title: The Rate-Distortion Risk in Estimation from Compressed Data

abstract:
  Consider the problem of estimating a latent signal from a lossy compressed
version of the data when the compressor is agnostic to the relation between the
signal and the data. This situation arises in a host of modern applications
when data is transmitted or stored prior to determining the downstream
inference task. Given a bitrate constraint and a distortion measure between the
data and its compressed version, let us consider the joint distribution
achieving Shannon's rate-distortion (RD) function. Given an estimator and a
loss function associated with the downstream inference task, define the
rate-distortion risk as the expected loss under the RD-achieving distribution.
We provide general conditions under which the operational risk in estimating
from the compressed data is asymptotically equivalent to the RD risk. The main
theoretical tools to prove this equivalence are transportation-cost
inequalities in conjunction with properties of compression codes achieving
Shannon's RD function. Whenever such equivalence holds, a recipe for designing
estimators from datasets undergoing lossy compression without specifying the
actual compression technique emerges: design the estimator to minimize the RD
risk. Our conditions simplified in the special cases of discrete memoryless or
multivariate normal data. For these scenarios, we derive explicit expressions
for the RD risk of several estimators and compare them to the optimal source
coding performance associated with full knowledge of the relation between the
latent signal and the data.


title: Efficient Second Order Online Learning by Sketching

abstract:
  We propose Sketched Online Newton (SON), an online second order learning
algorithm that enjoys substantially improved regret guarantees for
ill-conditioned data. SON is an enhanced version of the Online Newton Step,
which, via sketching techniques enjoys a running time linear in the dimension
and sketch size. We further develop sparse forms of the sketching methods (such
as Oja's rule), making the computation linear in the sparsity of features.
Together, the algorithm eliminates all computational obstacles in previous
second order online learning approaches.


title:
GDoF of the MISO BC: Bridging the Gap between Finite Precision and
  Perfect CSIT

abstract:
  For the $K=2$ user MISO BC, i.e., the wireless broadcast channel where a
transmitter equipped with $K=2$ antennas sends independent messages to $K=2$
receivers each of which is equipped with a single antenna, the sum generalized
degrees of freedom (GDoF) are characterized for arbitrary channel strength and
channel uncertainty levels for each of the channel coefficients. The result is
extended to $K>2$ users under additional restrictions which include the
assumption of symmetry.


abstract:
  In this paper, we study $\mathbb{A}^1$ curves on log K3 surfaces. We classify
all genuine log K3 surfaces of type II which admits countably infinite
$\mathbb{A}^1$ curves.


title:
On the Capacity of the Dirty Paper Channel with Fast Fading and Discrete
  Channel States

abstract:
  The "writing dirty paper" capacity result crucially dependents on the perfect
channel knowledge at the transmitter as the presence of even a small
uncertainty in the channel realization gravely hampers the ability of the
transmitter to pre-code its transmission against the channel state. This is
particularly disappointing as it implies that interference pre-coding in
practical systems is effective only when the channel estimates at the users
have very high precision, a condition which is generally unattainable in
wireless environments. In this paper we show that substantial improvements are
possible when the state sequence is drawn from a discrete distribution, such as
a constrained input constellation, for which state decoding can be
approximately optimal. We consider the "writing on dirty paper" channel in
which the state sequence is multiplied by a fast fading process and derive
conditions on the fading and state distributions for which state decoding
closely approaches capacity. These conditions intuitively relate to the ability
of the receiver to correctly identify both the input and the state realization
despite of the uncertainty introduced by fading.


title:
The Carbon Copy onto Dirty Paper Channel with Statistically Equivalent
  States

abstract:
  Costa's "writing on dirty paper" capacity result establishes that full state
pre-cancellation can be attained in Gelfand-Pinsker channel with additive state
and additive Gaussian noise. The "carbon copy onto dirty paper" channel is the
extension of Costa's model to the compound setting: M receivers each observe
the sum of the channel input, Gaussian noise and one of M Gaussian state
sequences and attempt to decode the same common message. The state sequences
are all non-causally known at the transmitter which attempts to simultaneously
pre-code its transmission against the channel state affecting each output. In
this correspondence we derive the capacity to within 2.25 bits-per-channel-use
of the carbon copying onto dirty paper channel in which the state sequences are
statistically equivalent, having the same variance and the same pairwise
correlation. For this channel capacity is approached by letting the channel
input be the superposition of two codewords: a base codeword, simultaneously
decoded at each user, and a top codeword which is pre-coded against the state
realization at each user for a portion 1/M of the time. The outer bound relies
on a recursive bounding in which incremental side information is provided at
each receiver. This result represents a significant first step toward
determining the capacity of the most general "carbon copy onto dirty paper"
channel in which state sequences appearing in the different channel outputs
have any jointly Gaussian distribution.


title: Non-universality for longest increasing subsequence of a random walk

abstract:
  The longest increasing subsequence of a random walk with mean zero and finite
variance is known to be $n^{1/2 + o(1)}$. We show that this is not universal
for symmetric random walks. In particular, the symmetric Ultra-fat tailed
random walk has a longest increasing subsequence that is asymptotically at
least $n^{0.690}$ and at most $n^{0.815}$. An exponent strictly greater than
$1/2$ is also shown for the symmetric stable-$\alpha$ distribution when
$\alpha$ is sufficiently small.


title:
A census of hyperbolic platonic manifolds and augmented knotted
  trivalent graphs

abstract:
  We call a 3-manifold Platonic if it can be decomposed into isometric Platonic
solids. Generalizing an earlier publication by the author and others where this
was done in case of the hyperbolic ideal tetrahedron, we give a census of
hyperbolic Platonic manifolds and all of their Platonic tessellations. For the
octahedral case, we also identify which manifolds are complements of an
augmented knotted trivalent graph and give the corresponding link. A (small
version of) the Platonic census and the related improved algorithms have been
incorporated into SnapPy. The census also comes in Regina format.
  In the appendix, we show that an ideal cubical tessellation can be subdivided
into an ideal geometric triangulation.


title: Displacement Data Assimilation

abstract:
  We show that modifying a Bayesian data assimilation scheme by incorporating
kinematically-consistent displacement corrections produces a scheme that is
demonstrably better at estimating partially observed state vectors in a setting
where feature information important. While the displacement transformation is
not tied to any particular assimilation scheme, here we implement it within an
ensemble Kalman Filter and demonstrate its effectiveness in tracking
stochastically perturbed vortices.


title: Classification accuracy as a proxy for two sample testing

abstract:
  When data analysts train a classifier and check if its accuracy is
significantly different from chance, they are implicitly performing a
two-sample test. We investigate the statistical properties of this flexible
approach in the high-dimensional setting. We prove two results that hold for
all classifiers in any dimensions: if its true error remains $\epsilon$-better
than chance for some $\epsilon>0$ as $d,n \to \infty$, then (a) the
permutation-based test is consistent (has power approaching to one), (b) a
computationally efficient test based on a Gaussian approximation of the null
distribution is also consistent. To get a finer understanding of the rates of
consistency, we study a specialized setting of distinguishing Gaussians with
mean-difference $\delta$ and common (known or unknown) covariance $\Sigma$,
when $d/n \to c \in (0,\infty)$. We study variants of Fisher's linear
discriminant analysis (LDA) such as "naive Bayes" in a nontrivial regime when
$\epsilon \to 0$ (the Bayes classifier has true accuracy approaching 1/2), and
contrast their power with corresponding variants of Hotelling's test.
Surprisingly, the expressions for their power match exactly in terms of
$n,d,\delta,\Sigma$, and the LDA approach is only worse by a constant factor,
achieving an asymptotic relative efficiency (ARE) of $1/\sqrt{\pi}$ for
balanced samples. We also extend our results to high-dimensional elliptical
distributions with finite kurtosis. Other results of independent interest
include minimax lower bounds, and the optimality of Hotelling's test when
$d=o(n)$. Simulation results validate our theory, and we present practical
takeaway messages along with natural open problems.


title: Fuzzy Maximum Satisfiability

abstract:
  In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to
{\L}ukasiewicz logic. The MaxSAT problem for a set of formulae {\Phi} is the
problem of finding an assignment to the variables in {\Phi} that satisfies the
maximum number of formulae. Three possible solutions (encodings) are proposed
to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer
Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem
(WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have
numerous applications in optimization problems that involve vagueness.


title:
$\rm{J}/\psi$ production at low transverse momentum in p+p and d+Au
  collisions at $\sqrt{s_{NN}}$ = 200 GeV

abstract:
  We report on the measurement of $\rm{J}/\psi$ production in the dielectron
channel at mid-rapidity (|y|<1) in p+p and d+Au collisions at $\sqrt{s_{NN}}$ =
200 GeV from the STAR experiment at the Relativistic Heavy Ion Collider. The
transverse momentum $p_{T}$ spectra in p+p for $p_{T}$ < 4 GeV/c and d+Au
collisions for $p_{T}$ < 3 GeV/c are presented. These measurements extend the
STAR coverage for $\rm{J}/\psi$ production in p+p collisions to low $p_{T}$.
The $<p_{T}^{2}>$ from the measured $\rm{J}/\psi$ invariant cross section in
p+p and d+Au collisions are evaluated and compared to similar measurements at
other collision energies. The nuclear modification factor for $\rm{J}/\psi$ is
extracted as a function of $p_{T}$ and collision centrality in d+Au and
compared to model calculations using the modified nuclear Parton Distribution
Function and a final-state $\rm{J}/\psi$ nuclear absorption cross section.


title:
Diagnosing $\Lambda$HDE model with statefinder hierarchy and fractional
  growth parameter

abstract:
  Recently, a new dark energy model called $\Lambda$HDE was proposed. In this
model, dark energy consists of two parts: cosmological constant $\Lambda$ and
holographic dark energy (HDE). Two key parameters of this model are the
fractional density of cosmological constant $\Omega_{\Lambda0}$, and the
dimensionless HDE parameter $c$. Since these two parameters determine the
dynamical properties of DE and the destiny of universe, it is important to
study the impacts of different values of $\Omega_{\Lambda0}$ and $c$ on the
$\Lambda$HDE model. In this paper, we apply various DE diagnostic tools to
diagnose $\Lambda$HDE models with different values of $\Omega_{\Lambda0}$ and
$c$; these tools include statefinder hierarchy \{$S_3^{(1)}, S_4^{(1)}$\},
fractional growth parameter $\epsilon$, and composite null diagnostic (CND),
which is a combination of \{$S_3^{(1)}, S_4^{(1)}$\} and $\epsilon$. We find
that: (1) adopting different values of $\Omega_{\Lambda0}$ only has
quantitative impacts on the evolution of the $\Lambda$HDE model, while adopting
different $c$ has qualitative impacts; (2) compared with $S_3^{(1)}$,
$S_4^{(1)}$ can give larger differences among the cosmic evolutions of the
$\Lambda$HDE model associated with different $\Omega_{\Lambda0}$ or different
$c$; (3) compared with the case of using a single diagnostic, adopting a CND
pair has much stronger ability to diagnose the $\Lambda$HDE model.


title: Strong Mechanical Squeezing and its Detection

abstract:
  We report an efficient mechanism to generate a squeezed state of a mechanical
mirror in an optomechanical system. We use especially tuned parametric
amplifier (PA) inside the cavity and the parametric photon phonon processes to
transfer quantum squeezing from photons to phonons with almost 100\%
efficiency. We get 50\% squeezing of the mechanical mirror which is limited by
the PA. We present analytical results for the mechanical squeezing thus
enabling one to understand the dependence of squeezing on system parameters
like gain of PA, cooperativity, temperature. As in cooling experiments the
detrimental effects of mirror's Brownian and zero point noises are strongly
suppressed by the pumping power. By judicious choice of the phases, the cavity
output is squeezed only if the mirror is squeezed thus providing us a direct
measure of the mirror's squeezing. Further considerable larger squeezing of the
mirror can be obtained by adding the known feedback techniques.


title: Swivel: Improving Embeddings by Noticing What's Missing

abstract:
  We present Submatrix-wise Vector Embedding Learner (Swivel), a method for
generating low-dimensional feature embeddings from a feature co-occurrence
matrix. Swivel performs approximate factorization of the point-wise mutual
information matrix via stochastic gradient descent. It uses a piecewise loss
with special handling for unobserved co-occurrences, and thus makes use of all
the information in the matrix. While this requires computation proportional to
the size of the entire matrix, we make use of vectorized multiplication to
process thousands of rows and columns at once to compute millions of predicted
values. Furthermore, we partition the matrix into shards in order to
parallelize the computation across many nodes. This approach results in more
accurate embeddings than can be achieved with methods that consider only
observed co-occurrences, and can scale to much larger corpora than can be
handled with sampling methods.


title:
Smoothing Brascamp-Lieb Inequalities and Strong Converses for Common
  Randomness Generation

abstract:
  We study the infimum of the best constant in a functional inequality, the
Brascamp-Lieb-like inequality, over auxiliary measures within a neighborhood of
a product distribution. In the finite alphabet and the Gaussian cases, such an
infimum converges to the best constant in a mutual information inequality.
Implications for strong converse properties of two common randomness (CR)
generation problems are discussed. In particular, we prove the strong converse
property of the rate region for the omniscient helper CR generation problem in
the discrete and the Gaussian cases. The latter case is perhaps the first
instance of a strong converse for a continuous source when the rate region
involves auxiliary random variables.


title:
The Varying Light Curve and Timings of the Ultra-short Period Contact
  Binary KIC 9532219

abstract:
  KIC 9532219 is a W UMa-type eclipsing binary with an orbital period of
0.1981549 d that is below the short-period limit ($\sim$0.22 d) of the period
distribution for contact binaries. The {\it Kepler} light curve of the system
exhibits striking light changes in both eclipse depths and light maxima.
Applying third-body and spot effects, the light-curve synthesis indicates that
the eclipsing pair is currently in a marginal contact stage with a mass ratio
of $q$=1.20, an orbital inclination of $i$=66.0 deg, a temperature difference
of $\Delta$ ($T_{1}$--$T_{2}$)=172 K, and a third light of $l_3$=75.9 \%. To
understand the light variations with time, we divided up the light curve into
312 segments and separately analyzed them. The results reveal that variation of
eclipse depth is primarily caused by changing amounts of contamination due to
the nearby star KIC9532228 between the {\it Kepler} Quarters and that the
variable O'Connell effect originates from the starspot activity on the less
massive primary component. Based on our light-curve timings, a period study of
KIC 9532219 indicates that the orbital period has varied as a combination of a
downward parabola and a light-travel-time (LTT) effect due to a third body,
with a period of 1196 d and a minimum mass of 0.0892 $M_\odot$ in an eccentric
orbit of 0.150. The parabolic variation could be a small part of a second LTT
orbit due to a fourth component in a wider orbit, instead of either mass
transfer or angular momentum loss.


title: Strongly-Typed Recurrent Neural Networks

abstract:
  Recurrent neural networks are increasing popular models for sequential
learning. Unfortunately, although the most effective RNN architectures are
perhaps excessively complicated, extensive searches have not found simpler
alternatives. This paper imports ideas from physics and functional programming
into RNN design to provide guiding principles. From physics, we introduce type
constraints, analogous to the constraints that forbids adding meters to
seconds. From functional programming, we require that strongly-typed
architectures factorize into stateless learnware and state-dependent firmware,
reducing the impact of side-effects. The features learned by strongly-typed
nets have a simple semantic interpretation via dynamic average-pooling on
one-dimensional convolutions. We also show that strongly-typed gradients are
better behaved than in classical architectures, and characterize the
representational power of strongly-typed nets. Finally, experiments show that,
despite being more constrained, strongly-typed architectures achieve lower
training and comparable generalization error to classical architectures.


title: Variational Hamiltonian Monte Carlo via Score Matching

abstract:
  Traditionally, the field of computational Bayesian statistics has been
divided into two main subfields: variational methods and Markov chain Monte
Carlo (MCMC). In recent years, however, several methods have been proposed
based on combining variational Bayesian inference and MCMC simulation in order
to improve their overall accuracy and computational efficiency. This marriage
of fast evaluation and flexible approximation provides a promising means of
designing scalable Bayesian inference methods. In this paper, we explore the
possibility of incorporating variational approximation into a state-of-the-art
MCMC method, Hamiltonian Monte Carlo (HMC), to reduce the required gradient
computation in the simulation of Hamiltonian flow, which is the bottleneck for
many applications of HMC in big data problems. To this end, we use a {\it
free-form} approximation induced by a fast and flexible surrogate function
based on single-hidden layer feedforward neural networks. The surrogate
provides sufficiently accurate approximation while allowing for fast
exploration of parameter space, resulting in an efficient approximate inference
algorithm. We demonstrate the advantages of our method on both synthetic and
real data problems.


title: Improved Dropout for Shallow and Deep Learning

abstract:
  Dropout has been witnessed with great success in training deep neural
networks by independently zeroing out the outputs of neurons at random. It has
also received a surge of interest for shallow learning, e.g., logistic
regression. However, the independent sampling for dropout could be suboptimal
for the sake of convergence. In this paper, we propose to use multinomial
sampling for dropout, i.e., sampling features or neurons according to a
multinomial distribution with different probabilities for different
features/neurons. To exhibit the optimal dropout probabilities, we analyze the
shallow learning with multinomial dropout and establish the risk bound for
stochastic optimization. By minimizing a sampling dependent factor in the risk
bound, we obtain a distribution-dependent dropout with sampling probabilities
dependent on the second order statistics of the data distribution. To tackle
the issue of evolving distribution of neurons in deep learning, we propose an
efficient adaptive dropout (named \textbf{evolutional dropout}) that computes
the sampling probabilities on-the-fly from a mini-batch of examples. Empirical
studies on several benchmark datasets demonstrate that the proposed dropouts
achieve not only much faster convergence and but also a smaller testing error
than the standard dropout. For example, on the CIFAR-100 data, the evolutional
dropout achieves relative improvements over 10\% on the prediction performance
and over 50\% on the convergence speed compared to the standard dropout.


title:
Photon-phonon parametric oscillation induced by the quadratic coupling
  in an optomechanical resonator

abstract:
  A direct photon-phonon parametric effect of the quadratic coupling on the
mean-field dynamics of an optomechanical resonator in the large-scale-movement
regime is found and investigated. Under a weak pumping power, the mechanical
resonator damps to steady state with a nonlinear static response sensitively
modified by the quadratic coupling. When the driving powerincreases beyond the
static energy balance, the steady states lose their stabilities via Hopf
bifurcations and the resonator produces stable self-sustained
oscillation(limit-circle behavior) of discrete energies with step-like
amplitudes due to the parametric effect of the quadratic coupling, which can be
understood roughly by the power balance between gain and loss on the resonator.
A further increase of the pumping power can induce chaotic dynamic of the
resonator via a typical routine of period-doubling bifurcation but which can be
stabilized by the parametric effect through an inversion bifurcation process
back to limit-circle states. The bifurcation-to-inverse-bifurcation transitions
are numerically verified by the maximal Lyapunov exponents of the dynamics and
which indicate an efficient way to suppress the chaotic behavior of the
optomechanical resonator by the quadratic coupling. Furthermore, the parametric
effect of the quadratic coupling on the dynamic transitions of an
optomechanical resonator can be conveniently detected or traced by the output
power spectrum of the cavity field.


title:
Study on the rare decays of $Y(4630)$ induced by final state
  interactions

abstract:
  A resonance $Y(4630)$ at the invariant mass spectrum of $\Lambda_c
\bar\Lambda_c$ observed by the Belle Collaboration triggers a hot discussion
about its inner structure. Since it preferably decays into two charmed baryons
$\Lambda_c\bar\Lambda_c$, it is tempted to conjecture it as a tetraquark.
Because the dominant decay portal $Y(4630)\to \Lambda_c \bar\Lambda_c$ is close
to the energy threshold, the final state interactions may be significant and
result in other baryonic and/or mesonic final states whose branching fractions
are sizable to be measured in the future experiments. In this work we calculate
the branching ratios of the $Y(4630)$ decays into $p\bar p$, $D^{(*)+}
D^{(*)-}$, $\pi^+\pi^-$, and $K^+K^-$ which are induced by the $\Lambda_c
\bar\Lambda_c$ re-scattering. The resultant decay patterns will be tested by
the future experiments and the consistency degree with the data composes a
valuable probe for the tetraquark conjecture.


title:
Electromagnetic fields with electric and chiral magnetic conductivities
  in heavy ion collisions

abstract:
  We derive analytic formula for electric and magnetic fields produced by a
moving charged particle in a conducting medium with the electric conductivity
$\sigma$ and the chiral magnetic conductivity $\sigma_{\chi}$. We use the Green
function method and assume that $\sigma_{\chi}$ is much smaller than $\sigma$.
The compact algebraic expressions for electric and magnetic fields without any
integrals are obtained. They recover the Lienard-Wiechert formula at vanishing
conductivities. Exact numerical solutions are also found for any values of
$\sigma$ and $\sigma_{\chi}$ and are compared to analytic results. Both
numerical and analytic results agree very well for the scale of high energy
heavy ion collisions. The space-time profiles of electromagnetic fields in
non-central Au+Au collisions have been calculated based on these analytic
formula as well as exact numerical solutions.


title: A simplification of the unified gas kinetic scheme

abstract:
  Unified gas kinetic scheme (UGKS) is an asymptotic preserving scheme for the
kinetic equations. It is superior for transition flow simulations, and has been
validated in the past years. However, compared to the well known discrete
ordinate method (DOM) which is a classical numerical method solving the kinetic
equations, the UGKS needs more computational resources. In this study, we
propose a simplification of the unified gas kinetic scheme. It allows almost
identical numerical cost as the DOM, but predicts numerical results as accurate
as the UGKS. Based on the observation that the equilibrium part of the UGKS
fluxes can be evaluated analytically, the equilibrium part in the UGKS flux is
not necessary to be discretized in velocity space. In the simplified scheme,
the numerical flux for the velocity distribution function and the numerical
flux for the macroscopic conservative quantities are evaluated separately. The
simplification is equivalent to a flux hybridization of the gas kinetic scheme
for the Navier-Stokes (NS) equations and conventional discrete ordinate method.
Several simplification strategies are tested, through which we can identify the
key ingredient of the Navier-Stokes asymptotic preserving property. Numerical
tests show that, as long as the collision effect is built into the macroscopic
numerical flux, the numerical scheme is Navier-Stokes asymptotic preserving,
regardless the accuracy of the microscopic numerical flux for the velocity
distribution function.


title: Functional Brain Imaging: A Comprehensive Survey

abstract:
  Functional brain imaging allows measuring dynamic functionality in all brain
regions. It is broadly used in clinical cognitive neuroscience as, well as in
research. It will allow the observation of neural activities in the brain
simultaneously. From the beginning when functional brain imaging was initiated
by the mapping of brain functions proposed by phrenologists, many scientists
were asking why we need to image brain functionality since we have already
structural information. Simply, their important question was including a great
answer. Functional information of the human brain would definitely complement
structural information, helping to have a better understanding of what is
happening in the brain. This paper, which could be useful to those who have an
interest in functional brain imaging, such as engineers, will present a quick
review of modalities used in functional brain imaging. We will concentrate on
the most used techniques in functional imaging which are functional magnetic
resonance imaging (fMRI) and functional optical imaging, which is one of
novelties in this area of study.


title: Sample path large deviations for Laplacian models in $(1+1)$-dimensions

abstract:
  For Laplacian models in dimension $(1+1)$ we derive sample path large
deviations for the profile height function, that is, we study scaling limits of
Gaussian integrated random walks and Gaussian integrated random walk bridges
perturbed by an attractive force towards the zero-level, called pinning. We
study in particular the regime when the rate functions of the corresponding
large deviation principles admit more than one minimiser, in our models either
two, three, or five minimiser depending on the pinning strength and the
boundary conditions. This study complements corresponding large deviation
results for gradient systems with pinning for Gaussian random walk bridges in $
(1+1) $-dimension (\cite{FS04}) and in $(1+d) $-dimension (\cite{BFO}), and
recently in higher dimensions in \cite{BCF}. In particular it turns out that
the Laplacian cases, i.e., integrated random walks, show richer and more
complex structures of the minimiser of the rate functions which are linked to
different phases.


title: Relativistic stars in bigravity theory

abstract:
  Assuming static and spherically symmetric spacetimes in the ghost-free
bigravity theory, we find a relativistic star solution, which is very close to
that in general relativity. The coupling constants are classified into two
classes: Class [I] and Class [II]. Although the Vainshtein screening mechanism
is found in the weak gravitational field for both classes, we find that there
is no regular solution beyond the critical value of the compactness in Class
[I]. This implies that the maximum mass of a neutron star in Class [I] becomes
much smaller than that in GR. On the other hand, for the solution in Class
[II], the Vainshtein screening mechanism works well even in a relativistic star
and the result in GR is recovered.


title:
Perspectives of Racetrack Memory for Large-Capacity On-Chip Memory: From
  Device to System

abstract:
  Current-induced domain wall motion (CIDWM) is regarded as a promising way
towards achieving emerging high-density, high-speed and low-power non-volatile
devices. Racetrack memory is an attractive spintronic memory based on this
phenomenon, which can store and transfer a series of data along a magnetic
nanowire. However, storage capacity issue is always one of the most serious
bottlenecks hindering its application for practical systems. This paper focuses
on the potential of racetrack memory towards large capacity. The investigations
covering from device level to system level have been carried out. Various
alternative mechanisms to improve the capacity of racetrack memory have been
proposed and elucidated, e.g. magnetic field assistance, chiral DW motion and
voltage-controlled flexible DW pinning. All of them can increase nanowire
length, allowing enhanced feasibility of large-capacity racetrack memory. By
using SPICE compatible racetrack memory electrical model and commercial CMOS 28
nm design kit, mixed simulations are performed to validate their
functionalities and analyze their performance. System level evaluations
demonstrate the impact of capacity improvement on overall system. Compared with
traditional SRAM based cache, racetrack memory based cache shows its advantages
in terms of execution time and energy consumption.


title:
Basic Properties of Conductivity and Normal Hall Effect in the Periodic
  Anderson Model

abstract:
  Exact formulas of diagonal conductivity $\sigma_{xx}$ and Hall conductivity
$\sigma_{xy}$ are derived from the Kubo formula in hybridized two-orbital
systems with arbitrary band dispersions. On the basis of the theoretical
framework for the Fermi liquid based on these formulas, the ground-state
properties of the periodic Anderson model with electron correlation and weak
impurity scattering are studied on the square lattice. It is shown that
imbalance of the mass-renormalization factors in $\sigma_{xx}$ and
$\sigma_{xy}$ causes remarkable increase in the valence-fluctuation regime as
the f level increases while the cancellation of the renormalization factors
causes slight increase in $\sigma_{xx}$ and $\sigma_{xy}$ in the Kondo regime.
The Hall coefficient $R_{\rm H}$ shows almost constant behavior in both the
regimes. Near half filling, $R_{\rm H}$ is expressed by the total hole density
as $R_{\rm H}=1/(\bar{n}_{\rm hole}e)$ while $R_{\rm H}$ approaches zero near
quarter filling, which reflects the curvature of the Fermi surface. These
results hold as far as the damping rate for f electrons is less than about
$10~\%$ of the renormalized hybridization gap. From these results we discuss
pressure dependence of residual resistivity and normal Hall effect in Ce- and
Yb-based heavy electron systems.


title:
Magnetic monopole condensation in pyrochlore ice quantum spin liquid:
  application to Pr2Ir2O7 and Yb2Ti2O7

abstract:
  Pyrochlore iridates and pyrochlore ices are two families of materials where
novel quantum phenomena are intertwined with strong spin-orbit coupling,
substantial electron correlation and geometrical frustration. Motivated by the
puzzling experiments on two pyrochlore systems Pr2Ir2O7 and Yb2Ti2O7, we study
the proximate Ising orders and the quantum phase transition out of quantum spin
ice U(1) quantum spin liquid (QSL). We apply the electromagnetic duality of the
compact quantum electrodynamics to analyze the "magnetic monopoles"
condensation for U(1) QSL. The monopole condensation transition represents a
unconventional quantum criticality with unusual scaling laws. It naturally
leads to the Ising orders that belong to the "2-in 2-out" spin ice manifold and
generically have an enlarged magnetic unit cell. We demonstrate that the
antiferormagnetic Ising state with the ordering wavevector ${\bf Q} =
2\pi(001)$ is proximate to U(1) QSL while the ferromagnetic Ising state with
${\bf Q}=(000)$ is not proximate to U(1) QSL. This implies that if there exists
a direct transition from U(1) QSL to the ferromagnetic Ising state, the
transition must be strongly first order. We apply the theory to Pr2Ir2O7 and
Yb2Ti2O7.


title: Testing the mapping between redshift and cosmic scale factor

abstract:
  The canonical redshift-scale factor relation, 1/a=1+z, is a key element in
the standard LambdaCDM model of the big bang cosmology. Despite its fundamental
role, this relation has not yet undergone any observational tests since
Lemaitre and Hubble established the expansion of the Universe. It is strictly
based on the assumption of the Friedmann-Lemaitre-Robertson-Walker metric
describing a locally homogeneous and isotropic universe and that photons move
on null geodesics of the metric. Thus any violation of this assumption, within
general relativity or modified gravity, can yield a different mapping between
the model redshift z=1/a-1 and the actually observed redshift z_obs, i.e. z_obs
neq z. Here we perform a simple test of consistency for the standard
redshift-scale factor relation by determining simultaneous observational
constraints on the concordance LambdaCDM cosmological parameters and a
generalized redshift mapping z=f(z_obs). Using current baryon acoustic
oscillations (BAO) and Type Ia supernova (SN) data we demonstrate that the
generalized redshift mapping is strongly degenerated with dark energy.
Marginalization over a class of monotonic functions f(z_obs) changes
substantially degeneracy between matter and dark energy density: the density
parameters become anti correlated with nearly vertical axis of degeneracy.
Furthermore, we show that current SN and BAO data, analysed in a framework with
the generalized redshift mapping, do not constrain dark energy unless the BAO
data include the measurements from the Ly-alpha forest of high-redshift
quasars.


title:
Cauchy Problems for Parabolic Equations in Sobolev-Slobodeckii and
  H\"older Spaces on Uniformly Regular Riemannian Manifolds

abstract:
  In this paper we establish optimal solvability results, that is, maximal
regularity theorems, for the Cauchy problem for linear parabolic differential
equations of arbitrary order acting on sections of tensor bundles over
boundaryless complete Riemannian manifolds with bounded geometry. We employ an
anisotropic extension of the Fourier multiplier theorem for arbitrary Besov
spaces introduced in earlier by the author. This allows for a unified treatment
of Sobolev-Slobodeckii and little H\"older spaces. In the flat case we recover
classical results for Petrowskii-parabolic Cauchy problems.


title:
Activity Analyses for Solar-Type Stars Observed With Kepler. I. Proxies
  of Magnetic Activity

abstract:
  Light curves of solar-type stars often show gradual fluctuations due to
rotational modulation by magnetic features (starspots and faculae) on stellar
surfaces. Two quantitative measures of modulated light curves are employed as
the proxies of magnetic activity for solar-type stars observed with Kepler
telescope. The first is named autocorrelation index $i_{AC}$, which describes
the degree of periodicity of the light curve, the second is the effective
fluctuation range of the light curve $R_{eff}$, which reflects the depth of
rotational modulation. The two measures are complementary and depict different
aspects of magnetic activities on solar-type stars. By using the two proxies
$i_{AC}$ and $R_{eff}$, we analyzed activity properties of two carefully
selected solar-type stars observed with Kepler (Kepler ID: 9766237 and
10864581), which have distinct rotational periods (14.7 vs. 6.0 days). We also
applied the two measures to the Sun for a comparative study. The result shows
that both the measures can reveal cyclic activity variations (referred to as
$i_{AC}$-cycle and $R_{eff}$-cycle) on the two Kepler stars and the Sun. For
the Kepler star with the faster rotation rate, $i_{AC}$-cycle and
$R_{eff}$-cycle are in the same phase, while for the Sun (slower rotator), they
are in the opposite phase. By comparing the solar light curve with simultaneous
photospheric magnetograms, it is identified that the magnetic feature that
causes the periodic light curve during solar minima is the faculae of the
enhanced network region, which can also be a candidate of magnetic features
that dominate the periodic light curves on the two Kepler stars.


title: Categorical resolutions of a class of derived categories

abstract:
  Using the relative derived categories, we prove that if an Artin algebra $A$
has a module $T$ with ${\rm inj.dim}T<\infty$ such that $^\perp T$ is finite,
then the bounded derived category $D^b({\rm mod}A)$ admits a categorical
resolution; and that for CM-finite Gorenstein algebra, such a categorical
resolution is weakly crepant.


title:
Constructions of q-ary entanglement-assisted quantum MDS codes with
  minimum distance greater than q + 1

abstract:
  The entanglement-assisted stabilizer formalism provides a useful framework
for constructing quantum error-correcting codes (QECC), which can transform
arbitrary classical linear codes into entanglement-assisted quantum error
correcting codes (EAQECCs) by using pre-shared entanglement between the sender
and the receiver. In this paper, we construct five classes of
entanglement-assisted quantum MDS (EAQMDS) codes based on classical MDS codes
by exploiting one or more pre-shared maximally entangled states. We show that
these EAQMDS codes have much larger minimum distance than the standard quantum
MDS (QMDS) codes of the same length, and three classes of these EAQMDS codes
consume only one pair of maximally entangled states.


title:
The Infrared Medium-Deep Survey. V. A New Selection Strategy for Quasars
  at z > 5 based on Medium-Band Observation with SQUEAN

abstract:
  Multiple color selection techniques have been successful in identifying
quasars from wide-field broad-band imaging survey data. Among the quasars that
have been discovered so far, however, there is a redshift gap at $5 \lesssim
{\rm z} \lesssim 5.7$ due to the limitations of filter sets in previous
studies. In this work, we present a new selection technique of high redshift
quasars using a sequence of medium-band filters: nine filters with central
wavelengths from 625 to 1025 nm and bandwidths of 50 nm. Photometry with these
medium-bands traces the spectral energy distribution (SED) of a source, similar
to spectroscopy with resolution R $\sim$ 15. By conducting medium-band
observations of high redshift quasars at 4.7 $\leq$ z $\leq$ 6.0 and brown
dwarfs (the main contaminants in high redshift quasar selection) using the SED
camera for QUasars in EArly uNiverse (SQUEAN) on the 2.1-m telescope at the
McDonald Observatory, we show that these medium-band filters are superior to
multi-color broad-band color section in separating high redshift quasars from
brown dwarfs. In addition, we show that redshifts of high redshift quasars can
be determined to an accuracy of $\Delta{\rm z}/(1+{\rm z}) = 0.002$ -- $0.026$.
The selection technique can be extended to z $\sim$ 7, suggesting that the
medium-band observation can be powerful in identifying quasars even at the
re-ionization epoch.


title:
Reducing training requirements through evolutionary based dimension
  reduction and subject transfer

abstract:
  Training Brain Computer Interface (BCI) systems to understand the intention
of a subject through Electroencephalogram (EEG) data currently requires
multiple training sessions with a subject in order to develop the necessary
expertise to distinguish signals for different tasks. Conventionally the task
of training the subject is done by introducing a training and calibration stage
during which some feedback is presented to the subject. This training session
can take several hours which is not appropriate for on-line EEG-based BCI
systems. An alternative approach is to use previous recording sessions of the
same person or some other subjects that performed the same tasks (subject
transfer) for training the classifiers. The main aim of this study is to
generate a methodology that allows the use of data from other subjects while
reducing the dimensions of the data. The study investigates several
possibilities for reducing the necessary training and calibration period in
subjects and the classifiers and addresses the impact of i) evolutionary
subject transfer and ii) adapting previously trained methods (retraining) using
other subjects data. Our results suggest reduction to 40% of target subject
data is sufficient for training the classifier. Our results also indicate the
superiority of the approaches that incorporated evolutionary subject transfer
and highlights the feasibility of adapting a system trained on other subjects.


title: Who Benefits from the "Sharing" Economy of Airbnb?

abstract:
  Sharing economy platforms have become extremely popular in the last few
years, and they have changed the way in which we commute, travel, and borrow
among many other activities. Despite their popularity among consumers, such
companies are poorly regulated. For example, Airbnb, one of the most successful
examples of sharing economy platform, is often criticized by regulators and
policy makers. While, in theory, municipalities should regulate the emergence
of Airbnb through evidence-based policy making, in practice, they engage in a
false dichotomy: some municipalities allow the business without imposing any
regulation, while others ban it altogether. That is because there is no
evidence upon which to draft policies. Here we propose to gather evidence from
the Web. After crawling Airbnb data for the entire city of London, we find out
where and when Airbnb listings are offered and, by matching such listing
information with census and hotel data, we determine the socio-economic
conditions of the areas that actually benefit from the hospitality platform.
The reality is more nuanced than one would expect, and it has changed over the
years. Airbnb demand and offering have changed over time, and traditional
regulations have not been able to respond to those changes. That is why,
finally, we rely on our data analysis to envision regulations that are
responsive to real-time demands, contributing to the emerging idea of
"algorithmic regulation".


title: Lieb-Mattis ferrimagnetism in diluted magnetic semiconductors

abstract:
  We show the possibility of long-range ferrimagnetic ordering with a
saturation magnetisation of the order of 1 Bohr magneton per spin for
arbitrarily low concentration of magnetic impurities in semiconductors,
provided that the impurities form a superstructure satisfying the conditions of
the Lieb-Mattis theorem. Explicit examples of such superstructures are given
for the wurtzite lattice, and the temperature of ferrimagnetic transition is
estimated from a high-temperature expansion. Exact diagonalization studies show
that small fragments of the structure exhibit enhanced magnetic response and
isotropic superparamagnetism at low temperatures. A quantum transition in a
high magnetic field is considered and similar superstructures in cubic
semiconductors are discussed as well.


title: Exactly solvable dynamical models with a minimal length uncertainty

abstract:
  We present exact analytical solutions to the classical equations of motion
and analyze the dynamical consequences of the existence of a minimal length for
the free particle, particle in a linear potential, anti-symmetric constant
force oscillator, harmonic oscillator, vertical harmonic oscillator, linear
diatomic chain, and linear triatomic chain. It turns out that a minimal length
increases the speed of a free particle and the rate of fall of a particle that
is subject to the influence of a linear potential. Our results suggest that the
characteristic frequency of systems tend to increase when there is a minimal
length. This is a common feature that we observed for the oscillator systems
that we have considered.


title:
Adaptive Mean Queue Size and Its Rate of Change: Queue Management with
  Random Dropping

abstract:
  The Random early detection (RED) active queue management (AQM) scheme uses
the average queue size to calculate the dropping probability in terms of
minimum and maximum thresholds. The effect of heavy load enhances the frequency
of crossing the maximum threshold value resulting in frequent dropping of the
packets. An adaptive queue management with random dropping (AQMRD) algorithm is
proposed which incorporates information not just about the average queue size
but also the rate of change of the same. Introducing an adaptively changing
threshold level that falls in between lower and upper thresholds, our algorithm
demonstrates that these additional features significantly improve the system
performance in terms of throughput, average queue size, utilization and queuing
delay in relation to the existing AQM algorithms.


title:
Determination of single-bond association kinetics by tethered particle
  motion: concept and simulations

abstract:
  Tethered particle motion (TPM) --- the motion of a micro- or nanoparticle
tethered to a substrate by a macromolecule --- is a system that has proven
extremely useful for its ability to reveal physical features of the tether,
because the thermal motion of the bound particle reports sensitively on
parameters like the length, the rigidity, or the folding state of its tether.
In this paper, we discuss a novel application of TPM, surveying its utility in
probing the kinetics of single secondary bonds: bonds that form and break
between the tethered particle and a substrate due, for instance, to
receptor/ligand pairs on particle and substrate. Much like the tether itself
affects the motion pattern, so do the presence and absence of such secondary
connections. Keeping the tether properties constant, we demonstrate how raw
positional TPM data may be parsed to generate detailed insights into the
association and dissociation kinetics of single secondary bonds. We do this
using coarse-grained molecular dynamics simulations, specifically developed to
treat the motion of particles close to interfaces.

categories: physics.bio-ph cond-mat.soft physics.comp-ph q-bio.QM


title:
Bayesian analysis of cosmic-ray propagation: evidence against
  homogeneous diffusion

abstract:
  We present the results of the most complete ever scan of the parameter space
for cosmic ray (CR) injection and propagation. We perform a Bayesian search of
the main GALPROP parameters, using the MultiNest nested sampling algorithm,
augmented by the BAMBI neural network machine learning package. This is the
first such study to separate out low-mass isotopes ($p$, $\bar p$ and He) from
the usual light elements (Be, B, C, N, O). We find that the propagation
parameters that best fit $p$, $\bar p$, He data are significantly different
from those that fit light elements, including the B/C and $^{10}$Be/$^9$Be
secondary-to-primary ratios normally used to calibrate propagation parameters.
This suggests each set of species is probing a very different interstellar
medium, and that the standard approach of calibrating propagation parameters
using B/C can lead to incorrect results. We present posterior distributions and
best fit parameters for propagation of both sets of nuclei, as well as for the
injection abundances of elements from H to Si. The input GALDEF files with
these new parameters will be included in an upcoming public GALPROP update.


title:
Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank
  Approximation

abstract:
  There has been a large increase in the amount of work on hierarchical
low-rank approximation methods, where the interest is shared by multiple
communities that previously did not intersect. This objective of this article
is two-fold; to provide a thorough review of the recent advancements in this
field from both analytical and algebraic perspectives, and to present a
comparative benchmark of two highly optimized implementations of contrasting
methods for some simple yet representative test cases. We categorize the recent
advances in this field from the perspective of compute-memory tradeoff, which
has not been considered in much detail in this area. Benchmark tests reveal
that there is a large difference in the memory consumption and performance
between the different methods.


title:
High Order Hierarchical Asymptotic Preserving Nodal Discontinuous
  Galerkin IMEX Schemes For The BGK Equation

abstract:
  A class of high order asymptotic preserving (AP) schemes has been developed
for the BGK equation in Xiong et. al. (2015) [37], which is based on the
micro-macro formulation of the equation. The nodal discontinuous Galerkin (NDG)
method with Lagrangian basis functions for spatial discretization and globally
stiffly accurate implicit-explicit (IMEX) Runge-Kutta (RK) scheme as time
discretization are introduced with asymptotic preserving properties. However,
it is only necessary to solve the kinetic equation when the hydrodynamic
description breaks down. Motivated by the recent work in Filbet and Rey (2015)
[23], it is more naturally to construct a hierarchy scheme under the NDG-IMEX
framework without hybridization, as the formal analysis in [37] shows that when
$\epsilon$ is small, the NDG-IMEX scheme becomes a local discontinuous Galerkin
(LDG) scheme for the compressible Navier-Stokes equations, and when
$\epsilon=0$ it is a discontinuous Galerkin (DG) scheme for the compressible
Euler equations. Moveover, we propose to combine the kinetic regime with the
hydrodynamic regime including both the compressible Euler and Navier-Stokes
equations. Numerical experiments demonstrate very decent performance of the new
approach. In our numerics, all three regimes are clearly divided, leading to
great savings in terms of the computational cost.


title:
General properties of the Foldy-Wouthuysen transformation and
  applicability of the corrected original Foldy-Wouthuysen method

abstract:
  General properties of the Foldy-Wouthuysen transformation which is widely
used in quantum mechanics and quantum chemistry are considered. Merits and
demerits of the original Foldy-Wouthuysen transformation method are analyzed.
While this method does not satisfy the Eriksen condition of the
Foldy-Wouthuysen transformation, it can be corrected with the use of the
Baker-Campbell-Hausdorff formula. We show a possibility of such a correction
and propose an appropriate algorithm of calculations. An applicability of the
corrected Foldy-Wouthuysen method is restricted by the condition of convergence
of a series of relativistic corrections.


title:
Parametrising Epoch of Reionization foregrounds: A deep survey of
  low-frequency point-source spectra with the MWA

abstract:
  Experiments that pursue detection of signals from the Epoch of Reionization
(EoR) are relying on spectral smoothness of source spectra at low frequencies.
This article empirically explores the effect of foreground spectra on EoR
experiments by measuring high-resolution full-polarization spectra for the 586
brightest unresolved sources in one of the MWA EoR fields using 45 h of
observation. A novel peeling scheme is used to subtract 2500 sources from the
visibilities with ionospheric and beam corrections, resulting in the deepest,
confusion-limited MWA image so far. The resulting spectra are found to be
affected by instrumental effects, which limit the constraints that can be set
on source-intrinsic spectral structure. The sensitivity and power-spectrum of
the spectra are analysed, and it is found that the spectra of residuals are
dominated by PSF sidelobes from nearby undeconvolved sources. We release a
catalogue describing the spectral parameters for each measured source.


title:
Lepton flavour violating decays of $\mu$ and $\tau$ lepton in a gauge
  group $SU_L(2)\times SU_R(2)\times SU_l(2)$

abstract:
  The electroweak unification group $ SU(2)_L\times SU(2)_R\times SU(2)_Y $ is
proposed for the charged lepton flavor violating decays of the muon ($\mu$) and
tau ($\tau$) leptons. The group $SU(2)_Y$ is in the lepton space. The
left-handed leptons and anti-leptons are assigned to the fundamental
representation $(2,2,\bar{2})$ of the semi-simple group. The gauge group
$SU(2)_Y$ is spontaneously broken to $U(1)_{Y_1}$, where $Y_1=-L=\pm1$ is the
hypercharge, by introducing a scalar multiplet $\Sigma$ which belongs to the
triplet representation 3 of the $SU(2)_Y$ and is singlet under $SU(2)_L\times
SU(2)_R$. At this stage charged vector bosons $Y^\pm$ of $SU(2)_Y$ which
mediate the lepton flavor violating decays acquire masses and are decoupled
with one Higgs scalar $H_\Sigma^0$. The residual group $SU(2)_L\times
SU(2)_R\times U(1)_{Y_1}$ has all the features of the left-right electroweak
unification group extensively studied in the literature. The probability for
lepton flavor violating decays is
$\left(\frac{\sin^2\theta_W}{1-2\sin^2\theta_W}\right)^2\left(\frac{m_{W_L}}{m_Y}\right)^4$.


title:
A Processing In-Memory Realization Using QCA: Proposal and
  Implementation

abstract:
  Processing in Memory (PIM) is a computing paradigm that promises enormous
gain in processing speed by eradicating latencies in the typical von Neumann
architecture. It has gained popularity owing to its throughput by embedding
storage and computation of data in a single unit. We portray implementation of
Akers array architecture endowed with PIM computation using Quantum-dot
Cellular Automata (QCA). We present the proof of concept of PIM with its
realization in the QCA designer paradigm. We illustrate implementation of Ex-OR
gate with the help of QCA based Akers Array and put forth many interesting
potential possibilities.


title:
On the Limits of Coexisting Coverage and Capacity in Multi-RAT
  Heterogeneous Networks

abstract:
  This paper devises a general modeling and analyzing framework for a
heterogeneous wireless network (HetNet) in which several wireless subnetworks
coexist and use multiple radio access technologies (multi-RATs). The coexisting
coverage and network capacity in such a multi-RAT HetNet are hardly
investigated in prior works. To characterize the coexisting interactions in a
multi-RAT HetNet, in this paper we consider a HetNet consisting of K-tier APs
and two different RATs, RAT-L and RAT-U, are adopted in the HetNet. RAT-L is
adopted by the access points (APs) in the first K-1 tiers and APs in the Kth
tier only use RAT-U. Both noncrossing-RAT and crossing-RAT user association
scenarios are considered. In each scenario, the void probability and channel
access probability of the APs in each tier are first found and then the tight
lower bounds and their lowest limits on the proposed coexisting coverage and
network capacity are derived. We show that multi-RAT networks in general can
achieve higher link coverage and capacity by using opportunistic CSMA/CA that
avoids/alleviates severe interfering between all coexisting APs. Also,
crossing-RAT user association is shown to achieve much higher coexisting
coverage and network capacity than noncrossing-RAT user association. Finally,
numerical simulations for the LTE-U and WiFi networks coexisting in the HetNet
validate our findings.


title: Muon Calibration at SoLid

abstract:
  The SoLid experiment aims to make a measurement of very short distance
neutrino oscillations using reactor antineutrinos. Key to its sensitivity are
the experiments high spatial and energy resolution, combined with a very
suitable reactor source and efficient background rejection. The fine
segmentation of the detector (cubes of side 5cm), and ability to resolve
signals in space and time, gives SoLid the capability to track cosmic muons. In
principle a source of background, these turn into a valuable calibration source
if they can be cleanly identified. This work presents the first energy
calibration results, using cosmic muons, of the 288kg SoLid prototype SM1. This
includes the methodology of tracking at SoLid, cosmic ray angular analyses at
the reactor site, estimates of the time resolution, and calibrations at the
cube level.


title: A conformal group approach to the Dirac-K\"ahler system on the lattice

abstract:
  Starting from the representation of the $(n-1)+n-$dimensional Lorentz
pseudo-sphere on the projective space $\mathbb{P}\mathbb{R}^{n,n}$, we propose
a method to derive a class of solutions underlying to a Dirac-K\"ahler type
equation on the lattice. We make use of the Cayley transform $\varphi({\bf
w})=\dfrac{1+{\bf w}}{1-{\bf w}}$ to show that the resulting group
representation arise from the same mathematical framework as the conformal
group representation in terms of the {\it general linear group}
$GL\left(2,\Gamma(n-1,n-1)\cup\{ 0\}\right)$. That allows us to describe such
class of solutions as a commutative $n-$ary product, involving the
quasi-monomials $\varphi\left({\bf z}_j\right)^{-\frac{x_j}{h}}$ ($x_j \in
h\mathbb{Z}$) with membership in the paravector space $\mathbb{R}\oplus
\mathbb{R}{\bf e}_j{\bf e}_{n+j}$.


title: Philosophical foundations of interpretations of quantum mechanics

abstract:
  It is demonstrated that the reason for the diversity of interpretations of
quantum mechanics is that they are not connected by continuity relations with
classical physics, and also the reason is the impossibility of operationalist
definition of the vector of state. The problem lies in the incompatibility of
the philosophical foundations of interpretations, which results in the
difficulty of building a unified picture of the world. To solve the problem, we
identify general philosophical foundation of interpretations of quantum
mechanics and built their classification. We also show that in more general
theories, the part of which is quantum mechanics, it is possible to integrate
(reconcile) the philosophical foundations of interpretations.


title: Gaugings of four-dimensional N=3 supergravity and AdS4/CFT3 holography

abstract:
  We study matter-coupled $N=3$ gauged supergravity in four dimensions with
various semisimple gauge groups. When coupled to $n$ vector multiplets, the
gauged supergravity contains $3+n$ vector fields and $3n$ complex scalars
parametrized by $SU(3,n)/SU(3)\times SU(n)\times U(1)$ coset manifold.
Semisimple gauge groups take the form of $G_0\times H\subset SO(3,n)\subset
SU(3,n)$ with $H$ being a compact subgroup of $SO(n+3-\textrm{dim}(G_0))$. The
$G_0$ groups considered in this paper are of the form $SO(3)$, $SO(3,1)$,
$SO(2,2)$, $SL(3,\mathbb{R})$ and $SO(2,1)\times SO(2,2)$. We find that
$SO(3)\times SO(3)$, $SO(3,1)$ and $SL(3,\mathbb{R})$ gauge groups admit a
maximally supersymmetric $AdS_4$ critical point. The $SO(2,1)\times SO(2,2)$
gauge group admits a supersymmetric Minkowski vacuum while the remaining gauge
groups admit both half-supersymmetric domain wall vacua and $AdS_4$ vacua with
completely broken supersymmetry. For the $SO(3)\times SO(3)$ gauge group, there
exists another supersymmetric $N=3$ $AdS_4$ critical point with
$SO(3)_{\textrm{diag}}$ symmetry. We explicitly give a detailed study of
various holographic RG flows between $AdS_4$ critical points, flows to
non-conformal theories and supersymmetric domain walls in each gauge group. The
results provide gravity duals of $N=3$ Chern-Simons-Matter theories in three
dimensions.


title: Deep Cross-Modal Hashing

abstract:
  Due to its low storage cost and fast query speed, cross-modal hashing (CMH)
has been widely used for similarity search in multimedia retrieval
applications. However, almost all existing CMH methods are based on
hand-crafted features which might not be optimally compatible with the
hash-code learning procedure. As a result, existing CMH methods with
handcrafted features may not achieve satisfactory performance. In this paper,
we propose a novel cross-modal hashing method, called deep crossmodal hashing
(DCMH), by integrating feature learning and hash-code learning into the same
framework. DCMH is an end-to-end learning framework with deep neural networks,
one for each modality, to perform feature learning from scratch. Experiments on
two real datasets with text-image modalities show that DCMH can outperform
other baselines to achieve the state-of-the-art performance in cross-modal
retrieval applications.


title: A Tractable Fully Bayesian Method for the Stochastic Block Model

abstract:
  The stochastic block model (SBM) is a generative model revealing macroscopic
structures in graphs. Bayesian methods are used for (i) cluster assignment
inference and (ii) model selection for the number of clusters. In this paper,
we study the behavior of Bayesian inference in the SBM in the large sample
limit. Combining variational approximation and Laplace's method, a consistent
criterion of the fully marginalized log-likelihood is established. Based on
that, we derive a tractable algorithm that solves tasks (i) and (ii)
concurrently, obviating the need for an outer loop to check all model
candidates. Our empirical and theoretical results demonstrate that our method
is scalable in computation, accurate in approximation, and concise in model
selection.


title: The Anisotropic Four-State Clock Model in the Presence of Random Fields

abstract:
  A four-state clock ferromagnetic model is studied in the presence of
different configurations of anisotropies and random fields. The model is
considered in the limit of infinite-range interactions, for which the
mean-field approach becomes exact. Both representations of Cartesian spin
components and two Ising variables are used, in terms of which the physical
properties and phase diagrams are discussed. The random fields follow bimodal
probability distributions and the richest criticality is found when the fields,
applied in the two Ising systems, are not correlated. The phase diagrams
present new interesting topologies, with a wide variety of critical
points,which are expected to be useful in describing different complex
phenomena.


title: Simplicial orders and chordality

abstract:
  Chordal clutters in the sense of [14] and [3] are defined via simplicial
orders. Their circuit ideal has a linear resolution, independent of the
characteristic of the base field. We show that any Betti sequence of an ideal
with linear resolution appears as the Betti sequence of the circuit ideal of
such a chordal clutter. Associated with any simplicial order is a sequence of
integers which we call the $\lambda$-sequence of the chordal clutter. All
possible $\lambda$-sequences are characterized. They are intimately related to
the Hilbert function of a suitable standard graded $K$-algebra attached to the
chordal clutter. By the $\lambda$-sequence of a chordal clutter we determine
other numerical invariants of the circuit ideal, such as the
$\textbf{h}$-vector and the Betti numbers.


title: Three-body force for baryons from the D0-D4/D8 matrix model

abstract:
  This is an extensive work to our previous paper \cite{key-08} studied on the
D0-D4/D8 holographic system. We compute the three-body force for baryons with
the D0-D4/D8 matrix model derived in \cite{key-08} with considering the
non-zero QCD vacuum. We obtain the three-body force at short distances but
modified by the appearance of the smeared D0-branes i.e. considering the
effects from the non-trivial QCD vacuum. We firstly test our matrix model in
the case of 't Hooft instanton and then in two more realistic case: (1)
three-neutrons with averaged spins and (2) proton-proton-neutron (or
proton-neutron-proton). The three-body potential vanishes in the former case
while in two latter cases it is positive i.e. repulsive and makes sense only if
the constraint for stable baryonic state is satisfied. We require all the
baryons in our computation aligned on a line. These may indicate that the cases
in dense states of neutrons such as in neutron stars, Helium-3 or Tritium
nucleus all with the non-trivial QCD vacuum.


title: Teichm\"uller dynamics in the eyes of an algebraic geometer

abstract:
  This is an introduction to the algebraic aspect of Teichm\"uller dynamics,
with a focus on its interplay with the geometry of moduli spaces of curves as
well as recent advances in the field.


title: End-to-End Goal-Driven Web Navigation

abstract:
  We propose a goal-driven web navigation as a benchmark task for evaluating an
agent with abilities to understand natural language and plan on partially
observed environments. In this challenging task, an agent navigates through a
website, which is represented as a graph consisting of web pages as nodes and
hyperlinks as directed edges, to find a web page in which a query appears. The
agent is required to have sophisticated high-level reasoning based on natural
languages and efficient sequential decision-making capability to succeed. We
release a software tool, called WebNav, that automatically transforms a website
into this goal-driven web navigation task, and as an example, we make WikiNav,
a dataset constructed from the English Wikipedia. We extensively evaluate
different variants of neural net based artificial agents on WikiNav and observe
that the proposed goal-driven web navigation well reflects the advances in
models, making it a suitable benchmark for evaluating future progress.
Furthermore, we extend the WikiNav with question-answer pairs from Jeopardy!
and test the proposed agent based on recurrent neural networks against strong
inverted index based search engines. The artificial agents trained on WikiNav
outperforms the engined based approaches, demonstrating the capability of the
proposed goal-driven navigation as a good proxy for measuring the progress in
real-world tasks such as focused crawling and question-answering.


title:
Recovery guarantee of weighted low-rank approximation via alternating
  minimization

abstract:
  Many applications require recovering a ground truth low-rank matrix from
noisy observations of the entries, which in practice is typically formulated as
a weighted low-rank approximation problem and solved by non-convex optimization
heuristics such as alternating minimization. In this paper, we provide provable
recovery guarantee of weighted low-rank via a simple alternating minimization
algorithm. In particular, for a natural class of matrices and weights and
without any assumption on the noise, we bound the spectral norm of the
difference between the recovered matrix and the ground truth, by the spectral
norm of the weighted noise plus an additive error that decreases exponentially
with the number of rounds of alternating minimization, from either
initialization by SVD or, more importantly, random initialization. These
provide the first theoretical results for weighted low-rank via alternating
minimization with non-binary deterministic weights, significantly generalizing
those for matrix completion, the special case with binary weights, since our
assumptions are similar or weaker than those made in existing works.
Furthermore, this is achieved by a very simple algorithm that improves the
vanilla alternating minimization with a simple clipping step.
  The key technical challenge is that under non-binary deterministic weights,
na\"ive alternating steps will destroy the incoherence and spectral properties
of the intermediate solutions, which are needed for making progress towards the
ground truth. We show that the properties only need to hold in an average sense
and can be achieved by the clipping step.
  We further provide an alternating algorithm that uses a whitening step that
keeps the properties via SDP and Rademacher rounding and thus requires weaker
assumptions. This technique can potentially be applied in some other
applications and is of independent interest.


title: DOLPHIn - Dictionary Learning for Phase Retrieval

abstract:
  We propose a new algorithm to learn a dictionary for reconstructing and
sparsely encoding signals from measurements without phase. Specifically, we
consider the task of estimating a two-dimensional image from squared-magnitude
measurements of a complex-valued linear transformation of the original image.
Several recent phase retrieval algorithms exploit underlying sparsity of the
unknown signal in order to improve recovery performance. In this work, we
consider such a sparse signal prior in the context of phase retrieval, when the
sparsifying dictionary is not known in advance. Our algorithm jointly
reconstructs the unknown signal - possibly corrupted by noise - and learns a
dictionary such that each patch of the estimated image can be sparsely
represented. Numerical experiments demonstrate that our approach can obtain
significantly better reconstructions for phase retrieval problems with noise
than methods that cannot exploit such "hidden" sparsity. Moreover, on the
theoretical side, we provide a convergence result for our method.


title: Near equipartitions of colored point sets

abstract:
  Suppose that $nk$ points in general position in the plane are colored red and
blue, with at least $n$ points of each color. We show that then there exist $n$
pairwise disjoint convex sets, each of them containing $k$ of the points, and
each of them containing points of both colors. We also show that if $P$ is a
set of $n(d+1)$ points in general position in $\mathbb{R}^d$ colored by $d$
colors with at least $n$ points of each color, then there exist $n$ pairwise
disjoint $d$-dimensional simplices with vertices in $P$, each of them
containing a point of every color. These results can be viewed as a step
towards a common generalization of several previously known geometric
partitioning results regarding colored point sets.


title:
Achieving the Dispatchability of Distribution Feeders through Prosumers
  Data Driven Forecasting and Model Predictive Control of Electrochemical
  Storage

abstract:
  We propose and experimentally validate a control strategy to dispatch the
operation of a distribution feeder interfacing heterogeneous prosumers by using
a grid-connected battery energy storage system (BESS) as a controllable element
coupled with a minimally invasive monitoring infrastructure. It consists in a
two-stage procedure: day-ahead dispatch planning, where the feeder 5-minute
average power consumption trajectory for the next day of operation (called
\emph{dispatch plan}) is determined, and intra-day/real-time operation, where
the mismatch with respect to the \emph{dispatch plan} is corrected by applying
receding horizon model predictive control (MPC) to decide the BESS
charging/discharging profile while accounting for operational constraints. The
consumption forecast necessary to compute the \emph{dispatch plan} and the
battery model for the MPC algorithm are built by applying adaptive data driven
methodologies. The discussed control framework currently operates on a daily
basis to dispatch the operation of a 20~kV feeder of the EPFL university campus
using a 750~kW/500~kWh lithium titanate BESS.


title:
Unexpected phonon-transport properties of stanene among 2D group-IV
  materials from \textit{ab initio}

abstract:
  It has been argued that stanene has lowest lattice thermal conductivity among
2D group-IV materials because of largest atomic mass, weakest interatomic
bonding, and enhanced ZA phonon scattering due to the breaking of an
out-of-plane symmetry selection rule. However, we show that although the
lattice thermal conductivity $\kappa$ for graphene, silicene and germanene
decreases monotonically with decreasing Debye temperature, unexpected higher
$\kappa$ is observed in stanene. By enforcing all the invariance conditions in
2D materials and including Ge $3d$ and Sn $4d$ electrons as valence electrons
for germanene and stanene respectively, the lattice dynamics in these materials
are accurately described. A large acoustic-optical gap and the bunching of the
acoustic phonon branches significantly reduce phonon scattering in stanene,
leading to higher thermal conductivity than germanene. The vibrational origin
of the acoustic-optical gap can be attributed to the buckled structure.
Interestingly, a buckled system has two competing influences on phonon
transport: the breaking of the symmetry selection rule leads to reduced thermal
conductivity, and the enlarging of the acoustic-optical gap results in enhanced
thermal conductivity. The size dependence of thermal conductivity is
investigated as well. In nanoribbons, the $\kappa$ of silicene, germanene and
stanene is much less sensitive to size effect due to their short intrinsic
phonon mean free paths. This work sheds light on the nature of phonon transport
in buckled 2D materials.


title: Harmonic volume and its applications

abstract:
  The period is a classical complex analytic invariant for a compact Riemann
surface defined by integration of differential 1-forms. It has a strong
relationship with the complex structure of the surface. In this chapter, we
review another complex analytic invariant called the harmonic volume. It is a
natural extension of the period defined using Chen's iterated integrals and
captures more detailed information of the complex structure. It is also one of
a few explicitly computable examples of complex analytic invariants. As an
application, we give an algorithm in proving nontriviality for a class of
homologically trivial algebraic cycles obtained from special compact Riemann
surfaces. The moduli space of compact Riemann surfaces is the space of all
biholomorphism classes of compact Riemann surfaces. The harmonic volume can be
regarded as an analytic section of a local system on the moduli space. It
enables a quantitative study of the local structure of the moduli space. We
explain basic concepts related to the harmonic volume and its applications of
the moduli space.


title: Secure and Dependable Virtual Network Embedding

abstract:
  One of the fundamental problems in network virtualization is Virtual Network
Embedding (VNE). The VNE problem deals with finding an effective mapping of the
virtual nodes & links onto the substrate network. The recent advances in
network virtualization gave cloud operators the ability to extend their cloud
computing offerings with virtual networks. This trend, jointly with the
increasing evidence of incidents in cloud facilities demonstrate that security
and dependability is becoming a critical factor that should be considered by
VNE algorithms. In this abstract we propose a VNE solution that considers
security and dependability as first class citizens. The resiliency properties
of our solution are enhanced by assuming a multiple cloud provider model.


title:
Riemann-Stieltjes integrals driven by irregular signals in Banach spaces
  and rate-independent characteristics of their irregularity

abstract:
  We prove an inequality of the Lo\'{e}ve-Young type for the Riemann-Stieltjes
integrals driven by irregular signals attaining their values in Banach spaces
and, as a result, we derive a new theorem on the existence of the
Riemann-Stieltjes integrals driven by such signals. Also, for any $p\ge1$ we
introduce the space of regulated signals $f:[a,b] \rightarrow W$ ($a<b$ are
real numbers and $W$ is a Banach space), which may be uniformly approximated
with accuracy $\delta>0$ by signals whose total variation is of order
$\delta^{1-p}$ as $\delta\rightarrow 0+$ and prove that they satisfy the
assumptions of the theorem. Finally, we derive more exact, rate-independent
characterisations of the irregularity of the integrals driven by such signals.


title: Refining the taming of the Reverse Mathematics zoo

abstract:
  Reverse Mathematics is a program in the foundations of mathematics. It
provides an elegant classification in which the majority of theorems of
ordinary mathematics fall into only five categories, based on the 'Big Five'
logical systems. Recently, a lot of effort has been directed towards finding
exceptional theorems, i.e. which fall outside the Big Five. The so-called
Reverse Mathematics zoo is a collection of such exceptional theorems (and their
relations). It was shown in [17] that a number of uniform versions of the
zoo-theorems, i.e. where a functional computes the objects stated to exist,
fall in the third Big Five category arithmetical comprehension, inside
Kohlenbach's higher-order Reverse Mathematics. In this paper, we extend and
refine the results from [17]. In particular, we establish analogous results for
recent additions to the Reverse Mathematics zoo, thus establishing that the
latter disappear at the uniform level. Furthermore, we show that the
aforementioned equivalences can be proved using only intuitionistic logic.
Perhaps most surprisingly, these explicit equivalences are extracted from
nonstandard equivalences in Nelson's internal set theory, and we show that the
nonstandard equivalence can be recovered from the explicit ones.


title: On equality of ranks of local components of automorphic representations

abstract:
  We prove that the local components of an automorphic representation of an
adelic semisimple group have equal rank in the sense defined earlier by the
second author. Our theorem is an analogue of the results previously obtained by
Howe, Li, Dvorsky--Sahi, and Kobayashi--Savin. Unlike previous works which are
based on explicit matrix realizations and existence of parabolic subgroups with
abelian unipotent radicals, our proof works uniformly for all of the (classical
as well as exceptional) groups under consideration. Our result is an extension
of the statement known for several semisimple groups that if at least one local
component of an automorphic representation is a minimal representation, then
all of its local components are minimal.


title:
Images de repr\'esentations galoisiennes associ\'ees \`a certaines
  formes modulaires de Siegel de genre $2$

abstract:
  We study the image of the $\ell$-adic Galois representations associated to
the four vector valued Siegel modular forms appearing in the work of Chenevier
and Lannes. These representations are symplectic of dimension $4$. Following a
method of Dieulefait, we determine the primes $\ell$ for which these
representations are absolutely irreducible. In addition, we show that their
image is "full" for all primes $\ell$ such that the associated residual
representation is absolutely irreducible, except in two cases.


title:
The Riemann-Hilbert mapping for $\mathfrak{sl}_2$ -systems over genus
  two curves

abstract:
  We prove in two different ways that the monodromy map from the space of
irreducible $\mathfrak{sl}_2$-differential-systems on genus two Riemann
surfaces, towards the character variety of $\mathrm{SL}_2$-representations of
the fundamental group, is a local diffeomorphism. This is motivated by a
question raised by \'Etienne Ghys about Margulis' problem: existence of curves
of negative Euler characteristic in compact quotients of
$\mathrm{SL}_2(\mathbb{C})$.


title:
The physical and chemical structure of Sagittarius B2, I.
  Three-dimensional thermal dust and free-free continuum modeling on 100 au to
  45 pc scales

abstract:
  We model the dust and free-free continuum emission in the high-mass
star-forming region Sagittarius B2 in order to reconstruct the
three-dimensional density and dust temperature distribution, as a crucial input
to follow-up studies of the gas velocity field and molecular abundances. We
employ the three-dimensional radiative transfer program RADMC-3D to calculate
the dust temperature self-consistently, provided a given initial density
distribution. This density distribution of the entire cloud complex is then
recursively reconstructed based on available continuum maps, including both
single-dish and high-resolution interferometric maps covering a wide frequency
range (40 GHz - 4 THz). The model covers spatial scales from 45 pc down to 100
au, i.e. a spatial dynamic range of 10^5.
  We find that the density distribution of Sagittarius B2 can be reasonably
well fitted by applying a superposition of spherical cores with Plummer-like
density profiles. In order to reproduce the spectral energy distribution, we
position Sgr B2(N) along the line of sight behind the plane containing Sgr
B2(M). We find that the entire cloud complex comprises a total gas mass of 8.0
x 10^6 Msun within a diameter of 45 pc, corresponding to an averaged gas
density of 170 Msun/pc^3. We estimate stellar masses of 2400 Msun and 20700
Msun and luminosities of 1.8 x 10^6 Lsun and 1.2 x 10^7 Lsun for Sgr B2(N) and
Sgr B2(M), respectively. We report H_2 column densities of 2.9 x 10^24 cm^-2
for Sgr B2(N) and 2.5 x 10^24 cm^-2 for Sgr B2(M) in a 40" beam. For Sgr B2(S),
we derive a stellar mass of 1100 Msun, a luminosity of 6.6 x 10^5 Lsun and a
H_2 column density of 2.2 x 10^24 cm^-2 in a 40" beam. We calculate a star
formation efficiency of 5% for Sgr B2(N) and 50% for Sgr B2(M), indicating that
most of the gas content in Sgr B2(M) has already been converted to stars or
dispersed.


title:
Meta-stable low-level accretion rate states or neutron star crust
  cooling in the Be/X-ray transients V0332+53 and 4U 0115+63

abstract:
  The Be/X-ray transients V0332+53 and 4U 0115+63 exhibited giant, type-II
outbursts in 2015. Here we present Swift/XRT follow-up observations at the end
of those outbursts. Surprisingly, the sources did not decay back to their known
quiescent levels but stalled at a (slowly decaying) meta-stable state with
luminosities ~10 times that observed in quiescence. The spectra in these states
are considerably softer than the outburst spectra and appear to soften in time
when the luminosity decreases. The physical mechanism behind these meta-stable
states is unclear and they could be due to low-level accretion (either directly
onto the neutron stars or onto their magnetospheres) or due to cooling of the
accretion-heated neutron star crusts. Based on the spectra, the slowly
decreasing luminosities, and the spectral softening, we favour the crust
cooling hypothesis but we cannot exclude the accretion scenarios. On top of
this meta-stable state, weak accretion events were observed that occurred at
periastron passage and may thus be related to regular type-I outbursts.


title: First results of the CALICE SDHCAL technological prototype

abstract:
  The CALICE Semi-Digital Hadronic Calorimeter (SDHCAL) prototype, built in
2011, was exposed to beams of hadrons, electrons and muons in two short periods
in 2012 on two different beam lines of the CERN SPS. The prototype with its 48
active layers, made of Glass Resistive Plate Chambers and their embedded
readout electronics, was run in triggerless and power-pulsing mode. The
performance of the SDHCAL during the test beam was found to be very
satisfactory with an efficiency exceeding 90% for almost all of the 48 active
layers. A linear response (within 5%) and a good energy resolution are obtained
for a large range of hadronic energies (5-80GeV) by applying appropriate
calibration coefficients to the collected data for both the Digital (Binary)
and the Semi-Digital (Multi-threshold) modes of the SDHCAL prototype. The
Semi-Digital mode shows better performance at energies exceeding 30GeV


title: Chemical and nuclear catalysis driven by localized anharmonic vibrations

abstract:
  In many-body nonlinear systems with sufficient anharmonicity, a special kind
of lattice vibrations, namely, Localized Anharmonic Vibrations (LAV) can be
excited either thermally or by external triggering, in which the amplitude of
atomic oscillations greatly exceeds that of harmonic oscillations (phonons)
that determine the system temperature. Coherency and persistence of LAV may
have drastic effect on chemical and nuclear reaction rates due to time-periodic
modulation of reaction sites. One example is a strong acceleration of chemical
reaction rates driven by thermally-activated "jumps" over the reaction barrier
due to the time-periodic modulation of the barrier height in the LAV vicinity.
At sufficiently low temperatures, the reaction rate is controlled by quantum
tunneling through the barrier rather than by classical jumping over it. A giant
increase of sub-barrier transparency was demonstrated for a parabolic potential
well with the time-periodic eigenfrequency, when the modulation frequency
exceeds the eigenfrequency by a factor of ~2 (parametric regime). Such regime
can be realized for a hydrogen or deuterium atom in metal hydrides/deuterides,
such as NiH or PdD, in the vicinity of LAV. We present an analytical solution
of the Schrodinger equation for a nonstationary harmonic oscillator, analyze
the parametric regime in details and discuss its applications to the tunnel
effect and to D-D fusion in PdD lattice. We obtain simple analytical
expressions for the increase of amplitude and energy of zero-point oscillations
(ZPO) induced by the parametric modulation. Based on that, we demonstrate a
drastic increase of the D-D fusion rate with in-creasing number of modulation
periods evaluated in the framework of Schwinger model, which takes into account
suppression of the Coulomb barrier due to lattice vibrations.


title:
An organizing principle for two-dimensional strongly correlated
  superconductivity

abstract:
  Superconductivity in the cuprates exhibits many unusual features. We study
the two-dimensional Hubbard model with plaquette dynamical mean-field theory to
address these unusual features and relate them to other normal-state phenomena,
such as the pseudogap. Previous studies with this method found that upon doping
the Mott insulator at low temperature a pseudogap phase appears. The
low-temperature transition between that phase and the correlated metal at
higher doping is first-order. A series of crossovers emerge along the Widom
line extension of that first-order transition in the supercritical region. Here
we show that the highly asymmetric dome of the dynamical mean-field
superconducting transition temperature $T_c^d$, the maximum of the condensation
energy as a function of doping, the correlation between maximum $T_c^d$ and
normal-state scattering rate, the change from potential-energy driven to
kinetic-energy driven pairing mechanisms can all be understood as remnants of
the normal state first-order transition and its associated crossovers that also
act as an organizing principle for the superconducting state.


title:
An algorithm for approximating the second moment of the normalizing
  constant estimate from a particle filter

abstract:
  We propose a new algorithm for approximating the non-asymptotic second moment
of the marginal likelihood estimate, or normalizing constant, provided by a
particle filter. The computational cost of the new method is $O(M)$ per time
step, independently of the number of particles $N$ in the particle filter,
where $M$ is a parameter controlling the quality of the approximation. This is
in contrast to $O(MN)$ for a simple averaging technique using $M$ i.i.d.
replicates of a particle filter with $N$ particles. We establish that the
approximation delivered by the new algorithm is unbiased, strongly consistent
and, under standard regularity conditions, increasing $M$ linearly with time is
sufficient to prevent growth of the relative variance of the approximation,
whereas for the simple averaging technique it can be necessary to increase $M$
exponentially with time in order to achieve the same effect. Numerical examples
illustrate performance in the context of a stochastic Lotka\textendash Volterra
system and a simple AR(1) model.


title:
Pseudogap and superconductivity in two-dimensional doped charge-transfer
  insulators

abstract:
  High-temperature superconductivity emerges in the CuO$_2$ plane upon doping a
Mott insulator. To ascertain the influence of Mott physics plus short-range
correlations, we solve a three-band copper-oxide model in the charge-transfer
regime using cellular dynamical mean-field theory with continuous-time quantum
Monte Carlo as an impurity solver. We report the normal and superconducting
phase diagram of this model as a function of doping, interaction strength and
temperature. Upon hole doping of the charge-transfer insulator, the phase
boundary between pseudogap and correlated metal consists of a first-order
transition line at finite doping ending at a critical point, as in the one-band
model. Beyond the endpoint, the phase boundary continues as a Widom crossover
line, across which thermodynamic quantities peak. This phase boundary
determines changes in the pairing mechanism and is an emergent phenomenon
characteristic of doped Mott insulators, independent of many microscopic
details. Broader implications are discussed.


title: Universal wavenumber selection laws in apical growth

abstract:
  We study pattern-forming dissipative systems in growing domains. We
characterize classes of boundary conditions that allow for defect-free growth
and derive universal scaling laws for the wavenumber in the bulk of the domain.
Scalings are based on a description of striped patterns in semi-bounded domains
via strain-displacement relations. We compare predictions with direct
simulations in the Swift-Hohenberg, the Complex Ginzburg-Landau, the
Cahn-Hilliard, and reaction-diffusion equations.


title: Ladder Variational Autoencoders

abstract:
  Variational Autoencoders are powerful models for unsupervised learning.
However deep models with several layers of dependent stochastic variables are
difficult to train which limits the improvements obtained using these highly
expressive models. We propose a new inference model, the Ladder Variational
Autoencoder, that recursively corrects the generative distribution by a data
dependent approximate likelihood in a process resembling the recently proposed
Ladder Network. We show that this model provides state of the art predictive
log-likelihood and tighter log-likelihood lower bound compared to the purely
bottom-up inference in layered Variational Autoencoders and other generative
models. We provide a detailed analysis of the learned hierarchical latent
representation and show that our new inference model is qualitatively different
and utilizes a deeper more distributed hierarchy of latent variables. Finally,
we observe that batch normalization and deterministic warm-up (gradually
turning on the KL-term) are crucial for training variational models with many
stochastic layers.


title: Importance Sampling for Minibatches

abstract:
  Minibatching is a very well studied and highly popular technique in
supervised learning, used by practitioners due to its ability to accelerate
training through better utilization of parallel processing power and reduction
of stochastic variance. Another popular technique is importance sampling -- a
strategy for preferential sampling of more important examples also capable of
accelerating the training process. However, despite considerable effort by the
community in these areas, and due to the inherent technical difficulty of the
problem, there is no existing work combining the power of importance sampling
with the strength of minibatching. In this paper we propose the first {\em
importance sampling for minibatches} and give simple and rigorous complexity
analysis of its performance. We illustrate on synthetic problems that for
training data of certain properties, our sampling can lead to several orders of
magnitude improvement in training time. We then test the new sampling on
several popular datasets, and show that the improvement can reach an order of
magnitude.


title:
The number of unimodular zeros of self-reciprocal polynomials with
  coefficients in a finite set

abstract:
  We study the number of real zeros of trigonometric polynomials in a period
and the number of zeros of self-reciprocal algebraic polynomials on the unit
circle under the assumption that their coefficients are in a fixed finite set
of real numbers.


title: A Deep Learning Approach to Unsupervised Ensemble Learning

abstract:
  We show how deep learning methods can be applied in the context of
crowdsourcing and unsupervised ensemble learning. First, we prove that the
popular model of Dawid and Skene, which assumes that all classifiers are
conditionally independent, is {\em equivalent} to a Restricted Boltzmann
Machine (RBM) with a single hidden node. Hence, under this model, the posterior
probabilities of the true labels can be instead estimated via a trained RBM.
Next, to address the more general case, where classifiers may strongly violate
the conditional independence assumption, we propose to apply RBM-based Deep
Neural Net (DNN). Experimental results on various simulated and real-world
datasets demonstrate that our proposed DNN approach outperforms other
state-of-the-art methods, in particular when the data violates the conditional
independence assumption.


title:
Statistical-noise reduction in correlation analysis of high-energy
  nuclear collisions with event-mixing

abstract:
  The error propagation and statistical-noise reduction method of Reid and
Trainor for two-point correlation applications in high-energy collisions is
extended to include particle-pair references constructed by mixing two
particles from all event-pair combinations within event subsets of arbitrary
size. The Reid-Trainor method is also applied to other particle-pair mixing
algorithms commonly used in correlation analysis of particle production from
high-energy nuclear collisions. The statistical-noise reduction, inherent in
the Reid-Trainor event-mixing procedure, is shown to occur for these other
event-mixing algorithms as well. Monte Carlo simulation results are presented
which verify the predicted degree of noise reduction. In each case the final
errors are determined by the bin-wise particle-pair number, rather than by the
bin-wise single-particle count.


title:
The off-centered Seyfert-like compact emission in the nuclear region of
  NGC 3621

abstract:
  We analyze an optical data cube of the nuclear region of NGC 3621, taken with
the integral field unit of the Gemini Multi-object Spectrograph. We found that
the previously detected central line emission in this galaxy actually comes
from a blob, located at a projected distance of 2.14" +/- 0.08" (70.1 +/- 2.6
pc) from the stellar nucleus. Only diffuse emission was detected in the rest of
the field of view, with a deficit of emission at the position of the stellar
nucleus. Diagnostic diagram analysis reveals that the off-centered emitting
blob has a Seyfert 2 spectrum. We propose that the line-emitting blob may be a
"fossil" emission-line region or a light "echo" from an active galactic nucleus
(AGN), which was significantly brighter in the past. Our estimates indicate
that the bolometric luminosity of the AGN must have decreased by a factor of
~13 - 500 during the last ~230 years. A second scenario to explain the
morphology of the line-emitting areas in the nuclear region of NGC 3621
involves no decrease of the AGN bolometric luminosity and establishes that the
AGN is highly obscured toward the observer but not toward the line-emitting
blob. The third scenario proposed here assumes that the off-centered
line-emitting blob is a recoiling supermassive black hole, after the
coalescence of two black holes. Finally, an additional hypothesis is that the
central X-ray source is not an AGN, but an X-ray binary. This idea is
consistent with all the scenarios we proposed.


title:
Role of surface termination in realizing well-isolated topological
  surface states within the bulk band gap in TlBiSe$_2$ and TlBiTe$_2$

abstract:
  Electronic structures associated with the flat (polar) Se/Te- or
Tl-terminated surfaces of TlBiSe$_2$ and TlBiTe$_2$ are predicted to harbor not
only Dirac cone states, but also trivial dangling bond states near the Fermi
energy. However, the latter, trivial states have never been observed in
photoemission measurements. In order to address this discrepancy, we have
carried out {\it ab-initio} calculations for various surfaces of TlBiSe$_2$ and
TlBiTe$_2$. A rough nonpolar surface with an equal number of Se/Te and Tl atoms
in the surface atomic layer is found to destroy the trivial dangling bond
states, leaving only the Dirac cone states in the bulk energy gap. The
resulting energy dispersions of the Dirac states are in good accord with the
corresponding experimental dispersions in TlBiSe$_2$ as well as TlBiTe$_2$. We
also show that in the case of flat, Se terminated, high-index (221) and (112)
surfaces of TlBiSe$_2$, the trivial surface states shift energetically below
the Dirac node and become well-separated from the Dirac cone states.


title: Embedding tetrahedra into quasirandom hypergraphs

abstract:
  We investigate extremal problems for quasirandom hypergraphs. We say that a
$3$-uniform hypergraph $H=(V,E)$ is $(d,\eta)$-quasirandom if for any subset
$X\subseteq V$ and every set of pairs $P\subseteq V\times V$ the number of
pairs $(x,(y,z))\in X\times P$ with $\{x,y,z\}$ being a hyperedge of $H$ is in
the interval $d|X||P|\pm\eta|V|^3$. We show that for any $\varepsilon>0$ there
exists $\eta>0$ such that every sufficiently large
$(1/2+\varepsilon,\eta)$-quasirandom hypergraph contains a tetrahedron, i.e.,
four vertices spanning all four hyperedges. A known random construction shows
that the density $1/2$ is best possible. This result is closely related to a
question of Erd\H{o}s, whether every weakly quasirandom $3$-uniform hypergraph
$H$ with density bigger than $1/2$, i.e., every large subset of vertices
induces a hypergraph with density bigger than $1/2$, contains a tetrahedron.