  We consider Steklov eigenvalues on nearly spherical and nearly annular
domains in $d$ dimensions. By using the Green-Beltrami identity for spherical
harmonic functions, the derivatives of Steklov eigenvalues with respect to the
domain perturbation parameter can be determined by the eigenvalues of a matrix
involving the integral of the product of three spherical harmonic functions. By
using the addition theorem for spherical harmonic functions, we determine
conditions when the trace of this matrix becomes zero. These conditions can
then be used to determine when spherical and annular regions are critical
points while we optimize Steklov eigenvalues subject to a volume constraint. In
addition, we develop numerical approaches based on particular solutions and
show that numerical results in two and three dimensions are in agreement with
our analytic results.


  We consider a formulation of a non zero-sum n players game by an n+1 players
zero-sum game. We suppose the existence of the n+1-th player in addition to n
players in the main game, and virtual subsidies to the n players which is
provided by the n+1-th player. Its strategic variable affects only the
subsidies, and does not affect choice of strategies by the n players in the
main game. His objective function is the opposite of the sum of the payoffs of
the n players. We will show 1) The minimax theorem by Sion (Sion(1958)) implies
the existence of Nash equilibrium in the n players non zero-sum game. 2) The
maximin strategy of each player in {1, 2, \dots, n} with the minimax strategy
of the n+1-th player is equivalent to the Nash equilibrium strategy of the n
players non zero-sum game. 3) The existence of Nash equilibrium in the n
players non zero-sum game implies Sion's minimax theorem for pairs of each of
the n players and the n+1-th player.


  We present the results of the lattice QCD calculation of the average up-down
and strange quark masses and of the light meson pseudoscalar decay constants,
recently performed with Nf=2 dynamical fermions by the ETM Collaboration. The
simulation is carried out at a single value of the lattice spacing with the
twisted mass fermionic action at maximal twist, which guarantees automatic
O(a)-improvement of the physical quantities. Quark masses are renormalized by
implementing the non perturbative RI-MOM renormalization procedure. Our results
for the light quark masses are m_{ud}^{MSbar}(2 Gev)=3.85 +- 0.12 +- 0.40 MeV,
m_s^{MSbar}(2 Gev)=105 +- 3 +- 9 MeV and m_s/m_{ud}=27.3 +- 0.3 +- 1.2. We also
obtain f_K=161.7 +- 1.2 +- 3.1 MeV and the ratio f_K/f_pi=1.227 +- 0.009 +-
0.024. From this ratio, by using the experimental determination of Gamma(K ->
mu {bar nu}_mu (gamma))/Gamma(pi -> mu {bar nu}_mu (gamma)) and the average
value of |V_{ud}| from nuclear beta decays, we obtain |V_{us}|=0.2192(5)(45),
in agreement with the determination from K_{l3} decays and the unitarity
constraint.


  Parameter estimation is an important sub-field in statistics and system
identification. Various methods for parameter estimation have been proposed in
the literature, among which the Two-Stage (TS) approach is particularly
promising, due to its ease of implementation and reliable estimates. Among the
different statistical frameworks used to derive TS estimators, the min-max
framework is attractive due to its mild dependence on prior knowledge about the
parameters to be estimated. However, the existing implementation of the minimax
TS approach has currently limited applicability, due to its heavy computational
load. In this paper, we overcome this difficulty by using a gradient boosting
machine (GBM) in the second stage of TS approach. We call the resulting
algorithm the Two-Stage Gradient Boosting Machine (TSGBM) estimator. Finally,
we test our proposed TSGBM estimator on several numerical examples including
models of dynamical systems.


  The process of single W-boson production at the energies of Next Linear
Colliders is considered. We discuss in details the contributions from s and t
channel diagrams, technical aspects of the complete tree level calculation with
a finite W width, and the quark mass effects.


  Some key features of the overlap operator with a UV-filtered Wilson kernel
are discussed. The first part concerns spectral properties of the underlying
shifted hermitean Wilson operator and the relation to the observed speedup of
the overlap construction. Next, the localization of the filtered overlap and
its axial-vector renormalization constant are discussed. Finally, results of an
exploratory scaling study for $m_{ud}, m_s$ and $f_\pi, f_K$ are presented.


  We survey some basic geometric properties of the Funk metric of a convex set
in $\mathbb{R}^n$. In particular, we study its geodesics, its topology, its
metric balls, its convexity properties, its perpendicularity theory and its
isometries. The Hilbert metric is a symmetrization of the Funk metric, and we
show some properties of the Hilbert metric that follow directly from the
properties we prove for the Funk metric.


  In their 1960 book on finite Markov chains, Kemeny and Snell established that
a certain sum is invariant. The value of this sum has become known as {\it
Kemeny's constant}. Various proofs have been given over time, some more
technical than others. We give here a very simple physical justification, which
extends without a hitch to continuous-time Markov chains on a finite state
space.
  For Markov chains with denumerably infinite state space, the constant may be
infinite and even if it is finite, there is no guarantee that the physical
argument will hold. We show that the physical interpretation does go through
for the special case of a birth-and-death process with a finite value of
Kemeny's constant.
  Keywords: Kemeny's constant; discrete-time Markov chains; continuous-time
Markov chains; passage times; deviation matrix.


  The total number and luminosity function of the population of dwarf galaxies
of the Milky Way (MW) provide important constraints on the nature of the dark
matter and on the astrophysics of galaxy formation at low masses. However, only
a partial census of this population exists because of the flux limits and
restricted sky coverage of existing Galactic surveys. We combine the sample of
satellites recently discovered by the Dark Energy Survey (DES) with the
satellites found in Sloan Digital Sky Survey (SDSS) Data Release 9 (together
these surveys cover nearly half the sky) to estimate the total luminosity
function of satellites down to $M_{\rm V}=0$. We apply a new Bayesian inference
method in which we assume that the radial distribution of satellites
independently of absolute magnitude follows that of subhaloes selected
according to their peak maximum circular velocity. We find that there should be
at least $124^{+40}_{-27}$ (68 per cent CL, statistical error) satellites
brighter than $M_{\rm V}=0$ within $300$ kpc of the Sun. As a result of our use
of new data and better simulations, and a more robust statistical method, we
infer a much smaller population of satellites than reported in previous studies
using earlier SDSS data only; we also address an underestimation of the
uncertainties in earlier work by accounting for stochastic effects. We find
that the inferred number of faint satellites depends only weakly on the assumed
mass of the MW halo and we provide scaling relations to extend our results to
different assumed halo masses and outer radii. We predict that half of our
estimated total satellite population of the MW should be detected by the Large
Synoptic Survey Telescope. The code implementing our estimation method is
available online.


  On a smooth, compact and oriented manifold without boundary, we give a
complete description of the correlation function of a Morse-Smale gradient flow
satisfying a certain nonresonance assumption. This is done by analyzing
precisely the spectrum of the generator of such a flow acting on certain
anisotropic spaces of currents. In particular, we prove that this dynamical
spectrum is given by linear combinations with integer coefficients of the
Lyapunov exponents at the critical points of the Morse function. Via this
spectral analysis and in analogy with Hodge-de Rham theory, we give an
interpretation of the Morse complex as the image of the de Rham complex under
the spectral projector on the kernel of the generator of the flow. This allows
us to recover classical results from differential topology such as the Morse
inequalities and Poincar{\'e} duality.


  We prove a commutative algebra result which has consequences for congruences
between automorphic forms modulo prime powers. If C denotes the congruence
module for a fixed automorphic Hecke eigenform \pi_0 we prove an exact relation
between the p-adic valuation of the order of C and the sum of the exponents of
p-power congruences between the Hecke eigenvalues of \pi_0 and other
automorphic forms. We apply this result to several situations including the
congruences described by Mazur's Eisenstein ideal.


  Aftershocks of the 2012 Off-Coast of Sumatra Earthquake Sequence exhibit a
complex and diffuse spatial distribution. The first-order complexity in
aftershock distribution is clear and well beyond the influence of typical
earthquake location uncertainty. The sequence included rupture of multiple
fault segments, spatially separated. We use surface-wave based relative
centroid locations to examine whether, at the small scale, the distribution of
the aftershocks was influenced by location errors. Surface-wave based relative
location has delineated precise oceanic transform fault earthquake locations in
multiple regions. However, the relocated aftershocks off the coast of Sumatra
seldom align along simple linear trends that are compatible with the
corresponding fault strikes as estimated for the GCMT catalog. The relocation
of roughly 60 moderate-earthquake epicentroids suggests that the faulting
involved in the 2012 earthquake aftershock sequence included strain release
along many short fault segments. Statistical analysis and temporal variations
of aftershocks show a typical decay of the aftershocks but a relatively low
number of aftershocks, as is common for intraplate oceanic earthquakes. Coulomb
stress calculations indicate that most of the moderate-magnitude aftershocks
are compatible with stress changes predicted by the large-event slip models.
The patterns in the aftershocks suggest that the formation of the boundary and
eventual localization of deformation between the Indian and Australian plate is
a complicated process.


  Low latency rates are crucial for online video-based applications, such as
video conferencing and cloud gaming, which make improving video quality in
online scenarios increasingly important. However, existing quality enhancement
methods are limited by slow inference speed and the requirement for temporal
information contained in future frames, making it challenging to deploy them
directly in online tasks. In this paper, we propose a novel method, STLVQE,
specifically designed to address the rarely studied online video quality
enhancement (Online-VQE) problem. Our STLVQE designs a new VQE framework which
contains a Module-Agnostic Feature Extractor that greatly reduces the redundant
computations and redesign the propagation, alignment, and enhancement module of
the network. A Spatial-Temporal Look-up Tables (STL) is proposed, which
extracts spatial-temporal information in videos while saving substantial
inference time. To the best of our knowledge, we are the first to exploit the
LUT structure to extract temporal information in video tasks. Extensive
experiments on the MFQE 2.0 dataset demonstrate that our STLVQE achieves a
satisfactory performance-speed trade-off.


  The search for extraterrestrial intelligence (SETI) has been heavily
influenced by solutions to the Drake Equation, which returns an integer value
for the number of communicating civilisations resident in the Milky Way, and by
the Fermi Paradox, glibly stated as: "If they are there, where are they?". Both
rely on using average values of key parameters, such as the mean signal
lifetime of a communicating civilisation. A more accurate answer must take into
account the distribution of stellar, planetary and biological attributes in the
galaxy, as well as the stochastic nature of evolution itself. This paper
outlines a method of Monte Carlo realisation which does this, and hence allows
an estimation of the distribution of key parameters in SETI, as well as
allowing a quantification of their errors (and the level of ignorance therein).
Furthermore, it provides a means for competing theories of life and
intelligence to be compared quantitatively.


  Given the great threat of adversarial attacks against Deep Neural Networks
(DNNs), numerous works have been proposed to boost transferability to attack
real-world applications. However, existing attacks often utilize advanced
gradient calculation or input transformation but ignore the white-box model.
Inspired by the fact that DNNs are over-parameterized for superior performance,
we propose diversifying the high-level features (DHF) for more transferable
adversarial examples. In particular, DHF perturbs the high-level features by
randomly transforming the high-level features and mixing them with the feature
of benign samples when calculating the gradient at each iteration. Due to the
redundancy of parameters, such transformation does not affect the
classification performance but helps identify the invariant features across
different models, leading to much better transferability. Empirical evaluations
on ImageNet dataset show that DHF could effectively improve the transferability
of existing momentum-based attacks. Incorporated into the input
transformation-based attacks, DHF generates more transferable adversarial
examples and outperforms the baselines with a clear margin when attacking
several defense models, showing its generalization to various attacks and high
effectiveness for boosting transferability. Code is available at
https://github.com/Trustworthy-AI-Group/DHF.


  Current-induced spin-orbit torques in Co$_2$FeAl/Pt ultrathin bilayers are
studied using a magnetoresistive harmonic response technique, which
distinguishes the dampinglike and fieldlike contributions. The presence of a
temperature-dependent magnetic proximity effect is observed through the
anomalous Hall and anisotropic magnetoresistances, which are enhanced at low
temperatures for thin platinum thicknesses. The fieldlike torque efficiency
decreases steadily as the temperature is lowered for all Pt thicknesses
studied, which we propose is related to the influence of the magnetic proximity
effect on the fieldlike torque mechanism.


  The magnetoresistance associated with quantum interference corrections in a
high mobility, gated InGaAs/InP quantum well structure is studied as a function
of temperature, gate voltage, and angle of the tilted magnetic field.
Particular attention is paid to the experimental extraction of phase-breaking
and spin-orbit scattering times when weak anti- localization effects are
prominent. Compared with metals and low mobility semiconductors the
characteristic magnetic field $B_{tr} = \hbar/4eD \tau$ in high mobility
samples is very small and the experimental dependencies of the interference
effects extend to fields several hundreds of times larger. Fitting experimental
results under these conditions therefore requires theories valid for arbitrary
magnetic field. It was found, however, that such a theory was unable to fit the
experimental data without introducing an extra, empirical, scale factor of
about 2. Measurements in tilted magnetic fields and as a function of
temperature established that both the weak localization and the weak
anti-localization effects have the same, orbital origin. Fits to the data
confirmed that the width of the low field feature, whether a weak localization
or a weak anti-localization peak, is determined by the phase-breaking time and
also established that the universal (negative) magnetoresistance observed in
the high field limit is associated with a temperature independent spin-orbit
scattering time.


  Magneto-luminescence studies in electron bilayers reveal the hallmarks of the
even-denominator and other quantum Hall states in the intensities and energies
of the inter-band optical recombination lines. In the presence of a small
tunneling gap between the layers the magneto-optical emission from the lowest
anti-symmetric subband, not populated in a single-electron picture, displays
maxima at filling factors 1 and 2/3. These findings uncover a loss of
pseudospin polarization, where the pseudospin describes the layer index degree
of freedom, that is linked to an anomalous population of the anti-symmetric
level due to excitonic correlations. The results demonstrate a new realm to
probe the impact of inter-layer Coulomb interaction in quantum Hall bilayers.


  We characterize when a convex risk measure associated to a law-invariant
acceptance set in $L^\infty$ can be extended to $L^p$, $1\leq p<\infty$,
preserving finiteness and continuity. This problem is strongly connected to the
statistical robustness of the corresponding risk measures. Special attention is
paid to concrete examples including risk measures based on expected utility,
max-correlation risk measures, and distortion risk measures.


  Scene Graph Generation (SGG) endeavors to predict the relationships between
subjects and objects in a given image. Nevertheless, the long-tail distribution
of relations often leads to biased prediction on coarse labels, presenting a
substantial hurdle in SGG. To address this issue, researchers focus on unbiased
SGG and introduce data transfer methods to transfer coarse-grained predicates
into fine-grained ones across the entire dataset. However, these methods
encounter two primary challenges: 1) They overlook the inherent context
constraints imposed by subject-object pairs, leading to erroneous relations
transfer. 2) Additional retraining process are required after the data
transfer, which incurs substantial computational costs. To overcome these
limitations, we introduce the first plug-and-play one-stage data transfer
pipeline in SGG, termed Adaptive Label Finetuning (ALF), which eliminates the
need for extra retraining sessions and meanwhile significantly enhance models'
relation recognition capability across various SGG benchmark approaches.
Specifically, ALF consists of two components: Adaptive Label Construction (ALC)
and Adaptive Iterative Learning (AIL). By imposing Predicate-Context
Constraints within relation space, ALC adaptively re-ranks and selects
candidate relations in reference to model's predictive logits utilizing the
Restriction-Based Judgment techniques, achieving robust relation transfer.
Supervised with labels transferred by ALC, AIL iteratively finetunes the SGG
models in an auto-regressive manner, which mitigates the substantial
computational costs arising from the retraining process. Extensive experiments
demonstrate that ALF achieves a 16% improvement in mR@100 compared to the
typical SGG method Motif, with only a 6% increase in calculation costs compared
to the state-of-the-art method IETrans.


  In this paper we study the linear stability of the relative equilibria for
homogeneous and quasihomogeneous potentials. Firstly, in the case the potential
is a homogeneous function of degree $-a$, we find that any relative equilibrium
of the $n$-body problem with $a>2$ is spectrally unstable. We also find a
similar condition in the quasihomogeneous case. Then we consider the case of
three bodies and we study the stability of the equilateral triangle relative
equilibria. In the case of homogeneous potentials we recover the classical
result obtained by Routh in a simpler way. In the case of quasihomogeneous
potentials we find a generalization of Routh inequality and we show that, for
certain values of the masses, the stability of the relative equilibria depends
on the size of the configuration.


  Trapped ions constitute one of the most promising systems for implementing
quantum computing and networking. For large-scale ion-trap-based quantum
computers and networks, it is critical to have two types of qubits, one for
computation and storage, while the other for auxiliary operations like runtime
qubit detection, sympathetic cooling, and repetitive entanglement generation
through photon links. Dual-type qubits have previously been realized in hybrid
systems using two ion species, which, however, introduces significant
experimental challenges for laser setup, gate operations as well as the control
of the fraction and positioning of each qubit type within an ion crystal. Here
we solve these problems by implementing two coherently-convertible qubit types
using the same ion species. We encode the qubits into two pairs of clock states
of the 171Yb+ ions, and achieve fast and high-fidelity conversion between the
two types using narrow-band lasers. We further demonstrate that operations on
one qubit type, including sympathetic laser cooling, gates and qubit detection,
have crosstalk errors less than 0.03% on the other type, well below the error
threshold for fault-tolerant quantum computing. Our work showcases the
feasibility and advantages of using coherently convertible dual-type qubits
with the same ion species for future large-scale quantum computing and
networking.


  The link between hot and cool stellar outflows is shown to be critical for
correctly predicting the masses of the most massive black holes (BHs) below the
so-called pair-instability supernova (PISN) mass gap. Gravitational Wave (GW)
event 190521 allegedly hosted an "impossibly" heavy BH of 85 Solar Masses. Here
we show how our increased knowledge of both metallicity Z and temperature
dependent mass loss is critical for our evolutionary scenario of a low-Z blue
supergiant (BSG) progenitor of an initially approx 100 Solar Masses star to
work. We show using MESA stellar evolution modelling experiments that as long
as we can keep such stars above 8000 K such low-Z BSGs can avoid strong winds,
and keep a very large envelope mass intact before core collapse. This naturally
leads to the Cosmic Time dependent maximum BH function below the PISN gap.


  There is a widely held view in the astronomical community that unmanned
robotic space vehicles are, and will always be, more efficient explorers of
planetary surfaces than astronauts (e.g. Coates, 2001; Clements 2009; Rees
2011). Partly this is due to a common assumption that robotic exploration is
cheaper than human exploration (although, as we shall see, this isn't
necessarily true if like is compared with like), and partly from the
expectation that continued developments in technology will relentlessly
increase the capability, and reduce the size and cost, of robotic missions to
the point that human exploration will not be able to compete. I will argue
below that the experience of human exploration during the Apollo missions, more
recent field analogue studies, and trends in robotic space exploration actually
all point to exactly the opposite conclusion.


  We show that Spaltenstein varieties of classical groups are pure dimensional
when the Jordan type of the nilpotent element involved is an even or odd
partition. We further show that they are Lagrangian in the partial resolutions
of the associated nilpotent Slodowy slices, from which their dimensions are
known to be one half of the dimension of the partial resolution minus the
dimension of the nilpotent orbit. The results are then extended to the
$\sigma$-quiver-variety setting.


  Log Gromov-Witten invariants have recently been defined separately by Gross
and Siebert and Abramovich and Chen. This paper provides a dictionary between
log geometry and holomorphic exploded manifolds in order to compare
Gromov-Witten invariants defined using exploded manifolds or log schemes. The
gluing formula for Gromov-Witten invariants of exploded manifolds suggests an
approach to proving analogous gluing formulas for log Gromov-Witten invariants.


  New developments in empirical analyses of the proton-proton differential
cross section data at high energies are reported. Making use of an
unconstrained model-independent parametrization for the scattering amplitude
and two different fit procedures, all the experimental data in the
center-of-mass energy interval 19.4 - 62.5 GeV are quite well described
(optical point and data above the region of Coulomb-nuclear interference). The
contributions from the real and imaginary parts of the amplitude beyond the
forward direction are discussed and compared with the results from previous
analyses and phenomenological models. Extracted overlap functions (impact
parameter space) are outlined and a critical discussion on model-independent
analyses and results are also presented.


  Biological cells are often found to sense their chemical environment near the
single-molecule detection limit. Surprisingly, this precision is higher than
simple estimates of the fundamental physical limit, hinting towards active
sensing strategies. In this work, we analyse the effect of cell memory, e.g.
from slow biochemical processes, on the precision of sensing by cell-surface
receptors. We derive analytical formulas, which show that memory significantly
improves sensing in weakly fluctuating environments. However, surprisingly when
memory is adjusted dynamically, the precision is always improved, even in
strongly fluctuating environments. In support of this prediction we quantify
the directional biases in chemotactic Dictyostelium discoideum cells in a flow
chamber with alternating chemical gradients. The strong similarities between
cell sensing and control engineering suggest universal problem-solving
strategies of living matter.


  Various new physics models, e.g., theories of compositeness, can accommodate
the color singlet excited leptons that interact with the leptons, quarks,
leptoquarks, etc. A particular type of excited lepton, which at low energies
interacts with the Standard Model fermions mainly through the four-fermion
coupling to lepton and quark-antiquark (or lepton-antilepton) pair, we call
leptomeson. These new particles may contribute to variety of the experimental
anomalies such as the discrepancy in the muon g-2. We propose that the
leptomesons can generate also the baryon asymmetry that explains the imbalance
in ordinary matter and antimatter in the observable universe. We consider the
two types of scenarios for this baryogenesis via leptogenesis to occur from
either leptomeson oscillations or decays. Both possibilities do not contradict
to the small masses of the observable neutrinos and the proton stability.
Moreover they can be relevant for the near future collider experiments and do
not suffer from the gravitino problem.


  The discovery of rings around extrasolar planets ("exorings") is one of the
next breakthroughs in exoplanetary research. Previous studies have explored the
feasibility of detecting exorings with present and future photometric
sensitivities by seeking anomalous deviations in the residuals of a standard
transit light curve fit, at the level of ~100 ppm for Kronian rings. In this
work, we explore two much larger observational consequences of exorings: (1)
the significant increase in transit depth that may lead to the
misclassification of ringed planetary candidates as false-positives and/or the
underestimation of planetary density; and (2) the so-called "photo-ring"
effect, a new asterodensity profiling effect, revealed by a comparison of the
light curve derived stellar density to that measured with independent methods
(e.g., asteroseismology). While these methods do not provide an unambiguous
detection of exorings, we show that the large amplitude of these effects
combined with their relatively simple analytic description, makes them highly
suited to large-scale surveys to identify candidate ringed planets worthy of
more detailed investigation. Moreover, these methods lend themselves to
ensemble analyses seeking to uncover evidence of a population of ringed
planets. We describe the method in detail, develop the basic underlying
formalism and test it in the parameter space of rings and transit config-
uration. We discuss the prospects of using this method for the first systematic
search of exoplanetary rings in the Kepler database and provide a basic
computational code for implementing it.


  Observations of magnetic fields on scales up to several Mpc are important for
understanding cluster and large-scale structure evolution. Our current census
of such structures is heavily biased -- towards fields of several microG,
towards fields in deep potential wells, and towards high inferred field
strengths in cooling flow and other clusters from improper analysis of rotation
measure data. After reviewing these biases, I show some recent results on two
relics that are powered in very different ways. I describe new investigations
that are now uncovering weak diffuse fields in the outskirts of clusters and
other low density environments, and the good prospects for further progress.


  We identify a relationship between the solutions of a nonsymmetric algebraic
T-Riccati equation (T-NARE) and the deflating subspaces of a palindromic matrix
pencil, obtained by arranging the coefficients of the T-NARE. The interplay
between T-NARE and palindromic pencils allows one to derive both theoretical
properties of the solutions of the equation, and new methods for its numerical
solution. In particular, we propose methods based on the (palindromic) QZ
algorithm and the doubling algorithm, whose effectiveness is demonstrated by
several numerical tests


  Fine-Grained Named Entity Typing (FG-NET) is a key component in Natural
Language Processing (NLP). It aims at classifying an entity mention into a wide
range of entity types. Due to a large number of entity types, distant
supervision is used to collect training data for this task, which noisily
assigns type labels to entity mentions irrespective of the context. In order to
alleviate the noisy labels, existing approaches on FGNET analyze the entity
mentions entirely independent of each other and assign type labels solely based
on mention sentence-specific context. This is inadequate for highly overlapping
and noisy type labels as it hinders information passing across sentence
boundaries. For this, we propose an edge-weighted attentive graph convolution
network that refines the noisy mention representations by attending over
corpus-level contextual clues prior to the end classification. Experimental
evaluation shows that the proposed model outperforms the existing research by a
relative score of upto 10.2% and 8.3% for macro f1 and micro f1 respectively.


  We comment on a recently discussed possibility of oscillations between
neutrons and degenerate mirror neutrons in the context of mirror models for
particles and forces. It has been noted by Bento and Berezhiani that if these
oscillations occurred at a rate of $\tau^{-1}_{NN'}\sim sec^{-1}$, it would
help explain putative super GKZ cosmic ray events provided the temperature of
the mirror radiation is $\sim 0.3-0.4$ times that of familiar cosmic microwave
background radiation. We discuss how such oscillation time scales can be
realized in mirror models and find that the simplest nonsupersymmetric model
for this idea requires the existence of a low mass (30-3000 GeV) color triplet
scalar or vector boson. A supersymmetric model, where this constraint can be
avoided is severely constrained by the requirement of maintaining a cooler
mirror sector. We also find that the reheat temperature after inflation in
generic models that give fast $n-n'$ oscillation be less than about 300 GeV in
order to maintain the required relative coolness of the mirror sector.


  Comparison of the ISM properties of a wide range of metal-poor galaxies with
normal metal-rich galaxies reveals striking differences. We find that the
combination of the low dust abundance and the active star formation results in
a very porous ISM filled with hard photons, heating the dust in dwarf galaxies
to overall higher temperatures than their metal-rich counterparts. This results
in photodissociation of molecular clouds to greater depths, leaving relatively
large PDR envelopes and difficult-to-detect CO cores. From detailed modeling of
the low-metallicity ISM, we find significant fractions of CO-dark H2 - a
reservoir of molecular gas not traced by CO, but present in the [CII] and
[CI]-emitting envelopes. Self-consistent analyses of the neutral and ionized
gas diagnostics along with the dust SED is the necessary way forward in
uncovering the multiphase structure of galaxies


  We study the Gauss-Manin connection for the moduli space of an arrangement of
complex hyperplanes in the cohomology of a nonresonant complex rank one local
system. Aomoto and Kita determined this Gauss-Manin connection for arrangements
in general position. We use their results and an algorithm constructed in this
paper to determine this Gauss-Manin connection for all arrangements.


  Magnetic relaxation in a MgB$_2$ superconductor was measured. The temperature
dependence of the normalized relaxation rate was determined for three different
magnetic fields. By extrapolating these rates to T=0 K, we find that these
extrapolations do not approach zero, indicating quantum tunneling of vortices
in the superconductor. A quantum correction of the relaxation rate, followed by
the correction of the magnetic moment, is proposed. Using the quantum
correction, we find that $U_0$ increases with decreasing temperature and
approaches a maximum at T=0.


  Let $p(n)$ denote the partition function. In this article, we will show that
congruences of the form $$ p(m^j\ell^kn+B)\equiv 0\mod m \text{for all} n\ge 0
$$ exist for all primes $m$ and $\ell$ satisfying $m\ge 13$ and $\ell\neq
2,3,m$. Here the integer $k$ depends on the Hecke eigenvalues of a certain
invariant subspace of $S_{m/2-1}(\Gamma_0(576),\chi_{12})$ and can be
explicitly computed. More generally, we will show that for each integer $i>0$
there exists an integer $k$ such that for every non-negative integers $j\ge i$
with a properly chosen $B$ the congruence $$ p(m^j\ell^kn+B)\equiv 0\mod m^i $$
holds for all integers $n$ not divisible by $\ell$.


  We present near-infrared (nIR) and optical observations of the afterglow of
GRB 030115. Discovered in an infrared search at Kitt Peak 5 hours after the
burst trigger, this afterglow is amongst the faintest observed in the R-band at
an early epoch, and exhibits very red colors, with $R-K\approx 6$. The
magnitude of the optical afterglow of GRB 030115 is fainter than many upper
limits for other bursts, suggesting that without early nIR observations it
would have been classified as a ``dark'' burst. Both the color and optical
magnitude of the afterglow are likely due to dust extinction and indicate that
at least some optical afterglows are very faint due to dust along the line of
sight. Multicolor {\it Hubble Space Telescope} observations were also taken of
the host galaxy and the surrounding field. Photometric redshifts imply that the
host, and a substantial number of faint galaxies in the field are at $z \sim
2.5$. The overdensity of galaxies is sufficiently great that GRB 030115 may
have occurred in a rich high-redshift cluster. The host galaxy shows extremely
red colors (R-K=5) and is the first GRB host to be classified as an Extremely
Red Object (ERO). Some of the galaxies surrounding the host also show very red
colors, while the majority of the cluster are much bluer, indicating ongoing
unobscured star formation. As it is thought that much of high redshift star
formation occurs in highly obscured environments it may be that GRB 030115
represent a transition object, between the relatively unobscured afterglows
seen to date and a population which are very heavily extinguished, even in the
nIR.


  In recent years there has been a spate of papers describing systems for
probabilisitic reasoning which do not use numerical probabilities. In some
cases the simple set of values used by these systems make it impossible to
predict how a probability will change or which hypothesis is most likely given
certain evidence. This paper concentrates on such situations, and suggests a
number of ways in which they may be resolved by refining the representation.


  Part I of this work [2] developed the exact diffusion algorithm to remove the
bias that is characteristic of distributed solutions for deterministic
optimization problems. The algorithm was shown to be applicable to a larger set
of combination policies than earlier approaches in the literature. In
particular, the combination matrices are not required to be doubly stochastic,
which impose stringent conditions on the graph topology and communications
protocol. In this Part II, we examine the convergence and stability properties
of exact diffusion in some detail and establish its linear convergence rate. We
also show that it has a wider stability range than the EXTRA consensus
solution, meaning that it is stable for a wider range of step-sizes and can,
therefore, attain faster convergence rates. Analytical examples and numerical
simulations illustrate the theoretical findings.


  In this paper, we investigate the communication designs of over-the-air
computation (AirComp) empowered federated learning (FL) systems considering
uplink model aggregation and downlink model dissemination jointly. We first
derive an upper bound on the expected difference between the training loss and
the optimal loss, which reveals that optimizing the FL performance is
equivalent to minimizing the distortion in the received global gradient vector
at each edge node. As such, we jointly optimize each edge node transmit and
receive equalization coefficients along with the edge server forwarding matrix
to minimize the maximum gradient distortion across all edge nodes. We further
utilize the MNIST dataset to evaluate the performance of the considered FL
system in the context of the handwritten digit recognition task. Experiment
results show that deploying multiple antennas at the edge server significantly
reduces the distortion in the received global gradient vector, leading to a
notable improvement in recognition accuracy compared to the single antenna
case.


  In this Letter we present a theoretical scenario to explain the steep
correlation between disk accretion rates and stellar masses observed in
pre-main sequence stars. We show that the correlations and spread observed in
the two best studied regions, rho-Ophiuchus and Taurus, can be reproduced by a
simple model of single star formation from a rotating collapsing core and the
viscous evolution of the circumstellar disk. In this model, the rate of
rotation of the parent core sets the value of the `centrifugal radius' within
which the infalling matter is loaded onto the surface of the disk. As a
consequence, the disk accretion rate measured long after the dispersal of the
parental core bears the imprint of the initial conditions of star formation.
The observed trend results naturally if, at the onset of the collapse, cores of
all masses rotate with the same distribution of angular velocities, measured in
units of the break-up rotation rate.


  Mobile geo-location advertising, where mobile ads are targeted based on a
user's location, has been identified as a key growth factor for the mobile
market. As with online advertising, a crucial ingredient for their success is
the development of effective economic mechanisms. An important difference is
that mobile ads are shown sequentially over time and information about the user
can be learned based on their movements. Furthermore, ads need to be shown
selectively to prevent ad fatigue. To this end, we introduce, for the first
time, a user model and suitable economic mechanisms which take these factors
into account. Specifically, we design two truthful mechanisms which produce an
advertisement plan based on the user's movements. One mechanism is allocatively
efficient, but requires exponential compute time in the worst case. The other
requires polynomial time, but is not allocatively efficient. Finally, we
experimentally evaluate the tradeoff between compute time and efficiency of our
mechanisms.


  In Gauss-Bonnet braneworld cosmology, the Friedmann equation of our
four-dimensional universe on 3-brane is modified in a high energy regime
(Gauss-Bonnet regime), while the standard expansion law is reproduced in low
energies (standard regime). We investigate the Gauss-Bonnet braneworld
cosmological effect on the thermal relic density of cold dark matter when the
freeze-out of the dark matter occurs in the Gaugss-Bonnet regime. We find that
the resultant relic density is considerably reduced when the transition
temperature, which connects the Gauss-Bonnet regime with the standard regime,
is low enough. This result is in sharp contrast with the result previously
obtained in the Randall-Sundrum braneworld cosmology, where the relic density
is enhanced.


  We solve explicitly a certain minimization problem for probability measures
in one dimension involving an interaction energy that arises in the modelling
of aggregation phenomena. We show that in a certain regime minimizers are
absolutely continuous with an unbounded density, thereby settling a question
that was left open in previous works.


  We derive the expressions for the full angular distributions of $\bar B\to
D\ell\bar \nu_\ell$ and $\bar B\to D^{\ast }\ell\bar \nu_\ell$ decays and
discuss the spectra on each angle separately. The coefficient functions,
depending on helicity amplitudes, can then be combined in an ensemble of
observables which can then be used to check for the presence of New Physics. We
examine the sensitivity of each of these observables on the presence of
non-Standard Model interaction terms at low energies. The expressions presented
here are general and can be used for studying any other semileptonic
pseudoscalar to pseudoscalar/vector meson decay. We also examine the problem of
pollution of the $\bar B\to D^{\ast}(\to D\pi)_S\ell\bar \nu_\ell$ decay sample
by the $\bar B\to D_0^{\ast}(\to D\pi)\ell\bar \nu_\ell$ events, and point out
that a measurement of two particular quantities could clarify whether or not
the $(D\pi)_{S-\rm wave}$ in the vicinity of $D^\ast$-peak is (approximately)
described by the Breit-Wigner formula.


  Tuning-free long video diffusion has been proposed to generate
extended-duration videos with enriched content by reusing the knowledge from
pre-trained short video diffusion model without retraining. However, most works
overlook the fine-grained long-term video consistency modeling, resulting in
limited scene consistency (i.e., unreasonable object or background
transitions), especially with multiple text inputs. To mitigate this, we
propose the Consistency Noise Injection, dubbed CoNo, which introduces the
"look-back" mechanism to enhance the fine-grained scene transition between
different video clips, and designs the long-term consistency regularization to
eliminate the content shifts when extending video contents through noise
prediction. In particular, the "look-back" mechanism breaks the noise
scheduling process into three essential parts, where one internal noise
prediction part is injected into two video-extending parts, intending to
achieve a fine-grained transition between two video clips. The long-term
consistency regularization focuses on explicitly minimizing the pixel-wise
distance between the predicted noises of the extended video clip and the
original one, thereby preventing abrupt scene transitions. Extensive
experiments have shown the effectiveness of the above strategies by performing
long-video generation under both single- and multi-text prompt conditions. The
project has been available in https://wxrui182.github.io/CoNo.github.io/.


  This paper reports on the experimental implementation of the quantum baker's
map via a three bit nuclear magnetic resonance (NMR) quantum information
processor. The experiments tested the sensitivity of the quantum chaotic map to
perturbations. In the first experiment, the map was iterated forward and then
backwards to provide benchmarks for intrinsic errors and decoherence. In the
second set of experiments, the least significant qubit was perturbed in between
the iterations to test the sensitivity of the quantum chaotic map to applied
perturbations. These experiments are used to investigate previous predicted
properties of quantum chaotic dynamics.


  Modularity is a popular measure of community structure. However, maximizing
the modularity can lead to many competing partitions, with almost the same
modularity, that are poorly correlated with each other. It can also produce
illusory "communities" in random graphs where none exist. We address this
problem by using the modularity as a Hamiltonian at finite temperature, and
using an efficient Belief Propagation algorithm to obtain the consensus of many
partitions with high modularity, rather than looking for a single partition
that maximizes it. We show analytically and numerically that the proposed
algorithm works all the way down to the detectability transition in networks
generated by the stochastic block model. It also performs well on real-world
networks, revealing large communities in some networks where previous work has
claimed no communities exist. Finally we show that by applying our algorithm
recursively, subdividing communities until no statistically-significant
subcommunities can be found, we can detect hierarchical structure in real-world
networks more efficiently than previous methods.


  Let $G$ and $H$ be Hausdorff ample groupoids and let $R$ be a commutative
unital ring. We show that if $G$ and $H$ are equivalent in the sense of
Muhly-Renault-Williams, then the associated Steinberg algebras of locally
constant $R$-valued functions with compact support are Morita equivalent. We
deduce that collapsing a ``collapsible subgraph" of a directed graph in the
sense of Crisp and Gow does not change the Morita-equivalence class of the
associated Leavitt path $R$-algebra, and therefore a number of graphical
constructions which yield Morita equivalent $C^*$-algebras also yield Morita
equivalent Leavitt path algebras.


  The two dimensional square lattice hard-core boson Hubbard model with near
neighbor interactions has a `checkerboard' charge density wave insulating phase
at half-filling and sufficiently large intersite repulsion. When doped, rather
than forming a supersolid phase in which long range charge density wave
correlations coexist with a condensation of superfluid defects, the system
instead phase separates. However, it is known that there are other lattice
geometries and interaction patterns for which such coexistence takes place. In
this paper we explore the possibility that anisotropic hopping or anisotropic
near neighbor repulsion might similarly stabilize the square lattice
supersolid. By considering the charge density wave structure factor and
superfluid density for different ratios of interaction strength and
hybridization in the $\hat x$ and $\hat y$ directions, we conclude that phase
separation still occurs.


  The last several years have brought a growing body of work on ensuring that
recommender systems are in some sense consumer-fair -- that is, they provide
comparable quality of service, accuracy of representation, and other effects to
their users. However, there are many different strategies to make systems more
fair and a range of intervention points. In this position paper, we build on
ongoing work to highlight the need for researchers and practitioners to attend
to the details of their application, users, and the fairness objective they aim
to achieve, and adopt interventions that are appropriate to the situation. We
argue that consumer fairness should be a creative endeavor flowing from the
particularities of the specific problem to be solved.


  In this paper we study the bifurcations of a class of polycycles, called
lips, occurring in generic three-parameter smooth families of vector fields on
a M\"obius band. The lips consists of a set of polycycles formed by two
saddle-nodes, one attracting and the other repelling, connected by the
hyperbolic separatrices of the saddle-nodes and by orbits interior to both
nodal sectors. We determine, under certain genericity hypotheses, the maximum
number of limits cycles that may bifurcate from a graphic belonging to the lips
and we describe its bifurcation diagram.


  The control of strain in two-dimensional materials opens exciting
perspectives for the engineering of their electronic properties. While this
expectation has been validated by artificial-lattice studies, it remains
elusive in the case of atomic lattices. Remarkable results were obtained on
nanobubbles and nano-wrinkles, or using scanning probes; microscale strain
devices were implemented exploiting deformable substrates or external loads.
These devices lack, however, the flexibility required to fully control and
investigate arbitrary strain profiles. Here, we demonstrate a novel approach
making it possible to induce strain in graphene using polymeric micrometric
artificial muscles (MAMs) that contract in a controllable and reversible way
under an electronic stimulus. Our method exploits the mechanical response of
poly-methyl-methacrylate (PMMA) to electron-beam irradiation. Inhomogeneous
anisotropic strain and out-of-plane deformation are demonstrated and studied by
Raman, scanning-electron and atomic-force microscopy. These can all be easily
combined with the present device architecture. The flexibility of the present
method opens new opportunities for the investigation of strain and
nanomechanics in two-dimensional materials.


  We reveal a novel mathematical structure in physical observables, the mass of
tachyon fluctuation mode and the energy density, associated with a classical
solution of vacuum string field theory constructed previously [hep-th/0108150].
We find that they are expressed in terms of quantities which apparently vanish
identically due to twist even-odd degeneracy of eigenvalues of a Neumann
coefficient matrix defining the three-string interactions. However, they can
give non-vanishing values because of the breakdown of the degeneracy at the
edge of the eigenvalue distribution. We also present a general prescription of
correctly simplifying the expressions of these observables. Numerical
calculation of the energy density following our prescription indicates that the
present classical solution represents the configuration of two D25-branes.


  We report on the low temperature measurements of the magnetotransport in
Si-doped InAs quantum wire in the presence of a charged tip of an atomic force
microscope serving as a mobile gate, i.e. scanning gate microscopy (SGM). By
altering the carrier concentration with back gate voltage, we transfer the wire
through several transport regimes: from residual Coulomb blockade to nonlinear
resonance regime, followed by linear resonance regime and, finally, to almost
homogeneous diffusion regime. We demonstrate direct relations between patterns
measured with scanning gate microscopy and spectra of universal conductance
fluctuations. A clear sign of fractal behavior of magnetoconductance dependence
is observed for non-linear and linear resonance transport regimes.


  We report some new interesting features of the dynamics of a string axion
field (i.e., a (pseudo-)scalar field with tiny mass with sine-Gordon-type
self-interaction) around a rotating black hole in three respects. First, we
revisit the calculation of the growth rate of superradiant instability, and
show that in some cases, overtone modes have larger growth rates than the
fundamental mode with the same angular quantum numbers when the black hole is
rapidly rotating. Next, we study the dynamical evolution of the scalar field
caused by the nonlinear self-interaction, taking attention to the dependence of
the dynamical phenomena on the axion mass and the modes. The cases in which two
superradiantly unstable modes are excited simultaneously are also studied.
Finally, we report on our preliminary simulations for gravitational wave
emission from the dynamical axion cloud in the Schwarzschild background
approximation. Our result suggests that fairly strong gravitational wave burst
is emitted during the bosenova, which could be detected by the ground-based
detectors if it happens in Our Galaxy or nearby galaxies.


  A novel possibility of self-organized behaviour of stochastically driven
oscillators is presented. It is shown that synchronization by L\'evy stable
processes is significantly more efficient than that by oscillators with
Gaussian statistics. The impact of outlier events from the tail of the
distribution function was examined by artificially introducing a few additional
oscillators with very strong coupling strengths and it is found that remarkably
even one such rare and extreme event may govern the long term behaviour of the
coupled system. In addition to the multiplicative noise component, we have
investigated the impact of an external additive L\'evy distributed noise
component on the synchronisation properties of the oscillators.


  Properly regularized second-order degenerate perturbation theory is applied
to compute the contribution of higher Landau levels to the low-energy spectrum
of interacting electrons in a disk-shaped quantum dot. At ``filling factor''
near 1/2, this contribution proves to be larger than energy differences between
states with different spin polarizations. After checking convergence of the
method in small systems, we show results for a 12-electron quantum dot, a
system which is hardly tractable by means of exact diagonalization techniques.


  This is an old talk about Boardman's work in Z/2-equivariant unoriented
cobordism. It appeared long ago, but it discusses a useful geometric
interpretation of Tate cohomology which doesn't seem to be widely known. I'm
posting it in an attempt to advertise those ideas.


  In this overview, I discuss some of the open issues in Kaon physics. After
briefly touching on lattice calculations of Kaon dynamics and tests of CPT, my
main focus of attention is on epsilon prime over epsilon and on constraints on
the CKM model. The impact of rare K- decays and of experiments with B-mesons
for addressing the issue of CP-violation is also discussed. The importance of
looking for signals of flavor-conserving CP violating phases is emphasized.


  Notions of directional Chebyshev constant and transfinite diameter have
recently been studied on certain algebraic curves in $\mathbb{C}^2$. The theory
is extended here to curves in $\mathbb{C}^N$ for arbitrary $N$. The results are
analogous but require more methods from computational algebraic geometry.


  We consider the problem of fair allocation of indivisible goods to $n$
agents, with no transfers. When agents have equal entitlements, the well
established notion of the maximin share (MMS) serves as an attractive fairness
criterion, where to qualify as fair, an allocation needs to give every agent at
least a substantial fraction of her MMS.
  In this paper we consider the case of arbitrary (unequal) entitlements. We
explain shortcomings in previous attempts that extend the MMS to unequal
entitlements. Our conceptual contribution is the introduction of a new notion
of a share, the AnyPrice share (APS), that is appropriate for settings with
arbitrary entitlements. Even for the equal entitlements case, this notion is
new, and satisfies $APS \ge MMS$, where the inequality is sometimes strict. We
present two equivalent definitions for the APS (one as a minimization problem,
the other as a maximization problem), and provide comparisons between the APS
and previous notions of fairness.
  Our main result concerns additive valuations and arbitrary entitlements, for
which we provide a polynomial-time algorithm that gives every agent at least a
$\frac{3}{5}$-fraction of her APS. This algorithm can also be viewed as
providing strategies in a certain natural bidding game, and these strategies
secure each agent at least a $\frac{3}{5}$-fraction of her APS.


  This article investigates integer sequences that partition the sequence into
blocks of various lengths - irregular arrays. The main result of the article is
explicit formulas for numbering of irregular arrays. A generalization of Cantor
diagonal method is proposed. We also define and describe intra-block
permutations of natural numbers. Generalizations of reluctant sequences are
introduced, namely generalized reluctant sequences and generalized reverse
reluctant sequences. Explicit formulas are presented for these sequences. The
article provides numerous examples to illustrate all statements.


  Background: The energy consumption of machine learning and its impact on the
environment has made energy efficient ML an emerging area of research. However,
most of the attention stays focused on the model creation and the training and
inferencing phase. Data oriented stages like preprocessing, cleaning and
exploratory analysis form a critical part of the machine learning workflow.
However, the energy efficiency of these stages have gained little attention
from the researchers. Aim: Our study aims to explore the energy consumption of
different dataframe processing libraries as a first step towards studying the
energy efficiency of the data oriented stages of the machine learning pipeline.
Method: We measure the energy consumption of 3 popular libraries used to work
with dataframes, namely Pandas, Vaex and Dask for 21 different operations
grouped under 4 categories on 2 datasets. Results: The results of our analysis
show that for a given dataframe processing operation, the choice of library can
indeed influence the energy consumption with some libraries consuming 202 times
lesser energy over others. Conclusion: The results of our study indicates that
there is a potential for optimizing the energy consumption of the data oriented
stages of the machine learning pipeline and further research is needed in the
direction.


  In the domain of Large Language Model (LLM), LLMs demonstrate significant
capabilities in natural language understanding and generation. With the growing
needs of applying LLMs on various domains, it is a research question that how
to efficiently train and build a model that has expertise in different domains
but with a low training cost. We propose CCoE architecture, a framework of
easily coupling multiple strong domain experts together to fuse into a big LLM,
provides a collective way of utilizing the different domain expert LLMs.
Besides, training a large collaborative of multiple expert LLMs requires a high
requirements on training sources. CCoE bypasses this problem through isolating
other experts and train each expert separately. The design of CCoE assembles
multiple expert LLMs through the CoE (Collaboration of Experts) layer. Each CoE
layer could have one or more expert LLMs. Expert LLMs have different number of
layers and have been well-trained for different domain tasks. Each expert is
fine-tuned to be able to achieve the comparable results with SOTA domain LLMs.
We start from 5 experts in the domain of Code, Math, Law, text-to-SQL and
Medical. The results indicate that our CCoE framework can easily and
efficiently boost nearly 10%-20% performance on original base model in
different domains but using less resources on training, as well as inference.


  We study in this paper magnetic properties of a system of quantum Heisenberg
spins interacting with each other via a ferromagnetic exchange interaction J
and an in-plane Dzyaloshinskii-Moriya interaction D. The non-collinear ground
state due to the competition between J and D is determined. We employ a
self-consistent Green'function theory to calculate the spin-wave spectrum and
the layer magnetizations at finite T in two and three dimensions as well as in
a thin film with surface effects. Analytical details and the validity of the
method are shown and discussed.


  We propose the world first longitudinal gOSNR estimation by using correlation
template method at Rx, without any monitoring devices located in the middle of
the link. The proposed method is experimentally demonstrated in a 12-span link
with commercial transceiver.


  The cosmological reionization can be studied in the radio through the
tomographic view offered by the redshifted 21-cm line and the integrated
information carried out by the diffuse free-free emission, coupled to the
Comptonization distortion, relevant at higher frequencies. Current predictions
span a wide range of possibilities, while the recent EDGES observations
disagree with the standard models and call, if confirmed, for non-standard
physical processes and/or for an early population of extragalactic sources
producing a remarkable background at high redshifts almost consistent with the
ARCADE 2 claim of a significant excess of CMB absolute temperature at low
frequency. These signatures can be observed in global signal and fluctuations,
from very large to small angular scales. The observer peculiar motion with
respect to a reference frame in rest with respect to the CMB produces boosting
effects in various observable quantities, remarkable at low multipoles, and
particularly in the dipole, with frequency spectral behaviours depending on the
monopole emission spectrum. We present a novel investigation at radio
frequencies, aimed at predicting the imprints expected in the redshifted 21-cm
line signal and in the diffuse free-free emission plus the Comptonization
distortion for several models. Furthermore, we consider the same type of signal
but expected from the cosmological radio background determining the offset for
21-cm line. The combination of these signals and their relevance in the various
frequency ranges are studied. This approach, linking monopole and anisotropy
analyses, can be applied on wide sky coverage surveys as well as to sets of sky
patches. Relying only on the quality of interfrequency and relative data
calibration, it in principle by-passes the need for precise absolute
calibration, a critical point of current and future radio interferometric
facilities.


  In this note we give an asymptotic formula for the number of rational points
of bounded height on weighted projective spaces over global function fields.


  The presented results on top quark properties include measurements of the top
quark pair charge asymmetry, the top quark polarization in pair production and
single top production, the W helicity in top quark decays. Results of spin
correlation in top quark pairs are presented and interpreted in terms of the
Standard Model (SM) predicted values. The cross section of tt events produced
in association with a W, Z boson or a photon is also presented. The results are
compared with predictions from the standard model as well as new physics
models.


  We give an estimate of the quantum variance for $d$-regular graphs quantised
with boundary scattering matrices that prohibit back-scattering. For families
of graphs that are expanders, with few short cycles, our estimate leads to
quantum ergodicity for these families of graphs. Our proof is based on a
uniform control of an associated random walk on the bonds of the graph. We show
that recent constructions of Ramanujan graphs, and asymptotically almost
surely, random $d$-regular graphs, satisfy the necessary conditions to conclude
that quantum ergodicity holds.


  Runtime-tunable context-dependent network compression would make mobile deep
learning (DL) adaptable to often varying resource availability, input
"difficulty", or user needs. The existing compression techniques significantly
reduce the memory, processing, and energy tax of DL, yet, the resulting models
tend to be permanently impaired, sacrificing the inference power for reduced
resource usage. The existing tunable compression approaches, on the other hand,
require expensive re-training, do not support arbitrary strategies for adapting
the compression and do not provide mobile-ready implementations.
  In this paper we present Mobiprox, a framework enabling mobile DL with
flexible precision. Mobiprox implements tunable approximations of tensor
operations and enables runtime-adaptable approximation of individual network
layers. A profiler and a tuner included with Mobiprox identify the most
promising neural network approximation configurations leading to the desired
inference quality with the minimal use of resources. Furthermore, we develop
control strategies that depending on contextual factors, such as the input data
difficulty, dynamically adjust the approximation levels across a mobile DL
model's layers. We implement Mobiprox in Android OS and through experiments in
diverse mobile domains, including human activity recognition and spoken keyword
detection, demonstrate that it can save up to 15% system-wide energy with a
minimal impact on the inference accuracy.


  In the framework of the quasiparticle-phonon model, we study the
non-statistical proton decay of excited states in odd nuclei towards low-lying
collective states. Partial cross sections and branching ratios for the proton
decay of the high angular momentum states in $^{41}$Sc, $^{59}$Cu and $^{91}$Nb
%{\it excited by means of the ($^{7}$Li,$^{6}$He) reaction} are evaluated. The
calculated branching ratios predict strong direct proton decays to the
low-lying vibrational states in $^{41}$Sc and $^{91}$Nb. A general agreement
with existing experimental data is found.


  The climate belongs to the class of non-equilibrium forced and dissipative
systems, for which most results of quasi-equilibrium statistical mechanics,
including the fluctuation-dissipation theorem, do not apply. We show for the
first time how the Ruelle linear response theory, developed for studying
rigorously the impact of perturbations on general observables of
non-equilibrium statistical mechanical systems, can be applied to analyze the
climatic response. We choose as test bed the Lorenz 96 model, which has a
well-recognized prototypical value. We recapitulate the main aspects of the
response theory and propose some new results. We then analyze the frequency
dependence of the response of both local and global observables to
perturbations with localized as well as global spatial patterns. We derive
analytically the asymptotic behaviour, validity of Kramers-Kronig relations,
and sum rules for the susceptibilities, and related them to parameters
describing the unperturbed properties of the system. We verify the theoretical
predictions from the outputs of the simulations with great precision. The
theory is used to explain differences in the response of local and global
observables, in defining the intensive properties of the system and in
generalizing the concept of climate sensitivity to all time scales. We also
show how to reconstruct the linear Green function, which maps perturbations of
general time patterns into changes in the expectation value of the considered
observable. Finally, we propose a general methodology to study Climate Change
problems by resorting to few, well selected simulations and discuss the
specific case of surface temperature response to changes of the $CO_2$
concentration. This approach may provide a radically new perspective to study
rigorously the problem of climate sensitivity and climate change.


  We present both the observations and the data reduction procedures of the
Subaru COSMOS 20 project that is an optical imaging survey of the HST COSMOS
field, carried out by using Suprime-Cam on the Subaru Telescope with the
following 20 optical filters: 6 broad-band (B, g', V, r', i', and z'), 2
narrow-band (NB711 and NB816), and 12 intermediate-band filters (IA427, IA464,
IA484, IA505, IA527, IA574, IA624, IA679, IA709, IA738, IA767, and IA827). A
part of this project is described in Taniguchi et al. (2007) and Capak et al.
(2007) for the six broad-band and one narrow-band (NB816) filter data. In this
paper, we present details of the observations and data reduction for remaining
13 filters (the 12 IA filters and NB711). In particular, we describe the
accuracy of both photometry and astrometry in all the filter bands. We also
present optical properties of the Suprime-Cam IA filter system in Appendix.


  Let $1<\beta<2$. Given any $x\in[0, (\beta-1)^{-1}]$, a sequence
$(a_n)\in\{0,1\}^{\mathbb{N}}$ is called a $\beta$-expansion of $x$ if
$x=\sum_{n=1}^{\infty}a_n\beta^{-n}.$ For any $k\geq 1$ and any $(b_1b_2\cdots
b_k)\in\{0,1\}^{k}$, if there exists some $k_0$ such that
$a_{k_0+1}a_{k_0+2}\cdots a_{k_0+k}=b_1b_2\cdots b_k$, then we call $(a_n)$ a
universal $\beta$-expansion of $x$.
  Sidorov \cite{Sidorov2003}, Dajani and de Vries \cite{DajaniDeVrie} proved
that given any $1<\beta<2$, then Lebesgue almost every point has uncountably
many universal expansions. In this paper we consider the set $V_{\beta}$ of
points without universal expansions. For any $n\geq 2$, let $\beta_n$ be the
$n$-bonacci number satisfying the following equation:
$\beta^n=\beta^{n-1}+\beta^{n-2}+\cdots +\beta+1.$ Then we have
$\dim_{H}(V_{\beta_n})=1$, where $\dim_{H}$ denotes the Hausdorff dimension.
Similar results are still available for some other algebraic numbers. As a
corollary, we give some results of the Hausdorff dimension of the survivor set
generated by some open dynamical systems. This note is another application of
our paper \cite{KarmaKan}.


  In this paper, we develop an exact method for the determination of the
minimum sample size for estimating the proportion of a finite population with
prescribed margin of error and confidence level. By characterizing the behavior
of the coverage probability with respect to the proportion, we show that the
computational complexity can be significantly reduced and bounded regardless
population size.


  We examine the issue of dark radiation (DR) from string moduli decay into
axion-like particles (ALPs). In KKLT-type models of moduli stabilization, the
axionlike phases of moduli fields are expected to decouple whilst in LVS-type
moduli stabilization some can remain light and may constitute dark radiation.
We evaluate modulus decay to Minimal Supersymmetric Standard Model (MSSM)
particles and dark radiation for more general compactifications. In spite of
tightening error bars on \Delta N_{eff}, we find only mild constraints on
modulus-ALP couplings due to the somewhat suppressed modulus branching fraction
to DR owing to the large number of MSSM decay modes. We anticipate that future
CMB experiments with greater precision on \Delta N_{eff} may still turn up
evidence for DR if the ALP associated with the lightest modulus field is indeed
light.


  In this study, we propose a novel extended target tracking algorithm which is
capable of representing the extent of dynamic objects as an ellipsoid with a
time-varying orientation angle. A diagonal positive semi-definite matrix is
defined to model objects' extent within the random matrix framework where the
diagonal elements have inverse-Gamma priors. The resulting measurement equation
is non-linear in the state variables, and it is not possible to find a
closed-form analytical expression for the true posterior because of the absence
of conjugacy. We use the variational Bayes technique to perform approximate
inference, where the Kullback-Leibler divergence between the true and the
approximate posterior is minimized by performing fixed-point iterations. The
update equations are easy to implement, and the algorithm can be used in
real-time tracking applications. We illustrate the performance of the method in
simulations and experiments with real data. The proposed method outperforms the
state-of-the-art methods when compared with respect to accuracy and robustness.


  Optical Character Recognition (OCR) is the process of extracting digitized
text from images of scanned documents. While OCR systems have already matured
in many languages, they still have shortcomings in cursive languages with
overlapping letters such as the Arabic language. This paper proposes a complete
Arabic OCR system that takes a scanned image of Arabic Naskh script as an input
and generates a corresponding digital document. Our Arabic OCR system consists
of the following modules: Pre-processing, Word-level Feature Extraction,
Character Segmentation, Character Recognition, and Post-processing. This paper
also proposes an improved font-independent character segmentation algorithm
that outperforms the state-of-the-art segmentation algorithms. Lastly, the
paper proposes a neural network model for the character recognition task. The
system has experimented on several open Arabic corpora datasets with an average
character segmentation accuracy 98.06%, character recognition accuracy 99.89%,
and overall system accuracy 97.94% achieving outstanding results compared to
the state-of-the-art Arabic OCR systems.


  A simple model of a periodic ensemble of closely packed flux tubes sitting
atop a vertically stratified layer reveals that an incident fast wave from
below preferentially converts almost immediately to Alfv\'en waves in the flux
tubes, with kink waves restricted to at most a very few Fourier modes. This
suggests that observations of coronal kink modes in such structured systems may
greatly underestimate the net wave energy flux being transported into and
through the corona, much of which may reside in harder-to-observe Alfv\'en
waves. The processes of mode conversion/resonant absorption and Alfv\'en phase
mixing are implicated. It is suggested that the Sun's internal p-mode field --
the 5-minute oscillations -- may contribute substantially to the process by
supplying incident fast waves in the chromosphere that scatter and mode-convert
in the tube ensemble.


  The data functions that are studied in the course of functional data analysis
are assembled from discrete data, and the level of smoothing that is used is
generally that which is appropriate for accurate approximation of the
conceptually smooth functions that were not actually observed. Existing
literature shows that this approach is effective, and even optimal, when using
functional data methods for prediction or hypothesis testing. However, in the
present paper we show that this approach is not effective in classification
problems. There a useful rule of thumb is that undersmoothing is often
desirable, but there are several surprising qualifications to that approach.
First, the effect of smoothing the training data can be more significant than
that of smoothing the new data set to be classified; second, undersmoothing is
not always the right approach, and in fact in some cases using a relatively
large bandwidth can be more effective; and third, these perverse results are
the consequence of very unusual properties of error rates, expressed as
functions of smoothing parameters. For example, the orders of magnitude of
optimal smoothing parameter choices depend on the signs and sizes of terms in
an expansion of error rate, and those signs and sizes can vary dramatically
from one setting to another, even for the same classifier.


  In non-canonical two-field inflation models, deviations from the canonical
model can be captured by a parameter $\xi$. We show this parameter is usually
one half of the slow-roll order and analytically calculate the primordial power
spectra accurate to order $\xi^2$. The super-horizon perturbations are studied
with an improved method, which gives a correction of order $\xi^2$. Three
typical examples demonstrate that our analytical formulae of power spectra fit
well with numerical simulation.


  Results on LEP 2 e+e-->ffbar and gamma gamma (gamma) production are
presented. These are compared with Standard Model predictions, and then used to
set limits on various New Physics models, including Low Scale Gravity. Finally
the status of the LEP beam energy determination from radiative return events is
summarised.


  During the current Covid-19 pandemic in Italy, official data are collected
with medical swabs following a pure convenience criterion which, at least in an
early phase, has privileged the exam of patients showing evident symptoms.
However, there are evidences of a very high proportion of asymptomatic patients
(e. g. Aguilar et al., 2020; Chugthai et al, 2020; Li, et al., 2020; Mizumoto
et al., 2020a, 2020b and Yelin et al., 2020). In this situation, in order to
estimate the real number of infected (and to estimate the lethality rate), it
should be necessary to run a properly designed sample survey through which it
would be possible to calculate the probability of inclusion and hence draw
sound probabilistic inference. Some researchers proposed estimates of the total
prevalence based on various approaches, including epidemiologic models, time
series and the analysis of data collected in countries that faced the epidemic
in earlier time (Brogi et al., 2020). In this paper, we propose to estimate the
prevalence of Covid-19 in Italy by reweighting the available official data
published by the Istituto Superiore di Sanit\`a so as to obtain a more
representative sample of the Italian population. Reweighting is a procedure
commonly used to artificially modify the sample composition so as to obtain a
distribution which is more similar to the population (Valliant et al., 2018).
In this paper, we will use post-stratification of the official data, in order
to derive the weights necessary for reweighting them using age and gender as
post-stratification variables thus obtaining more reliable estimation of
prevalence and lethality.


  The rising use of information and communication technology in smart grids
likewise increases the risk of failures that endanger the security of power
supply, e.g., due to errors in the communication configuration, faulty control
algorithms, or cyber-attacks. Co-simulations can be used to investigate such
effects, but require precise modeling of the energy, communication, and
information domain within an integrated smart grid infrastructure model. Given
the complexity and lack of detailed publicly available communication network
models for smart grid scenarios, there is a need for an automated and
systematic approach to creating such coupled models. In this paper, we present
an approach to automatically generate smart grid infrastructure models based on
an arbitrary electrical distribution grid model using a generic architectural
template. We demonstrate the applicability and unique features of our approach
alongside examples concerning network planning, co-simulation setup, and
specification of domain-specific intrusion detection systems.


  We explore the robustness of the correlation matrix Hamiltonian
reconstruction technique with respect to the choice of operator basis, studying
the effects of bases that are undercomplete and over-complete -- too few or too
many operators respectively. An approximation scheme for reconstructing from an
undercomplete basis is proposed and performed numerically on select models. We
discuss the confounding effects of conserved quantities and symmetries on
reconstruction attempts. We apply these considerations to a variety of
one-dimensional systems in zero- and finite-temperature regimes.


  The deadly triad refers to the instability of a reinforcement learning
algorithm when it employs off-policy learning, function approximation, and
bootstrapping simultaneously. In this paper, we investigate the target network
as a tool for breaking the deadly triad, providing theoretical support for the
conventional wisdom that a target network stabilizes training. We first propose
and analyze a novel target network update rule which augments the commonly used
Polyak-averaging style update with two projections. We then apply the target
network and ridge regularization in several divergent algorithms and show their
convergence to regularized TD fixed points. Those algorithms are off-policy
with linear function approximation and bootstrapping, spanning both policy
evaluation and control, as well as both discounted and average-reward settings.
In particular, we provide the first convergent linear $Q$-learning algorithms
under nonrestrictive and changing behavior policies without bi-level
optimization.


  We study interactive imitation learning, where a learner interactively
queries a demonstrating expert for action annotations, aiming to learn a policy
that has performance competitive with the expert, using as few annotations as
possible. We focus on the general agnostic setting where the expert
demonstration policy may not be contained in the policy class used by the
learner. We propose a new oracle-efficient algorithm MFTPL-P (abbreviation for
Mixed Follow the Perturbed Leader with Poisson perturbations) with provable
finite-sample guarantees, under the assumption that the learner is given access
to samples from some ``explorative'' distribution over states. Our guarantees
hold for any policy class, which is considerably broader than prior state of
the art. We further propose Bootstrap-Dagger, a more practical variant that
does not require additional sample access. Empirically, MFTPL-P and
Bootstrap-Dagger notably surpass online and offline imitation learning
baselines in continuous control tasks.


  It is proved that the minimal free resolution of a module M over a Gorenstein
local ring R is eventually periodic if, and only if, the class of M is torsion
in a certain Z[t,t^{-1}]-module associated to R. This module, denoted J(R), is
the free Z[t,t^{-1}]-module on the isomorphism classes of finitely generated
R-modules modulo relations reminiscent of those defining the Grothendieck group
of R. The main result is a structure theorem for J(R) when R is a complete
Gorenstein local ring; the link between periodicity and torsion stated above is
a corollary.


  A new Hardy space Hardy space approach of Dirichlet type problem based on
Tikhonov regularization and Reproducing Hilbert kernel space is discussed in
this paper, which turns out to be a typical extremal problem located on the
upper upper-high complex plane. If considering this in the Hardy space, the
optimization operator of this problem will be highly simplified and an
efficient algorithm is possible. This is mainly realized by the help of
reproducing properties of the functions in the Hardy space of upper-high
complex plane, and the detail algorithm is proposed. Moreover, harmonic
mappings, which is a significant geometric transformation, are commonly used in
many applications such as image processing, since it describes the energy
minimization mappings between individual manifolds. Particularly, when we focus
on the planer mappings between two Euclid planer regions, the harmonic mappings
are exist and unique, which is guaranteed solidly by the existence of harmonic
function. This property is attractive and simulation results are shown in this
paper to ensure the capability of applications such as planer shape distortion
and surface registration.


  Self-attention based models are widely used in news recommendation tasks.
However, previous Attention architecture does not constrain repeated
information in the user's historical behavior, which limits the power of hidden
representation and leads to some problems such as information redundancy and
filter bubbles. To solve this problem, we propose a personalized news
recommendation model called DCAN.It captures multi-grained user-news matching
signals through news encoders and user encoders. We keep updating a coverage
vector to track the history of news attention and augment the vector in 4 types
of ways. Then we fed the augmented Coverage vector into the Multi-headed
Self-attention model to help adjust the future attention and added the Coverage
regulation to the loss function(CRL), which enabled the recommendation system
to consider more about differentiated information. Extensive experiments on
Microsoft News Recommendation Dataset (MIND) show that our model significantly
improve the diversity of news recommendations with minimal sacrifice in
accuracy.


  Bismuth Selenide (Bi$_{2}$Se$_{3}$) is a topological insulator (TI) with a
structure consisting of stacked quintuple layers. Single crystal surfaces are
commonly prepared by mechanical cleaving. This work explores the use of low
energy Ar$^{+}$ ion bombardment and annealing (IBA) as an alternative method to
produce reproducible and stable Bi$_{2}$Se$_{3}$ surfaces under ultra-high
vacuum (UHV). It is found that a well-ordered surface can be prepared by a
single cycle of 1 keV Ar$^{+}$ ion bombardment and 30 min of annealing. Low
energy electron diffraction (LEED) and detailed low energy ion scattering
(LEIS) measurements show no differences between IBA-prepared surfaces and those
prepared by $\textit{in situ}$ cleaving in UHV. Analysis of the LEED patterns
shows that the optimal annealing temperature is 450{\deg}C. Angular LEIS scans
reveal the formation of surface Se vacancies when the annealing temperature
exceeds 520{\deg}C.


  This letter reports our experimental results on magnetic-field-induced
aftereffects in solution derived Bi4Fe2TiO12 film, in which e' decreases as
much as 600 times after treated in a 5T magnetic field as that of the pristine
one. The phenomena are explained by an unusual spin-orbital coupling in film,
where strong magnetic field provides drive force for spin polarized electrons
of electrode to enter film, so as to form a ferromagnetic orbital state,
increase the relaxation time of defect dipoles and then produce giant
magnetodielectric effects. This process is reversible just by applying a
opposite 0.5T magnetic field. Our findings have potential applications on
magnetic fabrication of nanopatterns somehow to evade nanohazard, as well as on
integraged phononic or photonic crystals on chip.


  This survey paper contains an elementary exposition of Casson and Rivin's
technique for finding the hyperbolic metric on a 3-manifold M with toroidal
boundary. We also survey a number of applications of this technique.
  The method involves subdividing M into ideal tetrahedra and solving a system
of gluing equations to find hyperbolic shapes for the tetrahedra. The gluing
equations decompose into a linear and non-linear part. The solutions to the
linear equations form a convex polytope A. The solution to the non-linear part
(unique if it exists) is a critical point of a certain volume functional on
this polytope. The main contribution of this paper is an elementary proof of
Rivin's theorem that a critical point of the volume functional on A produces a
complete hyperbolic structure on M.


  A famous result of Stieltjes relates the zeroes of the classical orthogonal
polynomials with the configurations of points on the line that minimize a
suitable energy. The energy has logarithmic interactions and an external field
whose exponential is related to the weight of the classical orthogonal
polynomials.
  The optimal configuration satisfies an algebraic set of equations: we call
this set of algebraic equations the Stieltjes--Fekete problem or equivalently
the Stieltjes--Bethe equations. In this work we consider the Stieltjes-Fekete
problem when the derivative of the external field is an arbitrary rational
complex function. We show that its solutions are in one-to-one correspondence
with the zeroes of certain non-hermitean orthogonal polynomials that satisfy an
excess of orthogonality conditions and are thus termed "degenerate". This
generalizes the original result of Stieltjes.


  Prior to the launch of the Swift mission several X-ray line detections were
reported in Gamma Ray Burst afterglow spectra. To date, these pre-Swift era
results have not been conclusively confirmed. The most contentious issue in
this area is the choice of statistical method used to evaluate the significance
of these features. In this paper we compare three different methods already
extant in the literature for assessing the significance of possible line
features and discuss their relative advantages and disadvantages. The methods
are demonstrated by application to observations of 40 bursts from the archive
of Swift XRT at early times (< few ks post trigger in the rest frame of the
burst). Based on this thorough analysis we found no strong evidence for
emission lines. For each of the three methods we have determined detection
limits for emission line strengths in bursts with spectral parameters typical
of the Swift-era sample. We also discuss the effects of the current calibration
status on emission line detection.


  Borophene, an atomically thin, corrugated, crystalline two-dimensional boron
sheet, has been recently synthesized. We investigate mechanical properties and
lattice thermal conductivity of borophene via reactive molecular dynamics
simulations. We performed uniaxial tensile strain simulations at room
temperature along in-plane directions, and found 2D elastic moduli of 188 N/m
and 403 N/m along zigzag and armchair directions, respectively. The anisotropy
is attributed to the buckling of the borophene structure along the zigzag
direction. We also performed non-equilibrium molecular dynamics to calculate
the lattice thermal conductivity. We predict room-temperature lattice thermal
conductivities of $75.9 \pm 5.0$ W/m-K and $147 \pm 7.3$ W/m-K, respectively,
and estimate effective phonon mean free paths of $16.7 \pm 1.7$ nm and $21.4
\pm 1.0$ nm for the zigzag and armchair directions. The anisotropy is
attributed to differences in the density of states of low-frequency phonons,
with lower group velocities and possibly shorten phonon lifetimes along the
zigzag direction. We also observe that when borophene is strained along the
armchair direction there is a significant increase in thermal conductivity
along that direction. Meanwhile, when the sample is strained along the zigzag
direction there is a much smaller increase in thermal conductivity along that
direction. For a strain of 8\% along the armchair direction the thermal
conductivity increases by a factor of 3.5 (~250\%), whereas for the same amount
of strain along the zigzag direction the increase is only by a factor of 1.2
(~20\%). Our predictions are in agreement with recent first principles results,
at a fraction of the computational cost. The simulations shall serve as a guide
for experiments concerning mechanical and thermal properties of borophene and
related 2D materials.


  Social robots have been shown to help in language education for children.
This can be good aid for immigrant children that need additional help to learn
a second language their parents do not understand to attend school. We present
the setup for a long-term study that is being carried out in blinded to aid
immigrant children with poor skills in the Norwegian language to improve their
vocabulary. This includes additional tools to help parents follow along and
provide additional help at home.


  In a recent preprint of F. Gouvea and N. Yui (see arXiv:0902.1466) a detailed
account is given of a patching argument due to Serre that proves that the
modularity of all rigid Calabi-Yau threefolds defined over the rationals
follows from Serre's modularity conjecture. In this note (a letter to N. Yui)
we give an alternative proof of this implication. The main difference with
Serre's argument is that instead of using as main input residual modularity in
infinitely many characteristics we just require residual modularity in a
suitable characteristic. This is combined with effective Cebotarev.


  In the field of Automated Planning and Scheduling (APS), intelligent agents
by virtue require an action model (blueprints of actions whose interleaved
executions effectuates transitions of the system state) in order to plan and
solve real world problems. It is, however, becoming increasingly cumbersome to
codify this model, and is more efficient to learn it from observed plan
execution sequences (training data). While the underlying objective is to
subsequently plan from this learnt model, most approaches fall short as
anything less than a flawless reconstruction of the underlying model renders it
unusable in certain domains. This work presents a novel approach using long
short-term memory (LSTM) techniques for the acquisition of the underlying
action model. We use the sequence labelling capabilities of LSTMs to isolate
from an exhaustive model set a model identical to the one responsible for
producing the training data. This isolation capability renders our approach as
an effective one.


  In this note we prove that additive categories that occur as hearts of weight
structures are precisely the weakly idempotent completecategories, that is, the
categories where all split monomorphisms give direct sum decompositions. We
also give several other conditions equivalent to weak idempotent completeness
(some of them are completely new), and discuss weak idempotent completions of
additive categories.


  In recent work by L. Levine and Y. Peres, it was observed that three models
for particle aggregation on the lattice - the divisible sandpile, rotor-router
aggregation, and internal diffusion limited aggregation - share a common
scaling limit as the lattice spacing tends to zero, if they are started with
the same initial mass configuration. It is straightforward to observe that this
scaling limit is precisely the same as the potential-theoretic operation of
taking the partial balayage of this initial mass configuration to the Lebesgue
measure. However, from the theory of the partial balayage operation it is clear
that one may take the partial balayage of a mass configuration to a more
general measure than the Lebesgue measure, which one cannot do for the three
aggregation models described by Levine and Peres. In this paper we therefore
generalize one of these models, the divisible sandpile model, in mainly a
bounded setting, and show that a natural scaling limit of this generalization
is given by a general partial balayage operation.


  The miniaturization of electronic and mechanical components has allowed for
an unprecedented downscaling of spacecraft size and mass. Today, spacecraft
with a mass between 1 to 10 grams, AttoSats, have been developed and operated
in space. Due to their small size, they introduce a new paradigm in spacecraft
design, relying on agile development, rapid iterations, and massive redundancy.
However, no systematic survey of the potential advantages and unique mission
concepts based on AttoSats exists. This paper explores the potential of
AttoSats for future space missions. First, we present the state of the art of
AttoSats. Next, we identify unique AttoSat characteristics and map them to
future mission capabilities. Finally, we go beyond AttoSats and explore how
smart dust and nano-scale spacecraft could allow for even smaller spacecraft in
the milligram range: zepto- and yocto spacecraft.


  Simultaneously concentrating EM waves and heat fluxes to the same target
region within an on-chip system carries substantial academic research
importance and practical application value. Nevertheless, existing researches
are primarily aimed at the design and experimentation of concentrators for
individual EM waves or temperature fields. In this work, a thermal-EM
concentrator, capable of simultaneously concentrating EM waves and heat fluxes,
is designed using transformation optics/thermodynamics and fabricated with
engineered EM-thermal metamaterials. The concentrating effects of the proposed
thermal-EM concentrator on the thermal fluxes and EM waves are verified through
numerical simulations and experimental measurements, respectively, which are in
good agreement with each other. Both numerically simulated and experimentally
measured results demonstrate the concentrating capability of the proposed
thermal-EM concentrator, which can concentrate broadband TM-polarized EM waves
ranging from 8-12 GHz and heat/cold flows to the same target region within an
on-chip operating environment. The thermal-EM concentrator exhibits a thermal
focusing efficiency close to 100% and more than three times enhancement of the
magnetic field at the designed center frequency of 10 GHz. The proposed
thermal-EM concentrator can be utilized for efficient cooling for the specified
component and simultaneously enhancing the EM antenna's radiation/reception
efficiency within an on-chip system.


  We develop two new variants of alternating direction methods of multipliers
(ADMM) and two parallel primal-dual decomposition algorithms to solve a wide
range class of constrained convex optimization problems. Our approach relies on
a novel combination of the augmented Lagrangian framework, partial
alternating/linearization scheme, Nesterov's acceleration technique, and
adaptive strategy. The proposed algorithms have the following new features
compared to existing ADMM variants. First, they have a Nesterov's acceleration
step on the primal variables instead of the dual ones as in several ADMM
variants. Second, they possess an optimal $O(\frac{1}{k})$-convergence rate
guarantee in a non-ergodic sense without any smoothness or strong
convexity-type assumption, where $k$ is the iteration counter. When one
objective term is strongly convex, our algorithm achieves an optimal
$O(\frac{1}{k^2})$-non-ergodic rate. Third, our methods have better
per-iteration complexity than standard ADMM due to the linearization step in
the second subproblem. Fourth, we provide a set of conditions to derive update
rules for algorithmic parameters, and give a concrete update for these
parameters as an example. Finally, when the objective function is separable,
our methods can naturally be implemented in a parallel fashion. We also study
two extensions of our methods and a connection to existing primal-dual methods.
We verify our theoretical development via different numerical examples and
compare our methods with some existing state-of-the-art algorithms.


  Centre sector transitions in QCD-like theories with dynamical quark matter
are investigated. In the hadronic phase, these transitions still take place in
the infinite volume at zero temperature limit despite of the explicit breaking
of the centre symmetry by the matter fields. This finding is supported by
simulations of the SU(2) Yang-Mills theory with Higgs matter. The
phenomenological impact of the centre sector transitions for dense but confined
matter is explained: centre dressed quarks acquire Bose statistics and form a
so-called Fermi-Einstein condensate. This mechanism is further illustrated in
the Schwinger model where it solves the Silver-Blaze problem.