title:
The star-triangle relation, lens partition function, and hypergeometric
  sum/integrals

abstract:
  The aim of the present paper is to consider the hyperbolic limit of an
elliptic hypergeometric sum/integral identity, and associated lattice model of
statistical mechanics previously obtained by the second author. The hyperbolic
sum/integral identity obtained from this limit, has two important physical
applications in the context of the so-called gauge/YBE correspondence. For
statistical mechanics, this identity is equivalent to a new solution of the
star-triangle relation form of the Yang-Baxter equation, that directly
generalises the Faddeev-Volkov models to the case of discrete and continuous
spin variables. On the gauge theory side, this identity represents the duality
of lens ($S_b^3/\mathbb{Z}_r$) partition functions, for certain
three-dimensional $\mathcal N = 2$ supersymmetric gauge theories.

categories: math-ph cond-mat.stat-mech hep-th math.MP


title: Robust Utility Maximization in Discrete-Time Markets with Friction

abstract:
  We study a robust stochastic optimization problem in the quasi-sure setting
in discrete-time. We show that under a lineality-type condition the problem
admits a maximizer. This condition is implied by the no-arbitrage condition in
models of financial markets. As a corollary, we obtain existence of an utility
maximizer in the frictionless market model, markets with proportional
transaction costs and also more general convex costs, like in the case of
market impact.


title:
Integration Checker of JAVA P2P distributed System with Auto Source Code
  Composition

abstract:
  This paper presents an integrity checker of JAVA P2P distributed system with
auto source code composition. JAVA distributed system must guarantee the
integrity of program itself and the system components of JAVA virtual machine
against attackers, hackers, spies, cheaters, conspirators, etc. There are lots
of trusted computing methods to guarantee the integrity of the system. We here
present a novel method using just-in-time auto source code composition to
generate autocheck class for integrity measure and encrypt of integrity
reporting.
  By companies' effort, we have implemented and use it in DSCloud platform.


title: On the Fractional fixing number of graphs

abstract:
  An automorphism group of a graph $G$ is the set of all permutations of the
vertex set of $G$ that preserve adjacency and non adjacency of vertices in a
graph. A fixing set of a graph $G$ is a subset of vertices of $G$ such that
only the trivial automorphism fixes every vertex in $S$. Minimum cardinality of
a fixing set of $G$ is called the fixing number of $G$. In this article, we
define a fractional version of the fixing number of a graph. We formulate the
problem of finding the fixing number of a graph as an integer programming
problem. It is shown that a relaxation of this problem leads to a linear
programming problem and hence to a fractional version of the fixing number of a
graph. We also characterize the graphs $G$ with the fractional fixing number
$\frac{|V(G)|}{2}$ and the fractional fixing number of some families of graphs
is also obtained.


title:
Multiconfiguration calculations of electronic isotope shift factors in
  Al I

abstract:
  The present work reports results from systematic multiconfiguration
Dirac-Hartree-Fock calculations of electronic isotope shift factors for a set
of transitions between low-lying states in neutral aluminium. These electronic
quantities together with observed isotope shifts between different pairs of
isotopes provide the changes in mean-square charge radii of the atomic nuclei.
Two computational approaches are adopted for the estimation of the mass- and
field shift factors. Within these approaches, different models for electron
correlation are explored in a systematic way to determine a reliable
computational strategy and estimate theoretical error bars of the isotope shift
factors.


title: Super-Replication with Fixed Transaction Costs

abstract:
  We study super--replication of contingent claims in markets with fixed
transaction costs. This can be viewed as a stochastic impulse control problem
with a terminal state constraint. The first result in this paper reveals that
in reasonable continuous time financial market models the super--replication
price is prohibitively costly and leads to trivial buy--and--hold strategies.
Our second result derives nontrivial scaling limits of super--replication
prices for binomial models with small fixed costs.


title: A Tale of Two Turing Machines

abstract:
  Two Turing Machines may be able to answer questions about each other that
they cannot answer about themselves.


title: Hard X-rays as pump and probe of atomic motion in oxide glasses

abstract:
  Nowadays powerful X-ray sources like synchrotrons and free-electron lasers
are considered as ultimate tools for probing microscopic properties in
materials. However, the correct interpretation of such experiments requires a
good understanding on how the beam affects the properties of the sample,
knowledge that is currently lacking for intense X-rays. Here we use X-ray
photon correlation spectroscopy to probe static and dynamic properties of oxide
and metallic glasses. We find that although the structure does not depend on
the flux, strong fluxes do induce a non-trivial microscopic motion in oxide
glasses, whereas no such dependence is found for metallic glasses. These
results show that high fluxes can alter dynamical properties in hard materials,
an effect that needs to be considered in the analysis of X-ray data but which
also gives novel possibilities to study materials properties since the beam can
not only be used to probe the dynamics but also to pump it.


title: Learnable Visual Markers

abstract:
  We propose a new approach to designing visual markers (analogous to QR-codes,
markers for augmented reality, and robotic fiducial tags) based on the advances
in deep generative networks. In our approach, the markers are obtained as color
images synthesized by a deep network from input bit strings, whereas another
deep network is trained to recover the bit strings back from the photos of
these markers. The two networks are trained simultaneously in a joint
backpropagation process that takes characteristic photometric and geometric
distortions associated with marker fabrication and marker scanning into
account. Additionally, a stylization loss based on statistics of activations in
a pretrained classification network can be inserted into the learning in order
to shift the marker appearance towards some texture prototype. In the
experiments, we demonstrate that the markers obtained using our approach are
capable of retaining bit strings that are long enough to be practical. The
ability to automatically adapt markers according to the usage scenario and the
desired capacity as well as the ability to combine information encoding with
artistic stylization are the unique properties of our approach. As a byproduct,
our approach provides an insight on the structure of patterns that are most
suitable for recognition by ConvNets and on their ability to distinguish
composite patterns.


title: Strata of $k$-differentials

abstract:
  A $k$-differential on a Riemann surface is a section of the $k$-th power of
the canonical line bundle. Loci of $k$-differentials with prescribed number and
multiplicities of zeros and poles form a natural stratification of the moduli
space of $k$-differentials. In this paper we give a complete description for
the compactification of the strata of $k$-differentials in terms of pointed
stable $k$-differentials, for all $k$. The upshot is a global $k$-residue
condition that can also be reformulated in terms of admissible covers of stable
curves. Moreover, we study properties of $k$-differentials regarding their
deformations, residues, and flat geometric structure.


title: Curvature driven motion of soap cells in toroidal Hele-Shaw cells

abstract:
  We investigate the equilibrium properties of a single area-minimising bubble
trapped between two narrowly-separated parallel curved plates. We begin with
the simple case of a a bubble trapped between concentric spherical plates. We
develop a model that shows that the surface tension energy of the bubble is
lower when confined between spherical plates as compared to a bubble trapped
between flat plates. We confirm our findings by comparing against Surface
Evolver simulations. Next, we derive a simple model for a bubble between
arbitrarily curved parallel plates. The energy is found to be higher when the
local Gaussian curvature of the plates is negative and lower when the curvature
is positive. To check the validity of the the model we consider a bubble
trapped between concentric tori. In the toroidal case we find that the
sensitivity of the bubble's energy to the local curvature acts as a geometric
potential capable of driving bubbles from regions with negative to positive
curvature.


title:
Software Architecture Decision-Making Practices and Challenges: An
  Industrial Case Study

abstract:
  Software architecture decision-making is critical to the success of a
software system as software architecture sets the structure of the system,
determines its qualities, and has far-reaching consequences throughout the
system life cycle. The complex nature of the software development context and
the importance of the problem has led the research community to develop several
techniques, tools, and processes to assist software architects in making better
decisions. Despite these effort, the adoption of such systematic approaches
appears to be quite limited in practice. In addition, the practitioners are
also facing new challenges as different software development methods suggest
different approaches for architecture design. In this paper, we study the
current software architecture decision-making practices in the industry using a
case study conducted among professional software architects in three different
companies in Europe. As a result, we identified different software architecture
decision-making practices followed by the software teams as well as their
reasons for following them, the challenges associated with them, and the
possible improvements from the software architects' point of view. Based on
that, we recognized that improving software architecture knowledge management
can address most of the identified challenges and would result in better
software architecture decision-making.


title:
Nonconforming Finite Volume Methods for Second Order Elliptic Boundary
  Value Problems

abstract:
  This paper is devoted to analyze of nonconforming finite volume methods
(FVMs), whose trial spaces are chosen as the nonconforming finite element (FE)
spaces, for solving the second order elliptic boundary value problems. We
formulate the nonconforming FVMs as special types of Petrov-Galerkin methods
and develop a general convergence theorem, which serves as a guide for the
analysis of the nonconforming FVMs. As special examples, we shall present the
triangulation based Crouzeix-Raviart (C-R) FVM as well as the rectangle mesh
based hybrid Wilson FVM. Their optimal error estimates in the mesh dependent
$H^1$-norm will be obtained under the condition that the primary mesh is
regular. For the hybrid Wilson FVM, we prove that it enjoys the same optimal
error order in the $L^2$-norm as that of the Wilson FEM. Numerical experiments
are also presented to confirm the theoretical results.


title:
The microscopic structure of $\pi NN$, $\pi N\Delta$ and
  $\pi\Delta\Delta$ vertices in a hybrid constituent quark model

abstract:
  We present a microscopic description of the strong $\pi NN$, $\pi N\Delta$
and $\pi\Delta\Delta$ vertices. Our starting point is a constituent-quark model
supplemented by an additional $3q\pi$ non-valence component. In the spirit of
chiral constituent-quark models, quarks are allowed to emit and reabsorb a
pion. This multichannel system is treated in a relativistically invariant way
within the framework of point-form quantum mechanics. Starting with a common
$SU(6)$ spin-flavor-symmetric wave function for $N$ and $\Delta$, we calculate
the strength of the $\pi NN$, $\pi N\Delta$ and $\pi\Delta\Delta$ couplings and
the corresponding vertex form factors. Our results are in accordance with
phenomenological fits of these quantities that have been obtained within purely
hadronic multichannel models for baryon resonances.


title: Weyl Current, Scale-Invariant Inflation and Planck Scale Generation

abstract:
  Scalar fields, $\phi_i$ can be coupled non-minimally to curvature and satisfy
the general criteria: (i) the theory has no mass input parameters, including
the Planck mass; (ii) the $\phi_i$ have arbitrary values and gradients, but
undergo a general expansion and relaxation to constant values that satisfy a
nontrivial constraint, $K(\phi_i) =$ constant; (iii) this constraint breaks
scale symmetry spontaneously, and the Planck mass is dynamically generated;
(iv) there can be adequate inflation associated with slow roll in a scale
invariant potential subject to the constraint; (v) the final vacuum can have a
small to vanishing cosmological constant (vi) large hierarchies in vacuum
expectation values can naturally form; (vii) there is a harmless dilaton which
naturally eludes the usual constraints on massless scalars. These models are
governed by a global Weyl scale symmetry and its conserved current, $K_\mu$ .
At the quantum level the Weyl scale symmetry can be maintained by an invariant
specification of renormalized quantities.


title: An Application of Group Theory in Confidential Network Communications

abstract:
  A new proposal for group key exchange is introduced which proves to be both
efficient and secure and compares favorably with state of the art protocols.


title: On the cardinality of Hausdorff spaces and H-closed spaces

abstract:
  We introduce the cardinal invariant $aL^\prime(X)$ and show that $|X|\leq
2^{aL^\prime(X)\chi(X)}$ for any Hausdorff space $X$ (a corollary of Theorem
4.4. This invariant has the properties a) $aL^\prime(X)=\aleph_0$ if $X$ is
H-closed, and b) $aL(X)\leq aL^\prime(X)\leq aL_c(X)$. Theorem 4.4 then gives a
new improvement of the well-known Hausdorff bound $2^{L(X)\chi(X)}$ from which
it follows that $|X|\leq 2^{\psi_c(X)}$ if $X$ is H-closed (Dow/Porter [5]).
The invariant $aL^\prime(X)$ is constructed using convergent open ultrafilters
and an operator $c:\scr{P}(X)\to\scr{P}(X)$ with the property $clA\subseteq
c(A)\subseteq cl_\theta(A)$ for all $A\subseteq X$. As a comparison with this
open ultrafilter approach, in $\S 3$ we additionally give a $\kappa$-filter
variation of Hodel's proof [10] of the Dow-Porter result. Finally, for an
infinite cardinal $\kappa$, in $\S 5$ we introduce $\kappa$wH-closed spaces,
$\kappa H^\prime$-closed spaces, and $\kappa H^{\prime\prime}$-closed spaces.
The first two notions generalize the H-closed property. Key results in this
connection are that a) if $\kappa$ is an infinite cardinal and $X$ a
$\kappa$wH-closed space with a dense set of isolated points such that
$\chi(X)\leq\kappa$, then $|X|\leq 2^{\kappa}$, and b) if $X$ is $\kappa
H^\prime$-closed or $\kappa H^{\prime\prime}$-closed then
$aL^\prime(X)\leq\kappa$. This latter result relates these notions to the
invariant $aL^\prime(X)$ and the operator $c$.


title:
Feasibility of the $\beta^-$ Radio-Guided Surgery with a Variety of
  Radio-Nuclides of Interest to Nuclear Medicine

abstract:
  The $\beta^-$ based radio-guided surgery overcomes the corresponding $\gamma$
technique in case the background from healthy tissues is relevant. It can be
used only in case a radio-tracer marked with $^{90}$Y is available since the
current probe prototype was optimized for the emission spectrum of this
radio-nuclide. Here we study, with a set of laboratory tests and simulations,
the prototype capability in case a different radio-nuclide is chosen among
those used in nuclear medicine.
  As a result we estimate the probe efficiency on electrons and photons as a
function of energy and we evaluate the feasibility of a radio-guided surgery
exploiting the selected radio-nuclides. We conclude that requiring a 0.1~ml
residue to be detected within 1~s by administering 3~MBq/Kg of radio-isotope,
the current probe prototype would yield a significant signal in a vast range of
values of SUV and TNR in case $^{31}$Si,$^{32}$P, $^{97}$Zr, and $^{188}$Re are
used. Conversely, a tuning of the detector would be needed to efficiency use
$^{83}$Br, $^{133}$I, and $^{153}$Sm, although they could already be used in
case of high SUV or TNR values. Finally, $^{18}$F,$^{67}$Cu, $^{131}$I, and
$^{177}$Lu are not useable for radio-guided surgery with the current probe
design.


title: Generalized I-MMSE for K-User Gaussian Channels

abstract:
  In this paper, we generalize the fundamental relation between the mutual
information and the minimum mean squared error (MMSE) by Guo, Shamai, and Verdu
[1] to K-User Gaussian channels. We prove that the derivative of the multiuser
mutual information with respect to the signal to noise ratio (SNR) is equal to
the total MMSE plus a covariance term with respect to the cross correlation of
the multiuser input estimates, the channels and the precoding matrices. We shed
light that such relation is a generalized I-MMSE with one step lookahead and
lookback, applied to the Successive Interference Cancellation (SIC) in the
decoding process.


title: Radio Link Planning made easy with a Telegram Bot

abstract:
  Traditional radio planning tools present a steep learning curve. We present
BotRf, a Telegram Bot that facilitates the process by guiding non-experts in
assessing the feasibility of radio links. Built on open source tools, BotRf can
run on any smartphone or PC running Telegram. Using it on a smartphone has the
added value that the Bot can leverage the internal GPS to enter coordinates.
BotRf can be used in environments with low bandwidth as the generated data
traffic is quite limited. We present examples of its use in Venezuela.


title:
Estimates of time-periodic fundamental solutions to the linearized
  Navier-Stokes equations

abstract:
  Fundamental solutions to the time-periodic Stokes and Oseen linearizations of
the Navier-Stokes equations in dimension $n\geq 2$ are investigated.
Integrability properties and pointwise estimates are established.


title: Defining the q-analogue of a matroid

abstract:
  This paper defines the q-analogue of a matroid and establishes several
properties like duality, restriction and contraction. We discuss possible ways
to define a q-matroid, and why they are (not) cryptomorphic. Also, we explain
the motivation for studying q-matroids by showing that a rank metric code gives
a q-matroid.


title: Kelvin Waves and Dynamic Knots on Vortex-Membrane

abstract:
  Quantum mechanics is a successful theory that describes the behavior of
photons, electrons, and other atomic- and molecular-scale objects. However, it
is far from being well understood. In this paper, a new theory - knot physics
for entangled vortex-membranes is developed to explore the underline physics of
quantum mechanics. From point view of information, three dimensional quantum
Dirac model is developed to effectively describe the fluctuations of local
deformation of vortex-membranes: The elementary excitations are knots with
information unit; The physics quality to describe local deformation is knot
density that is defined by the density of zeros between two projected
vortex-membranes; The Biot-Savart equation for Kelvin waves becomes Schrodinger
equation for probability waves of knots; the classical functions for
perturbative Kelvin waves become wave functions for knots; The probability of
quantum mechanics comes from dynamic projection for inner observers owing to
"fast clock" effect; The angular frequency for leapfrogging motion plays the
role of the mass of knots; etc. This work would help people to understand the
mystery of quantum mechanics.


title: Comments on "Slowing of Bessel light beam group velocity"

abstract:
  In a recent article [R. R. Alfano and D. A. Nolan, Opt. Commun. 361 (2016)
25] the group velocity reduction below the speed of light in the case of
certain Bessel beam pulses has been considered and an idea of its application
for a natural optical buffer presented. However, the authors treat the problem
as if only one type of Bessel pulse existed, no matter how it is generated. The
deficiencies of the article stem from not being familiar with an extensive
literature on Bessel pulses, in particular, with a couple of papers published
much earlier in the J. Opt. Soc. Am. A, which have studied exactly the same
problem more thoroughly.


title:
Supporting novel biomedical research via multilayer collaboration
  networks

abstract:
  The value of research containing novel combinations of molecules can be seen
in many innovative and award-winning research programs. Despite calls to use
innovative approaches to address common diseases, an increasing majority of
research funding goes toward "safe" incremental research. Counteracting this
trend by nurturing novel and potentially transformative scientific research is
challenging, it must be supported in competition with established research
programs. Therefore, we propose a tool that helps to resolve the tension
between safe but fundable research vs. high-risk but potentially
transformational research. It does this by identifying hidden overlapping
interest around novel molecular research topics. Specifically, it identifies
paths of molecular interactions that connect research topics and hypotheses
that would not typically be associated, as the basis for scientific
collaboration. Because these collaborations are related to the scientists'
present trajectory, they are low risk and can be initiated rapidly. Unlike most
incremental steps, these collaborations have the potential for leaps in
understanding, as they reposition research for novel disease applications. We
demonstrate the use of this tool to identify scientists who could contribute to
understanding the cellular role of genes with novel associations with
Alzheimer's disease, which have not been thoroughly characterized, in part due
to the funding emphasis on established research.


title:
Partiality, Revisited: The Partiality Monad as a Quotient
  Inductive-Inductive Type

abstract:
  Capretta's delay monad can be used to model partial computations, but it has
the "wrong" notion of built-in equality, strong bisimilarity. An alternative is
to quotient the delay monad by the "right" notion of equality, weak
bisimilarity. However, recent work by Chapman et al. suggests that it is
impossible to define a monad structure on the resulting construction in common
forms of type theory without assuming (instances of) the axiom of countable
choice. Using an idea from homotopy type theory - a higher inductive-inductive
type - we construct a partiality monad without relying on countable choice. We
prove that, in the presence of countable choice, our partiality monad is
equivalent to the delay monad quotiented by weak bisimilarity. Furthermore we
outline several applications.


title: Observing the formation of flare-driven coronal rain

abstract:
  Flare-driven coronal rain can manifest from rapidly cooled plasma
condensations near coronal loop-tops in thermally unstable post-flare arcades.
We detect 5 phases that characterise the post-flare decay: heating,
evaporation, conductive cooling dominance for ~120 s, radiative / enthalpy
cooling dominance for ~4700 s and finally catastrophic cooling occurring within
35-124 s leading to rain strands with s periodicity of 55-70 s. We find an
excellent agreement between the observations and model predictions of the
dominant cooling timescales and the onset of catastrophic cooling. At the rain
formation site we detect co-moving, multi-thermal rain clumps that undergo
catastrophic cooling from ~1 MK to ~22000 K. During catastrophic cooling the
plasma cools at a maximum rate of 22700 K s-1 in multiple loop-top sources. We
calculated the density of the EUV plasma from the DEM of the multi-thermal
source employing regularised inversion. Assuming a pressure balance, we
estimate the density of the chromospheric component of rain to be 9.21x10^11
+-1.76x10^11 cm-3 which is comparable with quiescent coronal rain densities.
With up to 8 parallel strands in the EUV loop cross section, we calculate the
mass loss rate from the post-flare arcade to be as much as 1.98x10^12
+/-4.95x10^11 g s-1. Finally, we reveal a close proximity between the model
predictions of 10^5.8 K and the observed properties between 10^5.9 K and 10^6.2
K, that defines the temperature onset of catastrophic cooling. The close
correspondence between the observations and numerical models suggests that
indeed acoustic waves (with a sound travel time of 68 s) could play an
important role in redistributing energy and sustaining the enthalpy-based
radiative cooling.


title:
Performance Impact of LOS and NLOS Transmissions in Dense Cellular
  Networks under Rician Fading

abstract:
  In this paper, we analyse the performance of dense small cell network (SCNs).
We derive analytical expressions for both their coverage probability and their
area spectral efficiency (ASE) using a path loss model that considers both
line-of-sight (LOS) and non-LOS (NLOS) components. Due to the close proximity
of small cell base stations (BSs) and user equipments (UEs) in such dense SCNs,
we also consider Rician fading as the multi-path fading channel model for both
the LOS and NLOS fading transmissions. The Rayleigh fading used in most of
existing works analysing dense SCNs is not accurate enough. Then, we compare
the performance impact of LOS and NLOS transmissions in dense SCNs under Rician
fading with that based on Rayleigh fading. The analysis and the simulation
results show that in dense SCNs where LOS transmissions dominate the
performance, the impact of Rician fading on the overall system performance is
minor, and does not help to address the performance losses brought by the
transition of many interfering signals from NLOS to LOS.


title: Emergence of the world with Lie-N-algebra and M-dimensions from nothing

abstract:
  In this paper, we propose a new model in Lie-N-algebra that removes big bang
singularity and produces the world with all it's objects and dimensions from
nothing. We name this theory as G-theory. In this model, first, two types of
energies with opposite signs are produced from nothing such as the sum over
them be zero. They create two types of branes with opposite quantum numbers
which interact with each other by exchanging bosonic tensor fields like
graviton and compact. By compacting branes, fermionic tensor fields are emerged
which some of them play the role of the gravitinos. Also, some dimensions take
extra (i) factors, their properties become different and they behave like time
dimensions. Gravitons and gravitinos create two types of wormholes which lead
to the oscillation of branes between expansion and contracting branches. These
wormholes produce a repulsive gravity in compacted branes and cause that their
particles get away from each other and expansion branch begin. Also, they
create an attractive gravity in opening branes and lead to closing their
particles and starting the contraction epoch. Our universe is born on one of
these branes and oscillates between contraction and expansion branch.


title:
Design and advancement status of the Beam Expander Testing X-ray
  facility (BEaTriX)

abstract:
  The BEaTriX (Beam Expander Testing X-ray facility) project is an X-ray
apparatus under construction at INAF/OAB to generate a broad (200 x 60 mm2),
uniform and low-divergent X-ray beam within a small lab (6 x 15 m2). BEaTriX
will consist of an X-ray source in the focus a grazing incidence paraboloidal
mirror to obtain a parallel beam, followed by a crystal monochromation system
and by an asymmetrically-cut diffracting crystal to perform the beam expansion
to the desired size. Once completed, BEaTriX will be used to directly perform
the quality control of focusing modules of large X-ray optics such as those for
the ATHENA X-ray observatory, based on either Silicon Pore Optics (baseline) or
Slumped Glass Optics (alternative), and will thereby enable a direct quality
control of angular resolution and effective area on a number of mirror modules
in a short time, in full X-ray illumination and without being affected by the
finite distance of the X-ray source. However, since the individual mirror
modules for ATHENA will have an optical quality of 3-4 arcsec HEW or better,
BEaTriX is required to produce a broad beam with divergence below 1-2 arcsec,
and sufficient flux to quickly characterize the PSF of the module without being
significantly affected by statistical uncertainties. Therefore, the optical
components of BEaTriX have to be selected and/or manufactured with excellent
optical properties in order to guarantee the final performance of the system.
In this paper we report the final design of the facility and a detailed
performance simulation.


title: 3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes

abstract:
  We study CFT data of 3-dimensional superconformal field theories (SCFTs)
arising from wrapped two M5-branes on closed hyperbolic 3-manifolds. Via
so-called 3d/3d correspondence, central charges of these SCFTs are related to a
$SL(2)$ Chern-Simons (CS) invariant on the 3-manifolds. We give a rigorous
definition of the invariant in terms of resurgence theory and a state-integral
model for the complex CS theory. We numerically evaluate the central charges
for several closed 3-manifolds with small hyperbolic volume. The computation
suggests that the wrapped M5-brane systems give infinitely many discrete SCFTs
with small central charges. We also analyze these `minimal' SCFTs in the eye of
3d $\mathcal{N}=2$ superconformal bootstrap.


title: Introduction to abelian and non-abelian anyons

abstract:
  In this set of lectures, we will start with a brief pedagogical introduction
to abelian anyons and their properties. This will essentially cover the
background material with an introduction to basic concepts in anyon physics,
fractional statistics, braid groups and abelian anyons. The next topic that we
will study is a specific exactly solvable model, called the toric code model,
whose excitations have (mutual) anyon statistics. Then we will go on to discuss
non-abelian anyons, where we will use the one dimensional Kitaev model as a
prototypical example to produce Majorana modes at the edge. We will then
explicitly derive the non-abelian unitary matrices under exchange of these
Majorana modes.


title:
CHOPtrey: contextual online polynomial extrapolation for enhanced
  multi-core co-simulation of complex systems

abstract:
  The growing complexity of Cyber-Physical Systems (CPS), together with
increasingly available parallelism provided by multi-core chips, fosters the
parallelization of simulation. Simulation speed-ups are expected from
co-simulation and parallelization based on model splitting into weak-coupled
sub-models, as for instance in the framework of Functional Mockup Interface
(FMI). However, slackened synchronization between sub-models and their
associated solvers running in parallel introduces integration errors, which
must be kept inside acceptable bounds.
  CHOPtrey denotes a forecasting framework enhancing the performance of complex
system co-simulation, with a trivalent articulation. First, we consider the
framework of a Computationally Hasty Online Prediction system (CHOPred). It
allows to improve the trade-off between integration speed-ups, needing large
communication steps, and simulation precision, needing frequent updates for
model inputs. Second, smoothed adaptive forward prediction improves
co-simulation accuracy. It is obtained by past-weighted extrapolation based on
Causal Hopping Oblivious Polynomials (CHOPoly). And third, signal behavior is
segmented to handle the discontinuities of the exchanged signals: the
segmentation is performed in a Contextual \& Hierarchical Ontology of Patterns
(CHOPatt).
  Implementation strategies and simulation results demonstrate the framework
ability to adaptively relax data communication constraints beyond
synchronization points which sensibly accelerate simulation. The CHOPtrey
framework extends the range of applications of standard Lagrange-type methods,
often deemed unstable. The embedding of predictions in lag-dependent smoothing
and discontinuity handling demonstrates its practical efficiency.


title: Superconductivity and Fast Proton Transport in Nanoconfined Water

abstract:
  A real-space molecular-orbital description of Cooper pairing in conjunction
with the dynamic Jahn-Teller mechanism for high-Tc superconductivity predicts
that electron-doped water confined to the nanoscale environment of a carbon
nanotube or biological macromolecule should superconduct below and exhibit fast
proton transport above the transition temperature, Tc = 230 degK (-43 degC).


title: Flexible constrained sampling with guarantees for pattern mining

abstract:
  Pattern sampling has been proposed as a potential solution to the infamous
pattern explosion. Instead of enumerating all patterns that satisfy the
constraints, individual patterns are sampled proportional to a given quality
measure. Several sampling algorithms have been proposed, but each of them has
its limitations when it comes to 1) flexibility in terms of quality measures
and constraints that can be used, and/or 2) guarantees with respect to sampling
accuracy. We therefore present Flexics, the first flexible pattern sampler that
supports a broad class of quality measures and constraints, while providing
strong guarantees regarding sampling accuracy. To achieve this, we leverage the
perspective on pattern mining as a constraint satisfaction problem and build
upon the latest advances in sampling solutions in SAT as well as existing
pattern mining algorithms. Furthermore, the proposed algorithm is applicable to
a variety of pattern languages, which allows us to introduce and tackle the
novel task of sampling sets of patterns. We introduce and empirically evaluate
two variants of Flexics: 1) a generic variant that addresses the well-known
itemset sampling task and the novel pattern set sampling task as well as a wide
range of expressive constraints within these tasks, and 2) a specialized
variant that exploits existing frequent itemset techniques to achieve
substantial speed-ups. Experiments show that Flexics is both accurate and
efficient, making it a useful tool for pattern-based data exploration.


title:
Density matrix based time-dependent configuration interaction approach
  to ultrafast spin-flip dynamics

abstract:
  Recent developments in attosecond spectroscopy yield access to the correlated
motion of electrons on their intrinsic time scales. Spin-flip dynamics is
usually considered in the context of valence electronic states, where
spin-orbit coupling is weak and processes related to the electron spin are
usually driven by nuclear motion. However, for core-excited states, where the
core hole has a nonzero angular momentum, spin-orbit coupling is strong enough
to drive spin-flips on a much shorter time scale. Using density matrix based
time-dependent restricted active space configuration interaction including
spin-orbit coupling, we address an unprecedentedly short spin-crossover for the
example of L-edge (2p$\rightarrow$3d) excited states of a prototypical Fe(II)
complex. This process occurs on a time scale, which is faster than that of
Auger decay ($\sim$4\,fs) treated here explicitly. Modest variations of carrier
frequency and pulse duration can lead to substantial changes in the spin-state
yield, suggesting its control by soft X-ray light.


title:
Charge carrier transport and lifetimes in n-type and p-type phosphorene
  as 2D device active materials: an ab initio study

abstract:
  In this work, we provide a detailed analysis of phosphorene performance as
n-type and p-type active materials. The study is based on first principles
calculation of phosphorene electronic structure, and resulting electron and
hole scattering rates and lifetimes. Emphasis is put on extreme regimes
commonly found in semiconductor devices, i.e. high electric fields and heavy
doping, where impact ionization and Auger recombination can occur. We found
that electron-initiated impact ionization is weaker than the hole-initiated
process, when compared to carrier-phonon interaction rates, suggesting
resilience to impact ionization initiated breakdown. Moreover, calculated
minority electron lifetimes are limited by radiative recombination only, not by
Auger processes, suggesting that phosphorene could achieve good quantum
efficiencies in optoelectronic devices. The provided scattering rates and
lifetimes are critical input data for the modeling and understanding of
phosphorene-based device physics.


title:
Cohomological invariants of Abelian symplectic quotients of pure
  $r$-qubits

abstract:
  In this paper, we study cohomology rings and cohomological pairings over
Abelian symplectic quotients of special Hamiltonian tori manifolds. The
Hamiltonian group actions appear in quantum information theory where the tori
are maximal tori of some compact semi-simple Lie groups, so called the Local
Unitary groups, which act effectively and with non-trivial characters on
specific complex projective varieties. The complex projective spaces are in
fact spaces of pure multi-partite quantum states. By studying the geometry of
associated moment polytopes, we explicitly obtain cohomology rings, in terms of
elementary symmetric functions, and a recursive wall-crossing algorithm to
compute cohomological pairings over the corresponding Abelian symplectic
quotients. We propose algorithms for general $r$-qubit case and elaborate
discussions with explicit examples for the cases with $r=2,3$.


title: Novel Grid Topology Estimation Technique Exploiting PLC Modems

abstract:
  A fundamental requirement to develop routing strategies in power line
networks is the knowledge of the network topology, which might not be complete.
In this work, we present a novel method to derive the topology of a
distribution network that exploits the capability of Power Line Communication
modems to measure the network admittance, and we report the most significant
results.


title: Small Subalgebras of Polynomial Rings and Stillman's Conjecture

abstract:
  We show that in a polynomial ring $R$ in $N$ variables over an algebraically
closed field $K$ of arbitrary characteristic, any $K$-subalgebra of $R$
generated over $K$ by at most $n$ forms of degree at most $d$ is contained in a
$K$-subalgebra of $R$ generated by $B \leq {}^\eta\mathcal{B}(n,d)$ forms
$G_1,..., G_B$ of degree $\leq d$, where ${}^\eta\mathcal{B}(n,d)$ does not
depend on $N$ or $K$, such that these forms are a regular sequence and such
that for any ideal $J$ generated by forms that are in the $K$-span of $G_1,
..., G_B$, the ring $R/J$ satisfies the Serre condition $R_\eta$. These results
imply a conjecture of M. Stillman asserting that the projective dimension of an
$n$-generator ideal $I$ of $R$ whose generators are forms of degree $\leq d$ is
bounded independent of $N$. We also show that there is a primary decomposition
of $I$ such that all numerical invariants of the decomposition (e.g., the
number of primary components and the degrees and numbers of generators of all
of the prime and primary ideals occurring) are bounded independent of $N$.


title: Hierarchical Clustering via Spreading Metrics

abstract:
  We study the cost function for hierarchical clusterings introduced by
[arXiv:1510.05043] where hierarchies are treated as first-class objects rather
than deriving their cost from projections into flat clusters. It was also shown
in [arXiv:1510.05043] that a top-down algorithm returns a hierarchical
clustering of cost at most $O\left(\alpha_n \log n\right)$ times the cost of
the optimal hierarchical clustering, where $\alpha_n$ is the approximation
ratio of the Sparsest Cut subroutine used. Thus using the best known
approximation algorithm for Sparsest Cut due to Arora-Rao-Vazirani, the top
down algorithm returns a hierarchical clustering of cost at most
$O\left(\log^{3/2} n\right)$ times the cost of the optimal solution. We improve
this by giving an $O(\log{n})$-approximation algorithm for this problem. Our
main technical ingredients are a combinatorial characterization of ultrametrics
induced by this cost function, deriving an Integer Linear Programming (ILP)
formulation for this family of ultrametrics, and showing how to iteratively
round an LP relaxation of this formulation by using the idea of \emph{sphere
growing} which has been extensively used in the context of graph partitioning.
We also prove that our algorithm returns an $O(\log{n})$-approximate
hierarchical clustering for a generalization of this cost function also studied
in [arXiv:1510.05043]. Experiments show that the hierarchies found by using the
ILP formulation as well as our rounding algorithm often have better projections
into flat clusters than the standard linkage based algorithms. We also give
constant factor inapproximability results for this problem.


title: Independence in randomizations

abstract:
  The randomization of a complete first order theory $T$ is the complete
continuous theory $T^R$ with two sorts, a sort for random elements of models of
$T$, and a sort for events in an underlying atomless probability space. We
study independence relations and related ternary relations on the randomization
of $T$. We show that if $T$ has the exchange property and
$\operatorname{acl}=\operatorname{dcl}$, then $T^R$ has a strict independence
relation in the home sort, and hence is real rosy. In particular, if $T$ is
o-minimal, then $T^R$ is real rosy.


title: Canonical bases arising from quantum symmetric pairs

abstract:
  We develop a general theory of canonical bases for quantum symmetric pairs
$(\mathbf{U}, \mathbf{U}^\imath)$ with parameters of arbitrary finite type. We
construct new canonical bases for the simple integrable $\mathbf{U}$-modules
and their tensor products regarded as $\mathbf{U}^\imath$-modules. We also
construct a canonical basis for the modified form of the $\imath$quantum group
$\mathbf{U}^\imath$. To that end, we establish several new structural results
on quantum symmetric pairs, such as bilinear forms, braid group actions,
integral forms, Levi subalgebras (of real rank one), and integrality of the
intertwiners.


title:
Root-n consistent estimation of the marginal density in some time series
  models

abstract:
  In this paper, we consider the problem of estimating the marginal density in
some nonlinear autoregressive time series models for which the conditional mean
and variance have a parametric specification. Under some regularity conditions,
we show that a kernel type estimate based on the residuals can be root-n
consistent even if the noise density is unknown. Our results, which are shown
to be valid for classical time series models such as ARMA or GARCH processes,
extend substantially the existing results obtained for some homoscedatic time
series models. Asymptotic expansion of our estimator is obtained by combining
some martingale type arguments and a coupling method for time series which is
of independent interest. We also study the uniform convergence of our estimator
on compact intervals.


title:
On the invariant method for the time-dependent non-Hermitian
  Hamiltonians

abstract:
  We propose a scheme to deal with certain time-dependent non-Hermitian
Hamiltonian operators $H(t)$ that generate a real phase in their
time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that
are pseudo-Hermitian with respect to the time-dependent metric operator, which
implies that the dynamics is governed by unitary time evolution. Furthermore,
$H(t)$ is not generally quasi-Hermitian and does not define an observable of
the system but $I_{PH}(t)$ obeys a quasi-hermiticity transformation as in the
completely time-independent Hamiltonian systems case. The harmonic oscillator
with a time-dependent frequency under the action of a complex time-dependent
linear potential is considered as an illustrative example.


title:
Toward Implicit Sample Noise Modeling: Deviation-driven Matrix
  Factorization

abstract:
  The objective function of a matrix factorization model usually aims to
minimize the average of a regression error contributed by each element.
However, given the existence of stochastic noises, the implicit deviations of
sample data from their true values are almost surely diverse, which makes each
data point not equally suitable for fitting a model. In this case, simply
averaging the cost among data in the objective function is not ideal.
Intuitively we would like to emphasize more on the reliable instances (i.e.,
those contain smaller noise) while training a model. Motivated by such
observation, we derive our formula from a theoretical framework for optimal
weighting under heteroscedastic noise distribution. Specifically, by modeling
and learning the deviation of data, we design a novel matrix factorization
model. Our model has two advantages. First, it jointly learns the deviation and
conducts dynamic reweighting of instances, allowing the model to converge to a
better solution. Second, during learning the deviated instances are assigned
lower weights, which leads to faster convergence since the model does not need
to overfit the noise. The experiments are conducted in clean recommendation and
noisy sensor datasets to test the effectiveness of the model in various
scenarios. The results show that our model outperforms the state-of-the-art
factorization and deep learning models in both accuracy and efficiency.


title: Long-Range Repulsion Between Spatially Confined van der Waals Dimers

abstract:
  It is an undisputed textbook fact that non-retarded van der Waals (vdW)
interactions between isotropic dimers are attractive, regardless of the
polarizability of the interacting systems or spatial dimensionality. The
universality of vdW attraction is attributed to the dipolar coupling between
fluctuating electron charge densities. Here we demonstrate that the long-range
interaction between \textit{spatially confined} vdW dimers becomes repulsive
when accounting for the full Coulomb interaction between charge fluctuations.
Our analytic results are obtained by using the Coulomb potential as a
perturbation over dipole-correlated states for two quantum harmonic oscillators
embedded in spaces with reduced dimensionality, however the long-range
repulsion is expected to be a general phenomenon for spatially-confined quantum
systems. We suggest optical experiments to test our predictions, analyze their
relevance in the context of intermolecular interactions in nanoscale
environments, and rationalize the recent observation of anomalously strong
screening of the lateral vdW interactions between aromatic hydrocarbons
adsorbed on metal surfaces.


title: Boundary amenability of groups via ultrapowers

abstract:
  We use $\mathrm{C}^{\ast}$-algebra ultrapowers to give a new construction of
the Stone-Cech compactification of a separable, locally compact space. We use
this construction to give a new proof of the fact that groups that act
isometrically, properly, and transitively on trees are boundary amenable.


title: The birth of the universe in a new G-Theory approach

abstract:
  Recently, Padmanabhan has discussed that the expansion of the cosmic space is
due to the difference between the number of degrees of freedom on the boundary
surface and the number of degrees of freedom in a bulk region. Now, a natural
question arises that how these degrees of freedom are emerged from nothing? We
try to address this issue in a new theory which is more complete than M-theory
and reduces to it with some limitations. In M-theory, there isn't any stable
object like stable M3-branes that our universe is formed on it and for this
reason can't help us to explain cosmological events. In this research, we
propose a new theory, named G -theory which could be the mother of M-theory and
superstring theory. In G-theory, at the beginning, two types of G0-branes, one
with positive energy and one with negative energy are produced from nothing in
fourteen dimensions. Then, these branes are compactified on three circles via
two different ways (symmetrically and anti-symmetrically), and two bosonic and
fermionic parts of action for M0-branes are produced. By joining M0-branes,
supersymmetric Mp-branes are created which contain the equal number of degrees
of freedom for fermions and bosons. Our universe is constructed on one of
Mp-branes and other Mp-brane and extra energy play the role of bulk. By
dissolving extra energy which is produced by compacting actions of Gp-branes,
into our universe, the number of degrees of freedom on it and also it's scale
factor increase and universe expands. We test G-theory with observations and
find that the the magnitude of the slow-roll parameters and the
tensor-to-scalar ratio in this model are very smaller than one which are in
agreement with predictions of experimental data. Finally, we consider the
origin of the extended theories of gravity in G-theory and show that these
theories could be anomaly free.


title: The TUM LapChole dataset for the M2CAI 2016 workflow challenge

abstract:
  In this technical report we present our collected dataset of laparoscopic
cholecystectomies (LapChole). Laparoscopic videos of a total of 20 surgeries
were recorded and annotated with surgical phase labels, of which 15 were
randomly pre-determined as training data, while the remaining 5 videos are
selected as test data. This dataset was later included as part of the M2CAI
2016 workflow detection challenge during MICCAI 2016 in Athens.


title: Preliminary quantification of freely exploring Atta insularis

abstract:
  In this paper, we study the "free exploration" of individual ants of the
species Atta insularis, i.e., their motion on a featureless flat, horizontal
surface. Two basic preliminary results emerge from our work (a) the free
exploration is super-diffusive and (b) ants tend to turn more frequently to the
left than to the right -so we call them "let-handed"-. More statistics is
needed, however, to confirm those findings.


title: On Composite Moduli from the Viewpoint of Idempotent Numbers

abstract:
  The purpose of this paper is to introduce basic concepts that are fundamental
in the examination of composite moduli, while avoiding the notoriously
difficult problem of prime-factorization. We introduce a new class of numbers,
called idempotent numbers, that is unavoidable when researching composite
moduli. Among many interesting results, we give generalizations of well-known
theorems and definitions, such as the Euler-Fermat Theorem and the concept of
primitive roots. We consider the generalization of the equivalence condition
for the solvability of a binomial congruence to be the main result of our
paper.


title: First-principles lattice-gas Hamiltonian revisited: O-Pd(100)

abstract:
  The methodology of deriving an adatom lattice-gas Hamiltonian (LGH) from
first principles (FP) calculations is revisited. Such LGH cluster expansions
compute a large set of lateral pair-, trio-, quarto interactions by solving a
set of linear equations modelling regular adatom configurations and their FP
energies. The basic assumption of truncating interaction terms beyond fifth
nearest neighbors does not hold when adatoms show longer range interactions,
e.g. substrate mediated elastic interactions. O-Pd(100) as a popular reference
is used to propose a long range elastic interaction alternative including
many-body trio- and quarto terms with just 3 parameters fitted to FP
calculations. A key feature of the interaction alternative is its analytic
nature, allowing statistical methods different from Monte Carlo simulations to
derive surface order. The assumptions made are discussed and ways to further
verify and apply the model are outlined.


title: Synthetic polarimetric spectra from stellar prominences

abstract:
  Stellar prominences detected in rapidly rotating stars serve as probes of the
magnetism in the corona of cool stars. We have synthesized the temporal
evolution of the Stokes profiles generated in the He I 10830 and 5876 A
triplets during the rotation of a prominence around a star. The synthesis was
performed with the HAZEL code using a cloud model in which the prominence is
characterized by a slab located at a fixed latitude and height. It accounts for
the scattering polarization and Zeeman and Hanle effects. Several cases with
different prominence magnetic field strengths and orientations have been
analyzed. The results show an emission feature that drifts across the profile
while the prominence is out of the stellar disk. When the prominence eclipses
the star, the intensity profile shows an absorption. The scattering induced by
the prominence generates linear polarization signals in Stokes Q and U
profiles, which are modified by the Hanle effect when a magnetic field is
present. Due to the Zeeman effect, Stokes V profiles show a signal with very
low amplitude when the magnetic field along the line-of-sight is different from
zero. The estimated linear polarization signals could potentially be detected
with the future spectropolarimeter MIRADAS, to be attached to GTC telescope.


title:
Universal thermodynamics in different gravity theories: Conditions for
  generalized second law of thermodynamics and thermodynamical equilibrium on
  the horizons

abstract:
  The present work deals with a detailed study of universal thermodynamics in
different modified gravity theories. The validity of the generalized second law
of thermodynamics (GSLT) and thermodynamical equilibrium (TE) of the Universe
bounded by a horizon (apparent/event) in f(R)-gravity, Einstein-Gauss-Bonnet
gravity, RS-II brane scenario and DGP brane model has been investigated. In the
perspective of recent observational evidences, the matter in the Universe is
chosen as interacting holographic dark energy model. The entropy on the
horizons are evaluated from the validity of the unified first law and as a
result there is a correction (in integral form) to the usual Bekenstein
entropy. The other thermodynamical parameter namely temperature on the horizon
is chosen as the recently introduced corrected Hawking temperature. The above
thermodynamical analysis is done for homogeneous and isotropic flat FLRW model
of the Universe. The restrictions for the validity of GSLT and the TE are
presented in tabular form for each gravity theory. Finally, due to complicated
expressions, the validity of GSLT and TE are also examined from graphical
representation, using three Planck data sets.


title: Recent Progress in Lorentz and CPT Violation

abstract:
  This contribution to the CPT'16 meeting briefly highlights some of the recent
progress in the phenomenology of Lorentz and CPT violation, with emphasis on
research performed at the Indiana University Center for Spacetime Symmetries.


title:
Rigidity of Entire Convex Self-Shrinking Solutions to Hessian Quotient
  Flows

abstract:
  We prove that all entire smooth strictly convex self-shrinking solutions on
$\mathbb{R}^n$ to the Hessian quotient flows must be quadratic. This
generalizes the rigidity theorem for entire self-shrinking solutions to the
Lagrangian mean curvature flow in pseudo-Euclidean space due to Ding-Xin
\cite{DX}. Moreover, we show that our argument works for a larger class of
equations. In particular, we obtain rigidity results for entire self-shrinking
solutions on $\mathbb{C}^n$ to the K\"{a}hler-Ricci flow under certain
conditions.


title: Quasicrystalline three-dimensional foams

abstract:
  We present a numerical study of quasiperiodic foams, in which the bubbles are
generated as duals of quasiperiodic Frank-Kasper phases. These foams are
investigated as potential candidates to the celebrated Kelvin problem for the
partition of three-dimensional space with equal volume bubbles and minimal
surface area. Interestingly, one of the computed structures falls close (but
still slightly above) the best known Weaire-Phelan periodic candidate. This
gives additional clues to understanding the main geometrical ingredients
driving the Kelvin problem.


title: Generalized Dual Sudakov Minoration via Dimension Reduction - A Program

abstract:
  We propose a program for establishing a conjectural extension to the class of
(origin-symmetric) log-concave probability measures $\mu$, of the classical
dual Sudakov Minoration on the expectation of the supremum of a Gaussian
process: \begin{equation} \label{eq:abstract} M(Z_p(\mu), C \int ||x||_K d\mu
\cdot K) \leq \exp(C p) \;\;\, \forall p \geq 1 . \end{equation} Here $K$ is an
origin-symmetric convex body, $Z_p(\mu)$ is the $L_p$-centroid body associated
to $\mu$, $M(A,B)$ is the packing-number of $B$ in $A$, and $C > 0$ is a
universal constant. The Program consists of first establishing a Weak
Generalized Dual Sudakov Minoration, involving the dimension $n$ of the ambient
space, which is then self-improved to a dimension-free estimate after applying
a dimension-reduction step. The latter step may be thought of as a conjectural
"small-ball one-sided" variant of the Johnson--Lindenstrauss
dimension-reduction lemma. We establish the Weak Generalized Dual Sudakov
Minoration for a variety of log-concave probability measures and convex bodies
(for instance, this step is fully resolved assuming a positive answer to the
Slicing Problem). The Separation Dimension-Reduction step is fully established
for ellipsoids and, up to logarithmic factors in the dimension, for cubes,
resulting in a corresponding Generalized (regular) Dual Sudakov Minoration
estimate for these bodies and arbitrary log-concave measures, which are shown
to be (essentially) best-possible. Along the way, we establish a regular
version of (\ref{eq:abstract}) for all $p \geq n$ and provide a new direct
proof of Sudakov Minoration via The Program.


title:
Polyakov loop effects on the phase diagram in strong-coupling lattice
  QCD

abstract:
  We investigate the Polyakov loop effects on the QCD phase diagram by using
the strong-coupling (1/g^2) expansion of the lattice QCD (SC-LQCD) with one
species of unrooted staggered quark, including O}(1/g^4) effects. We take
account of the effects of Polyakov loop fluctuations in Weiss mean-field
approximation (MFA), and compare the results with those in the Haar-measure MFA
(no fluctuation from the mean-field). The Polyakov loops strongly suppress the
chiral transition temperature in the second-order/crossover region at small
chemical potential, while they give a minor modification of the first-order
phase boundary at larger chemical potential. The Polyakov loops also account
for a drastic increase of the interaction measure near the chiral phase
transition. The chiral and Polyakov loop susceptibilities have their peaks
close to each other in the second-order/crossover region. In particular in
Weiss MFA, there is no indication of the separated deconfinement transition
boundary from the chiral phase boundary at any chemical potential. We discuss
the interplay between the chiral and deconfinement dynamics via the bare quark
mass dependence of susceptibilities.


title:
Generalized Common Informations: Measuring Commonness by the Conditional
  Maximal Correlation

abstract:
  In literature, different common informations were defined by G\'acs and
K\"orner, by Wyner, and by Kumar, Li, and Gamal, respectively. In this paper,
we define two generalized versions of common informations, named approximate
and exact information-correlation functions, by exploiting the conditional
maximal correlation as a commonness or privacy measure. These two generalized
common informations encompass the notions of G\'acs-K\"orner's, Wyner's, and
Kumar-Li-Gamal's common informations as special cases. Furthermore, to give
operational characterizations of these two generalized common informations, we
also study the problems of private sources synthesis and common information
extraction, and show that the information-correlation functions are equal to
the minimum rates of commonness needed to ensure that some conditional maximal
correlation constraints are satisfied for the centralized setting versions of
these problems. As a byproduct, the conditional maximal correlation has been
studied as well.

categories: cs.IT cs.CR math.IT math.PR math.ST stat.TH


title: The Observational Future of Cosmological Scalar-Tensor Theories

abstract:
  The next generation of surveys will greatly improve our knowledge of
cosmological gravity. In this paper we focus on how Stage IV photometric
redshift surveys, including weak lensing and multiple tracers of the matter
distribution and radio experiments combined with measurements of the cosmic
microwave background will lead to precision constraints on deviations from
General Relativity. We use a broad subclass of Horndeski scalar-tensor theories
to forecast the accuracy with which we will be able to determine these
deviations and their degeneracies with other cosmological parameters. Our
analysis includes relativistic effects, does not rely on the quasi-static
evolution and makes conservative assumptions about the effect of screening on
small scales. We define a figure of merit for cosmological tests of gravity and
show how the combination of different types of surveys, probing different
length scales and redshifts, can be used to pin down constraints on the
gravitational physics to better than a few percent, roughly an order of
magnitude better than present probes. Future cosmological experiments will be
able to constrain the Brans-Dicke parameter at a level comparable to Solar
System and astrophysical tests


title: Very Long-period Pulsations before the Onset of Solar Flares

abstract:
  Solar flares are the most powerful explosions occurring in the solar system,
which may lead to disastrous space weather events and impact various aspects of
our Earth. So far, it is still a big challenge in modern astrophysics to
understand the origin of solar flares and predict their onset. Based on the
analysis of soft X-ray emission observed by the Geostationary Operational
Environmental Satellite (GOES), this work reported a new discovery of very
long-periodic pulsations occurred in the preflare phase before the onset of
solar flares (preflare-VLPs). These pulsations are typically with period of 8 -
30 min and last for about 1 - 2 hours. They are possibly generated from LRC
oscillations of plasma loops where electric current dominates the physical
process during magnetic energy accumulation in the source region. The
preflare-VLP provides an essential information for understanding the triggering
mechanism and origin of solar flares, and may help us to response to solar
explosions and the corresponding disastrous space weather events as a
convenient precursory indicator.


title: Optimal Shrinkage Estimator for High-Dimensional Mean Vector

abstract:
  In this paper we derive the optimal linear shrinkage estimator for the
high-dimensional mean vector using random matrix theory. The results are
obtained under the assumption that both the dimension $p$ and the sample size
$n$ tend to infinity in such a way that $p/n \to c\in(0,\infty)$. Under weak
conditions imposed on the underlying data generating mechanism, we find the
asymptotic equivalents to the optimal shrinkage intensities and estimate them
consistently. The proposed nonparametric estimator for the high-dimensional
mean vector has a simple structure and is proven to minimize asymptotically,
with probability $1$, the quadratic loss when $c\in(0,1)$. When $c\in(1,
\infty)$ we modify the estimator by using a feasible estimator for the
precision covariance matrix. To this end, an exhaustive simulation study and an
application to real data are provided where the proposed estimator is compared
with known benchmarks from the literature. It turns out that the existing
estimators of the mean vector, including the new proposal, converge to the
sample mean vector when the true mean vector has an unbounded Euclidean norm.


title:
Non-perturbative analysis of the spectrum of meson resonances in an
  ultraviolet-complete composite-Higgs model

abstract:
  We consider a vector-like gauge theory of fermions that confines at the
multi-TeV scale, and that realizes the Higgs particle as a composite Goldstone
boson. The weak interactions are embedded in the unbroken subgroup $Sp(4)$ of a
spontaneously broken $SU(4)$ flavour group. The meson resonances appear as
poles in the two-point correlators of fermion bilinears, and include the
Goldstone bosons plus a massive pseudoscalar $\eta'$, as well as scalars,
vectors and axial vectors. We compute the mass spectrum of these mesons, as
well as their decay constants, in the chiral limit, in the approximation where
the hypercolour $Sp(2N)$ dynamics is described by four-fermion operators, \`a
la Nambu-Jona Lasinio. By resumming the leading diagrams in the $1/N$
expansion, we find that the spin-one states lie beyond the LHC reach, while
spin-zero electroweak-singlet states may be as light as the Goldstone-boson
decay constant, $f\sim 1$ TeV. We also confront our results with a set of
available spectral sum rules. In order to supply composite top-quark partners,
the theory contains additional fermions carrying both hypercolour and ordinary
colour, with an associated flavour symmetry-breaking pattern $SU(6)/SO(6)$. We
identify and analyse several non-trivial features of the complete two-sector
gauge theory: the 't~Hooft anomaly matching conditions; the higher-dimension
operator which incorporates the effects of the hypercolour axial-singlet
anomaly; the coupled mass-gap equations; the mixing between the singlet mesons
of the two sectors, resulting in an extra Goldstone boson $\eta_0$, and novel
spectral sum rules. Assuming that the strength of the four-fermion interaction
is the same in the two sectors, we find that the coloured vector and scalar
mesons have masses $\gtrsim 4 f$, while the masses of coloured pseudo-Goldstone
bosons, induced by gluon loops, are $\gtrsim 1.5f$.


title: The coordinate-based meta-analysis of neuroimaging data

abstract:
  Neuroimaging meta-analysis is an area of growing interest in statistics. The
special characteristics of neuroimaging data render classical meta-analysis
methods inapplicable and therefore new methods have been developed. We review
existing methodologies, explaining the benefits and drawbacks of each. A
demonstration on a real dataset of emotion studies is included. We discuss some
still-open problems in the field to highlight the need for future research.


title: Rigidity of minimizers in nonlocal phase transitions

abstract:
  We obtain the classification of certain global bounded solutions for
semilinear nonlocal equations of the type $$\triangle^s u=W'(u)$$ in
$\mathbb{R}^n$,with $s \in (1/2 ,1),$ where $W$ is a double well potential.


title: Improving Sampling from Generative Autoencoders with Markov Chains

abstract:
  We focus on generative autoencoders, such as variational or adversarial
autoencoders, which jointly learn a generative model alongside an inference
model. Generative autoencoders are those which are trained to softly enforce a
prior on the latent distribution learned by the inference model. We call the
distribution to which the inference model maps observed samples, the learned
latent distribution, which may not be consistent with the prior. We formulate a
Markov chain Monte Carlo (MCMC) sampling process, equivalent to iteratively
decoding and encoding, which allows us to sample from the learned latent
distribution. Since, the generative model learns to map from the learned latent
distribution, rather than the prior, we may use MCMC to improve the quality of
samples drawn from the generative model, especially when the learned latent
distribution is far from the prior. Using MCMC sampling, we are able to reveal
previously unseen differences between generative autoencoders trained either
with or without a denoising criterion.


title:
Analysis of a growth model inspired by Gompertz and Korf laws, and an
  analogous birth-death process

abstract:
  We propose a new deterministic growth model which captures certain features
of both the Gompertz and Korf laws. We investigate its main properties, with
special attention to the correction factor, the relative growth rate, the
inflection point, the maximum specific growth rate, the lag time and the
threshold crossing problem. Some data analytic examples and their performance
are also considered. Furthermore, we study a stochastic counterpart of the
proposed model, that is a linear time-inhomogeneous birth-death process whose
mean behaves as the deterministic one. We obtain the transition probabilities,
the moments and the population ultimate extinction probability for this
process. We finally treat the special case of a simple birth process, which
better mimics the proposed growth model.


title: Testing dynamic stabilisation in complex Langevin simulations

abstract:
  Complex Langevin methods have been successfully applied in theories that
suffer from a sign problem such as QCD with a chemical potential. We present
and illustrate a novel method (dynamic stabilisation) that ensures that Complex
Langevin simulations stay close to the SU(3) manifold, which lead to correct
and improved results in the framework of pure Yang-Mills simulations and QCD in
the limit of heavy quarks.


title: Testing the hadronic spectrum in the strange sector

abstract:
  Heavier resonances are continually being added to the hadronic spectrum from
the Particle Data Group that follow an exponentially increasing mass spectrum.
However, it has been suggested that even further states predicted from Quark
Models are needed in the hadronic spectrum in order to improve the agreement
between the hadron resonance gas model predictions and lattice QCD data. We
find that the inclusion of such states with extrapolated branching ratios
slightly decreases the freezeout temperature. To eliminate ambiguities, we
introduce a first principle method to extract the freeze-out temperature for
charged kaons from experimental data, which yields a lower bound of
$T_{\text{fo}} \gtrsim $145 MeV for the highest collision energy at RHIC.


title:
Globally Optimal Training of Generalized Polynomial Neural Networks with
  Nonlinear Spectral Methods

abstract:
  The optimization problem behind neural networks is highly non-convex.
Training with stochastic gradient descent and variants requires careful
parameter tuning and provides no guarantee to achieve the global optimum. In
contrast we show under quite weak assumptions on the data that a particular
class of feedforward neural networks can be trained globally optimal with a
linear convergence rate with our nonlinear spectral method. Up to our knowledge
this is the first practically feasible method which achieves such a guarantee.
While the method can in principle be applied to deep networks, we restrict
ourselves for simplicity in this paper to one and two hidden layer networks.
Our experiments confirm that these models are rich enough to achieve good
performance on a series of real-world datasets.


title: A Maximum Principle for the controlled Sweeping Process

abstract:
  We consider the free endpoint Mayer problem for a controlled Moreau process,
the control acting as a perturbation of the dynamics driven by the normal cone,
and derive necessary optimality conditions of Pontryagin's Maximum Principle
type. The results are also discussed through an example. We combine techniques
from M. Sene, L. Thibault, Journal of Nonlinear and Convex Analysis 15 (2014)
and from M. Brokate and P. Krejci, Discrete and continuous dynamical systems
series B. Volume 18 (2013), 331-348, which in particular deals with a different
but related control problem. Our assumptions include the smoothness of the
boundary of the moving set $C(t)$, but do not require its strict convexity.
Rather, a kind of inward/outward pointing condition is assumed on the reference
optimal trajectory at the times where the boundary of $C(t)$ is touched. The
state space is finite dimensional.


title: Anisotropic invariance and the distribution of quantum correlations

abstract:
  We report the discovery of two new invariants for three-qubit states which,
similarly to the 3-tangle, are invariant under local unitary transformations
and permutations of the parties. These quantities have a direct interpretation
in terms of the anisotropy of pairwise spin correlations. Applications include
a universal ordering of pairwise quantum correlation measures for pure
three-qubit states; tradeoff relations for anisotropy, 3-tangle and Bell
nonlocality; strong monogamy relations for Bell inequalities,
Einstein-Podolsky-Rosen steering inequalities, geometric discord and fidelity
of remote state preparation (including results for arbitrary three-party
states); and a statistical and reference-frame-independent form of quantum
secret sharing.


title:
Measurements of $\psi(2S)$ and $X(3872) \to J/\psi\pi^+\pi^-$ production
  in $pp$ collisions at $\sqrt{s} = 8$ TeV with the ATLAS detector

abstract:
  Differential cross sections are presented for the prompt and non-prompt
production of the hidden-charm states $X(3872)$ and $\psi(2S)$, in the decay
mode $J/\psi \pi^+\pi^-$, measured using 11.4 fb$^{-1}$ of $pp$ collisions at
$\sqrt{s} = 8$ TeV by the ATLAS detector at the LHC. The ratio of
cross-sections $X(3872)/\psi(2S)$ is also given, separately for prompt and
non-prompt components, as well as the non-prompt fractions of $X(3872)$ and
$\psi(2S)$. Assuming independent single effective lifetimes for non-prompt
$X(3872)$ and $\psi(2S)$ production gives $R_B = \frac{\mathcal{B}(B
\rightarrow X(3872)\textrm{ + any}) \mathcal{B}(X(3872 \rightarrow
J/\psi\pi^+\pi^-)}{\mathcal{B}(B \rightarrow \psi(2S)\textrm{ + any})
\mathcal{B}(\psi(2S) \rightarrow J/\psi\pi^+\pi^-)} = (3.95 \pm 0.32
\mathrm{(stat)} \pm 0.08\mathrm{(sys)}) \times 10^{-2}$, while separating
short- and long-lived contributions, assuming that the short-lived component is
due to $B_c$ decays, gives $R_B = (3.57 \pm 0.33\mathrm{(stat)} \pm
0.11\mathrm{(sys)}) \times 10^{-2}$, with the fraction of non-prompt $X(3872)$
produced via $B_c$ decays for $p_\mathrm{T}(X(3872)) > 10$ GeV being $(25 \pm
13\mathrm{(stat)} \pm 2\mathrm{(sys)} \pm 5\mathrm{(spin)})\%$. The
distributions of the dipion invariant mass in the $X(3872)$ and $\psi(2S)$
decays are also measured and compared to theoretical predictions.


title:
Cohen Lenstra Heuristics for \'Etale Group Schemes and Symplectic
  Pairings

abstract:
  We generalize the Cohen-Lenstra heuristics over function fields to \'{e}tale
group schemes $G$ (with the classical case of abelian groups corresponding to
constant group schemes). By using the results of
Ellenberg-Venkatesh-Westerland, we make progress towards the proof of these
heuristics. Moreover, by keeping track of the image of the Weil-pairing as an
element of $\wedge^2G(1)$, we formulate more refined heuristics which nicely
explain the deviation from the usual Cohen-Lenstra heuristics for abelian
$\ell$-groups in cases where $\ell\mid q-1$; the nature of this failure was
suggested already in the works of Garton, EVW, and others. On the purely large
random matrix side, we provide a natural model which has the correct moments,
and we conjecture that these moments uniquely determine a limiting probability
measure.


title:
Conditions that the quotient of $L$-fuzzy up-sets forms a complete
  lattice

abstract:
  This paper deals with conditions under which the quotient of $L$-fuzzy
up-sets forms a complete lattice by using terminologies of closure operators.
It first gives a condition that a family of some subsets of a nonempty set can
be represented by $L$-fuzzy up-sets, which is then used to formulate a
necessary and sufficient condition under which the quotient of $L$-fuzzy
up-sets forms a complete lattice. This paper finally shows that the quotient of
a kind of $L$-fuzzy up-sets is isomorphic to an interval generated by an
$L$-fuzzy up-set.


title: Calls, zonoids, peacocks and log-concavity

abstract:
  The main results are two characterisations of log-concave densities in terms
of the collection of lift zonoids corresponding to a peacock. These notions are
recalled and connected to arbitrage-free asset pricing in financial
mathematics.


title:
Correlated-PCA: Principal Components' Analysis when Data and Noise are
  Correlated

abstract:
  Given a matrix of observed data, Principal Components Analysis (PCA) computes
a small number of orthogonal directions that contain most of its variability.
Provably accurate solutions for PCA have been in use for a long time. However,
to the best of our knowledge, all existing theoretical guarantees for it assume
that the data and the corrupting noise are mutually independent, or at least
uncorrelated. This is valid in practice often, but not always. In this paper,
we study the PCA problem in the setting where the data and noise can be
correlated. Such noise is often also referred to as "data-dependent noise". We
obtain a correctness result for the standard eigenvalue decomposition (EVD)
based solution to PCA under simple assumptions on the data-noise correlation.
We also develop and analyze a generalization of EVD, cluster-EVD, that improves
upon EVD in certain regimes.


title: Rotational tumbling of Escherichia coli aggregates under shear

abstract:
  Growing living cultures of Escherichia coli bacteria were investigated using
real-time in situ rheology and rheo-imaging measurements. In the early stages
of growth (lag phase), and when subjected to a constant stationary shear, the
viscosity slowly increases with the cell's population. As the bacteria reach
the exponential phase of growth, the viscosity increases rapidly, with sudden
and temporary abrupt decreases and recoveries. At a certain stage,
corresponding grossly to the late phase of growth, when the population
stabilises, the viscosity also keeps its maximum constant value, with drops and
recoveries, for a long period of time. This complex rheological behaviour,
which was observed to be shear strain dependent, is a consequence of two
coupled effects: the cell density continuous increase and its changing
interacting properties. Particular attention was given to the late phase of
growth of E. coli populations under shear. Rheo-imaging measurements revealed,
near the static plate, a rotational motion of E. coli aggregates, collectively
tumbling and flowing in the shear direction. To explain this behaviour, we
introduce a simple theoretical model, in which the individual cells are
transported by the flow, but remain rigidly attached to the other cells of the
aggregate.


title: Ground states of classical magnetic dipole rings

abstract:
  We investigate the two well-known ground states of rings of $N$ classical
magnetic dipoles that are given by clockwise or anti-clockwise spin
orientations tangent to the circle encompassing the dipole ring. In particular,
we formulate a rigorous proof of the ground state property of the states in
question. The problem can be reduced to the determination of the lowest
eigenvalue of a $3N\times 3N$ matrix ${\mathbf J}$. We show that all
eigenvalues of ${\mathbf J}$ can be analytically calculated and, at least for
$N=3,\ldots,8$, the lowest one can be directly determined. The main part of the
paper is devoted to the completion of the proof for $N\ge 9$ based on various
estimates and case distinctions. We also discuss the question to what extent
computer-algebraic results should be allowed to contribute to a mathematical
proof.


title: Analysis of random walks on a hexagonal lattice

abstract:
  We consider a discrete-time random walk on the nodes of an unbounded
hexagonal lattice. We determine the probability generating functions, the
transition probabilities and the relevant moments. The convergence of the
stochastic process to a 2-dimensional Brownian motion is also discussed.
Furthermore, we obtain some results on its asymptotic behavior making use of
large deviation theory. Finally, we investigate the first-passage-time problem
of the random walk through a vertical straight-line. Under suitable symmetry
assumptions we are able to determine the first-passage-time probabilities in a
closed form, which deserve interest in applied fields.


title:
Photoionisation of Be-like and Li-like atomic oxygen{\it K}-shell
  photoionisation of O$^{4+}$ and O$^{5+}$ ions : experiment and theory

abstract:
  Absolute cross sections for the {\it K}-shell photoionisation of Be-like
(O$^{4+}$) and Li-like (O$^{5+}$) atomic oxygen ions were measured for the
first time (in their respective {\it K}-shell regions) by employing the
ion-photon merged-beam technique at the SOLEIL synchrotron-radiation facility
in Saint-Aubin, France. High-resolution spectroscopy with E/$\Delta$E $\approx$
3200 ($\approx$ 170 meV, FWHM)was achieved with photon energy from 550 eV up to
670 eV. Rich resonance structure observed in the experimental spectra is
analysed using the R-matrix with pseudo-states (RMPS) method. Results are also
compared with the screening constant by unit nuclear charge (SCUNC)
calculations. We characterise and identify the strong $\rm 1s \rightarrow 2p$
resonances for both ions and the weaker $\rm 1s \rightarrow np$ resonances ($ n
\ge 3$) observed in the {\it K}-shell spectra of O$^{4+}$.


title:
User Cooperation for Enhanced Throughput Fairness in Wireless Powered
  Communication Networks

abstract:
  This paper studies a novel user cooperation method in a wireless powered
cooperative communication network (WPCN) in which a pair of distributed
terminal users first harvest wireless energy broadcasted by one energy node
(EN) and then use the harvested energy to transmit information to a destination
node (DN). In particular, the two cooperating users exchange their independent
information with each other so as to form a virtual antenna array and transmit
jointly to the DN. By allowing the users to share their harvested energy to
transmit each other's information, the proposed method can effectively mitigate
the inherent user unfairness problem in WPCN, where one user may suffer from
very low data rate due to poor energy harvesting performance and high data
transmission consumptions. Depending on the availability of channel state
information at the transmitters, we consider the two users cooperating using
either coherent or non-coherent data transmissions. In both cases, we derive
the maximum common throughput achieved by the cooperation schemes through
optimizing the time allocation on wireless energy transfer, user message
exchange, and joint information transmissions in a fixed-length time slot. We
also perform numerical analysis to study the impact of channel conditions on
the system performance. By comparing with some existing benchmark schemes, our
results demonstrate the effectiveness of the proposed user cooperation in a
WPCN under different application scenarios.


title: On infinitesimally weakly non-decreasable Beltrami differentials

abstract:
  Z. Zhou et al. proved that in a Teichm\"uller equivalence class, there exists
an extremal quasiconformal mapping with a weakly non-decreasable dilatation. In
this paper, we prove that in an infinitesimal equivalence class, there exists a
weakly non-decreasable extremal Beltrami differential.


title: A rheological state diagram for rough colloids in shear flow

abstract:
  The flow of dense suspensions, glasses, and granular materials is heavily
influenced by frictional interactions between constituent particles. However,
neither hydrodynamics nor friction has successfully explained the full range of
flow phenomena in concentrated suspensions. Particles with asperities represent
a case in point. Lubrication hydrodynamics fail to completely capture two key
rheological properties - namely, that the viscosity increases drastically and
the first normal stress difference can switch signs as volume fraction
increases. Yet, simulations that account for interparticle friction are also
unable to fully predict these properties. Furthermore, experiments show that
rheological behavior can vary depending on particle roughness and
deformability. We seek to resolve these apparent contradictions by
systematically tuning the roughness of model colloids, investigating their
viscosity and first normal stress differences under steady shear, and finally
generating a rheological state diagram that demonstrates how surface roughness
influences the transition between shear thickening and dilatancy. Our
simulations, which are in good agreement with the experiments, suggest that
friction between rough particles is significant. In addition, we find that
roughness progressively lowers the critical conditions required for the onset
of shear thickening and dilatancy. Our results thus provides a major
contribution in the field of suspension rheology with broad relevance to
granular and particulate materials. For instance, particle geometry can be
tuned to increase the efficacy of materials that turn solid-like on the
application of stimuli. On the other hand, engineers who work with concentrated
slurries can now use images of the constituent particles to estimate optimal
flow processing conditions.


title: Pressure induced magnetic order in FeSe

abstract:
  The magnetic order induced by the pressure was studied in single crystalline
FeSe by means of muon-spin rotation ($\mu$SR) technique. By following the
evolution of the oscillatory part of the $\mu$SR signal as a function of angle
between the initial muon-spin polarization and 101 axis of studied crystal it
was found that the pressure induced magnetic order in FeSe corresponds either
to the collinear (single-stripe) antiferromagnetic order as observed in parent
compounds of various FeAs-based superconductors or to the Bi-Collinear order as
obtained in FeTe system, but with the Fe spins turned by 45$^{\rm o}$. The
value of the magnetic moment per Fe atom was estimated to be $\simeq
0.13-0.14$~$\mu_{\rm B}$ at $p\simeq 1.9$~GPa.


title: Entanglement critical length at the many-body localization transition

abstract:
  We study the details of the distribution of the entanglement spectrum
(eigenvalues of the reduced density matrix) of a disordered spin chain
exhibiting a many-body localization (MBL) transition. In the thermalizing
region we identify the evolution under increasing system size of the
eigenvalues distribution function, whose thermodynamic limit is close (but
possibly different from) the Marchenko-Pastur distribution. From the analysis
we extract a correlation length $L_s(h)$ determining the minimum system size to
enter the asymptotic region. We find that $L_s(h)$ diverges at the MBL
transition. We discuss the nature of the subleading corrections to the
entanglement spectrum distribution and to the entanglement entropy.


title: Pseudo-bosons and Riesz bi-coherent states

abstract:
  After a brief review on $\D$-pseudo-bosons we introduce what we call {\em
Riesz bi-coherent states}, which are pairs of states sharing with ordinary
coherent states most of their features. In particular, they produce a
resolution of the identity and they are eigenstates of two different
annihilation operators which obey pseudo-bosonic commutation rules.


title: Lorentz Violation in Deep Inelastic Electron-Proton Scattering

abstract:
  Lorentz violation in the quark sector induces a sidereal time dependence in
electron-proton, proton-antiproton and proton-proton cross sections. At high
energies nonperturbative effects are buried in universal nucleon parton
distribution functions and Lorentz violating effects are calculable in
perturbation theory. We focus on deep inelastic electron-proton scattering data
collected from ZEUS and H1 at HERA and show that a sideral time analysis of
these events is able to set strong constraints on most of the coefficients we
consider.


title:
Scalar self-force for highly eccentric equatorial orbits in Kerr
  spacetime

abstract:
  If a small "particle" of mass $\mu M$ (with $\mu \ll 1$) orbits a black hole
of mass $M$, the leading-order radiation-reaction effect is an
$\mathcal{O}(\mu^2)$ "self-force" acting on the particle, with a corresponding
$\mathcal{O}(\mu)$ "self-acceleration" of the particle away from a geodesic.
Such "extreme--mass-ratio inspiral" systems are likely to be important
gravitational-wave sources for future space-based gravitational-wave detectors.
Here we consider the "toy model" problem of computing the self-force for a
scalar-field particle on a bound eccentric orbit in Kerr spacetime. We use the
Barack-Golbourn-Vega-Detweiler effective-source regularization with a 4th order
puncture field, followed by an $e^{im\phi}$ ("m-mode") Fourier decomposition
and a separate time-domain numerical evolution in $2+1$ dimensions for each
$m$. We introduce a finite worldtube that surrounds the particle worldline and
define our evolution equations in a piecewise manner so that the effective
source is only used within the worldtube. Viewed as a spatial region, the
worldtube moves to follow the particle's orbital motion. We use slices of
constant Boyer-Lindquist time in the region of the particle's motion, deformed
to be asymptotically hyperboloidal and compactified near the horizon and
$\mathcal{J}^+$. We present numerical results for a number of test cases with
orbital eccentricities as high as $0.98$. In some cases we find large
oscillations ("wiggles") in the self-force shortly after periastron passage.


title:
A Polynomial-time Algorithm for Detecting the Possibility of Braess
  Paradox in Directed Graphs

abstract:
  A directed multigraph is said vulnerable if it can generate Braess paradox in
Traffic Networks. In this paper, we give a graph-theoretic characterisation of
vulnerable directed multigraphs; analogous results appeared in the literature
only for undirected multigraphs and for a specific family of directed
multigraphs. The proof of our characterisation also provides an algorithm that
checks if a multigraph is vulnerable in O(|V| |E|^2); this is the first
polynomial time algorithm that checks vulnerability for general directed
multigraphs. The resulting algorithm also contributes to another well known
problem, i.e. the directed subgraph homeomorphism problem without node mapping,
by providing another pattern graph for which a polynomial time algorithm
exists.


title: Biased Tracers in Redshift Space in the EFT of Large-Scale Structure

abstract:
  The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a
novel formalism that is able to accurately predict the clustering of
large-scale structure (LSS) in the mildly non-linear regime. Here we provide
the first computation of the power spectrum of biased tracers in redshift space
at one loop order, and we make the associated code publicly available. We
compare the multipoles $\ell=0,2$ of the redshift-space halo power spectrum,
together with the real-space matter and halo power spectra, with data from
numerical simulations at $z=0.67$. For the samples we compare to, which have a
number density of $\bar n=3.8 \cdot 10^{-2}(h \ {\rm Mpc}^{-1})^3$ and $\bar
n=3.9 \cdot 10^{-4}(h \ {\rm Mpc}^{-1})^3$, we find that the calculation at
one-loop order matches numerical measurements to within a few percent up to
$k\simeq 0.43 \ h \ {\rm Mpc}^{-1}$, a significant improvement with respect to
former techniques. By performing the so-called IR-resummation, we find that the
Baryon Acoustic Oscillation peak is accurately reproduced. Based on the results
presented here, long-wavelength statistics that are routinely observed in LSS
surveys can be finally computed in the EFTofLSS. This formalism thus is ready
to start to be compared directly to observational data.


title: Homotopy Analysis for Tensor PCA

abstract:
  Developing efficient and guaranteed nonconvex algorithms has been an
important challenge in modern machine learning. Algorithms with good empirical
performance such as stochastic gradient descent often lack theoretical
guarantees. In this paper, we analyze the class of homotopy or continuation
methods for global optimization of nonconvex functions. These methods start
from an objective function that is efficient to optimize (e.g. convex), and
progressively modify it to obtain the required objective, and the solutions are
passed along the homotopy path. For the challenging problem of tensor PCA, we
prove global convergence of the homotopy method in the "high noise" regime. The
signal-to-noise requirement for our algorithm is tight in the sense that it
matches the recovery guarantee for the best degree-4 sum-of-squares algorithm.
In addition, we prove a phase transition along the homotopy path for tensor
PCA. This allows to simplify the homotopy method to a local search algorithm,
viz., tensor power iterations, with a specific initialization and a noise
injection procedure, while retaining the theoretical guarantees.


title: On $(p,r)$-Filtrations and Tilting Modules

abstract:
  We study the relationship between Donkin's Tilting Module Conjecture and
Donkin's Good $(p,r)$-Filtration Conjecture. Our main result was motivated by a
result of Kildetoft and Nakano showing that the Tilting Module Conjecture
implies one direction of the Good $(p,r)$-Filtration Conjecture. We observe
that the converse nearly holds; in particular a weaker version of the Good
$(p,r)$-Filtration Conjecture implies the Tilting Module Conjecture.


title:
Moduli Structures, Separability of the Kinematic Hilbert Space and
  Frames in Loop Quantum Gravity

abstract:
  We reassess the problem of separability of the kinematic Hilbert space in
loop quantum gravity under a new mathematical point of view. We use the
formalism of frames, a tool used in signal analysis, in order to remove the
redundancy of the moduli structures in high valence graphs, without resorting
to set extension of diffeomorphism group. For this, we introduce a local
redundancy which encodes the concentration of frame vectors on the tangent
spaces $T_pM$ around points of intersections $p$ of smooth loops $\alpha$ in
$\mathbb{R}^{3}$.


title:
Liquid phase stabilization versus bubble formation at a nanoscale-curved
  interface

abstract:
  We investigate the nature of vapor bubble nucleation near a nanoscale-curved
convex liquid-solid interface using two models; an equilibrium Gibbs model for
homogenous formation, and a nonequilibrium dynamic van der Waals/diffuse
interface model for phase change in an initially cool liquid. Vapor bubble
formation is shown to occur for sufficiently large radius of curvature and is
suppressed for smaller radii. Solid-fluid interactions are accounted for and it
is shown that liquid-vapor interfacial energy, hence Laplace pressure, has
limited influence over bubble formation. The dominant factor is the energetic
cost of creating the solid-vapor interface from the existing solid-liquid
interface, as demonstrated via both equilibrium and non-equilibrium arguments.


title: A Projector Quantum Monte Carlo Method for non-linear wavefunctions

abstract:
  We reformulate the projected imaginary-time evolution of Full Configuration
Interaction Quantum Monte Carlo in terms of a Lagrangian minimization. This
naturally leads to the admission of polynomial complex wavefunction
parameterizations, circumventing the exponential scaling of the approach. While
previously these functions have traditionally inhabited the domain of
Variational Monte Carlo, we consider recently developments for the
identification of deep-learning neural networks to optimize this Lagrangian,
which can be written as a modification of the propagator for the wavefunction
dynamics. We demonstrate this approach with a form of Tensor Network State, and
use it to find solutions to the strongly-correlated Hubbard model, as well as
its application to a fully periodic ab-initio Graphene sheet. The number of
variables which can be simultaneously optimized greatly exceeds alternative
formulations of Variational Monte Carlo, allowing for systematic improvability
of the wavefunction flexibility towards exactness for a number of different
forms, whilst blurring the line between traditional Variational and Projector
quantum Monte Carlo approaches.


title:
Understanding the periodicities in radio and GeV emission from LS
  I+61303

abstract:
  Accretion models predict two ejections along the eccentric orbit of LS I +61
303: one major ejection at periastron and a second, lower ejection towards
apastron. We develop a physical model for LS I +61 303 in which relativistic
electrons are ejected twice along the orbit. The ejecta form a conical jet that
is precessing with P2. The jet radiates in the radio band by the synchrotron
process and the jet radiates in the GeV energy band by the external inverse
Compton and synchrotron self-Compton processes. We compare the output fluxes of
our physical model with two available large archives: OVRO radio and Fermi
Large Area Telescope (LAT) GeV observations, the two databases overlapping for
five years. The larger ejection around periastron passage results in a slower
jet, and severe inverse Compton losses result in the jet also being short.
While large gamma-ray emission is produced, there is only negligible radio
emission. Our results are that the periastron jet has a length of 3.0 10^6 rs
and a velocity beta ~ 0.006, whereas the jet at apastron has a length of 6.3
10^7 rs and beta ~ 0.5.


title:
Positive solutions for the fractional Laplacian in the almost critical
  case in a bounded domain

abstract:
  We prove existence of multiple positive solutions for a {\sl fractional
scalar field equation} in a bounded domain, whenever $p$ tends to the critical
Sobolev exponent. By means of the "photography method", we prove that the
topology of the domain furnishes a lower bound on the number of positive
solutions.


title:
Stationary Scalar Clouds Around Maximally Rotating Linear Dilaton Black
  Holes

abstract:
  We investigate the wave dynamics of a charged massive scalar field
propagating in a maximally rotating (extremal) linear dilaton black hole
geometry. We prove the existence of a discrete and infinite family of
resonances describing non-decaying stationary scalar configurations (clouds)
enclosing these rapidly rotating black holes. The results obtained signal the
potential stationary scalar field distributions (dark matter) around the
extremal linear dilaton black holes. In particular, we analytically compute the
effective heights of those clouds above the center of the black hole.