title: First-principles study of $\langle c+a \rangle$ dislocations in Mg

abstract:
  We use first-principles density functional theory to study the generalized
stacking fault energy surfaces for pyramidal-I and pyramidal-II slip systems in
Mg. We demonstrate that the additional relaxation of atomic motions normal to
the slip direction allows for the appropriate local minimum in the generalized
stacking fault energy (GSFE) curve to be found. The fault energy calculations
suggest that formation of pyramidal-I dislocations would be slightly more
energetically favorable than that for pyramidal-II dislocations. The calculated
pyramidal-II GSFE curves also indicate that the full pyramidal II dislocations
would dissociate into the Stohr and Poirier (SP) configuration, consisting of
two $\frac{1}{2}\langle c+a \rangle$ partials, $\frac{1}{6}[11{\bar2}3] +
\frac{1}{6}[11{\bar2}3]$ , but the pyramidal-I GSFE curves, while also
possessing a local minimum, would not dissociate into the same SP
configuration. We report observation of these partials here emanating from a
$\{10{\bar1}2 \}$ twin boundary. Using MD simulations with MEAM potential for
Mg, we find that the full pyramidal-II $\langle c+a \rangle $ dislocation
splits into two equal value partials $\frac{1}{6}[11{\bar2}3] +
\frac{1}{6}[11{\bar2}3]$ separated by ~22.6 $\AA$. We reveal that the full
pyramidal-I $\langle c+a \rangle$ dislocation dissociates also into two equal
value partials but onto alternating $(30{\bar3}4)$ and $(30{\bar3}2)$ planes
with $\frac{1}{6} [20{\bar2}3]$ and $\frac{1}{6} [02{\bar2}3]$ Burgers vectors
separated by a 30.4 $\AA$ wide stacking fault. When a stress is applied, edge
and mixed dislocations of the extended pyramidal-II dislocation can move on
their glide plane; however, pyramidal-I dislocations of similar character
cannot.


title: Parametric set-wise injective maps

abstract:
  We introduce the notion of set-wise injective maps and provide results about
fiber embeddings. Our results improve some previous results in this area.


title: Homological dimension and homogeneous ANR spaces

abstract:
  The homological dimension $d_G$ of metric compacta was introduced by
Alexandroff. In this paper we provide some general properties of $d_G$, mainly
with an eye towards describing the dimensional full-valuedness of compact
metric spaces. As a corollary of the established properties of $d_G$, we prove
that any two-dimensional $lc^2$ metric compactum is dimensionally full-valued.
This improves the well known result of Kodama that every two-dimensional $ANR$
is dimensionally full-valued. Applications for homogeneous metric
$ANR$-compacta are also given.


title: On the breaking of mu-tau flavor symmetry

abstract:
  In light of the observation of a relatively large $\theta^{}_{13}$, one has
to consider breaking the $\mu$-$\tau$ symmetry properly which would otherwise
result in a vanishing $\theta^{}_{13}$ (as well as $\theta^{}_{23} = \pi/4$).
Therefore, we investigate various symmetry-breaking patterns and accordingly
identify those that are phenomenologically viable. Furthermore, the
symmetry-breaking effects arising from some specific physics (e.g., the
renormalization group equation running effect) are discussed as well.


title:
Four-divergence as a paravector operator. Invariance of the wave
  equation under orthogonal paravector transformation

abstract:
  The article presents four identities containing the spatio-temporal
differential operator also known as four-divergence. These equations are used
to prove the invariance of wave equation under orthogonal paravector
transformations. Moreover, the transformation of equations containing
spatio-temporal differential operators under the rotation of reference frame
has been presented.


title:
Hybridization and Field Driven Phase Transitions in Hexagonally Warped
  Topological Insulators

abstract:
  In this paper we discuss the role of material parameters and external field
effects on a thin film topological insulator(TI) in the context of quantum
phase transition(QPT). First, we consider an in-plane tilted magnetic field and
determine the band structure of the surface states as a function of the tilt
angle. We show that the presence of either a hybridization term or hexagonal
warping or a combination of both leads to a semi-metal to insulator phase
transition which is facilitated by their ${\cal PT}$ symmetry breaking
character. We then note that while the introduction of an electric field does
not allow for this QPT since it doesn't break ${\cal PT}$ symmetry, it can be
used in conjunction with a tunneling element to reach a phase transition
efficiently. The corresponding critical point is then non-trivially depend on
the electric field, which is pointed out here. Then, we demonstrate that
including a hexagonal warping term leads to an immediate ${\cal PT}$ symmetry
violating QPT.


title: On the Number of Rainbow Spanning Trees in Edge-Colored Complete Graphs

abstract:
  A spanning tree of a properly edge-colored complete graph, $K_n$, is rainbow
provided that each of its edges receives a distinct color. In 1996, Brualdi and
Hollingsworth conjectured that if $K_{2m}$ is properly $(2m-1)$-edge-colored,
then the edges of $K_{2m}$ can be partitioned into $m$ rainbow spanning trees
except when $m=2$. By means of an explicit, constructive approach, in this
paper we construct $\lfloor \sqrt{6m+9}/3 \rfloor$ mutually edge-disjoint
rainbow spanning trees for any positive value of $m$. Not only are the rainbow
trees produced, but also some structure of each rainbow spanning tree is
determined in the process. This improves upon best constructive result to date
in the literature which produces exactly three rainbow trees.


title:
Joint Learning of Siamese CNNs and Temporally Constrained Metrics for
  Tracklet Association

abstract:
  In this paper, we study the challenging problem of multi-object tracking in a
complex scene captured by a single camera. Different from the existing tracklet
association-based tracking methods, we propose a novel and efficient way to
obtain discriminative appearance-based tracklet affinity models. Our proposed
method jointly learns the convolutional neural networks (CNNs) and temporally
constrained metrics. In our method, a Siamese convolutional neural network
(CNN) is first pre-trained on the auxiliary data. Then the Siamese CNN and
temporally constrained metrics are jointly learned online to construct the
appearance-based tracklet affinity models. The proposed method can jointly
learn the hierarchical deep features and temporally constrained segment-wise
metrics under a unified framework. For reliable association between tracklets,
a novel loss function incorporating temporally constrained multi-task learning
mechanism is proposed. By employing the proposed method, tracklet association
can be accomplished even in challenging situations. Moreover, a new dataset
with 40 fully annotated sequences is created to facilitate the tracking
evaluation. Experimental results on five public datasets and the new
large-scale dataset show that our method outperforms several state-of-the-art
approaches in multi-object tracking.


title: The Numbers of Distinct Squares and Cubes in the Tribonacci Sequence

abstract:
  The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution
$\sigma(a,b,c)=(ab,ac,a)$. In this note, we give the explicit expressions of
the numbers of distinct squares and cubes in $\mathbb{T}[1,n]$ (the prefix of
$\mathbb{T}$ of length $n$).


title:
Effective numerical treatment of sub-diffusion equation with non-smooth
  solution

abstract:
  In this paper we investigate a sub-diffusion equation for simulating the
anomalous diffusion phenomenon in real physical environment. Based on an
equivalent transformation of the original sub-diffusion equation followed by
the use of a smooth operator, we devise a high-order numerical scheme by
combining the Nystrom method in temporal direction with the compact finite
difference method and the spectral method in spatial direction. The distinct
advantage of this approach in comparison with most current methods is its high
convergence rate even though the solution of the anomalous sub-diffusion
equation usually has lower regularity on the starting point. The effectiveness
and efficiency of our proposed method are verified by several numerical
experiments.


title: The Square Trees in the Tribonacci Sequence

abstract:
  The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution
$\sigma(a,b,c)=(ab,ac,a)$. In this note, we get the explicit expressions of all
squares, and then establish the tree structure of the positions of repeated
squares in $\mathbb{T}$, called square trees. Using the square trees, we give a
fast algorithm for counting the number of repeated squares in $\mathbb{T}[1,n]$
for all $n$, where $\mathbb{T}[1,n]$ is the prefix of $\mathbb{T}$ of length
$n$. Moreover we get explicit expressions for some special $n$ such as $n=t_m$
(the Tribonacci number) etc.


title:
Nematic order in a simple-cubic lattice-spin model with full-ranged
  dipolar interactions

abstract:
  In a previous paper [Phys. Rev. E 90, 022506 (2014)], we had studied
thermodynamic and structural properties of a three-dimensional simple-cubic
lattice model with dipolar-like interaction, truncated at nearest-neighbor
separation, for which the existence of an ordering transition at finite
temperature had been proven mathematically; here we extend our investigation
addressing the full-ranged counterpart of the model, for which the critical
behavior had been investigated theoretically and experimentally. In addition
the existence of an ordering transition at finite temperature had been proven
mathematically as well. Both models exhibited the same continuously degenerate
ground-state configuration, possessing full orientational order with respect to
a suitably defined staggered magnetization (polarization), but no nematic
second-rank order; in both cases, thermal fluctuations remove the degeneracy,
so that nematic order does set in at low but finite temperature via a mechanism
of order by disorder. On the other hand, there were recognizable quantitative
differences between the two models as for ground-state energy and critical
exponent estimates; the latter were found to agree with early Renormalization
Group calculations and with experimental results.


title: Short proofs of theorems of Malyutin and Margulis

abstract:
  The Ghys-Margulis alternative asserts that a subgroup $G$ of homeomorphisms
of the circle which does not contain a free subgroup on two generators must
admit an invariant probability measure. Malyutin's theorem classifies minimal
actions of $G$. We present a short proof of Malyutin's theorem and then deduce
Margulis' theorem which confirms the G-M alternative. The basic ideas are
borrowed from the original work of Malyutin but the use of the apparatus of the
enveloping semigroup enables us to shorten the proof considerably.


title: Probing the Heavy Neutrinos of Inverse Seesaw Model at the LHeC

abstract:
  We consider the production of a heavy neutrino and its possible signals at
the Large Hadron-electron Collider (LHeC) in the context of an inverse-seesaw
model for neutrino mass generation. The inverse seesaw model extends the
Standard Model (SM) particle content by adding two neutral singlet fermions for
each lepton generation. It is a well motivated model in the context of
generating non-zero neutrino masses and mixings. The proposed future LHeC
machine presents us with a particularly interesting possibility to probe such
extensions of the SM with new leptons due to the presence of an electron beam
in the initial state. We show that the LHeC will be able to probe an inverse
scenario with much better efficacy compared to the LHC with very nominal
integrated luminosities as well as exploit the advantage of having the electron
beam polarized to enhance the heavy neutrino production rates.


title:
Optical force on diseased blood cells: towards the optical sorting of
  biological matter

abstract:
  By employing a series of massively parallel ab-initio simulations, we study
how optical forces act on biological matter subject to morphological disease.
As a representative case study, we here consider the case of Plasmodium
Falciparum on red blood cells (RBC) illuminated by a monochromatic plane wave.
Realistic parameters for the geometry and the refractive index are then taken
from published experiments. In our theoretical campaign, we study the
dependence of the optical force on the disease stage for different incident
wavelengths. We show that optical forces change significantly with the disease,
with amplitude variation in the hundreds of pN range. Our results open up new
avenues for the design of new optical systems for the treatment of human
disease.

categories: physics.optics physics.bio-ph physics.comp-ph physics.med-ph


title: Coding for Improved Throughput Performance in Network Switches

abstract:
  Network switches and routers need to serve packet writes and reads at rates
that challenge the most advanced memory technologies. As a result, scaling the
switching rates is commonly done by parallelizing the packet I/Os using
multiple memory units. For improved read rates, packets can be coded upon
write, thus giving more flexibility at read time to achieve higher utilization
of the memory units. This paper presents a detailed study of coded network
switches, and in particular how to design them to maximize the throughput
advantages over standard uncoded switches. Toward that objective the paper
contributes a variety of algorithmic and analytical tools to improve and
evaluate the throughput performance. The most interesting finding of this study
is that the placement of packets in the switch memory is the key to both high
performance and algorithmic efficiency. One particular placement policy we call
"design placement" is shown to enjoy the best combination of throughput
performance and implementation feasibility.


title:
A hybrid multiscale coarse-grained method for dynamics on complex
  networks

abstract:
  Brute-force simulations for dynamics on very large networks are quite
expensive. While phenomenological treatments may capture some macroscopic
properties, they often ignore important microscopic details. Fortunately, one
may be only interested in the property of local part and not in the whole
network. Here, we propose a hybrid multiscale coarse-grained(HMCG) method which
combines a fine Monte Carlo(MC) simulation on the part of nodes of interest
with a more coarse Langevin dynamics on the rest part. We demonstrate the
validity of our method by analyzing the equilibrium Ising model and the
nonequilibrium susceptible-infected-susceptible model. It is found that HMCG
not only works very well in reproducing the phase transitions and critical
phenomena of the microscopic models, but also accelerates the evaluation of
dynamics with significant computational savings compared to microscopic MC
simulations directly for the whole networks. The proposed method is general and
can be applied to a wide variety of networked systems just adopting appropriate
microscopic simulation methods and coarse graining approaches.


title: Helicity oscillations of Dirac and Majorana neutrinos

abstract:
  The helicity of a Dirac neutrino with mass $m$ evolves under the influence of
a $B$-field because it has a magnetic dipole moment proportional to $m$.
Moreover, it was recently shown that a polarized or anisotropic medium
engenders the same effect for both Dirac and Majorana neutrinos. Because a
$B$-field polarizes a background medium, it instigates helicity oscillations
even for Majorana neutrinos unless the medium is symmetric between matter and
antimatter. Motivated by these observations, we review the impact of a
$B$-field and of an anisotropic or polarized medium on helicity oscillations
for Dirac and Majorana neutrinos from the common perspective of in-medium
dispersion.


title: On keen Heegaard splittings

abstract:
  In this paper, we introduce a new concept of {\it strongly keen} for Heegaard
splittings, and show that, for any integers $n\geq 2$ and $g\geq 3$, there
exists a strongly keen Heegaard splitting of genus $g$ whose Hempel distance is
$n$.


title:
Band-Renormalization Effects and Predominant Antiferromagnetic Order in
  Two-Dimensional Hubbard Model

abstract:
  Band renormalization effects (BRE) are comprehensively studied for a mixed
state of dx2-y2-wave superconducting (d-SC) and antiferromagnetic (AF) orders,
in addition to simple d-SC, AF, and normal (paramagnetic) states, by applying a
variational Monte Carlo method to a two-dimensional Hubbard (t-t'-U) model. In
a weakly correlated regime (U=t<~6), BRE are negligible on all the states
studied. As previously shown, the effective band of d-SC is greatly
renormalized but the modifications of physical quantities, including energy
improvement, are negligible. In contrast, BRE on the AF state considerably
affects various features of the system. Because the energy is markedly improved
for t'/t<0, the AF state occupies almost the whole underdoped regime in phase
diagrams. A doped metallic AF state undergoes a kind of Lifshitz transition at
t'= t'L~-0.05t as t'/t varies, irrespective of the values of U/t and delta
(doping rate). Pocket Fermi surfaces arise around (pi,0)[(pi/2,pi/2)] for
t'>t'L [t'<t'L], which corresponds to the electron-hole asymmetry observed in
angle-resolved photoemission spectroscopy (ARPES) spectra. The coexistent state
of the two orders is possible basically for t'>t'L, because the existence of
Fermi surfaces near (pi,0) is a requisite for the electron scattering of
q=(pi,pi). Actually, the coexistent state appears mainly for t'L/t<t'/t<~0.2 in
the mixed state. Nevertheless, the AF and coexisting states become unstable
toward phase separation for -0.05<~t'/t<~0.2 but become stable at other values
of t'/t owing to the energy reduction by the diagonal hopping of doped holes.
We show that this instability does not directly correlate with the strength of
d-SC.


title: Machine Translation Evaluation Resources and Methods: A Survey

abstract:
  We introduce the Machine Translation (MT) evaluation survey that contains
both manual and automatic evaluation methods. The traditional human evaluation
criteria mainly include the intelligibility, fidelity, fluency, adequacy,
comprehension, and informativeness. The advanced human assessments include
task-oriented measures, post-editing, segment ranking, and extended criteriea,
etc. We classify the automatic evaluation methods into two categories,
including lexical similarity scenario and linguistic features application. The
lexical similarity methods contain edit distance, precision, recall, F-measure,
and word order. The linguistic features can be divided into syntactic features
and semantic features respectively. The syntactic features include part of
speech tag, phrase types and sentence structures, and the semantic features
include named entity, synonyms, textual entailment, paraphrase, semantic roles,
and language models. The deep learning models for evaluation are very newly
proposed. Subsequently, we also introduce the evaluation methods for MT
evaluation including different correlation scores, and the recent quality
estimation (QE) tasks for MT.
  This paper differs from the existing works
\cite{GALEprogram2009,EuroMatrixProject2007} from several aspects, by
introducing some recent development of MT evaluation measures, the different
classifications from manual to automatic evaluation measures, the introduction
of recent QE tasks of MT, and the concise construction of the content.
  We hope this work will be helpful for MT researchers to easily pick up some
metrics that are best suitable for their specific MT model development, and
help MT evaluation researchers to get a general clue of how MT evaluation
research developed. Furthermore, hopefully, this work can also shine some light
on other evaluation tasks, except for translation, of NLP fields.


title: Permutation groups, pattern involvement, and Galois connections

abstract:
  There is a connection between permutation groups and permutation patterns:
for any subgroup $G$ of the symmetric group $S_\ell$ and for any $n \geq \ell$,
the set of $n$-permutations involving only members of $G$ as $\ell$-patterns is
a subgroup of $S_n$. Making use of the monotone Galois connection induced by
the pattern avoidance relation, we characterize the permutation groups that
arise via pattern avoidance as automorphism groups of relations of a certain
special form. We also investigate a related monotone Galois connection for
permutation groups and describe its closed sets and kernels as automorphism
groups of relations.


title: Conformal symmetry breaking differential operators on differential forms

abstract:
  We study conformal symmetry breaking differential operators which map
differential forms on $\mathbb{R}^n$ to differential forms on a codimension one
subspace $\mathbb{R}^{n-1}$. These operators are equivariant with respect to
the conformal Lie algebra of the subspace $\mathbb{R}^{n-1}$. They correspond
to homomorphisms of generalized Verma modules for ${\mathfrak so}(n,1)$ into
generalized Verma modules for ${\mathfrak so}(n+1,1)$ both being induced from
fundamental form representations of a parabolic subalgebra. We apply the
F-method to derive explicit formulas for such homomorphisms. In particular, we
find explicit formulas for the generators of the intertwining operators of the
related branching problems restricting generalized Verma modules for
${\mathfrak so}(n+1,1)$ to ${\mathfrak so}(n,1)$. As consequences, we find
closed formulas for all conformal symmetry breaking differential operators in
terms of the first-order operators $d$, $\delta$, $\bar{d}$ and $\bar{\delta}$
and certain hypergeometric polynomials. A dominant role in these studies will
be played by two infinite sequences of symmetry breaking differential operators
which depend on a complex parameter $\lambda$. These will be termed the
conformal first and second type symmetry breaking operators. Their values at
special values of $\lambda$ appear as factors in two systems of factorization
identities which involve the Branson-Gover operators of the Euclidean metrics
on $\mathbb{R}^n$ and $\mathbb{R}^{n-1}$ and the operators $d$, $\delta$,
$\bar{d}$ and $\bar{\delta}$ as factors, respectively. Moreover, they are shown
to naturally recover the gauge companion and $Q$-curvature operators of the
Euclidean metric on the subspace $\mathbb{R}^{n-1}$, respectively.


title:
Minimax representation of nonexpansive functions and application to
  zero-sum recursive games

abstract:
  We show that a real-valued function on a topological vector space is
positively homogeneous of degree one and nonexpansive with respect to a weak
Minkowski norm if and only if it can be written as a minimax of linear forms
that are nonexpansive with respect to the same norm. We derive a representation
of monotone, additively and positively homogeneous functions on $L^\infty$
spaces and on $\mathbb{R}^n$, which extend results of Kolokoltsov, Rubinov,
Singer, and others. We apply this representation to nonconvex risk measures and
to zero-sum games. We derive in particular results of representation and
polyhedral approximation for the class of Shapley operators arising from games
without instantaneous payments (Everett's recursive games).


title: Role of phytochemicals in the chemoprevention of tumors

abstract:
  Phytochemicals are plant-derived secondary metabolites, which may exert many
biological activities in humans, including anticancer properties. Although
recent findings appear to support their role in cancer prevention and
treatment, this issue is still controversial. Anti-cancer activity of
phytochemicals mainly depends on their multi-target mechanism of action,
including antimutagenic, antioxidant and antiproliferative activities.
Furthermore, they may modulate the host immune response to cancer, reducing
inflammatory microenvironment and enhancing lymphocyte onco-surveillance. Since
carcinogenesis is multi-factorial and involves several signaling pathways,
multi-targeted agents as phytochemicals may represent promising anticancer
compounds. This narrative review aims to analyze the current literature on
phytochemicals highlighting their specific targets on carcinogenic molecular
pathways and their chemopreventive role. A full comprehension of their activity
at molecular and cellular levels will contribute for a better understanding of
phytochemical clinical efficacy, thus promoting the identification of new
effective plant-derived therapeutics.


title: An Accretive Operator Approach to Ergodic Problems for Zero-Sum Games

abstract:
  Mean payoff stochastic games can be studied by means of a nonlinear spectral
problem involving the Shapley operator: the ergodic equation. A solution
consists in a scalar, called the ergodic constant, and a vector, called bias.
The existence of such a pair entails that the mean payoff per time unit is
equal to the ergodic constant for any initial state, and the bias gives
stationary strategies. By exploiting two fundamental properties of Shapley
operators, monotonicity and additive homogeneity, we give a necessary and
sufficient condition for the solvability of the ergodic equation for all the
Shapley operators obtained by perturbation of the transition payments of a
given stochastic game with finite state space. If the latter condition is
satisfied, we establish that the bias is unique (up to an additive constant)
for a generic perturbation of the transition payments. To show these results,
we use the theory of accretive operators, and prove in particular some
surjectivity condition.


title:
Parallel preconditioners for high order discretizations arising from
  full system modeling for brain microwave imaging

abstract:
  This paper combines the use of high order finite element methods with
parallel preconditioners of domain decomposition type for solving
electromagnetic problems arising from brain microwave imaging. The numerical
algorithms involved in such complex imaging systems are computationally
expensive since they require solving the direct problem of Maxwell's equations
several times. Moreover, wave propagation problems in the high frequency regime
are challenging because a sufficiently high number of unknowns is required to
accurately represent the solution. In order to use these algorithms in practice
for brain stroke diagnosis, running time should be reasonable. The method
presented in this paper, coupling high order finite elements and parallel
preconditioners, makes it possible to reduce the overall computational cost and
simulation time while maintaining accuracy.


title: Thermal fission rates with temperature dependent fission barriers

abstract:
  The fission processes of thermal excited nuclei are conventionally studied by
statistical models which rely on inputs of phenomenological level densities and
potential barriers. Therefore the microscopic descriptions of spontaneous
fission and induced fission are very desirable for a unified understanding of
various fission processes.
  We propose to study the fission rates, at both low and high temperatures,
with microscopically calculated temperature-dependent fission barriers and
collective mass parameters.
  The fission barriers are calculated by the finite-temperature
Skyrme-Hartree-Fock+BCS method. The mass parameters are calculated by the
temperature-dependent cranking approximation. The thermal fission rates can be
obtained by the imaginary free energy approach at all temperatures, in which
fission barriers are naturally temperature dependent. The fission at low
temperatures can be described mainly as a barrier-tunneling process. While the
fission at high temperatures has to incorporate the reflection above barriers.
Our results of spontaneous fission rates reasonably agree with other studies
and experiments. The temperature dependencies of fission barrier heights and
curvatures have been discussed. The temperature dependent behaviors of mass
parameters have also been discussed. The thermal fission rates from low to high
temperatures with a smooth connection have been given by different approaches.
\item[Conclusions] Since the temperature dependencies of fission barrier
heights and curvatures, and the mass parameters can vary rapidly for different
nuclei, the microscopic descriptions of thermal fission rates are very
valuable. Our studies without free parameters provide a consistent picture to
study various fissions such as that in fast-neutron reactors, astrophysical
environments and fusion reactions for superheavy nuclei.


title: The centre of the bidual of Fourier algebras (discrete groups)

abstract:
  For a discrete group G with Fourier algebra A(G), we study the topological
centre $Z_t$ of the bidual. If G is amenable, then $Z_t$ = A(G). But if G
contains a non-abelian free group $F_r$, we show that $Z_t$ is strictly larger
than A(G). Furthermore, it is shown that the subalgebra of radial functions in
A(G) is Arens regular.


title:
Precoding design for single-RF massive MIMO systems: A large system
  analysis

abstract:
  This work revisits a recently proposed precoding design for massive
multiple-input multiple output (MIMO) systems that is based on the use of an
instantaneous total power constraint. The main advantages of this technique lie
in its suitability to single RF MIMO systems coupled with a very-high power
efficiency. Such features have been proven using simulations for uncorrelated
channels. Based on tools from random matrix theory, we propose in this work to
analyze the performance of this precoder for more involved channels accounting
for spatial correlation. The obtained expressions are then optimized in order
to maximize the signal-to-interference-plus-noise ratio (SINR). Simulation
results are provided in order to illustrate the performance of the optimized
precoder in terms of peak-to-average power ratio (PAPR) and
signal-to-interference-plus-noise ratio (SINR).


title: Minimum output entropy of a non-Gaussian quantum channel

abstract:
  We introduce a model of non-Gaussian quantum channel that stems from the
combination of two physically relevant processes occurring in open quantum
systems, namely amplitude damping and dephasing. For it we find input states
approaching zero output entropy, while respecting the input energy constraint.
These states fully exploit the infinite dimensionality of the Hilbert space.
Upon truncation of the latter, the minimum output entropy remains finite and
optimal input states for such a case are conjectured thanks to numerical
evidences.


title: From Inverse to Delayed Magnetic Catalysis in Strong Magnetic Field

abstract:
  We study magnetic field effect on chiral phase transition in a
Nambu--Jona-Lasinio model. In comparison with mean field approximation
containing quarks only, including mesons as quantum fluctuations in the model
leads to a transition from inverse to delayed magnetic catalysis at finite
temperature and delays the transition at finite baryon chemical potential. The
location of the critical end point depends on the the magnetic field
non-monotonously.


title:
Existence and Stability the Lagrangian point $L_4$ for the Earth-Sun
  system under a relativistic framework

abstract:
  It is well known that, from the Newtonian point of view, the Lagrangian point
$L_4$ in the circular restricted three body is stable if $\mu<
\frac{1}{18}(9-\sqrt{19})\approx 0.03852$. In this paper we will provide a
formula that allows us to compute the eigenvalues of the matrix that determines
the stability of the equilibrium points of a family of ordinary differential
equations. As an application we will show that, under the relativistic
framework, the Lagrangian point $L_4$ is also stable for the Sun-Earth system.
Similar arguments show the stability for $L_4$ not only for the Sun-Earth
system but for systems coming from a range of values for $\mu$ similar to those
in the Newtonian restricted three body problem.


title:
Explicit implementation strategy of high order edge finite elements and
  Schwarz preconditioning for the time-harmonic Maxwell's equations

abstract:
  In this paper we focus on high order finite element approximations of the
electric field combined with suitable preconditioners, to solve the
time-harmonic Maxwell's equations in waveguide configurations. The
implementation of high order curl-conforming finite elements is quite delicate,
especially in the three-dimensional case. Here, we explicitly describe an
implementation strategy, which has been embedded in the open source finite
element software FreeFem++ (http://www.freefem.org/ff++/). In particular, we
use the inverse of a generalized Vandermonde matrix to build a basis of
generators in duality with the degrees of freedom, resulting in an easy-to-use
but powerful interpolation operator. We carefully address the problem of
applying the same Vandermonde matrix to possibly differently oriented
tetrahedra of the mesh over the computational domain. We investigate the
preconditioning for Maxwell's equations in the time-harmonic regime, which is
an underdeveloped issue in the literature, particularly for high order
discretizations. In the numerical experiments, we study the effect of varying
several parameters on the spectrum of the matrix preconditioned with
overlapping Schwarz methods, both for 2d and 3d waveguide configurations.


title: Bures distance and transition probability for $\alpha$-CPD-kernels

abstract:
  If the symmetry (fixed invertible self adjoint map) of Krein spaces is
replaced by a fixed unitary, then we obtain the notion of S-spaces which was
introduced by Szafraniec. Assume $\alpha$ to be an automorphism on a
$C^*$-algebra. In this article, we obtain the Kolmogorov decomposition of
$\alpha$-completely positive definite (or $\alpha$-CPD-kernels for short) and
investigate the Bures distance between $\alpha$-CPD-kernels. We also define
transition probability for these kernels and find a characterization of the
transition probability.


title: On derived equivalence of general Clifford double mirrors

abstract:
  We show that general Clifford double mirrors constructed in "On Clifford
double mirrors of toric complete intersections" are derived equivalent.


title:
Interfacial Phase Competition Induced Kondo-like Effect in
  Manganite-insulator Composites

abstract:
  Kondo-like effect, namely the upturn of resistivity at low temperatures, has
been observed in perovskite manganite when nonmagnetic insulators were doped as
the secondary phase. In this paper, the low-temperature resistivity upturn
effect was argued to be originated from the interfacial magnetic phase
reconstruction. Heisenberg spin lattices have been simulated using Monte Carlo
method to reveal the phase competition around the secondary phase boundary,
namely the manganite-insulator boundary behaves a weak antiferromagnetic
tendency. And the resistor-network model based on the double-exchange
conductive mechanism indeed reproduces the low-temperature resistivity upturn
effect. Our work provide a reasonable physical mechanism to understand novel
transport behaviors in micro-structures of correlated electron systems.


title: Circle-valued Morse theory for frame spun knots and surface-links

abstract:
  Let N be a closed oriented k-dimensional submanifold of the (k+2)-dimensional
sphere; denote its complement by C(N). Denote by x the 1-dimensional cohomology
class in C(N), dual to N. The Morse-Novikov number of C(N) is by definition the
minimal possible number of critical points of a regular Morse map f from C(N)
to a circle, such that f belongs to x. In the first part of this paper we study
the case when N is the twist frame spun knot associated to an m-knot K. We
obtain a formula which relates the Morse-Novikov numbers of N and K and
generalizes the classical results of D. Roseman and E.C. Zeeman about
fibrations of spun knots. In the second part we apply the obtained results to
the computation of Morse-Novikov numbers of surface-links in 4-sphere.


title:
Advantages of EEG phase patterns for the detection of gait intention in
  healthy and stroke subjects

abstract:
  One use of EEG-based brain-computer interfaces (BCIs) in rehabilitation is
the detection of movement intention. In this paper we investigate for the first
time the instantaneous phase of movement related cortical potential (MRCP) and
its application to the detection of gait intention. We demonstrate the utility
of MRCP phase in two independent datasets, in which 10 healthy subjects and 9
chronic stroke patients executed a self-initiated gait task in three sessions.
Phase features were compared to more conventional amplitude and power features.
The neurophysiology analysis showed that phase features have higher
signal-to-noise ratio than the other features. Also, BCI detectors of gait
intention based on phase, amplitude, and their combination were evaluated under
three conditions: session specific calibration, intersession transfer, and
intersubject transfer. Results show that the phase based detector is the most
accurate for session specific calibration (movement intention was correctly
detected in 66.5% of trials in healthy subjects, and in 63.3% in stroke
patients). However, in intersession and intersubject transfer, the detector
that combines amplitude and phase features is the most accurate one and the
only that retains its accuracy (62.5% in healthy subjects and 59% in stroke
patients) w.r.t. session specific calibration. Thus, MRCP phase features
improve the detection of gait intention and could be used in practice to remove
time-consuming BCI recalibration.


title:
Fluctuations of the SNR at the output of the MVDR with Regularized Tyler
  Estimators

abstract:
  This paper analyzes the statistical properties of the signal-to-noise ratio
(SNR) at the output of the Capon's minimum variance distortionless response
(MVDR) beamformers when operating over impulsive noises. Particularly, we
consider the supervised case in which the receiver employs the regularized
Tyler estimator in order to estimate the covariance matrix of the
interference-plus-noise process using $n$ observations of size $N\times 1$. The
choice for the regularized Tylor estimator (RTE) is motivated by its resilience
to the presence of outliers and its regularization parameter that guarantees a
good conditioning of the covariance estimate. Of particular interest in this
paper is the derivation of the second order statistics of the SINR. To achieve
this goal, we consider two different approaches. The first one is based on
considering the classical regime, referred to as the $n$-large regime, in which
$N$ is assumed to be fixed while $n$ grows to infinity. The second approach is
built upon recent results developed within the framework of random matrix
theory and assumes that $N$ and $n$ grow large together. Numerical results are
provided in order to compare between the accuracies of each regime under
different settings.


title: A^1-connectedness in reductive algebraic groups

abstract:
  Using sheaves of A^1-connected components, we prove that the Morel-Voevodsky
singular construction on a reductive algebraic group fails to be A^1-local if
the group does not satisfy suitable isotropy hypotheses. As a consequence, we
show the failure of A^1-invariance of torsors for such groups on smooth affine
schemes over infinite perfect fields. We also characterize A^1-connected
reductive algebraic groups over a field of characteristic 0.


title:
Finite-key analysis of a practical decoy-state high-dimensional quantum
  key distribution

abstract:
  Compared with two-level quantum key distribution (QKD), highdimensional QKD
enable two distant parties to share a secret key at a higher rate. We provide a
finite-key security analysis for the recently proposed practical
highdimensional decoy-state QKD protocol based on time-energy entanglement. We
employ two methods to estimate the statistical fluctuation of the postselection
probability and give a tighter bound on the secure-key capacity. By numerical
evaluation, we show the finite-key effect on the secure-key capacity in
different conditions. Moreover, our approach could be used to optimize
parameters in practical implementations of highdimensional QKD.


title:
The Pila-Wilkie theorem for subanalytic families: a complex analytic
  approach

abstract:
  We present a complex analytic proof of the Pila-Wilkie theorem for
subanalytic sets. In particular, we replace the use of $C^r$-smooth
parametrizations by a variant of Weierstrass division.


title:
Hopsets with Constant Hopbound, and Applications to Approximate Shortest
  Paths

abstract:
  A $(\beta,\epsilon)$-hopset for a weighted undirected $n$-vertex graph
$G=(V,E)$ is a set of edges, whose addition to the graph guarantees that every
pair of vertices has a path between them that contains at most $\beta$ edges,
whose length is within $1+\epsilon$ of the shortest path. In her seminal paper,
Cohen \cite[JACM 2000]{C00} introduced the notion of hopsets in the context of
parallel computation of approximate shortest paths, and since then it has found
numerous applications in various other settings, such as dynamic graph
algorithms, distributed computing, and the streaming model.
  Cohen \cite{C00} devised efficient algorithms for constructing hopsets with
{\em polylogarithmic} in $n$ number of hops. Her constructions remain the
state-of-the--art since the publication of her paper in STOC'94, i.e., for more
than two decades.
  In this paper we exhibit the first construction of sparse hopsets with a {\em
constant number of hops}. We also find efficient algorithms for hopsets in
various computational settings, improving the best known constructions.
Generally, our hopsets strictly outperform the hopsets of \cite{C00}, both in
terms of their parameters, and in terms of the resources required to construct
them.
  We demonstrate the applicability of our results for the fundamental problem
of computing approximate shortest paths from $s$ sources. Our results improve
the running time for this problem in the parallel, distributed and streaming
models, for a vast range of $s$.


title: On the angular dependence of the photoemission time delay in helium

abstract:
  We investigate an angular dependence of the photoemission time delay in
helium as measured by the RABBITT (Reconstruction of Attosecond Beating By
Interference of Two-photon Transitions) technique. The measured time delay $
\tau_a=\tau_W+\tau_{cc} $ contains two distinct components: the Wigner time
delay $\tau_W$ and the continuum-continuum CC) correction $\tau_{cc}$. In the
case of helium with only one $1s\to Ep$ photoemission channel, the Wigner time
delay $\tau_W$ does not depend on the photoelectron detection angle relative to
the polarization vector. However, the CC correction $\tau_{cc}$ shows a
noticeable angular dependence. We illustrate these findings by performing two
sets of calculations. In the first set, we solve the time-dependent
Schr\"odinger equation for the helium atom ionized by an attosecond pulse train
and probed by an IR pulse. In the second approach, we employ the lowest order
perturbation theory which describes absorption of the XUV and IR photons. Both
calculations produce close results in a fair agreement with experiment.


title: Analytical Solutions for Beams Passing Apertures with Sharp Boundaries

abstract:
  An approximation is elaborated for the paraxial propagation of diffracted
beams, with both one- and two-dimensional cross sections, which are released
from apertures with sharp boundaries. The approximation applies to any beam
under the condition that the thickness of its edges is much smaller than any
other length scale in the beam's initial profile. The approximation can be
easily generalized for any beam whose initial profile has several sharp
features. Therefore, this method can be used as a tool to investigate the
diffraction of beams on complex obstacles. The analytical results are compared
to numerical solutions and experimental findings, which demonstrates high
accuracy of the approximation. For an initially uniform field confined by sharp
boundaries, this solution becomes exact for any propagation distance and any
sharpness of the edges. Thus, it can be used as an efficient tool to represent
the beams, produced by series of slits with a complex structure, by a simple
but exact analytical solution.


title:
Modelling and closed loop control of near-field acoustically levitated
  objects

abstract:
  The present paper introduces a novel approach for modelling the governing,
slow dynamics of near-field acoustically levitated objects. This model is
sufficiently simple and concise to enable designing a closed-loop controller,
capable of accurate vertical positioning of a carried object. The near-field
acoustic levitation phenomenon exploits the compressibility, the nonlinearity
and the viscosity of the gas trapped between a rapidly oscillating surface and
a freely suspended planar object, to elevate its time averaged pressure above
the ambient pressure. By these means, the vertical position of loads weighing
up to several kilograms can be varied between dozens and hundreds of
micrometers. The simplified model developed in this paper is a second order
ordinary differential equation where the height-dependent stiffness and damping
terms of the gas layer are derived explicitly. This simplified model replaces a
traditional model consisting of the equation of motion of the levitated object,
coupled to a nonlinear partial differential equation, accounting for the
behavior of the entrapped gas. Due to the relatively simple form of the model
developed here, it constitutes a convenient foundation for model based control
algorithms, governing the slow dynamics of near-field acoustically levitated
objects. Indeed, based on the former, a height dependent, gain scheduled PID
controller is developed and verified numerically and experimentally, both
providing satisfying results.


title: On stepwise regression

abstract:
  Given data $y$ and $k$ covariates $x$ one problem in linear regression is to
decide which in any of the covariates to include when regressing $y$ on the
$x$. If $k$ is small it is possible to evaluate each subset of the $x$. If
however $k$ is large then some other procedure must be use. Stepwise regression
and the lasso are two such procedures but they both assume a linear model with
error term. A different approach is taken here which does not assume a model. A
covariate is included if it is better than random noise. This defines a
procedure which is simple both conceptually and algorithmically


title: Propagation of Thermally Induced Magnonic Spin Currents

abstract:
  The propagation of magnons in temperature gradients is investigated within
the framework of an atomistic spin model with the stochastic
Landau-Lifshitz-Gilbert equation as underlying equation of motion. We analyze
the magnon accumulation, the magnon temperature profile as well as the
propagation length of the excited magnons. The frequency distribution of the
generated magnons is investigated in order to derive an expression for the
influence of the anisotropy and the damping parameter on the magnon propagation
length. For soft ferromagnetic insulators with low damping a propagation length
in the range of some $\mu$m can be expected for exchange driven magnons.


title: Searching for Sterile Neutrinos with MINOS

abstract:
  This document presents the latest results for a 3+1 sterile neutrino search
using the $10.56 \times 10^{20}$ protons-on-target data set taken from 2005 -
2012. By searching for oscillations driven by a large mass splitting, MINOS is
sensitive to the existence of sterile neutrinos through any energy dependent
deviations using a charged current sample, as well as looking at any relative
deficit between neutral current events between the far and near detectors. This
document will discuss the novel analysis that enabled a search for sterile
neutrinos setting a limit in the previously unexplored regions in the parameter
space $\{\Delta m^{2}_{41}, \sin^2\theta_{24}\}$. The results presented can be
compared to the parameter space suggested by LSND and MiniBooNE and complements
other previous experimental searches for sterile neutrinos in the electron
neutrino appearance channel.


title: Tests of CPT symmetry in B0-B0bar mixing and in B0 -> c cbar K0 decays

abstract:
  Using the eight time dependences for the decays Upsilon(4S)-> B0 B0bar -> fj
fk with the dacay into a flavor-specific state fj = ell+- X before or after the
decay into a CP eigenstate fk = c cbar KS,KL, as measured by the BABAR
experiment, we determine the three CPT-sensitive parameters Re(z) and Im(z) in
B0-B0bar mixing and |Abar/A| in B0 -> c cbar K0 decays. We find Im(z) = 0.010
+- 0.030 +- 0.013, Re(z) = -0.065 +- 0.028 +- 0.014, and |Abar/A| = 0.999 +-
0.023 +- 0.017, in agreement with CPT symmetry.


title:
Phase transitions for Quantum Markov Chains associated with Ising type
  models on a Cayley tree

abstract:
  The main aim of the present paper is to prove the existence of a phase
transition in quantum Markov chain (QMC) scheme for the Ising type models on a
Cayley tree. Note that this kind of models do not have one-dimensional
analogous, i.e. the considered model persists only on trees. In this paper, we
provide a more general construction of forward QMC. In that construction, a QMC
is defined as a weak limit of finite volume states with boundary conditions,
i.e. QMC depends on the boundary conditions. Our main result states the
existence of a phase transition for the Ising model with competing interactions
on a Cayley tree of order two. By the phase transition we mean the existence of
two distinct QMC which are not quasi-equivalent and their supports do not
overlap. We also study some algebraic property of the disordered phase of the
model, which is a new phenomena even in a classical setting.

categories: math-ph cond-mat.stat-mech math.FA math.MP math.OA quant-ph


title: From geometric optics to plants: eikonal equation for buckling

abstract:
  Optimal embedding in the three-dimensional space of exponentially growing
squeezed surfaces, like plants leaves, or 2D colonies of exponentially
reproducing cells, is considered in the framework of conformal approach. It is
shown that the boundary profile of a growing tissue is described by the 2D
eikonal equation, which provides the geometric optic approximation for the wave
front propagating in the media with inhomogeneous refraction coefficient. The
variety of optimal surfaces embedded in 3D is controlled by spatial dependence
of the refraction coefficient which, in turn, is dictated by the local growth
protocol.


title:
The minimal regular model of a Fermat curve of odd squarefree exponent
  and its dualizing sheaf

abstract:
  We construct the minimal regular model of the Fermat curve of odd squarefree
composite exponent $N$ over the $N$-th cyclotomic integers. As an application,
we compute upper and lower bounds for the arithmetic self-intersection of the
dualizing sheaf of this model.


title:
Derivation of Generalized Camassa-Holm Equations from Boussinesq-type
  Equations

abstract:
  In this paper we derive generalized forms of the Camassa-Holm (CH) equation
from a Boussinesq-type equation using a two-parameter asymptotic expansion
based on two small parameters characterizing nonlinear and dispersive effects
and strictly following the arguments in the asymptotic derivation of the
classical CH equation. The resulting equations generalize the CH equation in
two different ways. The first generalization replaces the quadratic
nonlinearity of the CH equation with a general power-type nonlinearity while
the second one replaces the dispersive terms of the CH equation with
fractional-type dispersive terms. In the absence of both higher-order
nonlinearities and fractional-type dispersive effects, the generalized
equations derived reduce to the classical CH equation that describes
unidirectional propagation of shallow water waves. The generalized equations
obtained are compared to similar equations available in the literature, and
this leads to the observation that the present equations have not appeared in
the literature.


title: Finite-size effects and percolation properties of Poisson geometries

abstract:
  Random tessellations of the space represent a class of prototype models of
heterogeneous media, which are central in several applications in physics,
engineering and life sciences. In this work, we investigate the statistical
properties of $d$-dimensional isotropic Poisson geometries by resorting to
Monte Carlo simulation, with special emphasis on the case $d=3$. We first
analyse the behaviour of the key features of these stochastic geometries as a
function of the dimension $d$ and the linear size $L$ of the domain. Then, we
consider the case of Poisson binary mixtures, where the polyhedra are assigned
two `labels' with complementary probabilities. For this latter class of random
geometries, we numerically characterize the percolation threshold, the strength
of the percolating cluster and the average cluster size.


title:
Cyclic Cohomology and Chern Connes pairing of some crossed product
  algebras

abstract:
  We compute the cyclic and Hochschild cohomology groups for the algebras
$\mathcal A_\theta^{alg} \rtimes \mathbb Z_3, \mathcal A_\theta^{alg} \rtimes
\mathbb Z_4$ and $\mathcal A_\theta^{alg} \rtimes \mathbb Z_6$. We also compute
the partial Chern-Connes index table for each of these algebras.


title:
Boundary modeling in model-based calibration for automotive engines via
  the vertex representation of the convex hulls

abstract:
  When using the convex hull approach in the boundary modeling process,
Model-Based Calibration (MBC) software suites -- such as Model-Based
Calibration Toolbox from MathWorks -- can be computationally intensive
depending on the amount of data modeled. The reason for this is that the
half-space representation of the convex hull is used. We discuss here another
representation of the convex hull, the vertex representation, which proves
capable to reduce the computational cost. Numerical comparisons in this article
are executed in MATLAB by using MBC Toolbox commands, and show that for certain
conditions, the vertex representation outperforms the half-space
representation.


title: A Proposal for Linguistic Similarity Datasets Based on Commonality Lists

abstract:
  Similarity is a core notion that is used in psychology and two branches of
linguistics: theoretical and computational. The similarity datasets that come
from the two fields differ in design: psychological datasets are focused around
a certain topic such as fruit names, while linguistic datasets contain words
from various categories. The later makes humans assign low similarity scores to
the words that have nothing in common and to the words that have contrast in
meaning, making similarity scores ambiguous. In this work we discuss the
similarity collection procedure for a multi-category dataset that avoids score
ambiguity and suggest changes to the evaluation procedure to reflect the
insights of psychological literature for word, phrase and sentence similarity.
We suggest to ask humans to provide a list of commonalities and differences
instead of numerical similarity scores and employ the structure of human
judgements beyond pairwise similarity for model evaluation. We believe that the
proposed approach will give rise to datasets that test meaning representation
models more thoroughly with respect to the human treatment of similarity.


title: Free fermions, W-algebras and isomonodromic deformations

abstract:
  We consider the theory of multicomponent free massless fermions in two
dimensions and use it for construction of representations of W-algebras at
integer Virasoro central charges. We define the vertex operators in this theory
in terms of solutions of the corresponding isomonodromy problem. We use this
construction to get some new insights on tau-functions of the multicomponent
Toda type hierarchies for the class of solutions, given by the isomonodromy
vertex operators and get useful representation for the tau-function of
isomonodromic deformations.


title: Generalized derivations of n-Hom Lie superalgebras

abstract:
  It is well known that n-Hom Lie superalgebras are certain generalizations of
n-Lie algebras. This paper is devoted to investigate the generalized
derivations of multiplicative n-Hom Lie superalgebras. We generalize the main
results of Leger and Luks to the case of multiplicative n-Hom Lie
superalgebras. Firstly, we review some concepts associated with a
multiplicative n-Hom Lie superalgebra $N$. Furthermore, we give the definitions
of the generalized derivations, quasiderivations, center derivations, centroids
and quasicentroids. Obviously, we have the following tower $ZDer(N)\subseteq
Der(N)\subseteq QDer(N)\subseteq GDer(N)\subseteq End(N)$. Later on, we give
some useful properties and connections between these derivations. Moreover, we
obtain that the quasiderivation of $N$ can be embedded as a derivation in a
larger multiplicative n-Hom Lie superalgebra. Finally, we conclude that the
derivation of the larger multiplicative n-Hom Lie superalgebra has a direct sum
decomposition when the center of $N$ is equal to zero.


title: Cohomology in singular blocks for a quantum group at a root of unity

abstract:
  Let $U_\zeta$ be a Lusztig quantum enveloping algebra associated to a complex
semisimple Lie algebra $\mathfrak g$ and a root of unity $\zeta$. When $L,L'$
are irreducible $U_\zeta$-modules having regular highest weights, the dimension
of $\operatorname{Ext}^n_{U_\zeta}(L,L')$ can be calculated in terms of the
coefficients of appropriate Kazhdan-Lusztig polynomials associated to the
affine Weyl group of $U_\zeta$. This paper shows for $L,L'$ irreducible modules
in a singular block that $\dim\operatorname{Ext}^n_{U_\zeta}(L,L')$ is
explicitly determined using the coefficients of parabolic Kazhdan-Lusztig
polynomials. This also computes the corresponding cohomology for $q$-Schur
algebras and many generalized $q$-Schur algebras. The result depends on a
certain parity vanishing property which we obtain from the Kazhdan-Lusztig
correspondence and a Koszul grading of Shan-Varagnolo-Vasserot for the
corresponding affine Lie algebra.


title: Social contagions on time-varying community networks

abstract:
  Time-varying community structures widely exist in various real-world
networks. However, the spreading dynamics on this kind of network has not been
fully studied. To this end, we systematically study the effects of time-varying
community structures on social contagions. We first propose a non-Markovian
social contagion model on time-varying community networks based on the activity
driven network model, in which an individual adopts a behavior if and only if
the accumulated behavioral information it has ever received reaches a
threshold. Then, we develop a mean-field theory to describe the proposed model.
From theoretical analyses and numerical simulations, we find that behavior
adoption in the social contagions exhibits a hierarchical feature, i.e., the
behavior first quickly spreads in one of the communities, and then outbreaks in
the other. Moreover, under different behavioral information transmission rates,
the final behavior adoption proportion in the whole network versus the
community strength shows one of the patterns, which are a monotone increasing
pattern, a non-monotonic changing pattern, and a monotone decreasing pattern.
An optimal community strength maximizing the final behavior adoption can be
found in a suitable range of behavioral information transmission rate. Finally,
for a given average degree, increasing the number of edges generated by active
nodes is more beneficial to the social contagions than increasing the average
activity potential.


title:
Multicomponent Gas-Particle Flow and Heat/Mass Transfer Induced by a
  Localized Laser Irradiation on a Urethane-Coated Stainless Steel Substrate

abstract:
  A three-dimensional numerical simulation is conducted for a complex process
in a laser-material system, which involves heat and mass transfer in a
compressible gaseous phase and chemical reaction during laser irradiation on a
urethane paint coated on a stainless steel substrate. A finite volume method
(FVM) with a co-located grid mesh that discretizes the entire computational
domain is employed to simulate the heating process. The results show that when
the top surface of the paint reaches a threshold temperature of 560 K, the
polyurethane starts to decompose through chemical reaction. As a result,
combustion products CO2, H2O and NO2 are produced and chromium (III) oxide,
which serves as pigment in the paint, is ejected as solid parcels from the
paint into the gaseous domain. Variations of temperature, density and velocity
at the center of the laser irradiation spot, and the concentrations of reaction
reactant/products in the gaseous phase are presented and discussed, by
comparing six scenarios with different laser powers ranging from 2.5 kW to 15
kW with an increment of 2.5 kW.


title: Bitcoin Beacon

abstract:
  We examine a protocol $\pi_{\text{beacon}}$ that outputs unpredictable and
publicly verifiable randomness, meaning that the output is unknown at the time
that $\pi_{\text{beacon}}$ starts, yet everyone can verify that the output is
close to uniform after $\pi_{\text{beacon}}$ terminates. We show that
$\pi_{\text{beacon}}$ can be instantiated via Bitcoin under sensible
assumptions; in particular we consider an adversary with an arbitrarily large
initial budget who may not operate at a loss indefinitely. In case the
adversary has an infinite budget, we provide an impossibility result that stems
from the similarity between the Bitcoin model and Santha-Vazirani sources. We
also give a hybrid protocol that combines trusted parties and a Bitcoin-based
beacon.


title:
Forecasting Long-Lived Lagrangian Vortices from their Objective Eulerian
  Footprints

abstract:
  We derive a non-dimensional metric to quantify the expected Lagrangian
persistence of objectively defined Eulerian vortices in two-dimensional
unsteady flows. This persistence metric is the averaged deviation of the
vorticity from its spatial mean over the Eulerian vortex, normalized by the
instantaneous material leakage from the Eulerian vortex. The metric offers a
model-independent and frame-independent tool for uncovering the instantaneous
Eulerian signature of long-lived Lagrangian vortices. Using satellite-derived
ocean velocity data, we show that Lagrangian vortex-persistence predictions by
our metric significantly outperform those inferred from other customary
Eulerian diagnostics, such as the potential vorticity gradient and the
Okubo-Weiss criterion.


title:
Solutions of First Order Linear Partial Differential Equations Related
  to Urn Models and Central Limit Theorems

abstract:
  We study first order linear partial differential equations that appear, for
example, in the analysis of dimishing urn models with the help of the method of
characteristics and formulate sufficient conditions for a central limit
theorem.


title: New Electrically Charged Black Hole in Higher Derivative Gravity

abstract:
  In this paper, new electrically charged asymptotically flat black hole
solutions are numerically derived in the context of higher derivative gravity.
These solutions can be interpreted as generalizations of two different classes
of non-charged asymptotically flat spacetimes: Schwarzschild and
non-Schwarzschild solutions. Extreme black hole solutions and black holes with
negative mass were found.


title: Group actions and scattering problems in Teichm\"uller theory

abstract:
  In recent years, Teichm\"uller theory, which is the study of moduli spaces of
marked Riemann surfaces, has come to be considered more and more from the point
of view of actions of surface groups inside certain semi-simple Lie groups. In
particular, we consider the case where the Lie groups in question have
symmetric spaces which are lorentzian spacetimes. Indeed, this can be
considered as the starting point of Mess' seminal work, which led to the
development of new and strikingly simpler proofs of many results of
Teichm\"uller theory by considering them in terms of geometric objects inside
these symmetric spaces. Our aim is to provide a brief and straightforward
introduction to this approach, whilst developing what we consider to be a
useful mental framework for organising known results and open problems.


title: Localization in inelastic rate dependent shearing deformations

abstract:
  Metals deformed at high strain rates can exhibit failure through formation of
shear bands, a phenomenon often attributed to Hadamard instability and
localization of the strain into an emerging coherent structure. We verify
formation of shear bands for a nonlinear model exhibiting strain softening and
strain rate sensitivity. The effects of strain softening and strain rate
sensitivity are first assessed by linearized analysis, indicating that the
combined effect leads to Turing instability. For the nonlinear model a class of
self-similar solutions is constructed, that depicts a coherent localizing
structure and the formation of a shear band. This solution is associated to a
heteroclinic orbit of a dynamical system. The orbit is constructed numerically
and yields explicit shear localizing solutions.


title: Hierarchical Models for Independence Structures of Networks

abstract:
  We introduce a new family of network models, called hierarchical network
models, that allow us to represent in an explicit manner the stochastic
dependence among the dyads (random ties) of the network. In particular, each
member of this family can be associated with a graphical model defining
conditional independence clauses among the dyads of the network, called the
dependency graph. Every network model with dyadic independence assumption can
be generalized to construct members of this new family. Using this new
framework, we generalize the Erd\"os-R\'enyi and beta-models to create
hierarchical Erd\"os-R\'enyi and beta-models. We describe various methods for
parameter estimation as well as simulation studies for models with sparse
dependency graphs.


title: Realisation of Qudits in Coupled Potential Wells

abstract:
  Quantum computation strongly relies on the realisation, manipulation and
control of qubits. A central method for realizing qubits is by creating a
double-well potential system with a significant gap between the first two
eigenvalues and the rest. In this work we first revisit the theoretical grounds
underlying the double-well qubit dynamics, then proceed to suggest novel
extensions of these principles to a triple-well qutrit with periodic boundary
conditions, followed by a general d-well analysis of qudits. These analyses are
based on representations of the special unitary groups SU(d) which expose the
systems' symmetry and employ them for performing computations. We conclude with
a few notes on coherence and scalability of d-well systems.


title:
Chiral Magnetic Effect due to Inhomogeneous Magnetic Fields in
  Noncentrosymmetric Weyl Semimetals

abstract:
  The chiral magnetic effect is a phenomenon where an electromagnetic current
is generated along a magnetic field. Recently, in nonequilibrium systems,
negative longitudinal magnetoresistance has been observed experimentally in
Dirac/Weyl semimetals, which provides evidence for the chiral magnetic effect
as a nonequilibrium current. On the other hand, the emergence of the chiral
magnetic effect as an equilibrium current is still controversial. We propose a
possible realization of the chiral magnetic effect as an equilibrium current
using inhomogeneous magnetic fields. By employing tight-binding calculations
and linear response theory, we demonstrate that a finite current density is
generated by inhomogeneous magnetic fields, while the spatial integration of
the current is equal to zero, which is consistent with the so-called "no-go
theorem" of the chiral magnetic effect in real lattice systems. Moreover, we
propose an experimental setup to detect the effect in Weyl semimetal materials.


title:
The bellows conjecture for small flexible polyhedra in non-Euclidean
  spaces

abstract:
  The bellows conjecture claims that the volume of any flexible polyhedron of
dimension 3 or higher is constant during the flexion. The bellows conjecture
was proved for flexible polyhedra in the Euclidean spaces of dimensions 3 and
higher, and for bounded flexible polyhedra in the odd-dimensional Lobachevsky
spaces. Counterexamples to the bellows conjecture are known in all open
hemispheres of dimensions 3 and higher. The aim of this paper is to prove that,
nonetheless, the bellows conjecture is true for all flexible polyhedra in
either spheres or Lobachevsky spaces of dimensions greater than or equal to 3
with sufficiently small edge lengths.


title: Syntactically Guided Neural Machine Translation

abstract:
  We investigate the use of hierarchical phrase-based SMT lattices in
end-to-end neural machine translation (NMT). Weight pushing transforms the
Hiero scores for complete translation hypotheses, with the full translation
grammar score and full n-gram language model score, into posteriors compatible
with NMT predictive probabilities. With a slightly modified NMT beam-search
decoder we find gains over both Hiero and NMT decoding alone, with practical
advantages in extending NMT to very large input and output vocabularies.


title:
Real-time dynamics of lattice gauge theories with a few-qubit quantum
  computer

abstract:
  Gauge theories are fundamental to our understanding of interactions between
the elementary constituents of matter as mediated by gauge bosons. However,
computing the real-time dynamics in gauge theories is a notorious challenge for
classical computational methods. In the spirit of Feynman's vision of a quantum
simulator, this has recently stimulated theoretical effort to devise schemes
for simulating such theories on engineered quantum-mechanical devices, with the
difficulty that gauge invariance and the associated local conservation laws
(Gauss laws) need to be implemented. Here we report the first experimental
demonstration of a digital quantum simulation of a lattice gauge theory, by
realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a
few-qubit trapped-ion quantum computer. We are interested in the real-time
evolution of the Schwinger mechanism, describing the instability of the bare
vacuum due to quantum fluctuations, which manifests itself in the spontaneous
creation of electron-positron pairs. To make efficient use of our quantum
resources, we map the original problem to a spin model by eliminating the gauge
fields in favour of exotic long-range interactions, which have a direct and
efficient implementation on an ion trap architecture. We explore the Schwinger
mechanism of particle-antiparticle generation by monitoring the mass production
and the vacuum persistence amplitude. Moreover, we track the real-time
evolution of entanglement in the system, which illustrates how particle
creation and entanglement generation are directly related. Our work represents
a first step towards quantum simulating high-energy theories with atomic
physics experiments, the long-term vision being the extension to real-time
quantum simulations of non-Abelian lattice gauge theories.


title: Cosmological Constant, Fine Structure Constant and Beyond

abstract:
  In the present work, we consider the cosmological constant model
$\Lambda\propto\alpha^{-6}$, which is well motivated from three independent
approaches. As is well known, the hint of varying fine structure constant
$\alpha$ was found in 1998. If $\Lambda\propto\alpha^{-6}$ is right, it means
that the cosmological constant $\Lambda$ should also be varying. Here, we try
to develop a suitable framework to model this varying cosmological constant
$\Lambda\propto\alpha^{-6}$, in which we view it from an interacting vacuum
energy perspective. Then, we consider the observational constraints on these
models by using the 293 $\Delta\alpha/\alpha$ data from the absorption systems
in the spectra of distant quasars. We find that the model parameters can be
tightly constrained to the very narrow ranges of ${\cal O}(10^{-5})$ typically.
On the other hand, we can also view the varying cosmological constant model
$\Lambda\propto\alpha^{-6}$ from another perspective, namely it can be
equivalent to a model containing "dark energy" and "warm dark matter", but
there is no interaction between them. We find that this is also fully
consistent with the observational constraints on warm dark matter.


title:
Geodesic rays in the uniform infinite half-planar quadrangulation return
  to the boundary

abstract:
  We show that all geodesic rays in the uniform infinite half-planar
quadrangulation (UIHPQ) intersect the boundary infinitely many times, answering
thereby a recent question of Curien. However, the possible intersection points
are sparsely distributed along the boundary. As an intermediate step, we show
that geodesic rays in the UIHPQ are proper, a fact that was recently
established by Caraceni and Curien (2015) by a reasoning different from ours.
Finally, we argue that geodesic rays in the uniform infinite half-planar
triangulation behave in a very similar manner, even in a strong quantitative
sense.


title: Relativistic equations for the generalized Chapman-Enskog hierarchy

abstract:
  From the Boltzmann equation Chapman and Cowling have firstly motivated a
hierarchy of differential equations. I consider a general version of these
differential equations which contain the Navier-Stokes system. In the paper I
derive a relativistic version of these partial differential equations. This is
interesting because in the derivation a covariant version of a time direction
is used. This time direction is needed to derive a reduction of the
differential equations.


title: Predicting Pediatric Surgical Durations

abstract:
  Effective management of operating room resources relies on accurate
predictions of surgical case durations. This prediction problem is known to be
particularly difficult in pediatric hospitals due to the extreme variation in
pediatric patient populations. We propose a novel metric for measuring accuracy
of predictions which captures key issues relevant to hospital operations. With
this metric in mind we propose several tree-based prediction models. Some are
automated (they do not require input from surgeons) while others are
semi-automated (they do require input from surgeons). We see that many of our
automated methods generally outperform currently used algorithms and even
achieve the same performance as surgeons. Our semi-automated methods can
outperform surgeons by a significant margin. We gain insights into the
predictive value of different features and suggest avenues of future work.


title:
Relating Domination, Exponential Domination, and Porous Exponential
  Domination

abstract:
  The domination number $\gamma(G)$ of a graph $G$, its exponential domination
number $\gamma_e(G)$, and its porous exponential domination number
$\gamma_e^*(G)$ satisfy $\gamma_e^*(G)\leq \gamma_e(G)\leq \gamma(G)$. We
contribute results about the gaps in these inequalities as well as the graphs
for which some of the inequalities hold with equality. Relaxing the natural
integer linear program whose optimum value is $\gamma_e^*(G)$, we are led to
the definition of the fractional porous exponential domination number
$\gamma_{e,f}^*(G)$ of a graph $G$. For a subcubic tree $T$ of order $n$, we
show $\gamma_{e,f}^*(T)=\frac{n+2}{6}$ and $\gamma_e(T)\leq
2\gamma_{e,f}^*(T)$. We characterize the two classes of subcubic trees $T$ with
$\gamma_e(T)=\gamma_{e,f}^*(T)$ and $\gamma(T)=\gamma_e(T)$, respectively.
Using linear programming arguments, we establish several lower bounds on the
fractional porous exponential domination number in more general settings.


title: Why is Deep Random suitable for cryptology

abstract:
  We present a new form of randomness, called Deep Randomness, generated in
such a way that probability distribution of the output signal is made
unknowledgeable for an observer. By limiting, thanks to Deep Randomness, the
capacity of the opponent observer to perform bayesian inference over public
information to estimate private information, we can design protocols, beyond
Shannon limit, enabling two legitimate partners, sharing originally no common
private information, to exchange secret information with accuracy as close as
desired from perfection, and knowledge as close as desired from zero by any
unlimitedly powered opponent. We discuss the theoretical foundation of Deep
Randomness, which lies on Prior Probability theory, introduced and developped
by authors like Laplace, Cox, Carnap, Jefferys and Jaynes ; and we introduce
computational method to generate such Deep Randomness.
  V2: we add a commented example of Perfact Secrecy Protocol based on Deep
Random assumption
  V3: we provide a major update of the article. The logic foundation of Deep
Random assumption is highly strengthened by avoiding the inconsistency attached
to rare events. Such inconsistency could lead to security flaws in previous
proposition. At the same time, several variants of the protocol are commented
with improved performances.
  V4: we correct an error due to lack of symmetry in the example of protocol
given in annex. We also make some writing improvements in perspective of
conference publication.
  V5: we introduce parallel with former article from Maurer presenting a model
of Perfect security based on partially independent channels.


title: New assessment on the nonlocality of correlation boxes

abstract:
  Correlation boxes are hypothetical systems capable of producing the maximal
algebraic violation of Bell inequalities, beyond the quantum bound and without
superluminal signaling. The fact that these systems show stronger correlations
than those presented by maximally entangled quantum states has been regarded as
a demonstration that the former are more nonlocal than the latter. By employing
an alternative, consistent measure of nonlocality, we show that this conclusion
is not necessarily true. In addition, we find a class of correlation boxes that
are less nonlocal than the quantum singlet with respect to the
Clauser-Horne-Shimony-Holt inequality, being, at the same time, more nonlocal
with respect to the 3322 inequality.


title:
Monotonicity formulas for static metrics with non-zero cosmological
  constant

abstract:
  In this paper we study non-singular vacuum static space-times with non-zero
cosmological constant. We introduce new integral quantities, and under suitable
assumptions we prove their monotonicity along the level set flow of the static
potential. We then show how to use these properties to derive a number of sharp
geometric and analytic inequalities, whose equality case can be used to
characterize the rotational symmetry of the underlying static solutions. As a
consequence, we are able to prove some new uniqueness statements for the de
Sitter and the anti-de Sitter metrics. In particular, we show that the de
Sitter solution has the least possible surface gravity among three-dimensional
static metrics with connected boundary and positive cosmological constant.


title:
Communicating One Bit over a Delay Constrained Gaussian MIMO Channel
  with Feedback

abstract:
  The energy-optimal scheme is found for communicating one bit over a
memoryless Gaussian channel with an ideal feedback channel. It is assumed that
the channel is allowed to be used at most N times before decoding. The optimal
coding/decoding strategy is derived by dynamic programming. It is found that
feedback gives a significant performance gain and that the optimal strategies
are discontinuous. It is also shown that most of the performance increase can
be obtained even with a one-bit feedback channel. The optimal scheme is
compared with the strategy by Kailath-Schalkwijk and is found to be
significantly more effective. For the case of a diagonal MIMO channel where
measurement noise variances are equal along the sub channels we also show that
the problem can be reduced to the previous case of transmitting one bit over a
scalar feedback channel.


title:
TwinCG: Dual Thread Redundancy with Forward Recovery for Conjugate
  Gradient Methods

abstract:
  Even though iterative solvers like the Conjugate Gradients method (CG) have
been studied for over fifty years, fault tolerance for such solvers has seen
much attention in recent years. For iterative solvers, two major reliable
strategies of recovery exist: checkpoint-restart for backward recovery, or some
type of redundancy technique for forward recovery. Important redundancy
techniques like ABFT techniques for sparse matrix-vector products (SpMxV) have
recently been proposed, which increase the resilience of CG methods. These
techniques offer limited recovery options, and introduce a tolerable overhead.
In this work, we study a more powerful resilience concept, which is redundant
multithreading. It offers more generic and stronger recovery guarantees,
including any soft faults in CG iterations (among others covering ABFT SpMxV),
but also requires more resources. We carefully study this redundancy/efficiency
conflict. We propose a fault tolerant CG method, called TwinCG, which
introduces minimal wallclock time overhead, and significant advantages in
detection and correction strategies. Our method uses Dual Modular Redundancy
instead of the more expensive Triple Modular Redundancy; still, it retains the
TMR advantages of fault correction. We describe, implement, and benchmark our
iterative solver, and compare it in terms of efficiency and fault tolerance
capabilities to state-of-the-art techniques. We find that before
parallelization, TwinCG introduces around 5-6% runtime overhead compared to
standard CG, and after parallelization efficiently uses BLAS. In the presence
of faults, it reliably performs forward recovery for a range of problems,
outperforming SpMxV ABFT solutions.


title:
A remainder term for H\"older's inequality for matrices and quantum
  entropy inequalities

abstract:
  We prove a sharp remainder term for H\"older's inequality for traces as a
consequence of the uniform convexity properties of the Schatten trace norms. We
then show how this implies a novel family of Pinsker type bounds for the
quantum Renyi entropy. Finally, we show how the sharp form of the usual quantum
Pinsker inequality for relative entropy may be obtained as a fairly direct
consequence of uniform convexity.


title:
A Foray into Efficient Mapping of Algorithms to Hardware Platforms on
  Heterogeneous Systems

abstract:
  Heterogeneous computing can potentially offer significant performance and
performance per watt improvements over homogeneous computing, but the question
"what is the ideal mapping of algorithms to architectures?" remains an open
one. In the past couple of years new types of computing devices such as FPGAs
have come into general computing use. In this work we attempt to add to the
body of scientific knowledge by comparing Kernel performance and performance
per watt of seven key algorithms according to Berkley's dwarf taxonomy. We do
so using the Rodinia benchmark suite on three different high-end hardware
architecture representatives from the CPU, GPU and FPGA families. We find
results that support some distinct mappings between the architecture and
performance per watt. Perhaps the most interesting finding is that, for our
specific hardware representatives, FPGAs should be considered as alternatives
to GPUs and CPUs in several key algorithms: N-body simulations, dense linear
algebra and structured grid.


title: Quantum key distribution over multicore fiber

abstract:
  We present the first quantum key distribution (QKD) experiment over multicore
fiber. With space division multiplexing, we demonstrate that weak QKD signals
can coexist with classical data signals launched at full power in a 53 km
7-core fiber, while showing negligible degradation in performance. Based on a
characterization of intercore crosstalk, we perform additional simulations
highlighting that classical data bandwidths beyond 1Tb/s can be supported with
high speed QKD on the same fiber.


title:
On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent
  Premiums

abstract:
  This paper concerns the dual risk model, dual to the risk model for insurance
applications, where premiums are surplus-dependent. In such a model premiums
are regarded as costs, while claims refer to profits. We calculate the mean of
the cumulative discounted dividends paid until ruin, if the barrier strategy is
applied. We formulate associated Hamilton-Jacobi-Bellman equation and identify
sufficient conditions for a barrier strategy to be optimal. Some numerical
examples are provided when profits have exponential law.


title: Small subgraphs in the trace of a random walk

abstract:
  We consider the combinatorial properties of the trace of a random walk on the
complete graph and on the random graph $G(n,p)$. In particular, we study the
appearance of a fixed subgraph in the trace. We prove that for a subgraph
containing a cycle, the threshold for its appearance in the trace of a random
walk of length $m$ is essentially equal to the threshold for its appearance in
the random graph drawn from $G(n,m)$. In the case where the base graph is the
complete graph, we show that a fixed forest appears in the trace typically much
earlier than it appears in $G(n,m)$.


title: Circumplanetary disk or circumplanetary envelope?

abstract:
  We present three-dimensional simulations with nested meshes of the dynamics
of the gas around a Jupiter mass planet with the JUPITER and FARGOCA codes. We
implemented a radiative transfer module into the JUPITER code to account for
realistic heating and cooling of the gas. We focus on the circumplanetary gas
flow, determining its characteristics at very high resolution ($80\%$ of
Jupiter's diameter). In our nominal simulation where the temperature evolves
freely by the radiative module and reaches 13000 K at the planet, a
circumplanetary envelope was formed filling the entire Roche-lobe. Because of
our equation of state is simplified and probably overestimates the temperature,
we also performed simulations with limited maximal temperatures in the planet
region (1000 K, 1500 K, and 2000 K). In these fixed temperature cases
circumplanetary disks (CPDs) were formed. This suggests that the capability to
form a circumplanetary disk is not simply linked to the mass of the planet and
its ability to open a gap. Instead, the gas temperature at the planet's
location, which depends on its accretion history, plays also fundamental role.
The CPDs in the simulations are hot and cooling very slowly, they have very
steep temperature and density profiles, and are strongly sub-Keplerian.
Moreover, the CPDs are fed by a strong vertical influx, which shocks on the CPD
surfaces creating a hot and luminous shock-front. In contrast, the pressure
supported circumplanetary envelope is characterized by internal convection and
almost stalled rotation.


title: Exceptional cosmetic surgeries on homology spheres

abstract:
  The cosmetic surgery conjecture is a longstanding conjecture in 3-manifold
theory. We present a theorem about exceptional cosmetic surgery for homology
spheres. Along the way we prove that if the surgery is not a small seifert
$\mathbb{Z}/2\mathbb{Z}$-homology sphere or a toroidal irreducible non-Seifert
surgery then there is at most one pair of exceptional truly cosmetic slope. We
also prove that toroidal truly cosmetic surgeries on integer homology spheres
must be integer homology spheres.


title:
Comment on "On the unphysical solutions of the Kadanoff--Baym equations
  in linear response: Correlation-induced homogeneous density-distribution and
  attractors"

abstract:
  In a recent Rapid Communication [A. Stan, Phys. Rev. B \textbf{93}, 041103(R)
(2016)], the reliability of the Keldysh--Kadanoff--Baym equations (KBE) using
correlated selfenergy approximations applied to linear and nonlinear response
has been questioned. In particular, the existence of a universal attractor has
been predicted that would drive the dynamics of any correlated system towards
an unphysical homogeneous density distribution regardless of the system type,
the interaction and the many-body approximation. Moreover, it was conjectured
that even the mean-field dynamics would be damped. Here, by performing accurate
solutions of the KBE for situations studied in that paper, we prove these
claims wrong being caused by numerical inaccuracies.


title:
Nonlocal correlations in the vicinity of the $\alpha$-$\gamma$ phase
  transition in iron within a DMFT plus spin-fermion model approach

abstract:
  We consider nonlocal correlations in iron in the vicinity of the
$\alpha$-$\gamma$ phase transition within the spin-rotationally-invariant
dynamical mean-field theory (DMFT) approach, combined with the recently
proposed spin-fermion model of iron. The obtained nonlocal corrections to DMFT
yield a decrease of the Curie temperature of the $\alpha$ phase, leading to an
agreement with its experimental value. We show that the corresponding nonlocal
corrections to the energy of the $\alpha$ phase are crucially important to
obtain the proximity of energies of $\alpha$ and $\gamma$ phases in the
vicinity of the iron $\alpha$-$\gamma$ transformation.


title: Mod 3 Chern classes and generators

abstract:
  We show the non-triviality of the mod 3 Chern class of degree 324 of the
adjoint representation of the exceptional Lie group E_8.


title:
Ordinary Differential Equation Methods For Markov Decision Processes and
  Application to Kullback-Leibler Control Cost

abstract:
  A new approach to computation of optimal policies for MDP (Markov decision
process) models is introduced. The main idea is to solve not one, but an entire
family of MDPs, parameterized by a weighting factor $\zeta$ that appears in the
one-step reward function. For an MDP with $d$ states, the family of value
functions $\{ h^*_\zeta : \zeta\in\Re\}$ is the solution to an ODE, $$
\frac{d}{d\zeta} h^*_\zeta = {\cal V}(h^*_\zeta) $$ where the vector field
${\cal V}\colon\Re^d\to\Re^d$ has a simple form, based on a matrix inverse.
  This general methodology is applied to a family of average-cost optimal
control models in which the one-step reward function is defined by
Kullback-Leibler divergence. The motivation for this reward function in prior
work is computation: The solution to the MDP can be expressed in terms of the
Perron-Frobenius eigenvector for an associated positive matrix. The drawback
with this approach is that no hard constraints on the control are permitted. It
is shown here that it is possible to extend this framework to model randomness
from nature that cannot be modified by the controller. Perron-Frobenius theory
is no longer applicable -- the resulting dynamic programming equations appear
as complex as a completely unstructured MDP model. Despite this apparent
complexity, it is shown that this class of MDPs admits a solution via this new
ODE technique. This approach is new and practical even for the simpler problem
in which randomness from nature is absent.


title:
Constructing an Element of a Banach Space with Given Deviation from its
  Nested Subspaces

abstract:
  This paper contains two improvements on a theorem of S. N. Bernstein for
Banach spaces. We show that if $X$ is an arbitrary infinite-dimensional Banach
space, $\{Y_n\}$ is a sequence of strictly nested subspaces of $ X$ and if
$\{d_n\}$ is a non-increasing sequence of non-negative numbers tending to 0,
then for any $c\in(0,1]$ we can find $x_{c} \in X$, such that the distance
$\rho(x_{c}, Y_n)$ from $x_{c}$ to $Y_n$ satisfies $$ c d_n \leq
\rho(x_{c},Y_n) \leq 4c d_n,~\mbox{for all $n\in\mathbb N$}. $$ We prove the
above inequality by first improving Borodin (2006)'s result for Banach spaces
by weakening his condition on the sequence $\{d_n\}$. The weakened condition on
$d_n$ requires refinement of Borodin's construction to extract an element in
$X$, whose distances from the nested subspaces are precisely the given values
$d_n$.


title:
An explicit relaxation filtering framework based upon Perona-Malik
  anisotropic diffusion for shock capturing and subgrid scale modeling of
  Burgers turbulence

abstract:
  In this paper, we introduce a relaxation filtering closure approach to
account for subgrid scale effects in explicitly filtered large eddy simulations
using the concept of anisotropic diffusion. We utilize the Perona-Malik
diffusion model and demonstrate its shock capturing ability and spectral
performance for solving the Burgers turbulence problem, which is a simplified
prototype for more realistic turbulent flows showing the same quadratic
nonlinearity. Our numerical assessments present the behavior of various
diffusivity functions in conjunction with a detailed sensitivity analysis with
respect to the free modeling parameters. In comparison to direct numerical
simulation (DNS) and under-resolved DNS results, we find that the proposed
closure model is efficient in the prevention of energy accumulation at grid
cut-off and is also adept at preventing any possible spurious numerical
oscillations due to shock formation under the optimal parameter choices. In
contrast to other relaxation filtering approaches, it is also shown that a
larger inertial range can be obtained by the proposed anisotropic diffusion
model using a compact stencil scheme in an efficient way.


title: A directly phase-modulated light source

abstract:
  The art of imparting information onto a light wave by optical signal
modulation is fundamental to all forms of optical communication. Among many
schemes, direct modulation of laser diodes stands out as a simple, robust, and
cost effective method. However, the simultaneous changes in intensity,
frequency and phase are a drawback which has prevented its application in the
field of secure quantum communication. Here, we propose and experimentally
demonstrate a directly phase-modulated light source which overcomes the main
disadvantages associated with direct modulation and is suitable for diverse
applications such as coherent communications and quantum cryptography. The
source separates the tasks of phase preparation and pulse generation between a
pair of semiconductor lasers leading to very pure phase states. Moreover, the
cavity enhanced electro-optic effect enables the first example of sub-volt
halfwave phase modulation at high signal rates. The source is compact, stable
and versatile, and we show its potential to become the standard transmitter for
future quantum communication networks.


title: Quantum Tunneling from the Charged Non-Rotating BTZ Black Hole with GUP

abstract:
  In the present paper, the quantum corrections to the temperature, entropy and
specific heat capacity of the charged non-rotating BTZ black hole are studied
by generalized uncertainty principle in tunneling formalism. It is shown that
quantum corrected entropy would be of the form of predicted entropy in quantum
gravity theories like string theory and loop quantum gravity.


title:
Modelling a network where the opinion of each unit varies according to a
  majority ruling of its neighbouring units

abstract:
  The complexity of human behaviour can lead to very unpredictable patterns in
social activity and structure. Here we demonstrate the instability of a
community network controlled by majority ruling, where an element adopts the
most popular opinion of their peers. We modelled a community as a square
lattice, and performed sequential time step numerical calculations upon each
cell in parallel. Depending on the initial ratio of two opinions, the community
can segregate either into separate gangs and cliques, or get dominated by a
single opinion. We also note that gangs are separated by neutral or confused
groups of individuals, buffering the transition. The behaviors shown by this
model can be comfortably applied to many other real life situations, such as
neural or ecological networks. The results of this paper have been preliminary
published in the Ref. [34].


title: Small sumsets in real line : a continuous 3k-4 theorem

abstract:
  We prove a continuous Freiman's $3k-4$ theorem for small sumsets in
$\mathbb{R}$ by using some ideas from Ruzsa's work on measure of sumsets in
$\mathbb{R}$ as well as some graphic representation of density functions of
sets. We thereby get some structural properties of $A$, $B$ and $A+B$ when
$\lambda(A+B)<\lambda(A)+\lambda(B)+\min(\lambda(A),\lambda(B))$. We also give
some structural information for sets of large density with small sumset and
characterize the extremal sets for which equality holds in the lower bounds for
$\lambda(A+B)$.


title:
Constrained Linear Representability of Polymatroids and Algorithms for
  Computing Achievability Proofs in Network Coding

abstract:
  The constrained linear representability problem (CLRP) for polymatroids
determines whether there exists a polymatroid that is linear over a specified
field while satisfying a collection of constraints on the rank function. Using
a computer to test whether a certain rate vector is achievable with vector
linear network codes for a multi-source network coding instance and whether
there exists a multi-linear secret sharing scheme achieving a specified
information ratio for a given secret sharing instance are shown to be special
cases of CLRP. Methods for solving CLRP built from group theoretic techniques
for combinatorial generation are developed and described. These techniques form
the core of an information theoretic achievability prover, an implementation
accompanies the article, and several computational experiments with interesting
instances of network coding and secret sharing demonstrating the utility of the
method are provided.


title: Modified teleparallel gravity with higher-derivative torsion terms

abstract:
  We construct $F(T,\left(\nabla{T}\right)^2,\Box {T})$ gravitational
modifications, which are novel classes of modified theories arising from
higher-derivative torsional terms in the action, and are different than their
curvature analogue. Applying them in a cosmological framework we obtain an
effective dark energy sector that comprises of the novel torsional
contributions. We perform a detailed dynamical analysis for two specific
examples, extracting the stable late-time solutions and calculating the
corresponding observables. We show that the thermal history of the universe can
be reproduced, and it can result in a dark-energy dominated, accelerating
universe, where the dark-energy equation-of-state parameter lies in the
quintessence regime, or may exhibit the phantom-divide crossing during the
cosmological evolution. Finally, the scale factor behaves asymptotically either
as a power-law or as an exponential, in agreement with observations.