title: Dynamic network models and graphon estimation

abstract:
  In the present paper we consider a dynamic stochastic network model. The
objective is estimation of the tensor of connection probabilities $\Lambda$
when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic
graphon. In particular, in the context of the DSBM, we derive a penalized least
squares estimator $\widehat{\Lambda}$ of $\Lambda$ and show that
$\widehat{\Lambda}$ satisfies an oracle inequality and also attains minimax
lower bounds for the risk. We extend those results to estimation of $\Lambda$
when it is generated by a dynamic graphon function. The estimators constructed
in the paper are adaptive to the unknown number of blocks in the context of the
DSBM or to the smoothness of the graphon function. The technique relies on the
vectorization of the model and leads to much simpler mathematical arguments
than the ones used previously in the stationary set up. In addition, all
results in the paper are non-asymptotic and allow a variety of extensions.


title: Estimation of anthracnose dynamics by nonlinear filtering

abstract:
  In this paper, we apply the nonlinear filtering theory to the estimation of
the partially observed dynamics of anthracnose which is a phytopathology. The
signal here is the inhibition rate and the observations are the fruit volume
ant the rotted volume. We propose stochastic models based on the deterministic
models given in the references [21, 22], in order to represent the noise
introduced by uncontrolled variation on parameters and errors on the
measurements. Under the assumption of Brownian noises we prove the
well-posedness the models either they take into account the space variable or
not. The filtering problem is solved for the non-spatial model giving Zakai and
Kushner-Stratonovich equations satisfied respectively by the unnormalized and
the normalized conditional distribution of the signal with respect to the
observations. A prevision problem and a discrete filtering problem are also
studied for the realistic cases of discrete and possibly incomplete
observations. We illustrate the filter behaviour through numerical simulations
corresponding to different scenarios
  KeyWords: Anthracnose modelling, State estimation, Nonlinear filtering.


title: Statistical physics of linear and bilinear inference problems

abstract:
  The recent development of compressed sensing has led to spectacular advances
in the understanding of sparse linear estimation problems as well as in
algorithms to solve them. It has also triggered a new wave of developments in
the related fields of generalized linear and bilinear inference problems, that
have very diverse applications in signal processing and are furthermore a
building block of deep neural networks. These problems have in common that they
combine a linear mixing step and a nonlinear, probabilistic sensing step,
producing indirect measurements of a signal of interest. Such a setting arises
in problems as different as medical or astronomical imaging, clustering, matrix
completion or blind source separation. The aim of this thesis is to propose
efficient algorithms for this class of problems and to perform their
theoretical analysis. To this end, it uses belief propagation, thanks to which
high-dimensional distributions can be sampled efficiently, thus making a
Bayesian approach to inference tractable. The resulting algorithms undergo
phase transitions just as physical systems do. These phase transitions can be
analyzed using the replica method, initially developed in statistical physics
of disordered systems. The analysis reveals phases in which inference is easy,
hard or impossible. These phases correspond to different energy landscapes of
the problem. The main contributions of this thesis can be divided into three
categories. First, the application of known algorithms to concrete problems:
community detection, superposition codes and an innovative imaging system.
Second, a new, efficient message-passing algorithm for a class of problems
called blind sensor calibration. Third, a theoretical analysis of matrix
compressed sensing and of instabilities in Bayesian bilinear inference
algorithms.


title: Study of MSSM heavy Higgs bosons decaying into charginos and neutralinos

abstract:
  A multitude of searches have already been performed by the ATLAS and CMS
collaborations at the LHC to probe the heavy Higgses of the Minimal
Supersymmetric Standard Model (MSSM) through their decay to the Standard Model
particles. In this paper, we study the decay of the MSSM heavy Higgses into
neutralino and chargino pairs and estimate the maximum possible branching
ratios for these `ino' modes being consistent with the present LHC data. After
performing a random scan of the relevant electroweakino parameters, we impose
the SM 125 GeV Higgs constraints, low energy flavour data as well as current
bounds on heavy Higgses from the LHC run-I and run-II data. The present limits
on the electroweakino masses and couplings are also considered in our analysis.
We choose a few representative benchmark points satisfying all the
above-mentioned constraints, and then perform a detailed collider simulation,
including fast detector effects, and analyze all the potential SM backgrounds
in order to estimate the discovery reach of these heavy Higgses at the LHC. We
restrict ourselves within the leptonic cascade decay modes of these heavy
Higgses and study the mono-X + MET (X=W,Z) and trilepton + MET signatures in
the context of high luminosity run of the 14 TeV LHC.


title:
On equicontinuity of some class of mappings, which are quasiconformal in
  the mean

abstract:
  A behavior of open discrete mappings, which are quasiconformal in the mean,
is investigated. It is proved that the classes of mappings mentioned above are
equicontinuous (normal).


title: Optimizing the Expected Mean Payoff in Energy Markov Decision Processes

abstract:
  Energy Markov Decision Processes (EMDPs) are finite-state Markov decision
processes where each transition is assigned an integer counter update and a
rational payoff. An EMDP configuration is a pair s(n), where s is a control
state and n is the current counter value. The configurations are changed by
performing transitions in the standard way. We consider the problem of
computing a safe strategy (i.e., a strategy that keeps the counter
non-negative) which maximizes the expected mean payoff.


title:
Drag reduction in turbulent channel flow laden with finite-size oblate
  spheroids

abstract:
  We study suspensions of oblate rigid particles in a viscous fluid for
different values of the particle volume fractions. Direct numerical simulations
have been performed using a direct-forcing immersed boundary method to account
for the dispersed phase, combined with a soft-sphere collision model and
lubrication corrections for short-range particle-particle and particle-wall
interactions. With respect to the single phase flow, we show that in flows
laden with oblate spheroids the drag is reduced and the turbulent fluctuations
attenuated. In particular, the turbulence activity decreases to lower values
than those obtained by only accounting for the effective suspension viscosity.
To explain the observed drag reduction we consider the particle dynamics and
the interactions of the particles with the turbulent velocity field and show
that the particle wall layer, previously observed and found to be responsible
for the increased dissipation in suspensions of spheres, disappears in the case
of oblate particles. These rotate significantly slower than spheres near the
wall and tend to stay with their major axes parallel to the wall, which leads
to a decrease of the Reynolds stresses and turbulence production and so to the
overall drag reduction.


title: Metallic phase of hydrogen at the pressure 500GPa

abstract:
  The first-principle method of mathematical modeling was used to calculate the
structural, electronic, phonon, and other characteristics of the normal
metallic phase of hydrogen at a pressure of 500 GPa. It has been shown that
metal hydrogen having a lattice symmetry I41 / AMD cell is a stable phase under
a high pressure hydrostatic compression. The resulting structure is a locally
stable one with respect to the phonon spectrum.


title:
Local well-posedness and Global stability of the Two-Phase Stefan
  problem

abstract:
  The two-phase Stefan problem describes the temperature distribution in a
homogeneous medium undergoing a phase transition such as ice melting to water.
This is accomplished by solving the heat equation on a time-dependent domain,
composed of two regions separated by an a priori unknown moving boundary which
is transported by the difference (or jump) of the normal derivatives of the
temperature in each phase. We establish local-in-time well-posedness and a
global-in-time stability result for arbitrary sufficiently smooth domains and
small initial temperatures. To this end, we develop a higher-order energy with
natural weights adapted to the problem and combine it with Hopf-type
inequalities. This extends the previous work by Hadzic and Shkoller [31,32] on
the one-phase Stefan problem to the setting of two-phase problems, and
simplifies the proof significantly.


title:
Large time asymptotics for the parabolic Anderson model driven by space
  and time correlated noise

abstract:
  We consider the linear stochastic heat equation on $\mathbb{R}^\ell$, driven
by a Gaussian noise which is colored in time and space. The spatial covariance
satisfies general assumptions and includes examples such as the Riesz kernel in
any dimension and the covariance of the fractional Brownian motion with Hurst
parameter $H\in (\frac 14, \frac 12]$ in dimension one. First we establish the
existence of a unique mild solution and we derive a Feynman-Kac formula for its
moments using a family of independent Brownian bridges and assuming a general
integrability condition on the initial data. In the second part of the paper we
compute Lyapunov exponents and lower and upper exponential growth indices in
terms of a variational quantity.


title: Destruction or Preservation As You Like It

abstract:
  The Gap Forcing Theorem, a key contribution of this paper, implies
essentially that after any reverse Easton iteration of closed forcing, such as
the Laver preparation, every supercompactness measure on a supercompact
cardinal extends a measure from the ground model. Thus, such forcing can create
no new supercompact cardinals, and, if the GCH holds, neither can it increase
the degree of supercompactness of any cardinal; in particular, it can create no
new measurable cardinals. In a crescendo of what I call exact preservation
theorems, I use this new technology to perform a kind of partial Laver
preparation, and thereby finely control the class of posets which preserve a
supercompact cardinal. Eventually, I prove the `As You Like It' Theorem, which
asserts that the class of ${<}\kappa$-directed closed posets which preserve a
supercompact cardinal $\kappa$ can be made by forcing to conform with any
pre-selected local definition which respects the equivalence of forcing. Along
the way I separate completely the levels of the superdestructibility hierarchy,
and, in an epilogue, prove that the notions of fragility and
superdestructibility are orthogonal---all four combinations are possible.


title: Small Forcing Makes Any Cardinal Superdestructible

abstract:
  Small forcing always ruins the indestructibility of an indestructible
supercompact cardinal. In fact, after small forcing, any cardinal $\kappa$
becomes superdestructible---any further ${<}\kappa$-closed forcing which adds a
subset to $\kappa$ will destroy the measurability, even the weak compactness,
of $\kappa$. Nevertheless, after small forcing indestructible cardinals remain
resurrectible, but never strongly resurrectible.


title:
Meta-conformal invariance and the boundedness of two-point correlation
  functions

abstract:
  The covariant two-point functions, derived from Ward identities in direct
space, can be affected by consistency problems and can become unbounded for
large time- or space-separations. This difficulty arises for several extensions
of dynamical scaling, for example Schr\"odinger-invariance, conformal Galilei
invariance or meta-conformal invariance, but not for standard ortho-conformal
invariance. For meta-conformal invariance in 1+1 dimensions, these difficulties
can be cured by going over to a dual space and an extension of these dynamical
symmetries through the construction of a new generator in the Cartan
sub-algebra. This provides a canonical interpretation of meta-conformally
covariant two-point functions as correlators. Galilei-conformal correlators can
be obtained from meta-conformal invariance through a simple contraction. In
contrast, by an analogus construction, Schr\"odinger-covariant two-point
functions are causal response functions. All these two-point functions are
bounded at large separations, for sufficiently positive values of the scaling
exponents.

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


title:
The structure of graphs with forbidden $C_4$, $\overline{C}_4$, $C_5$,
  chair and co-chair

abstract:
  We find the structure of graphs that have no $C_4$, $\overline{C}_4$, $C_5$,
chair and co-chair as induced subgraphs.


title: Fuchs' problem for dihedral groups

abstract:
  More than 50 years ago, Laszlo Fuchs asked which abelian groups can be the
group of units of a ring. Though progress has been made, the question remains
open. One could equally well pose the question for various classes of
nonabelian groups. In this paper, we prove that D_2, D_4, D_6, D_8, and D_12
are the only dihedral groups that appear as the group of units of a ring of
positive characteristic (or, equivalently, of a finite ring), and D_2 and D_4k,
where k is odd, are the only dihedral groups that appear as the group of units
of a ring of characteristic 0.


title:
HATS-22b, HATS-23b and HATS-24b: Three new transiting Super-Jupiters
  from the HATSouth Project

abstract:
  We report the discovery of three moderately high-mass transiting hot Jupiters
from the HATSouth survey: HATS-22b, HATS-23b and HATS-24b. These planets add to
the numbers of known planets in the ~2MJ regime. HATS-22b is a 2.74+/-0.11 MJ
mass and 0.953+0.048/-0.029 RJ radius planet orbiting a V = 13.455 +/- 0.040
sub-silar mass (M_star = 0.759+/-0.019 M_sun; R_star = 0.759+/-0.019 R_sun)
K-dwarf host star on an eccentric (e = 0.079 +/- 0.026) orbit. This planet's
high planet-to-stellar mass ratio is further evidence that migration mechanisms
for hot Jupiters may rely on exciting orbital eccentricities that bring planets
closer to their parent stars followed by tidal circularisation. HATS-23b is a
1.478 +/- 0.080 MJ mass and 1.69 +/- 0.24 RJ radius planet on a grazing orbit
around a V = 13.901 +/- 0.010 G-dwarf with properties very similar to those of
the Sun (M_star = 1.115 +/- 0.054 M_sun; R_star = 1.145 +/- 0.070 R_sun).
HATS-24b orbits a moderately bright V = 12.830 +/- 0.010 F-dwarf star (M_star =
1.218 +/- 0.036 M_sun; R_star = 1.194+0.066/-0.041 R_sun). This planet has a
mass of 2.39 +0.21/-0.12 MJ and an inflated radius of 1.516 +0.085/-0.065 RJ.


title:
Besov continuity for pseudo-differential operators on compact
  homogeneous manifolds

abstract:
  In this paper we study the Besov continuity of pseudo-differential operators
on compact homogeneous manifolds $M=G/K.$ We use the global quantization of
these operators in terms of the representation theory of compact homogeneous
manifolds.


title: Isobaric multiplet mass equation in the $A=31$ $T = 3/2$ quartets

abstract:
  The observed mass excesses of analog nuclear states with the same mass number
$A$ and isospin $T$ can be used to test the isobaric multiplet mass equation
(IMME), which has, in most cases, been validated to a high degree of precision.
A recent measurement [Kankainen et al., Phys. Rev. C 93 041304(R) (2016)] of
the ground-state mass of $^{31}$Cl led to a substantial breakdown of the IMME
for the lowest $A = 31, T = 3/2$ quartet. The second-lowest $A = 31, T = 3/2$
quartet is not complete, due to uncertainties associated with the identity of
the $^{31}$S member state. Using a fast $^{31}$Cl beam implanted into a plastic
scintillator and a high-purity Ge $\gamma$-ray detection array, $\gamma$ rays
from the $^{31}$Cl$(\beta\gamma)$$^{31}$S sequence were measured. Shell-model
calculations using USDB and the recently-developed USDE interactions were
performed for comparison. Isospin mixing between the $^{31}$S isobaric analog
state (IAS) at 6279.0(6) keV and a nearby state at 6390.2(7) keV was observed.
The second $T = 3/2$ state in $^{31}$S was observed at $E_x = 7050.0(8)$ keV.
Isospin mixing in $^{31}$S does not by itself explain the IMME breakdown in the
lowest quartet, but it likely points to similar isospin mixing in the mirror
nucleus $^{31}$P, which would result in a perturbation of the $^{31}$P IAS
energy. USDB and USDE calculations both predict candidate $^{31}$P states
responsible for the mixing in the energy region slightly above $E_x = 6400$
keV. The second quartet has been completed thanks to the identification of the
second $^{31}$S $T = 3/2$ state, and the IMME is validated in this quartet.


title: Mapping the Structure of Directed Networks: Beyond the "Bow-tie" Diagram

abstract:
  We reveal a hierarchical, multilayer organization of finite components --
i.e., tendrils and tubes -- around the giant connected components in directed
networks and propose efficient algorithms allowing one to uncover the entire
organization of key real-world directed networks, such as the World Wide Web,
the neural network of \emph{Caenorhabditis elegans}, and others. With
increasing damage, the giant components decrease in size while the number and
size of tendril layers increase, enhancing the susceptibility of the networks
to damage.


title:
Three-Dimensional Simulations of Tearing and Intermittency in Coronal
  Jets

abstract:
  Observations of coronal jets increasingly suggest that local fragmentation
and intermittency play an important role in the dynamics of these events. In
this work we investigate this fragmentation in high-resolution simulations of
jets in the closed-field corona. We study two realizations of the
embedded-bipole model, whereby impulsive helical outflows are driven by
reconnection between twisted and untwisted field across the domed fan plane of
a magnetic null. We find that the reconnection region fragments following the
onset of a tearing-like instability, producing multiple magnetic null points
and flux-rope structures within the current layer. The flux ropes formed within
the weak-field region in the center of the current layer are associated with
"blobs" of density enhancement that become filamentary threads as the flux
ropes are ejected from the layer, whereupon new flux ropes form behind them.
This repeated formation and ejection of flux ropes provides a natural
explanation for the intermittent outflows, bright blobs of emission, and
filamentary structure observed in some jets. Additional observational
signatures of this process are discussed. Essentially all jet models invoke
reconnection between regions of locally closed and locally open field as the
jet-generation mechanism. Therefore, we suggest that this repeated tearing
process should occur at the separatrix surface between the two flux systems in
all jets. A schematic picture of tearing-mediated jet reconnection in three
dimensions is outlined.


title:
Exploring the locally low dimensional structure in solving random
  elliptic PDEs

abstract:
  We propose a stochastic multiscale finite element method (StoMsFEM) to solve
random elliptic partial differential equations with a high stochastic
dimension. The key idea is to simultaneously upscale the stochastic solutions
in the physical space for all random samples and explore the low stochastic
dimensions of the stochastic solution within each local patch. We propose two
effective methods to achieve this simultaneous local upscaling. The first
method is a high order interpolation method in the stochastic space that
explores the high regularity of the local upscaled quantities with respect to
the random variables. The second method is a reduced-order method that explores
the low rank property of the multiscale basis functions within each coarse grid
patch. Our complexity analysis shows that compared with the standard FEM on a
fine grid, the StoMsFEM can achieve computational saving in the order of
$(H/h)^{d}/(\log(H/h))^k$, where $H/h$ is the ratio between the coarse and the
fine gird sizes, $d$ is the physical dimension and $k$ is the local stochastic
dimension. Several numerical examples are presented to demonstrate the accuracy
and effectiveness of the proposed methods. In the high contrast example, we
observe a factor of 2000 speed-up.


title: Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics

abstract:
  We show that the proper inclusion of soft reparameterization modes in the
Sachdev-Ye-Kitaev model of $N$ randomly interacting Majorana fermions reduces
its long-time behavior to that of Liouville quantum mechanics. As a result, all
zero temperature correlation functions decay with the universal exponent
$\propto \tau^{-3/2}$ for times larger than the inverse single particle level
spacing $\tau\gg N\ln N$. In the particular case of the single particle Green
function this behavior is manifestation of the zero-bias anomaly, or scaling in
energy as $\epsilon^{1/2}$. We also present exact diagonalization study
supporting our conclusions.


title: Can we reach Pareto optimal outcomes using bottom-up approaches?

abstract:
  Traditionally, researchers in decision making have focused on attempting to
reach Pareto Optimality using horizontal approaches, where optimality is
calculated taking into account every participant at the same time. Sometimes,
this may prove to be a difficult task (e.g., conflict, mistrust, no information
sharing, etc.). In this paper, we explore the possibility of achieving Pareto
Optimal outcomes in a group by using a bottom-up approach: discovering Pareto
optimal outcomes by interacting in subgroups. We analytically show that Pareto
optimal outcomes in a subgroup are also Pareto optimal in a supergroup of those
agents in the case of strict, transitive, and complete preferences. Then, we
empirically analyze the prospective usability and practicality of bottom-up
approaches in a variety of decision making domains.


title: Variational limits of k-NN graph based functionals on data clouds

abstract:
  This paper studies the large sample asymptotics of data analysis procedures
based on the optimization of functionals defined on $k$-NN graphs on point
clouds. The paper is framed in the context of minimization of balanced cut
functionals, but our techniques, ideas and results can be adapted to other
functionals of relevance. We rigorously show that provided the number of
neighbors in the graph $k:=k_n$ scales with the number of points in the cloud
as $n \gg k_n \gg \log(n)$, then with probability one, the solution to the
graph cut optimization problem converges towards the solution of an analogue
variational problem at the continuum level.


title: Neural ideals and stimulus space visualization

abstract:
  A neural code $\mathcal{C}$ is a collection of binary vectors of a given
length n that record the co-firing patterns of a set of neurons. Our focus is
on neural codes arising from place cells, neurons that respond to geographic
stimulus. In this setting, the stimulus space can be visualized as subset of
$\mathbb{R}^2$ covered by a collection $\mathcal{U}$ of convex sets such that
the arrangement $\mathcal{U}$ forms an Euler diagram for $\mathcal{C}$. There
are some methods to determine whether such a convex realization $\mathcal{U}$
exists; however, these methods do not describe how to draw a realization. In
this work, we look at the problem of algorithmically drawing Euler diagrams for
neural codes using two polynomial ideals: the neural ideal, a pseudo-monomial
ideal; and the neural toric ideal, a binomial ideal. In particular, we study
how these objects are related to the theory of piercings in information
visualization, and we show how minimal generating sets of the ideals reveal
whether or not a code is $0$, $1$, or $2$-inductively pierced.


title: The Econometrics of Randomized Experiments

abstract:
  In this review, we present econometric and statistical methods for analyzing
randomized experiments. For basic experiments we stress randomization-based
inference as opposed to sampling-based inference. In randomization-based
inference, uncertainty in estimates arises naturally from the random assignment
of the treatments, rather than from hypothesized sampling from a large
population. We show how this perspective relates to regression analyses for
randomized experiments. We discuss the analyses of stratified, paired, and
clustered randomized experiments, and we stress the general efficiency gains
from stratification. We also discuss complications in randomized experiments
such as non-compliance. In the presence of non-compliance we contrast
intention-to-treat analyses with instrumental variables analyses allowing for
general treatment effect heterogeneity. We consider in detail estimation and
inference for heterogeneous treatment effects in settings with (possibly many)
covariates. These methods allow researchers to explore heterogeneity by
identifying subpopulations with different treatment effects while maintaining
the ability to construct valid confidence intervals. We also discuss optimal
assignment to treatment based on covariates in such settings. Finally, we
discuss estimation and inference in experiments in settings with interactions
between units, both in general network settings and in settings where the
population is partitioned into groups with all interactions contained within
these groups.


title: The State of Applied Econometrics - Causality and Policy Evaluation

abstract:
  In this paper we discuss recent developments in econometrics that we view as
important for empirical researchers working on policy evaluation questions. We
focus on three main areas, where in each case we highlight recommendations for
applied work. First, we discuss new research on identification strategies in
program evaluation, with particular focus on synthetic control methods,
regression discontinuity, external validity, and the causal interpretation of
regression methods. Second, we discuss various forms of supplementary analyses
to make the identification strategies more credible. These include placebo
analyses as well as sensitivity and robustness analyses. Third, we discuss
recent advances in machine learning methods for causal effects. These advances
include methods to adjust for differences between treated and control units in
high-dimensional settings, and methods for identifying and estimating
heterogeneous treatment effects.


title: G\'en\'eralisation des congruences de Wolstenholme et de Morley

abstract:
  In this paper, we prove that for any odd prime $p$ and for any $p$-integer
$\alpha $,we have $ \binom{\alpha p-1}{p-1}\equiv 1-\alpha (\alpha -1)(\alpha
^{2}-\alpha -1)p\sum_{k=1}^{p-1}\frac{1}{k}+\alpha ^{2}
(\alpha-1)^{2}p^{2}\sum_{1\leq i<j\leq p-1}\frac{1}{ij} \ \pmod{p^{m}}$, where
$m=7$ if $p\neq 7$ and $m=6$ if $p=7$. this congruence generalizes the
congruences of Wolstenholme, Morley, Glaisher, Carlitz, McIntosh, Tauraso and
Me\v{s}trovi\'c. It allows one to rediscover the congruences of Glaisher,
Carlitz and Zhao in a simple way


title:
Reanalysis of the $X(4140)$ as axialvector tetraquark state with QCD sum
  rules

abstract:
  In this article, we take the $X(4140)$ as the diquark-antidiquark type
$cs\bar{c}\bar{s}$ tetraquark state with $J^{PC}=1^{++}$, and study the mass
and pole residue with the QCD sum rules in details by constructing two types
interpolating currents. The numerical results
$M_{X_{L,+}}=3.95\pm0.09\,\rm{GeV}$ and $M_{X_{H,+}}=5.00\pm0.10\,\rm{GeV}$
disfavor assigning the $X(4140)$ to be the $J^{PC}=1^{++}$ diquark-antidiquark
type $cs\bar{c}\bar{s}$ tetraquark state. Moreover, we obtain the masses of the
$J^{PC}=1^{+-}$ diquark-antidiquark type $cs\bar{c}\bar{s}$ tetraquark states
as a byproduct. The present predictions can be confronted to the experimental
data in the future.


title:
A sparse decomposition of low rank symmetric positive semi-definite
  matrices

abstract:
  Suppose that $A \in \mathbb{R}^{N \times N}$ is symmetric positive
semidefinite with rank $K \le N$. Our goal is to decompose $A$ into $K$
rank-one matrices $\sum_{k=1}^K g_k g_k^T$ where the modes $\{g_{k}\}_{k=1}^K$
are required to be as sparse as possible. In contrast to eigen decomposition,
these sparse modes are not required to be orthogonal. Such a problem arises in
random field parametrization where $A$ is the covariance function and is
intractable to solve in general. In this paper, we partition the indices from 1
to $N$ into several patches and propose to quantify the sparseness of a vector
by the number of patches on which it is nonzero, which is called patch-wise
sparseness. Our aim is to find the decomposition which minimizes the total
patch-wise sparseness of the decomposed modes. We propose a
domain-decomposition type method, called intrinsic sparse mode decomposition
(ISMD), which follows the "local-modes-construction + patching-up" procedure.
The key step in the ISMD is to construct local pieces of the intrinsic sparse
modes by a joint diagonalization problem. Thereafter a pivoted Cholesky
decomposition is utilized to glue these local pieces together. Optimal sparse
decomposition, consistency with different domain decomposition and robustness
to small perturbation are proved under the so called regular-sparse assumption
(see Definition 1.2). We provide simulation results to show the efficiency and
robustness of the ISMD. We also compare the ISMD to other existing methods,
e.g., eigen decomposition, pivoted Cholesky decomposition and convex relaxation
of sparse principal component analysis [25] and [40].


title: Topological complexity and efficiency of motion planning algorithms

abstract:
  We introduce a variant of Farber's topological complexity, defined for smooth
compact orientable Riemannian manifolds, which takes into account only motion
planners with the lowest possible "average length" of the output paths. We
prove that it never differs from topological complexity by more than $1$, thus
showing that the latter invariant addresses the problem of the existence of
motion planners which are "efficient".


title: Neutrino Flux Predictions for the NuMI Beam

abstract:
  Knowledge of the neutrino flux produced by the Neutrinos at the Main Injector
(NuMI) beamline is essential to the neutrino oscillation and neutrino
interaction measurements of the MINERvA, MINOS+, NOvA and MicroBooNE
experiments at Fermi National Accelerator Laboratory. We have produced a flux
prediction which uses all available and relevant hadron production data,
incorporating measurements of particle production off of thin targets as well
as measurements of particle yields from a spare NuMI target exposed to a 120
GeV proton beam. The result is the most precise flux prediction achieved for a
neutrino beam in the one to tens of GeV energy region. We have also compared
the prediction to in situ measurements of the neutrino flux and find good
agreement.


title: Towards a Numerical Unitarity Approach for Two-loop Amplitudes in QCD

abstract:
  The numerical unitarity approach has been important for obtaining reliable
QCD predictions for the LHC. Here I discuss the extension of the approach
beyond the leading quantum corrections for computing multi-loop amplitudes. The
numerical unitarity approach requires a suitable parametrisation of the loop
integrands as a sum of terms that integrate to zero (surface terms) and master
integrands. The construction and classification of suitable surface terms which
match the propagators structures of Feynman amplitudes is the main technical
advance discussed. A number of spin-offs for integral reduction and further
formal questions are briefly reviewed.


title:
A Semi-supervised learning approach to enhance health care
  Community-based Question Answering: A case study in alcoholism

abstract:
  Community-based Question Answering (CQA) sites play an important role in
addressing health information needs. However, a significant number of posted
questions remain unanswered. Automatically answering the posted questions can
provide a useful source of information for online health communities. In this
study, we developed an algorithm to automatically answer health-related
questions based on past questions and answers (QA). We also aimed to understand
information embedded within online health content that are good features in
identifying valid answers. Our proposed algorithm uses information retrieval
techniques to identify candidate answers from resolved QA. In order to rank
these candidates, we implemented a semi-supervised leaning algorithm that
extracts the best answer to a question. We assessed this approach on a curated
corpus from Yahoo! Answers and compared against a rule-based string similarity
baseline. On our dataset, the semi-supervised learning algorithm has an
accuracy of 86.2%. UMLS-based (health-related) features used in the model
enhance the algorithm's performance by proximately 8 %. A reasonably high rate
of accuracy is obtained given that the data is considerably noisy. Important
features distinguishing a valid answer from an invalid answer include text
length, number of stop words contained in a test question, a distance between
the test question and other questions in the corpus as well as a number of
overlapping health-related terms between questions. Overall, our automated QA
system based on historical QA pairs is shown to be effective according to the
data set in this case study. It is developed for general use in the health care
domain which can also be applied to other CQA sites.


title:
Iteration formulae of the Maslov-type index theory in weak symplectic
  Hilbert spaces

abstract:
  In this paper, we prove a splitting formula for the Maslov-type indices of
symplectic paths induced by the splitting of the nullity in weak symplectic
Hilbert space. Then we give a direct proof of iteration formulae for the
Maslov-type indices of symplectic paths.


title:
Vortex motion and flux-flow resistivity in dirty multiband
  superconductors

abstract:
  The conductivity of vortex lattices in multiband superconductors with high
concentration of impurities is calculated based on microscopic kinetic theory.
Both the limits of high and low fields are considered, when the magnetic
induction is close to or much smaller than the critical field strength
$H_{c2}$, respectively. It is shown that in contrast to single-band
superconductors the resistive properties are not universal but depend on the
pairing constants and ratios of diffusivities in different bands. The low-field
magneto-resistance can strongly exceed Bardeen-Stephen estimation in a
quantitative agreement with experimental data for two-band superconductor
MgB$_2$.


title: New computations of the Riemann zeta function on the critical line

abstract:
  We present highlights of computations of the Riemann zeta function around
large values and high zeros. The main new ingredient in these computations is
an implementation of the second author's fast algorithm for numerically
evaluating quadratic exponential sums. In addition, we use a new simple
multi-evaluation method to compute the zeta function in a very small range at
little more than the cost of evaluation at a single point.


title: Automatic Generation of Probabilistic Programming from Time Series Data

abstract:
  Probabilistic programming languages represent complex data with intermingled
models in a few lines of code. Efficient inference algorithms in probabilistic
programming languages make possible to build unified frameworks to compute
interesting probabilities of various large, real-world problems. When the
structure of model is given, constructing a probabilistic program is rather
straightforward. Thus, main focus have been to learn the best model parameters
and compute marginal probabilities. In this paper, we provide a new perspective
to build expressive probabilistic program from continue time series data when
the structure of model is not given. The intuition behind of our method is to
find a descriptive covariance structure of time series data in nonparametric
Gaussian process regression. We report that such descriptive covariance
structure efficiently derives a probabilistic programming description
accurately.


title:
Optimal Energy Allocation For Delay-Constrained Traffic Over Fading
  Multiple Access Channels

abstract:
  In this paper, we consider a multiple-access fading channel where $N$ users
transmit to a single base station (BS) within a limited number of time slots.
We assume that each user has a fixed amount of energy available to be consumed
over the transmission window. We derive the optimal energy allocation policy
for each user that maximizes the total system throughput under two different
assumptions on the channel state information. First, we consider the offline
allocation problem where the channel states are known a priori before
transmission. We solve a convex optimization problem to maximize the
sum-throughput under energy and delay constraints. Next, we consider the online
allocation problem, where the channels are causally known to the BS and obtain
the optimal energy allocation via dynamic programming when the number of users
is small. We also develop a suboptimal resource allocation algorithm whose
performance is close to the optimal one. Numerical results are presented
showing the superiority of the proposed algorithms over baseline algorithms in
various scenarios.


title:
Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of
  Constant Curvature

abstract:
  We review the theory of orthogonal separation of variables of the
Hamilton-Jacobi equation on spaces of constant curvature, highlighting key
contributions to the theory by Benenti. This theory revolves around a special
type of conformal Killing tensor, hereafter called a concircular tensor. First,
we show how to extend original results given by Benenti to intrinsically
characterize all (orthogonal) separable coordinates in spaces of constant
curvature using concircular tensors. This results in the construction of a
special class of separable coordinates known as Kalnins-Eisenhart-Miller
coordinates. Then we present the Benenti-Eisenhart-Kalnins-Miller separation
algorithm, which uses concircular tensors to intrinsically search for
Kalnins-Eisenhart-Miller coordinates which separate a given natural
Hamilton-Jacobi equation. As a new application of the theory, we show how to
obtain the separable coordinate systems in the two dimensional spaces of
constant curvature, Minkowski and (Anti-)de Sitter space. We also apply the
Benenti-Eisenhart-Kalnins-Miller separation algorithm to study the separability
of the three dimensional Calogero-Moser and Morosi-Tondo systems.


title: Deformations and generalized derivations of Hom-Lie conformal algebras

abstract:
  The purpose of this paper is to extend the cohomology and conformal
derivation theories of the classical Lie conformal algebras to Hom-Lie
conformal algebras. In this paper, we develop cohomology theory of Hom-Lie
conformal algebras and discuss some applications to the study of deformations
of regular Hom-Lie conformal algebras. Also, we introduce
$\alpha^k$-derivations of multiplicative Hom-Lie conformal algebras and study
their properties.


title: Stochastic Modeling of Hybrid Cache Systems

abstract:
  In recent years, there is an increasing demand of big memory systems so to
perform large scale data analytics. Since DRAM memories are expensive, some
researchers are suggesting to use other memory systems such as non-volatile
memory (NVM) technology to build large-memory computing systems. However,
whether the NVM technology can be a viable alternative (either economically and
technically) to DRAM remains an open question. To answer this question, it is
important to consider how to design a memory system from a "system
perspective", that is, incorporating different performance characteristics and
price ratios from hybrid memory devices.
  This paper presents an analytical model of a "hybrid page cache system" so to
understand the diverse design space and performance impact of a hybrid cache
system. We consider (1) various architectural choices, (2) design strategies,
and (3) configuration of different memory devices. Using this model, we provide
guidelines on how to design hybrid page cache to reach a good trade-off between
high system throughput (in I/O per sec or IOPS) and fast cache reactivity which
is defined by the time to fill the cache. We also show how one can configure
the DRAM capacity and NVM capacity under a fixed budget. We pick PCM as an
example for NVM and conduct numerical analysis. Our analysis indicates that
incorporating PCM in a page cache system significantly improves the system
performance, and it also shows larger benefit to allocate more PCM in page
cache in some cases. Besides, for the common setting of performance-price ratio
of PCM, "flat architecture" offers as a better choice, but "layered
architecture" outperforms if PCM write performance can be significantly
improved in the future.


title: Path planning with Inventory-driven Jump-Point-Search

abstract:
  In many navigational domains the traversability of cells is conditioned on
the path taken. This is often the case in video-games, in which a character may
need to acquire a certain object (i.e., a key or a flying suit) to be able to
traverse specific locations (e.g., doors or high walls). In order for
non-player characters to handle such scenarios we present invJPS, an
"inventory-driven" pathfinding approach based on the highly successful
grid-based Jump-Point-Search (JPS) algorithm. We show, formally and
experimentally, that the invJPS preserves JPS's optimality guarantees and its
symmetry breaking advantages in inventory-based variants of game maps.


title:
An Algebraic Approach to Non-Orthogonal General Joint Block
  Diagonalization

abstract:
  The exact/approximate non-orthogonal general joint block diagonalization
({\sc nogjbd}) problem of a given real matrix set $\mathcal{A}=\{A_i\}_{i=1}^m$
is to find a nonsingular matrix $W\in\mathbb{R}^{n\times n}$ (diagonalizer)
such that $W^T A_i W$ for $i=1,2,\dots, m$ are all exactly/approximately block
diagonal matrices with the same diagonal block structure and with as many
diagonal blocks as possible. In this paper, we show that a solution to the
exact/approximate {\sc nogjbd} problem can be obtained by finding the
exact/approximate solutions to the system of linear equations $A_iZ=Z^TA_i$ for
$i=1,\dots, m$, followed by a block diagonalization of $Z$ via similarity
transformation. A necessary and sufficient condition for the equivalence of the
solutions to the exact {\sc nogjbd} problem is established. Two numerical
methods are proposed to solve the {\sc nogjbd} problem, and numerical examples
are presented to show the merits of the proposed methods.


title: Some Conformal Positive Mass Theorems

abstract:
  W. Simon proved a conformal positive mass theorem, which was used to prove
uniqueness of black holes later. In this note, we will generalize Simon's
conformal positive mass theorem in two directions. First we will consider
spacetime version of conformal positive mass theorems on asymptotically flat
initial data set. Next, we will prove a conformal positive mass theorem on
asymptotically hyperbolic manifolds.


title:
Towards Abstraction from Extraction: Multiple Timescale Gated Recurrent
  Unit for Summarization

abstract:
  In this work, we introduce temporal hierarchies to the sequence to sequence
(seq2seq) model to tackle the problem of abstractive summarization of
scientific articles. The proposed Multiple Timescale model of the Gated
Recurrent Unit (MTGRU) is implemented in the encoder-decoder setting to better
deal with the presence of multiple compositionalities in larger texts. The
proposed model is compared to the conventional RNN encoder-decoder, and the
results demonstrate that our model trains faster and shows significant
performance gains. The results also show that the temporal hierarchies help
improve the ability of seq2seq models to capture compositionalities better
without the presence of highly complex architectural hierarchies.


title: Coarse2Fine: Two-Layer Fusion For Image Retrieval

abstract:
  This paper addresses the problem of large-scale image retrieval. We propose a
two-layer fusion method which takes advantage of global and local cues and
ranks database images from coarse to fine (C2F). Departing from the previous
methods fusing multiple image descriptors simultaneously, C2F is featured by a
layered procedure composed by filtering and refining. In particular, C2F
consists of three components. 1) Distractor filtering. With holistic
representations, noise images are filtered out from the database, so the number
of candidate images to be used for comparison with the query can be greatly
reduced. 2) Adaptive weighting. For a certain query, the similarity of
candidate images can be estimated by holistic similarity scores in
complementary to the local ones. 3) Candidate refining. Accurate retrieval is
conducted via local features, combining the pre-computed adaptive weights.
Experiments are presented on two benchmarks, \emph{i.e.,} Holidays and Ukbench
datasets. We show that our method outperforms recent fusion methods in terms of
storage consumption and computation complexity, and that the accuracy is
competitive to the state-of-the-arts.


title: An Empirical Evaluation Of Social Influence Metrics

abstract:
  Predicting when an individual will adopt a new behavior is an important
problem in application domains such as marketing and public health. This paper
examines the perfor- mance of a wide variety of social network based
measurements proposed in the literature - which have not been previously
compared directly. We study the probability of an individual becoming
influenced based on measurements derived from neigh- borhood (i.e. number of
influencers, personal network exposure), structural diversity, locality,
temporal measures, cascade mea- sures, and metadata. We also examine the
ability to predict influence based on choice of classifier and how the ratio of
positive to negative samples in both training and testing affect prediction
results - further enabling practical use of these concepts for social influence
applications.


title: Recursive utility optimization with concave coefficients

abstract:
  This paper concerns the recursive utility maximization problem. We assume
that the coefficients of the wealth equation and the recursive utility are
concave. Then some interesting and important cases with nonlinear and nonsmooth
coefficients satisfy our assumption. After given an equivalent backward
formulation of our problem, we employ the Fenchel-Legendre transform and derive
the corresponding variational formulation. By the convex duality method, the
primal "sup-inf" problem is translated to a dual minimization problem and the
saddle point of our problem is derived. Finally, we obtain the optimal terminal
wealth. To illustrate our results, three cases for investors with ambiguity
aversion are explicitly worked out under some special assumptions.


title: On the cluster nature and quantization of geometric $R$-matrices

abstract:
  We define cluster $R$-matrices as sequences of mutations in triangular grid
quivers on a cylinder, and show that the affine geometric $R$-matrix of
symmetric power representations for the quantum affine algebra
$U_q^\prime(\hat{\mathfrak{sl}}_n)$ can be obtained from our cluster
$R$-matrix. A quantization of the affine geometric $R$-matrix is defined,
compatible with the cluster structure. We construct invariants of the quantum
affine geometric $R$-matrix as quantum loop symmetric functions.


title: The Ground Axiom

abstract:
  The ground axiom is the assertion that the set-theoretic universe is not
obtainable by forcing over any inner model. Although this appears at first to
be a second-order assertion, it is actually first-order expressible in the
language of set theory. This article is the extended abstract for a talk at the
2005 Workshop in Set Theory at the Mathematisches Forschungsinstitut
Oberwolfach.


title: Optimal Dividend and Investment Problems under Sparre Andersen Model

abstract:
  In this paper we study a class of optimal dividend and investment problems
assuming that the underlying reserve process follows the Sparre Andersen model,
that is, the claim frequency is a "renewal" process, rather than a standard
compound Poisson process. The main feature of such problems is that the
underlying reserve dynamics, even in its simplest form, is no longer Markovian.
By using the backward Markovization technique we recast the problem in a
Markovian framework with expanded dimension representing the time elapsed after
the last claim, with which we investigate the regularity of the value function,
and validate the dynamic programming principle. Furthermore, we show that the
value function is the unique constrained viscosity solution} to the associated
HJB equation on a cylindrical domain on which the problem is well-defined.


title: Location of Gamma-ray emission and magnetic field strengths in OJ 287

abstract:
  The Gamma-ray BL Lac object OJ 287 is known to exhibit inner-parsec
"jet-wobbling", high degrees of variability at all wavelengths and
quasi-stationary features including an apparent (~100 deg) position angle
change in projection on the sky plane. Sub-50 micro-arcsecond resolution 86 GHz
observations with the global mm-VLBI array (GMVA) supplement ongoing
multi-frequency VLBI blazar monitoring at lower frequencies. Using these maps
together with cm/mm total intensity and Gamma-ray observations from Fermi/LAT
from 2008-2014, we aimed to determine the location of Gamma-ray emission and to
explain the inner-mas structural changes. Observations with the GMVA offer
approximately double the angular resolution compared with 43 GHz VLBA
observations and allow us to observe above the synchrotron self-absorption peak
frequency. The jet was spectrally decomposed at multiple locations along the
jet. From this we derived estimates of the magnetic field. How the field
decreases down the jet allowed an estimate of the distance to the jet apex and
an estimate of the magnetic field strength at the jet apex and in the broad
line region. Combined with accurate kinematics we attempt to locate the site of
Gamma-ray activity, radio flares and spectral changes. Strong Gamma-ray flares
appeared to originate from either the "core" region, a downstream stationary
feature, or both, with Gamma-ray activity significantly correlated with radio
flaring in the downstream quasi-stationary feature. Magnetic field estimates
were determined at multiple locations along the jet, with the magnetic field
found to be >1.6 G in the "core" and >0.4 G in the downstream quasi-stationary
feature. We therefore found upper limits on the location of the "core" as >6.0
pc from the jet apex and determined an upper limit on the magnetic field near
the jet base of the order of thousands of Gauss.


title: Frobenius-Chern-Simons gauge theory

abstract:
  Given a set of differential forms on an odd-dimensional noncommutative
manifold valued in an internal associative algebra H, we show that the most
general cubic covariant Hamiltonian action, without mass terms, is controlled
by an Z_2-graded associative algebra F with a graded symmetric nondegenerate
bilinear form. The resulting class of models provide a natural generalization
of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957
as an off-shell formulation of the minimal bosonic four-dimensional higher spin
gravity theory. If F is unital and the Z_2-grading is induced from a Klein
operator that is outer to a proper Frobenius subalgebra, then the action can be
written on a form akin to topological open string field theory in terms of a
superconnection valued in the direct product of H and F. We give a new model of
this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual
complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be
truncated consistently as to zero-form constraints on-shell. Two examples
thereof are a twisting of C[(Z_2)^3] that yields the original model, and the
Clifford algebra Cl_2n which provides an FCS formulation of the bosonic
Konstein--Vasiliev model with gauge algebra hu(4^{n-1},0).


title: Differential Poisson Sigma Models with Extended Supersymmetry

abstract:
  The induced two-dimensional topological N=1 supersymmetric sigma model on a
differential Poisson manifold M presented in arXiv:1503.05625 is shown to be a
special case of the induced Poisson sigma model on the bi-graded supermanifold
T[0,1]M. The bi-degree comprises the standard N-valued target space degree,
corresponding to the form degree on the worldsheet, and an additional Z-valued
fermion number, corresponding to the degree in the differential graded algebra
of forms on M. The N=1 supersymmetry stems from the compatibility between the
(extended) differential Poisson bracket and the de Rham differential on M. The
latter is mapped to a nilpotent vector field Q of bi-degree (0,1) on
T*[1,0](T[0,1]M), and the covariant Hamiltonian action is Q-exact. New extended
supersymmetries arise as inner derivatives along special bosonic Killing
vectors on M that induce Killing supervector fields of bi-degree (0,-1) on
T*[1,0](T[0,1]M).


title: Higher Spin Currents in the Enhanced N=3 Kazama-Suzuki Model

abstract:
  The N=3 Kazama-Suzuki model at the `critical' level has been found by
Creutzig, Hikida and Ronne. We construct the lowest higher spin currents of
spins (3/2, 2,2,2,5/2, 5/2, 5/2, 3) in terms of various fermions. In order to
obtain the operator product expansions (OPEs) between these higher spin
currents, we describe three N=2 OPEs between the two N=2 higher spin currents
denoted by (3/2, 2, 2, 5/2) and (2, 5/2, 5/2, 3) (corresponding 36 OPEs in the
component approach). Using the various Jacobi identities, the coefficient
functions appearing on the right hand side of these N=2 OPEs are determined in
terms of central charge completely. Then we describe them as one single N=3 OPE
in the N=3 superspace. The right hand side of this N=3 OPE contains the
SO(3)-singlet N=3 higher spin multiplet of spins (2, 5/2, 5/2, 5/2, 3,3,3,
7/2), the SO(3)-singlet N=3 higher spin multiplet of spins (5/2, 3,3,3, 7/2,
7/2, 7/2, 4), and the SO(3)-triplet N=3 higher spin multiplets where each
multiplet has the spins (3, 7/2, 7/2, 7/2, 4,4,4, 9/2), in addition to N=3
superconformal family of the identity operator. Finally, by factoring out the
spin-1/2 current of N=3 linear superconformal algebra generated by eight
currents of spins (1/2, 1,1,1, 3/2, 3/2, 3/2, 2), we obtain the extension of
so-called SO(3) nonlinear Knizhnik Bershadsky algebra.


title: Retrofitting mutual authentication to GSM using RAND hijacking

abstract:
  As has been widely discussed, the GSM mobile telephony system only offers
unilateral authentication of the mobile phone to the network; this limitation
permits a range of attacks. While adding support for mutual authentication
would be highly beneficial, changing the way GSM serving networks operate is
not practical. This paper proposes a novel modification to the relationship
between a Subscriber Identity Module (SIM) and its home network which allows
mutual authentication without changing any of the existing mobile
infrastructure, including the phones; the only necessary changes are to the
authentication centres and the SIMs. This enhancement, which could be deployed
piecemeal in a completely transparent way, not only addresses a number of
serious vulnerabilities in GSM but is also the first proposal for enhancing GSM
authentication that possesses such transparency properties.


title:
A Two-Streamed Network for Estimating Fine-Scaled Depth Maps from Single
  RGB Images

abstract:
  Estimating depth from a single RGB image is an ill-posed and inherently
ambiguous problem. State-of-the-art deep learning methods can now estimate
accurate 2D depth maps, but when the maps are projected into 3D, they lack
local detail and are often highly distorted. We propose a fast-to-train
two-streamed CNN that predicts depth and depth gradients, which are then fused
together into an accurate and detailed depth map. We also define a novel set
loss over multiple images; by regularizing the estimation between a common set
of images, the network is less prone to over-fitting and achieves better
accuracy than competing methods. Experiments on the NYU Depth v2 dataset shows
that our depth predictions are competitive with state-of-the-art and lead to
faithful 3D projections.


title: Perspectives on Kuperberg flows

abstract:
  The "Seifert Conjecture" asks, "Does every non-singular vector field on the
3-sphere ${\mathbb S}^3$ have a periodic orbit?" In a celebrated work, Krystyna
Kuperberg gave a construction of a smooth aperiodic vector field on a plug,
which is then used to construct counter-examples to the Seifert Conjecture for
smooth flows on the $3$-sphere, and on compact 3-manifolds in general. The
dynamics of the flows in these plugs have been extensively studied, with more
precise results known in special "generic" cases of the construction. Moreover,
the dynamical properties of smooth perturbations of Kuperberg's construction
have been considered. In this work, we recall some of the results obtained to
date for the Kuperberg flows and their perturbations. Then the main point of
this work is to focus attention on how the known results for Kuperberg flows
depend on the assumptions imposed on the flows, and to discuss some of the many
interesting questions and problems that remain open about their dynamical and
ergodic properties.


title:
Ultrahigh-Energy Cosmic Ray Production by Turbulence in Gamma-Ray Burst
  Jets and Cosmogenic Neutrinos

abstract:
  We propose a novel model to produce ultrahigh-energy cosmic-rays (UHECRs) in
gamma-ray burst jets. After the prompt gamma-ray emission, hydrodynamical
turbulence is excited in the GRB jets at or before the afterglow phase. The
mildly relativistic turbulence stochastically accelerates protons. The
acceleration rate is much slower than the usual first-order shock acceleration
rate, but in this case it can be energy-independent. The resultant UHECR
spectrum is so hard that the bulk energy is concentrated in the highest energy
range, resulting in a moderate requirement for the typical cosmic ray
luminosity of $\sim 10^{53.5}~\mbox{erg}~\mbox{s}^{-1}$. In this model, the
secondary gamma-ray and neutrino emissions initiated by photopion production
are significantly suppressed. Although the UHECR spectrum at injection shows a
curved feature, this does not conflict with the observed UHECR spectral shape.
The cosmogenic neutrino spectrum in the $10^{17}$--$10^{18}$ eV range becomes
distinctively hard in this model, which may be verified by future observations.


title: Generalized multiplicities of edge ideals

abstract:
  We explore connections between the generalized multiplicities of square-free
monomial ideals and the combinatorial structure of the underlying hypergraphs
using methods of commutative algebra and polyhedral geometry. For instance, we
show the $j$-multiplicity is multiplicative over the connected components of a
hypergraph, and we explicitly relate the $j$-multiplicity of the edge ideal of
a properly connected uniform hypergraph to the Hilbert-Samuel multiplicity of
its special fiber ring. In addition, we provide general bounds for the
generalized multiplicities of the edge ideals and compute these invariants for
classes of uniform hypergraphs.


title:
Insights into Phase Transitions and Entanglement from Density Functional
  Theory

abstract:
  Density functional theory has made great success in solid state physics,
quantum chemistry and in computational material sciences. In this work we show
that density functional theory could shed light on phase transitions and
entanglement at finite temperatures. Specifically, we show that the equilibrium
state of an interacting quantum many-body system which is in thermal
equilibrium with a heat bath at a fixed temperature is a universal functional
of the first derivatives of the free energy with respect to temperature and
other control parameters respectively. This insight from density functional
theory enables us to express the average value of any physical observable and
any entanglement measure as a universal functional of the first derivatives of
the free energy with respect to temperature and other control parameters. Since
phase transitions are marked by the nonanalytic behavior of free energy with
respect to control parameters, the physical quantities and entanglement
measures may present nonanalytic behavior at critical point inherited from
their dependence on the first derivative of free energy. We use an
experimentally realizable model to demonstrate the idea. These results give new
insights for phase transitions and provide new profound connections between
entanglement and phase transition in interacting quantum many-body physics.


title: Global nilpotent cone is isotropic : parahoric torsors on curves

abstract:
  In this article, we investigate an analogue of the global nilpotent cone in
the case of the cotangent stack of the moduli stack of parahoric torsors on
curves.


title: Duality theorems of multiple zeta values with parameters

abstract:
  In this paper, we introduce the method of adding additional factors and a
parameter to multiple zeta values and prove some generalizations of the duality
theorem and several relations among multiple zeta values. In particular, we are
able to evaluate some special (truncated) sums in terms of Riemann zeta values
of different weights.


title: Study of WIMP annihilations into a pair of on-shell scalar mediators

abstract:
  In this article, we focus on a new scalar $\phi$ mediated scalar/vectorial
WIMPs (weakly interacting massive particles) with $\phi$'s mass slightly below
the WIMP mass. To explain the Galactic center 1 - 3 GeV gamma-ray excess, here
we consider the case that a WIMP pair predominantly annihilates into an
on-shell $\phi \phi$ pair with $\phi$ mainly decaying to $\tau \bar{\tau}$. The
masses of WIMPs are in a range about 14 - 22 GeV, and the annihilations of
WIMPs are phase space suppressed today. In this annihilation scheme, the
couplings of the $\phi$ - standard model (SM) particles are almost arbitrary
small, and the WIMP-nucleus spin-independent scattering can be tolerant by the
present dark matter (DM) direct detections. A scalar mediator-Higgs field
mixing is introduced, which is small and available. The lower limit on the
couplings of the $\phi$-SM particles set by the thermal equilibrium in the
early universe is derived, and this constraint is above the neutrino background
for scalar DM in direct detections. The WIMPs may be detectable at the upgraded
DM direct detection experiment in the next few years, and the exotic decay $h
\rightarrow \phi \phi$, the production of $\phi$ may be observable at future
high-luminosity $e^+ e^-$ collider.


title:
Determination of the number of $J/\psi$ events with inclusive $J/\psi$
  decays

abstract:
  A measurement of the number of $J/\psi$ events collected with the BESIII
detector in 2009 and 2012 is performed using inclusive decays of the $J/\psi$ .
The number of $J/\psi$ events taken in 2009 is recalculated to be
$(223.7\pm1.4)\times 10^6$, which is in good agreement with the previous
measurement, but with significantly improved precision due to improvements in
the BESIII software. The number of $J/\psi$ events taken in 2012 is determined
to be $(1086.9\pm 6.0)\times 10^6$. In total, the number of $J/\psi$ events
collected with the BESIII detector is measured to be $(1310.6\pm 7.0)\times
10^6$, where the uncertainty is dominated by systematic effects and the
statistical uncertainty is negligible.


title:
Existence and Stability of standing waves for supercritical NLS with a
  Partial Confinement

abstract:
  We prove the existence of orbitally stable ground states to NLS with a
partial confinement together with qualitative and symmetry properties. This
result is obtained for nonlinearities which are $L^2$-supercritical, in
particular we cover the physically relevant cubic case. The equation that we
consider is the limit case of the cigar-shaped model in BEC.


title: On Gromov-Witten theory of projective bundles

abstract:
  Given two equivariant vector bundles over an algebraic GKM manifold with the
same equivariant Chern classes, we show that the genus zero equivariant
Gromov--Witten theory of their projective bundles are naturally isomorphic.


title:
Direct Testing of Gradual PostPeak Softening of Notched Specimens of
  Fiber Composites Stabilized by Enhanced Stiffness and Mass

abstract:
  Static and dynamic analysis of the fracture tests of fiber composites in
hydraulically servo-controlled testing machines currently in use shows that
their grips are much too soft and light for observing the postpeak softening.
Based on static and dynamic analysis of the test setup, far stiffer and heavier
grips are proposed. Tests of compact-tension fracture specimens of woven
carbon-epoxy laminates prove this theoretical conclusion. Sufficiently stiff
grips allow observation of a stable postpeak, even under load-point
displacement control. Dynamic stability analysis further indicates that stable
postpeak can be observed under CMOD control provided that a large mass is
rigidly attached to the current soft grips. The fracture energy deduced from
the area under the measured complete load-deflection curve with stable postpeak
agrees closely with the fracture energy deduced from the size effect tests of
the same composite. Previous suspicions of dynamic snapback in the testing of
composites are dispelled. So is the previous view that fracture mechanics was
inapplicable to the fiber-polymer composites.


title:
First-principles investigations into the thermodynamics of cation
  disorder and it's impact on electronic structure and magnetic properties of
  spinel $Co\left(Cr_{1-x}Mn_{x} \right)_{2}O_{4}$

abstract:
  Recent experiments on Mn doped multiferroic $CoCr_{2}O_{4}$ indicate that a
possible distribution of Mn atoms among tetrahedrally and octahedrally
coordinated sites in the spinel lattice give rise to different variations in
the structural parameters and saturation magnetisations in different
concentration regimes of Mn atoms substituting the Cr. A composition dependent
magnetic compensation behaviour points to the role conversions of the magnetic
constituents. In this work, we have investigated the thermodynamics of cation
disorder in $Co\left(Cr_{1-x}Mn_{x}\right)_{2}O_{4}$ system and it's
consequences on the structural, electronic and magnetic properties, using
results from first-principles electronic structure calculations. We have
computed the variations in the cation-disorder as a function of Mn
concentration and the temperature and found that at the annealing temperature
of the experiment many of the systems exhibit cation disorder. Our results
support the interpretations of the experimental results regarding the
qualitative variations in the sub-lattice occupancies and the associated
magnetisation behaviour, with composition. We have analysed the variations in
structural, magnetic and electronic properties of this system with variations
in the compositions and the degree of cation disorder from the variations in
their electronic structures and by using the ideas from crystal field theory.
Our study provides a complete microscopic picture of the effects that are
responsible for composition dependent behavioural differences of the properties
of this system. This work lays down a general framework, based upon results
from first-principles calculations, to understand and analyse the
substitutional magnetic spinel oxides $A\left(B_{1-x}C_{x} \right)_{2}O_{4}$ in
presence of cation disorder.


title:
A Residual Bootstrap for High-Dimensional Regression with Near Low-Rank
  Designs

abstract:
  We study the residual bootstrap (RB) method in the context of
high-dimensional linear regression. Specifically, we analyze the distributional
approximation of linear contrasts $c^{\top} (\hat{\beta}_{\rho}-\beta)$, where
$\hat{\beta}_{\rho}$ is a ridge-regression estimator. When regression
coefficients are estimated via least squares, classical results show that RB
consistently approximates the laws of contrasts, provided that $p\ll n$, where
the design matrix is of size $n\times p$. Up to now, relatively little work has
considered how additional structure in the linear model may extend the validity
of RB to the setting where $p/n\asymp 1$. In this setting, we propose a version
of RB that resamples residuals obtained from ridge regression. Our main
structural assumption on the design matrix is that it is nearly low rank --- in
the sense that its singular values decay according to a power-law profile.
Under a few extra technical assumptions, we derive a simple criterion for
ensuring that RB consistently approximates the law of a given contrast. We then
specialize this result to study confidence intervals for mean response values
$X_i^{\top} \beta$, where $X_i^{\top}$ is the $i$th row of the design. More
precisely, we show that conditionally on a Gaussian design with near low-rank
structure, RB simultaneously approximates all of the laws
$X_i^{\top}(\hat{\beta}_{\rho}-\beta)$, $i=1,\dots,n$. This result is also
notable as it imposes no sparsity assumptions on $\beta$. Furthermore, since
our consistency results are formulated in terms of the Mallows (Kantorovich)
metric, the existence of a limiting distribution is not required.


title:
Fine-tuning problems in quantum field theory and Lorentz invariance: A
  scalar-fermion model with a physical momentum cutoff

abstract:
  We study the consistency of having Lorentz invariance as a low energy
approximation within the quantum field theory framework. A model with a scalar
and a fermion field is used to show how a Lorentz invariance violating high
momentum scale, a physical cutoff rendering the quantum field theory finite,
can be made compatible with a suppression of Lorentz invariance violations at
low momenta. The fine tuning required to get this suppression and to have a
light scalar particle in the spectrum is determined at one loop.


title:
Results of an all-sky high-frequency Einstein@Home search for continuous
  gravitational waves in LIGO's fifth science run

abstract:
  We present results of a high-frequency all-sky search for continuous
gravitational waves from isolated compact objects in LIGO's 5th Science Run
(S5) data, using the computing power of the Einstein@Home volunteer computing
project. This is the only dedicated continuous gravitational wave search that
probes this high frequency range on S5 data. We find no significant candidate
signal, so we set 90%-confidence level upper-limits on continuous gravitational
wave strain amplitudes. At the lower end of the search frequency range, around
1250 Hz, the most constraining upper-limit is $5.0\times 10^{-24}$, while at
the higher end, around 1500 Hz, it is $6.2\times 10^{-24}$. Based on these
upper-limits, and assuming a fiducial value of the principal moment of inertia
of $10^{38}$kg$\,$m$^2$, we can exclude objects with ellipticities higher than
roughly $2.8\times10^{-7}$ within 100 pc of Earth with rotation periods between
1.3 and 1.6 milliseconds.


title: Micromagnetic study of equilibrium states in nano hemispheroidal shells

abstract:
  We present results of micromagnetic simulations of thin ferromagnetic nano
hemispheroidal shells with sizes ranging from 1 to 50 nm (inside dimensions).
Depending on the geometrical and magnetic parameters of the hemispheroidal
shell, there exist four different magnetic phases: easy axis, easy plane, onion
and vortex. The profile for the vortex magnetization distribution is analyzed
and the limitations and applicability of different vortex ansatzes are
discussed. In addition, we investigate the total energy density for each of the
magnetic distributions as a function of the hemispheroidal shell dimensions.


title:
High-harmonic generation in alpha-quartz by the electron-hole
  recombination

abstract:
  A calculation of the high-harmonic generation (HHG) in $\alpha$-quartz using
the time-dependent density functional theory is reported. The inter-band
process is attributed to the dominant in HHG above the band gap. The photon
energy is set to 1.55 eV, and the cutoff energy of the plateau region is found
to be limited at the 19th harmonic (30 eV). The dependence of the HHG
efficiency at the cutoff energy region on laser intensity is consistent with
that of the hole density in the lowest-lying valence band. Numerical results
indicate that electron-hole recombination plays a crucial role in HHG in
$\alpha$-quartz. It is found that a 200 attosecond pulse train is produced
using HHG around the plateau cutoff energy.


title: Perfect Sampling and Gradient Simulation for Fork-Join Networks

abstract:
  Fork-join network is a class of queueing networks with applications in
manufactory, healthcare and computation systems. In this paper, we develop a
simulation algorithm that (1) generates i.i.d. samples of the job sojourn time,
jointly with the number of waiting tasks, exactly following the steady-state
distribution, and (2) unbiased estimators of the derivatives of the job sojourn
time with respect to the service rates of the servers in the network. The
algorithm is designed based on the Coupling from the Past (CFTP) and
Infinitesimal Perturbation Analysis (IPA) techniques. Two numerical examples
are reported, including the special 2-station case where analytic results on
the steady-state distribution is known and a 10-station network with a
bottleneck.


title: Graded comodule categories with enough projectives

abstract:
  It is well-known that the category of comodules over a flat Hopf algebroid is
abelian but typically fails to have enough projectives, and more generally, the
category of graded comodules over a graded flat Hopf algebroid is abelian but
typically fails to have enough projectives. In this short paper we prove that
the category of connective graded comodules over a connective, graded, flat,
finite-type Hopf algebroid has enough projectives. Applications in algebraic
topology are given: the Hopf algebroids of stable co-operations in complex
bordism, Brown-Peterson homology, and classical mod $p$ homology all have the
property that their categories of connective graded comodules have enough
projectives.


title:
Many-Body-Localization Transition : sensitivity to twisted boundary
  conditions

abstract:
  For disordered interacting quantum systems, the sensitivity of the spectrum
to twisted boundary conditions depending on an infinitesimal angle $\phi$ can
be used to analyze the Many-Body-Localization Transition. The sensitivity of
the energy levels $E_n(\phi)$ is measured by the level curvature $K_n=E_n"(0)$,
or more precisely by the Thouless dimensionless curvature $k_n=K_n/\Delta_n$,
where $\Delta_n$ is the level spacing that decays exponentially with the size
$L$ of the system. For instance $\Delta_n \propto 2^{-L}$ in the middle of the
spectrum of quantum spin chains of $L$ spins, while the Drude weight $D_n=L
K_n$ studied recently by M. Filippone, P.W. Brouwer, J. Eisert and F. von Oppen
[arxiv:1606.07291v1] involves a different rescaling. The sensitivity of the
eigenstates $\vert \psi_n(\phi) > $ is characterized by the susceptibility
$\chi_n=-F_n"(0)$ of the fidelity $F_n =\vert < \psi_n(0) \vert \psi_n(\phi)
>\vert $. Both observables are distributed with probability distributions
displaying power-law tails $P_{\beta}(k) \simeq A_{\beta} \vert k
\vert^{-(2+\beta)} $ and $Q(\chi) \simeq B_{\beta} \chi^{-\frac{3+\beta}{2}} $,
where $\beta$ is the level repulsion index taking the values $\beta^{GOE}=1$ in
the ergodic phase and $\beta^{loc}=0$ in the localized phase. The amplitudes
$A_{\beta}$ and $B_{\beta}$ of these two heavy tails are given by some moments
of the off-diagonal matrix element of the local current operator between two
nearby energy levels, whose probability distribution has been proposed as a
criterion for the Many-Body-Localization transition by M. Serbyn, Z. Papic and
D.A. Abanin [Phys. Rev. X 5, 041047 (2015)].


title: (Weak) diamond can fail at the least inaccessible cardinal

abstract:
  Starting from suitable large cardinals, we force the failure of (weak)
diamond at the least inaccessible cardinal. The result improves an unpublished
theorem of Woodin and a recent result of Ben-Neria, Garti and Hayut.


title:
Symmetries, conservation laws and Noether's theorem for
  differential-difference equations

abstract:
  This paper mainly contributes to the extension of Noether's theorem to
differential-difference equations. For that purpose, we first investigate the
prolongation formula for continuous symmetries, which makes a characteristic
representation possible. The relations of symmetries, conservation laws and the
Fr\'echet derivative are also investigated. For non-variational equations,
since Noether's theorem is now available, the self-adjointness method is
adapted to the computation of conservation laws for differential-difference
equations. A couple of differential-difference equations are investigated as
illustrative examples, including the Toda lattice and semi-discretisations of
the Korteweg-de Vries (KdV) equation. In particular, the Volterra equation is
taken as a running example.


title: Minimal growth harmonic functions on lamplighter groups

abstract:
  We study the minimal possible growth of harmonic functions on lamplighters.
We find that $(\mathbb{Z}/2)\wr \mathbb{Z}$ has no sublinear harmonic
functions, $(\mathbb{Z}/2)\wr \mathbb{Z}^2$ has no sublogarithmic harmonic
functions, and neither has the repeated wreath product
$(\dotsb(\mathbb{Z}/2\wr\mathbb{Z}^2)\wr\mathbb{Z}^2)\wr\dotsb\wr\mathbb{Z}^2$.
These results have implications on attempts to quantify the
Derriennic-Kaimanovich-Vershik theorem.


title:
Minimax Extrapolation Problem For Harmonizable Stable Sequences With
  Noise Observations

abstract:
  We consider the problem of optimal linear estimation of the functional $A
\xi~=~\sum_{j = 0}^{\infty} a_j \xi_j$ that depends on the unknown values
$\xi_j,j=0,1,\dots, $ of a random sequence $\{\xi_j,j\in\mathbb Z\}$ from
observations of the sequence
  $\{\xi_k+\eta_k,k\in\mathbb Z\}$ at points $k = -1, -2, \dots$, where
$\{\xi_k,k\in\mathbb Z\}$ and $\{\eta_k,k\in\mathbb Z\}$ are mutually
independent harmonizable symmetric $\alpha$-stable random sequences which have
the spectral densities $f(\theta)>0$ and $g(\theta)>0$ satisfying the
minimality condition.
  The problem is investigated under the condition of spectral certainty as well
as under the condition of spectral uncertainty.
  Formulas for calculating the value of the error and the spectral
characteristic of the optimal linear estimate of the functional are derived
under the condition of spectral certainty where spectral densities of the
sequences are exactly known.
  In the case of spectral uncertainty where spectral densities of the sequences
are not exactly known, while a class of admissible spectral densities is given,
relations that determine the least favorable spectral densities and the minimax
spectral characteristic are derived.


title: Nonlinear fiber gyroscope for quantum metrology

abstract:
  We examine the performance of a nonlinear fiber gyroscope for improved signal
detection beating the quantum limits of its linear counterparts. The
performance is examined when the nonlinear gyroscope is illuminated by
practical field states, such as coherent and quadrature squeezed states. This
is compared with the case of more ideal probes such as photon-number states.


title:
Comments on the BCBS proposal for a New Standardized Approach for
  Operational Risk

abstract:
  On March 4th 2016 the Basel Committee on Banking Supervision published a
consultative document where a new methodology, called the Standardized
Measurement Approach (SMA), is introduced for computing Operational Risk
regulatory capital for banks. In this note, the behavior of the SMA is studied
under a variety of hypothetical and realistic conditions, showing that the
simplicity of the new approach is very costly on other aspects: we find that
the SMA does not respond appropriately to changes in the risk profile of a
bank, nor is it capable of differentiating among the range of possible risk
profiles across banks; that SMA capital results generally appear to be more
variable across banks than the previous AMA option of fitting the loss data;
that the SMA can result in banks over- or under-insuring against operational
risks relative to previous AMA standards. Finally, we argue that the SMA is not
only retrograde in terms of its capability to measure risk, but perhaps more
importantly, it fails to create any link between management actions and capital
requirement.


title: Intrinsic reflections in Coxeter systems

abstract:
  Let $(W,S)$ be a Coxeter system and let $s \in S$. We call $s$ a right-angled
generator of $(W,S)$ if $st = ts$ or $st$ has infinite order for each $t \in
S$. We call $s$ an intrinsic reflection of $W$ if $s \in R^W$ for all Coxeter
generating sets $R$ of $W$. We give necessary and sufficient conditions for a
right-angled generator $s \in S$ of $(W,S)$ to be an intrinsic reflection of
$W$.


title:
Universality of quantum computation with cluster states and (X,Y)-plane
  measurements

abstract:
  Measurement-based quantum computing (MBQC) is a model of quantum computation
where quantum information is coherently processed by means of projective
measurements on highly entangled states. Following the introduction of MBQC,
cluster states have been studied extensively both from the theoretical and
experimental point of view. Indeed, the study of MBQC was catalysed by the
realisation that cluster states are universal for MBQC with (X,Y)-plane and Z
measurements. Here we examine the question of whether the requirement for Z
measurements can be dropped while maintaining universality. We answer this
question in the affirmative by showing that universality is possible in this
scenario.


title:
Fuchsia and master integrals for splitting functions from differential
  equations in QCD

abstract:
  We report on the recent progress in reducing differential equations for
Feynman master integrals to canonical form with the help of a method proposed
by Roman Lee. For the first time, we present Fuchsia --- our open-source
implementation of the Lee algorithm written in Python using mathematical
routines of a free computer algebra system SageMath. We demonstrate Fuchsia by
reducing differential equations for NLO contributions to splitting functions in
QCD, which contain both loops and legs integrals.


title: Global fluctuations for 1D log-gas dynamics

abstract:
  We study in this article the hydrodynamic limit in the macroscopic regime of
the coupled system of stochastic differential equations, \begin{equation}
d\lambda_t^i=\frac{1}{\sqrt{N}} dW_t^i - V'(\lambda_t^i) dt+ \frac{\beta}{2N}
\sum_{j\not=i} \frac{dt}{\lambda^i_t-\lambda^j_t}, \qquad i=1,\ldots,N,
\end{equation} with $\beta>1$, sometimes called generalized Dyson's Brownian
motion, describing the dissipative dynamics of a log-gas of $N$ equal charges
with equilibrium measure corresponding to a $\beta$-ensemble, with sufficiently
regular convex potential $V$. The limit $N\to\infty$ is known to satisfy a
mean-field Mac-Kean-Vlasov equation. We prove that, for suitable initial
conditions, fluctuations around the limit are Gaussian and satisfy an explicit
PDE.
  The proof is very much indebted to the harmonic potential case treated in
Israelsson \cite{Isr}. Our key argument consists in showing that the
time-evolution generator may be written in the form of a transport operator on
the upper half-plane, plus a bounded non-local operator interpreted in terms of
a signed jump process. As an essential technical argument ensuring the
convergence of the above scheme, we give an $N$-independent large-deviation
type estimate for the probability that $\sup_{t\in[0,T]}\max_{i=1,\ldots,N}
|\lambda_t^i|$ is large, based on a multi-scale argument and entropic bounds.

categories: math.PR cond-mat.stat-mech math-ph math.MP


title: Fate of spinons at the Mott point

abstract:
  Gapless spin liquids have recently been observed in several frustrated Mott
insulators, with elementary spin excitations - "spinons" - reminiscent of
degenerate Fermi systems. However, their precise role at the Mott point, where
charge fluctuations begin to proliferate, remains controversial and
ill-understood. Here we present the simplest theoretical framework that treats
the dynamics of emergent spin and charge excitations on the same footing,
providing a new physical picture of the Mott metal-insulator transition at half
filing. We identify a generic orthogonality mechanism leading to strong damping
of spinons, arising as soon as the Mott gap closes. Our results indicates that
spinons should not play a significant role within the high-temperature quantum
critical regime above the Mott point - in striking agreement with all available
experiments.


title:
A Constrained Coding Scheme for Correcting Asymmetric Magnitude-$1$
  Errors in $q$-ary Channels

abstract:
  We present a constraint-coding scheme to correct asymmetric magnitude-$1$
errors in multi-level non-volatile memories. For large numbers of such errors,
the scheme is shown to deliver better correction capability compared to known
alternatives, while admitting low-complexity of decoding. Our results include
an algebraic formulation of the constraint, necessary and sufficient conditions
for correctability, a maximum-likelihood decoder running in complexity linear
in the alphabet size, and upper bounds on the probability of failing to correct
$t$ errors. Besides the superior rate-correction tradeoff, another advantage of
this scheme over standard error-correcting codes is the flexibility to vary the
code parameters without significant modifications.


title:
On the maximal use of Monte Carlo samples: re-weighting events at NLO
  accuracy

abstract:
  Accurate Monte Carlo simulations for high-energy events at CERN's Large
Hadron Collider, are very expensive, both from the computing and storage points
of view. We describe a method that allows to consistently re-use parton-level
samples accurate up to NLO in QCD under different theoretical hypotheses. We
implement it in MadGraph5_aMC@NLO and show its validation by applying it to
several cases of practical interest for the search of new physics at the LHC.


title: New solutions for non-Abelian cosmic strings

abstract:
  We study the properties of classical vortex solutions in a non-Abelian gauge
theory. A system of two adjoint Higgs fields breaks the SU(2) gauge symmetry to
$Z_2$, producing 't Hooft-Polyakov monopoles trapped on cosmic strings, termed
beads; there are two charges of monopole and two degenerate string solutions.
The strings break an accidental discrete $Z_2$ symmetry of the theory,
explaining the degeneracy of the ground state. Further symmetries of the model,
not previously appreciated, emerge when the masses of the two adjoint Higgs
fields are degenerate. The breaking of the enlarged discrete symmetry gives
rise to additional string solutions and splits the monopoles into four types of
`semipole': kink solutions that interpolate between the string solutions,
classified by a complex gauge invariant magnetic flux and a $Z_4$ charge. At
special values of the Higgs self-couplings, the accidental symmetry broken by
the string is continuous, giving rise to supercurrents on the strings. The
SU(2) theory can be embedded in a wide class of Grand Unified Theories,
including SO(10). We argue that semipoles and supercurrents are generic on GUT
strings.


title:
Multi-Objective Design of State Feedback Controllers Using Reinforced
  Quantum-Behaved Particle Swarm Optimization

abstract:
  In this paper, a novel and generic multi-objective design paradigm is
proposed which utilizes quantum-behaved PSO(QPSO) for deciding the optimal
configuration of the LQR controller for a given problem considering a set of
competing objectives. There are three main contributions introduced in this
paper as follows. (1) The standard QPSO algorithm is reinforced with an
informed initialization scheme based on the simulated annealing algorithm and
Gaussian neighborhood selection mechanism. (2) It is also augmented with a
local search strategy which integrates the advantages of memetic algorithm into
conventional QPSO. (3) An aggregated dynamic weighting criterion is introduced
that dynamically combines the soft and hard constraints with control objectives
to provide the designer with a set of Pareto optimal solutions and lets her to
decide the target solution based on practical preferences. The proposed method
is compared against a gradient-based method, seven meta-heuristics, and the
trial-and-error method on two control benchmarks using sensitivity analysis and
full factorial parameter selection and the results are validated using
one-tailed T-test. The experimental results suggest that the proposed method
outperforms opponent methods in terms of controller effort, measures associated
with transient response and criteria related to steady-state.


title:
An improved upper bound for the number of distinct eigenvalues of a
  matrix after perturbation

abstract:
  An upper bound for the number of distinct eigenvalues of a perturbed matrix
has been recently established by P. E. Farrell [1, Theorem 1.3]. The estimate
is the central result in Farrell's work and can be applied to estimate the
number of Krylov iterations required for solving a perturbed linear system. In
this paper, we present an improved upper bound for the number of distinct
eigenvalues of a matrix after perturbation. Furthermore, some results based on
the improved estimate are presented.


title: Universal $\alpha$-central extensions of hom-Leibniz $n$-algebras

abstract:
  We construct homology with trivial coefficients of Hom-Leibniz $n$-algebras.
We introduce and characterize universal ($\alpha$)-central extensions of
Hom-Leibniz $n$-algebras. In particular, we show their interplay with the
zeroth and first homology with trivial coefficients. When $n=2$ we recover the
corresponding results on universal central extensions of Hom-Leibniz algebras.
The notion of non-abelian tensor product of Hom-Leibniz $n$-algebras is
introduced and we establish its relationship with the universal central
extensions. We develop a generalization of the concept and properties of
unicentral Leibniz algebras to the setting of Hom-Leibniz $n$-algebras.


title: Corrugation of relativistic magnetized shock waves

abstract:
  As a shock front interacts with turbulence, it develops corrugation which
induces outgoing wave modes in the downstream plasma. For a fast shock wave,
the incoming wave modes can either be fast magnetosonic waves originating from
downstream, outrunning the shock, or eigenmodes of the upstream plasma drifting
through the shock. Using linear perturbation theory in relativistic MHD, this
paper provides a general analysis of the corrugation of relativistic magnetized
fast shock waves resulting from their interaction with small amplitude
disturbances. Transfer functions characterizing the linear response for each of
the outgoing modes are calculated as a function of the magnetization of the
upstream medium and as a function of the nature of the incoming wave.
Interestingly, if the latter is an eigenmode of the upstream plasma, we find
that there exists a resonance at which the (linear) response of the shock
becomes large or even diverges. This result may have profound consequences on
the phenomenology of astrophysical relativistic magnetized shock waves.


title:
Well-conditioned boundary integral equation formulations and Nystr\"om
  discretizations for the solution of Helmholtz problems with impedance
  boundary conditions in two-dimensional Lipschitz domains

abstract:
  We present a regularization strategy that leads to well-conditioned boundary
integral equation formulations of Helmholtz equations with impedance boundary
conditions in two-dimensional Lipschitz domains. We consider both the case of
classical impedance boundary conditions, as well as the case of transmission
impedance conditions wherein the impedances are certain coercive operators. The
latter type of problems is instrumental in the speed up of the convergence of
Domain Decomposition Methods for Helmholtz problems. Our regularized
formulations use as unknowns the Dirichlet traces of the solution on the
boundary of the domain. Taking advantage of the increased regularity of the
unknowns in our formulations, we show through a variety of numerical results
that a graded-mesh based Nystr\"om discretization of these regularized
formulations leads to efficient and accurate solutions of interior and exterior
Helmholtz problems with impedance boundary conditions.


title:
NaFe$_{0.56}$Cu$_{0.44}$As: A pnictide insulating phase induced by
  on-site Coulomb interaction

abstract:
  In the studies of iron-pnictides, a key question is whether their bad-metal
state from which the superconductivity emerges lies in close proximity with a
magnetically ordered insulating phase. Recently it was found that at low
temperatures, the heavily Cu-doped NaFe$_{1-x}$Cu$_x$As ($x > 0.3$)
iron-pnictide is an insulator with long-range antiferromagnetic order, similar
to the parent compound of cuprates but distinct from all other iron-pnictides.
Using angle-resolved photoemission spectroscopy, we determined the
momentum-resolved electronic structure of NaFe$_{1-x}$Cu$_x$As ($x = 0.44$) and
identified that its ground state is a narrow-gap insulator. Combining the
experimental results with density functional theory (DFT) and DFT+U
calculations, our analysis reveals that the on-site Coulombic (Hubbard) and
Hund's coupling energies play crucial roles in formation of the band gap about
the chemical potential. We propose that at finite temperatures charge carriers
are thermally excited from the Cu-As-like valence band into the conduction
band, which is of Fe $3d$-like character. With increasing temperature, the
number of electrons in the conduction band becomes larger and the hopping
energy between Fe sites increases, and finally the long-range antiferromagnetic
order is destroyed at $T > T_\mathrm{N}$. Our study provides a basis for
investigating the evolution of the electronic structure of a Mott insulator
transforming into a bad metallic phase, and eventually forming a
superconducting state in iron-pnictidesa superconducting state in
iron-pnictides.


title:
OpenGeoBase: Information Centric Networking meets Spatial Database
  applications - Extended Version

abstract:
  This paper explores methodologies, advantages and challenges related to the
use of Information Centric Networking (ICN) for realizing distributed spatial
databases. Our findings show that the ICN functionality perfectly fits database
requirements: routing-by-name can be used to dispatch queries and insertions,
in-network caching to accelerate queries, and data-centric security to
implement secure multi-tenancy. We present an ICN-based distributed spatial
database, named OpenGeoBase, and describe its design choices. Thanks to ICN,
OpenGeoBase can quickly and efficiently provide information to database users;
easily operate in a distributed way, deploying and using many database engines
in parallel; secure every piece of content; naturally slice resources, so that
several tenants and users can concurrently and independently use the database.
We also show how OpenGeoBase can support a real world Intelligent Transport
System application, by enabling discovery of geo-referenced public
transportation information.


title: Internetwork magnetic field as revealed by 2D inversions

abstract:
  Properties of magnetic field in the internetwork regions are still fairly
unknown due to rather weak spectropolarimetric signals. We address the matter
by using the 2D inversion code that is able to retrieve the information on
smallest spatial scales, up to the diffraction limit, while being less
susceptible to noise than most of the previous methods used. Performance of the
code and the impact of the various effects on the retrieved field distribution
is tested first on the realistic MHD simulations. The best inversion scenario
is then applied to the real Hinode/SP data. Tests on simulations show: (1) the
best choice of node position ensures a decent retrieval of all parameters, (2)
code performs well for different configurations of magnetic field, (3) slightly
different noise level or slightly different defocus included in the spatial PSF
produces no significant effect on the results and (4) temporal integration
shifts the field distribution to the stronger, more horizontally inclined
field. Although the contribution of the weak field is slightly overestimated
due to noise, the 2D inversions are able to recover well the overall
distribution of the magnetic field strength. Application of the 2D inversion
code on the Hinode/SP internetwork observations reveals a monotonic field
strength distribution. The mean field strength at optical depth unity is $\sim
130$~G. At the higher layers, field strength drops as the field becomes more
horizontal. Regarding the distribution of the field inclination, tests show
that we cannot directly retrieve it with the observations/tools at hand,
however the obtained distributions are consistent with those expected from
simulations with a quasi-isotropic field inclination after accounting for
observational effects.