title: Entropy product of rotating black holes in three-dimensions

abstract:
  It has been shown that the product of the entropies of the inner Cauchy and
outer event horizon of the charged axisymmetric and stationary black holes is a
universal formula, which is independent of the black hole's mass. In this
paper, we investigate this universality for the two kinds of rotating black
holes in the three-dimensional gravity models. In fact, we study the spacelike
warped anti-de Sitter black hole in the new massive gravity and the Ba~nados,
Teitelboim, and Zanelli black hole in the minimal massive gravity. We show that
this rule is held in the first theory. By contrast, in the latter case which
includes a holographic gravitational anomalous term, we obtain that the
universality does not work and the product depends on the mass. As a complement
to the above verification, we also study the thermodynamic properties of these
black holes.


title: Nonlocality in Remote State Preparation vis-a-vis Teleportation

abstract:
  The hitherto unexplored nonlocality of quantum correlations in the
information transfer protocol of remote state preparation (RSP) is investigated
in terms of a unified nonlocality argument formulated for teleportation as well
as for two distinct RSP schemes. The argument differs only in the respective
types of local measurements used in each scenario. One of the RSP schemes uses
single particle projective measurements, while the other uses joint Bell-basis
measurements. Interestingly, the quantum mechanical violations of the Bell-CHSH
type inequalities formulated for each of the RSP setups, while being equal to
each other, also turn out to be equal to that of the corresponding Bell-CHSH
type local realist inequality for teleportation, using the common resource of
non-maximally entangled state. This reveals that for such a resource state, the
maximum amount of extractable nonlocality of correlations involved in the
transfer of information is the same for the standard teleportation protocol and
the two RSP schemes considered here, thereby implying that the essential
difference between teleportation and remote state preparation lies in the
amount of classical information required to be exchanged between parties, and
not in the nonlocality of underlying correlations.


title: The equilibrium measure for a nonlocal dislocation energy

abstract:
  In this paper we characterise the equilibrium measure for a nonlocal and
anisotropic weighted energy describing the interaction of positive dislocations
in the plane. We prove that the minimum value of the energy is attained by a
measure supported on the vertical axis and distributed according to the
semi-circle law, a well-known measure which also arises as the minimiser of
purely logarithmic interactions in one dimension. In this way we give a
positive answer to the conjecture that positive dislocations tend to form
vertical walls. This result is one of the few examples where the minimiser of a
nonlocal energy is explicitly computed and the only one in the case of
anisotropic kernels.


title: Approximations and Mittag-Leffler conditions --- the tools

abstract:
  Mittag-Leffler modules occur naturally in algebra, algebraic geometry, and
model theory, [18], [12], [17]. If $R$ is a non-right perfect ring, then it is
known that in contrast with the classes of all projective and flat modules, the
class of all flat Mittag-Leffler modules is not deconstructible [14], and it
does not provide for approximations when $R$ has cardinality $\leq \aleph_0$,
[6]. We remove the cardinality restriction on $R$ in the latter result. We also
prove an extension of the Countable Telescope Conjecture [21]: a cotorsion pair
$(\mathcal A,\mathcal B)$ is of countable type whenever the class $\mathcal B$
is closed under direct limits.
  In order to prove these results, we develop new general tools combining
relative Mittag-Leffler conditions with set-theoretic homological algebra. They
make it possible to trace the facts above to their ultimate, countable, origins
in the properties of Bass modules. These tools have already found a number of
applications: e.g., they yield a positive answer to Enochs' problem on module
approximations for classes of modules associated with tilting [4], and enable
investigation of new classes of flat modules occurring in algebraic geometry
[24]. Finally, the ideas from Section 3 have led to the solution of a
long-standing problem due to Auslander on the existence of right almost split
maps [20].


title:
Giant Metrewave Radio Telescope detection of associated HI 21cm
  absorption at $z = 1.2230$ towards TXS1954+513

abstract:
  We have used the 610 MHz receivers of the Giant Metrewave Radio Telescope
(GMRT) to detect associated HI 21cm absorption from the $z = 1.2230$ blazar
TXS1954+513. The GMRT HI 21cm absorption is likely to arise against either the
milli-arcsecond-scale core or the one-sided milli-arcsecond-scale radio jet,
and is blueshifted by $\approx 328$ km s$^{-1}$ from the blazar redshift. This
is consistent with a scenario in which the HI cloud giving rise to the
absorption is being driven outward by the radio jet. The integrated HI 21cm
optical depth is $(0.716 \pm 0.037)$ km s$^{-1}$, implying a high HI column
density, $N_{\rm HI} = (1.305 \pm 0.067) \times ({\rm T_s/100\: K}) \times
10^{20}$ cm$^{-2}$, for an assumed HI spin temperature of 100 K. We use Nickel
Telescope photometry of TXS1954+513 to infer a high rest-frame 1216 \AA\
luminosity of $(4.1 \pm 1.2) \times 10^{23}$ W Hz$^{-1}$. The $z = 1.2230$
absorber towards TXS1954+513 is only the fifth case of a detection of
associated HI 21cm absorption at $z > 1$, and is also the first case of such a
detection towards an active galactic nucleus (AGN) with a rest-frame
ultraviolet luminosity $\gg 10^{23}$ W Hz$^{-1}$, demonstrating that neutral
hydrogen can survive in AGN environments in the presence of high ultraviolet
luminosities.


title: Approximations and Mittag-Leffler conditions --- the applications

abstract:
  A classic result by Bass says that the class of all projective modules is
covering, if and only if it is closed under direct limits. Enochs extended the
if-part by showing that every class of modules $\mathcal C$, which is
precovering and closed under direct limits, is covering, and asked whether the
converse is true. We employ the tools developed in [18] and give a positive
answer when $\mathcal C = \mathcal A$, or $\mathcal C$ is the class of all
locally $\mathcal A ^{\leq \omega}$-free modules, where $\mathcal A$ is any
class of modules fitting in a cotorsion pair $(\mathcal A, \mathcal B)$ such
that $\mathcal B$ is closed under direct limits. This setting includes all
cotorsion pairs and classes of locally free modules arising in
(infinite-dimensional) tilting theory. We also consider two particular
applications: to pure-semisimple rings, and artin algebras of infinite
representation type.


title: Multiranks and classical theta functions

abstract:
  Multiranks and new rank/crank analogs for a variety of partitions are given,
so as to imply combinatorially some arithmetic properties enjoyed by these
types of partitions. Our methods are elementary relying entirely on the three
classical theta functions, and are motivated by the seminal work of Ramanujan,
Garvan, Hammond and Lewis.


title: Abrikosov vortices in SF bilayers

abstract:
  We study the spatial distribution of supercurrent circulated around an
Abrikosov vortex in an SF bilayer in perpendicular magnetic field. Within the
dirty limit regime and circular cell approximation for the vortex lattice, we
derive the conditions when the Usadel equations the F layer can be solved
analytically. Using the obtained solutions, we demonstrate the possibility of
reversal of direction of proximity induced supercurrents around the vortex in
the F layer compared to that in the S-layer. The direction of currents can be
controlled either by varying transparency of the SF interface or by changing an
exchange field in a ferromagnet. We argue that the origin of this effect is due
the phase shift between singlet and triplet order parameter components induced
in the F-layer. Possible ways of experimental detection of the predicted effect
are discussed.


title: A note on the binary additive divisor problem

abstract:
  In this note we show that the methods of Motohashi and Meurman yield the same
upper bound on the error term in the binary additive divisor problem. With this
goal, we improve an estimate in the proof of Motohashi.


title: Flexible affine cones and flexible coverings

abstract:
  We provide a new criterion for flexibility of cones over varieties covered by
flexible affine varieties. We apply this criterion to prove flexibility of
affine cones over secant varieties of Segre--Veronese embeddings and over
certain Fano threefolds. We further prove flexibility of total coordinate
spaces of Cox rings of del Pezzo surfaces.


title: Garling sequence spaces

abstract:
  By generalizing a construction of Garling, for each $1\leqslant p<\infty$ and
each normalized, nonincreasing sequence of positive numbers $w\in
c_0\setminus\ell_1$ we exhibit an $\ell_p$-saturated, complementably
homogeneous Banach space $g(w,p)$ related to the Lorentz sequence space
$d(w,p)$. Using methods originally developed for studying $d(w,p)$, we show
that $g(w,p)$ admits a unique (up to equivalence) subsymmetric basis, although
when $w=(n^{-\theta})_{n=1}^\infty$ for some $0<\theta<1$, it does not admit a
symmetric basis. We then discuss some additional properties of $g(w,p)$ related
to uniform convexity and superreflexivity.


title: On mixing and sparse ergodic theorems

abstract:
  We consider Bourgain's ergodic theorem regarding arithmetic averages in the
cases where quantitative mixing is present in the dynamical system. Focusing on
the case of the horocyclic flow, those estimates allows us to bound from above
the Hausdorff dimension of the exceptional set, providing evidence towards
conjectures by Margulis,Shah and Sarnak regarding equidistribution of
arithmetic averages in homogeneous spaces. We also prove the existence of a
uniform upper bound for the Hausdorff dimension of the exceptional set which is
independent from the spectral gap.


title: The limits of SDP relaxations for general-valued CSPs

abstract:
  It has been shown that for a general-valued constraint language $\Gamma$ the
following statements are equivalent: (1) any instance of
$\operatorname{VCSP}(\Gamma)$ can be solved to optimality using a constant
level of the Sherali-Adams LP hierarchy; (2) any instance of
$\operatorname{VCSP}(\Gamma)$ can be solved to optimality using the third level
of the Sherali-Adams LP hierarchy; (3) the support of $\Gamma$ satisfies the
"bounded width condition", i.e., it contains weak near-unanimity operations of
all arities.
  We show that if the support of $\Gamma$ violates the bounded width condition
then not only is $\operatorname{VCSP}(\Gamma)$ not solved by a constant level
of the Sherali-Adams LP hierarchy but it is also not solved by $\Omega(n)$
levels of the Lasserre SDP hierarchy (also known as the sum-of-squares SDP
hierarchy). For $\Gamma$ corresponding to linear equations in an Abelian group,
this result follows from existing work on inapproximability of Max-CSPs. By a
breakthrough result of Lee, Raghavendra, and Steurer [STOC'15], our result
implies that for any $\Gamma$ whose support violates the bounded width
condition no SDP relaxation of polynomial-size solves
$\operatorname{VCSP}(\Gamma)$.
  We establish our result by proving that various reductions preserve exact
solvability by the Lasserre SDP hierarchy (up to a constant factor in the level
of the hierarchy). Our results hold for general-valued constraint languages,
i.e., sets of functions on a fixed finite domain that take on rational or
infinite values, and thus also hold in notable special cases of
$\{0,\infty\}$-valued languages (CSPs), $\{0,1\}$-valued languages
(Min-CSPs/Max-CSPs), and $\mathbb{Q}$-valued languages (finite-valued CSPs).


title:
Massless Dirac-like fermions under external fields: a nonminimal
  coupling approach

abstract:
  We investigate the unusual properties of quasirelativistic massless fermions
under a magnetic or electric field by means of nonminimal couplings. Within
this approach, the spin-orbit coupling (SOC) effects are properly generated in
the energy spectrum of the quasiparticles. By including a magnetic field, $B$,
we show that the spin splitting of Landau Levels (LL) obeys a $\sqrt{B}$ linear
dependence with SOC, typical of relativistic particles. Moreover, our
calculated spectrum of LLs resembles the behavior of the three-dimensional (3D)
massless Kane fermions. Using a nonminimal coupling with an external electric
field, we demonstrate that a Rashba-like SOC naturally appears into the
relativistic equations and apply to the case of two-dimensional (2D) massless
Dirac fermions. Still considering our proposed approach, the Hall conductivity
is also computed for the 2D case under transverse electric field both at zero
and finite temperatures for a general chemical potential. The results feature a
typical quantization of the Hall conductivity at low temperatures, when the
absolute value of the gap opened by the electric field is larger than the
considered chemical potential.


title:
Nikishin systems on star-like sets: Ratio asymptotics of the associated
  multiple orthogonal polynomials

abstract:
  We investigate the ratio asymptotic behavior of the sequence
$(Q_{n})_{n=0}^{\infty}$ of multiple orthogonal polynomials associated with a
Nikishin system of $p\geq 1$ measures that are compactly supported on the
star-like set of $p+1$ rays $S_{+}=\{z\in\mathbb{C}: z^{p+1}\geq 0\}$. The main
algebraic property of these polynomials is that they satisfy a three-term
recurrence relation of the form $zQ_{n}(z)=Q_{n+1}(z)+a_{n} Q_{n-p}(z)$ with
$a_{n}>0$ for all $n\geq p$. Under a Rakhmanov-type condition on the measures
generating the Nikishin system, we prove that the sequence of ratios
$Q_{n+1}(z)/Q_{n}(z)$ and the sequence $a_{n}$ of recurrence coefficients are
limit periodic with period $p(p+1)$. Our results complement some results
obtained by the first author and Mi\~{n}a-D\'{i}az in a recent paper in which
algebraic properties and weak asymptotics of these polynomials were
investigated. Our results also extend some results obtained by the first author
in the case $p=2$.


title: The grammar of mammalian brain capacity

abstract:
  Uniquely human abilities may arise from special-purpose brain circuitry, or
from concerted general capacity increases due to our outsized brains. We
forward a novel hypothesis of the relation between computational capacity and
brain size, linking mathematical formalisms of grammars with the allometric
increases in cortical-subcortical ratios that arise in large brains. In sum, i)
thalamocortical loops compute formal grammars; ii) successive cortical regions
describe grammar rewrite rules of increasing size; iii) cortical-subcortical
ratios determine the quantity of stacks in single-stack pushdown grammars; iii)
quantitative increase of stacks yields grammars with qualitatively increased
computational power. We arrive at the specific conjecture that human brain
capacity is equivalent to that of indexed grammars, far short of full
Turing-computable (recursively enumerable) systems. The work provides a
candidate explanatory account of a range of existing human and animal data,
addressing longstanding questions of how repeated similar brain algorithms can
be successfully applied to apparently dissimilar computational tasks (e.g.,
perceptual versus cognitive, phonological versus syntactic); and how
quantitative increases to brains can confer qualitative changes to their
computational repertoire.


title: ${\cal N}$ = $1$ Euler Anomaly from RG-dependent metric-Background

abstract:
  We consider ${\cal N}=1$ supersymmetric gauge theories in the conformal
window. By applying a suitable matter superfield rescaling and a
Weyl-transformation the renormalisation group running (matter and gauge field
$Z$-factors) are absorbed into the metric. The latter becomes a function of the
$Z$-factors. The Euler flow $\Delta a \equiv a_{\rm UV} - a_{\rm IR} |_{{\cal
N}=1}$ is then obtained by free field theory computation with the non-trivial
dynamics coming from expanding the Euler invariant in the flow dependent
metric. The result is therefore directly obtained in terms of the infrared
anomalous dimension confirming an earlier result using the matching of
conserved currents.


title: Global Results for Eikonal Hamilton-Jacobi Equations on Networks

abstract:
  We study a one-parameter family of Eikonal Hamilton-Jacobi equations on an
embedded network, and prove that there exists a unique critical value for which
the corresponding equation admits global solutions, in a suitable viscosity
sense. Such a solution is identified, via an Hopf-Lax type formula, once an
admissible trace is assigned on an intrinsic boundary. The salient point of our
method is to associate to the network an abstract graph, encoding all of the
information on the complexity of the network, and to relate the differential
equation to a discrete functional equation on the graph. Comparison principles
and representation formulae are proven in the supercritical case as well.


title: Closed Ideals of Operators between the Classical Sequence Spaces

abstract:
  We prove that the spaces $\mathcal L(\ell_p,\mathrm{c}_0)$, $\mathcal
L(\ell_p,\ell_\infty)$ and $\mathcal L(\ell_1,\ell_q)$ of operators with
$1<p,q<\infty$ have continuum many closed ideals. This extends and improves
earlier works by Schlumprecht and Zs\'ak, by Wallis, and by Sirotkin and
Wallis. Several open problems remain. Key to our construction of closed ideals
are matrices with the Restricted Isometry Property that come from Compressed
Sensing.


title: Weakly Broken Galileon Symmetry in Cosmology

abstract:
  In the present thesis, using an effective field theory point of view, we
explore theories of single-field inflation where higher derivative operators
become relevant, affecting in a novel way the dynamics and therefore the
observations. For instance, concerning the scalar spectrum, they allow for
measurable equilateral non-Gaussianity, whose amplitude can differ
significantly from the predictions of other existing models. Moreover, we show
that the stability and the consistency of such theories are ensured by an
approximate Galileon symmetry. Indeed, being generically possible to build an
invariant theory under Galileon transformations in flat space-time, it is
instead well known that such a symmetry is unavoidably broken by gravity. In
principle, this might ruin the nice and interesting properties of the Galileons
in flat backgrounds, such as the non-renormalization theorem. However, we find
that this does not happen if the Galileon invariance is broken only weakly, in
a well defined sense, by a suitable coupling to gravity, providing therefore an
extension of the quantum non-renormalization properties in curved space-times.
Hence, besides discussing the phenomenological consequences and the
observational predictions for inflation, we apply such Galileon theories to the
context of the late-time acceleration of the Universe. In the last part, in
order to probe non-standard primordial scenarios, they are also employed in a
cosmology where the Big Bang singularity is smoothed down and the Universe
emerges from a Minkowski space-time, in a well defined extension at all times
of the Galilean Genesis scenario.


title: A Multifaceted Panel Data Gravity Model Analysis of Peru's Foreign Trade

abstract:
  Peru's abundant natural resources and friendly trade policies has made the
country a major economic player in both South America and the global community.
Consequently, exports are playing an increasingly important role in Peru's
national economy. Indeed, growing from 13.1% as of 1994, exports now contribute
approximately 21% of the GDP of Peru as of 2015. Given Peru's growing global
influence, the time is ripe for a thorough analysis of the most important
factors governing its export performance. Thus, within the framework of the
augmented gravity model of trade, this paper examines Peru's export performance
and attempts to identify the dominant economic factors that should be further
developed to increase the value of exports. The analysis was conducted from
three different aspects: (1) general economic parameters' effect on Peru's
export value, (2) more specific analysis into a major specific trade good,
copper, and (3) the impact that regional trade agreements have had on Peru's
export performance. Our panel data analysis results for each dataset revealed
interesting economic trends and were consistent with the theoretical
expectations of the gravity model: namely positive coefficients for economic
size and negative coefficients for distance. This report's results can be a
reference for the proper direction of Peruvian economic policy so as to enhance
economic growth in a sustainable direction.


title:
One-dimensional electron gas in strained lateral heterostructures of
  single layer materials

abstract:
  Confinement of the electron gas along one of the spatial directions opens an
avenue for studying fundamentals of quantum transport along the side of
numerous practical electronic applications, with high-electron-mobility
transistors being a prominent example. A heterojunction of two materials with
dissimilar electronic polarisation can be used for engineering of the
conducting channel. Extension of this concept to single-layer materials leads
to one-dimensional electron gas (1DEG). MoS2/WS2 lateral heterostructure is
used as a prototype for the realisation of 1DEG. The electronic polarisation
discontinuity is achieved by straining the heterojunction taking advantage of
dissimilarities in the piezoelectric coupling between MoS2 and WS2. A complete
theory that describes an induced electric field profile in lateral
heterojunctions of two-dimensional materials is proposed and verified by first
principle calculations.


title: Ternary universal sums of generalized polygonal numbers

abstract:
  An integer of the form $p_m(x)= \frac{(m-2)x^2-(m-4)x}{2} \ (m\ge 3)$, for
some integer $x$ is called a generalized polygonal number of order $m$. A
ternary sum $\Phi_{i,j,k}^{a,b,c}(x,y,z)=ap_{i+2}(x)+bp_{j+2}(y)+cp_{k+2}(z)$
of generalized polygonal numbers, for some positive integers $a,b,c$ and some
integers $1\leq i\leq j \leq k$, is said to be universal over $\mathbb{Z}$ if
the equation $\Phi_{i,j,k}^{a,b,c}(x,y,z)=n$ has an integer solution $x,y,z$
for any nonnegative integer $n$. In this article, we prove the universalities
of $17$ ternary sums of generalized polygonal numbers, which was conjectured by
Sun.


title: Properties and Bayesian fitting of restricted Boltzmann machines

abstract:
  A restricted Boltzmann machine (RBM) is an undirected graphical model
constructed for discrete or continuous random variables, with two layers, one
hidden and one visible, and no conditional dependency within a layer. In recent
years, RBMs have risen to prominence due to their connection to deep learning.
By treating a hidden layer of one RBM as the visible layer in a second RBM, a
deep architecture can be created. RBMs are thought to thereby have the ability
to encode very complex and rich structures in data, making them attractive for
supervised learning. However, the generative behavior of RBMs is largely
unexplored and typical fitting methodology does not easily allow for
uncertainty quantification in addition to point estimates. In this paper, we
discuss the relationship between RBM parameter specification in the binary case
and model properties such as degeneracy, instability and uninterpretability. We
also describe the associated difficulties that can arise with likelihood-based
inference and further discuss the potential Bayes fitting of such (highly
flexible) models, especially as Gibbs sampling (quasi-Bayes) methods are often
advocated for the RBM model structure.


title: On the instability and degeneracy of deep learning models

abstract:
  A probability model exhibits instability if small changes in a data outcome
result in large, and often unanticipated, changes in probability. This
instability is a property of the probability model, given by a distributional
form and a given configuration of parameters. For correlated data structures
found in several application areas, there is increasing interest in identifying
such sensitivity in model probability structure. We consider the problem of
quantifying instability for general probability models defined on sequences of
observations, where each sequence of length N has a finite number of possible
values that can be taken at each point. A sequence of probability models
results, indexed by N, and an associated parameter sequence, that accommodates
data of expanding dimension. Model instability is formally shown to occur when
a certain log-probability ratio under such models grows faster than N. In this
case, a one component change in the data sequence can shift probability by
orders of magnitude. Also, as instability becomes more extreme, the resulting
probability models are shown to tend to degeneracy, placing all their
probability on potentially small portions of the sample space. These results on
instability apply to large classes of models commonly used in random graphs,
network analysis, and machine learning contexts.


title: General models for rational cameras and the case of two-slit projections

abstract:
  The rational camera model recently introduced in [19] provides a general
methodology for studying abstract nonlinear imaging systems and their
multi-view geometry. This paper builds on this framework to study "physical
realizations" of rational cameras. More precisely, we give an explicit account
of the mapping between between physical visual rays and image points (missing
in the original description), which allows us to give simple analytical
expressions for direct and inverse projections. We also consider "primitive"
camera models, that are orbits under the action of various projective
transformations, and lead to a general notion of intrinsic parameters. The
methodology is general, but it is illustrated concretely by an in-depth study
of two-slit cameras, that we model using pairs of linear projections. This
simple analytical form allows us to describe models for the corresponding
primitive cameras, to introduce intrinsic parameters with a clear geometric
meaning, and to define an epipolar tensor characterizing two-view
correspondences. In turn, this leads to new algorithms for structure from
motion and self-calibration.


title:
Ultrafast stratified diffusion of water inside carbon nanotubes. Direct
  experimental evidence with 2D (D-T2) NMR spectroscopy

abstract:
  Water, when confined at the nanoscale acquires extraordinary transport
properties. And yet there is no direct experimental evidence of these
properties at nanoscale resolution. Here, by using 2D NMR diffusion-relaxation
(D-T2) and spin-lattice - spin-spin relaxation (T1-T2) spectroscopy, we
succeeded to resolve at the nanoscale water diffusion in single and
double-walled carbon nanotubes (SWCNT/DWCNT). In SWCNTs, spectra display the
characteristic shape of uniform water diffusion restricted in one dimension.
Remarkably, in DWCNTs water is shown to split into two axial components with
the inner one acquiring unusual flow properties: high fragility, ultrafast
self-diffusion coefficient, and "rigid" molecular environment, revealing a
stratified cooperative motion mechanism to underlie fast diffusion in water
saturated CNTs.


title:
Early GRB afterglows from reverse shocks in ultra-relativistic
  long-lasting winds

abstract:
  We develop a model of early GRB afterglows with the dominant $X$-ray
contribution from the reverse shock (RS) propagating in highly relativistic
(Lorentz factor $\gamma_w \sim 10^6$) magnetized wind of a long-lasting central
engine. The model reproduces, in a fairly natural way, the overall trends and
yet allows for variations in the temporal and spectral evolution of early
optical and $X$-ray afterglows. The high energy and the optical synchrotron
emission from the RS particles occurs in the fast cooling regime; the resulting
synchrotron power $L_s$ is a large fraction of the wind luminosity, $L_s
\approx L_w/\sqrt{1+\sigma_w}$ ($L_w$ and $\sigma_w$ are wind power and
magnetization). Thus, plateaus - parts of afterglow light curves that show
slowly decreasing spectral power - are a natural consequence of the RS
emission. Contribution from the forward shock (FS) is negligible in the
$X$-rays, but in the optical both FS and RS contribute similarly: the FS
optical emission is in the slow cooling regime, producing smooth components,
while the RS optical emission is in the fast cooling regime, and thus can both
produce optical plateaus and account for fast optical variability correlated
with the $X$-rays, e.g., due to changes in the wind properties. We discuss how
the RS emission in the $X$-rays and combined FS and RS emission in the optical
can explain many of puzzling properties of early GRB afterglows.


title:
QoS-based Computing Resources Partitioning between Virtual Machines in
  the Cloud Architecture

abstract:
  Cloud services have been used very widely, but configuration of the
parameters, including the efficient allocation of resources, is an important
objective for the system architect. The article is devoted to solving the
problem of choosing the architecture of computers based on simulation and
developed program for monitoring computing resources. Techniques were developed
aimed at providing the required quality of service and efficient use of
resources. The article describes the monitoring program of computing resources
and time efficiency of the target application functions. On the basis of this
application the technique is shown and described in the experiment, designed to
ensure the requirements for quality of service, by isolating one process from
the others on different virtual machines inside the hypervisor.


title: The monodromy of $F$-isocrystals with log-decay

abstract:
  Let U be a smooth geometrically connected affine curve over $\mathbb{F}_p$
with compactification X. Following Dwork and Katz, a $p$-adic representation
$\rho$ of $\pi_1(U)$ corresponds to an \'etale $F$-isocrystal. By work of
Tsuzuki and Crew an $F$-isocrystal is overconvergent precisely when $\rho$ has
finite monodromy at each $x \in X-U$. However, in practice most F-isocrystals
arising geometrically are not overconvergent and have logarithmic growth at
singularities (e.g. characters of the Igusa tower over a modular curve). We
give a Galois-theoretic interpretation of these log growth $F$-isocrystals in
terms of asymptotic properties of higher ramification groups.


title:
Effects of cavity-cavity interaction on the entanglement dynamics of a
  generalized double Jaynes-Cummings model

abstract:
  We consider a generalized double Jaynes-Cummings model consisting of two
isolated two-level atoms, each contained in a lossless cavity, with the
cavities interacting with each other through a controlled photon hopping
mechanism. The temporal dynamics of entanglement between the two atoms, as the
atom-cavity system evolves with time, is investigated for different values of
the mediated cavity-cavity interaction. We analytically show that at low values
of such an interaction, entanglement between the atoms evolves under the
effects of cavity perturbation and exhibits the well-known phenomenon of
entanglement sudden death. Interestingly, using moderately large values of the
interaction, a complete preclusion of sudden death of entanglement can be
achieved, irrespective of its value in the initial two-atom state. Our results,
thus allow us to design a model to sustain bipartite entanglement between two
atomic qubits under the adverse effect of cavity induced environmental
perturbation, by introducing a non-intrusive inter-cavity photon exchange that
can be physically realized through cavity-QED setups in contemporary
experiments. For completeness, we also compare the effects of inter-cavity
interaction on entanglement with the case of direct spin-exchange interaction
between the two isolated atoms.


title:
Robust discretization in quantized tensor train format for elliptic
  problems in two dimensions

abstract:
  In this work we propose an efficient black-box solver for two-dimensional
stationary diffusion equations, which is based on a new robust discretization
scheme. The idea is to formulate an equation in a certain form without
derivatives with a non-local stencil, which leads us to a linear system of
equations with dense matrix. This matrix and a right-hand side are represented
in a low-rank parametric representation -- the quantized tensor train (QTT-)
format, and then all operations are performed with logarithmic complexity and
memory consumption. Hence very fine grids can be used, and very accurate
solutions with extremely high spatial resolution can be obtained. Numerical
experiments show that this formulation gives accurate results and can be used
up to $2^{60}$ grid points with no problems with conditioning, while total
computational time is around several seconds.


title: Heavy Flavour production as probe of Gluon Sivers Function

abstract:
  Heavy flavour production like $J/\psi$ and $D$- meson production in
scattering of electrons/unpolarized protons off polarized proton target offer
promising probes to investigate gluon Sivers function. In this talk, I will
summarize our recent work on trasverse single spin asymmetry in $J/\psi $
-production and $D$ - meson production in $p p^\uparrow$ scattering using a
generalized parton model approach. We compare predictions obtained using
different models of gluon Sivers function within this approach and then, taking
into account the transverse momentum dependent evolution of the unpolarized
parton distribution functions and gluon Sivers function, we study the effect of
evolution on asymmetry.


title:
Algebraic isomonodromic deformations of the five punctured sphere
  arising from quintic plane curves

abstract:
  In this paper, we classify the algebraic isomonodromic deformations that can
be obtained through restriction to generic lines of logarithmic flat
connections on the complex projective plane $\mathbb{P}^2_\mathbb{C}$ whose
singular locus is a quintic curve. We then explicitly compute the (finite)
finite mapping class group orbits of the associated points in the character
variety and describe the new algebraic Garnier solutions that can be obtained
through this procedure.


title: Bounds for entries of $\gamma$-vectors of flag homology spheres

abstract:
  We present some enumerative and structural results for flag homology spheres.
For a flag homology sphere $\Delta$, we show that its $\gamma$-vector
$\gamma^\Delta=(1,\gamma_1,\gamma_2,\ldots)$ satisfies: \begin{align*}
  \gamma_j=0,\text{ for all } j>\gamma_1, \quad
\gamma_2\leq\binom{\gamma_1}{2}, \quad \gamma_{\gamma_1}\in\{0,1\}, \quad
\text{ and }\gamma_{\gamma_1-1}\in\{0,1,2,\gamma_1\}, \end{align*} supporting a
conjecture of Nevo and Petersen. Further we characterize the possible
structures for $\Delta$ in extremal cases. As an application, the techniques
used produce infinitely many $f$-vectors of flag balanced simplicial complexes
that are not $\gamma$-vectors of flag homology spheres (of any dimension);
these are the first examples of this kind.
  In addition, we prove a flag analog of Perles' 1970 theorem on $k$-skeleta of
polytopes with "few" vertices, specifically: the number of combinatorial types
of $k$-skeleta of flag homology spheres with $\gamma_1\leq b$, of any given
dimension, is bounded independently of the dimension.


title: A simple AF algebra not isomorphic to its opposite

abstract:
  We show that it is consistent with ZFC that there is a simple nuclear
non-separable C*-algebra which is not isomorphic to its opposite algebra. We
can furthermore guarantee that this example is an inductive limit of unital
copies of the Cuntz algebra O_2, or of the CAR algebra.


title:
The limited blessing of low dimensionality: when $1-1/d$ is the best
  possible exponent for $d$-dimensional geometric problems

abstract:
  We are studying $d$-dimensional geometric problems that have algorithms with
$1-1/d$ appearing in the exponent of the running time, for example, in the form
of $2^{n^{1-1/d}}$ or $n^{k^{1-1/d}}$. This means that these algorithms perform
somewhat better in low dimensions, but the running time is almost the same r
all large values $d$ of the dimension. Our main result is showing that for some
of these problems the dependence on $1-1/d$ is best possible under a standard
complexity assumption. We show that, assuming the Exponential Time Hypothesis,
  --- $d$-dimensional Euclidean TSP on $n$ points cannot be solved in time
$2^{O(n^{1-1/d-\epsilon})}$ for any $\epsilon>0$, and
  --- the problem of finding a set of $k$ pairwise nonintersecting
$d$-dimensional unit balls/axis parallel unit cubes cannot be solved in time
$f(k)n^{o(k^{1-1/d})}$ for any computable function $f$.
  These lower bounds essentially match the known algorithms for these problems.
To obtain these results, we first prove lower bounds on the complexity of
Constraint Satisfaction Problems (CSPs) whose constraint graphs are
$d$-dimensional grids. We state the complexity results on CSPs in a way to make
them convenient starting points for problem-specific reductions to particular
$d$-dimensional geometric problems and to be reusable in the future for further
results of similar flavor.


title:
Clouds effect on the Atmospheric Total Column Carbon Dioxide Retrieval
  by Space Orbiting Argus 1000 Micro-spectrometer: Introductory Study

abstract:
  Carbon Dioxide (CO2) is one of the most important greenhouse gases after
water vapor (H2O) which plays significant role in the climate process. Accurate
space-based measurement of CO2 is of great significance in inferring the
location of CO2 sources and sinks. Uncertainties in greenhouse gases (GHG)
retrieval process must be minimized to accurately infer the actual amount of
the atmospheric species. Clouds pose a large uncertainty in CO2 space-based
retrieval process leading, mostly, to an underestimation in the CO2 absorption
amount above the cloud layer provided that photons do not perform multiple
paths. In this paper, three different cases of data collected over cloudy and
clear skies by Argus 1000 micro-spectrometer were analyzed. Findings show that
the CO2 absorption in the absence of clouds is approximately 4.5% higher than
when clouds are present.


title:
Analysis of nonlocal phonon thermal conductivity simulations showing the
  ballistic to diffusive crossover

abstract:
  Simulations (e.g. Zhou et al., Phys. Rev. B 79, 115201 (2009)) show nonlocal
effects of the ballistic/diffusive crossover. The local temperature has
nonlinear spatial variation not contained in the local Fourier law
$\vec{j}(\vec{r})=-\kappa\vec{\nabla}T(\vec{r})$. The heat current
$\vec{j}(\vec{r})$ depends not just on the local temperature gradient
$\vec{\nabla}T(\vec{r})$, but also on temperatures at points $\vec{r}^{ \
\prime}$ within phonon mean free paths, which can be micrometers long. This
paper uses the Peierls-Boltzmann transport theory in non-local form to analyze
the spatial variation $\Delta T(\vec{r})$. The relaxation-time approximation
(RTA) is used because full solution is very challenging. Improved methods of
extrapolation to obtain the bulk thermal conductivity $\kappa$ are proposed.
Callaway invented an approximate method of correcting RTA for the $\vec{q}$
(phonon wavevector or crystal momentum) conservation of N (normal as opposed to
Umklapp) anharmonic collisions This method is generalized to the non-local case
where $\kappa(\vec{k})$ depends on wavevector of the current $\vec{j}(\vec{k})$
and temperature gradient $i\vec{k}\Delta T(\vec{k})$.


title: On nonlinear fractional maps: Nonlinear maps with power-law memory

abstract:
  This article is a short review of the recent results on properties of
nonlinear fractional maps which are maps with power- or asymptotically
power-law memory. These maps demonstrate the new type of attractors - cascade
of bifurcations type trajectories, power-law convergence/divergence of
trajectories, period doubling bifurcations with changes in the memory
parameter, intersection of trajectories, and overlapping of attractors. In the
limit of small time steps these maps converge to nonlinear fractional
differential equations.


title: Who is Mistaken?

abstract:
  Recognizing when people have false beliefs is crucial for understanding their
actions. We introduce the novel problem of identifying when people in abstract
scenes have incorrect beliefs. We present a dataset of scenes, each visually
depicting an 8-frame story in which a character has a mistaken belief. We then
create a representation of characters' beliefs for two tasks in human action
understanding: predicting who is mistaken, and when they are mistaken.
Experiments suggest that our method for identifying mistaken characters
performs better on these tasks than simple baselines. Diagnostics on our model
suggest it learns important cues for recognizing mistaken beliefs, such as
gaze. We believe models of people's beliefs will have many applications in
action understanding, robotics, and healthcare.


title: An algebraic model for the pion's valence-quark GPD

abstract:
  We briefly report on a recent computation, with the help of a fruitful
algebraic model, sketching the pion valence dressed-quark generalized parton
distribution. Then, preliminary, we introduce on a sensible procedure to get
reliable results in both Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and
Efremov-Radyushkin-Brodsky-Lepage (ERBL) kinematical regions, grounded on the
GPD overlap representation and its parametrization of a Radon transform of the
so-called double distribution (DD).


title: Approximation numbers of weighted composition operators

abstract:
  We study the approximation numbers of weighted composition operators
$f\mapsto w\cdot(f\circ\varphi)$ on the Hardy space $H^2$ on the unit disc. For
general classes of such operators, upper and lower bounds on their
approximation numbers are derived. For the special class of weighted lens map
composition operators with specific weights, we show how much the weight $w$
can improve the decay rate of the approximation numbers, and give sharp upper
and lower bounds. These examples are motivated from applications to the
analysis of relative commutants of special inclusions of von Neumann algebras
appearing in quantum field theory (Borchers triples).


title: Adaptive Work-Efficient Connected Components on the GPU

abstract:
  This report presents an adaptive work-efficient approach for implementing the
Connected Components algorithm on GPUs. The results show a considerable
increase in performance (up to 6.8$\times$) over current state-of-the-art
solutions.


title: On the limit relation for the quantum relative entropy

abstract:
  Recently, Di\'osi et al. (Int. J. Quant. Inf. 4, 99 (2006)) introduced a
simple, yet very interesting model for reservoirs, in order to study the
relationship between thermodynamic entropy production of a system and the
corresponding von Neumann entropy (or informatic entropy, as it was called by
the authors). They came up with a conjecture about the asymptotic behaviour of
the state introduced in the model. The conjecture was proven later by Csisz\'ar
et al. (J. Math. Phys. 48, 092102 (2007)). In this paper we give a different
interpretation of the original question and extend the result to a collection
of more general states.


title:
Molecular organization in the twist-bend nematic phase by resonant X-ray
  scattering at the Se K-edge and by SAXS, WAXS and GIXRD

abstract:
  Using a novel Se-labelled dimer mixed with DTC5C7 aligned by magnetic field,
the twist-bend nematic phase (Ntb) in dimers was studied by hard X-ray resonant
scattering and by small and wide angle X-ray scattering (SAXS, WAXS). Resonant
diffraction spots indicated a helix with a 9-12 nm pitch in the Ntb phase.
Unprecedentedly high helix orien-tation enabled deconvolution of global and
local order parameters. This, combined with simultaneous resonant and
non-resonant SAXS and WAXS data, allowed us to construct a modified model of
the Ntb phase matching twisted molecular conformations and the local
heliconical director field.


title:
Spin- and velocity-dependent non-relativistic potentials in modified
  electrodynamics

abstract:
  We investigate the interparticle potential between spin-0, -1/2 and -1
sources interacting in modified electrodynamics in the non-relativistic regime.
By keeping terms of $\mathcal{O}( |{\bf p}|^2/m^2 )$ in the amplitudes, we
obtain spin- and velocity-dependent interaction energies. We find well-known
effects such as spin-orbit couplings, as well as spin-spin (dipole-dipole)
interactions. For concreteness, we consider the cases of electrodynamics with
higher derivatives (Podolsky-Lee-Wick) and hidden photons.


title:
Phase Retrieval from Local Measurements: Improved Robustness via
  Eigenvector-Based Angular Synchronization

abstract:
  We improve a phase retrieval approach that uses correlation-based
measurements with compactly supported measurement masks [27]. The improved
algorithm admits deterministic measurement constructions together with a
robust, fast recovery algorithm that consists of solving a system of linear
equations in a lifted space, followed by finding an eigenvector (e.g., via an
inverse power iteration). Theoretical reconstruction error guarantees from [27]
are improved as a result for the new and more robust reconstruction approach
proposed herein. Numerical experiments demonstrate robustness and computational
efficiency that outperforms competing approaches on large problems. Finally, we
show that this approach also trivially extends to phase retrieval problems
based on windowed Fourier measurements.


title: AMP-Inspired Deep Networks for Sparse Linear Inverse Problems

abstract:
  Deep learning has gained great popularity due to its widespread success on
many inference problems. We consider the application of deep learning to the
sparse linear inverse problem, where one seeks to recover a sparse signal from
a few noisy linear measurements. In this paper, we propose two novel
neural-network architectures that decouple prediction errors across layers in
the same way that the approximate message passing (AMP) algorithms decouple
them across iterations: through Onsager correction. First, we propose a
"learned AMP" network that significantly improves upon Gregor and LeCun's
"learned ISTA." Second, inspired by the recently proposed "vector AMP" (VAMP)
algorithm, we propose a "learned VAMP" network that offers increased robustness
to deviations in the measurement matrix from i.i.d. Gaussian. In both cases, we
jointly learn the linear transforms and scalar nonlinearities of the network.
Interestingly, with i.i.d. signals, the linear transforms and scalar
nonlinearities prescribed by the VAMP algorithm coincide with the values
learned through back-propagation, leading to an intuitive interpretation of
learned VAMP. Finally, we apply our methods to two problems from 5G wireless
communications: compressive random access and massive-MIMO channel estimation.


title: Order eight non-symplectic automorphisms on elliptic K3 surfaces

abstract:
  In this paper we classify complex K3 surfaces with non-symplectic
automorphism of order 8 that leaves invariant a smooth elliptic curve. We show
that the rank of the Picard group is either 10, 14 or 18 and the fixed locus is
the disjoint union of elliptic curves, rational curves and points, whose number
does not exceed 1, 2, respectively 14. We give examples corresponding to
several types of fixed locus in the classification.


title: Spontaneous polariton currents in periodic lateral chains

abstract:
  We predict spontaneous generation of superfluid polariton currents in planar
microcavities with lateral periodic modulation of both potential and decay
rate. A spontaneous breaking of spatial inversion symmetry of a polariton
condensate emerges at a critical pumping, and the current direction is
stochastically chosen. We analyse the stability of the current with respect to
the fluctuations of the condensate. A peculiar spatial current domain structure
emerges, where the current direction is switched at the domain walls, and the
characteristic domain size and lifetime scale with the pumping power.


title: Vector Approximate Message Passing for the Generalized Linear Model

abstract:
  The generalized linear model (GLM), where a random vector $\boldsymbol{x}$ is
observed through a noisy, possibly nonlinear, function of a linear transform
output $\boldsymbol{z}=\boldsymbol{Ax}$, arises in a range of applications such
as robust regression, binary classification, quantized compressed sensing,
phase retrieval, photon-limited imaging, and inference from neural spike
trains. When $\boldsymbol{A}$ is large and i.i.d. Gaussian, the generalized
approximate message passing (GAMP) algorithm is an efficient means of MAP or
marginal inference, and its performance can be rigorously characterized by a
scalar state evolution. For general $\boldsymbol{A}$, though, GAMP can
misbehave. Damping and sequential-updating help to robustify GAMP, but their
effects are limited. Recently, a "vector AMP" (VAMP) algorithm was proposed for
additive white Gaussian noise channels. VAMP extends AMP's guarantees from
i.i.d. Gaussian $\boldsymbol{A}$ to the larger class of rotationally invariant
$\boldsymbol{A}$. In this paper, we show how VAMP can be extended to the GLM.
Numerical experiments show that the proposed GLM-VAMP is much more robust to
ill-conditioning in $\boldsymbol{A}$ than damped GAMP.


title:
UV-extended E-MILES stellar population models: young components in
  massive early-type galaxies

abstract:
  We present UV-extended E-MILES stellar population synthesis models covering
the spectral range 1680-50000A at moderately high resolution. We employ the
NGSL space-based stellar library to compute spectra of single-age,
single-metallicity stellar populations in the wavelength range from 1680 to
3540A. These models represent a significant improvement in resolution and
age/metallicity coverage over previous studies based on earlier space-based
libraries. These model spectra were joined with those we computed in the
visible using MILES, and other empirical libraries for redder wavelengths. The
models span the metallicity range -1.79<[M/H]<+0.26 and ages above 30 Myr, for
a suite of IMF types with varying slopes. We focus on the behaviour of colours,
spectra and line-strength indices in the UV range as a function of relevant
stellar population parameters. Whereas some indices strengthen with increasing
age and metallicity, as most metallicity indicators in the visible, other
indices peak around 3 Gyr for metal-rich stellar populations, such as Mg at
2800A. Our models provide reasonably good fits to the integrated colours and
most line-strengths of the stellar clusters of the Milky-Way and LMC. Our
full-spectrum fits in the UV range for a representative set of ETGs of varying
mass yield age and metallicity estimates in very good agreement with those
obtained in the optical range. The comparison of UV colours and line-strengths
of massive ETGs with our models reveals the presence of young stellar
components, with ages in the range 0.1-0.5 Gyr and mass fractions 0.1-0.5%, on
the top of an old stellar population.


title: Privacy on the Blockchain: Unique Ring Signatures

abstract:
  Ring signatures are cryptographic protocols designed to allow any member of a
group to produce a signature on behalf of the group, without revealing the
individual signer's identity. This offers group members a level of anonymity
not attainable through generic digital signature schemes. We call this property
'plausible deniability', or anonymity with respect to an anonymity set. We
concentrate in particular on implementing privacy on the blockchain,
introducing a unique ring signature scheme that works with existing blockchain
systems. We implement a unique ring signature (URS) scheme using secp256k1,
creating the first implementation compatible with blockchain libraries in this
way, so as for easy implementation as an Ethereum smart contract. We review the
privacy and security properties offered by the scheme we have constructed, and
compare its efficiency with other commonly suggested approaches to privacy on
the blockchain.


title:
Cache-Enabled Physical-Layer Security for Video Streaming in Wireless
  Networks with Limited Backhaul

abstract:
  In this paper, we investigate for the first time the benefits of wireless
caching for the physical layer security (PLS) of wireless networks. In
particular, a caching scheme enabling power-efficient PLS is proposed for
cellular video streaming with constrained backhaul capacity. By sharing video
data across a subset of base stations (BSs) through both caching and backhaul
loading, secure cooperative transmission of several BSs is dynamically enabled
in accordance with the cache status, the channel conditions, and the backhaul
capacity. Thereby, caching reduces the data sharing overhead over the
capacity-constrained backhaul links. More importantly, caching introduces
additional secure degrees of freedom and enables a power-efficient design. We
investigate the optimal caching and transmission policies for minimizing the
total transmit power while providing quality of service (QoS) and guaranteeing
secrecy during video delivery. A two-stage non-convex mixed-integer
optimization problem is formulated, which optimizes the caching policy in an
offline video caching stage and the cooperative transmission policy in an
online video delivery stage. As the problem is NP-hard, suboptimal
polynomial-time algorithms are proposed for low-complexity cache training and
delivery control, respectively. Sufficient optimality conditions, under which
the proposed schemes attain global optimal solutions, are also provided.
Simulation results show that the proposed schemes achieve low secrecy outage
probability and high power efficiency simultaneously.


title:
Search for heavy neutrinos or third-generation leptoquarks in final
  states with two hadronically decaying tau leptons and two jets in
  proton-proton collisions at sqrt(s) = 13 TeV

abstract:
  A search for new particles has been conducted using events with two high
transverse momentum (pt) tau leptons that decay hadronically, at least two
high-pt jets, and missing transverse energy from the tau lepton decays. The
analysis is performed using data from proton-proton collisions, collected by
the CMS experiment in 2015 at sqrt(s) = 13 TeV, corresponding to an integrated
luminosity of 2.1 inverse femtobarns. The results are interpreted in two
physics models. The first model involves heavy right-handed neutrinos, N[l] (l
= e, mu, tau), and right-handed charged bosons, W[R], arising in a left-right
symmetric extension of the standard model. Masses of the W[R] boson below 2.35
(1.63) TeV are excluded at 95% confidence level, assuming the N[tau] mass is
0.8 (0.2) times the mass of the W[R] boson and that only the N[tau] flavor
contributes to the W[R] decay width. In the second model, pair production of
third-generation scalar leptoquarks that decay into tau tau bb is considered.
Third-generation scalar leptoquarks with masses below 740 GeV are excluded,
assuming a 100% branching fraction for the leptoquark decay to a tau lepton and
a bottom quark. This is the first search at hadron colliders for the
third-generation Majorana neutrino, as well as the first search for
third-generation leptoquarks in the final state with a pair of hadronically
decaying tau leptons and jets.


title:
The study of massive stars with 50 Msun initial mass at different
  evolutionary stages

abstract:
  We will present results of studies of several massive stars at different
evolutionary stages, but with similar values of the initial mass: O-supergiants
belonging to association Cyg OB2, unique LBV/post-LBV - Romano's star and two
Wolf-Rayet stars - WR156 and FSZ35. All these stars have similar initial mass
of about 50 Msun. It allows us to consider them a single star at different
moments of life, and it gives an opportunity to track changes in the physical
parameters (such as effective temperature, luminosity, mass loss rate, wind
velocity) and chemical abundances during the life of a massive star. It is
important to test the current evolution theories of such objects.


title:
Exclusion limits on a scalar decaying to photons and distinguishing its
  production mechanisms

abstract:
  LHC run-II has a great potential to search for new resonances in the diphoton
channel. Latest 13 TeV data already put stringent limits on the cross sections
in the diphoton channel assuming the resonance is produced through the
gluon-gluon fusion. Many beyond the Standard Model (SM) theories predict
TeV-scale scalars, which copiously decay to diphotons. Apart from the
gluon-gluon fusion production, these scalars can also be dominantly produced in
other ways too at the LHC namely through the quark-quark fusion or the gauge
boson fusions like the photon-photon, photon-$Z$, $WW$ or $ZZ$ fusions. In this
paper, we use an effective field theory approach where a heavy scalar can be
produced in various ways and recast the latest ATLAS diphoton resonance search
to put model-independent limits on its mass and effective couplings to the SM
particles. If a new scalar is discovered at the LHC, it would be very important
to identify its production mechanism in order to probe the nature of the
underlying theory. We show that combining various kinematic variables in a
multivariate analysis can be very powerful to distinguish different production
mechanisms one from the other.


title:
Optimal transport over nonlinear systems via infinitesimal generators on
  graphs

abstract:
  We present a set-oriented graph-based computational framework for
continuous-time optimal transport over nonlinear dynamical systems. We recover
provably optimal control laws for steering a given initial distribution in
phase space to a final distribution in prescribed finite time for the case of
non-autonomous nonlinear control-affine systems, while minimizing a quadratic
control cost. The resulting control law can be used to obtain approximate
feedback laws for individual agents in a swarm control application. Using
infinitesimal generators, the optimal control problem is reduced to a modified
Monge-Kantorovich optimal transport problem, resulting in a convex
Benamou-Brenier type fluid dynamics formulation on a graph. The well-posedness
of this problem is shown to be a consequence of the graph being
strongly-connected, which in turn is shown to result from controllability of
the underlying dynamical system. Using our computational framework, we study
optimal transport of distributions where the underlying dynamical systems are
chaotic, and non-holonomic. The solutions to the optimal transport problem
elucidate the role played by invariant manifolds, lobe-dynamics and
almost-invariant sets in efficient transport of distributions in finite time.
Our work connects set-oriented operator-theoretic methods in dynamical systems
with optimal mass transportation theory, and opens up new directions in design
of efficient feedback control strategies for nonlinear multi-agent and swarm
systems operating in nonlinear ambient flow fields.


title: Online Localization and Prediction of Actions and Interactions

abstract:
  This paper proposes a person-centric and online approach to the challenging
problem of localization and prediction of actions and interactions in videos.
Typically, localization or recognition is performed in an offline manner where
all the frames in the video are processed together. This prevents timely
localization and prediction of actions and interactions - an important
consideration for many tasks including surveillance and human-machine
interaction.
  In our approach, we estimate human poses at each frame and train
discriminative appearance models using the superpixels inside the pose bounding
boxes. Since the pose estimation per frame is inherently noisy, the conditional
probability of pose hypotheses at current time-step (frame) is computed using
pose estimations in the current frame and their consistency with poses in the
previous frames. Next, both the superpixel and pose-based foreground
likelihoods are used to infer the location of actors at each time through a
Conditional Random. The issue of visual drift is handled by updating the
appearance models, and refining poses using motion smoothness on joint
locations, in an online manner. For online prediction of action (interaction)
confidences, we propose an approach based on Structural SVM that operates on
short video segments, and is trained with the objective that confidence of an
action or interaction increases as time progresses. Lastly, we quantify the
performance of both detection and prediction together, and analyze how the
prediction accuracy varies as a time function of observed action (interaction)
at different levels of detection performance. Our experiments on several
datasets suggest that despite using only a few frames to localize actions
(interactions) at each time instant, we are able to obtain competitive results
to state-of-the-art offline methods.


title:
Accurate potential energy curve for helium dimer retrieved from
  viscosity coefficient data at very low temperatures

abstract:
  The long range potential of helium-helium interaction, which requires
accurate 'ab initio' calculation, due to the small value of the potential
depth, approximately 11 K (0.091 kJ/mol) at 2.96 angstrom, will be obtained in
this study by an alternative technique. This work presents a robust and
consistent procedure that provides the long range potential directly from
experimental data. However, it is difficult to obtain experimental data
containing information regarding such a small potential depth. Thereby,
sensitivity analysis will be used to circumvent this difficulty, from which
viscosity data at lower temperatures (<5K) were chosen as appropriate data to
be used to retrieve the potential function between 3 and 4 angstrom. The linear
relationship between the potential energy function and the viscosity
coefficient will be established under quantum assumptions and the Bose-Einstein
statistic. The use of quantum theory is essential, since the temperatures are
below 5K. The potential obtained in this study describes the viscosity with an
average error of 1.68% that is less than the experimental error (5%), with the
results being similar to those obtained for recent 'ab initio' potentials.


title: On the nature of anomalous reddening of Cygnus OB2 #12 hypergiant

abstract:
  To explain the nature of the anomalously high reddening (Av~10 mag) towards
one of the most luminous stars in the Galaxy - Cyg OB2 #12 (B5 Ia-0), also
known as MT304, we carried out spectro-photometric observations of 24 stars
located in its vicinity. We included five new B-stars to the members of Cygnus
OB2, and for five more photometrically selected stars we spectroscopically
confirmed their membership. We constructed the map of interstellar extinction
within 2.5 arcmin radius and found that interstellar extinction increases
towards MT304. The increase of reddening suggests that the reddening excess may
be caused by the circumstellar shell ejected by the star during its evolution.
We also report the detection of a second component of MT304, and discovery of
an even fainter third component, based on data of speckle interferometric
observations taken with the Russian 6-m telescope.


title:
Neural Symbolic Machines: Learning Semantic Parsers on Freebase with
  Weak Supervision (Short Version)

abstract:
  Extending the success of deep neural networks to natural language
understanding and symbolic reasoning requires complex operations and external
memory. Recent neural program induction approaches have attempted to address
this problem, but are typically limited to differentiable memory, and
consequently cannot scale beyond small synthetic tasks. In this work, we
propose the Manager-Programmer-Computer framework, which integrates neural
networks with non-differentiable memory to support abstract, scalable and
precise operations through a friendly neural computer interface. Specifically,
we introduce a Neural Symbolic Machine, which contains a sequence-to-sequence
neural "programmer", and a non-differentiable "computer" that is a Lisp
interpreter with code assist. To successfully apply REINFORCE for training, we
augment it with approximate gold programs found by an iterative maximum
likelihood training process. NSM is able to learn a semantic parser from weak
supervision over a large knowledge base. It achieves new state-of-the-art
performance on WebQuestionsSP, a challenging semantic parsing dataset, with
weak supervision. Compared to previous approaches, NSM is end-to-end, therefore
does not rely on feature engineering or domain specific knowledge.


title: Implementing and Evaluating Candidate-Based Invariant Generation

abstract:
  The discovery of inductive invariants lies at the heart of static program
verification. Presently, many automatic solutions to inductive invariant
generation are inflexible, only applicable to certain classes of programs, or
unpredictable. An automatic technique that circumvents these deficiencies to
some extent is candidate-based invariant generation. This paper describes our
efforts to apply candidate-based invariant generation in GPUVerify, a static
checker for programs that run on GPUs. We study a set of GPU programs that
contain loops, drawn from a number of open source suites and vendor SDKs.
  We describe the methodology we used to incrementally improve the invariant
generation capabilities of GPUVerify to handle these benchmarks, through
candidate-based invariant generation, using cheap static analysis to speculate
potential program invariants. We also describe a set of experiments that we
used to examine the effectiveness of our rules for candidate generation,
assessing rules based on their generality (the extent to which they generate
candidate invariants), hit rate (the extent to which the generated candidates
hold), worth (the extent to which provable candidates actually help in allowing
verification to succeed), and influence (the extent to which the success of one
generation rule depends on candidates generated by another rule).
  The candidates produced by GPUVerify help to verify 231 of the 253 programs.
This increase in precision, however, makes GPUVerify sluggish: the more
candidates that are generated, the more time is spent determining which are
inductive invariants. To speed up this process, we have investigated four
under-approximating program analyses that aim to reject false candidates
quickly and a framework whereby these analyses can run in sequence or in
parallel.


title: Gaussian Boson Sampling

abstract:
  Boson Sampling has emerged as a tool to explore the advantages of quantum
over classical computers as it does not require a universal control over the
quantum system, which favours current photonic experimental platforms.Here, we
introduce Gaussian Boson Sampling, a classically hard-to-solve problem that
uses squeezed states as a non-classical resource. We relate the probability to
measure specific photon patterns from a general Gaussian state in the Fock
basis to a matrix function called the hafnian, which answers the last remaining
question of sampling from Gaussian states. Based on this result, we design
Gaussian Boson Sampling, a #P hard problem, using squeezed states. This
approach leads to a more efficient photonic boson sampler with significant
advantages in generation probability and measurement time over currently
existing protocols.


title: Intra-day Activity Better Predicts Chronic Conditions

abstract:
  In this work we investigate intra-day patterns of activity on a population of
7,261 users of mobile health wearable devices and apps. We show that: (1) using
intra-day step and sleep data recorded from passive trackers significantly
improves classification performance on self-reported chronic conditions related
to mental health and nervous system disorders, (2) Convolutional Neural
Networks achieve top classification performance vs. baseline models when
trained directly on multivariate time series of activity data, and (3) jointly
predicting all condition classes via multi-task learning can be leveraged to
extract features that generalize across data sets and achieve the highest
classification performance.


title: Andreev bound states probed in three-terminal quantum dots

abstract:
  We demonstrate several new electron transport phenomena mediated by Andreev
bound states (ABSs) that form on three-terminal carbon nanotube (CNT) QDs, with
one superconducting (S) contact in the center and two adjacent normal metal (N)
contacts. Three-terminal spectroscopy allows us to identify the coupling to the
N contacts as the origin of the Andreev resonance (AR) linewidths and to
determine the critical coupling strengths to S, for which a ground state
transition S-QD systems can occur. We ascribe replicas of the lowest-energy ABS
resonance to transitions between the ABS and odd-parity excited QD states, a
process called excited state ABS resonances. In the conductance between the two
N contacts we find a characteristic pattern of positive and negative
differential subgap conductance, which we explain by considering two nonlocal
processes, the creation of Cooper pairs in S by electrons from both N
terminals, and a novel mechanism called resonant ABS tunneling. In the latter,
electrons are transferred via the ABS without creating Cooper pairs in S. The
three-terminal geometry also allows spectroscopy experiments with different
boundary conditions, for example by leaving S floating. Surprisingly, we find
that, depending on the boundary conditions, the experiments either show
single-particle Coulomb blockade resonances, ABS characteristics, or both in
the same measurements, seemingly contradicting the notion of ABSs replacing the
single particle states as eigenstates of the QD. We qualitatively explain these
results as originating from the finite time scale required for the coherent
oscillations between the superposition states after a single electron tunneling
event. These experiments demonstrate that three-terminal experiments on a
single complex quantum object can also be useful to investigate charge dynamics
otherwise not accessible due to the very high frequencies.


title: DenseReg: Fully Convolutional Dense Shape Regression In-the-Wild

abstract:
  In this paper we propose to learn a mapping from image pixels into a dense
template grid through a fully convolutional network. We formulate this task as
a regression problem and train our network by leveraging upon manually
annotated facial landmarks "in-the-wild". We use such landmarks to establish a
dense correspondence field between a three-dimensional object template and the
input image, which then serves as the ground-truth for training our regression
system. We show that we can combine ideas from semantic segmentation with
regression networks, yielding a highly-accurate "quantized regression"
architecture.
  Our system, called DenseReg, allows us to estimate dense image-to-template
correspondences in a fully convolutional manner. As such our network can
provide useful correspondence information as a stand-alone system, while when
used as an initialization for Statistical Deformable Models we obtain landmark
localization results that largely outperform the current state-of-the-art on
the challenging 300W benchmark. We thoroughly evaluate our method on a host of
facial analysis tasks and also provide qualitative results for dense human body
correspondence. We make our code available at http://alpguler.com/DenseReg.html
along with supplementary materials.


title:
The holographic Hadamard condition on asymptotically Anti-de Sitter
  spacetimes

abstract:
  In the setting of asymptotically Anti-de Sitter spacetimes, we consider
Klein-Gordon fields subject to Dirichlet boundary conditions, with mass
satisfying the Breitenlohner-Freedman bound. We introduce a condition on the
b-wave front set of two-point functions of quantum fields, which locally in the
bulk amounts to the usual Hadamard condition, and which moreover allows to
estimate wave front sets for the holographically induced theory on the
boundary. We prove the existence of two-point functions satisfying this
condition, and show their uniqueness modulo terms that have smooth Schwartz
kernel in the bulk and have smooth restriction to the boundary. Finally, using
Vasy's propagation of singularities theorem, we prove an analogue of
Duistermaat and H\"ormander's theorem on distinguished parametrices.


title:
Phenomenological Parameters of the Prototype Eclipsing Binaries Algol,
  $\beta$ Lyrae and W UMa

abstract:
  The phenomenological parameters of eclipsing binary stars, which are the
prototypes of the EA, EB and EW systems are determined using the expert complex
of computer programs, which realizes the NAV ("New Algol Variable") algorithm
(Andronov 2010, 2012) and its possible modifications are discussed, as well as
constrains for estimates of some physical parameters of the systems in a case
of photometric observations only, such as the degree of eclipse, ratio of the
mean surface brightnesses of the components. The half-duration of the eclipse
is 0.0617(7), 0.1092(18) and 0.1015(7) for Algol, $\beta$ Lyrae and W UMa,
respectively. The brightness ratio is 6.8$\pm$1.0, 4.9$\pm$1.0 and
1.15$\pm$0.13. These results show that the eclipses have distinct begin and end
not only in EA (as generally assumed), but also in EB and EW - type systems as
well. The algorithm may be applied to classification and study of the newly
discovered (or poorly studied) eclipsing variables based on own observations or
that obtained using photometric surveys.


title: Optimal and Adaptive Off-policy Evaluation in Contextual Bandits

abstract:
  We study the off-policy evaluation problem---estimating the value of a target
policy using data collected by another policy---under the contextual bandit
model. We consider the general (agnostic) setting without access to a
consistent model of rewards and establish a minimax lower bound on the mean
squared error (MSE). The bound is matched up to constants by the inverse
propensity scoring (IPS) and doubly robust (DR) estimators. This highlights the
difficulty of the agnostic contextual setting, in contrast with multi-armed
bandits and contextual bandits with access to a consistent reward model, where
IPS is suboptimal. We then propose the SWITCH estimator, which can use an
existing reward model (not necessarily consistent) to achieve a better
bias-variance tradeoff than IPS and DR. We prove an upper bound on its MSE and
demonstrate its benefits empirically on a diverse collection of data sets,
often outperforming prior work by orders of magnitude.


title: Nontautological Bielliptic Cycles

abstract:
  Let $[\overline{\mathcal{B}}_{2,0,20}]$ and $[\mathcal{B}_{2,0,20}]$ be the
classes of the loci of stable resp. smooth bielliptic curves with 20 marked
points where the bielliptic involution acts on the marked points as the
permutation (1 2)...(19 20). Graber and Pandharipande proved that these classes
are nontatoulogical. In this note we show that their result can be extended to
prove that $[\overline{\mathcal{B}}_{g}]$ is nontautological for $g\geq 12$ and
that $[\mathcal{B}_{12}]$ is nontautological.


title: Perverse sheaves and the reductive Borel-Serre compactification

abstract:
  We briefly introduce the theory of perverse sheaves with special attention to
the topological situation where strata can have odd dimension. This is part of
a project to use perverse sheaves on the topological reductive Borel-Serre
compactification of a Hermitian locally symmetric space as a tool to study
perverse sheaves on the Baily-Borel compactification, a projective algebraic
variety. We sketch why the decomposition theorem holds for the natural map
between the reductive Borel-Serre and the Baily-Borel compactifications. We
demonstrate how to calculate extensions of simple perverse sheaves on the
reductive Borel-Serre compactification and illustrate with the example of
Sp(4,R).


title:
The effect of $SU(2)$ symmetry on many-body localization and
  thermalization

abstract:
  The many-body localized (MBL) phase is characterized by a complete set of
quasi-local integrals of motion and area-law entanglement of excited
eigenstates. We study the effect of non-Abelian continuous symmetries on MBL,
considering the case of $SU(2)$ symmetric disordered spin chains. The $SU(2)$
symmetry imposes strong constraints on the entanglement structure of the
eigenstates, precluding conventional MBL. We construct a fixed-point
Hamiltonian, which realizes a non-ergodic (but non-MBL) phase characterized by
eigenstates having logarithmic scaling of entanglement with the system size, as
well as an incomplete set of quasi-local integrals of motion. We study the
response of such a phase to local symmetric perturbations, finding that even
weak perturbations induce multi-spin resonances. We conclude that the
non-ergodic phase is generally unstable and that $SU(2)$ symmetry implies
thermalization. The approach introduced in this work can be used to study
dynamics in disordered systems with non-Abelian symmetries, and provides a
starting point for searching non-ergodic phases beyond conventional MBL.

categories: cond-mat.dis-nn cond-mat.stat-mech cond-mat.str-el quant-ph


title: Throughput of Infrastructure-based Cooperative Vehicular Networks

abstract:
  In this paper, we provide detailed analysis of the achievable throughput of
infrastructure-based vehicular network with a finite traffic density under a
cooperative communication strategy, which explores combined use of
vehicle-to-infrastructure (V2I) communications, vehicle-to-vehicle (V2V)
communications, mobility of vehicles and cooperations among vehicles and
infrastructure to facilitate the data transmission. A closed form expression of
the achievable throughput is obtained, which reveals the relationship between
the achievable throughput and its major performance-impacting parameters such
as distance between adjacent infrastructure points, radio ranges of
infrastructure and vehicles, transmission rates of V2I and V2V communications
and vehicular density. Numerical and simulation results show that the proposed
cooperative communication strategy significantly increases the throughput of
vehicular networks, compared with its non-cooperative counterpart, even when
the traffic density is low. Our results shed insight on the optimum deployment
of vehicular network infrastructure and optimum design of cooperative
communication strategies in vehicular networks to maximize the throughput.


title:
On the regular conditional distribution of a multivariate Normal given a
  linear transformation

abstract:
  We show that the orthogonal projection operator onto the range of the adjoint
of a linear operator T can be represented as UT, where U is an invertible
linear operator. Using this representation we obtain a decomposition of a
multivariate Normal random variable Y as the sum of a linear transformation of
Y that is independent of TY and an affine transformation of TY. We then use
this decomposition to prove that the regular conditional distribution of a
multivariate Normal random variable Y given a linear transformation TY is again
a multivariate Normal distribution. This result is equivalent to the well-known
result that given a k-dimensional component of a n-dimensional multivariate
Normal random variable, where k < n, the regular conditional distribution of
the remaining (n - k)-dimensional component is a (n - k)-dimensional
multivariate Normal distribution.


title: Gaussian Process Model Predictive Control of Unknown Nonlinear Systems

abstract:
  Model Predictive Control (MPC) of an unknown system that is modelled by
Gaussian Process (GP) techniques is studied in this paper. Using GP, the
variances computed during the modelling and inference processes allow us to
take model uncertainty into account. The main issue in using MPC to control
systems modelled by GP is the propagation of such uncertainties within the
control horizon. In this paper, two approaches to solve this problem, called
GPMPC1 and GPMPC2, are proposed. With GPMPC1, the original Stochastic Model
Predictive Control (SMPC) problem is relaxed to a deterministic nonlinear MPC
based on a basic linearized GP local model. The resulting optimization problem,
though non-convex, can be solved by the Sequential Quadratic Programming (SQP).
By incorporating the model variance into the state vector, an extended local
model is derived. This model allows us to relax the non-convex MPC problem to a
convex one which can be solved by an active-set method efficiently. The
performance of both approaches is demonstrated by applying them to two
trajectory tracking problems. Results show that both GPMPC1 and GPMPC2 produce
effective controls but GPMPC2 is much more efficient computationally.


title: Counting numerical semigroups by genus and even gaps

abstract:
  Let $n_g$ be the number of numerical semigroups of genus $g$. We present an
approach to compute $n_g$ by using even gaps, and the question: Is it true that
$n_{g+1}>n_g$? is investigated. Let $N_\gamma(g)$ be the number of numerical
semigroups of genus $g$ whose number of even gaps equals $\gamma$. We show that
$N_\gamma(g)=N_\gamma(3\gamma)$ for $\gamma \leq \lfloor g/3\rfloor$ and
$N_\gamma(g)=0$ for $\gamma > \lfloor 2g/3\rfloor$; thus the question above is
true provided that $N_\gamma(g+1) > N_\gamma(g)$ for $\gamma = \lfloor g/3
\rfloor +1, \ldots, \lfloor 2g/3\rfloor$. We also show that $N_\gamma(3\gamma)$
coincides with $f_\gamma$, the number introduced by Bras-Amor\'os in conection
with semigroup-closed sets. Finally, the stronger possibility $f_\gamma \sim
\varphi^{2\gamma}$ arises being $\varphi = (1+\sqrt{5})/2$ the golden number.


title: Deep Metric Learning via Facility Location

abstract:
  Learning the representation and the similarity metric in an end-to-end
fashion with deep networks have demonstrated outstanding results for clustering
and retrieval. However, these recent approaches still suffer from the
performance degradation stemming from the local metric training procedure which
is unaware of the global structure of the embedding space.
  We propose a global metric learning scheme for optimizing the deep metric
embedding with the learnable clustering function and the clustering metric
(NMI) in a novel structured prediction framework.
  Our experiments on CUB200-2011, Cars196, and Stanford online products
datasets show state of the art performance both on the clustering and retrieval
tasks measured in the NMI and Recall@K evaluation metrics.


title: Maximally entangled mixed states for qubit-qutrit systems

abstract:
  We consider the problems of maximizing the entanglement negativity of X-form
qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed
purity. In the first case, the problem is solved in full generality whereas, in
the latter, partial solutions are obtained by imposing extra spectral
constraints such as rank-deficiency and degeneracy, which enable a semidefinite
programming treatment for the optimization problem at hand. Despite the
technically-motivated assumptions, we provide strong numerical evidence that
three-fold degenerate X states of purity $P$ reach the highest entanglement
negativity accessible to arbitrary qubit-qutrit density matrices of the same
purity, hence characterizing a sparse family of likely qubit-qutrit maximally
entangled mixed states.


title:
Do What I Want, Not What I Did: Imitation of Skills by Planning
  Sequences of Actions

abstract:
  We propose a learning-from-demonstration approach for grounding actions from
expert data and an algorithm for using these actions to perform a task in new
environments. Our approach is based on an application of sampling-based motion
planning to search through the tree of discrete, high-level actions constructed
from a symbolic representation of a task. Recursive sampling-based planning is
used to explore the space of possible continuous-space instantiations of these
actions. We demonstrate the utility of our approach with a magnetic structure
assembly task, showing that the robot can intelligently select a sequence of
actions in different parts of the workspace and in the presence of obstacles.
This approach can better adapt to new environments by selecting the correct
high-level actions for the particular environment while taking human
preferences into account.


title: Decentralized Frank-Wolfe Algorithm for Convex and Non-convex Problems

abstract:
  Decentralized optimization algorithms have received much attention due to the
recent advances in network information processing. However, conventional
decentralized algorithms based on projected gradient descent are incapable of
handling high dimensional constrained problems, as the projection step becomes
computationally prohibitive to compute. To address this problem, this paper
adopts a projection-free optimization approach, a.k.a.~the Frank-Wolfe (FW) or
conditional gradient algorithm. We first develop a decentralized FW (DeFW)
algorithm from the classical FW algorithm. The convergence of the proposed
algorithm is studied by viewing the decentralized algorithm as an inexact FW
algorithm. Using a diminishing step size rule and letting $t$ be the iteration
number, we show that the DeFW algorithm's convergence rate is ${\cal O}(1/t)$
for convex objectives; is ${\cal O}(1/t^2)$ for strongly convex objectives with
the optimal solution in the interior of the constraint set; and is ${\cal
O}(1/\sqrt{t})$ towards a stationary point for smooth but non-convex
objectives. We then show that a consensus-based DeFW algorithm meets the above
guarantees with two communication rounds per iteration. Furthermore, we
demonstrate the advantages of the proposed DeFW algorithm on low-complexity
robust matrix completion and communication efficient sparse learning. Numerical
results on synthetic and real data are presented to support our findings.


title: Superconductivity in Solid Benzene Molecular Crystal

abstract:
  Light-element compounds hold great promise of high critical temperature
superconductivity judging from the theoretical perspective. Hydrogen-rich
material, benzene, is such a kind of candidate but also an organic compound. A
series of first-principles calculations are performed on the electronic
structures, dynamics properties, and electron-phonon interactions of solid
benzene at high pressures. Benzene is found to be dynamically stable in the
pressure range of 180 - 200 GPa and to exhibit superconductivity with a maximum
transition temperature of 20 K at 195 GPa. The phonon modes of carbon atoms are
identified to mainly contribute to the electron-phonon interactions driving
this superconductivity. The predicted superconductivity in this simplest
pristine hydrocarbon shows a common feature in aromatic hydrocarbons and also
makes it a bridge to organic and hydrogen-rich superconductors.


title: On the spinor norm in the unitary groups

abstract:
  Let $F$ be a field of odd characteristic, $E$ be a finite extension of $F$
equipped an involution with subfield of fixed points $E_0$ containing $F$ and
$V$ be a finite dimensional $E$-vector space with a non-degenerate hermitian
form $h$. We show a link between the spinor norm in the unitary group $U(V,h)$
and the calculus of determinants and discriminants. Then we show a formula
which links the spinor norm in $U(V,h)$ and the spinor norm in the orthogonal
group $O(V,b_h)$ defined by a non-degenerate symmetric bilinear form $b_h$
associated to $h$.


title:
Uniform regularity for linear kinetic equations with random input based
  on hypocoercivity

abstract:
  In this paper we study the effect of randomness in kinetic equations that
preserve mass. Our focus is in proving the analyticity of the solution with
respect to the randomness, which naturally leads to the convergence of
numerical methods. The analysis is carried out in a general setting, with the
regularity result not depending on the specific form of the collision term, the
probability distribution of the random variables, or the regime the system is
in, and thereby termed "uniform". Applications include the linear Boltzmann
equation, BGK model, Carlemann model, among many others; and the results hold
true in kinetic, parabolic and high field regimes. The proof relies on the
explicit expression of the high order derivatives of the solution in the random
space, and the convergence in time is mainly based on hypocoercivity, which,
despite the popularity in PDE analysis of kinetic theory, has rarely been used
for numerical algorithms.


title: Perverse obstructions to flat regular compactifications

abstract:
  Suppose $\pi:W\to S$ is a smooth, proper morphism over a variety $S$
contained as a Zariski open subset in a smooth, complex variety $\bar S$. The
goal of this note is to consider the question of when $\pi$ admits a regular,
flat compactification. In other words, when does there exists a flat, proper
morphism $\bar\pi:\overline{W}\to\bar S$ extending $\pi$ with $\overline{W}$
regular? One interesting recent example of this occurs in the preprint
arXiv:1602.05534 of Laza, Sacca and Voisin where $\pi$ is a family of abelian
$5$-folds over a Zariski open subset $S$ of $\bar S=\mathbb{P}^5$. In that
paper, the authors construct $\overline{W}$ using the theory of compactified
Prym varieties and show that it is a holomorphic symplectic manifold
(deformation equivalent to O'Grady's $10$-dimensional example).
  In this note I observe that non-vanishing of the local intersection
cohomology of $R^1\pi_*\mathbb{Q}$ in degree at least $2$ provides an
obstruction to finding a $\bar\pi$. Moreover, non-vanishing in degree $1$
provides an obstruction to finding a $\bar\pi$ with irreducible fibers. Then I
observe that, in some cases of interest, results of Brylinski, Beilinson and
Schnell can be used to compute the intersection cohomology. I also give
examples involving cubic $4$-folds, and ask a question about palindromicity of
hyperplane sections.


title:
A Systematic Study of the Thermal and Nonthermal Emission in the
  Supernova Remnant RCW 86 with Suzaku

abstract:
  Diffusive shock acceleration by the shockwaves in supernova remnants (SNRs)
is widely accepted as the dominant source for Galactic cosmic rays. However, it
is unknown what determines the maximum energy of accelerated particles. The
surrounding environment could be one of the key parameters. The SNR RCW 86
shows both thermal and non-thermal X-ray emission with different spatial
morphologies. These emission originate from the shock-heated plasma and
accelerated electrons respectively, and their intensities reflect their density
distributions. Thus, the remnant provides a suitable laboratory to test
possible association between the acceleration efficiency and the environment.
In this paper, we present results of spatially resolved spectroscopy of the
entire remnant with Suzaku. The spacially-resolved spectra are well reproduced
with a combination of a power-law for synchrotron emission and a two-component
optically thin thermal plasma, corresponding to the shocked interstellar medium
(ISM) with kT of 0.3-0.6 keV and Fe-dominated ejecta. It is discovered that the
photon index of the nonthermal component becomes smaller with decreasing the
emission measure of the shocked ISM, where the shock speed has remained high.
This result implies that the maximum energy of accelerated electrons in RCW 86
is higher in the low-density and higher shock speed regions.


title: Time-delay Induced Dimensional Crossover in Voter Model

abstract:
  We investigate the ordering dynamics of the voter model with time-delayed
interactions. The dynamical process in the $d$-dimensional lattice is shown to
be equivalent to the first passage problem of a random walker in the
$(d+1)$-dimensional strip of a finite width determined by the delay time. The
equivalence reveals that the time delay leads to the dimensional crossover from
the $(d+1)$-dimensional scaling behavior at short time to the $d$-dimensional
scaling behavior in the long time. The scaling property in both regimes and the
crossover time scale are obtained analytically, which are confirmed with the
numerical simulation results.


title: Search for dark matter from the first data of the PandaX-II experiment

abstract:
  Results of WIMP dark matter search from the first data of the PandaX-II
experiment are presented. PandaX-II experiment uses a 500 kg scale dual phase
liquid xenon time projection chamber, operating at the China JinPing
Underground Laboratory. The first data correspond to a total exposure of
$3.1\times10^{4}$ kg-day. The observed data after selections are found to be
consistent with background expection, and upper limits of the spin-independent
WIMP-nucleon cross sections are derived for a range of WIMP mass between 5
GeV/c$^2$ and 1000 GeV/$c^{2}$. The lowest cross section limit obtained is
2.5$\times$10$^{-46}$ cm$^2$ at a WIMP mass of 40 GeV/c$^2$.

categories: hep-ex astro-ph.CO hep-ph physics.ins-det


title:
Numerical simulations of the Princeton magneto-rotational instability
  experiment with conducting axial boundaries

abstract:
  We investigate numerically the Princeton magneto-rotational instability (MRI)
experiment and the effect of conducting axial boundaries or endcaps. MRI is
identified and found to reach a much higher saturation than for insulating
endcaps. This is probably due to stronger driving of the base flow by the
magnetically rather than viscously coupled boundaries. Although the
computations are necessarily limited to lower Reynolds numbers ($\Re$) than
their experimental counterparts, it appears that the saturation level becomes
independent of $\Re$ when $\Re$ is sufficiently large, whereas it has been
found previously to decrease roughly as $\Re^{-1/4}$ with insulating endcaps.
The much higher saturation levels will allow for the first positive detection
of MRI beyond its theoretical and numerical predictions.

categories: physics.flu-dyn astro-ph.EP astro-ph.SR physics.plasm-ph


title: Deep Multi-Modal Image Correspondence Learning

abstract:
  Inference of correspondences between images from different modalities is an
extremely important perceptual ability that enables humans to understand and
recognize cross-modal concepts. In this paper, we consider an instance of this
problem that involves matching photographs of building interiors with their
corresponding floorplan. This is a particularly challenging problem because a
floorplan, as a stylized architectural drawing, is very different in appearance
from a color photograph. Furthermore, individual photographs by themselves
depict only a part of a floorplan (e.g., kitchen, bathroom, and living room).
We propose the use of a number of different neural network architectures for
this task, which are trained and evaluated on a novel large-scale dataset of 5
million floorplan images and 80 million associated photographs. Experimental
evaluation reveals that our neural network architectures are able to identify
visual cues that result in reliable matches across these two quite different
modalities. In fact, the trained networks are able to even outperform human
subjects in several challenging image matching problems. Our result implies
that neural networks are effective at perceptual tasks that require long
periods of reasoning even for humans to solve.


title: Computing the Fixed Field of $\text{Aut}(\mathbb{F}(x)/\mathbb{F})$

abstract:
  For a finite field $\mathbb{F}$, it is a basic result of Galois theory that
the fixed field $E$ of $\text{Aut}(\mathbb{F}(x)/\mathbb{F})$ is a proper
extension of $\mathbb{F}$. In this expository paper we construct, for all
finite fields, an element $f\in \mathbb{F}(x)$ such that $E = \mathbb{F}(f)$.
This element is shown to be easily computable in all cases using a simple
formula. The approach is entirely elementary, and aimed at the student level;
only a basic familiarity with Galois theory and field extensions is assumed.


title:
Deep Blur Mapping: Exploiting High-Level Semantics by Deep Neural
  Networks

abstract:
  The human visual system excels at detecting local blur of visual images, but
the underlying mechanism is not well understood. Traditional views of blur such
as reduction in energy at high frequencies and loss of phase coherence at
localized features have fundamental limitations. For example, they cannot well
discriminate flat regions from blurred ones. Here we propose that high-level
semantic information is critical in successfully identifying local blur.
Therefore, we resort to deep neural networks that are proficient at learning
high-level features and propose the first end-to-end local blur mapping
algorithm based on a fully convolutional network. By analyzing various
architectures with different depths and design philosophies, we empirically
show that high-level features of deeper layers play a more important role than
low-level features of shallower layers in resolving challenging ambiguities for
this task. We test the proposed method on a standard blur detection benchmark
and demonstrate that it significantly advances the state-of-the-art (ODS
F-score of 0.853). Furthermore, we explore the use of the generated blur maps
in three applications, including blur region segmentation, blur degree
estimation, and blur magnification.


title: On uniqueness of static black hole with conformal scalar hair

abstract:
  We discuss the uniqueness of the static black hole in the Einstein gravity
with a conformally coupled scalar field. In particular, we prove the uniqueness
of the region outside of the photon surface, not event horizon.