title:
Asymptotic expansions of the contact angle in nonlocal capillarity
  problems

abstract:
  We consider a family of nonlocal capillarity models, where surface tension is
modeled by exploiting the family of fractional interaction kernels
$|z|^{-n-s}$, with $s\in(0,1)$ and $n$ the dimension of the ambient space. The
fractional Young's law (contact angle condition) predicted by these models
coincides, in the limit as $s\to 1^-$, with the classical Young's law
determined by the Gauss free energy. Here we refine this asymptotics by showing
that, for $s$ close to $1$, the fractional contact angle is always smaller than
its classical counterpart when the relative adhesion coefficient $\sigma$ is
negative, and larger if $\sigma$ is positive. In addition, we address the
asymptotics of the fractional Young's law in the limit case $s\to 0^+$ of
interaction kernels with heavy tails. Interestingly, near $s=0$, the dependence
of the contact angle from the relative adhesion coefficient becomes linear.


title:
Rigorous Results in Existence and Selection of Saffman-Taylor Fingers by
  Kinetic Undercooling

abstract:
  The selection of Saffman-Taylor fingers by surface tension has been
extensively investigated. In this paper we are concerned with the existence and
selection of steadily translating symmetric finger solutions in a Hele-Shaw
cell by small but non-zero kinetic undercooling ($\epsilon^2 $). We rigorously
conclude that for relative finger width $\lambda$ near one half, symmetric
finger solutions exist in the asymptotic limit of undercooling $\epsilon^2
~\rightarrow ~0$ if the Stokes multiplier for a relatively simple nonlinear
differential equation is zero. This Stokes multiplier $S$ depends on the
parameter $\alpha \equiv \frac{2 \lambda
-1}{(1-\lambda)}\epsilon^{-\frac{4}{3}} $ and earlier calculations have shown
this to be zero for a discrete set of values of $\alpha$. While this result is
similar to that obtained previously for Saffman-Taylor fingers by surface
tension, the analysis for the problem with kinetic undercooling exhibits a
number of subtleties as pointed out by Chapman and King (2003) [The selection
of Saffman-Taylor fingers by kinetic undercooling, Journal of Engineering
Mathematics 46, 1-32]. The main subtlety is the behavior of the Stokes lines at
the finger tip, where the analysis is complicated by non-analyticity of
coefficients in the governing equation.


title:
Position and content paradigms in genome rearrangements: the wild and
  crazy world of permutations in genomics

abstract:
  Modellers of large scale genome rearrangement events, in which segments of
DNA are inverted, moved, swapped, or even inserted or deleted, have found a
natural syntax in the language of permutations. Despite this, there has been a
wide range of modelling choices, assumptions and interpretations that make
navigating the literature a significant challenge. Indeed, even authors of
papers that use permutations to model genome rearrangement can struggle to
interpret each others' work, because of subtle differences in basic assumptions
that are often deeply ingrained (and consequently sometimes not even
mentioned). In this paper, we describe the different ways in which permutations
have been used to model genomes and genome rearrangement events, presenting
some features and limitations of each approach, and show how the various models
are related. This paper will help researchers navigate the landscape of genome
rearrangement models, and make it easier for authors to present clear and
consistent models.


title: Local Hausdorff Measure

abstract:
  A local Hausdorff dimension is defined on a metric space. We study its
properties and use it to define a local Hausdorff measure. We show that in the
case that in the local Hausdorff measure is finite we can recover the global
Hausdorff dimension from the local one. Lastly, for a variable Ahlfors
Q-regular measure on a compact metric space, we show the Ahlfors regular
measure is strongly equivalent to the local Hausdorff measure and that the
function $Q$ is equal to the local Hausdorff dimension.


title:
Finite Element Formulation for a Poroelasticity Problem Stemming from
  Mixture Theory

abstract:
  A finite element formulation is developed for a poroelastic medium consisting
of an incompressible hyperelastic skeleton saturated by an incompressible
fluid. The governing equations stem from mixture theory and the application is
motivated by the study of interstitial fluid flow in brain tissue. The
formulation is based on the adoption of an ALE perspective. We focus on a flow
regime in which inertia forces are negligible. The stability and convergence of
the formulation is discussed, and numerical results demonstrate agreement with
the theory.


title: Soliton crystals in Kerr resonators

abstract:
  Strongly interacting solitons confined to an optical resonator would offer
unique capabilities for experiments in communication, computation, and sensing
with light. Here we report on the discovery of soliton crystals in monolithic
Kerr microresonators-spontaneously and collectively ordered ensembles of
co-propagating solitons whose interactions discretize their allowed temporal
separations. We unambiguously identify and characterize soliton crystals
through analysis of their 'fingerprint' optical spectra, which arise from
spectral interference between the solitons. We identify a rich space of soliton
crystals exhibiting crystallographic defects, and time-domain measurements
directly confirm our inference of their crystal structure. The crystallization
we observe is explained by long-range soliton interactions mediated by
resonator mode degeneracies, and we probe the qualitative difference between
soliton crystals and a soliton liquid that forms in the absence of these
interactions. Our work explores the rich physics of monolithic Kerr resonators
in a new regime of dense soliton occupation and offers a way to greatly
increase the efficiency of Kerr combs; further, the extreme degeneracy of the
configuration space of soliton crystals suggests an implementation for a robust
on-chip optical buffer.


title:
Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows
  Prediction

abstract:
  Forecasting the flow of crowds is of great importance to traffic management
and public safety, yet a very challenging task affected by many complex
factors, such as inter-region traffic, events and weather. In this paper, we
propose a deep-learning-based approach, called ST-ResNet, to collectively
forecast the in-flow and out-flow of crowds in each and every region through a
city. We design an end-to-end structure of ST-ResNet based on unique properties
of spatio-temporal data. More specifically, we employ the framework of the
residual neural networks to model the temporal closeness, period, and trend
properties of the crowd traffic, respectively. For each property, we design a
branch of residual convolutional units, each of which models the spatial
properties of the crowd traffic. ST-ResNet learns to dynamically aggregate the
output of the three residual neural networks based on data, assigning different
weights to different branches and regions. The aggregation is further combined
with external factors, such as weather and day of the week, to predict the
final traffic of crowds in each and every region. We evaluate ST-ResNet based
on two types of crowd flows in Beijing and NYC, finding that its performance
exceeds six well-know methods.


title:
PTAS for Ordered Instances of Resource Allocation Problems with
  Restrictions on Inclusions

abstract:
  We consider the problem of allocating a set $I$ of $m$ indivisible resources
(items) to a set $P$ of $n$ customers (players) competing for the resources.
Each resource $j \in I$ has a same value $v_j > 0$ for a subset of customers
interested in $j$, and zero value for the remaining customers. The utility
received by each customer is the sum of the values of the resources allocated
to her. The goal is to find a feasible allocation of the resources to the
interested customers such that for the Max-Min allocation problem (Min-Max
allocation problem) the minimum of the utilities (maximum of the utilities)
received by the customers is maximized (minimized). The Max-Min allocation
problem is also known as the \textit{Fair Allocation problem}, or the
\textit{Santa Claus problem}. The Min-Max allocation problem is the problem of
Scheduling on Unrelated Parallel Machines, and is also known as the $R \, | \,
| C_{\max}$ problem.
  In this paper, we are interested in instances of the problem that admit a
Polynomial Time Approximation Scheme (PTAS). We show that an ordering property
on the resources and the customers is important and paves the way for a PTAS.
For the Max-Min allocation problem, we start with instances of the problem that
can be viewed as a \textit{convex bipartite graph}; a bipartite graph for which
there exists an ordering of the resources such that each customer is interested
in (has a positive evaluation for) a set of \textit{consecutive} resources. We
demonstrate a PTAS for the inclusion-free cases. This class of instances is
equivalent to the class of bipartite permutation graphs. For the Min-Max
allocation problem, we also obtain a PTAS for inclusion-free instances. These
instances are not only of theoretical interest but also have practical
applications.


title:
Estimating stellar atmospheric parameters, absolute magnitudes and
  elemental abundances from the LAMOST spectra with Kernel-based Principal
  Component Analysis

abstract:
  Accurate determination of stellar atmospheric parameters and elemental
abundances is crucial for Galactic archeology via large-scale spectroscopic
surveys. In this paper, we estimate stellar atmospheric parameters -- effective
temperature T_{\rm eff}, surface gravity log g and metallicity [Fe/H], absolute
magnitudes M_V and M_{Ks}, {\alpha}-element to metal (and iron) abundance ratio
[{\alpha}/M] (and [{\alpha}/Fe]), as well as carbon and nitrogen abundances
[C/H] and [N/H] from the LAMOST spectra with amultivariate regressionmethod
based on kernel-based principal component analysis, using stars in common with
other surveys (Hipparcos, Kepler, APOGEE) as training data sets. Both internal
and external examinations indicate that given a spectral signal-to-noise ratio
(SNR) better than 50, our method is capable of delivering stellar parameters
with a precision of ~100K for Teff, ~0.1 dex for log g, 0.3 -- 0.4mag for M_V
and M_{Ks}, 0.1 dex for [Fe/H], [C/H] and [N/H], and better than 0.05 dex for
[{\alpha}/M] ([{\alpha}/Fe]). The results are satisfactory even for a spectral
SNR of 20. The work presents first determinations of [C/H] and [N/H] abundances
from a vast data set of LAMOST, and, to our knowledge, the first reported
implementation of absolute magnitude estimation directly based on the observed
spectra. The derived stellar parameters for millions of stars from the LAMOST
surveys will be publicly available in the form of value-added catalogues.


title: Spectral asymptotics for Kac-Murdock-Szeg\H{o} matrices

abstract:
  Szeg\H{o}'s First Limit Theorem provides the limiting statistical
distribution (LSD) of the eigenvalues of large Toeplitz matrices. Szeg\H{o}'s
Second (or Strong) Limit Theorem for Toeplitz matrices gives a second order
correction to the First Limit Theorem, and allows one to calculate asymptotics
for the determinants of large Toeplitz matrices. In this paper we survey
results extending the first and strong limit theorems to Kac-Murdock-Szeg\H{o}
(KMS) matrices. These are matrices whose entries along the diagonals are not
necessarily constants, but modeled by functions. We clarify and extend some
existing results, and explain some apparently contradictory results in the
literature.


title: Latent Tree Analysis

abstract:
  Latent tree analysis seeks to model the correlations among a set of random
variables using a tree of latent variables. It was proposed as an improvement
to latent class analysis --- a method widely used in social sciences and
medicine to identify homogeneous subgroups in a population. It provides new and
fruitful perspectives on a number of machine learning areas, including cluster
analysis, topic detection, and deep probabilistic modeling. This paper gives an
overview of the research on latent tree analysis and various ways it is used in
practice.


title:
Consistency Ensuring in Social Web Services Based on Commitments
  Structure

abstract:
  Web Service is one of the most significant current discussions in information
sharing technologies and one of the examples of service oriented processing. To
ensure accurate execution of web services operations, it must be adaptable with
policies of the social networks in which it signs up. This adaptation
implements using controls called 'Commitment'. This paper describes commitments
structure and existing research about commitments and social web services, then
suggests an algorithm for consistency of commitments in social web services. As
regards the commitments may be executed concurrently, a key challenge in web
services execution based on commitment structure is consistency ensuring in
execution time. The purpose of this research is providing an algorithm for
consistency ensuring between web services operations based on commitments
structure.


title: Very Deep Convolutional Neural Networks for Raw Waveforms

abstract:
  Learning acoustic models directly from the raw waveform data with minimal
processing is challenging. Current waveform-based models have generally used
very few (~2) convolutional layers, which might be insufficient for building
high-level discriminative features. In this work, we propose very deep
convolutional neural networks (CNNs) that directly use time-domain waveforms as
inputs. Our CNNs, with up to 34 weight layers, are efficient to optimize over
very long sequences (e.g., vector of size 32000), necessary for processing
acoustic waveforms. This is achieved through batch normalization, residual
learning, and a careful design of down-sampling in the initial layers. Our
networks are fully convolutional, without the use of fully connected layers and
dropout, to maximize representation learning. We use a large receptive field in
the first convolutional layer to mimic bandpass filters, but very small
receptive fields subsequently to control the model capacity. We demonstrate the
performance gains with the deeper models. Our evaluation shows that the CNN
with 18 weight layers outperform the CNN with 3 weight layers by over 15% in
absolute accuracy for an environmental sound recognition task and matches the
performance of models using log-mel features.


title:
Malcev algebras corresponding to smooth Almost Left Automorphic Moufang
  Loops

abstract:
  In this note we introduce the concept of an almost left automorphic Moufang
loop and study the properties of tangent algebras of smooth loops of this
class.


title:
System Identification of NN-based Model Reference Control of RUAV during
  Hover

abstract:
  UAV control system is a huge and complex system, and to design and test a UAV
control system is time-cost and money-cost. This paper considered the
simulation of identification of a nonlinear system dynamics using artificial
neural networks approach. This experiment develops a neural network model of
the plant that we want to control. In the control design stage, experiment uses
the neural network plant model to design (or train) the controller. We use
Matlab to train the network and simulate the behavior. This chapter provides
the mathematical overview of MRC technique and neural network architecture to
simulate nonlinear identification of UAV systems. MRC provides a direct and
effective method to control a complex system without an equation-driven model.
NN approach provides a good framework to implement MEC by identifying
complicated models and training a controller for it.


title: The Complex-Time Segal-Bargmann Transform

abstract:
  We introduce a new form of the Segal--Bargmann transform for a Lie group $K$
of compact type. We show that the heat kernel $(\rho_{t}(x))_{t>0,x\in K}$ has
a space-time analytic continuation to a holomorphic function \[
(\rho_{\mathbb{C}}(\tau,z))_{\mathrm{Re}\,\tau>0,z\in K_{\mathbb{C}}} \] where
$K_{\mathbb{C}}$ is the complexification of $K$. The new transform is defined
by the integral \[
(B_{\tau}f)(z)=\int_{K}\rho_{\mathbb{C}}(\tau,zk^{-1})f(k)\,dk,\quad z\in
K_{\mathbb{C}}. \] If $s>0$ and $\tau\in\mathbb{D}(s,s)$ (the disk of radius
$s$ centered at $s$), this integral defines a holomorphic function on
$K_{\mathbb{C}}$ for each $f\in L^{2}(K,\rho_{s})$. We construct a heat kernel
density $\mu_{s,\tau}$ on $K_{\mathbb{C}}$ such that, for all $s,\tau$ as
above, $B_{s,\tau}:=B_{\tau}|_{L^{2}(K,\rho_{s})}$ is an isometric isomorphism
from $L^{2}(K,\rho_{s})$ onto the space of holomorphic functions in
$L^{2}(K_{\mathbb{C}},\mu_{s,\tau})$. When $\tau=t=s$, the transform $B_{t,t}$
coincides with the one introduced by the second author for compact groups and
extended by the first author to groups of compact type. When $\tau=t\in
(0,2s)$, the transform $B_{s,t}$ coincides with the one introduced by the first
two authors.


title: The ccbar Pentaquarks by a Quark Model

abstract:
  Recent LHCb experiments have shown us that there are two resonances in the
$J/\psi p$ channel in the $\Lambda_b$ decay, whose spin and parity are most
probably (3/2$^-$ 5/2$^+$). In this work, we investigate the
$I(J^P)=1/2(1/2^-)$, $1/2(3/2^-)$, and $1/2(5/2^-)$ $uudc{\bar c}$ pentaquark
states by employing the quark cluster model. It is found that the color-octet
isospin-1/2 spin-3/2 $uud$ configuration gives an attraction to such five-quark
systems. This configuration together with the color-octet $c{\bar c}$ pair
gives structures around the $\Sigma_c^{(*)}{\bar D}{}^{(*)}$ thresholds: one
bound state, two resonances, and one large cusp are found in the $uudc{\bar c}$
negative parity channels. We argue that these resonances and cusp may
correspond to, or combine to form, the negative parity pentaquark peak observed
by LHCb.


title:
Bockstein homomorphisms for Hochschild cohomology of group algebras and
  of block algebras of finite groups

abstract:
  We give an explicit approach for Bockstein homomorphisms of the Hochschild
cohomology of a group algebra and of a block algebra of a finite group and we
show some properties. To give explicit definitions for these maps we use an
additive decomposition and a Product Formula for the Hochschild cohomology of
group algebras given by Siegel and Witherspoon in 1999. For k an algebraically
closed field of characteristic p and G a finite group we prove an additive
decomposition and a Product Formula for the cohomology algebra of a defect
group of a block ideal of kG with coefficients in the source algebra of this
block, and we define similar Bockstein homomorphisms.


title: Frobenius induction for algebras

abstract:
  Let $B\rightarrow A$ be a homomorphism of Hopf algebras and let $C$ be an
algebra. We consider the induction from $B$ to $A$ of $C$ in two cases: when
$C$ is a $B$-interior algebra and when $C$ is a $B$-module algebra. Our main
results establish the connection between the two inductions. The inspiration
comes from finite group representation theory, and some constructions work in
even more general contexts.


title:
Estimating the second-order parameter of regular variation and bias
  reduction in tail index estimation under random truncation

abstract:
  In this paper, we propose an estimator of the second-order parameter of
randomly right-truncated Pareto-type distributions data and establish its
consistency and asymptotic normality. Moreover, we derive an asymptotically
unbiased estimator of the tail index and study its asymptotic behaviour. Our
considerations are based on a useful Gaussian approximation of the tail
product-limit process recently given by Benchaira et al. [Tail product-limit
process for truncated data with application to extreme value index estimation.
Extremes, 2016; 19: 219-251] and the results of Gomes et al. [Semi-parametric
estimation of the second order parameter in statistics of extremes. Extremes,
2002; 5: 387-414]. We show, by simulation, that the proposed estimators behave
well, in terms of bias and mean square error.


title: On cohomology of saturated fusion systems and support varieties

abstract:
  In this short note we study the cohomology algebra of saturated fusion
systems using finite groups which realize saturated fusion systems and
Hochschild cohomology of group algebras. A similar result to a theorem of
Alperin is proved for varieties of cohomology algebras of fusions systems
associated to block algebras of finite groups.


title: Magnetic MoS2 Interface Monolayer on CdS Nanowire by Cation Exchange

abstract:
  MoS2 atomic layers have recently attracted much interest because of their
two-dimensional structure as well as tunable optical, electrical, and
mechanical properties for next generation electronic and electro-optical
devices. Here we have achieved facile fabrication of MoS2 thin films on CdS
nanowires by cation exchange in solution at room temperature and importantly
observed their extraordinary magnetic properties. We establish the atomic
structure of the MoS2/CdS heterostructure by taking atomic images of the
MoS2/CdS interface as well as performing first-principles density functional
geometry optimizations and STEM-ADF image simulations. Furthermore, our first
principles density functional calculations for the MoS2/CdS heterostructure
reveal that the magnetism in the MoS2/CdS heterostructure stems from the
ferromagnetic MoS2 monolayer next to the MoS2/CdS interface. The ferromagnetism
is attributed to the partial occupation of the Mo dx2-y2/dxy conduction band in
the interfacial MoS2 monolayer caused by the mixed covalent-ionic bonding among
the MoS2 and CdS monolayers near the MoS2/CdS interface. The present findings
of the ferromagnetic MoS2 monolayer with large spin polarization at the
MoS2-semiconductor interface suggest a new route for fabrication of the
transition metal dichalcogenide-based magnetic semiconductor multilayers for
applications in spintronic devices.


title: Refinement types for precisely named cache locations

abstract:
  Many programming language techniques for incremental computation employ
programmer-specified names for cached information. At runtime, each name
identifies a "cache location" for a dynamic data value or a sub-computation; in
sum, these cache location choices guide change propagation and incremental
(re)execution.
  We call a cache location name precise when it identifies at most one value or
subcomputation; we call all other names imprecise, or ambiguous. At a minimum,
cache location names must be precise to ensure that change propagation works
correctly; yet, reasoning statically about names in incremental programs
remains an open problem.
  As a first step, this paper defines and solves the precise name problem,
where we verify that incremental programs with explicit names use them
precisely. To do so, we give a refinement type and effect system, and prove it
sound (every well-typed program uses names precisely). We also demonstrate that
this type system is expressive by verifying example programs that compute over
efficient representations of incremental sequences and sets. Beyond verifying
these programs, our type system also describes their dynamic naming strategies,
e.g., for library documentation purposes.


title:
Explicit formulas for the Dunkl dihedral kernel and the $(\kappa,
  a)$-generalized Fourier kernel

abstract:
  In this paper, a new method is developed to obtain explicit and integral
expressions for the kernel of the $(\kappa, a)$-generalized Fourier transform
for $\kappa =0$. In the case of dihedral groups, this method is also applied to
the Dunkl kernel as well as the Dunkl Bessel function. The method uses the
introduction of an auxiliary variable in the series expansion of the kernel,
which is subsequently Laplace transformed. The kernel in the Laplace domain
takes on a much simpler form, by making use of the Poisson kernel. The inverse
Laplace transform can then be computed using the generalized Mittag-Leffler
function to obtain integral expressions. In case the parameters involved are
integers, explicit formulas are obtained using partial fraction decomposition.
  New bounds for the kernel of the $(\kappa, a)$-generalized Fourier transform
are obtained as well.


title:
Finite-momentum nematic fluctuations soften phonons in the
  superconducting state of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$

abstract:
  Nematic order is ubiquitous in liquid crystals and is characterized by a
rotational symmetry breaking in an otherwise uniform liquid. Recently a similar
phenomenon has been observed in some electronic phases of quantum materials
related to high temperature superconductivity, particularly in the Fe-based
superconductors. While several experiments have probed nematic fluctuations,
they have been primarily restricted to the uniform nematic susceptibility, i.e.
q = 0 fluctuations. Here, we investigate the behavior of finite-momentum
nematic fluctuations by measuring transverse acoustic phonon modes with
wavelengths of up to 25 unit cells in the prototypical Fe-based compound
Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. While the slope of the phonon dispersion gives
information about the uniform nematic susceptibility, deviations from this
linear behavior at finite but small wave-vectors are attributed to
finite-momentum nematic fluctuations. Surprisingly, these non-zero q
fluctuations lead to a softening of the phonon mode below the superconducting
transition temperature, in contrast to the behavior of the phonon velocity at q
= 0, which increases below $T_c$. Our work not only establishes a sound method
to probe long wavelength nematic fluctuations, but also sheds light on the
unique interplay between nematicity and superconductivity in Fe-based
compounds.


title:
L shell x-ray production in high-Z elements using 4-6 MeV/u fluorine
  ions

abstract:
  L shell line and total x-ray production cross sections in 78Pt, 79Au, 82Pb,
83Bi, 90Th, and 92U targets ionized by 4-6 MeV/u fluorine ions were measured.
These cross sections are compared with available theories for L shell
ionization using single- and multiple-hole fluorescence and the Coster-Kronig
yields. The ECPSSR and the ECUSAR theories exhibit good agreement with the
measured data, whereas, the FBA theory overestimates them by a factor of two.
Although for the F ion charge states q = 6-8 the multiple-hole atomic
parameters do not significantly differ from the single-hole values, after an
account for the multiple-holes, our data are better in agreement with the
ECUSAR than the ECPSSR theory.


title: Measuring effective temperatures in a generalized Gibbs ensemble

abstract:
  The local physical properties of an isolated quantum statistical system in
the stationary state reached long after a quench are generically described by
the Gibbs ensemble, which involves only its Hamiltonian and the temperature as
a parameter. If the system is instead integrable, additional quantities
conserved by the dynamics intervene in the description of the stationary state.
The resulting generalized Gibbs ensemble involves a number of temperature-like
parameters, the determination of which is practically difficult. Here we argue
that in a number of simple models these parameters can be effectively
determined by using fluctuation-dissipation relationships between response and
correlation functions of natural observables, quantities which are accessible
in experiments.


title:
Observing Nonclassical Paths by Measuring Bohmian Velocities in
  Multi-Slit Interferometer with Electron

abstract:
  Superposition principle of wave function in multi-slit interference
experiment has been widely accepted by many quantum mechanics textbooks,
however the expression ${\psi _{AB}} = {\psi _A} + {\psi _B}$ does not strictly
hold. The non-classical paths in Feynman path integral provide an explanation
to the multi-path interference effect, and can be used to quantitatively
analyse the multi-slit interference effect. In this work, we apply quantities
in Bohmian mechanics to the measurement of multi-order interference by
analysing the contribution of non-classical paths to Bohmian velocity in
electron's multi-slit interferometer. The result shows that the non-classical
paths effect will cause a relative deviation of $10^{-3}$ in electron's Bohmian
velocity, which is observable by doing weak measurement similar to previous
work.


title:
On Non-Newtonian fluids and phase field approach: Existence and
  Regularity

abstract:
  The object of this paper is twofold. Firstly, we study a class of generalized
Newtonian fluid related to "power law ". For the corresponding non-Newtonian
Navier-Stokes problems, the existence of a weak and periodic solutions is
proved in the large for a bounded domain in $\mathbb{R}^3$. Further,
variational inequalities and local-in-time well-posedness of the
initial-boundary value problem are investigated. Secondly, we deduce a
generalization of the Graffi-Kazhikhov-Smagulov model based on an
advective-diffusion process in the context of multiphase theory. Local-in-time
well-posedness of the initial-boundary value problem is investigated


title: A Note on the Entropy of Entanglement and Entanglement Swapping Bounds

abstract:
  Using the information content of correlations between multipartite systems,
together with the notion of partitioning, we show that some general results
about the evolution of correlations in quantum systems can be derived with only
elementary methods. In particular, we show that for 2 quantum systems A and B,
each comprised of a number of sub-systems, in which a partition of A interacts
unitarily with a partition of B, then the total correlation can only increase
(or remain unchanged) and is given simply by the sum of the initial correlation
and the correlation that develops as a result of the interaction. We then show
that in a 4 qubit entanglement swapping process the transferred degree of
entanglement is bounded by the lower of the initial degrees of entanglements of
the qubits.


title: Quantum Information as a Measure of Multipartite Correlation

abstract:
  The mutual information has been successfully used as a measure of correlation
strength between quantum systems, especially for bipartite systems. Here we
examine the use of this measure for multipartite quantum systems. For system of
qubits we find that the difference between `classical' and `quantum' regimes of
correlation strength amounts to just 1 bit of information, at most. We show
that the information content of a correlation can be expanded into correlations
between pairwise components and demonstrate that in terms of this
information-based measure of correlation the GHZ states are the only states
that simultaneously optimize these pairwise correlations for systems of qubits.


title:
The influence of magnetic fields on absorption and emission
  spectroscopies

abstract:
  Spectroscopic observations play a fundamental role in astrophysics. They are
crutial to determine important physical parameters, provide information about
the composition of various objects in the universe, as well as depict motions
in the universe. However, spectroscopic studies often do not consider the
influence of magnetic fields. In this paper, we explore the influence of
magnetic fields on the spectroscopic observations using the concept of atomic
alignment. Synthetic spectra are generated to show the measurable changes of
the spectra due to atomic alignment. The influences of atomic alignment on
absorption from DLAs, emission from H\,{\sc ii} Regions, submillimeter
fine-structure lines from star forming regions are presented as examples to
show this effect in diffuse gas. Furthermore, we demonstrate the influence of
atomic alignment on physical parameters derived from atomic line ratios, such
as the alpha-to-iron ratio([X/Fe]), interstellar temperature, and ionization
rate. We conclude that Ground State Alignment (GSA) should be taken into
consideration in the error budget of spectroscopic studies with high
signal-to-noise(S/N) ratio.


title: Cubic graphs and the golden mean

abstract:
  The connective constant $\mu(G)$ of a graph $G$ is the exponential growth
rate of the number of self-avoiding walks starting at a given vertex. We
investigate the validity of the inequality $\mu \ge \phi$ for infinite,
transitive, simple, cubic graphs, where $\phi:= \frac12(1+\sqrt 5)$ is the
golden mean. The inequality is proved for several families of graphs including
(i) Cayley graphs of infinite groups with three generators and strictly
positive first Betti number, (ii) infinite, transitive, topologically locally
finite (TLF) planar, cubic graphs, and (iii) cubic Cayley graphs with two ends.
Bounds for $\mu$ are presented for transitive cubic graphs with girth either
$3$ or $4$, and for certain quasi-transitive cubic graphs.


title: A digit reversal property for Stern polynomials

abstract:
  We consider the following polynomial generalization of Stern's diatomic
series: let $s_1(x,y)=1$, and for $n\geq 1$ set $s_{2n}(x,y)=s_n(x,y)$ and
$s_{2n+1}(x,y)=x\,s_n(x,y)+y\,s_{n+1}(x,y)$. The coefficient $[x^iy^j]s_n(x,y)$
is the number of hyperbinary expansions of $n-1$ with exactly $i$ occurrences
of the digit $\mathtt 2$ and $j$ occurrences of $\mathtt 0$. We prove that the
polynomials $s_n$ are invariant under \emph{digit reversal}, that is,
$s_n=s_{n^R}$, where $n^R$ is obtained from $n$ by reversing the binary
expansion of $n$.


title: Current-Density Functional Theory for the superconductor

abstract:
  We present the current-density functional theory for the superconductor
immersed in the magnetic field. The order parameter of the superconducting
state, transverse component of the paramagnetic current-density, and electron
density are chosen as basic variables that uniquely determine the equilibrium
properties of the system. In order to construct this theory, the development of
the approximate form of the exchange-correlation (xc) energy functional is
indispensable as well as the derivation of the effective single-particle
equation which makes it possible to reproduce the equilibrium densities
mentioned above. The rigorous expression of the xc-energy functional is derived
using the technique of the coupling-constant integration. Furthermore, the
approximate form of the xc energy functional is proposed such that the energy
gap resulting from the effective single-particle equation is consistent with
the attractive interaction energy of the system.


title: Superconducting energy gap of $2H$-NbSe$_2$ in phonon spectroscopy

abstract:
  We present a high energy-resolution inelastic x-ray scattering data
investigation of the charge-density-wave (CDW) soft phonon mode upon entering
the superconducting state in $2H$-NbSe$_2$. Measurements were done close to the
CDW ordering wavevector $\mathbf{q}_{CDW}$ at
$\mathbf{q}=\mathbf{q}_{CDW}+(0,0,l)$,$0.15\leq l \leq 0.5$, for $T=10\,\rm{K}$
(CDW order) and $3.8\,\rm{K}$ (CDW order + superconductivity). We observe
changes of the phonon lineshape that are characteristic for systems with strong
electron-phonon coupling in the presence of a superconducting energy gap
$2\Delta_c$ and from which we can demonstrate an $l$-dependence of the
superconducting gap. Reversely, our data imply that the CDW energy gap is
strongly localized along the $c^*$ direction. The confinement of the CDW gap to
a very small momentum region explains the rather low competition and easy
coexistence of CDW order and superconductivity in $2H$-NbSe$_2$. However, the
energy gained by opening $\Delta_{CDW}$ seems to be too small to be the driving
force of the phase transition at $T_{CDW}=33\,\rm{K}$ , which is better
described as an electron-phonon coupling driven structural phase transition.


title: Norms of vector functionals

abstract:
  We examine the question of when, and how, the norm of a vector functional on
an operator algebra can be controlled by the invariant subspace lattice of the
algebra. We introduce a related operator algebraic property, and show that it
is satisfied by all von Neumann algebras and by all CSL algebras. We exhibit
examples of operator algebras that do not satisfy the property or any scaled
version of it.


title:
Nanoscale Charge Balancing Mechanism in Alkali Substituted
  Calcium-Silicate-Hydrate Gels

abstract:
  Alkali-activated materials and related alternative cementitious systems are
sustainable material technologies that have the potential to substantially
lower CO$_2$ emissions associated with the construction industry. However, the
impact of augmenting the chemical composition of the material on the main
binder phase, calcium-silicate-hydrate gel, is far from understood,
particularly since this binder phase is disordered at the nanoscale. Here, we
reveal the presence of a charge balancing mechanism at the molecular level,
which leads to stable structures when alkalis (i.e., Na or K) are incorporated
into a calcium-silicate-hydrate gel, as modeled using crystalline 14{\AA}
tobermorite. These alkali containing charge balanced structures possess
superior mechanical properties compared to their charge unbalanced
counterparts. Our results, which are based on first-principles simulations
using density functional theory, include the impact of charge balancing on the
optimized geometries of the new model phases, formation energies, local bonding
environments, bulk moduli and diffusion barriers of the alkali atoms within the
crystals.


title:
Formation of spin droplet at nu = 5/2 in an asymmetric quantum dot under
  quantum Hall conditions

abstract:
  In this work, a quantum dot that is defined asymmetrically by electrostatic
means induced on a GaAs/AlGaAs heterostructure is investigated to unravel the
effect of geometric constrains on the formation of spin droplets under
quantised Hall conditions. The incompressibility of exciting nu = 5/2 state is
explored by solving the Schrodinger equation within spin density functional
theory, where the confinement potential is obtained self-consistently utilising
the Thomas-Fermi approximation. Our numerical investigations show that the
spatial distribution of the nu = 2 incompressible strips and electron
occupation in the second lowest Landau level considerably differ from the
results of the laterally symmetric quantum dots. Our findings yield two
important consequences, first the incompressibility of the intriguing nu = 5/2
state is strongly affected by the asymmetry, and second, since the
Aharonov-Bohm interference patterns depend on the velocity of the particles,
asymmetry yields an additional parameter to adjust the oscillation period,
which imposes a boundary condition dependency in observing quasi-particle
phases.


title: Emergence of collective dynamical chirality for achiral active particles

abstract:
  Emergence of collective dynamical chirality (CDC) at mesoscopic scales plays
a key role in many formation processes of chiral structures in nature, which
may also provide possible routines for people to fabricate complex chiral
architectures. So far, most of reported CDCs are found in systems of active
objects with individual structure chirality or/and dynamical chirality, and
whether CDC can arise from simple and achiral units is still an attractive
mystery. Here, we report a spontaneous formation of CDC in a system of both
dynamically and structurally achiral particles motivated by active motion of
cells. Active moving, confinement and hydrodynamic interaction are found to be
the three key factors. Detailed analysis shows that the system can support
abundant collective dynamical behaviors, including rotating droplet, rotating
bubble, CDC oscillation, array of collective rotation, as well as interesting
transitions such as chirality transition, structure transition and state
reentrance.


title:
Power-law modulation of the scalar power spectrum from a heavy field
  with a monomial potential

abstract:
  The effects of heavy fields modulate the scalar power spectrum during
inflation. We analytically calculate the modulations of the scalar power
spectrum from a heavy field with a separable monomial potential, i.e.
V(\phi)~\phi^n. In general the modulation is characterized by a power-law
oscillation which is reduced to the logarithmic oscillation in the case of n=2.


title: An improved Moore bound for mixed graphs

abstract:
  A mixed graph $G$ can contain both (undirected) edges and arcs (directed
edges). Here we derive an improved Moore-like bound for the maximum number of
vertices of a mixed graph with diameter at least three. Moreover, a complete
enumeration of all optimal $(1,1)$-regular mixed graphs with diameter three is
presented, so proving that, in general, the proposed bound cannot be improved.


title: Robustness of graph properties

abstract:
  A typical result in graph theory says that a graph $G$, satisfying certain
conditions, has some property $\cal P$. Once such a theorem is established, it
is natural to ask how strongly $G$ satisfies $\cal P$. Can one strengthen the
result by showing that $G$ possesses $\cal P$ in a robust way? What measures of
robustness can one utilize? In this survey, we discuss various measures that
can be used to study robustness of graph properties, illustrating them with
examples.


title:
Low Complexity Channel Estimation for Millimeter Wave Systems with
  Hybrid A/D Antenna Processing

abstract:
  The availability of large bandwidth at millimeter wave (mmWave) frequencies
is one of the major factors that rendered very high frequencies a promising
candidate enabler for fifth generation (5G) mobile communication networks. To
confront with the intrinsic characteristics of signal propagation at
frequencies of tens of GHz and being able to achieve data rates of the order of
gigabits per second, mmWave systems are expected to employ large antenna arrays
that implement highly directional beamforming. In this paper, we consider
mmWave wireless systems comprising of nodes equipped with large antenna arrays
and being capable of performing hybrid analog and digital (A/D) processing.
Intending at realizing channel-aware transmit and receive beamforming, we focus
on designing low complexity compressed sensing channel estimation. In
particular, by adopting a temporally correlated mmWave channel model, we
present two compressed sensing algorithms that exploit the temporal correlation
to reduce the complexity of sparse channel estimation, one being greedy and the
other one being iterative. Our representative performance evaluation results
offer useful insights on the interplay among some system and operation
parameters, and the accuracy of channel estimation.


title: On the sigma sigma term

abstract:
  We give some estimates for the light-quark mass dependence of the pole
position of the sigma ($f_{0}(500)$) resonance in the complex energy plane,
with the help of a chiral Lagrangian for the resonance field and some input
from hadronic models constrained by Chiral Perturbation Theory and elastic
unitarity. We also speculate on the fate of the sigma resonance when the quark
masses become unphysically large.


title:
Nonequilibrium fluctuation response relation in a time scale separated
  system

abstract:
  We present a theoretical framework to analyze the violation of
fluctuation-response relation (FRR) for any observable from a finite Markov
system with two well-separated time scales. We find that, generally for both
slow and fast observables, a broad plateau exists in the intermediate frequency
region, which contributes to a finite hidden entropy production. Assuming that
non-equilibrium behavior arises only from coupling of slow and fast processes,
we find that, at large observation time scae, the effective temperature for a
slow observable deviates only slightly from the bath temperature, accompanied
by an emerging well-defined effective potential landscape, while the deviation
is significant for a fast observable. Our study also identifies a wider range
of applicability of the Harada-Sasa equality in Markov jumping systems.


title:
Prediction of Prokaryotic and Eukaryotic Promoters Using Convolutional
  Deep Learning Neural Networks

abstract:
  Accurate computational identification of promoters remains a challenge as
these key DNA regulatory regions have variable structures composed of
functional motifs that provide gene specific initiation of transcription. In
this paper we utilize Convolutional Neural Networks (CNN) to analyze sequence
characteristics of prokaryotic and eukaryotic promoters and build their
predictive models. We trained the same CNN architecture on promoters of four
very distant organisms: human, plant (Arabidopsis), and two bacteria
(Escherichia coli and Mycoplasma pneumonia). We found that CNN trained on
sigma70 subclass of Escherichia coli promoter gives an excellent classification
of promoters and non-promoter sequences (Sn=0.90, Sp=0.96, CC=0.84). The
Bacillus subtilis promoters identification CNN model achieves Sn=0.91, Sp=0.95,
and CC=0.86. For human and Arabidopsis promoters we employ CNNs for
identification of two well-known promoter classes (TATA and non-TATA
promoters). CNNs models nicely recognize these complex functional regions. For
human Sn/Sp/CC accuracy of prediction reached 0.95/0.98/0,90 on TATA and
0.90/0.98/0.89 for non-TATA promoter sequences, respectively. For Arabidopsis
we observed Sn/Sp/CC 0.95/0.97/0.91 (TATA) and 0.94/0.94/0.86 (non-TATA)
promoters. Thus, the developed CNN models (implemented in CNNProm program)
demonstrated the ability of deep learning with grasping complex promoter
sequence characteristics and achieve significantly higher accuracy compared to
the previously developed promoter prediction programs. As the suggested
approach does not require knowledge of any specific promoter features, it can
be easily extended to identify promoters and other complex functional regions
in sequences of many other and especially newly sequenced genomes. The CNNProm
program is available to run at web server http://www.softberry.com.


title:
Symmetry of Solutions to Semilinear Equations Involving the Fractional
  Laplacian on $\mathbb{R}^n$ and $\mathbb{R}^n_+$

abstract:
  Let $0<\alpha<2$ be any real number. In this paper, we investigate the
following semilinear equations involving the fractional Laplacian
\begin{equation}(-\bigtriangleup)^{\alpha/2} u(x)=f(u),\end{equation} on
$\mathbb{R}^n$ and $\mathbb{R}^n_+$.
  Applying a direct method of moving planes for the fractional Laplacian, we
prove symmetry and nonexistence of positive solutions on $\mathbb{R}^n$ and
$\mathbb{R}^n_+$ under mild conditions on $f$.


title: On Newton-Cartan local renormalization group and anomalies

abstract:
  Weyl consistency conditions are a powerful tool to study the irreversibility
properties of the renormalization group. We apply this formalism to
non-relativistic theories in 2 spatial dimensions with boost invariance and
dynamical exponent z=2. Different possibilities are explored, depending on the
structure of the gravitational background used as a source for the
energy-momentum tensor.


title:
Signatures of bifurcation on quantum correlations: Case of the quantum
  kicked top

abstract:
  Quantum correlations reflect the quantumness of a system and are useful
resources for quantum information and computational processes. The measures of
quantum correlations do not have a classical analog and yet are influenced by
the classical dynamics. In this work, by modelling the quantum kicked top as a
multi-qubit system, the effect of classical bifurcations on the measures of
quantum correlations such as quantum discord, geometric discord, Meyer and
Wallach $Q$ measure is studied. The quantum correlation measures change rapidly
in the vicinity of a classical bifurcation point. If the classical system is
largely chaotic, time averages of the correlation measures are in good
agreement with the values obtained by considering the appropriate random matrix
ensembles. The quantum correlations scale with the total spin of the system,
representing its semiclassical limit. In the vicinity of the trivial fixed
points of the kicked top, scaling function decays as a power-law. In the
chaotic limit, for large total spin, quantum correlations saturate to a
constant, which we obtain analytically, based on random matrix theory, for the
$Q$ measure. We also suggest that it can have experimental consequences.


title:
Dithen: A Computation-as-a-Service Cloud Platform For Large-Scale
  Multimedia Processing

abstract:
  We present Dithen, a novel computation-as-a-service (CaaS) cloud platform
specifically tailored to the parallel execution of large-scale multimedia
tasks. Dithen handles the upload/download of both multimedia data and
executable items, the assignment of compute units to multimedia workloads, and
the reactive control of the available compute units to minimize the cloud
infrastructure cost under deadline-abiding execution. Dithen combines three key
properties: (i) the reactive assignment of individual multimedia tasks to
available computing units according to availability and predetermined
time-to-completion constraints; (ii) optimal resource estimation based on
Kalman-filter estimates; (iii) the use of additive increase multiplicative
decrease (AIMD) algorithms (famous for being the resource management in the
transport control protocol) for the control of the number of units servicing
workloads. The deployment of Dithen over Amazon EC2 spot instances is shown to
be capable of processing more than 80,000 video transcoding, face detection and
image processing tasks (equivalent to the processing of more than 116 GB of
compressed data) for less than $1 in billing cost from EC2. Moreover, the
proposed AIMD-based control mechanism, in conjunction with the Kalman
estimates, is shown to provide for more than 27% reduction in EC2 spot instance
cost against methods based on reactive resource estimation. Finally, Dithen is
shown to offer a 38% to 500% reduction of the billing cost against the current
state-of-the-art in CaaS platforms on Amazon EC2 (Amazon Lambda and Amazon
Autoscale). A baseline version of Dithen is currently available at
http://www.dithen.com under the "AutoScale" option.


title:
Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for
  Phase-Space Manipulations of High-Intensity Beams

abstract:
  In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV)
distribution, formulated on the basis of the single-particle Courant-Snyder
(CS) invariants, has served as a fundamental theoretical basis for the analyses
of the equilibrium, stability, and transport properties of high-intensity beams
for the past several decades. Recent applications of high-intensity beams,
however, require beam phase-space manipulations by intentionally introducing
strong coupling. In this Letter, we report the full generalization of the KV
model by including all of the linear (both external and space-charge) coupling
forces, beam energy variations, and arbitrary emittance partition, which all
form essential elements for phase-space manipulations. The new generalized KV
model yields spatially uniform density profiles and corresponding linear
self-field forces as desired. The corresponding matrix envelope equations and
beam matrix for the generalized KV model provide important new theoretical
tools for the detailed design and analysis of high-intensity beam
manipulations, for which previous theoretical models are not easily applicable.


title: Auditing Australian Senate Ballots

abstract:
  We explain why the Australian Electoral Commission should perform an audit of
the paper Senate ballots against the published preference data files. We
suggest four different post-election audit methods appropriate for Australian
Senate elections. We have developed prototype code for all of them and tested
it on preference data from the 2016 election.


title: A note on rational points near planar curves

abstract:
  Under fairly natural assumptions, Huang counted the number of rational points
lying close to an arc of a planar curve. He obtained upper and lower bounds of
the correct order of magnitude, and conjectured an asymptotic formula. In this
note, we establish the conjectured asymptotic formula.


title: On the non-thermal energy content of cosmic structures

abstract:
  1) Background: the budget of non-thermal energy in galaxy clusters is not
well constrained, owing to the observational and theoretical difficulties in
studying these diluted plasmas on large scales. 2) Method: we use recent
cosmological simulations with complex physics in order to connect the emergence
of non-thermal energy to the underlying evolution of gas and dark matter. 3)
Results: the impact of non-thermal energy (e.g. cosmic rays, magnetic fields
and turbulent motions) is found to increase in the outer region of galaxy
clusters. Within numerical and theoretical uncertainties, turbulent motions
dominate the budget of non-thermal energy in most of the cosmic volume. 4)
Conclusion: assessing the distribution non-thermal energy in galaxy clusters is
crucial to perform high-precision cosmology in the future. Constraining the
level of non-thermal energy in cluster outskirts will improve our understanding
of the acceleration of relativistic particles by cosmic shocks and of the
origin of extragalactic magnetic fields.


title: Fast and Compact Planar Embeddings

abstract:
  There are many representations of planar graphs, but few are as elegant as
Tur\'an's (1984): it is simple and practical, uses only 4 bits per edge, can
handle self-loops and multi-edges, and can store any specified embedding. Its
main disadvantage has been that "it does not allow efficient searching"
(Jacobson, 1989). In this paper we show how to add a sublinear number of bits
to Tur\'an's representation such that it supports fast navigation while
retaining simplicity. As a consequence of the inherited simplicity, we offer
the first efficient parallel construction of a compact encoding of a planar
graph embedding. Our experimental results show that the resulting
representation uses about 6 bits per edge in practice, supports basic
navigation operations within a few microseconds, and can be built sequentially
at a rate below 1 microsecond per edge, featuring a linear speedup with a
parallel efficiency around 50\% for large datasets.


title:
Magnetooptical Properties of Rydberg Excitons - Center-of-Mass
  Quantization Approach

abstract:
  We show how to compute the magnetooptical functions (absorption, reflection,
and transmission) when Rydberg Exciton-Polaritons appear, including the effect
of the coherence between the electron-hole pair and the electromagnetic field,
and the polaritonic effect. Using the Real Density Matrix Approach the
analytical expressions for magnetooptical functions are obtained and numerical
calculations for Cu$_2$0 crystal are performed. The influence of the strength
of applied external magnetic field on the resonance displacement of excitonic
spectra is discussed. We report a good agreement with recently published
experimental data.


title:
Charles Sanders Peirce and the Abduction of Einstein: On the
  Comprehensibility of the World

abstract:
  Einstein was deeply puzzled by the success of natural science, and thought
that we would never be able to explain it. He came to this conclusion on the
ground that we cannot extract the basic laws of physics from experience using
induction or deduction, and he took this to mean that they cannot be arrived at
in a logical manner at all. In this paper I use Charles Peirce's logic of
abduction, a third mode of reasoning different from deduction and induction,
and show that it can be used to explain how laws in physics are arrived at,
thereby addressing Einstein's puzzle about the incomprehensible
comprehensibility of the universe. Interpreting Einstein's reflections in terms
of Peirce's abduction also sheds light on abduction itself, by seeing it
applied in an area where our common sense, and with that our intuitions, give
us little or no guidance, and is even prone to lead us astray.


title: Riemann surface of complex logarithm and multiplicative calculus

abstract:
  Could elementary complex analysis, which covers the topics such as algebra of
complex numbers, elementary complex functions, complex differentiation and
integration, series expansions of complex functions, residues and
singularities, and introduction to conformal mappings, be made more elementary?
In this paper we demonstrate that a little reorientation of existing elementary
complex analysis brings a lot of benefits, including operating with
single-valued logarithmic and power functions, making the Cauchy integral
formula as a part of fundamental theorem of calculus, removal of residues and
singularities, etc. Implicitly, this reorientation consists of resolving the
multivalued nature of complex logarithm by considering its Riemann surface. But
instead of the advanced mathematical concepts such as manifolds, differential
forms, integration on manifolds, etc, which are necessary for introducing
complex analysis in Riemann surfaces, we use rather elementary methods of
multiplicative calculus. We think that such a reoriented elementary complex
analysis could be especially successful as a first course in complex analysis
for the students of engineering, physics, even applied mathematics programs who
indeed do not see a second and more advanced course in complex analysis. It
would be beneficial for the students of pure mathematics programs as well
because it is more appropriate introduction to complex analysis on Riemann
surfaces rather than the existing one.


title:
How Transferable are CNN-based Features for Age and Gender
  Classification?

abstract:
  Age and gender are complementary soft biometric traits for face recognition.
Successful estimation of age and gender from facial images taken under
real-world conditions can contribute improving the identification results in
the wild. In this study, in order to achieve robust age and gender
classification in the wild, we have benefited from Deep Convolutional Neural
Networks based representation. We have explored transferability of existing
deep convolutional neural network (CNN) models for age and gender
classification. The generic AlexNet-like architecture and domain specific
VGG-Face CNN model are employed and fine-tuned with the Adience dataset
prepared for age and gender classification in uncontrolled environments. In
addition, task specific GilNet CNN model has also been utilized and used as a
baseline method in order to compare with transferred models. Experimental
results show that both transferred deep CNN models outperform the GilNet CNN
model, which is the state-of-the-art age and gender classification approach on
the Adience dataset, by an absolute increase of 7% and 4.5% in accuracy,
respectively. This outcome indicates that transferring a deep CNN model can
provide better classification performance than a task specific CNN model, which
has a limited number of layers and trained from scratch using a limited amount
of data as in the case of GilNet. Domain specific VGG-Face CNN model has been
found to be more useful and provided better performance for both age and gender
classification tasks, when compared with generic AlexNet-like model, which
shows that transfering from a closer domain is more useful.


title:
Effect of scalar field mass on gravitating charged scalar solitons and
  black holes in a cavity

abstract:
  We study soliton and black hole solutions of Einstein charged scalar field
theory in cavity. We examine the effect of introducing a scalar field mass on
static, spherically symmetric solutions of the field equations. We focus
particularly on the spaces of soliton and black hole solutions, as well as
studying their stability under linear, spherically symmetric perturbations of
the metric, electromagnetic field, and scalar field.


title: Locking of length scales in two-band superconductors

abstract:
  A model of a clean two-band s-wave superconductor with cylindrical Fermi
surfaces, different Fermi velocities v_{1,2}, and a general 2x2 coupling matrix
V_{alpha beta} is used to study the order parameter distribution in vortex
lattices. The Eilenberger weak coupling formalism is used to calculate
numerically the spatial distributions of the pairing amplitudes Delta_1_ and
Delta_2_ of the two bands for vortices parallel to the Fermi cylinders. For
generic values of the interband coupling V_{12}, it is shown that,
independently of the couplings V_{alpha beta}, of the ratio v_1 /v_2, of the
temperature, and the applied field, the length scales of spatial variation of
Delta_1 and of Delta_2 are the same within the accuracy of our calculations.
The only exception from this single length-scale behavior is found for V_{12}
--> 0, i.e., for nearly decoupled bands.


title: A vanishing theorem for Dirac cohomology of standard modules

abstract:
  This paper studies the Dirac cohomology of standard modules in the setting of
graded Hecke algebras with geometric parameters. We prove that the Dirac
cohomology of a standard module vanishes if and only if the module is not
twisted-elliptic tempered. The proof makes use of two deep results. One is some
structural information from the generalized Springer correspondence obtained by
S. Kato and Lusztig. Another one is a computation of the Dirac cohomology of
tempered modules by Barbasch-Ciubotaru-Trapa and Ciubotaru.
  We apply our result to compute the Dirac cohomology of ladder representations
for type $A_n$. For each of such representations with non-zero Dirac
cohomology, we associate to a canonical Weyl group representation. We use the
Dirac cohomology to conclude that such representations appear with multiplicity
one.


title:
Cooperative resonances in light scattering from two-dimensional atomic
  arrays

abstract:
  We consider light scattering off a two-dimensional (2D) dipolar array and
show how it can be tailored by properly choosing the lattice constant of the
order of the incident wavelength. In particular, we demonstrate that such
arrays can operate as nearly perfect mirrors for a wide range of incident
angles and frequencies close to the individual atomic resonance. These results
can be understood in terms of the cooperative resonances of the surface modes
supported by the 2D array. Experimental realizations are discussed, using
ultracold arrays of trapped atoms and excitons in 2D semiconductor materials,
as well as potential applications ranging from atomically thin metasurfaces to
single photon nonlinear optics and nanomechanics.


title: Constructing Orthogonal Latin Squares from Linear Cellular Automata

abstract:
  We undertake an investigation of combinatorial designs engendered by cellular
automata (CA), focusing in particular on orthogonal Latin squares and
orthogonal arrays. The motivation is of cryptographic nature. Indeed, we
consider the problem of employing CA to define threshold secret sharing schemes
via orthogonal Latin squares. We first show how to generate Latin squares
through bipermutive CA. Then, using a characterization based on Sylvester
matrices, we prove that two linear CA induce a pair of orthogonal Latin squares
if and only if the polynomials associated to their local rules are relatively
prime.


title: Induced bisecting families for hypergraphs

abstract:
  Two $n$-dimensional vectors $A$ and $B$, $A,B \in \mathbb{R}^n$, are said to
be \emph{trivially orthogonal} if in every coordinate $i \in [n]$, at least one
of $A(i)$ or $B(i)$ is zero. Given the $n$-dimensional Hamming cube
$\{0,1\}^n$, we study the minimum cardinality of a set $\mathcal{V}$ of
$n$-dimensional $\{-1,0,1\}$ vectors, each containing exactly $d$ non-zero
entries, such that every `possible' point $A \in \{0,1\}^n$ in the Hamming cube
has some $V \in \mathcal{V}$ which is orthogonal, but not trivially orthogonal,
to $A$. We give asymptotically tight lower and (constructive) upper bounds for
such a set $\mathcal{V}$ except for the even values of $d \in
\Omega(n^{0.5+\epsilon})$, for any $\epsilon$, $0< \epsilon \leq 0.5$.


title:
Optical-flow-based background-oriented schlieren technique for measuring
  a laser-induced underwater shock wave

abstract:
  The background-oriented schlieren (BOS) technique with the physics-based
optical flow method (OF-BOS) is developed for measuring the pressure field of a
laser-induced underwater shock wave. Compared to BOS with the conventional
cross-correlation method in PIV (called PIV-BOS), by using the OF-BOS, the
displacement field generated by the small density gradient in water can be
obtained at the spatial resolution of one vector per pixel. The corresponding
density and pressure fields can be further extracted. It is particularly
demonstrated that the sufficiently high spatial resolution of the extracted
displacement vector field is required in the tomographic reconstruction to
correctly infer the pressure field of the spherical underwater shock wave. The
capability of the OF-BOS is critically evaluated based on synchronized
hydrophone measurements. Special emphasis is placed on direct comparison
between the OF-BOS with the PIV-BOS.


title: A Networks-Science Investigation into the Epic Poems of Ossian

abstract:
  In 1760 James Macpherson published the first volume of a series of epic poems
which he claimed to have translated into English from ancient Scottish-Gaelic
sources. The poems, which purported to have been composed by a third-century
bard named Ossian, quickly achieved wide international acclaim. They invited
comparisons with major works of the epic tradition, including Homer's Iliad and
Odyssey, and effected a profound influence on the emergent Romantic period in
literature and the arts. However, the work also provoked one of the most famous
literary controversies of all time, colouring the reception of the poetry to
this day. The authenticity of the poems was questioned by some scholars, while
others protested that they misappropriated material from Irish mythological
sources. Recent years have seen a growing critical interest in Ossian,
initiated by revisionist and counter-revisionist scholarship and by the
two-hundred-and-fiftieth anniversary of the first collected edition of the
poems in 1765. Here we investigate Ossian from a networks-science point of
view. We compare the connectivity structures underlying the societies described
in the Ossianic narratives with those of ancient Greek and Irish sources.
Despite attempts, from the outset, to position Ossian alongside the Homeric
epics and to distance it from Irish sources, our results indicate significant
network-structural differences between Macpherson's text and those of Homer.
They also show a strong similarity between Ossianic networks and those of the
narratives known as Acallam na Sen\'orach (Colloquy of the Ancients) from the
Fenian Cycle of Irish mythology.


title:
On the regularization of impact without collision: the Painlev\'e
  paradox and compliance

abstract:
  We consider the problem of a rigid body, subject to a unilateral constraint,
in the presence of Coulomb friction. We regularize the problem by assuming
compliance (with both stiffness and damping) at the point of contact, for a
general class of normal reaction forces. Using a rigorous mathematical
approach, we recover impact without collision (IWC) in both the inconsistent
and indeterminate Painlev\'e paradoxes, in the latter case giving an exact
formula for conditions that separate IWC and lift-off. We solve the problem for
arbitrary values of the compliance damping and give explicit asymptotic
expressions in the limiting cases of small and large damping, all for a large
class of rigid bodies.


title: The projective Leavitt complex

abstract:
  Let Q be a finite quiver without sources, and A be the corresponding algebra
with radical square zero. We construct an explicit compact generator for the
homotopy category of acyclic complexes of projective A-modules. We call such a
generator the projective Leavitt complex of Q. This terminology is justified by
the following result: the opposite differential graded endomorphism algebra of
the projective Leavitt complex of Q is quasi-isomorphic to the Leavitt path
algebra of Q^{ op}. Here, Q^{op} is the opposite quiver of Q and the Leavitt
path algebra of Q^{op} is naturally Z-graded and viewed as a differential
graded algebra with trivial differential.


title: On definable subgroups of the fundamental group

abstract:
  We present several new theorems concerning the first fundamental group of a
path connected metric space. Among the results proven are strengthenings of the
main theorems of \cite{Sh2} and \cite{CoCo}. A compactness theorem for the
fundamental group of a Peano continuum is given. A useful characterization for
the shape kernel of a locally path connected space is presented, along with a
very succinct proof of the fact that for such a space the Spanier and shape
kernel subgroups coincide (see \cite{BF}). We also show that a free
decomposition of the fundamental group of a locally path connected Polish space
cannot be nonconstructive. Numerous other results and examples illustrating the
sharpness of our theorems are provided.


title:
Thermal Inflation with a Thermal Waterfall Scalar Field Coupled to a
  Light Spectator Scalar Field

abstract:
  This thesis begins with an introduction to the state of the art of modern
Cosmology. The field of Particle Cosmology is then introduced and explored, in
particular with regard to the study of cosmological inflation. We then
introduce a new model of Thermal Inflation, in which the mass of the thermal
waterfall field responsible for the inflation is dependent on a light spectator
scalar field. The model contains a variety of free parameters, two of which
control the power of the coupling term and the non-renormalizable term. We use
the $\delta N$ formalism to investigate the "end of inflation" and modulated
decay scenarios in turn to see whether they are able to produce the dominant
contribution to the primordial curvature perturbation $\zeta$. We constrain the
model and then explore the parameter space. We explore key observational
signatures, such as non-Gaussianity, the scalar spectral index and the running
of the scalar spectral index. We find that for some regions of the parameter
space, the ability of the model to produce the dominant contribution to $\zeta$
is excluded. However, for other regions of the parameter space, we find that
the model yields a sharp prediction for a variety of parameters within the
model.


title: Data Fusion for Correcting Measurement Errors

abstract:
  Often in surveys, key items are subject to measurement errors. Given just the
data, it can be difficult to determine the distribution of this error process,
and hence to obtain accurate inferences that involve the error-prone variables.
In some settings, however, analysts have access to a data source on different
individuals with high quality measurements of the error-prone survey items. We
present a data fusion framework for leveraging this information to improve
inferences in the error-prone survey. The basic idea is to posit models about
the rates at which individuals make errors, coupled with models for the values
reported when errors are made. This can avoid the unrealistic assumption of
conditional independence typically used in data fusion. We apply the approach
on the reported values of educational attainments in the American Community
Survey, using the National Survey of College Graduates as the high quality data
source. In doing so, we account for the informative sampling design used to
select the National Survey of College Graduates. We also present a process for
assessing the sensitivity of various analyses to different choices for the
measurement error models. Supplemental material is available online.


title: On hamiltonian colorings of trees

abstract:
  A hamiltonian coloring $c$ of a graph $G$ of order $n$ is a mapping $c$ :
$V(G) \rightarrow \{0,1,2,...\}$ such that $D(u, v)$ + $|c(u) - c(v)|$ $\geq$
$n-1$, for every two distinct vertices $u$ and $v$ of $G$, where $D(u, v)$
denotes the detour distance between $u$ and $v$ which is the length of a
longest $u,v$-path in $G$. The value $hc(c)$ of a hamiltonian coloring $c$ is
the maximum color assigned to a vertex of $G$. The hamiltonian chromatic
number, denoted by $hc(G)$, is the min{$hc(c)$} taken over all hamiltonian
coloring $c$ of $G$. In this paper, we present a lower bound for the
hamiltonian chromatic number of trees and give a sufficient condition to
achieve this lower bound. Using this condition we determine the hamiltonian
chromatic number of symmetric trees, firecracker trees and a special class of
caterpillars.


title:
Data-Unit-Size Distribution Model with Retransmitted Packet Size
  Preservation Property and Its Application to Goodput Analysis for
  Stop-and-Wait Protocol: Case of Independent Packet Losses

abstract:
  This paper proposes a data-unit-size distribution model to represent the
retransmitted packet size preservation (RPSP) property in a scenario where
independently lost packets are retransmitted by a stop-and-wait protocol. RPSP
means that retransmitted packets with the same sequence number are equal in
size to the packet of the original transmission, which is identical to the
packet generated from a message through the segmentation function, namely,
generated packet. Furthermore, we derive goodput formula using an approach to
derive the data-unit-size distribution. We investigate the effect of RPSP on
frame size distributions and goodput in a simple case when no collision happens
over the bit-error prone wireless network equipped with IEEE 802.11 Distributed
Coordination Function, which is a typical example of the stop-and-wait
protocol. Numerical results show that the effect gets stronger as bit error
rate increases and the maximum size of the generated packets is larger than the
mean size for large enough packet retry limits because longer packets will be
repeatedly corrupted and retransmitted more times as a result of RPSP.


title: Higgs Potential from Derivative Interactions

abstract:
  A formulation of the linear $\sigma$ model with derivative interactions is
studied. The classical theory is on-shell equivalent to the $\sigma$ model with
the standard quartic Higgs potential. The mass of the scalar mode only appears
in the quadratic part and not in the interaction vertices, unlike in the
ordinary formulation of the theory. Renormalization of the model is discussed.
A non power-counting renormalizable extension, obeying the defining functional
identities of the theory, is presented. This extension is physically equivalent
to the tree-level inclusion of a dimension six effective operator $\partial_\mu
(\Phi^\dagger \Phi) \partial^\mu (\Phi^\dagger \Phi)$. The resulting UV
divergences are arranged in a perturbation series around the power-counting
renormalizable theory. The application of the formalism to the Standard Model
in the presence of the dimension-six operator $\partial_\mu (\Phi^\dagger \Phi)
\partial^\mu (\Phi^\dagger \Phi)$ is discussed.


title: A compact representation for minimizers of $k$-submodular functions

abstract:
  A $k$-submodular function is a generalization of submodular and bisubmodular
functions. This paper establishes a compact representation for minimizers of a
$k$-submodular function by a poset with inconsistent pairs (PIP). This is a
generalization of Ando-Fujishige's signed poset representation for minimizers
of a bisubmodular function. We completely characterize the class of PIPs
(elementary PIPs) arising from $k$-submodular functions. We give algorithms to
construct the elementary PIP of minimizers of a $k$-submodular function $f$ for
three cases: (i) a minimizing oracle of $f$ is available, (ii) $f$ is
network-representable, and (iii) $f$ arises from a Potts energy function.
Furthermore, we provide an efficient enumeration algorithm for all maximal
minimizers of a Potts $k$-submodular function. Our results are applicable to
obtain all maximal persistent labelings in actual computer vision problems. We
present experimental results for real vision instances.


title: An ultrafast polarised single photon source at 220 K

abstract:
  A crucial requirement for the realisation of efficient and scalable on-chip
quantum communication is an ultrafast polarised single photon source operating
beyond the Peltier cooling barrier of 200 K. While a few systems based on
different materials and device structures have achieved single photon
generation above this threshold, there has been no report of single quantum
emitters with deterministic polarisation properties at the same high
temperature conditions. Here, we report the first device to simultaneously
achieve single photon emission with a g(2)(0) of only 0.21, a high polarisation
degree of 0.80, a fixed polarisation axis determined by the underlying
crystallography, and a GHz repetition rate with a radiative lifetime of 357 ps
at 220 K. The temperature insensitivity of these properties, together with the
simple planar growth method, and absence of complex device geometries, makes
this system an excellent candidate for on-chip applications in integrated
systems.


title:
Study of the lowest tensor and scalar resonances in the $\tau \to
  \pi\pi\pi \nu_\tau$ decay

abstract:
  In this note we present a new parametrization of the hadronic current for the
decay $\tau \to \pi\pi\pi \nu_\tau$ derived from the chiral lagrangian with
explicit inclusion of resonances. We have included both scalar, vector and
axial-vector resonances. For the first time, the lowest tensor resonance
($f_2(1270)$) is included as well. Both single and double-resonance
contributions to the hadronic form factors are taken into account. To satisfy
the correct high energy behaviour of the hadronic form factors, constraints on
numerical values of the vertex constants are obtained.


title:
Optomechanical dual-beam backaction-evading measurement beyond the
  rotating-wave approximation

abstract:
  We present the exact analytical solution of the explicitly time-periodic
quantum Langevin equation describing the dual-beam backaction-evasion
measurement of a single mechanical oscillator quadrature due to Braginsky,
Vorontsov and Thorne beyond the commonly used rotating-wave approximation. We
show that counterrotating terms lead to extra sidebands in the optical and
mechanical spectra and to a modification of the main peak. Physically, the
backaction of the measurement is due to periodic coupling of the mechanical
resonator to a light field quadrature that only contains cavity-filtered shot
noise. Since this fact is independent of other degrees of freedom the resonator
might be coupled to, our solution can be generalized, including to
dissipatively or parametrically squeezed oscillators, as well as recent
two-mode backaction evasion measurements.


title: How many three-dimensional Hilbert curves are there?

abstract:
  Hilbert's two-dimensional space-filling curve is appreciated for its good
locality-preserving properties and easy implementation for many applications.
However, Hilbert did not describe how to generalize his construction to higher
dimensions. In fact, the number of ways in which this may be done ranges from
zero to infinite, depending on what properties of the Hilbert curve one
considers to be essential.
  In this work we take the point of view that a Hilbert curve should at least
be self-similar and traverse cubes octant by octant. We organize and explore
the space of possible three-dimensional Hilbert curves and the potentially
useful properties which they may have. We discuss a notation system that allows
us to distinguish the curves from one another and enumerate them. This system
has been implemented in a software prototype, available from the author's
website. Several examples of possible three-dimensional Hilbert curves are
presented, including a curve that visits the points on most sides of the unit
cube in the order of the two-dimensional Hilbert curve; curves of which not
only the eight octants are similar to each other, but also the four quarters; a
curve with excellent locality-preserving properties and endpoints that are not
vertices of the cube; a curve in which all but two octants are each other's
images with respect to reflections in axis-parallel planes; and curves that can
be sketched on a grid without using vertical line segments. In addition, we
discuss several four-dimensional Hilbert curves.


title:
Ab initio model of amorphous zinc oxide (a-ZnO) and a-X_0.375 Z_0.625 O
  (X=Al, Ga and In)

abstract:
  Density functional theory (DFT) calculations are carried out to study the
structure and electronic structure of amorphous zinc oxide (a-ZnO). The models
were prepared by the "melt-quench" method. The models are chemically ordered
with some coordination defects. The effect of trivalent dopants in the
structure and electronic properties of a-ZnO is investigated. Models of
a-X_0.375 Z_0.625 O (X=Al, Ga and In) were also prepared by the "melt- quench"
method. The trivalent dopants reduce the four-fold Zn and O, thereby
introducing some coordination defects in the network. The dopants prefer to
bond with O atom. The network topology is discussed in detail. Dopants reduce
the gap in EDOS by producing defect states minimum while maintaining the
extended nature of the conduction band edge.


title: A Performance-Based Scheme for Pricing Resources in the Cloud

abstract:
  With the rapid growth of the cloud computing marketplace, the issue of
pricing resources in the cloud has been the subject of much study in recent
years. In this paper, we identify and study a new issue: how to price resources
in the cloud so that the customer's risk is minimized, while at the same time
ensuring that the provider accrues his fair share. We do this by correlating
the revenue stream of the customer to the prices charged by the provider. We
show that our mechanism is incentive compatible in that it is in the best
interest of the customer to provide his true revenue as a function of the
resources rented. We next add another restriction to the price function, i.e.,
that it be linear. This removes the distortion that creeps in when the customer
has to pay more money for less resources. Our algorithms for both the schemes
mentioned above are efficient.


title: Topological resolutions in K(2)-local homotopy theory at the prime 2

abstract:
  We provide a topological duality resolution for the spectrum
$E_2^{h\mathbb{S}_2^1}$, which itself can be used to build the $K(2)$-local
sphere. The resolution is built from spectra of the form $E_2^{hF}$ where $E_2$
is the Morava spectrum for the formal group of a supersingular curve at the
prime $2$ and $F$ is a finite subgroup of the automorphisms of that formal
group. The results are in complete analogy with the resolutions of Goerss,
Henn, Mahowald, and Rezk at the prime $3$, but the methods are of necessity
very different. As in the prime $3$ case, the main difficulty is in identifying
the top fiber; to do this, we make calculations using Henn's centralizer
resolution.


title: On the complexity of the permanent in various computational models

abstract:
  We answer a question in [Landsberg, Ressayre, 2015], showing the regular
determinantal complexity of the determinant det_m is O(m^3). We answer
questions in, and generalize results of [Aravind, Joglekar, 2015], showing
there is no rank one determinantal expression for perm_m or det_m when m >= 3.
Finally we state and prove several "folklore" results relating different models
of computation.


title:
Testing Einstein's gravity and dark energy with growth of matter
  perturbations: Indications for new Physics?

abstract:
  The growth index of matter fluctuations is computed for ten distinct
accelerating cosmological models and confronted to the latest growth rate data
via a two-step process. First, we implement a joint statistical analysis in
order to place constraints on the free parameters of all models using solely
background data. Second, using the observed growth rate of clustering from
various galaxy surveys we test the performance of the current cosmological
models at the perturbation level while either marginalizing over $\sigma_8$ or
having it as a free parameter. As a result, we find that at a statistical
level, i.e. after considering the best-fit $\chi^2$ or the value of the Akaike
information criterion, most models are in very good agreement with the growth
rate data and are practically indistinguishable from $\Lambda$CDM. However,
when we also consider the internal consistency of the models by comparing the
theoretically predicted values of $(\gamma_0, \gamma_1)$, i.e. the value of the
growth index $\gamma(z)$ and its derivative today, with the best-fit ones, we
find that the predictions of three out of ten dark energy models are in mild
tension with the best-fit ones when $\sigma_8$ is marginalized over. When
$\sigma_8$ is free we find that most models are not only in mild tension, but
also predict low values for $\sigma_8$. This could be attributed to either a
systematic problem with the growth-rate data or the emergence of new physics at
low redshifts, with the latter possibly being related to the well-known issue
of the lack of power at small scales. Finally, by utilizing mock data based on
an LSST-like survey we show that with future surveys and by using the growth
index parameterization, it will be possible to resolve the issue of the low
$\sigma_8$ but also the tension between the fitted and theoretically predicted
values of $(\gamma_0, \gamma_1)$.


title: Towards deep learning with segregated dendrites

abstract:
  Deep learning has led to significant advances in artificial intelligence, in
part, by adopting strategies motivated by neurophysiology. However, it is
unclear whether deep learning could occur in the real brain. Here, we show that
a deep learning algorithm that utilizes multi-compartment neurons might help us
to understand how the brain optimizes cost functions. Like neocortical
pyramidal neurons, neurons in our model receive sensory information and
higher-order feedback in electrotonically segregated compartments. Thanks to
this segregation, the neurons in different layers of the network can coordinate
synaptic weight updates. As a result, the network can learn to categorize
images better than a single layer network. Furthermore, we show that our
algorithm takes advantage of multilayer architectures to identify useful
representations---the hallmark of deep learning. This work demonstrates that
deep learning can be achieved using segregated dendritic compartments, which
may help to explain the dendritic morphology of neocortical pyramidal neurons.


title:
Pumping electrons in graphene to the $\mathbf{M}$-point in the Brillouin
  zone: The emergence of anisotropic plasmons

abstract:
  We consider the existence of plasmons in a non-equilibrium situation where
electrons from the valence band of graphene are pumped to states in the
Brillouin zone around the $\mathbf{M}$-point by a high intensity UV
electromagnetic field. The resulting out-of-equilibrium electron gas is later
probed by a weak electromagnetic field of different frequency. We show that the
optical properties of the system and the dispersion of the plasmons are
strongly anisotropic, depending on the pumping radiation properties: its
intensity, polarization, and frequency. This anisotropy has its roots in the
saddle-like nature of the electronic dispersion relation around that particular
point in the Brillouin zone.
  It is found that despite the strong anisotropy, the dispersion of the
plasmons scales with the square root of the wave number but is characterized an
effective Fermi energy, which depends on the properties of the pumping
radiation. Our calculations go beyond the usual Dirac cone approximation taking
the full band structure of graphene into account. This is a necessary condition
for discussing plasmons at the $\mathbf{M}$-point in the Brillouin zone.


title: X-CNN: Cross-modal Convolutional Neural Networks for Sparse Datasets

abstract:
  In this paper we propose cross-modal convolutional neural networks (X-CNNs),
a novel biologically inspired type of CNN architectures, treating gradient
descent-specialised CNNs as individual units of processing in a larger-scale
network topology, while allowing for unconstrained information flow and/or
weight sharing between analogous hidden layers of the network---thus
generalising the already well-established concept of neural network ensembles
(where information typically may flow only between the output layers of the
individual networks). The constituent networks are individually designed to
learn the output function on their own subset of the input data, after which
cross-connections between them are introduced after each pooling operation to
periodically allow for information exchange between them. This injection of
knowledge into a model (by prior partition of the input data through domain
knowledge or unsupervised methods) is expected to yield greatest returns in
sparse data environments, which are typically less suitable for training CNNs.
For evaluation purposes, we have compared a standard four-layer CNN as well as
a sophisticated FitNet4 architecture against their cross-modal variants on the
CIFAR-10 and CIFAR-100 datasets with differing percentages of the training data
being removed, and find that at lower levels of data availability, the X-CNNs
significantly outperform their baselines (typically providing a 2--6% benefit,
depending on the dataset size and whether data augmentation is used), while
still maintaining an edge on all of the full dataset tests.


title:
Traces, high powers and one level density for families of curves over
  finite fields

abstract:
  The zeta function of a curve $C$ over a finite field may be expressed in
terms of the characteristic polynomial of a unitary matrix $\Theta_C$.
  We develop and present a new technique to compute the expected value of
$\mathrm{Tr}(\Theta_C^n)$ for various moduli spaces of curves of genus $g$ over
a fixed finite field in the limit as $g$ is large, generalizing and extending
the work of Rudnick and Chinis.
  This is achieved by using function field zeta functions, explicit formulae,
and the densities of prime polynomials with prescribed ramification types at
certain places as given by Bucur, David, Feigon, Kaplan, Lal\'in and Wood
[BDF$^+$16] and by Zhao.
  We extend [BDF$^+$16] by describing explicit dependence on the place and give
an explicit proof of the Lindel\"{o}f bound for function field Dirichlet
$L$-functions $L(1/2 + it, \chi)$.
  As applications, we compute the one-level density for hyperelliptic curves,
cyclic $\ell$-covers, and cubic non-Galois covers.


title:
Microscopic Observation of the Light-Cone-Like Thermal Correlations in
  Cracking Excitations

abstract:
  Many seemingly intractable systems can be reduced to a system of interacting
spins. Here, we introduce a system of artificial acoustic spins which are
manipulated with ultrasound excitations associated with micro-cracking sources
in thin sheets of crystals. Our spin-like system shows a peculiar relaxation
mechanism after inducing an impulsive stress-ramp akin to splitting, or
rupturing, of the system. Using real-time construction of correlations between
spins states, we observe a clear emergence of the light cone effect. It has
been proposed that equilibration horizon occurs on a local scale in systems
where correlations between distant sites are established at a finite speed. The
observed equilibration horizon in our observations defines a region where
elements of the material are in elastic communication through excited
elementary excitations. These results yield important insights into dynamic
communication between failing elements in brittle materials during processes
such as brittle fragmentation and dynamic stress triggering of
earthquake-generating faults.


title: Periods of quaternionic Shimura varieties. I

abstract:
  We study "quadratic periods" on quaternionic Shimura varieties and formulate
an integral refinement of Shimura's conjecture regarding Petersson inner
products of automorphic forms that are related by the Jacquet-Langlands
correspondence. The main result is that this integral refinement is implied by
another conjecture (Conjecture D below) regarding integrality of theta lifts
between certain quaternionic unitary groups.


title: Structure of attractors for boundary maps associated to Fuchsian groups

abstract:
  We study dynamical properties of generalized Bowen-Series boundary maps
associated to cocompact torsion-free Fuchsian groups. These maps are defined on
the unit circle (the boundary of the Poincar\'e disk) by the generators of the
group and have a finite set of discontinuities. We study the two forward orbits
of each discontinuity point and show that for a family of such maps the cycle
property holds: the orbits coincide after finitely many steps. We also show
that for an open set of discontinuity points the associated two-dimensional
natural extension maps possess global attractors with finite rectangular
structure. These two properties belong to the list of "good" reduction
algorithms, equivalence or implications between which were suggested by Don
Zagier.


title: Learning Optimized Risk Scores

abstract:
  Risk scores are simple classification models that let users make quick risk
predictions by adding and subtracting a few small numbers. These models are
widely used in medicine and criminal justice, but are difficult to learn from
data because they need to be calibrated, sparse, use small integer
coefficients, and obey application-specific operational constraints. In this
paper, we present a new machine learning approach to learn risk scores. We
formulate the risk score problem as a mixed integer nonlinear program, and
present a cutting plane algorithm for non-convex settings to efficiently
recover its optimal solution. We improve our algorithm with specialized
techniques to generate feasible solutions, narrow the optimality gap, and
reduce data-related computation. Our approach can fit risk scores in a way that
scales linearly in the number of samples, provides a certificate of optimality,
and obeys real-world constraints without parameter tuning or post-processing.
We benchmark the performance benefits of this approach through an extensive set
of numerical experiments, comparing to risk scores built using heuristic
approaches. We also discuss its practical benefits through a real-world
application where we build a customized risk score for ICU seizure prediction
in collaboration with the Massachusetts General Hospital.


title: Covariant Quantization of CPT-violating Photons

abstract:
  We perform the covariant canonical quantization of the CPT- and
Lorentz-symmetry-violating photon sector of the minimal Standard-Model
Extension, which contains a general (timelike, lightlike, or spacelike) fixed
background tensor $k_{AF}^\mu$. Well-known stability issues, arising from
complex-valued energy states, are solved by introducing a small photon mass,
orders of magnitude below current experimental bounds. We explicitly construct
a covariant basis of polarization vectors, in which the photon field can be
expanded. We proceed to derive the Feynman propagator and show that the theory
is microcausal. Despite the occurrence of negative energies and
vacuum-Cherenkov radiation, we do not find any runaway stability issues,
because the energy remains bounded from below. An important observation is that
the ordering of the roots of the dispersion relations is the same in any
observer frame, which allows for a frame-independent condition that selects the
correct branch of the dispersion relation. This turns out to be critical for
the consistency of the quantization. To our knowledge, this is the first system
for which quantization has consistently been performed, in spite of the fact
that the theory contains negative energies in some observer frames.


title:
High-performance coherent population trapping clock with polarization
  modulation

abstract:
  We demonstrate a vapor cell atomic clock prototype based on continuous-wave
(CW) interrogation and double-modulation coherent population trapping (DM-CPT)
technique. The DM-CPT technique uses a synchronous modulation of polarization
and relative phase of a bi-chromatic laser beam in order to increase the number
of atoms trapped in a dark state, i.e. a non-absorbing state. The narrow
resonance, observed in transmission of a Cs vapor cell, is used as a narrow
frequency discriminator in an atomic clock. A detailed characterization of the
CPT resonance versus numerous parameters is reported. A short-term frequency
stability of $3.2 \times 10^{-13} \tau^{-1/2}$ up to 100 s averaging time is
measured. These performances are more than one order of magnitude better than
industrial Rb clocks and comparable to those of best laboratory-prototype vapor
cell clocks. The noise budget analysis shows that the short and mid-term
frequency stability is mainly limited by the power fluctuations of the
microwave used to generate the bi-chromatic laser. These preliminary results
demonstrate that the DM-CPT technique is well-suited for the development of a
high-performance atomic clock, with potential compact and robust setup due to
its linear architecture. This clock could find future applications in industry,
telecommunications, instrumentation or global navigation satellite systems.


title:
Personalized Prediction of Vehicle Energy Consumption based on
  Participatory Sensing

abstract:
  The advent of abundant on-board sensors and electronic devices in vehicles
populates the paradigm of participatory sensing to harness crowd-sourced data
gathering for intelligent transportation applications, such as
distance-to-empty prediction and eco-routing. While participatory sensing can
provide diverse driving data, there lacks a systematic study of effective
utilization of the data for personalized prediction. There are considerable
challenges on how to interpolate the missing data from a sparse dataset, which
often arises from participatory sensing. This paper presents and compares
various approaches for personalized vehicle energy consumption prediction,
including a blackbox framework that identifies
driver/vehicle/environment-dependent factors and a collaborative filtering
approach based on matrix factorization. Furthermore, a case study of
distance-to-empty prediction for electric vehicles by participatory sensing
data is conducted and evaluated empirically, which shows that our approaches
can significantly improve the prediction accuracy.


title: Regularity of Milne Problem with Geometric Correction in 3D

abstract:
  Consider the Milne problem with geometric correction in a 3D convex domain.
Via bootstrapping arguments, we establish $W^{1,\infty}$ regularity for its
solutions. Combined with a uniform $L^6$ estimate, such regularity leads to the
validity of diffusive expansion for the neutron transport equation with
diffusive boundary conditions.