title: Saliency Integration: An Arbitrator Model

abstract:
  Saliency integration has attracted much attention on unifying saliency maps
from multiple saliency models. Previous offline integration methods usually
face two challenges: 1. if most of the candidate saliency models misjudge the
saliency on an image, the integration result will lean heavily on those
inferior candidate models; 2. an unawareness of the ground truth saliency
labels brings difficulty in estimating the expertise of each candidate model.
To address these problems, in this paper, we propose an arbitrator model (AM)
for saliency integration. Firstly, we incorporate the consensus of multiple
saliency models and the external knowledge into a reference map to effectively
rectify the misleading by candidate models. Secondly, our quest for ways of
estimating the expertise of the saliency models without ground truth labels
gives rise to two distinct online model-expertise estimation methods. Finally,
we derive a Bayesian integration framework to reconcile the saliency models of
varying expertise and the reference map. To extensively evaluate the proposed
AM model, we test twenty-seven state-of-the-art saliency models, covering both
traditional and deep learning ones, on various combinations over four datasets.
The evaluation results show that the AM model improves the performance
substantially compared to the existing state-of-the-art integration methods,
regardless of the chosen candidate saliency models.


title: Distributed Scheduling of Event Analytics across Edge and Cloud

abstract:
  Internet of Things (IoT) domains generate large volumes of high velocity
event streams from sensors, which need to be analyzed with low latency to drive
decisions. Complex Event Processing (CEP) is a Big Data technique to enable
such analytics, and is traditionally performed on Cloud Virtual Machines (VM).
Leveraging captive IoT edge resources in combination with Cloud VMs can offer
better performance, flexibility and monetary costs for CEP. Here, we formulate
an optimization problem for energy-aware placement of CEP queries, composed as
an analytics dataflow, across a collection of edge and Cloud resources, with
the goal of minimizing the end-to-end latency for the dataflow. We propose a
Genetic Algorithm (GA) meta-heuristic to solve this problem, and compare it
against a brute-force optimal algorithm (BF). We perform detailed real-world
benchmarks on the compute, network and energy capacity of edge and Cloud
resources. These results are used to define a realistic and comprehensive
simulation study that validates the BF and GA solutions for 45 diverse CEP
dataflows, LAN and WAN setup, and different edge resource availability. We
compare the GA and BF solutions against random and Cloud-only baselines for
different configurations, for a total of 1764 simulation runs. Our study shows
that GA is within 97% of the optimal BF solution that takes hours, maps
dataflows with 4 - 50 queries in 1 - 26 secs, and only fails to offer a
feasible solution <= 20% of the time.


title: News from strong interactions program of the NA61/SHINE experiment

abstract:
  The NA61/SHINE experiment aims to discover the critical point of strongly
interacting matter and study the properties of the onset of deconfinement. This
is performed by a two dimensional phase diagram ($T-\mu_B$) scan of
measurements of particle spectra and fluctuations in proton-proton,
proton-nucleus and nucleus-nucleus interactions as a function of collision
energy and system size.
  In this contribution new NA61/SHINE results on negative pion production, as
well as transverse momentum and multiplicity fluctuations in Ar+Sc collisions
are presented. Moreover, the latest results on higher order moments of
net-charge multiplicity distribution in p+p collisions are also discussed. The
Ar+Sc results are compared to NA61 p+p and Be+Be data, as well as to NA49 $A+A$
results.


title:
Essential Spectrum of the Weighted Laplacian on Noncompact Manifolds and
  Applications

abstract:
  We obtain upper estimates for the bottom (that is, greatest lower bound) of
the essential spectrum of weighted Laplacian operator of a weighted manifold
under assumptions of the volume growth of their geodesic balls and spheres.
Furthermore, we find examples where the equality occurs in the estimates
obtained. As a consequence, we give estimates for the weighted mean curvature
of complete noncompact hypersurfaces into weighted manifolds.


title: Dividing goods or bads under additive utilities

abstract:
  We compare the Egalitarian Equivalent and the Competitive Equilibrium with
Equal Incomes rules to divide a bundle of goods (heirlooms) or a bundle of bads
(chores).
  For goods the Competitive division fares better, as it is Resource Monotonic,
and makes it harder to strategically misreport preferences. But for bads, the
Competitive rule, unlike the Egalitarian one, is multivalued, harder to
compute, and admits no continuous selection.
  We also provide an axiomatic characterization of the Competitive rule based
on the simple formulation of Maskin Monotonicity under additive utilities.


title: A repulsive force in the Einstein theory

abstract:
  The Laser Interferometer Gravitational-Wave Observatory (LIGO) detection of
gravitational waves that take away 5 per cent of the total mass of two merging
black holes points out on the importance of considering varying gravitational
mass of a system in the framework of the Einstein general theory of relativity.
We calculate the acceleration of a particle in the non-stationary field of a
quasi-spherical system composed of a large number of objects emitting
gravitational waves. It is shown that reduction of the gravitational mass of
the system due to emitting gravitational waves leads to a repulsive
gravitational force that diminishes with time but never disappears. This
repulsive force may be related to the observed expansion of the Universe.


title: Lower Bounds on the mim-width of Some Graph Classes

abstract:
  mim-width is a recent graph width measure that has seen applications in graph
algorithms and problems related to propositional satisfiability. In this paper,
we show linear lower bounds for the mim-width of strongly chordal split graphs,
co-comparability graphs and circle graphs. This improves and refines lower
bounds that were known before, some of them only conditionally. In the case of
strongly chordal graphs not even a conditional lower bound was known before.
All of the bounds given are optimal up to constants.


title: Hermitian Hamiltonians: Matrix versus Schr${\"o}$dinger's

abstract:
  We draw attention to the fact that a Hermitian matrix is always
diagonalizable and has real discrete spectrum whereas the Hermitian
Schr{\"o}dinger Hamiltonian: $H=p^2/2\mu+V(x)$, may not be so. For instance
when $V(x)=x, x^3, -x^2$, $H$ does not have even one real discrete eigenvalue.
Textbooks do not highlight this distinction. However, if $H$ has real discrete
spectrum, by virtue of the expansion theorem, one can convert the eigenvalue
problem $H\psi_n=E_n \psi_n$ into a matrix and get eigenvalues $E_n$ by
diagonalizing the matrix. We show, that the thus obtained $E_n$ could be
accurate, provided $H$ is devoid of scattering states. We suggest that this
could be a simple and apt way to introduce the method of Linear Combination of
Atomic Orbitals (LCAO) for finding the spectra of molecules. In textbooks,
usually the method of matrix-diagonalization appears meagerly as a degenerate
perturbation theory for more than one dimensions.


title:
On the Conventionality of Simultaneity and the Huygens-Fresnel-Miller
  Model of Wave Propagation

abstract:
  We identify a fundamental space-time invariance principle by combining the
thesis of the conventionality of simultaneity with the Hugyens-Fresnel-Miller
model of wave propagation. By following the standard gauge prescription, we
show that the classical electromagnetic potentials influence the one-way speed
of light.


title: Linkage principle for ortho-symplectic supergroups

abstract:
  The purpose of the paper is to derive linkage principle for modular
representations of ortho-symplectic supergroups. We follow the approach of Doty
and investigate in detail the representation theory of the orthosymplectic
group $OSP(2|1)$ and that of its Frobenius thickening. Using the description of
flags and adjacent Borel supersubgroups we derive first the strong linkage for
the Frobenius thickening $G_rT$ of the orthosymplectic supergroup $G$ of type
$SpO(2m|2n+1)$ and $SpO(2m|2n)$. Based on this, we derive the linkage principle
for orthosymplectic supergroup $SpO(2m|2n+1)$ and $SpO(2m|2n)$.


title: Self-similar Turing Patterns: An Anomalous diffusion consequence

abstract:
  In this work we show that under specific anomalous diffusion conditions,
chemical systems can produce well-ordered self-similar concentration patterns
through a diffusion-driven instability. We also find spiral patterns and
patterns with mixtures of rotational symmetries not reported before. The type
of anomalous diffusion discussed in this work, either subdiffusion or
superdiffusion, is a consequence of the medium heterogeneity, and is modelled
through a space-dependent diffusion coefficient with a power-law functional
form.


title:
Improved Separability Criteria Based on Bloch Representation of Density
  Matrices

abstract:
  The correlation matrices or tensors in the Bloch representation of density
matrices are encoded with entanglement properties. In this paper, based on the
Bloch representation of density matrices, we give some new separability
criteria for bipartite and multipartite quantum states. Theoretical analysis
and some examples show that the proposed criteria can be more efficient than
the previous related criteria.


title:
Phonon blockade in a nanomechanical resonator resonantly coupled to a
  qubit

abstract:
  We study phonon statistics in a nanomechanical resonator (NAMR) which is
resonantly coupled to a qubit. We find that there are two different mechanisms
for phonon blockade in such a resonantly coupled NAMR-qubit system. One is due
to the strong anharmonicity of the NAMR-qubit system with large coupling
strength; the other one is due to the destructive interference between
different paths for two-phonon excitation in the NAMR-qubit system with a
moderate coupling strength. We find that the phonon blockade is fragile towards
thermal mode occupations and can only be observed for NAMR being at ultracold
effective temperature. In order to enlarge the mean phonon number for strong
phonon antibunching with a moderate NAMR-qubit coupling strength, we assume
that two external driving fields are applied to the NAMR and qubit,
respectively. In this case, we find that the phonon blockades under two
mechanisms can appear at the same frequency regime by optimizing the strength
ratio and phase difference of the two external driving fields.


title:
New Suns in the Cosmos II: Differential rotation in Kepler Sun-like
  stars

abstract:
  The present study reports the discovery of Sun-like stars, namely
main-sequence stars with $T_{\rm eff}$, $\log g$ and rotation periods $P_{rot}$
similar to solar values, presenting evidence of surface differential rotation.
An autocorrelation of the time series was used to select stars presenting
photometric signal stability from a sample of 881 stars with light curves
collected by the $Kepler$ space-borne telescope, in which we have identified 17
stars with stable signals. A simple two-spot model together with a Bayesian
information criterion were applied to these stars in the search for indications
of differential rotation; in addition, for all 17 stars, it was possible to
compute the spot rotation period $P$, the mean values of the individual spot
rotation periods and their respective colatitudes, and the relative amplitude
of the differential rotation.


title: Asymmetric dynamics of outer automorphisms

abstract:
  We consider the action of an irreducible outer automorphism $\phi$ on the
closure of Culler--Vogtmann Outer space. This action has north-south dynamics
and so, under iteration, points converge exponentially to $[T^\phi_+]$.
  For each $N \geq 3$, we give a family of outer automorphisms $\phi_k \in
\textrm{Out}(\mathbb{F}_N)$ such that as, $k$ goes to infinity, the rate of
convergence of $\phi_k$ goes to infinity while the rate of convergence of
$\phi_k^{-1}$ goes to one. Even if we only require the rate of convergence of
$\phi_k$ to remain bounded away from one, no such family can be constructed
when $N < 3$.
  This family also provides an explicit example of a property described by
Handel and Mosher: that there is no uniform upper bound on the distance between
the axes of an automorphism and its inverse.


title:
Minimal degrees of invariants of (super)groups - a connection to
  cryptology

abstract:
  We investigate questions related to the minimal degree of invariants of
finitely generated diagonalizable groups. These questions were raised in
connection to security of a public key cryptosystem based on invariants of
diagonalizable groups. We derive results for minimal degrees of invariants of
finite groups, abelian groups and algebraic groups. For algebraic groups we
relate the minimal degree of the group to the minimal degrees of its tori.
Finally, we investigate invariants of certain supergroups that are superanalogs
of tori. It is interesting to note that a basis of these invariants is not
given by monomials.


title:
Ideological Consumerism in Colombian Elections, 2015: Links between
  Political Ideology, Twitter Activity and Electoral Results

abstract:
  Propagation of political ideologies in social networks has shown a notorious
impact on voting behavior. Both the contents of the messages (the ideology) and
the politicians' influence on their online audiences (their followers) have
been associated with such an impact. Here we evaluate which of these factors
exerted a major role in deciding electoral results of the 2015 Colombian
regional elections by evaluating the linguistic similarity of political
ideologies and their influence on the Twitter sphere. The electoral results
proved to be strongly associated with tweets and retweets and not with the
linguistic content of their ideologies or their Twitter followers. Suggestions
on new ways to analyze electoral processes are finally discussed.


title: Stochastic higher spin six vertex model and Madconald measures

abstract:
  We prove an identity that relates the q-Laplace transform of the height
function of a (higher spin inhomogeneous) stochastic six vertex model in a
quadrant on one side, and a multiplicative functional of a Macdonald measure on
the other. The identity is used to prove the GUE Tracy-Widom asymptotics for
two instances of the stochastic six vertex model via asymptotics analysis of
the corresponding Schur measures.


title: The Birth and Death of a Universe

abstract:
  This letter is meant to be a brief survey of several recent publications
providing a simple, sequential explanation of Dark Energy, Inflation and Dark
Matter, which leads to a simple picture of the why and the how of the Big Bang,
and thence to a possible understanding of the birth and death of a Universe.


title: On the zeros of the zeta function and eigenvalue problems

abstract:
  In this paper we provide a proof of the Riemann Hypothesis by relating the
non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue
problem on a finite interval.


title:
FIR extended emission from cold gas and dust in Blue Compact Dwarf
  Galaxies: the anomalous cases of POX 186 and UM 461

abstract:
  FIR observation of BCD galaxies with Herschel has revealed a wealth of new
insights in these objects which are thought to resemble high-redshift forming
galaxies. Dust and cold gas showed to be colder, in more or less quantities
than expected and of uncertain origin. However, not unlike in the local
universe, not all the dust or the cold gas is accounted for, making it more
challenging. SPICA and its factor 10 to 100 in sensitivity will allow to image
the faint extended cold gas/dusty disks in BCDGs in addition to detect faint C
and O lines only marginally or not at all detected by Herschel/


title: Moments Match between the KPZ Equation and the Airy Point Process

abstract:
  The results of Amir-Corwin-Quastel, Calabrese-Le Doussal-Rosso, Dotsenko, and
Sasamoto-Spohn imply that the one-point distribution of the solution of the KPZ
equation with the narrow wedge initial condition coincides with that for a
multiplicative statistics of the Airy determinantal random point process.
Taking Taylor coefficients of the two sides yields moment identities. We
provide a simple direct proof of those via a combinatorial match of their
multivariate integral representations.


title:
Mean-field message-passing equations in the Hopfield model and its
  generalizations

abstract:
  Motivated by recent progress in using restricted Boltzmann machines as
preprocessing algorithms for deep neural network, we revisit the mean-field
equations (belief-propagation and TAP equations) in the best understood such
machine, namely the Hopfield model of neural networks, and we explicit how they
can be used as iterative message-passing algorithms, providing a fast method to
compute the local polarizations of neurons. In the "retrieval phase" where
neurons polarize in the direction of one memorized pattern, we point out a
major difference between the belief propagation and TAP equations : the set of
belief propagation equations depends on the pattern which is retrieved, while
one can use a unique set of TAP equations. This makes the latter method much
better suited for applications in the learning process of restricted Boltzmann
machines. In the case where the patterns memorized in the Hopfield model are
not independent, but are correlated through a combinatorial structure, we show
that the TAP equations have to be modified. This modification can be seen
either as an alteration of the reaction term in TAP equations, or, more
interestingly, as the consequence of message passing on a graphical model with
several hidden layers, where the number of hidden layers depends on the depth
of the correlations in the memorized patterns. This layered structure is
actually necessary when one deals with more general restricted Boltzmann
machines.


title: Sketches for arithmetic universes

abstract:
  A theory of sketches for arithmetic universes (AUs) is developed.
  A restricted notion of sketch, called here "context", is defined with the
property that every non-strict model is uniquely isomorphic to a strict model.
This allows us to reconcile the syntactic, dealt with strictly using universal
algebra, with the semantic, in which non-strict models must be considered.
  For any context T, a concrete construction is given of the AU AU<T> freely
generated by it.
  A 2-category Con of contexts is defined, with a full and faithful 2-functor
to the 2-category of AUs and strict AU-functors, given by T |-> AU<T>. It has
finite pie limits, and also all pullbacks of a certain class of "extension"
maps. Every object, morphism or 2-cell of Con is a finite structure.


title: On partial traces and compactification of $*$-autonomous Mix-categories

abstract:
  We study the question when a $*$-autonomous Mix-category has a representation
as a $*$-autonomous Mix-subcategory of a compact one. We define certain partial
trace-like operation on morphisms of a Mix-category, which we call a mixed
trace, and show that any structure preserving embedding of a Mix-category into
a compact one induces a mixed trace on the former. We also show that,
conversely, if a Mix-category ${\bf K}$ has a mixed trace, then we can
construct a compact category and structure preserving embedding of ${\bf K}$
into it, which induces the same mixed trace.
  Finally, we find a specific condition expressed in terms of interaction of
Mix- and coevaluation maps on a Mix-category ${\bf K}$, which is necessary and
sufficient for a structure preserving embedding of ${\bf K}$ into a compact one
to exist. When this condition is satisfied, we construct a "free" or "minimal"
mixed trace on ${\bf K}$ directly from the Mix-category structure, which gives
us also a "free" compactification of ${\bf K}$.


title:
UsingWord Embeddings for Query Translation for Hindi to English Cross
  Language Information Retrieval

abstract:
  Cross-Language Information Retrieval (CLIR) has become an important problem
to solve in the recent years due to the growth of content in multiple languages
in the Web. One of the standard methods is to use query translation from source
to target language. In this paper, we propose an approach based on word
embeddings, a method that captures contextual clues for a particular word in
the source language and gives those words as translations that occur in a
similar context in the target language. Once we obtain the word embeddings of
the source and target language pairs, we learn a projection from source to
target word embeddings, making use of a dictionary with word translation
pairs.We then propose various methods of query translation and aggregation. The
advantage of this approach is that it does not require the corpora to be
aligned (which is difficult to obtain for resource-scarce languages), a
dictionary with word translation pairs is enough to train the word vectors for
translation. We experiment with Forum for Information Retrieval and Evaluation
(FIRE) 2008 and 2012 datasets for Hindi to English CLIR. The proposed word
embedding based approach outperforms the basic dictionary based approach by 70%
and when the word embeddings are combined with the dictionary, the hybrid
approach beats the baseline dictionary based method by 77%. It outperforms the
English monolingual baseline by 15%, when combined with the translations
obtained from Google Translate and Dictionary.


title: Convex domino towers

abstract:
  We study convex domino towers using a classic dissection technique on
polyominoes to find the generating function and an asymptotic approximation.


title: On the enumeration of k-omino towers

abstract:
  We describe a class of fixed polyominoes called $k$-omino towers that are
created by stacking rectangular blocks of size $k\times 1$ on a convex base
composed of these same $k$-omino blocks. By applying a partition to the set of
$k$-omino towers of fixed area $kn$, we give a recurrence on the $k$-omino
towers therefore showing the set of $k$-omino towers is enumerated by a Gauss
hypergeometric function. The proof in this case implies a more general
hypergeometric identity with parameters similar to those given in a classical
result of Kummer.


title: The ASEP and determinantal point processes

abstract:
  We introduce a family of discrete determinantal point processes related to
orthogonal polynomials on the real line, with correlation kernels defined via
spectral projections for the associated Jacobi matrices. For classical weights,
we show how such ensembles arise as limits of various hypergeometric orthogonal
polynomials ensembles.
  We then prove that the q-Laplace transform of the height function of the ASEP
with step initial condition is equal to the expectation of a simple
multiplicative functional on a discrete Laguerre ensemble --- a member of the
new family. This allows us to obtain the large time asymptotics of the ASEP in
three limit regimes: (a) for finitely many rightmost particles; (b) GUE
Tracy-Widom asymptotics of the height function; (c) KPZ asymptotics of the
height function for the ASEP with weak asymmetry. We also give similar results
for two instances of the stochastic six vertex model in a quadrant. The proofs
are based on limit transitions for the corresponding determinantal point
processes.


title: The CONNIE experiment

abstract:
  The CONNIE experiment uses fully depleted, high resistivity CCDs as particle
detectors in an attempt to measure for the first time the Coherent
Neutrino-Nucleus Elastic Scattering of antineutrinos from a nuclear reactor
with silicon nuclei.This talk, given at the XV Mexican Workshop on Particles
and Fields (MWPF), discussed the potential of CONNIE to perform this
measurement, the installation progress at the Angra dos Reis nuclear power
plant, as well as the plans for future upgrades.


title:
Modelling Censored Losses Using Splicing: a Global Fit Strategy With
  Mixed Erlang and Extreme Value Distributions

abstract:
  In risk analysis, a global fit that appropriately captures the body and the
tail of the distribution of losses is essential. Modelling the whole range of
the losses using a standard distribution is usually very hard and often
impossible due to the specific characteristics of the body and the tail of the
loss distribution. A possible solution is to combine two distributions in a
splicing model: a light-tailed distribution for the body which covers light and
moderate losses, and a heavy-tailed distribution for the tail to capture large
losses. We propose a splicing model with a mixed Erlang (ME) distribution for
the body and a Pareto distribution for the tail. This combines the flexibility
of the ME distribution with the ability of the Pareto distribution to model
extreme values. We extend our splicing approach for censored and/or truncated
data. Relevant examples of such data can be found in financial risk analysis.
We illustrate the flexibility of this splicing model using practical examples
from risk measurement.


title: On the decay of the off-diagonal singular values in cyclic reduction

abstract:
  It was recently observed that the singular values of the off-diagonal blocks
of the matrix sequences generated by the Cyclic Reduction algorithm decay
exponentially. This property was used to solve, with a higher efficiency,
certain quadratic matrix equations encountered in the analysis of queueing
models. In this paper, we provide a sharp theoretical bound to the basis of
this exponential decay together with a tool for its estimation based on a
rational interpolation problem. Applications to solving $n\times n$ block
tridiagonal block Toeplitz systems with $n\times n$ semiseparable blocks and
certain generalized Sylvester equations in $O(n^2\log n)$ arithmetic operations
are shown.


title:
Derandomizing Chernoff Bound with Union Bound with an Application to
  $k$-wise Independent Sets

abstract:
  Derandomization of Chernoff bound with union bound is already proven in many
papers. We here give another explicit version of it that obtains a construction
of size that is arbitrary close to the probabilistic nonconstructive size.
  We apply this to give a new simple polynomial time constructions of almost
$k$-wise independent sets. We also give almost tight lower bounds for the size
of $k$-wise independent sets.


title: Very High Energy outburst of Markarian 501 in May 2009

abstract:
  The very high energy (VHE; E $>$ 100 GeV) blazar Markarian 501 was observed
between April 17 and May 5 (MJD 54938--54956), 2009, as part of an extensive
multi-wavelength campaign from radio to VHE. Strong VHE $\gamma$-ray activity
was detected on May 1st with Whipple and VERITAS, when the flux (E $>$ 400 GeV)
increased to 10 times the pre-flare baseline flux ($3.9{\times 10^{-11}}~{\rm
ph~cm^{-2}~s^{-1}}$), reaching five times the flux of the Crab Nebula. This
coincided with a decrease in the optical polarization and a rotation of the
polarization angle by 15$^{\circ}$. This VHE flare showed a fast flux variation
with an increase of a factor $\sim$4 in 25 minutes, and a falling time of
$\sim$50 minutes. We present the observations of the quiescent state previous
to the flare and of the high state after the flare, focusing on the flux and
spectral variability from Whipple, VERITAS, Fermi-LAT, RXTE, and Swift combined
with optical and radio data.


title: Meridional Rank of Knots Whose Exterior is a Graph Manifold

abstract:
  We prove for a large class of knots that the meridional rank coincides with
the bridge number. This class contains all knots whose exterior is a graph
manifold. This gives a partial answer to a question of S. Cappell and J.
Shaneson, see problem 1.11 on Kirby's list.


title: Two-Photon Blockade in an Atom-Driven Cavity QED System

abstract:
  Photon blockade is a dynamical quantum-nonlinear effect that occurs in driven
systems with an anharmonic excitation ladder. For a single atom strongly
coupled to an optical cavity, we show that driving the atom gives a decisively
larger optical nonlinearity than driving the cavity. This enhances
single-photon blockade and allows for the implementation of two-photon blockade
where the absorption of two photons suppresses the absorption of further
photons. As a signature, we report on three-photon antibunching with
simultaneous two-photon bunching observed in the light emitted from the cavity.
Our experiment constitutes a significant step towards multi-photon
quantum-nonlinear optics.


title: Global topological control for synchronized dynamics on networks

abstract:
  A general scheme is proposed and tested to control the symmetry breaking
instability of a homogeneous solution of a spatially extended multispecies
model, defined on a network. The inherent discreteness of the space makes it
possible to act on the topology of the inter-nodes contacts to achieve the
desired degree of stabilization, without altering the dynamical parameters of
the model. Both symmetric and asymmetric couplings are considered. In this
latter setting the web of contacts is assumed to be balanced, for the
homogeneous equilibrium to exist. The performance of the proposed method are
assessed, assuming the Complex Ginzburg-Landau equation as a reference model.
In this case, the implemented control allows one to stabilize the synchronous
limit cycle, hence time-dependent, uniform solution. A system of coupled real
Ginzburg-Landau equations is also investigated to obtain the topological
stabilization of a homogeneous and constant fixed point.


title:
Local Term Weight Models from Power Transformations: Development of
  BM25IR: A Best Match Model based on Inverse Regression

abstract:
  In this article we show how power transformations can be used as a common
framework for the derivation of local term weights. We found that under some
parametric conditions, BM25 and inverse regression produce equivalent results.
As a special case of inverse regression, we show that the largest increment in
term weight occurs when a term is mentioned for the second time. A model based
on inverse regression (BM25IR) is presented. Simulations suggest that BM25IR
works fairly well for different BM25 parametric conditions and document
lengths.


title:
Stochastic thermodynamics based on incomplete information: Generalized
  Jarzynski equality with measurement errors with or without feedback

abstract:
  In the derivation of fluctuation relations, and in stochastic thermodynamics
in general, it is tacitly assumed that we can measure the system perfectly,
i.e., without measurement errors. We here demonstrate for a driven system
immersed in a single heat bath, for which the classic Jarzynski equality
$\langle e^{-\beta(W-\Delta F)}\rangle = 1$ holds, how to relax this
assumption. Based on a general measurement model akin to Bayesian inference we
derive a general expression for the fluctuation relation of the measured work
and we study the case of an overdamped Brownian particle and of a two-level
system in particular. We then generalize our results further and incorporate
feedback in our description. We show and argue that, if measurement errors are
fully taken into account by the agent who controls and observes the system, the
standard Jarzynski-Sagawa-Ueda relation should be formulated differently. We
again explicitly demonstrate this for an overdamped Brownian particle and a
two-level system where the fluctuation relation of the measured work differs
significantly from the efficacy parameter introduced by Sagawa and Ueda.
Instead, the generalized fluctuation relation under feedback control, $\langle
e^{-\beta(W-\Delta F)-I}\rangle = 1$, holds only for a superobserver having
perfect access to both the system and detector degrees of freedom,
independently of whether or not the detector yields a noisy measurement record
and whether or not we perform feedback.


title:
Almost everywhere convergence of Bochner-Riesz means on some Sobolev
  type spaces

abstract:
  In this paper, we investigate the convergence of the Bochner-Riesz means on
some Sobolev type spaces including $L^p$-Sobolev spaces $(p\geq 1)$ and
$H^q$-Sobolev spaces $(0<q<1)$. The relation between the smoothness imposed on
functions and the rate of almost everywhere convergence of the generalized
Bochner-Riesz means is given.


title:
Decay bounds for the numerical quasiseparable preservation in matrix
  functions

abstract:
  Given matrices $A$ and $B$ such that $B=f(A)$, where $f(z)$ is a holomorphic
function, we analyze the relation between the singular values of the
off-diagonal submatrices of $A$ and $B$. We provide family of bounds which
depend on the interplay between the spectrum of the argument $A$ and the
singularities of the function. In particular, these bounds guarantee the
numerical preservation of quasiseparable structures under mild hypotheses. We
extend the Dunford-Cauchy integral formula to the case in which some poles are
contained inside the contour of integration. We use this tool together with the
technology of hierarchical matrices ($\mathcal H$-matrices) for the effective
computation of matrix functions with quasiseparable arguments.


title: Almost all trees are almost graceful

abstract:
  The Graceful Tree Conjecture of Rosa from 1967 asserts that the vertices of
each tree T of order n can be injectively labelled by using the numbers
{1,2,...,n} in such a way that the absolute differences induced on the edges
are pairwise distinct.
  We prove the following relaxation of the conjecture for each c>0 and for all
n>n_0(c). Suppose that (i) the maximum degree of T is bounded by O(n/log n),
and (ii) the vertex labels are chosen from the set {1,2,..., (1+c)n}. Then
there is an injective labelling of V(T) such that the absolute differences on
the edges are pairwise distinct. In particular, asymptotically almost all trees
on n vertices admit such a labelling.
  As a consequence, for any such tree T we can pack (2+2c)n-1 copies of T into
the complete graph of order (2+2c)n-1 cyclically. This proves an approximate
version of the Ringel-Kotzig conjecture (which asserts the existence of a
cyclic packing of 2n-1 copies of any T into the complete graph of order 2n-1)
for these trees.
  The proof proceeds by showing that a certain very natural randomized
algorithm produces a desired labelling with high probability.


title: Basis for the linear space of matrices under equivalence

abstract:
  The semi-tensor product (STP) of matrices which was proposed by Daizhan Cheng
in 2001 [2], is a natural generalization of the standard matrix product and
well defined at every two finite-dimensional matrices. In 2016, Cheng proposed
a new concept of semi-tensor addition (STA) which is a natural generalization
of the standard matrix addition and well defined at every two
finite-dimensional matrices with the same ratio between the numbers of rows and
columns [1]. In addition, an identify equivalence relation between matrices was
defined in [1], STP and STA were proved valid for the corresponding identify
equivalence classes, and the corresponding quotient space was endowed with an
algebraic structure and a manifold structure. In this follow-up paper, we give
a new concise basis for the quotient space, which also shows that the Lie
algebra corresponding to the quotient space is of countably infinite dimension.


title: Rotation Forms and Local Hamiltonian Monodromy

abstract:
  The monodromy of torus bundles associated to completely integrable systems
can be computed using geometric techniques (constructing homology cycles) or
analytic arguments (computing discontinuities of abelian integrals). In this
article we give a general approach to the computation of monodromy that
resembles the analytical one, reducing the problem to the computation of
residues of polar 1-forms. We apply our technique to three celebrated examples
of systems with monodromy (the champagne bottle, the spherical pendulum, the
hydrogen atom) and to the case of non degenerate focus-focus singularities,
re-obtaining the classical results. An advantage of this approach is that the
residue-like formula can be shown to be local in a neighborhood of a
singularity, hence allowing the definition of monodromy also in the case of
non-compact fibers. This idea has been introduced in the literature under the
name of scattering monodromy. We prove the coincidence of the two definitions
with the monodromy of an appropriately chosen compactification.


title:
Faraday and resonant waves in binary collisionally-inhomogeneous
  Bose-Einstein condensates

abstract:
  We study Faraday and resonant waves in two-component quasi-one-dimensional
(cigar-shaped) collisionally inhomogeneous Bose-Einstein condensates subject to
periodic modulation of the radial confinement. We show by means of extensive
numerical simulations that, as the system exhibits stronger spatially-localised
binary collisions (whose scattering length is taken for convenience to be of
Gaussian form), the system becomes effectively a linear one. In other words, as
the scattering length approaches a delta-function, we observe that the two
nonlinear configurations typical for binary cigar-shaped condensates, namely
the segregated and the symbiotic one, turn into two overlapping Gaussian wave
functions typical for linear systems, and that the instability onset times of
the Faraday and resonant waves become longer. Moreover, our numerical
simulations show that the spatial period of the excited waves (either resonant
or Faraday ones) decreases as the inhomogeneity becomes stronger. Our results
also demonstrate that the topology of the ground state impacts the dynamics of
the ensuing density waves, and that the instability onset times of Faraday and
resonant waves, for a given level of inhomogeneity in the two-body
interactions, depend on whether the initial configuration is segregated or
symbiotic.


title:
Strain Engineering of the Band Gap of HgTe Quantum Wells using
  Superlattice Virtual Substrates

abstract:
  The HgTe quantum well (QW) is a well-characterized two-dimensional
topological insulator (2D-TI). Its band gap is relatively small (typically on
the order of 10 meV), which restricts the observation of purely topological
conductance to low temperatures. Here, we utilize the strain-dependence of the
band structure of HgTe QWs to address this limitation. We use
$\text{CdTe}-\text{Cd}_{0.5}\text{Zn}_{0.5}\text{Te}$ strained-layer
superlattices on GaAs as virtual substrates with adjustable lattice constant to
control the strain of the QW. We present magneto-transport measurements, which
demonstrate a transition from a semi- metallic to a 2D-TI regime in wide QWs,
when the strain is changed from tensile to compressive. Most notably, we
demonstrate a much enhanced energy gap of 55 meV in heavily compressively
strained QWs. This value exceeds the highest possible gap on common II-VI
substrates by a factor of 2-3, and extends the regime where the topological
conductance prevails to much higher temperatures.


title:
One-loop corrections to the Higgs self-couplings in the singlet
  extension

abstract:
  We investigate predictions on the triple Higgs boson couplings with radiative
corrections in the model with an additional real singlet scalar field. In this
model, the second physical scalar state ($H$) appears in addition to the Higgs
boson ($h$) with the mass 125 GeV. The $hhh$ vertex is calculated at the
one-loop level, and its possible deviation from the predictions in the standard
model is evaluated under various theoretical constraints. The decay rate of $H
\to hh$ is also computed at the one-loop level. We also take into account the
bound from the precise measurement of the $W$ boson mass, which gives the upper
limit on the mixing angle $\alpha$ between two physical Higgs bosons for a
given value of the mass of $H$ ($m_H^{}$). We find that the deviation in the
$hhh$ coupling from the prediction in the standard model can maximally be about
250\%, 150\% and 75\% for $m_H^{}=300$, 500 and 1000 GeV, respectively, under
the requirement that the cutoff scale of the model is higher than 3 TeV. We
also discuss deviations from the standard model prediction in double Higgs
boson production from the gluon fusion at the LHC using the one-loop corrected
Higgs boson vertices.


title: Undistorted purely pseudo-Anosov groups

abstract:
  In this paper we prove that groups as in the title are convex cocompact in
the mapping class group.


title: Four-dimensional unsubtraction with massive particles

abstract:
  We extend the four-dimensional unsubtraction method, which is based on the
loop-tree duality (LTD), to deal with processes involving heavy particles. The
method allows to perform the summation over degenerate IR configurations
directly at integrand level in such a way that NLO corrections can be
implemented directly in four space-time dimensions. We define a general
momentum mapping between the real and virtual kinematics that accounts properly
for the quasi-collinear configurations, and leads to an smooth massless limit.
We illustrate the method first with an scalar toy example, and then analyse the
case of the decay of a scalar or vector boson into a pair of massive quarks.
The results presented in this paper are suitable for the application of the
method to any multipartonic process.


title: Pre-Courant Algebroids

abstract:
  Pre-Courant algebroids are `Courant algebroids' without the Jacobi identity
for the Courant-Dorfman bracket. In this paper we examine the corresponding
supermanifold description of pre-Courant algebroids and some direct
consequences thereof - such as the definition of (sub-)Dirac structures and the
notion of the naive quasi-cochain complex. In particular we define symplectic
almost Lie 2-algebroids and show how they correspond to pre-Courant algebroids.
Moreover, the framework of supermanifolds allows us to economically define and
work with pre-Courant algebroids equipped with a compatible non-negative
grading. VB-Courant algebroids are natural examples of what we call weighted
pre-Courant algebroids, and our approach drastically simplifies working with
them. We remark that examples of pre-Courant algebroids are plentiful - natural
examples include the cotangent bundle of any almost Lie algebroid.


title:
On the exact discrete Lagrangian function for variational integrators:
  theory and applications

abstract:
  In this paper, we will give a rigorous construction of the exact discrete
Lagrangian formulation associated to a continuous Lagrangian problem. Moreover,
we work in the setting of Lie groupoids and Lie algebroids which is enough
general to simultaneously cover several cases of interest in discrete and
continuous descriptions as, for instance, Euler-Lagrange equations,
Euler-Poincar\'e equations, Lagrange-Poincar\'e equations... The construction
of an exact discrete Lagrangian is of considerable interest for the analysis of
the error between an exact trajectory and the discrete trajectory derived by a
variational integrator.


title: Absorption of Very High Energy Gamma Rays in the Milky Way

abstract:
  Galactic Gamma ray astronomy at very high energy (E > 30 TeV) is a vital tool
in the study of the non-thermal universe. The interpretation of the
observations in this energy region requires the precise modeling of the
attenuation of photons due to pair production interactions, where the targets
are the radiation fields present in interstellar space. For gamma rays with
energy E > 300 TeV the attenuation is mostly due to the photons of the Cosmic
Microwave Background Radiation (CMBR). At lower energy the most important
target are infrared photons with wavelengths in the range 50-500 micron emitted
by dust. The evaluation of the attenuation requires a good knowledge of the
density, and energy and angular distributions of the target photons for all
positions in the Galaxy. In this work we discuss a simple model for the
infrared radiation that depends on only few parameters associated to the space
and temperature distributions of the emitting dust. The model allows to compute
with good accuracy the effects of absorption for any space and energy
distribution of the diffuse Galactic gamma ray emission. The absorption
probability due to the Galactic infrared radiation is maximum for E around 150
TeV, and can be as large as P_abs around 0.45 for distant sources on lines of
sight that pass close to the Galactic Center. The systematic uncertainties on
the absorption probability are estimated as Delta P_abs < 0.08.


title: Outage Behavior of Integer Forcing With Random Unitary Pre-Processing

abstract:
  Integer forcing is an equalization scheme for the multiple-input
multiple-output communication channel that has been demonstrated to allow
operating close to capacity for "most" channels. In this work, the measure of
"bad" channels is quantified by considering a compound channel setting where
the transmitter communicates over a fixed channel but knows only its mutual
information. The transmitter encodes the data into independent streams, all
taken from the same linear code. The coded streams are transmitted after
applying a unitary transformation. At the receiver side, integer-forcing
equalization is applied, followed by standard single-stream decoding.
Considering pre-processing matrices drawn from a random ensemble, outage
corresponds to the event that the target rate exceeds the achievable rate of
integer forcing for a given channel matrix. For the case of the circular
unitary ensemble, an explicit universal bound on the outage probability for a
given target rate is derived that holds for any channel in the compound class.
The derived bound depends only on the gap-to-capacity and the number of
transmit antennas. The results are also applied to obtain universal bounds on
the gap-to-capacity of multiple-antenna closed-loop multicast, achievable via
linear pre-processed integer forcing.


title: Coloring curves on surfaces

abstract:
  We study the chromatic number of the curve graph of a surface. We show that
the chromatic number grows like k log k for the graph of separating curves on a
surface of Euler characteristic -k. We also show that the graph of curves that
represent a fixed non-zero homology class is uniquely t-colorable, where t
denotes its clique number. Together, these results lead to the best known
bounds on the chromatic number of the curve graph. We also study variations for
arc graphs and obtain exact results for surfaces of low complexity. Our
investigation leads to connections with Kneser graphs, the Johnson
homomorphism, and hyperbolic geometry.


title:
Compositional abstraction for networks of control systems: A
  dissipativity approach

abstract:
  In this paper we propose a compositional scheme for the construction of
abstractions for networks of control systems using the interconnection matrix
and joint dissipativity-type properties of subsystems and their abstractions.
In the proposed framework, the abstraction, itself a control system (possibly
with a lower dimension), can be used as a substitution of the original system
in the controller design process. Moreover, we provide a procedure for
constructing abstractions of a class of nonlinear control systems by using the
bounds on the slope of system nonlinearities. We illustrate the proposed
results on a network of linear control systems by constructing its abstraction
in a compositional way without requiring any condition on the number or gains
of the subsystems. We use the abstraction as a substitute to synthesize a
controller enforcing a certain linear temporal logic specification. This
example particularly elucidates the effectiveness of dissipativity-type
compositional reasoning for large-scale systems.


title:
Resonance Damping of the THz-frequency Transverse Acoustic Phonon in the
  Relaxor Ferroelectric KTa1-xNbxO3

abstract:
  The damping ($\Gamma_a$) of the transverse acoustic (TA) phonon in single
crystals of the relaxor $KTa_{1-x}Nb_xO_3$ with x=0.15-0.17 was studied by
means of high resolution inelastic cold neutron scattering near the (200) B.Z.
point where diffuse scattering is absent, although it is present near (110). In
a wide range of temperatures centered on the phase transition, T=195K-108K, the
TA phonon width (damping) exhibits a step increase around momentum q=0.07, goes
through a shallow maximum at q=0.09-0.12 and remains high up to the highest
momentum studied of q=0.16. These experimental results are explained in terms
of a resonant interaction between the TA phonon and the collective or
correlated reorientation through tunneling of the off-center Nb+5 ions. The
observed TA damping is successfully reproduced in a simple model that includes
an interaction between the TA phonon and a dispersionless localized mode (LM)
with frequency $\omega_L$ and damping $\Gamma_L$ ($\Gamma_L < \omega_L$),
itself coupled to the transverse optic (TO) mode. Maximum damping of the TA
phonon occurs when its frequency $\omega_a \approx{\omega_L}$. $\omega_L$ and
$\Gamma_L$ are moderately dependent on temperature but the oscillator strength,
$M_2$, of the resonant damping exhibits a strong maximum in the range
$T\sim{150 K-120 K}$ in which neutron diffuse scattering near the (110) B.Z.
point is also maximum and the dielectric susceptibility exhibits the relaxor
behavior. The maximum value of M appears to be due to the increasing number of
polar nanodomains. In support of the proposed model, the observed value of
$\omega_L$ is found to be similar to the estimate previously obtained by
Girshberg and Yacoby. Alternatively, the TA phonon damping can be successfully
fitted in the framework of an empirical Havriliak - Negami (HN) relaxation
model that includes a strong resonance-like transient contribution.


title: Bounds on Multipartite Concurrence and Tangle

abstract:
  We present an analytical lower bound of multipartite concurrence based on the
generalized Bloch representations of density matrices. It is shown that the
lower bound can be used as an effective entanglement witness of genuine
multipartite entanglement. Tight lower and upper bounds for multipartite
tangles are also derived. Since the lower bounds depend on just part of the
correlation tensors, the result is experimentally feasible.


title: Generalized Additive Models for Pair-Copula Constructions

abstract:
  Pair-copula constructions are flexible dependence models that use bivariate
copulas as building blocks. In this paper, we use generalized additive models
to extend them by allowing covariates effects. Borrowing ideas from a
traditionally univariate context, we let each pair-copula parameter depend
directly on the covariates in a parametric, semiparametric or nonparametric
way. We propose a sequential estimation method that we study by simulation, and
apply it to investigate the time-varying dependence structure between the
intraday returns on four major foreign exchange rates. An R package, a script
reproducing the results in this article, and additional simulation results are
provided as supplementary material.


title:
Precise Complexity Guarantees for Pointer Analysis via Datalog with
  Extensions

abstract:
  Pointer analysis is a fundamental static program analysis for computing the
set of objects that an expression can refer to. Decades of research has gone
into developing methods of varying precision and efficiency for pointer
analysis for programs that use different language features, but determining
precisely how efficient a particular method is has been a challenge in itself.
  For programs that use different language features, we consider methods for
pointer analysis using Datalog and extensions to Datalog. When the rules are in
Datalog, we present the calculation of precise time complexities from the rules
using a new algorithm for decomposing rules for obtaining the best
complexities. When extensions such as function symbols and universal
quantification are used, we describe algorithms for efficiently implementing
the extensions and the complexities of the algorithms.
  This paper is under consideration for acceptance in TPLP.


title: Results from the OPERA experiment

abstract:
  The OPERA long baseline experiment located in the INFN Gran Sasso underground
Laboratory was designed to establish the $\nu_{\mu}$ $\rightarrow$ $\nu_{\tau}$
oscillations in appearance mode, using the CNGS neutrino beam. Five
$\nu_{\tau}$ candidate events have been detected in a data sample from the
2008-2012 runs, with a expected background of 0.25 events. The background only
hypothesis is rejected with a significance larger than 5${\sigma}$. The
analysis of the tau neutrino sample in the framework of the 3+1 neutrino model
is presented. OPERA is able to identify $\nu_{e}$ CC events due to the good
tracking capabilities of its target. The electron neutrino sample is also used
to set limits on the 3+1 oscillation parameters.


title: Heat kernel estimates on connected sums of parabolic manifolds

abstract:
  We obtain matching two sided estimates of the heat kernel on a connected sum
of parabolic manifolds, each of them satisfying the Li-Yau estimate. The key
result is the on-diagonal upper bound of the heat kernel at a central point.
Contrary to the nonparabolic case (which was settled in [15]), the on-diagonal
behavior of the heat kernel in our case is determined by the end with the
maximal volume growth function. As examples, we give explicit heat kernel
bounds on the connected sums $R^2#R^2$ and $R^1#R^2$ where $R^1 =
R_+\timesS^1$.


title: Intertwinings of beta-Dyson Brownian motions of different dimensions

abstract:
  We show that for all positive beta the semigroups of beta-Dyson Brownian
motions of different dimensions are intertwined. The proof relates beta-Dyson
Brownian motions directly to Jack symmetric polynomials and omits an
approximation of the former by discrete space Markov chains, thereby disposing
of the technical assumption beta>1 in [GS]. The corresponding results for
beta-Dyson Ornstein-Uhlenbeck processes are also presented.


title:
Logarithmic Corrections to the Black Hole Entropy Product of ${\cal
  H}^{\pm}$ via Cardy Formula

abstract:
  We compute the logarithmic corrections to black hole (BH) entropy product of
${\cal H}^{\pm}$ \footnote{ ${\cal H}^{+}$ and ${\cal H}^{-}$ denote outer
(event) horizon and inner (Cauchy) horizons} by using \emph{Cardy
prescription}. We particularly apply this formula for \emph{BTZ BH}. We
speculate that the logarithmic corrections to entropy product of ${\cal
H}^{\pm}$ when computed \emph{via Cardy formula} the product should be neither
\emph{mass-independent (universal)} nor be \emph{quantized}.


title:
Deligne's determinant functors and the RHom of connected homotopy
  $2$-types

abstract: The determinant functeurs are the RHom of connected homotopy $2$-types.


title:
Transport and Optical Conductivity in the Hubbard Model: A
  High-Temperature Expansion Perspective

abstract:
  We derive analytical expressions for the spectral moments of the dynamical
response functions of the Hubbard model using the high-temperature series
expansion. We consider generic dimension $d$ as well as the infinite-$d$ limit,
arbitrary electron density $n$, and both finite and infinite repulsion $U$. We
use moment-reconstruction methods to obtain the one-electron spectral function,
the self-energy, and the optical conductivity. They are all smooth functions at
high-temperature and, at large-$U$, they are featureless with characteristic
widths of order the lattice hopping parameter $t$. In the infinite-$d$ limit we
compare the series expansion results with accurate numerical renormalization
group and interaction expansion quantum Monte-Carlo results. We find excellent
agreement down to surprisingly low temperatures, throughout most of the
bad-metal regime which applies for $T \gtrsim (1-n)D$, the Brinkman-Rice scale.
The resistivity increases linearly in $T$ at high-temperature without
saturation. This results from the $1/T$ behaviour of the compressibility or
kinetic energy, which play the role of the effective carrier number. In
contrast, the scattering time (or diffusion constant) saturate at high-$T$. We
find that $\sigma(n,T) \approx (1-n)\sigma(n=0,T)$ to a very good approximation
for all $n$, with $\sigma(n=0,T)\propto t/T$ at high temperatures. The
saturation at small $n$ occurs due to a compensation between the
density-dependence of the effective number of carriers and that of the
scattering time. The $T$-dependence of the resistivity displays a knee-like
feature which signals a cross-over to the intermediate-temperature regime where
the diffusion constant (or scattering time) start increasing with decreasing
$T$. At high-temperatures, the thermopower obeys the Heikes formula, while the
Wiedemann-Franz law is violated with the Lorenz number vanishing as $1/T^2$.


title:
Elucidating Dark Energy with Future 21 cm Observations at the Epoch of
  Reionization

abstract:
  We investigate how precisely we can determine the nature of dark energy such
as the equation of state (EoS) and its time dependence by using future
observations of 21 cm fluctuations at the epoch of reionization (6.8 <~ z <~
10) such as Square Kilometre Array (SKA) and Omniscope in combination with
those from cosmic microwave background, baryon acoustic oscillation, type Ia
supernovae and direct measurement of the Hubble constant. We consider several
parametrizations for the EoS and find that future 21 cm observations will be
powerful in constraining models of dark energy, especially when its EoS varies
at high redshifts.


title: Renormalization Group Analysis of the Hierarchical Anderson Model

abstract:
  We apply Feshbach-Krein-Schur renormalization techniques in the hierarchical
Anderson model to establish a criterion on the single-site distribution which
ensures exponential dynamical localization as well as positive inverse
participation ratios and Poisson statistics of eigenvalues. Our criterion
applies to all cases of exponentially decaying hierarchical hopping strengths
and holds even for spectral dimension $d > 2$, which corresponds to the regime
of transience of the underlying hierarchical random walk. This challenges
recent numerical findings that the spectral dimension is significant as far as
the Anderson transition is concerned.

categories: math-ph cond-mat.dis-nn math.MP math.PR math.SP


title: Stable Models for Infinitary Formulas with Extensional Atoms

abstract:
  The definition of stable models for propositional formulas with infinite
conjunctions and disjunctions can be used to describe the semantics of answer
set programming languages. In this note, we enhance that definition by
introducing a distinction between intensional and extensional atoms. The
symmetric splitting theorem for first-order formulas is then extended to
infinitary formulas and used to reason about infinitary definitions. This note
is under consideration for publication in Theory and Practice of Logic
Programming.


title: Query Answering in Resource-Based Answer Set Semantics

abstract:
  In recent work we defined resource-based answer set semantics, which is an
extension to answer set semantics stemming from the study of its relationship
with linear logic. In fact, the name of the new semantics comes from the fact
that in the linear-logic formulation every literal (including negative ones)
were considered as a resource. In this paper, we propose a query-answering
procedure reminiscent of Prolog for answer set programs under this extended
semantics as an extension of XSB-resolution for logic programs with negation.
We prove formal properties of the proposed procedure.
  Under consideration for acceptance in TPLP.


title:
Reply to the Comment on "The Lifshitz-Matsubara sum formula for the
  Casimir pressure between magnetic metallic mirrors"

abstract:
  We reply to the "Comment on 'The Lifshitz-Matsubara sum formula for the
Casimir pressure between magnetic metallic mirrors'" [arXiv:1604.06432]. We
believe the comment misrepresents our papers, and fails to provide a plausible
resolution to the conflict between theory and experiment.


title: Particle Traces for Detecting Divergent Robot Behavior

abstract:
  The motion of robots and objects in our world is often highly dependent upon
contact. When contact is expected but does not occur or when contact is not
expected but does occur, robot behavior diverges from plan, often disastrously.
This paper describes an approach that uses simulation to detect possible such
behavioral divergences on real robots. This approach, and others like it, could
be applied to validation of robot behaviors, mechanism design, and even online
planning.
  The particle trace approach samples robot modeling parameters, sensory
readings, and state estimates to evaluate a robot's behavior statistically over
a range of conditions. We demonstrate that combining even coarse estimates of
state and modeling parameters with fast multibody simulation can be sufficient
to detect divergent robot behavior and characterize robot performance in the
real world. Correspondingly, this approach could be used to assess risk and
find and analyze likely failures, given the extensive data that such
simulations can generate.
  We assess this approach on actuated, high degree-of-freedom robot locomotion
examples, a picking task with a fixed-base manipulator, and an unpowered
passive dynamic walker. This research works toward understanding how
multi-rigid body simulations can better characterize the behavior of robots
without significantly compliant elements.


title: The detector calibration system for the CUORE cryogenic bolometer array

abstract:
  The Cryogenic Underground Observatory for Rare Events (CUORE) is a ton-scale
cryogenic experiment designed to search for neutrinoless double-beta decay of
$^{130}$Te and other rare events. The CUORE detector consists of 988 TeO$_2$
bolometers operated underground at 10 mK in a dilution refrigerator at the
Laboratori Nazionali del Gran Sasso. Candidate events are identified through a
precise measurement of their energy. The absolute energy response of the
detectors is established by the regular calibration of each individual
bolometer using gamma sources. The close-packed configuration of the CUORE
bolometer array combined with the extensive shielding surrounding the detectors
requires the placement of calibration sources within the array itself. The
CUORE Detector Calibration System is designed to insert radioactive sources
into and remove them from the cryostat while respecting the stringent heat
load, radiopurity, and operational requirements of the experiment. This paper
describes the design, commissioning, and performance of this novel source
calibration deployment system for ultra-low-temperature environments.


title:
Future evolution in a backreaction model and the analogous scalar field
  cosmology

abstract:
  We investigate the future evolution of the universe using the Buchert
framework for averaged backreaction in the context of a two-domain partition of
the universe. We show that this approach allows for the possibility of the
global acceleration vanishing at a finite future time, provided that none of
the subdomains accelerate individually. The model at large scales is
analogously described in terms of a homogeneous scalar field emerging with a
potential that is fixed and free from phenomenological parametrization. The
dynamics of this scalar field is explored in the analogous FLRW cosmology.
  We use observational data from Type Ia Supernovae, Baryon Acoustic
Oscillations, and Cosmic Microwave Background to constrain the parameters of
the model for a viable cosmology, providing the corresponding likelihood
contours.


title: Designing peg solitaire puzzles

abstract:
  Peg solitaire is an old puzzle with a 300 year history. We consider two ways
a computer can be utilized to find interesting peg solitaire puzzles. It is
common for a peg solitaire puzzle to begin from a symmetric board position, we
have computed solvable symmetric board positions for four board shapes. A new
idea is to search for board positions which have a unique starting jump leading
to a solution. We show many challenging puzzles uncovered by this search
technique. Clever solvers can take advantage of the uniqueness property to help
solve these puzzles.


title:
Lower limit on the gravitino mass in low-scale gauge mediation with
  $m_H\simeq 125$GeV

abstract:
  We revisit low-scale gauge mediation models in light of recent observations
of CMB Lensing and Cosmic Shear which put a severe upper limit on the gravitino
mass, $m_{3/2} \lesssim 4.7$eV. With such a stringent constraint, many models
of low-scale gauge mediation are excluded when the squark masses are required
to be rather large to explain the observed Higgs boson mass. In this note, we
discuss a type of low-scale gauge mediation models which satisfy both the
observed Higgs boson mass and the upper limit on the gravitino mass. We also
show that the gravitino mass cannot be smaller than about 1eV even in such
models, which may be tested in future observations of 21 cm line fluctuations.


title:
Deploying learning materials to game content for serious education game
  development: A case study

abstract:
  The ultimate goals of serious education games (SEG) are to facilitate
learning and maximizing enjoyment during playing SEGs. In SEG development,
there are normally two spaces to be taken into account: knowledge space
regarding learning materials and content space regarding games to be used to
convey learning materials. How to deploy the learning materials seamlessly and
effectively into game content becomes one of the most challenging problems in
SEG development. Unlike previous work where experts in education have to be
used heavily, we proposed a novel approach that works toward minimizing the
efforts of education experts in mapping learning materials to content space.
For a proof-of-concept, we apply the proposed approach in developing an SEG
game, named \emph{Chem Dungeon}, as a case study in order to demonstrate the
effectiveness of our proposed approach. This SEG game has been tested with a
number of users, and the user survey suggests our method works reasonably well.


title: Separators in region intersection graphs

abstract:
  For undirected graphs $G=(V,E)$ and $G_0=(V_0,E_0)$, say that $G$ is a region
intersection graph over $G_0$ if there is a family of connected subsets $\{ R_u
\subseteq V_0 : u \in V \}$ of $G_0$ such that $\{u,v\} \in E \iff R_u \cap R_v
\neq \emptyset$.
  We show if $G_0$ excludes the complete graph $K_h$ as a minor for some $h
\geq 1$, then every region intersection graph $G$ over $G_0$ with $m$ edges has
a balanced separator with at most $c_h \sqrt{m}$ nodes, where $c_h$ is a
constant depending only on $h$. If $G$ additionally has uniformly bounded
vertex degrees, then such a separator is found by spectral partitioning.
  A string graph is the intersection graph of continuous arcs in the plane. The
preceding result implies that every string graph with $m$ edges has a balanced
separator of size $O(\sqrt{m})$. This bound is optimal, as it generalizes the
planar separator theorem. It confirms a conjecture of Fox and Pach (2010), and
improves over the $O(\sqrt{m} \log m)$ bound of Matousek (2013).


title: On augmented superfield approach to vector Schwinger model

abstract:
  We exploit the techniques of Bonora-Tonin superfield formalism to derive the
off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as
(anti-)co-BRST symmetry transformations for the (1+1)-dimensional (2D)
bosonized vector Schwinger model. In the derivation of above symmetries, we
invoke the (dual)-horizontality conditions as well as gauge and (anti-)co-BRST
invariant restrictions on the superfields that are defined onto the (2,
2)-dimensional supermanifold. We provide geometrical interpretation of the
above nilpotent symmetries (and their corresponding charges). We also express
the nilpotency and absolute anticommutativity of the (anti-)BRST and
(anti-)co-BRST charges within the framework of augmented superfield formalism.


title:
Detecting the Integer Decomposition Property and Ehrhart Unimodality in
  Reflexive Simplices

abstract:
  A long-standing open conjecture in combinatorics asserts that a Gorenstein
lattice polytope with the integer decomposition property (IDP) has a unimodal
(Ehrhart) $h^\ast$-polynomial. This conjecture can be viewed as a strengthening
of a previously disproved conjecture which stated that any Gorenstein lattice
polytope has a unimodal $h^\ast$-polynomial. The first counterexamples to
unimodality for Gorenstein lattice polytopes were given in even dimensions
greater than five by Musta{\c{t}}{\v{a}} and Payne, and this was extended to
all dimensions greater than five by Payne. While there exist numerous examples
in support of the conjecture that IDP reflexives are $h^\ast$-unimodal, its
validity has not yet been considered for families of reflexive lattice
simplices that closely generalize Payne's counterexamples. The main purpose of
this work is to prove that the former conjecture does indeed hold for a natural
generalization of Payne's examples. The second purpose of this work is to
extend this investigation to a broader class of lattice simplices, for which we
present new results and open problems.


title:
Dynamics of Large Boson Systems with Attractive Interaction and a
  Derivation of the Cubic Focusing NLS in $\mathbb{R}^3$

abstract:
  We consider a system of $N$ bosons where the particles experience a short
range two-body interaction given by $N^{-1}v_N(x)=N^{3\beta-1}v(N^\beta x)$
where $v \in C^\infty_c(\mathbb{R}^3)$, without a definite sign on $v$. We
extend the results of M. Grillakis and M. Machedon, Comm. Math. Phys.,
$\textbf{324}$, 601(2013) and E. Kuz, Differ. Integral Equ., $\textbf{137}$,
1613(2015) regarding the second-order correction to the mean-field evolution of
systems with repulsive interaction to systems with attractive interaction for
$0<\beta<\frac{1}{2}$. Our extension allows for a more general set of initial
data which includes coherent states. Inspired by the works of X. Chen and J.
Holmer, Arch. Ration. Mech. Anal., $\textbf{221}$, 631(2016) and Int. Math.
Res. Not., $\textbf{2017}$, 4173(2017), and P. T. Nam and M. Napi\'orkowski,
Adv. Theor. Math. Phys., $\textbf{21}$, 683(2017), we also provide both a
derivation of the focusing nonlinear Schr\"odinger equation (NLS) in $3$D from
the many-body system and its rate of convergence toward mean-field for
$0<\beta<\frac{1}{3}$. In particular, we give two derivations of the focusing
NLS, one based on the $N$-norm approximation given in the work of Nam and
Napi\'orkowski and the other via a method introduced in P. Pickl, J. Stat.
Phys., $\textbf{140}$, 76(2010). The techniques used in this article are
standard in the literature of dispersive PDEs. Nevertheless, the derivation of
the focusing NLS had only previously been studied for the 1D \& 2D cases and
conditionally answered for the 3D case for $0<\beta<\frac{1}{6}$.


title:
Projective Dimensions and Extensions of Modules from Titled to
  Cluster-Tilted Algebras

abstract:
  We study the module categories of a tilted algebra C and the corresponding
cluster-tilted algebra B. We investigate how various properties of a C-module
are affected when considered in the module category of B. We give a complete
classification of the projective dimension of a C-module inside the module
category of B. If a C-module M is rigid, we show two sufficient conditions for
M to be a rigid B-module. In particular, if M is an indecomposable and rigid
C-module, we prove M is always a rigid B-module.


title:
Black Phosphorus Plasmonics: Anisotropic Elliptical Propagation and
  Nonlocality-Induced Canalization

abstract:
  We investigate unusual surface plasmons polariton (SPP) propagation and
light-matter interactions in ultrathin black phosphorus (BP) films, a 2D
material that exhibits exotic electrical and physical properties due to its
extremely anisotropic crystal structure. Recently, it has been speculated that
the ultra-confined surface plasmons supported by BP may present various
topologies of wave propagation bands, ranging from anisotropic elliptic to
hyperbolic, across the mid- and near-infrared regions of the electromagnetic
spectrum. By carefully analyzing the natural nonlocal anisotropic optical
conductivity of BP, derived using the Kubo formalism and an effective
low-energy Hamiltonian, we demonstrate here that the SPP wavenumber cutoff
imposed by nonlocality prohibits that they acquire an arbitrary hyperbolic
topology, forcing operation in the canalization regime. The resulting
nonlocality-induced canalization presents interesting properties, as it is
inherently broadband, enables large light-matter interactions in the very near
field, and allows extreme device miniaturization. We also determine fundamental
bounds to the confinement of BP plasmons, which are significantly weaker than
for graphene, thus allowing a larger local density of states. Our results
confirm the potential of BP as a promising reconfigurable plasmonic platform,
with exciting applications, such as planar hyperlenses, optoelectronic
components, imaging, and communication systems.


title:
Extracting Majorana Properties in the Throat of Neutrinoless Double Beta
  Decay

abstract:
  Assuming that neutrinos are Majorana particles, we explore what information
can be inferred from future strong limits (i.e. non-observation) for
neutrinoless double beta decay. Specifically we consider the case where the
mass hierarchy is normal and the different contributions to the effective mass
$\langle m \rangle_{ee}$ partly cancel. We discuss how this fixes the two
Majorana CP phases simultaneously from the Majorana Triangle and how it limits
the lightest neutrino mass $m_1$ within a narrow window. The two Majorana CP
phases are in this case even better determined than in the usual case for
larger $\langle m \rangle_{ee}$. We show that the uncertainty in these
predictions can be significantly reduced by the complementary measurement of
reactor neutrino experiments, especially the medium baseline version
JUNO/RENO-50. We also estimate the necessary precision on $\langle m
\rangle_{ee}$ to infer non-trivial Majorana CP phases and the upper limit
$\langle m \rangle_{ee} \lesssim 1\,\mbox{meV}$ sets a target for the design of
future neutrinoless double beta decay experiments.


title: A Gauss--Newton iteration for Total Least Squares problems

abstract:
  The Total Least Squares solution of an overdetermined, approximate linear
equation $Ax \approx b$ minimizes a nonlinear function which characterizes the
backward error. We show that a globally convergent variant of the Gauss--Newton
iteration can be tailored to compute that solution. At each iteration, the
proposed method requires the solution of an ordinary least squares problem
where the matrix $A$ is perturbed by a rank-one term.


title: Physical limits to biomechanical sensing

abstract:
  Cells actively probe and respond to the stiffness of their surroundings.
Since mechanosensory cells in connective tissue are surrounded by a disordered
network of biopolymers, their in vivo mechanical environment can be extremely
heterogeneous. Here, we investigate how this heterogeneity impacts
mechanosensing by modeling the cell as an idealized local stiffness sensor
inside a disordered fiber network. For all types of networks we study,
including experimentally-imaged collagen and fibrin architectures, we find that
measurements applied at different points throughout a given network yield a
strikingly broad range of local stiffnesses, spanning roughly two decades. We
verify via simulations and scaling arguments that this broad range of local
stiffnesses is a generic property of disordered fiber networks, and show that
the range can be further increased by tuning specific network features,
including the presence of long fibers and the proximity to elastic transitions.
These features additionally allow for a highly tunable dependence of stiffness
on probe length. Finally, we show that to obtain optimal, reliable estimates of
global tissue stiffness, a cell must adjust its size, shape, and position to
integrate multiple stiffness measurements over extended regions of space.

categories: cond-mat.soft cond-mat.dis-nn physics.bio-ph q-bio.CB q-bio.TO


title:
Open-ended versus guided laboratory activities: Impact on students'
  beliefs about experimental physics

abstract:
  Improving students' understanding of the nature of experimental physics is
often an explicit or implicit goal of undergraduate laboratory physics courses.
However, lab activities in traditional lab courses are typically characterized
by highly structured, guided labs that often do not require or encourage
students to engage authentically in the process of experimental physics.
Alternatively, open-ended laboratory activities can provide a more authentic
learning environment by, for example, allowing students to exercise greater
autonomy in what and how physical phenomena are investigated. Engaging in
authentic practices may be a critical part of improving students' beliefs
around the nature of experimental physics. Here, we investigate the impact of
open-ended activities in undergraduate lab courses on students' epistemologies
and expectations about the nature of experimental physics, as well as their
confidence and affect, as measured by the Colorado Learning Attitudes about
Science Survey for Experimental Physics (E-CLASS). Using a national data set of
student responses to the E-CLASS, we find that the inclusion of some open-ended
lab activities in a lab course correlates with more expert-like postinstruction
responses relative to courses that include only traditional guided lab
activities. This finding holds when examining postinstruction E-CLASS scores
while controlling for the variance associated with preinstruction scores,
course level, student major, and student gender.


title:
Split-facets for Balanced Minimal Evolution Polytopes and the
  Permutoassociahedron

abstract:
  Understanding the face structure of the balanced minimal evolution (BME)
polytope, especially its top-dimensional facets, is crucially important to
phylogenetic applications. We show that BME polytope has a sub-lattice of its
poset of faces which is isomorphic to a quotient of the well-studied
permutoassociahedron. This sub-lattice corresponds to compatible sets of splits
displayed by phylogenetic trees, and extends the lattice of faces of the BME
polytope found by Hodge, Haws, and Yoshida. Each of the maximal elements in our
new poset of faces corresponds to a single split of the leaves. Nearly all of
these turn out to actually be facets of the BME polytope, a collection of
facets which grows exponentially.


title:
Radiation-induced mobility of small defect clusters in covalent
  materials

abstract:
  Although defect clusters are detrimental to electronic and mechanical
properties of semiconductor materials, annihilation of such clusters is limited
by their lack of thermal mobility due to high migration barriers. Here, we find
that small clusters in bulk SiC (a covalent material of importance for both
electronic and nuclear applications) can become mobile at room temperature
under the influence of electron radiation. So far, direct observation of
radiation-induced diffusion of defect clusters in bulk materials has not been
demonstrated yet. This finding was made possible by low angle annular dark
field (LAADF) scanning transmission electron microscopy (STEM) combined with
non-rigid registration technique to remove sample instability, which enables
atomic resolution imaging of small migrating defect clusters. We show that the
underlying mechanism of this athermal diffusion is ballistic collision between
incoming electrons and cluster atoms. Our findings suggest that defect clusters
may be mobile under certain irradiation conditions, changing current
understanding of cluster annealing process in irradiated covalent materials.


title:
Making maps of Cosmic Microwave Background polarization for B-mode
  studies: the POLARBEAR example

abstract:
  Analysis of cosmic microwave background (CMB) datasets typically requires
some filtering of the raw time-ordered data. Filtering is frequently used to
minimize the impact of low frequency noise, atmospheric contributions and/or
scan synchronous signals on the resulting maps. In this work we explicitly
construct a general filtering operator, which can unambiguously remove any set
of unwanted modes in the data, and then amend the map-making procedure in order
to incorporate and correct for it. We show that such an approach is
mathematically equivalent to the solution of a problem in which the sky signal
and unwanted modes are estimated simultaneously and the latter are marginalized
over. We investigate the conditions under which this amended map-making
procedure can render an unbiased estimate of the sky signal in realistic
circumstances. We then study the effects of time-domain filtering on the noise
correlation structure in the map domain, as well as impact it may have on the
performance of the popular pseudo-spectrum estimators. We conclude that
although maps produced by the proposed estimators arguably provide the most
faithful representation of the sky possible given the data, they may not
straightforwardly lead to the best constraints on the power spectra of the
underlying sky signal and special care may need to be taken to ensure this is
the case. By contrast, simplified map-makers which do not explicitly correct
for time-domain filtering, but leave it to subsequent steps in the data
analysis, may perform equally well and be easier and faster to implement. We
focus on polarization-sensitive measurements targeting the B-mode component of
the CMB signal and apply the proposed methods to realistic simulations based on
characteristics of an actual CMB polarization experiment, POLARBEAR.


title: Coarsening dynamics of zero-range processes

abstract:
  We consider a class of zero-range processes exhibiting a condensation
transition in the stationary state, with a critical single-site distribution
decaying faster than a power law. We present the analytical study of the
coarsening dynamics of the system on the complete graph, both at criticality
and in the condensed phase. In contrast with the class of zero-range processes
with critical single-site distribution decaying as a power law, in the present
case the role of finite-time corrections are essential for the understanding of
the approach to scaling.


title: Proving Infinitary Formulas

abstract:
  The infinitary propositional logic of here-and-there is important for the
theory of answer set programming in view of its relation to strongly equivalent
transformations of logic programs. We know a formal system axiomatizing this
logic exists, but a proof in that system may include infinitely many formulas.
In this note we describe a relationship between the validity of infinitary
formulas in the logic of here-and-there and the provability of formulas in some
finite deductive systems. This relationship allows us to use finite proofs to
justify the validity of infinitary formulas. This note is under consideration
for publication in Theory and Practice of Logic Programming.


title: Cut-and-join description of generalized Brezin-Gross-Witten model

abstract:
  We investigate the Brezin-Gross-Witten model, a tau-function of the KdV
hierarchy, and its natural one-parameter deformation, the generalized
Brezin-Gross-Witten tau-function. In particular, we derive the Virasoro
constraints, which completely specify the partition function. We solve them in
terms of the cut-and-join operator. The Virasoro constraints lead to the loop
equations, which we solve in terms of the correlation functions. Explicit
expressions for the coefficients of the tau-function and the free energy are
derived, and a compact formula for the genus zero contribution is conjectured.
A family of polynomial solutions of the KdV hierarchy, given by the Schur
functions, is obtained for the half-integer values of the parameter. The
quantum spectral curve and its classical limit are discussed.


title: Binarisation for Valued Constraint Satisfaction Problems

abstract:
  We study methods for transforming valued constraint satisfaction problems
(VCSPs) to binary VCSPs. First, we show that the standard dual encoding
preserves many aspects of the algebraic properties that capture the
computational complexity of VCSPs. Second, we extend the reduction of CSPs to
binary CSPs described by Bulin et al. [LMCS'15] to VCSPs. This reduction
establishes that VCSPs over a fixed valued constraint language are
polynomial-time equivalent to Minimum-Cost Homomorphism Problems over a fixed
digraph.


title: Few-body quantum physics with strongly interacting Rydberg polaritons

abstract:
  We present an extension of our recent paper [Bienias et al., Phys. Rev. A 90,
053804 (2014)] in which we demonstrated the scattering properties and
bound-state structure of two Rydberg polaritons, as well as the derivation of
the effective low-energy many-body Hamiltonian. Here, we derive a microscopic
Hamiltonian describing the propagation of Rydberg slow light polaritons in one
dimension. We describe possible decoherence processes within a Master equation
approach, and derive equations of motion in a Schroedinger picture by using an
effective non-Hermitian Hamiltonian. We illustrate diagrammatic methods on two
examples: First, we show the solution for a single polariton in an external
potential by exact summation of Feynman diagrams. Secondly, we solve the two
body problem in a weakly interacting regime exactly.


title:
Sharp local boundedness and maximum principle in the infinitely
  degenerate regime via DeGiorgi iteration

abstract:
  We obtain local boundedness and maximum principles for weak subsolutions to
certain infinitely degenerate elliptic divergence form equations, and the local
boundedness turns out to be sharp in more than two dimensions, answering the
`Moser gap' problem left open in arXiv:1506.09203v5. Finally we obtain a
maximum principle for weak solutions under the same condition on the
degeneracy.


title: Massless sector of AdS_3 superstrings: a geometric interpretation

abstract:
  We study the recently discovered q-deformed Poincare' supersymmetry of the
AdS_3/CFT_2 integrable massless scattering, and demonstrate how the S-matrix is
invariant under boosts. The boost generator has a non-local coproduct, which
acts on the scattering matrix as a differential operator, annihilating it. We
propose to reinterpret the boost action in terms of covariant derivatives on
bundles, and derive an expression for the S-matrix as the path-ordered
exponential of a flat connection. We provide a list of possible alternative
interpretations of this emergent geometric picture, including a one-dimensional
auxiliary Schroedinger problem. We support our claims by performing a
simplified algebraic Bethe ansatz, which bears some resemblance to
antiferromagnets.


title: Cooperation-based Routing in Cognitive Radio Networks

abstract:
  Primary user activity is a major bottleneck for existing routing protocols in
cognitive radio networks. Typical routing protocols avoid areas that are highly
congested with primary users, leaving only a small fragment of available links
for secondary route construction. In addition, wireless links are prone to
channel impairments such as multipath fading; which renders the quality of the
available links highly fluctuating. In this paper, we investigate using
cooperative communication mechanisms to reveal new routing opportunities,
enhance route qualities, and enable true coexistence of primary and secondary
networks. As a result, we propose Undercover: a cooperative routing protocol
that utilizes the available location information to assist in the routing
process. Specifically, our protocol revisits a fundamental assumption taken by
the state of the art routing protocols designed for cognitive radio networks.
Using Undercover, secondary users can transmit in the regions of primary users
activity through utilizing cooperative communication techniques to null out
transmission at primary receivers via beamforming. In addition, the secondary
links qualities are enhanced using cooperative diversity. To account for the
excessive levels of interference typically incurred due to cooperative
transmissions, we allow our protocol to be interference-aware. Thus,
cooperative transmissions are penalized in accordance to the amount of
negatively affected secondary flows. We evaluate the performance of our
proposed protocol via NS2 simulations which show that our protocol can enhance
the network goodput by a ratio reaches up to 250% compared to other popular
cognitive routing protocols with minimal added overhead.


title: Managing resonant trapped orbits in our Galaxy

abstract:
  Galaxy modelling is greatly simplified by assuming the existence of a global
system of angle-action coordinates. Unfortunately, global angle-action
coordinates do not exist because some orbits become trapped by resonances,
especially where the radial and vertical frequencies coincide. We show that in
a realistic Galactic potential such trapping occurs only on thick-disc and halo
orbits (speed relative to the guiding centre >~80 km/s). We explain how the
Torus Mapper code (TM) behaves in regions of phase space in which orbits are
resonantly trapped, and we extend TM so trapped orbits can be manipulated as
easily as untrapped ones. The impact that the resonance has on the structure of
velocity space depends on the weights assigned to trapped orbits. The impact is
everywhere small if each trapped orbit is assigned the phase space density
equal to the time average along the orbit of the DF for untrapped orbits. The
impact could be significant with a different assignment of weights to trapped
orbits.


title:
On-shell methods for off-shell quantities in N=4 Super Yang-Mills: from
  scattering amplitudes to form factors and the dilatation operator

abstract:
  Planar maximally supersymmetric Yang-Mills theory (N=4 SYM) is a special
quantum field theory. A few of its remarkable features are conformal symmetry
at the quantum level, evidence of integrability and, moreover, it is a prime
example of the AdS/CFT duality. Triggered by Witten's twistor string theory,
the past 15 years have witnessed enormous progress in reformulating this theory
to make as many of these special features manifest, from the choice of
convenient variables to recursion relations that allowed new mathematical
structures to appear, like the Grassmannian. These methods are collectively
referred to as on-shell methods. The ultimate hope is that, by understanding
N=4 SYM in depth, one can learn about other, more realistic quantum field
theories. The overarching theme of this thesis is the investigation of how
on-shell methods can aid the computation of quantities other than scattering
amplitudes. In this spirit we study form factors and correlation functions,
said to be partially and completely off-shell quantities, respectively. More
explicitly, we compute form factors of half-BPS operators up to two loops, and
study the dilatation operator in the SO(6) and SU(2|3) sectors using techniques
originally designed for amplitudes. A second part of the work is dedicated to
the study of scattering amplitudes beyond the planar limit, an area of research
which is still in its infancy, and not much is known about which special
features of the planar theory survive in the non-planar regime. In this
context, we generalise some aspects of the on-shell diagram formulation of
Arkani-Hamed et al. to take into account non-planar corrections.


title: Unrectifiable normal currents in Euclidean spaces

abstract:
  We construct in $\mathbb{R}^{k+2}$ a $k$-dimensional simple normal current
whose support is purely $2$-unrectifiable. The result is sharp because the
support of a normal current cannot be purely $1$-unrectifiable and a
$(k+1)$-dimensional normal current can be represented as an integral of
$(k+1)$-rectifiable currents. This gives a negative answer to the (revised
version) of a question of Frank Morgan (1984).


title: On the criteria for integrability of the Li\'{e}nard equation

abstract:
  The Li\'{e}nard equation is of a high importance from both mathematical and
physical points of view. However a question about integrability of this
equation has not been completely answered yet. Here we provide a new criterion
for integrability of the Li\'{e}nard equation using an approach based on
nonlocal transformations. We also obtain some of previously known criteria for
integrability of the Li\'{e}nard equation as a straightforward consequences of
our approach's application. We illustrate our results by several new examples
of integrable Li\'{e}nard equations.


title:
The Mechanism Behind Beauty: Golden Ratio Appears in Red Blood Cell
  Shape

abstract:
  In the past two decades, under the conditions that both the osmotic pressure
$\Delta p$ and tensile stress $\lambda$ equal zero, a rigorous solution (RS) of
human red blood cell (RBC) with a minus spontaneous curvature $c_{0}$ has been
derived with Helfrich model. And, by fitting with observed shapes of RBC,
$c_{0}R_{0}$ has been predicted to be -1.62 as minus golden ratio, where
$R_{0}$ is the radius of a sphere with the same area of RBC. In this Lett., it
is also found $\rho_{max}$ /$\rho_{B}\approx$ 1.6 shows a approximately
beautiful golden cross section of RBC, where $\rho_{max}$ is the radius of RBC
and $\rho_{B}$ is the radius at maximal thickness of RBC. With a complete
numerical calculation, we find the mechanism behind the beauty that minus
golden ratio of $c_{0}R_{0}$ is the balance between economical surface area and
enough deformability to pass spleen, the so called "physical fitness test".


title:
A Modified Stern-Gerlach Experiment Using a Quantum Two-State Magnetic
  Field

abstract:
  The Stern-Gerlach experiment has played an important role in our
understanding of quantum behavior. We propose and analyze a modified version of
this experiment where the magnetic field of the detector is in a quantum
superposition, which may be experimentally realized using a superconducting
flux qubit. We show that if incident spin-$1/2$ particles couple with the
two-state magnetic field, a discrete target distribution results that resembles
the distribution in the classical Stern-Gerlach experiment. As an application
of the general result, we compute the distribution for a square waveform of the
incident fermion. This experimental setup allows us to establish: (1) the
quantization of the intrinsic angular momentum of a spin-$1/2$ particle, and
(2) a correlation between EPR pairs leading to nonlocality, without necessarily
collapsing the particle's spin wavefunction.


title:
The attribute of rotational profile to the hyperon puzzle in the
  prediction of heaviest compact star

abstract:
  In this theoretical study, we report an investigation of the equations of
state (EoSs) ofhyper-nuclear matter and its composition as a function of
density within the framework of effective field theory motivated relativistic
mean field model. We have used G2 force parameter along with various
hyperon-meson coupling ratios by allowing the mixing and the breaking of SU(6)
symmetry to predict the EoSs, keeping the nucleonic coupling constant intact.
We have estimated the properties of non-rotating and rapidly rotating
configuration of compact stars by employing four different representative sets
of equations of state. The obtained results of the mass and radius for the
compact stars are compared with the recent mass observations. Further, we have
studied the stability and sensitivity of rotational frequency (at
sub-millisecond period) on the configuration of the compact stars, because the
angular frequency is significantly smaller than the mass-shedding (Keplerian)
frequency in slow rotation regime. Moreover, the yield of hyperon as a function
of density for various hyperon-meson couplings are also estimated.


title: Comment on "Particle Path Through a Nested Mach-Zehnder Interferometer"

abstract:
  In a recent paper, arXiv:1604.04596, Griffiths questioned - based on an
informative consistent-histories (CH) argument - the counterfactuality, for one
of the bit choices, of Salih et al.'s protocol for communicating without
sending physical particles, Phys. Rev. Lett. 110, 170502 (2013). Here, we first
show that for the Mach-Zehnder version used to explain our protocol, no family
of consistent histories exists where any history has the photon travelling
through the communication channel, thus rendering the question of whether the
photon was in the communication channel meaningless from a CH viewpoint. We
then show that for the actual Michelson-type protocol, there are
consistent-histories families that include histories where the photon travels
through the communication channel. We show that the probability of finding the
photon in the communication channel is zero - thus proving complete
counterfactuality.


title: Holonomic modules over Cherednik algebras, I

abstract:
  The goal of this paper is to generalize several basic results from the theory
of $\cal{D}$-modules to the representation theory of rational Cherednik
algebras. We relate characterizations of holonomic modules in terms of singular
support and Gelfand-Kirillov dimension. We study pullback, pushforward, and
dual on the derived category of (holonomic) Cherednik modules for certain
classes of maps between varieties. We prove, in the case of generic parameters
for the rational Cherednik algebra, that pushforward with respect to an open
affine inclusion preserves holonomicity.


title: Extending the graviton propagator with a Lorentz-violating vector field

abstract:
  I discuss progress towards "bootstrapping" a Lorentz-violating gravity
theory: namely, extending a linear Lorentz-violating theory of a rank-2 tensor
to a non-linear theory by coupling this field to its own stress-energy tensor.