  Stochastic models for collections of interacting populations have crucial
roles in scientific fields such as epidemiology and ecology, yet the standard
approach to extending an ordinary differential equation model to a Markov chain
does not have sufficient flexibility in the mean-variance relationship to match
data. To handle that, over-dispersed Markov chains have previously been
constructed using gamma white noise on the rates. We develop new approaches
using Dirichlet noise to construct collections of independent or dependent
noise processes. This permits the modeling of high-frequency variation in
transition rates both within and between the populations under study. Our
theory is developed in a general framework of time-inhomogeneous Markov
processes equipped with a graphical structure, for which ecological and
epidemiological models provide motivating examples. We demonstrate our approach
on a widely analyzed measles dataset, adding Dirichlet noise to a classical
SEIR (Susceptible-Exposed-Infected-Recovered) model. Our methodology shows
improved statistical fit measured by log-likelihood and provides new insights
into the dynamics of this biological system.


  We consider the localization landscape function $u$ and ground state
eigenvalue $\lambda$ for operators on graphs. We first show that the maximum of
the landscape function is comparable to the reciprocal of the ground state
eigenvalue if the operator satisfies certain semigroup kernel upper bounds.
This implies general upper and lower bounds on the landscape product
$\lambda\|u\|_\infty$ for several models, including the Anderson model and
random hopping (bond-disordered) models, on graphs that are roughly isometric
to $\mathbb{Z}^d$, as well as on some fractal-like graphs such as the
Sierpinski gasket graph. Next, we specialize to a random hopping model on
$\mathbb{Z}$, and show that as the size of the chain grows, the landscape
product $\lambda\|u\|_\infty$ approaches $\pi^2/8$ for Bernoulli off-diagonal
disorder, and has the same upper bound of $\pi^2/8$ for Uniform([0,1])
off-diagonal disorder. We also numerically study the random hopping model when
the band width (hopping distance) is greater than one, and provide strong
numerical evidence that a similar approximation holds for low-lying energies in
the spectrum.


  In this paper we obtain new estimates of the number of edges in subgraphs of
the special distance graph. Bibliography: 21 item.


  The Hamiltonian interprets how the system evolves, while the scattering
coefficients describe how the system responds to inputs. Recent studies on
non-Hermitian physics have revealed many unconventional effects. However, in
all cases, the non-Hermiticity such as material loss is only considered for the
Hamiltonian, even when studying scattering properties. Another important
component-the scattering channel, is always assumed to be lossless and
time-reversal symmetric. This assumption hinders the exploration on the more
general and fundamental properties of non-Hermitian scattering. Here, we
identify a novel kind of scattering channel that obeys time-reversal
anti-symmetry. Such diffusive scattering channels overturn the conventional
understanding about scattering symmetry by linking the positive and negative
frequencies. By probing non-Hermitian systems with the diffusive channels, we
reveal a hidden anti-parity-time (APT) scattering symmetry, which is distinct
from the APT symmetry of Hamiltonians studied before. The symmetric and
symmetry broken scattering phases are observed for the first time as the
collapse and revival of temperature oscillation. Our work highlights the
overlooked role of scattering channels in the symmetry and phase transition of
non-Hermitian systems, thereby gives the diffusion the new life as a signal
carrier. Our findings can be utilized to the analysis and control of strongly
dissipative phenomena such as heat transfer and charge diffusion.


  In this paper, we study the commuting variety of symmetric pairs associated
to parabolic subalgebras with abelian unipotent radical in a simple complex Lie
algebra. By using the ``cascade'' construction of Kostant, we construct a
Cartan subspace which in turn provides, in certain cases, useful information on
the centralizers of non $\mathfrak{p}$-regular semisimple elements. In the case
of the rank 2 symmetric pair $(\mathrm{so}_{p+2},\mathrm{so}_{p}\times
\mathrm{so}_{2})$, $p\geq 2$, this allows us to apply induction, in view of
previous results of the authors, and reduce the problem of the irreducibility
of the commuting variety to the consideration of evenness of
$\mathfrak{p}$-distinguished elements. Finally, via the correspondence of
Kostant-Sekiguchi, we check that in this case, $\mathfrak{p}$-distinguished
elements are indeed even, and consequently, the commuting variety is
irreducible.


  Four-dimensional string theories predict in general the existence of light
exotic particles with fractional electric charges. Such particles could escape
present observations if they are confined by a gauge group of the "hidden"
sector into integrally charged states. It is conceivable that the same gauge
group is also responsible for dynamical supersymmetry breaking, via gaugino and
scalar condensation. The communication of the breaking to the observable sector
is now mediated by ordinary gauge interactions, implying that the confining
scale can be in the TeV-region. We study the main phenomenological implications
of this possibility. In particular, we analyze the pattern of supersymmetry
breaking and the mass-spectrum of the sparticles. We also show that this
scenario can be consistent with the unification of all coupling constants at
the string scale.


  In this paper we design efficient quadrature rules for finite element
discretizations of nonlocal diffusion problems with compactly supported kernel
functions. Two of the main challenges in nonlocal modeling and simulations are
the prohibitive computational cost and the nontrivial implementation of
discretization schemes, especially in three-dimensional settings. In this work
we circumvent both challenges by introducing a parametrized mollifying function
that improves the regularity of the integrand, utilizing an adaptive
integration technique, and exploiting parallelization. We first show that the
"mollified" solution converges to the exact one as the mollifying parameter
vanishes, then we illustrate the consistency and accuracy of the proposed
method on several two- and three-dimensional test cases. Furthermore, we
demonstrate the good scaling properties of the parallel implementation of the
adaptive algorithm and we compare the proposed method with recently developed
techniques for efficient finite element assembly.


  To enable wireless federated learning (FL) in communication
resource-constrained networks, two communication schemes, i.e., digital and
analog ones, are effective solutions. In this paper, we quantitatively compare
these two techniques, highlighting their essential differences as well as
respectively suitable scenarios. We first examine both digital and analog
transmission schemes, together with a unified and fair comparison framework
under imbalanced device sampling, strict latency targets, and transmit power
constraints. A universal convergence analysis under various imperfections is
established for evaluating the performance of FL over wireless networks. These
analytical results reveal that the fundamental difference between the digital
and analog communications lies in whether communication and computation are
jointly designed or not. The digital scheme decouples the communication design
from FL computing tasks, making it difficult to support uplink transmission
from massive devices with limited bandwidth and hence the performance is mainly
communication-limited. In contrast, the analog communication allows
over-the-air computation (AirComp) and achieves better spectrum utilization.
However, the computation-oriented analog transmission reduces power efficiency,
and its performance is sensitive to computation errors from imperfect channel
state information (CSI). Furthermore, device sampling for both schemes are
optimized and differences in sampling optimization are analyzed. Numerical
results verify the theoretical analysis and affirm the superior performance of
the sampling optimization.


  We use ultra-high resolution, tunable, VUV laser-based, angle-resolved
photoemission spectroscopy (ARPES) and temperature and field dependent
resistivity and thermoelectric power (TEP) measurements to study the electronic
properties of WTe2, a compound that manifests exceptionally large, temperature
dependent magnetoresistance. The temperature dependence of the TEP shows a
change of slope at T=175 K and the Kohler rule breaks down above 70-140 K
range. The Fermi surface consists of two electron pockets and two pairs of hole
pockets along the X-Gamma-X direction. Upon increase of temperature from 40K,
the hole pockets gradually sink below the chemical potential. Like BaFe2As2,
WTe2 has clear and substantial changes in its Fermi surface driven by modest
changes in temperature. In WTe2, this leads to a rare example of temperature
induced Lifshitz transition, associated with the complete disappearance of the
hole pockets. These dramatic changes of the electronic structure naturally
explain unusual features of the transport data.


  We prove integral representations of the approximation forms in zeta values
constructed in arXiv:1801.09895 and arXiv:1803.08905.


  Despite the popularity of Vision Transformers (ViTs) and eXplainable AI
(XAI), only a few explanation methods have been designed specially for ViTs
thus far. They mostly use attention weights of the [CLS] token on patch
embeddings and often produce unsatisfactory saliency maps. This paper proposes
a novel method for explaining ViTs called ViT-CX. It is based on patch
embeddings, rather than attentions paid to them, and their causal impacts on
the model output. Other characteristics of ViTs such as causal
overdetermination are also considered in the design of ViT-CX. The empirical
results show that ViT-CX produces more meaningful saliency maps and does a
better job revealing all important evidence for the predictions than previous
methods. The explanation generated by ViT-CX also shows significantly better
faithfulness to the model. The codes and appendix are available at
https://github.com/vaynexie/CausalX-ViT.


  We discuss the use of comagnetometry in studying new physics that couples to
fermionic spin. Modern comagnetometry is -- in absolute energy units -- the
most sensitive experimental technique for measuring the energy difference
between quantum states, reaching sensitivities in the $10^{-26}\,$eV range. The
technique suppresses the magnetic interactions of the spins, making searches
for non-standard-model interactions possible. Many implementations have been
developed and optimized for various uses. New physics scenarios which can be
probed with comagnetometers include: EDMs, violations of Lorentz invariance,
Goldstone bosons of new high-energy symmetries, CP-violating long-range forces,
and axionic dark matter. We consider the prospects for improvements in the
technique, and show -- based purely on signal-to-noise ratio with existing
technology -- that there is room for several orders of magnitude in further
improvement. We also evaluate several sources of systematic error and
instability that may limit improvements.


  The principle of virtual work for dissipative systems is stated. Partially
controlled systems are discussed and the concept of a generating families of
forms is introduced. The notion of a critical point of a family of convex forms
is introduced and discussed. A number of examples is given.


  We study inelastic processes for ultracold three-body systems in which only
one interaction is resonant. We have found that the decay rates for weakly
bound molecules due to collisions with other atoms can be suppressed not only
without fermionic statistics but also when bosonic statistics applies. In
addition, we show that at ultracold temperatures three-body recombination
involving a single resonant pair of atoms leads mainly to formation of weakly
bound molecules which, in turn, are stable against decay. These results
indicate that recombination in three-component atomic gases can be used as an
efficient mechanism for molecular formation, allowing the achievement of high
molecular densities.


  We study incremental constituent parsers to assess their capacity to output
trees based on prefix representations alone. Guided by strictly left-to-right
generative language models and tree-decoding modules, we build parsers that
adhere to a strong definition of incrementality across languages. This builds
upon work that asserted incrementality, but that mostly only enforced it on
either the encoder or the decoder. Finally, we conduct an analysis against
non-incremental and partially incremental models.


  Long gamma-ray bursts (LGRBs) and superluminous supernovae (SLSNe) are both
explosive transients with very massive progenitor stars. Clues about the nature
of the progenitors can be found by investigating environments in which such
transients occur. While studies of LGRB host galaxies have a long history,
dedicated observational campaigns have only recently resulted in a high enough
number of photometrically and spectroscopically observed SLSN hosts to allow
statistically significant analysis of their properties. In this paper we make a
comparison of the host galaxies of hydrogen-poor (H-poor) SLSNe and the
Swift/BAT6 sample of LGRBs. In contrast to previous studies we use a complete
sample of LGRBs and we address a special attention to the comparison
methodology and the selection of SLSN sample whose data have been compiled from
the available literature. At intermediate redshifts (0.3 < z < 0.7) the two
classes of transients select galaxies whose properties (stellar mass,
luminosity, star-formation rate, specific star-formation rate and metallicity)
do not differ on average significantly. Moreover, the host galaxies of both
classes of objects follow the fundamental metallicity relation and the
fundamental plane of metallicity. In contrast to previous studies we show that
at intermediate redshifts the emission line equivalent widths of the two
populations are essentially the same and that the previous claims regarding the
higher fraction of SLSN hosts among the extreme emission line galaxies with
respect to LGRBs are mostly due to a larger fraction of strong-line emitters
among SLSN hosts at z < 0.3, where samples of LGRB hosts are small and poorly
defined.


  We review the theory of regenerative processes, which are processes that can
be intuitively seen as comprising of i.i.d.\ cycles. Although we focus on the
classical definition, we present a more general definition that allows for some
form of dependence between two adjacent cycles, and mention two further
extensions of the second definition. We mention the connection of regenerative
processes to the single-server queue, to multi-server queues and more generally
to Harris ergodic Markov chains and processes. In the main theorem, we pay some
attention to the conditions under which a limiting distribution exists and
provide references that should serve as a starting point for the interested
reader.


  We present the application of novel diagnostics to the spectroscopic
observation of a Coronal Mass Ejection (CME) on disk by the Extreme Ultraviolet
Imaging Spectrometer (EIS) on the Hinode spacecraft. We apply a recently
developed line profile asymmetry analysis to the spectroscopic observation of
NOAA AR 10930 on 14-15 December 2006 to three raster observations before and
during the eruption of a 1000km/s CME. We see the impact that the observer's
line-of-sight and magnetic field geometry have on the diagnostics used.
Further, and more importantly, we identify the on-disk signature of a
high-speed outflow behind the CME in the dimming region arising as a result of
the eruption. Supported by recent coronal observations of the STEREO
spacecraft, we speculate about the momentum flux resulting from this outflow as
a secondary momentum source to the CME. The results presented highlight the
importance of spectroscopic measurements in relation to CME kinematics, and the
need for full-disk synoptic spectroscopic observations of the coronal and
chromospheric plasmas to capture the signature of such explosive energy release
as a way of providing better constraints of CME propagation times to L1, or any
other point of interest in the heliosphere.


  We give a simple proof of a result originally due to Dimca and Suciu: a group
that is both Kaehler and the fundamental group of a closed three-manifold is
finite. We also prove that a group that is both the fundamental group of a
closed three-manifold and of a non-Kaehler compact complex surface is infinite
cyclic or the direct product of an infinite cyclic group and a group of order
two.


  This article reports on the development and experimental results of
commercial plasma display panels adapted for their potential use as
micropattern gas radiation detectors. The plasma panel sensors (PPS) design an
materials include glass substrates, metal electrodes and inert gas mixtures
which provide a physically robust, hermetically-sealed device. Plasma display
panels used as detectors were tested with cosmic ray muons, beta rays and gamma
rays, protons and thermal neutrons. The results demonstrated rise times and
time resolution of a few nanoseconds, as well as sub-millimeter spatial
resolution compatible with the pixel pitch.


  To support emerging real-time monitoring and control applications, the
timeliness of computation results is of critical importance to mobile-edge
computing (MEC) systems. We propose a performance metric called age of task
(AoT) based on the concept of age of information (AoI), to evaluate the
temporal value of computation tasks. In this paper, we consider a system
consisting of a single MEC server and one mobile device running several
applications. We study an age minimization problem by jointly considering task
scheduling, computation offloading and energy consumption. To solve the problem
efficiently, we propose a light-weight task scheduling and computation
offloading algorithm. Through performance evaluation, we show that our proposed
age-based solution is competitive when compared with traditional strategies.


  This paper has been withdrawn by the authors, due a crucial error in the
proof of the main theorem.


  In 1983 Kalai proved an incredible generalisation of Cayley's formula for the
number of trees on a labelled vertex set to a formula for a class of
$r$-dimensional simplicial complexes. These simplicial complexes generalise
trees by means of being homologically $\Bbb Q$-acyclic. In this text we
consider a different generalisation of trees to the class of pure dimensional
simplicial complexes that \textit{minimally connect a vertex set} (in the sense
that the removal of any top dimensional face disconnects the complex). Our main
result provides an upper and lower bound for the number of these minimally
connected complexes on a labelled vertex set. We also prove that they are
potentially vastly more topologically complex than the generalisation of Kalai.
As an application of our bounds we compute the threshold probability for the
connectivity of a random simplicial complex.


  The ability to generalize under distributional shifts is essential to
reliable machine learning, while models optimized with empirical risk
minimization usually fail on non-$i.i.d$ testing data. Recently, invariant
learning methods for out-of-distribution (OOD) generalization propose to find
causally invariant relationships with multi-environments. However, modern
datasets are frequently multi-sourced without explicit source labels, rendering
many invariant learning methods inapplicable. In this paper, we propose
Kernelized Heterogeneous Risk Minimization (KerHRM) algorithm, which achieves
both the latent heterogeneity exploration and invariant learning in kernel
space, and then gives feedback to the original neural network by appointing
invariant gradient direction. We theoretically justify our algorithm and
empirically validate the effectiveness of our algorithm with extensive
experiments.


  Same-day delivery for e-commerce has become a popular service. Companies
usually offer several time delivery options with the earliest one being next
hour delivery. Due to tight delivery deadlines and thin margins, companies
often find it challenging to provide efficient same-day delivery services. In
this work, we propose a holistic scheme that combines the optimization of
routing and pricing for same-day delivery. The proposed approach is able to
take into account uncertainty in travel times, a crucial factor for delivery
applications in urban environments. We model this problem as a Markov decision
process. We apply a value function approximation technique to compute
opportunity costs. Based on these opportunity costs, as well as the customer
choice model and travel time distribution, we optimize the prices for various
delivery deadlines. We perform extensive computational experiments to compare
the proposed model with baseline policies. We also investigate how the
(potentially wrong) choice of travel time distributions affect the performance
of the proposed optimization scheme. Through numerical simulations of realistic
scenarios, we observe that compared to the deterministic model, the proposed
approach can reduce the number of missed deliveries up to 40%; at the same
time, it can increase revenue by more than 5% compared to the baseline
policies. We explore new issues that arise due to the stochastic nature of the
problem such as the effect of penalties for missed deliveries on pricing
structure and overall revenue.


  We present the experimental generation of light with directly observable
close-to ideal thermal statistical properties. The thermal light state is
prepared using a spontaneous Raman emission in a warm atomic vapor. The photon
number statistics is evaluated by both the measurement of second-order
correlation function and by the detailed analysis of the corresponding photon
number distribution, which certifies the quality of the Bose-Einstein
statistics generated by natural physical mechanism. We further demonstrate the
extension of the spectral bandwidth of the generated light to hundreds of MHz
domain while keeping the ideal thermal statistics, which suggests a direct
applicability of the presented source in a broad range of applications
including optical metrology, tests of robustness of quantum communication
protocols, or quantum thermodynamics.


  The ubiquity of GPS enabled devices result into the generation of an enormous
amount of user movement data consisting of a sequence of locations together
with activities performed at those locations. Such data, commonly known as {\it
activity-trajectory data}, can be analysed to find common user movements and
preferred activities, which will have tremendous business value. However,
various countries have now introduced data privacy regulations that make it
mandatory to anonymize any data before releasing it. This makes it difficult to
look for patterns as the existing mining techniques may not be directly
applicable over anonymized data. User locations in an activity-trajectory
dataset are anonymized to regions of different shapes and sizes making them
uncomparable; therefore, it is unclear how to define suitable patterns over
those regions. In this paper, we propose a top-k pattern mining technique
called TopKMintra that employs a pre-processing step to transform anonymized
activity-trajectory into an intermediate representation that address the above
problem. Unlike usual sequential data, activity-trajectory data is
2-dimensional that can lead to generation of duplicate patterns. To handle
this, TopKMintra restricts arbitrary extensions in the two dimensions by
imposing an order over the search space; this also helps in addressing the
common problem of updating the threshold in top-k pattern mining algorithms
during various stages. We perform extensive experiments on real datasets to
demonstrate the efficiency and the effectiveness of TopKMintra. Our results
show that even after anonymization, certain patterns may remain in a dataset
and those could be mined efficiently.


  We study decompositions of the global NVALUE constraint. Our main
contribution is theoretical: we show that there are propagators for global
constraints like NVALUE which decomposition can simulate with the same time
complexity but with a much greater space complexity. This suggests that the
benefit of a global propagator may often not be in saving time but in saving
space. Our other theoretical contribution is to show for the first time that
range consistency can be enforced on NVALUE with the same worst-case time
complexity as bound consistency. Finally, the decompositions we study are
readily encoded as linear inequalities. We are therefore able to use them in
integer linear programs.


  We solve the Cauchy-Dirichlet problem for the minimal surface system in
arbitrary dimension and codimension assuming a condition on the variation of
the initial submanifold .


  Let $G$ be a simple graph with $2n$ vertices and a perfect matching. The
forcing number $f(G,M)$ of a perfect matching $M$ of $G$ is the smallest
cardinality of a subset of $M$ that is contained in no other perfect matching
of $G$. Among all perfect matchings $M$ of $G$, the minimum and maximum values
of $f(G,M)$ are called the minimum and maximum forcing numbers of $G$, denoted
by $f(G)$ and $F(G)$, respectively. Then $f(G)\leq F(G)\leq n-1$. Che and Chen
(2011) proposed an open problem: how to characterize the graphs $G$ with
$f(G)=n-1$. Later they showed that for a bipartite graph $G$, $f(G)=n-1$ if and
only if $G$ is a complete bipartite graph $K_{n,n}$. In this paper, we
completely solve the problem of Che and Chen, and show that $f(G)=n-1$ if and
only if $G$ is a complete multipartite graph or a graph obtained from complete
bipartite graph $K_{n,n}$ by adding arbitrary edges in the same partite set.
For all graphs $G$ with $F(G)=n-1$, we prove that the forcing spectrum of each
such graph $G$ forms an integer interval by matching 2-switches and the minimum
forcing numbers of all such graphs $G$ form an integer interval from
$\lfloor\frac{n}{2}\rfloor$ to $n-1$.


  Recent observations show a large concentration of galaxies at high redshift.
At first sight strong clustering of galaxies at high redshifts seems to be in
contradiction with the models of structure formation. In this paper we show
that such structures are a manifestation of the strong clustering of rare peaks
in the density field. We compute the frequency of occurrence of such large
concentrations of galaxies in some models of structure formation.


  Poster layout is a crucial aspect of poster design. Prior methods primarily
focus on the correlation between visual content and graphic elements. However,
a pleasant layout should also consider the relationship between visual and
textual contents and the relationship between elements. In this study, we
introduce a relation-aware diffusion model for poster layout generation that
incorporates these two relationships in the generation process. Firstly, we
devise a visual-textual relation-aware module that aligns the visual and
textual representations across modalities, thereby enhancing the layout's
efficacy in conveying textual information. Subsequently, we propose a geometry
relation-aware module that learns the geometry relationship between elements by
comprehensively considering contextual information. Additionally, the proposed
method can generate diverse layouts based on user constraints. To advance
research in this field, we have constructed a poster layout dataset named
CGL-Dataset V2. Our proposed method outperforms state-of-the-art methods on
CGL-Dataset V2. The data and code will be available at
https://github.com/liuan0803/RADM.


  Efficient synthesis recipes are needed both to streamline the manufacturing
of complex materials and to accelerate the realization of theoretically
predicted materials. Oftentimes the solid-state synthesis of multicomponent
oxides is impeded by undesired byproduct phases, which can kinetically trap
reactions in an incomplete non-equilibrium state. We present a thermodynamic
strategy to navigate high-dimensional phase diagrams in search of precursors
that circumvent low-energy competing byproducts, while maximizing the reaction
energy to drive fast phase transformation kinetics. Using a robotic inorganic
materials synthesis laboratory, we perform a large-scale experimental
validation of our precursor selection principles. For a set of 35 target
quaternary oxides with chemistries representative of intercalation battery
cathodes and solid-state electrolytes, we perform 224 reactions spanning 27
elements with 28 unique precursors. Our predicted precursors frequently yield
target materials with higher phase purity than when starting from traditional
precursors. Robotic laboratories offer an exciting new platform for data-driven
experimental science, from which we can develop new insights into materials
synthesis for both robot and human chemists.


  Genotype-phenotype (GP) maps specify how the random mutations that change
genotypes generate variation by altering phenotypes, which, in turn, can
trigger selection. Many GP maps share the following general properties: 1) The
number of genotypes $N_G$ is much larger than the number of selectable
phenotypes; 2) Neutral exploration changes the variation that is accessible to
the population; 3) The distribution of phenotype frequencies $F_p=N_p/N_G$,
with $N_p$ the number of genotypes mapping onto phenotype $p$, is highly
biased: the majority of genotypes map to only a small minority of the
phenotypes. Here we explore how these properties affect the evolutionary
dynamics of haploid Wright-Fisher models that are coupled to a simplified and
general random GP map or to a more complex RNA sequence to secondary structure
map. For both maps the probability of a mutation leading to a phenotype $p$
scales to first order as $F_p$, although for the RNA map there are further
correlations as well. By using mean-field theory, supported by computer
simulations, we show that the discovery time $T_p$ of a phenotype $p$ similarly
scales to first order as $1/F_p$ for a wide range of population sizes and
mutation rates in both the monomorphic and polymorphic regimes. These
differences in the rate at which variation arises can vary over many orders of
magnitude. Phenotypic variation with a larger $F_p$ is therefore be much more
likely to arise than variation with a small $F_p$. We show, using the RNA
model, that frequent phenotypes (with larger $F_p$) can fix in a population
even when alternative, but less frequent, phenotypes with much higher fitness
are potentially accessible. In other words, if the fittest never `arrive' on
the timescales of evolutionary change, then they can't fix. We call this highly
non-ergodic effect the `arrival of the frequent'.


  Microsphere-assisted imaging emerged as a surprisingly simple way of
achieving optical super-resolution imaging. In this work, we use movable PDMS
thin films with embedded high-index barium titanate glass microspheres a sample
scanning capability was developed, thus removing the main limitation of this
technology based on its small field-of-view.


  The opacity of spiral galaxies is examined by modelling the dust and stellar
content of individual galaxies. The model is applied to five late-type spiral
galaxies (NGC 4013, IC 2531, UGC 1082, NGC 5529 and NGC 5907). Having analyzed
a total of seven galaxies thus far, the five galaxies mentioned above plus UGC
2048 and NGC 891 presented in (Xilouris et al. 1997, 1998), we are able to draw
some general conclusions, the most significant of which are: 1) The face-on
central optical depth is less than one in all optical bands indicating that
typical spiral galaxies like the ones that we have modelled would be completely
transparent if they were to be seen face-on. 2) The dust scaleheight is about
half that of the stars, which means that the dust is more concentrated near the
plane of the disk. 3) The dust scalelength is about 1.4 times larger than that
of the stars and the dust is more radially extended than the stars. 4) The dust
mass is found to be about an order of a magnitude more than previously measured
using the IRAS fluxes, indicating the existence of a cold dust component. The
gas-to-dust mass ratio calculated is close to the value derived for our Galaxy.
5) The derived extinction law matches quite well the Galactic extinction law,
indicating a universal dust behaviour.


  Most recent works in optical flow extraction focus on the accuracy and
neglect the time complexity. However, in real-life visual applications, such as
tracking, activity detection and recognition, the time complexity is critical.
  We propose a solution with very low time complexity and competitive accuracy
for the computation of dense optical flow. It consists of three parts: 1)
inverse search for patch correspondences; 2) dense displacement field creation
through patch aggregation along multiple scales; 3) variational refinement. At
the core of our Dense Inverse Search-based method (DIS) is the efficient search
of correspondences inspired by the inverse compositional image alignment
proposed by Baker and Matthews in 2001.
  DIS is competitive on standard optical flow benchmarks with large
displacements. DIS runs at 300Hz up to 600Hz on a single CPU core, reaching the
temporal resolution of human's biological vision system. It is order(s) of
magnitude faster than state-of-the-art methods in the same range of accuracy,
making DIS ideal for visual applications.


  This report presents the application of polynomial regression for estimating
free energy differences using thermodynamic integration. We employ linear
regression to construct a polynomial that optimally fits the thermodynamic
integration data, and thus reduces the bias and uncertainty of the resulting
free energy estimate. Two test systems with analytical solutions were used to
verify the accuracy and precision of the approach. Our results suggest that
regression with a high degree of polynomials give the most accurate free energy
difference estimates, but often with a slightly larger variance, compared to
commonly used quadrature techniques. High degrees of polynomials possess the
flexibility to closely fit the thermodynamic integration data but are often
sensitive to small changes in data points. To further improve overall accuracy
and reduce uncertainty, we also examine the use of Chebyshev nodes to guide the
selection of non-equidistant lambda values for the thermodynamic integration
scheme. We conclude that polynomial regression with non-equidistant lambda
values delivers the most accurate and precise free energy estimates for
thermodynamic integration data. Software and documentation is available at
http://www.phys.uidaho.edu/ytreberg/software


  The phase diagram and surface critical behaviour of the vertex-interacting
self-avoiding walk are examined using transfer matrix methods extended using
DMRG and coupled with finite-size scaling. Particular attention is paid to the
critical exponents at the ordinary and special points along the collapse
transition line. The question of the bulk exponents ($\nu$ and $\gamma$) is
addressed, and the results found are at variance with previously conjectured
exact values.


  Recent work on the zero temperature phases and phase transitions of strongly
random electronic system is reviewed. The transition between the spin glass and
quantum paramagnet is examined, for both metallic and insulating systems.
Insight gained from the solution of infinite range models leads to a quantum
field theory for the transition between a metallic quantum paramagnetic and a
metallic spin glass. The finite temperature phase diagram is described and
crossover functions are computed in mean field theory. A study of fluctuations
about mean field leads to the formulation of scaling hypotheses.


  The challenge of labeling large example datasets for computer vision
continues to limit the availability and scope of image repositories. This
research provides a new method for automated data collection, curation,
labeling, and iterative training with minimal human intervention for the case
of overhead satellite imagery and object detection. The new operational scale
effectively scanned an entire city (68 square miles) in grid search and yielded
a prediction of car color from space observations. A partially trained yolov5
model served as an initial inference seed to output further, more refined model
predictions in iterative cycles. Soft labeling here refers to accepting label
noise as a potentially valuable augmentation to reduce overfitting and enhance
generalized predictions to previously unseen test data. The approach takes
advantage of a real-world instance where a cropped image of a car can
automatically receive sub-type information as white or colorful from pixel
values alone, thus completing an end-to-end pipeline without overdependence on
human labor.


  We express the real period of a family of elliptic curves in terms of
classical hypergeometric series. This expression is analogous to a result of
Ono which relates the trace of Frobenius of the same family of elliptic curves
to a Gaussian hypergeometric series. This analogy provides further evidence of
the interplay between classical and Gaussian hypergeometric series.


  We investigate the physical properties and electronic structure of
BaFe2-{\delta}Se3 crystals, which were grown out of tellurium flux. The crystal
structure of the compound, an iron-deficient derivative of the ThCr2Si2-type,
is built upon edge-shared FeSe4 tetrahedra fused into double chains. The
semiconducting BaFe2-{\delta}Se3 with {\delta} \approx 0.2 ({\rho}295K = 0.18
{\Omega}\cdotcm and Eg = 0.30 eV) does not order magnetically, however there is
evidence for short-range magnetic correlations of spin glass type (Tf \approx
50 K) in magnetization, heat capacity and neutron diffraction results. A
one-third substitution of selenium with sulfur leads to a slightly higher
electrical conductivity ({\rho}295K = 0.11 {\Omega}\cdotcm and Eg = 0.22 eV)
and a lower spin glass freezing temperature (Tf \approx 15 K), corroborating
with higher electrical conductivity reported for BaFe2S3. According to the
electronic structure calculations, BaFe2Se3 can be considered as a
one-dimensional ladder structure with a weak interchain coupling.


  This paper is a discussion of the physics of magnification in telescopes.
Special attention is given to the question of whether telescopes magnify stars.
Telescopes do magnify star images, although opinions to the contrary abound.


  We construct a non-trivial $U(1)/\mathbb{Z}_q$ principal bundle on~$T^4$ from
the compact $U(1)$ lattice gauge field by generalizing L\"uscher's constriction
so that the cocycle condition contains $\mathbb{Z}_q$ elements (the 't~Hooft
flux). The construction requires an admissibility condition on lattice gauge
field configurations. From the transition function so constructed, we have the
fractional topological charge that is $\mathbb{Z}_q$ one-form gauge invariant
and odd under the lattice time reversal transformation. Assuming a rescaling of
the vacuum angle $\theta\to q\theta$ suggested from the Witten effect, our
construction provides a lattice implementation of the mixed 't~Hooft anomaly
between the $\mathbb{Z}_q$ one-form symmetry and the time reversal symmetry in
the $U(1)$ gauge theory with matter fields of charge~$q\in2\mathbb{Z}$ when
$\theta=\pi$, which was studied by Honda and Tanizaki [J. High Energy Phys.
\textbf{12}, 154 (2020)] in the continuum framework.


  We present experimental observations and a study of quantum dynamics of
strongly interacting electronic spins, at room temperature in the solid state.
In a diamond substrate, a single nitrogen vacancy (NV) center coherently
interacts with two adjacent S = 1/2 dark electron spins. We quantify
NV-electron and electron-electron couplings via detailed spectroscopy, with
good agreement to a model of strongly interacting spins. The electron-electron
coupling enables an observation of coherent flip-flop dynamics between
electronic spins in the solid state, which occur conditionally on the state of
the NV. Finally, as a demonstration of coherent control, we selectively couple
and transfer polarization between the NV and the pair of electron spins. These
results demonstrate a key step towards full quantum control of electronic spin
registers in room temperature solids.


  The geometrical structure is among the most fundamental ingredients in
understanding complex systems. Is there any systematic approach in defining
structures quantitatively, rather than illustratively? If yes, what are the
basic principles to follow? By introducing the concept of extremal points at
different scale levels, a multi-level dissipation element approach has been
developed to define structures at different scale levels, in accordance with
the concept of structure hierarchy. Each dissipation element can be
characterized by the length scale and the scalar variance inside. Using the
two-dimensional fractal Brownian motion as a benchmark case, the conditional
mean of the scalar difference with respect to the length scale shows clearly a
power law and the scaling exponent is in agreement with the Hurst number. For
the 3D turbulence velocity component, the 1/3 scaling law can be represented.
These results indicate the important linkage between the turbulence physics and
ow structure, if well posed and defined. In principle, the multi-level
dissipation element idea is generally applicable in analyzing other multiscale
complex systems as well.


  We establish relations between geometric quantum discord and entanglement
quantifiers obtained by means of optimal witness operators. In particular, we
prove a relation between negativity and geometric discord in the
Hilbert-Schmidt norm, which is slightly different from a previous conjectured
one [Phys. Rev. A 84, 052110 (2011)].We also show that, redefining the
geometric discord with the trace norm, better bounds can be obtained. We
illustrate our results numerically.


  In this paper, we study a multi-user multiple-input-multiple-output secrecy
simultaneous wireless information and power transfer (SWIPT) channel which
consists of one transmitter, one cooperative jammer (CJ), multiple energy
receivers (potential eavesdroppers, ERs), and multiple co-located receivers
(CRs). We exploit the dual of artificial noise (AN) generation for facilitating
efficient wireless energy transfer and secure transmission. Our aim is to
maximize the minimum harvested energy among ERs and CRs subject to secrecy rate
constraints for each CR and total transmit power constraint. By incorporating
norm-bounded channel uncertainty model, we propose a iterative algorithm based
on sequential parametric convex approximation to find a near-optimal solution.
Finally, simulation results are presented to validate the performance of the
proposed algorithm outperforms that of the conventional AN-aided scheme and
CJ-aided scheme.


  We performed Raman studies and a dielectric characterization of the
pseudo-kagome Cu3Bi(SeO3)2O2X (X = Cl, Br). These compounds share competing
nearest-neighbour ferromagnetic exchange and frustrating next-nearest-neighbour
antiferromagnetic exchange as well as highly noncollinear magnetic ground
state. However, at low temperature they differ with respect to the existence of
inversion symmetry. For both compounds there exists a pronounced interplay of
polar phonon modes with quantum magnetic fluctuations. A novel Raman mode
appears for temperatures below the Neel temperature with a Fano lineshape and
an enormous intensity that exceeds most of the phonon lines. We discuss a
possible contribution of longitudinal magnons to this signal. In contrast, one
magnon scattering based on linear transvers magnons is excluded based on a
symmetry analysis of spin wave representations and Raman tensor calculations.
There exists evidence that in these pseudo-kagome compounds magnetic quantum
fluctuations carry an electric dipole moment. Our data as well as a comparison
with previous far-infrared spectra allow us to conclude that Cu3Bi(SeO3)2O2Cl
changes its symmetry most likely from Pmmn to P21mn with a second order
structural phase transition at T*=120 K and becomes multiferroic.
Cu3Bi(SeO3)2O2Br represents an interesting counter part as it does not show
this instability and stays inversion symmetric down to lowest temperatures,
investigated.


  We consider the dispersion managed nonlinear Schr\"dinger equations with
quintic and cubic nonlinearities in one and two dimensions, respectively. We
prove the global well-posedness and scattering in $L_x^2$ for small initial
data employing the $U^p$ and $V^p$ spaces.


  We analyse the primordial density perturbation when it is generated by a
`curvaton' field different from the inflaton. In some cases this perturbation
may have large isocurvature components, fully correlated or anti-correlated
with the adiabatic component. It may also have a significant non-Gaussian
component. All of these effects are calculated in a form which will enable
direct comparison with current and forthcoming observational data.


  Data sharing enables critical advances in many research areas and business
applications, but it may lead to inadvertent disclosure of sensitive summary
statistics (e.g., means or quantiles). Existing literature only focuses on
protecting a single confidential quantity, while in practice, data sharing
involves multiple sensitive statistics. We propose a novel framework to define,
analyze, and protect multi-secret summary statistics privacy in data sharing.
Specifically, we measure the privacy risk of any data release mechanism by the
worst-case probability of an attacker successfully inferring summary statistic
secrets. Given an attacker's objective spanning from inferring a subset to the
entirety of summary statistic secrets, we systematically design and analyze
tailored privacy metrics. Defining the distortion as the worst-case distance
between the original and released data distribution, we analyze the tradeoff
between privacy and distortion. Our contribution also includes designing and
analyzing data release mechanisms tailored for different data distributions and
secret types. Evaluations on real-world data demonstrate the effectiveness of
our mechanisms in practical applications.


  The origin of rovibrational H_2 emission in the central galaxies of cooling
flow clusters is poorly understood. Here we address this issue using data from
our near-infrared spectroscopic survey of 32 of the most line luminous such
systems, presented in the companion paper by Edge et al. (2002).
  We consider excitation by X-rays from the surrounding intracluster medium, UV
radiation from young stars, and shocks. The v=1-0 K-band lines with upper
levels within 10^4 K of the ground state appear to be mostly thermalised
(implying gas densities above ~10^5 cm^-3), with excitation temperatures
typically exceeding 2000K, as found earlier by Jaffe, Bremer and van der Werf
(2001). Together with the lack of strong v=2-0 lines in the H-band, this rules
out UV fluorescence.
  Using the CLOUDY photoionisation code, we deduce that the H_2 lines can
originate in a population of dense clouds, exposed to the same hot (T~50000K)
stellar continuum as the lower density gas which produces the bulk of the
forbidden optical line emission in the H-alpha luminous systems. This dense gas
may be in the form of self-gravitating clouds deposited directly by the cooling
flow, or may instead be produced in the high-pressure zones behind strong
shocks. Furthermore, the shocked gas is likely to be gravitationally unstable,
so collisions between the larger clouds may lead to the formation of globular
clusters.


  We have detected the weak lensing signal induced by the cluster of galaxies
MS 2053-04 (z=0.58) from a two-colour mosaic of 6 HST WFPC2 images. The best
fit singular isothermal sphere model to the observed tangential distortion
yields an Einstein radius r_E=6.2"+-1.8", which corresponds to a velocity
dispersion of 886^{+121}_{-139} km/s. This result is in good agreement with the
observed velocity dispersion of 817+-80 km/s from cluster members.
  MS 2053 is the third cluster we studied using mosaics of deep WFPC2 images.
For all three clusters we find good agreement between dynamical and weak
lensing velocity dispersions, in contrast to weak lensing studies based on
single WFPC2 pointings on cluster cores. This result demonstrates the
importance of wide field data. We have compared the ensemble averaged cluster
profile to the predicted NFW profile, and find that a NFW profile can fit the
observed lensing signal well. The best fit concentration parameter is found to
be 0.79^{+0.44}_{-0.15} (68% confidence) times the predicted value from an open
CDM model. The observed mass-to-light ratios of the clusters in our sample
evolve with redshift, and are inconsistent with a constant, non-evolving,
mass-to-light ratio at the 99% confidence level. The evolution is consistent
with the results derived from the evolution of the fundamental plane of early
type galaxies. The resulting average mass-to-light ratio for massive clusters
at z=0 is found to be 239+-18+-9 M/L_B. (abridged)


  High temperature expansions for the free energy, the susceptibility and the
second correlation moment of the classical N-vector model [also denoted as the
O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear
sigma model] have been extended to order beta^{21} on the simple cubic and the
body centered cubic lattices, for arbitrary N. The series for the second field
derivative of the susceptibility has been extended to order beta^{17}. An
analysis of the newly computed series yields updated estimates of the model's
critical parameters in good agreement with present renormalization group
estimates.


  We characterize the metric spaces whose free space has the bounded
approximation property through a Lipschitz analogue of the local reflexivity
principle. We show that there exist compact metric spaces whose free spaces
fail the approximation property.


  Quantum error correction plays an important role in fault-tolerant quantum
information processing. It is usually difficult to experimentally realize
quantum error correction, as it requires multiple qubits and quantum gates with
high fidelity. Here we propose a simple quantum error-correcting code for the
detected amplitude damping channel. The code requires only two qubits. We
implement the encoding, the channel, and the recovery on an optical platform,
the IBM Q System, and a nuclear magnetic resonance system. For all of these
systems, the error correction advantage appears when the damping rate exceeds
some threshold. We compare the features of these quantum information processing
systems used and demonstrate the advantage of quantum error correction on
current quantum computing platforms.


  Many dynamical models of the Milky Way halo require assumptions that the
distribution function of a tracer population should be independent of time
(i.e., a steady state distribution function) and that the underlying potential
is spherical. We study the limitations of such modelling by applying a general
dynamical model with minimal assumptions to a large sample of galactic haloes
from cosmological $N$-body and hydrodynamical simulations. Using dark matter
particles as dynamical tracers, we find that the systematic uncertainties in
the measured mass and concentration parameters typically have an amplitude of
25% to 40%. When stars are used as tracers, however, the systematic
uncertainties can be as large as a factor of $2-3$. The systematic
uncertainties are not reduced by increasing the tracer sample size and vary
stochastically from halo to halo. These systematic uncertainties are mostly
driven by underestimated statistical noise caused by correlated phase-space
structures that violate the steady state assumption. The number of independent
phase-space structures inferred from the uncertainty level sets a limiting
sample size beyond which a further increase no longer significantly improves
the accuracy of dynamical inferences. The systematic uncertainty level is
determined by the halo merger history, the shape and environment of the halo.
Our conclusions apply generally to any spherical steady-state model.


  Despite being so vital to success of Support Vector Machines, the principle
of separating margin maximisation is not used in deep learning. We show that
minimisation of margin variance and not maximisation of the margin is more
suitable for improving generalisation in deep architectures. We propose the
Halfway loss function that minimises the Normalised Margin Variance (NMV) at
the output of a deep learning models and evaluate its performance against the
Softmax Cross-Entropy loss on the MNIST, smallNORB and CIFAR-10 datasets.


  This paper proposes a direct coupling coherent quantum observer for a quantum
plant which consists of a two level quantum system. The quantum observer, which
is a quantum harmonic oscillator, includes homodyne detection measurements. It
is shown that the observer can be designed so that it does not affect the
quantum variable of interest in the quantum plant and that measured output
converges in a given sense to the plant variable of interest. Also, the plant
variable of interest-observer system can be described by a set of linear
quantum stochastic differential equations. A minimum variance unbiased
estimator form of the Kalman filter is derived for linear quantum systems and
applied to the direct coupled coherent quantum observer.


  Cytoskeletons are self-organized networks based on polymerized proteins:
actin, tubulin, and driven by motor proteins, such as myosin, kinesin and
dynein. Their positive Darwinian evolution enables them to approach optimized
functionality (self-organized criticality). Our theoretical analysis uses
hydropathic waves to identify and contrast the functional differences between
the polymerizing $\alpha$ and $\beta$ tubulin monomers, which are similar in
length and secondary structures, as well as having indistinguishable
phylogenetic trees. We show how evolution has improved water-driven flexibility
especially for $\alpha$ tubulin, and thus facilitated heterodimer microtubule
assembly, in agreement with recent atomistic simulations and topological
models. We conclude that the failure of phylogenetic analysis to identify
functionally specific positive Darwinian evolution has been caused by 20th
century technical limitations. These are overcome using 21st century
quantitative mathematical methods based on thermodynamic scaling and
hydropathic modular averaging. Our most surprising result is the identification
of large level sets, especially in hydrophobic extrema, with both
thermodynamically first- and second-order scaled water waves. Our calculations
include explicitly long-range water-protein interactions described by fractals.
We also suggest a much-needed corrective for large protein drug development
costs.


  We extend the study on the algebraic structure of the $su(n)$ color
Calogero-Sutherland models to the case of $gl(n|m)$ color CS model and show
that the generators of the super-Yangian $Y(gl(n|m))$ can be obtained from two
$gl(n|m)$ loop algebras. Also, a super $W_{\infty}$ algebra for the SUSY CS
model is constructed.


  We show that S-duality in four dimensional non-supersymmetric abelian gauge
theories can be formulated as a canonical transformation in the phase space of
the theory. This transformation is the usual interchange between electric and
magnetic degrees of freedom. It is shown that in phase space the modular
anomaly emerges as the result of integrating out the momenta degrees of
freedom. The generalization to d dimensional abelian gauge theories of p forms
is also considered. In the case of non-abelian gauge theories a careful
analysis of the constraints implied by the canonical transformation shows that
it does not relate Yang-Mills theories with inverted couplings. In fact the
dual theory is shown to be of Freedman- Townsend's type, also with ${\tilde
\tau}=-1/\tau$, $\tau=\frac{\theta}{2\pi}+\frac{4\pi i}{g^2}$.


  We provide an interior point method based on quasi-Newton iterations, which
only requires first-order access to a strongly self-concordant barrier
function. To achieve this, we extend the techniques of Dunagan-Harvey [STOC
'07] to maintain a preconditioner, while using only first-order information. We
measure the quality of this preconditioner in terms of its relative
excentricity to the unknown Hessian matrix, and we generalize these techniques
to convex functions with a slowly-changing Hessian. We combine this with an
interior point method to show that, given first-order access to an appropriate
barrier function for a convex set $K$, we can solve well-conditioned linear
optimization problems over $K$ to $\varepsilon$ precision in time
$\widetilde{O}\left(\left(\mathcal{T}+n^{2}\right)\sqrt{n\nu}\log\left(1/\varepsilon\right)\right)$,
where $\nu$ is the self-concordance parameter of the barrier function, and
$\mathcal{T}$ is the time required to make a gradient query. As a consequence
we show that:
  $\bullet$ Linear optimization over $n$-dimensional convex sets can be solved
in time
$\widetilde{O}\left(\left(\mathcal{T}n+n^{3}\right)\log\left(1/\varepsilon\right)\right)$.
This parallels the running time achieved by state of the art algorithms for
cutting plane methods, when replacing separation oracles with first-order
oracles for an appropriate barrier function.
  $\bullet$ We can solve semidefinite programs involving $m\geq n$ matrices in
$\mathbb{R}^{n\times n}$ in time
$\widetilde{O}\left(mn^{4}+m^{1.25}n^{3.5}\log\left(1/\varepsilon\right)\right)$,
improving over the state of the art algorithms, in the case where
$m=\Omega\left(n^{\frac{3.5}{\omega-1.25}}\right)$.
  Along the way we develop a host of tools allowing us to control the evolution
of our potential functions, using techniques from matrix analysis and Schur
convexity.


  Families of DFAs (FDFAs) have recently been introduced as a new
representation of $\omega$-regular languages. They target ultimately periodic
words, with acceptors revolving around accepting some representation $u\cdot
v^\omega$. Three canonical FDFAs have been suggested, called periodic,
syntactic, and recurrent. We propose a fourth one, limit FDFAs, which can be
exponentially coarser than periodic FDFAs and are more succinct than syntactic
FDFAs, while they are incomparable (and dual to) recurrent FDFAs. We show that
limit FDFAs can be easily used to check not only whether {\omega}-languages are
regular, but also whether they are accepted by deterministic B\"uchi automata.
We also show that canonical forms can be left behind in applications: the limit
and recurrent FDFAs can complement each other nicely, and it may be a good way
forward to use a combination of both. Using this observation as a starting
point, we explore making more efficient use of Myhill-Nerode's right
congruences in aggressively increasing the number of don't-care cases in order
to obtain smaller progress automata. In pursuit of this goal, we gain
succinctness, but pay a high price by losing constructiveness.


  We study photoionization of cold rubidium atoms in a strong infrared laser
field using a magneto-optical trap (MOT) recoil ion momentum spectrometer.
Three types of cold rubidium target are provided, operating in two-dimension
(2D) MOT, 2D molasses, and 3D MOT with densities in the orders of $10^7$
atoms/cm$^3$, $10^8$ atoms/cm$^3$, and $10^9$ atoms/cm$^3$, respectively. The
density profile and the temperature of 3D MOT are characterized using the
absorption imaging and photoionization. The momentum distributions of Rb$^+$
created by absorption of two- or three-photon illuminate a dipole-like
double-peak structure, in good agreement with the results in the strong field
approximation. The yielding momentum resolution of $0.12 \pm 0.03$ a.u. is
achieved in comparison with theoretical calculations, exhibiting the great
prospects for the study of electron correlations in alkali metal atoms through
interaction with strong laser pulses.


  We review attempts that have been made towards understanding the
computational properties and mechanisms of input-driven dynamical systems like
RNNs, and reservoir computing networks in particular. We provide details on
methods that have been developed to give quantitative answers to the questions
above. Following this, we show how self-organization may be used to improve
reservoirs for better performance, in some cases guided by the measures
presented before. We also present a possible way to quantify task performance
using an information-theoretic approach, and finally discuss promising future
directions aimed at a better understanding of how these systems perform their
computations and how to best guide self-organized processes for their
optimization.


  This paper deals with the determination of the S-curves in the theory of
non-hermitian orthogonal polynomials with respect to exponential weights along
suitable paths in the complex plane. It is known that the corresponding complex
equilibrium potential can be written as a combination of Abelian integrals on a
suitable Riemann surface whose branch points can be taken as the main
parameters of the problem. Equations for these branch points can be written in
terms of periods of Abelian differentials and are known in several equivalent
forms. We select one of these forms and use a combination of analytic an
numerical methods to investigate the phase structure of asymptotic zero
densities of orthogonal polynomials and of asymptotic eigenvalue densities of
random matrix models. As an application we give a complete description of the
phases and critical processes of the standard cubic model.


  We revisit the idea of generating primordial anisotropies at the end of
inflation in models of inflation with gauge fields. To be specific we consider
the charged hybrid inflation model where the waterfall field is charged under a
U(1) gauge field so the surface of end of inflation is controlled both by
inflaton and the gauge fields. Using delta N formalism properly we find that
the anisotropies generated at the end of inflation from the gauge field
fluctuations are exponentially suppressed on cosmological scales. This is
because the gauge field evolves exponentially during inflation while in order
to generate appreciable anisotropies at the end of inflation the spectator
gauge field has to be frozen and scale invariant. We argue that this is a
generic feature, that is, one can not generate observable anisotropies at the
end of inflation within an FRW background.


  The Luttinger's theorem has long been taken as the key feature of Landau's
Fermi liquid, which signals the presence of quasiparticles. Here, by the
unbiased Monte Carlo method, violation of Luttinger's theorem is clearly
revealed in the Falicov-Kimball (FK) model, indicating the robust
correlation-driven non-Fermi liquid characteristic under any electron density.
Introducing hole carriers to the half-filled FK leads to Mott insulator-metal
transition, where the Mott quantum criticality manifests unconventional scaling
behavior in transport properties. Further insight on the violation of the
Luttinger's theorem is examined by combining Hubbard-I approximation with a
composite fermion picture, which emphasizes the importance of a mixed
excitation of the itinerant electron and the composite fermion. Interestingly,
when compared FK model with a binary disorder system, it suggests that the
two-peak band structure discovered by Monte Carlo and Hubbard-I approaches is
underlying the violation of Luttinger's theorem.


  We present the optoelectronic characterization of two graphene/silicon
Schottky junctions, fabricated by transferring CVD-graphene on flat and
nanotip-patterned n-Si substrates, respectively. We demonstrate record photo
responsivity, exceeding 2.5 A/W under white light, which we attribute to the
contribution of charges photogenerated in the surrounding region of the flat
junction or to the internal gain by impact ionization caused by the enhanced
field on the nanotips.


  We introduce a deep recursive octree network for the compression of 3D voxel
data. Our network compresses a voxel grid of any size down to a very small
latent space in an autoencoder-like network. We show results for compressing
32, 64 and 128 grids down to just 80 floats in the latent space. We demonstrate
the effectiveness and efficiency of our proposed method on several publicly
available datasets with three experiments: 3D shape classification, 3D shape
reconstruction, and shape generation. Experimental results show that our
algorithm maintains accuracy while consuming less memory with shorter training
times compared to existing methods, especially in 3D reconstruction tasks.


  In this work, we use a Stackelberg infinite discrete-time dynamic game model
to study the optimal supply schedule and the optimal demand response under a
market-driven dynamic price. A two-layer optimization framework is established.
At the lower layer, for each user, different appliances are scheduled for
energy consumption. For enegy provider, different generators are utilized for
energy generation. At the upper level, with the supplier acting as a leader and
the users acting as followers, a Stackelberg dynamic game is used to capture
the interaction among the energy provider and the users where the energy
provider and the users care only about their own cost. We analyze the
one-leader-N-followers Stackelberg dynamic game and characterize the
Stackelberg equilibrium. We provide a closed-form Nash solution of the optimal
dynamic demand response problem when the supply is announced. A set of linear
constraints is developed to characterize the Stackeberg equilibrium. Simulation
results show that the price is driven to a reasonable value. Also, the total
demand and the supply is balanced.


  To help researchers conduct a systematic review or meta-analysis as
efficiently and transparently as possible, we designed a tool (ASReview) to
accelerate the step of screening titles and abstracts. For many tasks -
including but not limited to systematic reviews and meta-analyses - the
scientific literature needs to be checked systematically. Currently, scholars
and practitioners screen thousands of studies by hand to determine which
studies to include in their review or meta-analysis. This is error prone and
inefficient because of extremely imbalanced data: only a fraction of the
screened studies is relevant. The future of systematic reviewing will be an
interaction with machine learning algorithms to deal with the enormous increase
of available text. We therefore developed an open source machine learning-aided
pipeline applying active learning: ASReview. We demonstrate by means of
simulation studies that ASReview can yield far more efficient reviewing than
manual reviewing, while providing high quality. Furthermore, we describe the
options of the free and open source research software and present the results
from user experience tests. We invite the community to contribute to open
source projects such as our own that provide measurable and reproducible
improvements over current practice.


  This article reports the status of a $\nu_{\mu} \to \nu_{e}$ oscillation
search in MiniBooNE (Booster Neutrino Experiment) experiment. If an appearance
signal is observed, it will imply Physics Beyond the Standard Model such as the
existence of light sterile neutrino.


  Ever increasing computational power will require methods for automatic
programming. We present an alternative to genetic programming, based on a
general model of thinking and learning. The advantage is that evolution takes
place in the space of constructs and can thus exploit the mathematical
structures of this space. The model is formalized, and a macro language is
presented which allows for a formal yet intuitive description of the problem
under consideration. A prototype has been developed to implement the scheme in
PERL. This method will lead to a concentration on the analysis of problems, to
a more rapid prototyping, to the treatment of new problem classes, and to the
investigation of philosophical problems. We see fields of application in
nonlinear differential equations, pattern recognition, robotics, model
building, and animated pictures.


  We theoretically predict efficient optical second-harmonic generation (SHG)
from a few hundred nanometer thick slab consisting of a quadratic nonlinear
anisotropic medium whose linear principal permittivities are, at the
fundamental wavelength, very small and have different signs (indefinite
medium). We show that, by illuminating the slab with a p-polarized fundamental
wave (with intensity of a few MW/cm^2), a highly efficient scattering of the
second-harmonic field occurs when the conditions of linear complete slab
transparency for the fundamental wave are met. The high efficiency of the SHG
process, stems from the large non-plasmonic enhancement of the longitudinal
field, perpendicular to the slab surface, produced by the very small value of
the slab dielectric permittivities. A suitable nano-structured composite is
proposed and numerically designed for observing the novel non-phase-matched and
highly efficient SHG process from nano-structures.


  This note considers the finite linear independence of coherent systems. We
show by simple arguments that lattice coherent systems of amenable groups are
linearly independent whenever the associated twisted group ring does not
contain any nontrivial zero divisors. We verify the latter for discrete locally
indicable groups, which includes lattices in nilpotent Lie groups. For the
particular case of time-frequency translates of Euclidean space, our main
result recovers the Heil-Ramanathan-Topiwala (HRT) conjecture for subsets of
arbitrary lattices.


  The Extremely Low-Resource Optical Identifier (ELROI) is a concept for an
autonomous, low-power optical "license plate" that can be attached to anything
that goes into space. ELROI uses short, omnidirectional flashes of laser light
to encode a unique ID number which can be read by a small ground telescope
using a photon-counting sensor and innovative extreme background-rejection
techniques. ELROI is smaller and lighter than a typical radio beacon, low-power
enough to run on its own small solar cell, and can safely operate for the
entire orbital lifetime of a satellite or debris object. The concept has been
validated in ground tests, and orbital prototypes are scheduled for launch in
2018 and beyond. In this paper we focus on the details of the encoding scheme
and data analysis that allow a milliwatt optical signal to be read from orbit.
We describe the techniques of extreme background-rejection needed to achieve
this, including spectral filtering and temporal filtering using a period- and
phase-recovery algorithm, and discuss the requirements for an error-correcting
code to encode the ID number. Worked examples with both simulated and
experimental (long-range ground test) data illustrate the methods used. We
present these techniques to describe a new optical communication concept, and
to encourage others to consider observing and analyzing our upcoming test
flights.


  In this work we generalize the concept of injective module and develop a
theory of divisibility for modules over a general ring, which provides a
general and unified framework to study Kummer-like field extensions arising
from commutative algebraic groups. With these tools we provide an effective
bound for the degree of the field extensions arising from division points of
elliptic curves, extending previous results of Javan Peykar for CM curves and
of Lombardo and the author for the non-CM case.


  The main goal of the Jiangmen Underground Neutrino Observatory (JUNO) under
construction in China is to determine the neutrino mass hierarchy and to
measure oscillation parameters to the sub-percent level. The detector consists
of 20 ktons of liquid scintillator instrumented by 17612 20-inch
photo-multiplier tubes, and 25600 3-inch small PMTs, with photo-cathode
coverage of 77%. The electronics system is separated into two main parts. The
front-end system, sitting under water, performs analog signal processing. The
back-end electronics system, sitting outside water, consists of the DAQ and the
trigger. The current production status of the experiment as well as the design
of the electronics system will be reported in the presentation.


  Third-party resources ($e.g.$, samples, backbones, and pre-trained models)
are usually involved in the training of deep neural networks (DNNs), which
brings backdoor attacks as a new training-phase threat. In general, backdoor
attackers intend to implant hidden backdoor in DNNs, so that the attacked DNNs
behave normally on benign samples whereas their predictions will be maliciously
changed to a pre-defined target label if hidden backdoors are activated by
attacker-specified trigger patterns. To facilitate the research and development
of more secure training schemes and defenses, we design an open-sourced Python
toolbox that implements representative and advanced backdoor attacks and
defenses under a unified and flexible framework. Our toolbox has four important
and promising characteristics, including consistency, simplicity, flexibility,
and co-development. It allows researchers and developers to easily implement
and compare different methods on benchmark or their local datasets. This Python
toolbox, namely \texttt{BackdoorBox}, is available at
\url{https://github.com/THUYimingLi/BackdoorBox}.


  Two-field slow-roll inflation is the most conservative modification of a
single-field model. The main motivations to study it are its entropic mode and
non-Gaussianity. Several years ago, for a two-field model with additive
separable potentials, Vernizzi and Wands invented an analytic method to
estimate its non-Gaussianities. Later on, Choi et al. applied this method to
the model with multiplicative separable potentials. In this note, we design a
larger class of models whose non-Gaussianity can be estimated by the same
method. Under some simplistic assumptions, roughly these models are unlikely
able to generate a large non-Gaussianity. We look over some specific models of
this class by scanning the full parameter space, but still no large
non-Gaussianity appears in the slow-roll region. These models and scanning
techniques would be useful for future model hunt if observational evidence
shows up for two-field inflation.


  Given a finite set $V=\{v^1, \dots, v^n\} \subset \mathbb R^d$ with dim conv
$(V)=d$, a triangulation $T$ of $V$ is a collection of distinct subsets $\{T_1,
\dots, T_m\}$ where $T_i \subseteq V$ is the vertex set of a $d$-simplex,
$\mathrm{conv} (V)=\bigcup_{i=1}^m \mathrm{conv} (T_i)$, and $T_i \cap T_j$ is
a common (possibly empty) face of both $T_i$ and $T_j$. Associated with each
triangulation $T$ of $V$ is the GKZ-vector $\phi(T)=(z_1, \dots, z_n)$ where
$z_i$ is the sum of the volumes of all $d$-simplices of $T$ having $v^i \in V$
as a vertex. It is clear that given $V$ and a triangulation $T$ we can find
$\phi(T)$. The focus of this paper is recovering a lexicographic triangulation
from its GKZ-vector.
  The motivation for studying triangulations and their GKZ-vectors arises from
the work of Gel'fand, Kapranov, and Zelevinski\v{\i} in which they illuminate
connections between regular triangulations and subdivisions of Newton
polytopes, and generalized discriminants and determinants.
  The secondary polytope, $\Sigma (V)$, of an arbitrary finite point set $V
\subset \mathbb R^d$, introduced by Gel'fand, Kapranov, and Zelevinski\v{\i},
is defined to be the convex hull of the GKZ-vectors of all triangulations of
$V$. They showed the vertices of $\Sigma (V)$ are in one-to-one correspondence
with the regular triangulations of $V$. Since the GKZ-vector of a regular
triangulation is uniquely associated with that triangulation, a natural
question is how that triangulation can be recovered from its vector. We answer
this question in the case that the associated triangulation is lexicographic.


  We investigate the connection between the most luminous active galactic
nuclei (AGN), galaxy pairs, and post-mergers in the IllustrisTNG simulation. We
select galaxy pairs and post-mergers with a mass ratio between 1:10 $< \mu <$
1:1 and a redshift between $0<z<1$. We compare the incidence of luminous AGN in
pairs with matched non-pair controls, finding that AGN with luminosity
$L_{\mathrm{bol}}>10^{44}$ erg/s occur in $\sim $26\% of paired galaxies with a
companion within 20 kpc, compared with $\sim $14\% in controls (a fractional
excess of $\sim$2). The enhancement of AGN in galaxy pairs is luminosity
dependent, with the highest excess (a factor of $\sim6\pm2$ at the closest
separations) for AGN with $L_{\mathrm{bol}}>10^{45}$ erg/s. Additionally, pairs
exhibit a modest yet statistically significant excess of luminous AGN up to
$\sim$150 kpc in separation. For pairs which merge between $0<z<1$, AGN
fractions are elevated between 1.5 Gyr before and after coalescence, with the
highest excess closest to coalescence. Our results indicate that
pre-coalescence interactions drive excesses of luminous AGN, but that luminous
AGN in galaxy pairs are not ubiquitous. Finally, we investigate what fraction
of AGN can be associated with an interaction (either having a companion within
100 kpc or a merger within the last 500 Myr). For AGN with
$L_{\mathrm{bol}}>10^{45}$ erg/s, $\sim$55\% are interacting, compared with a
30\% interaction fraction in AGN with $10^{44}<L_{\mathrm{bol}}<10^{44.5}$
erg/s. Our results support a picture in which interactions play a dominant role
in (but are not the sole cause of) triggering the most luminous AGN.


  We show a degree formula for a type of orthogonal Deligne--Lusztig varieties
and their Pl\"ucker embeddings. This is an analog of work of Li on a unitary
case.


  To identify the superconducting gap structure in URu2Si2 we perform
field-angle-dependent specific heat measurements for the two principal
orientations in addition to field rotations, and theoretical analysis based on
microscopic calculations. The Sommerfeld coefficient \gamma(H)'s in the mixed
state exhibit distinctively different field-dependence. This comes from point
nodes and substantial Pauli paramagnetic effect of URu2Si2. These two features
combined give rise to a consistent picture of superconducting properties,
including a possible first order transition of Hc2 at low temperatures.


  In this paper we propose a measure of anisotropy as a quality parameter to
estimate the amount of noise in noisy images. The anisotropy of an image can be
determined through a directional measure, using an appropriate statistical
distribution of the information contained in the image. This new measure is
achieved through a stack filtering paradigm. First, we define a local
directional entropy, based on the distribution of 0's and 1's in the
neigborhood of every pixel location of each stack level. Then the entropy
variation of this directional entropy is used to define an anisotropic measure.
The empirical results have shown that this measure can be regarded as an
excellent image noise indicator, which is particularly relevant for quality
assessment of denoising algorithms. The method has been evaluated with
artificial and real-world degraded images.


  We study transmission and reflection properties of a perfectly amplifying as
well as absorbing medium analytically by using the tight binding equation.
Different expressions for transmittance and reflectance are obtained for even
and odd values of the sample length which is the origin of their oscillatory
behavior. In a weak amplifying medium, a cross-over length scale exists below
which transmittance and reflectance increase exponentially and above which
transmittance decays exponentially while the reflectance gets saturated.
Depending on amplification transmittance and reflectance show singular behavior
at the cross-over length. In a weak absorbing medium we do not find any
cross-over length scale. The transmission coefficient behaves similar to that
in an amplifying medium in the asymptotic limit. In a strong
amplifying/absorbing medium, the transmission coefficient decays exponentially
in the large length limit. In both weak as well as strong absorbing media the
logarithm of the reflection coefficient shows the same behavior as obtained in
an amplifying medium but with opposite sign.


  The secular instability and nonlinear evolution of the m=2 f-mode (bar-mode)
driven by gravitational radiation reaction in a rapidly rotating, newly formed
neutron star are reviewed. There are two types of rotating bars which generate
quite different gravitational waveforms: those with large internal rotation
relative to the bar figure (Dedekind-like bars) have GW frequency sweeping
downward during the evolution, and those with small internal rotation
(Jacobi-like) have GW frequency sweeping upward. Various sources of viscosity
(which affects the instability) in hot nuclear matter are reexamined, and the
possible effect of star-disk coupling on the bar-mode instability is also
discussed.


  We study the computational complexity of a Metropolis-Hastings algorithm for
Bayesian community detection. We first establish a posterior strong consistency
result for a natural prior distribution on stochastic block models under the
optimal signal-to-noise ratio condition in the literature. We then give a set
of conditions that guarantee rapid mixing of a simple Metropolis-Hastings
algorithm. The mixing time analysis is based on a careful study of posterior
ratios and a canonical path argument to control the spectral gap of the Markov
chain.


  One of the main challenges of modern cosmology is to understand the nature of
dark energy. The Integrated Sachs-Wolfe (ISW) effect is sensitive to dark
energy and presents an independent signature of dark energy in the absence of
modified gravity and curvature. The ISW effect occurs on large scales, where
cosmic variance is high and where there are large amounts of missing data in
the CMB and large scale structure maps due to Galactic confusion. Moreover,
existing methods in the literature often make strong assumptions about the
statistics of the underlying fields or estimators. Together these effects can
severely limit signal extraction. We review literature on the ISW effect,
comparing statistical subtleties between existing methods, and identifying
several limitations. We propose a novel method to detect and measure the ISW
signal. This method assumes only that the primordial CMB field is Gaussian. It
is based on a sparse inpainting method to reconstruct missing data and uses a
bootstrap technique to avoid assumptions about the statistics of the estimator.
It is a complete method, using three complementary statistical methods. We
apply our method to Euclid-like simulations and show we can expect a \sim
7\sigma model-independent detection of the ISW signal with WMAP7-like data,
even with missing data. Other tests return \sim 4.7\sigma detection levels for
a Euclid-like survey, with levels independent from whether the galaxy field is
normally or lognormally distributed. We apply our method to the 2 Micron All
Sky Survey (2MASS) and WMAP7 CMB data and find detections in the 1.1 -
2.0\sigma range, as expected from simulations. As a by-product, we reconstruct
the full-sky temperature ISW field due to 2MASS data. We have presented a novel
technique, based on sparse inpainting and bootstrapping, which accurately
detects and reconstructs the ISW effect.


  We prove equidistribution theorems for a family of holomorphic Siegel cusp
forms of general degree in the level aspect. Our main contribution is to
estimate unipotent contributions for general degree in the geometric side of
Arthur's invariant trace formula in terms of Shintani zeta functions. Several
applications including the vertical Sato-Tate theorem and low-lying zeros for
standard $L$-functions of holomorphic Siegel cusp forms are discussed. We also
show that the "non-genuine forms" which come from non-trivial endoscopic
contributions by Langlands functoriality classified by Arthur are negligible.


  The band structures of ordered and thermally disordered
Li$_2$Mo$_{12}$O$_{34}$ are calculated by use of ab-initio DFT-LMTO method with
focus on the behavior of the Mo 3d-core levels. It is shown that thermal
disorder and zero-point motion lead to substantial core level broadening, and
the broadening at room temperature is predicted to be sufficiently larger than
at zero degrees to allow for a detection by XPS measurements. However, real
purple bronze has 10 percent of Li vacancies and static disorder will attenuate
the $T$-dependent broadening. It is argued that core level spectroscopies could
be a useful tool for measuring of thermal disorders in many materials,
especially for those with minor static disorder. Studies of core levels in
magnetic materials will be helpful for an understanding of $T$-dependent spin
moments.


  The topic of this tutorial is Least Squares Sparse Principal Components
Analysis (LS SPCA) which is a simple method for computing approximated
Principal Components which are combinations of only a few of the observed
variables. Analogously to Principal Components, these components are
uncorrelated and sequentially best approximate the dataset. The derivation of
LS SPCA is intuitive for anyone familiar with linear regression. Since LS SPCA
is based on a different optimality from other SPCA methods and does not suffer
from their serious drawbacks. I will demonstrate on two datasets how useful and
parsimonious sparse PCs can be computed. An R package for computing LS SPCA is
available for download.


  We reexamine the thermodynamics of adS black holes with Ricci flat horizons
using the adS soliton as the thermal background. We find that there is a phase
transition which is dependent not only on the temperature, but also on the
black hole area, which is an independent parameter. As in the spherical adS
black hole, this phase transition is related via the adS/CFT correspondence to
a confinement-deconfinement transition in the large N gauge theory on the
conformal boundary at infinity.


  This work focuses on some key aspects of the General Relativistic
(GR)-magnetohydrodynamic (MHD) applications in High-Energy Astrophysics. We
discuss the relevance of the GR-HD counterparts formulation exploring the
geometrically thick disk models and constraints of the GR-MHD shaping the
physics of accreting configurations. Models of clusters of tori orbiting a
central super-massive black hole (SMBH) are described. These orbiting tori
aggregates form sets of geometrically thick, pressure supported, perfect fluid
tori, associated to complex instability processes including tori collision
emergence and empowering a wide range of activities related expectantly to the
embedding matter environment of Active Galaxy Nuclei. Some notes are included
on aggregates combined with proto-jets, represented by open cusped solutions
associated to the geometrically thick tori. This exploration of some key
concepts of the GR-MHD formulation in its applications to High-Energy
Astrophysics starts with the discussion of the initial data problem for a most
general Einstein-Euler-Maxwell system addressing the problem with a
relativistic geometric background. The system is then set in quasi linear
hyperbolic form, and the reduction procedure is argumented. Then,
considerations follow on the analysis of the stability problem for
self-gravitating systems with determined symmetries considering the
perturbations also of the geometry part on the quasi linear hyperbolic onset.
Thus we focus on the ideal GR-MHD and self-gravitating plasma ball. We conclude
with the models of geometrically thick GR-HD disks gravitating around a Kerr
SMBH in their GR-HD formulation and including in the force balance equation of
the disks the influence of a toroidal magnetic field, determining its impact in
tori topology and stability


  We present a new phase-field formulation for the non-equilibrium interface
kinetics. The diffuse interface is considered an integral of numerous
representative volume elements (RVEs), in which there is a two-phase mixture
with two conserved and two non-conserved concentration fields. This particular
way of separating concentration fields leads to two distinct dissipative
processes besides the phase boundary migration, i.e., trans-sharp-interface
diffusion between different phases within a single RVE and
trans-diffuse-interface diffusion between different RVEs within a single phase.
A two-part mechanism is proposed to balance the driving forces and energy
dissipation for diffusionless and diffusional processes in RVEs. Moreover, the
classical interface friction and solute drag can be recovered by integrating
the diffuse interface. Compared with the sharp interface theory, the present
diffuse interface can reproduce the atomic simulated partial-drag
self-consistently in thermodynamics.


  We study the issue of description of spinning particle dynamics by means of
recently proposed world sheet concept. A model of irreducible spinning particle
in the $3d$ Minkowski space with two gauge symmetries is considered. The
classical trajectories of free particle lie on a circular cylinder with a
time-like axis. The direction of cylinder axis is determined by the particle
momentum, and its position in space-time depends on the value of total angular
momentum. The radius of cylinder is determined by the representation. The model
admits inclusion of consistent interactions with a general (not necessarily
uniform) electromagnetic field. The classical trajectories of the particle lie
on the cylindrical hypersurface in space time, whose position is determined by
the initial values of the momentum and total angular momentum. All the world
paths that lie on one and the same representative in the set of hypersufaces
are connected by gauge transformations. The general construction is illustrated
by the example of unform electric field. In this case, the particle paths are
shown to be general pseudotoroidal lines.


  We show that, unlike other pure b -> d penguin processes, the decay Bs(t) ->
phi K_s is dominated by a single amplitude, that of the internal t-quark. The
contributions of the u- and c-quark operators each vanish due to a cancellation
between the (V-A) \otimes (V-A) and (V-A) \otimes (V+A) matrix elements. Thus,
the indirect CP asymmetry in this decay probes sin 2\beta. Although this
cancellation is complete only for certain values of the s- and b-quark masses,
the theoretical uncertainty on sin 2\beta is still less than 10% over most
(~80%) of the parameter space. By measuring the direct CP asymmetry, one can
get a better idea of the probable error on sin 2\beta.


  Under the assumption of hierarchical right-handed neutrino masses, masses of
right-handed neutrinos must be larger than $10^8$ GeV in the standard thermal
leptogenesis scenario, while the mass can be reduced to around 5 TeV in a
neutrinophilic two Higgs doublet model. On the other hand, resonant
leptogenesis can work with the masses of TeV-scale. However, necessary
degeneracy between the lightest and the second lightest right-handed neutrino
masses means unnatural fine-tuning of the order of $10^9$. In this paper, we
will investigate the resonant leptogenesis scenario in a neutrinophilic two
Higgs doublet model. We will find the mass can be reduced to 2 TeV and the
degeneracy becomes much milder as of the order of $10^4$. We will also show
that degenerate mass spectrum of active neutrinos is disfavored in this setup.


  Particle smoothers are SMC (Sequential Monte Carlo) algorithms designed to
approximate the joint distribution of the states given observations from a
state-space model. We propose dSMC (de-Sequentialized Monte Carlo), a new
particle smoother that is able to process $T$ observations in $\mathcal{O}(\log
T)$ time on parallel architecture. This compares favourably with standard
particle smoothers, the complexity of which is linear in $T$. We derive
$\mathcal{L}_p$ convergence results for dSMC, with an explicit upper bound,
polynomial in $T$. We then discuss how to reduce the variance of the smoothing
estimates computed by dSMC by (i) designing good proposal distributions for
sampling the particles at the initialization of the algorithm, as well as by
(ii) using lazy resampling to increase the number of particles used in dSMC.
Finally, we design a particle Gibbs sampler based on dSMC, which is able to
perform parameter inference in a state-space model at a $\mathcal{O}(\log(T))$
cost on parallel hardware.


  We consider quantum mechanics on the noncommutative spaces characterized by
the commutation relations $$ [x_a, x_b] \ =\ i\theta f_{abc} x_c\,, $$ where
$f_{abc}$ are the structure constants of a Lie algebra. We note that this
problem can be reformulated as an ordinary quantum problem in a commuting
momentum space. The coordinates are then represented as linear differential
operators $\hat x_a = -i\hat D_a = -iE_{ab} (p)\, \partial /\partial p_b $.
Generically, the matrix $E_{ab}(p)$ represents a certain infinite series over
the deformation parameter $\theta$: $E_{ab} = \delta_{ab} + \ldots$. The
deformed Hamiltonian, $\hat H = -\frac 12 \hat D_a^2\,,$ describes the motion
along the corresponding group manifolds with the characteristic size of order
$\theta^{-1}$. Their metrics are also expressed into certain infinite series in
$\theta$, with $E_{ab}$ having the meaning of vielbeins. For the algebras
$su(2)$ and $u(N)$, it has been possible to represent the operators $\hat x_a$
in a simple finite form. A byproduct of our study are new nonstandard formulas
for the metrics on all the spheres $S^n$, on the corresponding projective
spaces $RP^n$ and on $U(2)$.


  Monte Carlo simulations of mono-- and polydisperse two--dimensional crystals
are reported. The particles in the studied system, interacting through
hard--core repulsive Yukawa potential, form a solid phase of hexagonal lattice.
The elastic properties of crystalline Yukawa systems are determined in the
$NpT$ ensemble with variable shape of the periodic box. Effects of the Debye
screening length ($\kappa^{-1}$), contact value of the potential ($\epsilon$),
and the size polydispersity of particles on elastic properties of the system
are studied. The simulations show that the polydispersity of particles strongly
influences the elastic properties of the studied system, especially on the
shear modulus. It is also found that the elastic moduli increase with density
and their growth rate depends on the screening length. Shorter screening length
leads to faster increase of elastic moduli with density and decrease of the
Poisson's ratio. In contrast to its three-dimensional version, the studied
system is non-auxetic, i.e. shows positive Poisson's ratio.


  In this note we study linear systems on the blow-up of $(\mathbb{P}^1)^n$ at
$r$ points in very general position. We prove that the fibers of the
projections $(\mathbb{P}^1)^n \rightarrow (\mathbb{P}^1)^s, 1\leq s \leq n-1$
can give contribution to the speciality of the linear system. This allows us to
give a new definition of expected dimension of a linear system in
$(\mathbb{P}^1)^n$ which we call fiber dimension. Finally, we state a
conjecture about linear systems on $(\mathbb{P}^1)^3$.


  Naive scale invariance is not a true property of natural images. Natural
monochrome images posses a much richer geometrical structure, that is
particularly well described in terms of multiscaling relations. This means that
the pixels of a given image can be decomposed into sets, the fractal components
of the image, with well-defined scaling exponents (Turiel & Parga, submitted).
Here it is shown that multispectral representations of natural scenes also
exhibit multiscaling properties, observing the same kind of behavior. A precise
measure of the informational relevance of the fractal components is also given,
and it is shown that there are important differences between the intrinsically
redundant RGB system and the decorrelated one defined in (Ruderman, Cronin &
Chiao, 1998).


  This paper considers the uplink pilot overhead in a time division duplexing
(TDD) massive Multiple Input Multiple Output (MIMO) mobile systems. A common
scenario of conventional massive MIMO systems is a Base Station (BS) serving
all user terminals (UTs) in the cell with the same TDD frame format that fits
the coherence interval of the worst-case scenario of user mobility (e.g. a
moving train with velocity 300 Km/s). Furthermore, the BS has to estimate all
the channels each time-slot for all users even for those with long coherence
intervals. In fact, within the same cell, sensors or pedestrian with low
mobility UTs (e.g. moving 1.38 m/s) share the same short TDD frame and thus are
obliged to upload their pilots each time-slot. The channel coherence interval
of the pedestrian UTs with a carrier frequency of 1.9 GHz can be as long as 60
times that of the train passenger users. In other words, conventional
techniques waste 59-uploaded pilot sequences for channel estimation. In this
paper, we are aware of the resources waste due to various coherence intervals
among different user mobility. We classify users based on their coherence
interval length, and we propose to skip uploading pilots of UTs with large
coherence intervals. Then, we shift frames with the same pilot reused sequence
toward an empty pilot time-slot. Simulation results had proved that the
proposed technique overcome the performance of conventional massive MIMO
systems in both energy and spectral efficiency.


  We present the loop-loop correlation model that allows us to compute
confining flux tubes and to examine their effects and manifestations in
high-energy reactions.