynamically unstable and thus must be stabilized by the surrounding Al matrix.
Monte Carlo simulations and free-energy techniques are used to study the Al
rich side of the phase diagram with the current CE parameters, and kinetic
Monte Carlo simulations are used to study clustering in the disordered phase.
The implications of our findings are discussed in the framework of classical
nucleation theories, and we outline possible nucleation mechanisms.