title: Universal anyons at the irradiated surface of topological insulator

abstract:
  Anyons have recently received great attention due to their promising
application in topological quantum computation. The best validated system that
enjoys the anyonic excitations are the Laughlin states. The quasi-particles in
Laughlin states are neither fermions nor bosons but possess the discrete
statistical angle ? = ?=m, with m being an integer. Here we report a possible
realization of the universal Abelian anyons, whose statistical angle can be
tuned continuously by external parameters and can take any arbitrary values
interpolating ? = 0 and ? = ?. The proposed setup is the surface state of a
three dimensional topological insulator driven by an amplitude-modulated
circularly-polarized light. It is found that the external field leads to a
particular Floquet phase, which is a two-spatial-dimensional analogy of the
Weyl semimetal phase in the Floquet first Brillouin zone. The chiral anomaly of
this phase results in a U(1) Chern-Simons gauge theory with a tunable Floquet
Chern number. Owing to this underlying gauge field theory, the irradiated
surface of topological insulator constitutes a promising platform for the
observation of the universal anyons.


title:
Daily variability of Ceres' Albedo detected by means of radial
  velocities changes of the reflected sunlight

abstract:
  Bright features have been recently discovered by Dawn on Ceres, which extend
previous photometric and Space Telescope observations. These features should
produce distortions of the line profiles of the reflected solar spectrum and
therefore an apparent radial velocity variation modulated by the rotation of
the dwarf planet. Here we report on two sequences of observations of Ceres
performed in the nights of 31 July, 26-27 August 2015 by means of the
high-precision HARPS spectrograph at the 3.6-m La Silla ESO telescope. The
observations revealed a quite complex behaviour which likely combines a radial
velocity modulation due to the rotation with an amplitude of approx +/- 6 m/s
and an unexpected diurnal effect. The latter changes imply changes in the
albedo of Occator's bright features due to the blaze produced by the exposure
to solar radiation. The short-term variability of Ceres' albedo is on
timescales ranging from hours to months and can both be confirmed and followed
by means of dedicated radial velocity observations.


title:
Articulated Clinician Detection Using 3D Pictorial Structures on RGB-D
  Data

abstract:
  Reliable human pose estimation (HPE) is essential to many clinical
applications, such as surgical workflow analysis, radiation safety monitoring
and human-robot cooperation. Proposed methods for the operating room (OR) rely
either on foreground estimation using a multi-camera system, which is a
challenge in real ORs due to color similarities and frequent illumination
changes, or on wearable sensors or markers, which are invasive and therefore
difficult to introduce in the room. Instead, we propose a novel approach based
on Pictorial Structures (PS) and on RGB-D data, which can be easily deployed in
real ORs. We extend the PS framework in two ways. First, we build robust and
discriminative part detectors using both color and depth images. We also
present a novel descriptor for depth images, called histogram of depth
differences (HDD). Second, we extend PS to 3D by proposing 3D pairwise
constraints and a new method that makes exact inference tractable. Our approach
is evaluated for pose estimation and clinician detection on a challenging RGB-D
dataset recorded in a busy operating room during live surgeries. We conduct
series of experiments to study the different part detectors in conjunction with
the various 2D or 3D pairwise constraints. Our comparisons demonstrate that 3D
PS with RGB-D part detectors significantly improves the results in a visually
challenging operating environment.


title: Generating functions for purely crossing partitions

abstract:
  The generating function for the number of purely crossing partitions of
{1,...,n} is found in terms of the generating function for Bell numbers.
Further results about generating functions for asymptotic moments of certain
random Vandermonde matrices are derived.


title:
Note on "Diffusive quantum criticality in three-dimensional disordered
  Dirac semimetals"

abstract:
  We correct erroneous conclusions from Ref.[1] regarding the values of various
critical exponents, calculated to the two-loop order, and argue that
$\epsilon$-expansion near two spatial dimension, with $\epsilon=d-2$ may not be
reliable to address the critical properties of disorder driven Dirac
semimetal-metal quantum phase transition in $d=3$.


title: Improved group testing rates with constant column weight designs

abstract:
  We consider nonadaptive group testing where each item is placed in a constant
number of tests. The tests are chosen uniformly at random with replacement, so
the testing matrix has (almost) constant column weights. We show that
performance is improved compared to Bernoulli designs, where each item is
placed in each test independently with a fixed probability. In particular, we
show that the rate of the practical COMP detection algorithm is increased by
31% in all sparsity regimes. In dense cases, this beats the best possible
algorithm with Bernoulli tests, and in sparse cases is the best proven
performance of any practical algorithm. We also give an algorithm-independent
upper bound for the constant column weight case; for dense cases this is again
a 31% increase over the analogous Bernoulli result.


title: Far-infrared study of tracers of oxygen chemistry in diffuse clouds

abstract:
  Context. The chemistry of the diffuse interstellar medium rests upon three
pillars: exothermic ion-neutral reactions (" cold chemistry "), endothermic
neutral-neutral reactions with significant activation barriers (" warm
chemistry "), and reactions on the surfaces of dust grains. While warm
chemistry becomes important in the shocks associated with turbulent dissipation
regions, the main path for the formation of interstellar OH and H2O is that of
cold chemistry. Aims. The aim of this study is to observationally confirm the
association of atomic oxygen with both atomic and molecular gas phases, and to
understand the measured abundances of OH and OH + as a function of the
available reservoir of H2. Methods. We obtained absorption spectra of the
ground states of OH, OH+ and OI with high-velocity resolution, with GREAT
on-board SOFIA, and with the THz receiver at the APEX. We analyzed them along
with ancillary spectra of HF and CH from HIFI. To deconvolve them from the
hyperfine structure and to separate the blend that is due to various velocity
components on the sightline, we fit model spectra consisting of an appropriate
number of Gaussian profiles using a method combining simulated annealing with
downhill simplex minimization. Together with HF and/or CH as a surrogate for
H2, and HI $\lambda$21 cm data, the molecular hydrogen fraction f^N\_H2 = N(H
2)/(N(H) + 2N(H 2)) can be determined. We then investigated abundance ratios as
a function of f^N\_H2. Results. The column density of OI is correlated at a
high significance with the amount of available molecular and atomic hydrogen,
with an atomic oxygen abundance of $3 \times 10 ^{-4}$ relative to H nuclei.
While the velocities of the absorption features of OH and OH+ are loosely
correlated and reflect the spiral arm crossings on the sightline, upon closer
inspection they display an anticorrespondence. The arm-to-interarm density
contrast is found to be higher in OH than in OH+. While both species can
coexist, with a higher abundance in OH than in OH+, the latter is found less
frequently in absence of OH than the other way around, which is a direct
consequence of the rapid destruction of OH+ by dissociative recombination when
not enough H2 is available. This conjecture has been substantiated by a
comparison between the OH/OH+ ratio with f^N\_H2, showing a clear correlation.
The hydrogen abstraction reaction chain OH+ (H2,H) H2O+ (H2,H)H3O+ is confirmed
as the pathway for the production of OH and H 2 O. Our estimate of the
branching ratio of the dissociative recombination of H3O+ to OH and H2O is
confined within the interval of 84 to 91%, which matches laboratory
measurements (74 to 83%). -- A correlation between the linewidths and column
densities of OH+ features is found to be significant with a false-alarm
probability below 5%. Such a correlation is predicted by models of interstellar
MHD turbulence. For OH the same correlation is found to be insignificant
because there are more narrow absorption features. Conclusions. While it is
difficult to assess the contributions of warm neutral-neutral chemistry to the
observed abundances, it seems fair to conclude that the predictions of cold
ion-neutral chemistry match the abundance patterns we observed.


title: New results on sum-products in R

abstract:
  We improve a previous sum--products estimates in R, namely, we obtain that
max{|A+A|,|AA|} \gg |A|^{4/3+c}, where c any number less than 5/9813. New lower
bounds for sums of sets with small the product set are found. Also we prove
some pure energy sum--products results, improving a result of Balog and Wooley,
in particular.


title: On a linear runs and tumbles equation

abstract:
  We consider a linear runs and tumbles equation in dimension d $\ge$ 1 for
which we establish the existence of a unique positive and normalized steady
state as well as its asymptotic stability, improving similar results obtained
by Calvez et al. [5] in dimension d = 1. Our analysis is based on the
Krein-Rutman theory revisited in [18] together with some new moment estimates
for proving confinement mechanism as well as dispersion, multiplicator and
averaging lemma arguments for proving some regularity property of suitable
iterated averaging quantities.


title:
The Scientific and Historical Value of Annotations on Astronomical
  Photographic Plates

abstract:
  The application of photography to astronomy was a critical step in the
development of astrophysics at the end of the nineteenth century. Using
custom-built photographic telescopes and objective prisms, astronomers took
images of the sky on glass plates during a 100-year period from many observing
stations around the globe. After each plate was developed, astronomers and
their assistants studied and annotated the plates as they made astrometric,
photometric and spectroscopic measurements, counted galaxies, observed stellar
variability, tracked meteors, and calculated the ephemerides of asteroids and
comets. In this paper, the authors assess the importance of the plate
annotations for future scientific, historical, and educational programs.
Unfortunately, many of these interesting annotations are now being erased when
grime is removed from the plates before they are digitized to make the
photometric data available for time-domain astrophysics. To see what
professional astronomers and historians think about this situation, the authors
conducted a survey. This paper captures the lively discussion on the pros and
cons of the removal of plate markings, how to best to document them if they
must be cleaned off, and what to do with plates whose annotations are deemed
too valuable to be erased. Three appendices to the paper offer professional
guidance on the best practices for handling and cleaning the plates,
photographing any annotations, and rehousing them.


title:
Conditional Dependence via Shannon Capacity: Axioms, Estimators and
  Applications

abstract:
  We conduct an axiomatic study of the problem of estimating the strength of a
known causal relationship between a pair of variables. We propose that an
estimate of causal strength should be based on the conditional distribution of
the effect given the cause (and not on the driving distribution of the cause),
and study dependence measures on conditional distributions. Shannon capacity,
appropriately regularized, emerges as a natural measure under these axioms. We
examine the problem of calculating Shannon capacity from the observed samples
and propose a novel fixed-$k$ nearest neighbor estimator, and demonstrate its
consistency. Finally, we demonstrate an application to single-cell
flow-cytometry, where the proposed estimators significantly reduce sample
complexity.


title: Propagators of random walks on comb lattices of arbitrary dimension

abstract:
  We study diffusion on comb lattices of arbitrary dimension. Relying on the
loopless structure of these lattices and using first-passage properties, we
obtain exact and explicit formulae for the Laplace transforms of the
propagators associated to nearest-neighbour random walks in both cases where
either the first or the last point of the random walk is on the backbone of the
lattice, and where the two extremities are arbitrarily chosen. As an
application, we compute the mean-square displacement of a random walker on a
comb of arbitrary dimension. We also propose an alternative and consistent
approach of the problem using a master equation description, and obtain simple
and generic expressions of the propagators. This method is more general and is
extended to study the propagators of random walks on more complex comb-like
structures. In particular, we study the case of a two-dimensional comb lattice
with teeth of finite length.


title: Induced Gravity and Topological Quantum Field Theory

abstract:
  We construct an induced gravity (pregeometry) where both the Newton constant
and the cosmological constant appear as integration constants in solving field
equations. By adding the kinetic terms of ghosts and antighosts, an action of
the induced gravity is transformed to a topological field theory. Moreover, by
solving field equations of the topological field theory in the FRW universe, we
find an inflation solution. The present study might shed some light on a close
relationship between the induced gravity and the topological quantum field
theory.


title:
Commutators and Cartan subalgebras in Lie algebras of compact semisimple
  Lie groups

abstract:
  First we give a new proof of Goto's theorem for Lie algebras of compact
semisimple Lie groups using Coxeter transformations. Namely, every $x$ in $L =
\operatorname{Lie}(G)$ can be written as $x =[a, b]$ for some $a$, $b$ in $L$.
By using the same method, we give a new proof of the following theorem (thus
avoiding the classification tables of fundamental weights): in compact
semisimple Lie algebras, orthogonal Cartan subalgebras always exist (where one
of them can be chosen arbitrarily). Some of the consequences of this theorem
are the following. $(i)$ If $L=\operatorname{Lie}(G)$ is such a Lie algebra and
$C$ is any Cartan subalgebra of $L$, then the $G$-orbit of $C^{\perp}$ is all
of $L$. $(ii)$ The consequence in part $(i)$ answers a question by L. Florit
and W. Ziller on fatness of certain principal bundles. It also shows that in
our case, the commutator map $L \times L \to L$ is open at $(0, 0)$. $(iii)$
given any regular element $x$ of $L$, there exists a regular element $y$ such
that $L = [x, L] + [y,L]$ and $x$, $y$ are orthogonal. Then we generalize this
result about compact semisimple Lie algebras to the class of non-Hermitian real
semisimple Lie algebras having full rank.
  Finally, we survey some recent related results , and construct explicitly
orthogonal Cartan subalgebras in $\mathfrak{su}(n)$, $\mathfrak{sp}(n)$,
$\mathfrak{so}(n)$.


title: Representations and geometric structures

abstract:
  This note summarizes in an informal way some geometric properties of Anosov
representations into the symplectic group, which were presented in a talk at
the conference What is Next. The mathematical legacy of Bill Thurston, held in
June 2014 in Cornell.


title: Achieving Budget-optimality with Adaptive Schemes in Crowdsourcing

abstract:
  Crowdsourcing platforms provide marketplaces where task requesters can pay to
get labels on their data. Such markets have emerged recently as popular venues
for collecting annotations that are crucial in training machine learning models
in various applications. However, as jobs are tedious and payments are low,
errors are common in such crowdsourced labels. A common strategy to overcome
such noise in the answers is to add redundancy by getting multiple answers for
each task and aggregating them using some methods such as majority voting. For
such a system, there is a fundamental question of interest: how can we maximize
the accuracy given a fixed budget on how many responses we can collect on the
crowdsourcing system. We characterize this fundamental trade-off between the
budget (how many answers the requester can collect in total) and the accuracy
in the estimated labels. In particular, we ask whether adaptive task assignment
schemes lead to a more efficient trade-off between the accuracy and the budget.
  Adaptive schemes, where tasks are assigned adaptively based on the data
collected thus far, are widely used in practical crowdsourcing systems to
efficiently use a given fixed budget. However, existing theoretical analyses of
crowdsourcing systems suggest that the gain of adaptive task assignments is
minimal. To bridge this gap, we investigate this question under a strictly more
general probabilistic model, which has been recently introduced to model
practical crowdsourced annotations. Under this generalized Dawid-Skene model,
we characterize the fundamental trade-off between budget and accuracy. We
introduce a novel adaptive scheme that matches this fundamental limit. We
further quantify the fundamental gap between adaptive and non-adaptive schemes,
by comparing the trade-off with the one for non-adaptive schemes. Our analyses
confirm that the gap is significant.


title:
On the self-excitation mechanisms of Plasma Series Resonance
  oscillations in single- and multi-frequency capacitive discharges

abstract:
  The self-excitation of plasma series resonance (PSR) oscillations is a
prominent feature in the current of low pressure capacitive radio frequency
(RF) discharges. This resonance leads to high frequency oscillations of the
charge in the sheaths and enhances electron heating. Up to now, the phenomenon
has only been observed in asymmetric discharges. There, the nonlinearity in the
voltage balance, which is necessary for the self-excitation of resonance
oscillations with frequencies above the applied frequencies, is caused
predominantly by the quadratic contribution to the charge-voltage relation of
the plasma sheaths. Using PIC/MCC simulations of single- and multi- frequency
capacitive discharges and an equivalent circuit model, we demonstrate that
other mechanisms such as a cubic contribution to the charge-voltage relation of
the plasma sheaths and the time dependent bulk electron plasma frequency can
cause the self-excitation of PSR oscillations, as well. These mechanisms have
been neglected in previous models, but are important for the theoretical
description of the current in symmetric or weakly asymmetric discharges.


title: Learning Distributed Representations of Sentences from Unlabelled Data

abstract:
  Unsupervised methods for learning distributed representations of words are
ubiquitous in today's NLP research, but far less is known about the best ways
to learn distributed phrase or sentence representations from unlabelled data.
This paper is a systematic comparison of models that learn such
representations. We find that the optimal approach depends critically on the
intended application. Deeper, more complex models are preferable for
representations to be used in supervised systems, but shallow log-linear models
work best for building representation spaces that can be decoded with simple
spatial distance metrics. We also propose two new unsupervised
representation-learning objectives designed to optimise the trade-off between
training time, domain portability and performance.


title: Nontrivial rheological exponents in sheared yield stress fluids

abstract:
  In this work we discuss possible physical origins for non-trivial exponents
in the athermal rheology of soft materials at low but finite driving rates. A
key ingredient in our scenario is the presence of a self-consistent mechanical
noise that stems from the spatial superposition of long-range elastic responses
to localized plastically deforming regions. We study analytically a mean-field
model, in which this mechanical noise is accounted for by a stress diffusion
term coupled to the plastic activity. Within this description we show how a
dependence of the shear modulus and/or the local relaxation time on the shear
rate introduces corrections to the usual mean-field prediction, concerning the
Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the
mean-field picture is then shown to be robust with respect to structural
disorder and partial relaxation of the local stress. We test this prediction
numerically on a mesoscopic lattice model that implements explicitly the
long-range elastic response to localized shear transformations, and we conclude
on how our scenario might be tested in rheological experiments.


title:
Orientational ordering of confined hard rods: the effect of shape
  anisotropy on surface ordering and capillary nematization

abstract:
  We examine the ordering properties of rectangular hard rods with length L and
diameter D at a single planar wall and between two parallel hard walls using
the second-virial density functional theory. The theory is implemented in the
three-state Zwanzig approximation, where only three mutually perpendicular
directions are allowed for the orientations of hard rods. The effect of varying
shape anisotropy is examined at L/D=10, 15 and 20. In contact with a single
hard wall, the density profiles show planar ordering, damped oscillatory
behavior, and wall induced surface ordering transition below the coexisting
isotropic density of bulk isotropic-nematic (I-N) phase transition. Upon
approaching the coexisting isotropic density, the thickness of nematic film
diverges logarithmically, i.e. the nematic wetting is complete for any shape
anisotropy. In the case of confinement between two parallel hard walls, it is
found that the continuous surface ordering transition depends strongly on the
distance between confining walls (H) for H<L, while it depends weakly on H for
H>L. The minimal density at which a surface ordering transition can be realized
is located at around H~2D for all studied shape anisotropies due to the strong
interference effect between the two hard walls. The first order I-N phase
transition of the bulk system becomes surface ordered isotropic (IB)-capillary
nematic (NB) phase transition in the slit pore. This first order IB-NB
transition weakens with decreasing pore width and terminates in a critical
point for all studied shape anisotropies.


title: On $\zeta(2n)$. Even simpler

abstract:
  We solve an interpolation problem for computing $\zeta(2n)$ in a rather
elementary way, by generalizing the main idea in \cite{SE}.


title: Entanglement between two scalar fields in an expanding spacetime

abstract:
  We study the evolution of the two scalar fields entangled via a mutual
interaction in an expanding spacetime. We compute the logarithmic negativity to
leading order in perturbation theory and show that for lowest order in the
coupling constants, the mutual interaction will give rise to the survival of
the quantum correlations in the limit of the smooth expansion. The results
suggest that interacting fields can codify more information about the
underlying expansion spacetime and lead to interesting observable effects.


title: Measuring the Distribution and Excitation of Cometary CH3OH Using ALMA

abstract:
  The Atacama Large Millimeter/submillimeter Array (ALMA) was used to obtain
measurements of spatially and spectrally resolved CH$_3$OH emission from comet
C/2012 K1 (PanSTARRS) on 28-29 June 2014. Detection of 12-14 emission lines of
CH$_3$OH on each day permitted the derivation of spatially-resolved rotational
temperature profiles (averaged along the line of sight), for the innermost 5000
km of the coma. On each day, the CH$_3$OH distribution was centrally peaked and
approximately consistent with spherically symmetric, uniform outflow. The
azimuthally-averaged CH$_3$OH rotational temperature ($T_{rot}$) as a function
of sky-projected nucleocentric distance ($\rho$), fell by about 40 K between
$\rho=0$ and 2500 km on 28 June, whereas on 29 June, $T_{rot}$ fell by about 50
K between $\rho=$0 km and 1500 km. A remarkable ($\sim50$ K) rise in $T_{rot}$
at $\rho=$1500-2500 km on 29 June was not present on 28 June. The observed
variations in CH$_3$OH rotational temperature are interpreted primarily as a
result of variations in the coma kinetic temperature due to adiabatic cooling,
and heating through Solar irradiation, but collisional and radiative non-LTE
excitation processes also play a role.


title:
Results on the Spin-Dependent Scattering of Weakly Interacting Massive
  Particles on Nucleons from the Run 3 Data of the LUX Experiment

abstract:
  We present the first experimental constraints on the spin-dependent
WIMP-nucleon elastic cross sections from LUX data acquired in 2013. LUX is a
dual-phase xenon time projection chamber operating at the Sanford Underground
Research Facility (Lead, South Dakota), which is designed to observe the recoil
signature of galactic WIMPs scattering from xenon nuclei. A profile likelihood
ratio analysis of $1.4~\times~10^{4}~\text{kg}\cdot~\text{days}$ of fiducial
exposure allows 90% CL upper limits to be set on the WIMP-neutron (WIMP-proton)
cross section of $\sigma_n~=~9.4~\times~10^{-41}~\text{cm}^2$
($\sigma_p~=~2.9~\times~10^{-39}~\text{cm}^2$) at 33 GeV/c$^2$. The
spin-dependent WIMP-neutron limit is the most sensitive constraint to date.


title: Tremain equiangular tight frames

abstract:
  Equiangular tight frames provide optimal packings of lines through the
origin. We combine Steiner triple systems with Hadamard matrices to produce a
new infinite family of equiangular tight frames. This in turn leads to new
constructions of strongly regular graphs and distance-regular antipodal covers
of the complete graph.


title:
Non-equilibrium dynamics of non-linear Jaynes-Cummings model in cavity
  arrays

abstract:
  We analyze in detail an open cavity array using mean-field description, where
each cavity field is coupled to a number of three-level atoms. Such system is
highly tunable and can be described by a Jaynes-Cummings like Hamiltonian with
additional non-linear terms. In the single cavity case we provide simple
analytic solutions and show, that the system features a bistable region. The
extra non-linear term gives rise to a rich dynamical behaviour including
occurrence of limit cycles through Hopf bifurcations. In the limit of large
non-linearity, the system exhibits an Ising like phase transition as the
coupling between light and matter is varied. We then discuss how these results
extend to the two-dimensional case.


title: Wishart--Pickrell distributions and closures of group actions

abstract:
  Consider probabilistic distributions on the space of infinite Hermitian
matrices $Herm(\infty)$ invariant with respect to the unitary group
$U(\infty)$. We describe the closure of $U(\infty)$ in the space of spreading
maps (polymorphisms) of $Herm(\infty)$, this closure is a semigroup isomorphic
to the semigroup of all contractive operators.


title: Winning versus losing during gambling and its neural correlates

abstract:
  Humans often make decisions which maximize an internal utility function. For
example, humans often maximize their expected reward when gambling and this is
considered as a "rational" decision. However, humans tend to change their
betting strategies depending on how they "feel". If someone has experienced a
losing streak, they may "feel" that they are more likely to win on the next
hand even though the odds of the game have not changed. That is, their
decisions are driven by their emotional state. In this paper, we investigate
how the human brain responds to wins and losses during gambling. Using a
combination of local field potential recordings in human subjects performing a
financial decision-making task, spectral analyses, and non-parametric cluster
statistics, we investigated whether neural responses in different cognitive and
limbic brain areas differ between wins and losses after decisions are made. In
eleven subjects, the neural activity modulated significantly between win and
loss trials in one brain region: the anterior insula ($p=0.01$). In particular,
gamma activity (30-70 Hz) increased in the anterior insula when subjects just
realized that they won. Modulation of metabolic activity in the anterior insula
has been observed previously in functional magnetic resonance imaging studies
during decision making and when emotions are elicited. However, our study is
able to characterize temporal dynamics of electrical activity in this brain
region at the millisecond resolution while decisions are made and after
outcomes are revealed.


title:
Time and Frequency Domain Investigation of Selected Memristor based
  Analog Circuits

abstract:
  In this paper, we investigate few memristor-based analog circuits namely the
phase shift oscillator, integrator, and differentiator which have been explored
numerously using the traditional lumped components. We use LTspice-IV platform
for simulation of the above-said circuits. The investigation resorts to the
nonlinear dopant drift model of memristor and the window function portrayed in
the literature for nonlinearity realization. The results of our investigations
depict good agreement with the conventional lumped component based phase shift
oscillator, integrator, and differentiator circuits. The results are evident to
showcase the potential of the memristor as a promising candidate for the next
generation analog circuits.


title: Comments on New Ontology of Quantum Mechanics called CSM

abstract:
  A new quantum ontology of quantum mechanics has been proposed recently. This
ontology is based on impossible to realize measurements which need to be
performed repeatedly on the same single physical system or on the same pair of
physical systems. We agree that quantum mechanics is a contextual theory and
that the experimental contexts have to be a part of any description of quantum
phenomena but in our opinion this new ontology is neither convincing nor
useful. In particular the authors claim that their ontology explains the
peaceful coexistence between quantum mechanics and relativity in spin
polarization correlation experiments. We show that, contrary to their claim,
the authors are unable to explain why strong correlations, between the outcomes
of distant local measurements, do exist and why they preserve a condition of
parameter independence (non-signaling). Strangely enough the authors ignore
that these strong but imperfect correlations can be explained in a local and
causal way using statistical contextual interpretation of quantum mechanics
what was demonstrated in several articles.


title: A computational approach to Milnor fiber cohomology

abstract:
  In this note we consider the Milnor fiber $F$ associated to a reduced
projective plane curve $C$. A computational approach for the determination of
the characteristic polynomial of the monodromy action on the first cohomology
group of $F$, also known as the Alexander polynomial of the curve $C$, is
presented. This leads to an effective algorithm to detect all the monodromy
eigenvalues and, in many cases, explicit bases for the monodromy eigenspaces in
terms of polynomial differential forms.


title: Tau Now

abstract:
  UHECR and UHE neutrino map correlation seem to most inconclusive. We show
here that a few peculiar UHECR narrow clustering might be connected to a first
UHE muon neutrino tracks. Moreover we discuss the best filtered and amplified
UHE neutrino astronomy painted by up-going tau airshower. Their discover by new
projects could be reached soon.

categories: astro-ph.HE astro-ph.CO astro-ph.IM hep-ph


title: Analog Coding of a Source with Erasures

abstract:
  Analog coding decouples the tasks of protecting against erasures and noise.
For erasure correction, it creates an "analog redundancy" by means of
band-limited discrete Fourier transform (DFT) interpolation, or more generally,
by an over-complete expansion based on a frame. We examine the analog coding
paradigm for the dual setup of a source with "erasure" side-information (SI) at
the encoder. The excess rate of analog coding above the rate-distortion
function (RDF) is associated with the energy of the inverse of submatrices of
the frame, where each submatrix corresponds to a possible erasure pattern. We
give a partial theoretical as well as numerical evidence that a variety of
structured frames, in particular DFT frames with difference-set spectrum and
more general equiangular tight frames (ETFs), with a common MANOVA limiting
spectrum, minimize the excess rate over all possible frames. However, they do
not achieve the RDF even in the limit as the dimension goes to infinity.


title: Capacity of the range of random walk on $\mathbb{Z}^d$

abstract:
  We study the capacity of the range of a transient simple random walk on
$\mathbb{Z}^d$. Our main result is a central limit theorem for the capacity of
the range for $d\ge 6$. We present a few open questions in lower dimensions.


title: Primes in arithmetic progressions to spaced moduli.III

abstract:
  We obtain the analog of the Bombieri-Vinogradov theorem for square moduli up
to any power of x less than 1/2.


title: Algebraic Databases

abstract:
  Databases have been studied category-theoretically for decades. The database
schema---whose purpose is to arrange high-level conceptual entities---is
generally modeled as a category or sketch. The data itself, often called an
instance, is generally modeled as a set-valued functor, assigning to each
conceptual entity a set of examples. While mathematically elegant, these
categorical models have typically struggled with representing concrete data
such as integers or strings.
  In the present work, we propose an extension of the set-valued functor model,
making use of multisorted algebraic theories (a.k.a. Lawvere theories) to
incorporate concrete data in a principled way. This also allows constraints and
queries to make use of operations on data, such as multiplication or comparison
of numbers, helping to bridge the gap between traditional databases and
programming languages.
  We also show how all of the components of our model---including schemas,
instances, change-of-schema functors, and queries - fit into a single double
categorical structure called a proarrow equipment (a.k.a. framed bicategory).


title:
The influence of gain compression factor on dynamical properties of
  single level InAs/GaAs quantum dot lasers

abstract:
  In this paper, by representing a single level rate equation model for
InAs/GaAs quantum dot lasers and computations by fourth order Runge-Kutta
method some characteristics of the output laser are considered. The change of
photon number in time and current and also the output power versus current with
different gain compression factors are investigated for lasing from ground
state (GS). Afterwards, the response function of small signal modulation for
ground state in constant current but different gain compressions is surveyed.
At last, we find an optimum value for gain compression factor in lasing from
GS.


title: The number of polynomial solutions of polynomial Riccati equations

abstract:
  Consider real or complex polynomial Riccati differential equations $a(x) \dot
y=b_0(x)+b_1(x)y+b_2(x)y^2$ with all the involved functions being polynomials
of degree at most $\eta$. We prove that the maximum number of polynomial
solutions is $\eta+1$ (resp. 2) when $\eta\ge 1$ (resp. $\eta=0$) and that
these bounds are sharp.
  For real trigonometric polynomial Riccati differential equations with all the
functions being trigonometric polynomials of degree at most $\eta\ge 1$ we
prove a similar result. In this case, the maximum number of trigonometric
polynomial solutions is $2\eta$ (resp. $3$) when $\eta\ge 2$ (resp. $\eta=1$)
and, again, these bounds are sharp.
  Although the proof of both results has the same starting point, the classical
result that asserts that the cross ratio of four different solutions of a
Riccati differential equation is constant, the trigonometric case is much more
involved. The main reason is that the ring of trigonometric polynomials is not
a unique factorization domain.


title: Active Stabilization of a Diode Laser Injection Lock

abstract:
  We report on a device to electronically stabilize the optical injection lock
of a semiconductor diode laser. Our technique uses as discriminator the peak
height of the laser's transmission signal on a scanning Fabry-Perot cavity and
feeds back to the diode current, thereby maintaining maximum optical power in
the injected mode. A two-component feedback algorithm provides constant
optimization of the injection lock, keeping it robust to slow thermal drifts
and allowing fast recovery from sudden failures such as temporary occlusion of
the injection beam. We demonstrate the successful performance of our
stabilization method in a diode laser setup at 399 nm used for laser cooling of
Yb atoms. The device eases the requirements on passive stabilization and can
benefit any diode laser injection lock application, particularly those where
several such locks are employed.


title:
Basel III capital surcharges for G-SIBs fail to control systemic risk
  and can cause pro-cyclical side effects

abstract:
  In addition to constraining bilateral exposures of financial institutions,
there are essentially two options for future financial regulation of systemic
risk (SR): First, financial regulation could attempt to reduce the financial
fragility of global or domestic systemically important financial institutions
(G-SIBs or D-SIBs), as for instance proposed in Basel III. Second, future
financial regulation could attempt strengthening the financial system as a
whole. This can be achieved by re-shaping the topology of financial networks.
We use an agent-based model (ABM) of a financial system and the real economy to
study and compare the consequences of these two options. By conducting three
"computer experiments" with the ABM we find that re-shaping financial networks
is more effective and efficient than reducing leverage. Capital surcharges for
G-SIBs can reduce SR, but must be larger than those specified in Basel III in
order to have a measurable impact. This can cause a loss of efficiency. Basel
III capital surcharges for G-SIBs can have pro-cyclical side effects.


title: Research Priorities for Robust and Beneficial Artificial Intelligence

abstract:
  Success in the quest for artificial intelligence has the potential to bring
unprecedented benefits to humanity, and it is therefore worthwhile to
investigate how to maximize these benefits while avoiding potential pitfalls.
This article gives numerous examples (which should by no means be construed as
an exhaustive list) of such worthwhile research aimed at ensuring that AI
remains robust and beneficial.


title: Phase coexistence far from equilibrium

abstract:
  Investigation of simple far-from-equilibrium systems exhibiting phase
separation leads to the conclusion that phase coexistence is not well defined
in this context. This is because the properties of the coexisting
nonequilibrium systems depend on how they are placed in contact, as verified in
the driven lattice gas with attractive interactions, and in the two-temperature
lattice gas, under (a) weak global exchange between uniform systems, and (b)
phase-separated (nonuniform) systems. Thus, far from equilibrium, the notions
of universality of phase coexistence (i.e., independence of how systems
exchange particles and/or energy), and of phases with intrinsic properties
(independent of their environment) are lost.


title:
Energy Management in Heterogeneous Networks with Cell Activation, User
  Association and Interference Coordination

abstract:
  The densification and expansion of wireless network pose new challenges on
interference management and reducing energy consumption. This paper studies
energy-efficient resource management in heterogeneous networks by jointly
optimizing cell activation, user association and multicell multiuser channel
assignment, according to the long-term average traffic and channel conditions.
The proposed framework is built on characterizing the interference coupling by
pre-defined interference patterns, and performing resource allocation among
these patterns. In this way, the interference fluctuation caused by
(de)activating cells is explicitly taken into account when calculating the user
achievable rates. A tailored algorithm is developed to solve the formulated
problem in the dual domain by exploiting the problem structure, which gives a
significant complexity saving. Numerical results show a huge improvement in
energy saving achieved by the proposed scheme. The user association derived
from the proposed joint resource optimization is mapped to standard-compliant
cell selection biasing. This mapping reveals that the cell-specific biasing for
energy saving is quite different from that for load balancing investigated in
the literature.


title:
Implementing a search for gravitational waves from non-precessing,
  spinning binary black holes

abstract:
  Searching for gravitational waves (GWs) from binary black holes (BBHs) with
LIGO and Virgo involves matched-filtering data against a set of representative
signal waveforms --- a template bank --- chosen to cover the full signal space
of interest with as few template waveforms as possible. Although the component
black holes may have significant angular momenta (spin), previous searches for
BBHs have filtered LIGO and Virgo data using only waveforms where both
component spins are zero. This leads to a loss of signal-to-noise ratio for
signals where this is not the case. Combining the best available template
placement techniques and waveform models, we construct a template bank of GW
signals from BBHs with component spins $\chi_{1,2}\in [-0.99, 0.99]$ aligned
with the orbital angular momentum, component masses $m_{1,2}\in [2,
48]\,\mathrm{M}_\odot$, and total mass $M_\mathrm{total} \leq
50\,\mathrm{M}_\odot$. Using effective-one-body waveforms with spin effects, we
show that less than $3\%$ of the maximum signal-to-noise ratio (SNR) of these
signals is lost due to the discreetness of the bank, using the early advanced
LIGO noise curve. We use simulated advanced LIGO noise to compare the
sensitivity of this bank to a non-spinning bank covering the same parameter
space. In doing so, we consider the competing effects between improved SNR and
signal-based vetoes, and the increase in the rate of false alarms of the
aligned-spin bank due to covering a larger parameter space. We find that the
aligned-spin bank can be a factor of $1.3$ -- $5$ more sensitive than a
non-spinning bank to BBHs with dimensionless spins $> +0.6$ and component
masses $\gtrsim 20\,\mathrm{M}_\odot$. Even larger gains are obtained for
systems with equally high spins but smaller component masses.


title:
Describtion of normal basis of boundary algebras and factor languages of
  small growth

abstract:
  Let $A$ be an algebra with fixed set of generators $a_1,\dots,a_s$. $V_A(n)$
be dimension of the space, generated by worlds of length $\le n$ over $a_i$,
$T_A(n)=V_A(n)-V_A(n-1)$. If $T_A(n)<\mbox{Const}$, algebra $A$ is a {\it
boundary algebra}. We describe a normal basis of boundary algebras, i.e.
algebras with small growth.
  Let $\cal L$ be a factor language over alphabet $\cal A$. {\it Growth
function} $T_{\cal L}(n)$ is number of subwords $\cal L$ of degree $n$. We
describe factor languages of small growth such that $T_{\cal L}(n)\le
n+\mbox{const}$.


title:
Global Unscented Attitude Estimation via the Matrix Fisher Distributions
  on SO(3)

abstract:
  This paper is focused on probabilistic estimation for the attitude dynamics
of a rigid body on the special orthogonal group. We select the matrix Fisher
distribution to represent the uncertainties of attitude estimates and
measurements in a global fashion without need for local coordinates. Several
properties of the matrix Fisher distribution on the special orthogonal group
are presented, and an unscented transform is proposed to approximate a matrix
Fisher distribution by selected sigma points. Based on these, an intrinsic,
global framework for Bayesian attitude estimation is developed. It is shown
that the proposed approach can successfully deal with large initial estimator
errors and large uncertainties over complex maneuvers to obtain accurate
estimates of the attitude.


title: Extragalactic Background Light: Measurements and Applications

abstract:
  This review covers the measurements related to the extragalactic background
light (EBL) intensity from gamma-rays to radio in the electromagnetic spectrum
over 20 decades in the wavelength. The cosmic microwave background (CMB)
remains the best measured spectrum with an accuracy better than 1%. The
measurements related to the cosmic optical background (COB), centered at 1
microns, are impacted by the large zodiacal light associated with
interplanetary dust in the inner Solar system. The best measurements of COB
come from an indirect technique involving Gamma-ray spectra of bright blazars
with an absorption feature resulting from pair-production off of COB photons.
The cosmic infrared background (CIB) peaking at around 100 microns established
an energetically important background with an intensity comparable to the
optical background. This discovery paved the path for large aperture
far-infrared and sub-millimeter observations resulting in the discovery of
dusty, starbursting galaxies. Their role in galaxy formation and evolution
remains an active area of research in modern-day astrophysics. The extreme UV
background remains mostly unexplored and will be a challenge to measure due to
the high Galactic background and absorption of extragalactic photons by the
intergalactic medium at these EUV/soft X-ray energies. We also summarize our
understanding of the spatial anisotropies and angular power spectra of
intensity fluctuations. We motivate a precise direct measurement of the COB
between 0.1 to 5 microns using a small aperture telescope observing either from
the outer Solar system, at distances of 5 AU or more, or out of the ecliptic
plane. Other future applications include improving our understanding of the
background at TeV energies and spectral distortions of CMB and CIB.


title:
Hierarchy sensitivity of NO$\nu$A in light of T2K $\nu_e$ appearance
  data

abstract:
  The $\nu_e$ appearance data of T2K experiment has given a glimpse of the
allowed parameters in the hierarchy-$\delta_{CP}$ parameter space. In this
paper, we explore how this data affects our expectations regarding the
hierarchy sensitivity of the NO$\nu$A experiment. For the favourable
combinations of hierarchy and $\delta_{CP}$, the hierarchy sensitivity of
NO$\nu$A is unaffected by the addition of T2K data. For the unfavourable
combinations, NO$\nu$A data gives degenerate solutions. Among these degenerate
solutions, T2K data prefers IH and $\delta_{CP}$ in the lower half plane over
NH and $\delta_{CP}$ in the upper half plane. Hence, addition of the T2K data
to NO$\nu$A creates a bias towards IH and $\delta_{CP}$ in the lower half plane
irrespective of what the true combination is.


title:
Transition from reconstruction towards thin film on the (110) surface of
  strontium titanate

abstract:
  The surfaces of metal oxides often are reconstructed with a geometry and
composition that is considerably different from a simple termination of the
bulk. Such structures can also be viewed as ultrathin films, epitaxed on a
substrate. Here, the reconstructions of the SrTiO3 (110) surface are studied
combining scanning tunneling microscopy, transmission electron diffraction, and
X-ray absorption spectroscopy, and analyzed with density functional theory
calculations. While SrTiO3 (110) invariably terminates with an overlayer of
titania, with increasing density its structure switches from nx1 and 2xn. At
the same time the coordination of the Ti atoms changes from a network of
corner-sharing tetrahedra to a double layer of edge-shared octahedra with
bridging units of octahedrally coordinated strontium. This transition from the
nx1 to 2xn reconstructions is a transition from a pseudomorphically stabilized
tetrahedral network towards an octahedral titania thin film with stress-relief
from octahedral strontia units at the surface.


title:
Explicit versions of the prime ideal theorem for Dedekind zeta functions
  under GRH, II

abstract:
  We have proved recently several explicit versions of the prime ideal theorem
under GRH. Here we prove a version with optimal asymptotic behaviour.


title:
Probing anharmonicity of a quantum oscillator in an optomechanical
  cavity

abstract:
  We present a way of measuring with high precision the anharmonicity of a
quantum oscillator coupled to an optical field via radiation pressure. Our
protocol uses a sequence of pulsed interactions to perform a loop in the phase
space of the mechanical oscillator, which is prepared in a thermal state. We
show how the optical field acquires a phase depending on the anharmonicity.
Remarkably, one only needs small initial cooling of the mechanical motion to
probe even small anharmonicities. Finally, by applying tools from quantum
estimation theory, we calculate the ultimate bound on the estimation precision
posed by quantum mechanics and compare it with the precision obtainable with
feasible measurements such as homodyne and heterodyne detection on the cavity
field. In particular we demonstrate that homodyne detection is nearly optimal
in the limit of a large number of photons of the field and we discuss the
estimation precision of small anharmonicities in terms of its signal-to-noise
ratio.


title: Frequency comb formation in doubly resonant second-harmonic generation

abstract:
  We theoretically study the generation of optical frequency combs and
corresponding pulse trains in doubly resonant intracavity second-harmonic
generation (SHG). We find that, despite the large temporal walk-off
characteristic of realistic cavity systems, the nonlinear dynamics can be
accurately and efficiently modelled using a pair of coupled mean-field
equations. Through rigorous stability analysis of the system's steady-state
continuous wave solutions, we demonstrate that walk-off can give rise to a new,
previously unexplored regime of temporal modulation instability (MI). Numerical
simulations performed in this regime reveal rich dynamical behaviours,
including the emergence of temporal patterns that correspond to coherent
optical frequency combs. We also demonstrate that the two coupled equations
that govern the doubly resonant cavity behaviour can, under typical conditions,
be reduced to a single mean-field equation akin to that describing the dynamics
of singly resonant cavity SHG [F. Leo et al., Phys. Rev. Lett. 116, 033901
(2016)]. This reduced approach allows us to derive a simple expression for the
MI gain, thus permitting to acquire significant insight into the underlying
physics. We anticipate that our work will have wide impact on the study of
frequency combs in emerging doubly resonant cavity SHG platforms, including
quadratically nonlinear microresonators.


title: Generalized beta-transformations and the entropy of unimodal maps

abstract:
  Generalized beta-transformations are the class of piecewise continuous
interval maps given by taking the beta-transformation $x \mapsto \beta x ~\pmod
1$, where $\beta>1$, and replacing some of the branches with branches of
constant negative slope. If the orbit of 1 is finite, then the map is Markov,
and we call beta (which must be an algebraic number) a generalized Parry
number. We show that the Galois conjugates of such beta have modulus less than
2, and the modulus is bounded away from 2 apart from the exceptional case of
conjugates lying on the real line. We give a characterization of the closure of
all these Galois conjugates, and show that this set is path connected. Our
approach is based on an analysis of Solomyak for the case of
beta-transformations. One motivation for this work is that the entropy of a
post-critically finite (PCF) unimodal map is the logarithm of a generalized
Parry number. Thus, our results give a mild restriction on the set of entropies
that can be attained by PCF unimodal maps.


title:
Sharp asymptotics for the minimal mass blow up solution of critical gKdV
  equation

abstract:
  Let $S$ be a minimal mass blow up solution of the critical generalized KdV
equation as constructed by Martel, Merle and Rapha\"el in arXiv:1204.4624. We
prove both time and space sharp asymptotics for $S$ close to the blow up time.
Let $Q$ be the unique ground state of (gKdV), satisfying $Q"+Q^5=Q$.
  First, we show that there exist universal smooth profiles
$Q_k\in\mathcal{S}(\mathbb{R})$ (with $Q_0=Q$) and a constant
$c_0\in\mathbb{R}$ such that, fixing the blow up time at $t=0$ and appropriate
scaling and translation parameters, $S$ satisfies, for any $m\geqslant 0$, \[
\partial_x^m S(t) - \sum_{k=0}^{[m/2]} \frac 1{t^{\frac 12+m-2k}}
Q_k^{(m-k)}\left(\frac{\cdot+ \frac1t}{t}+c_0\right)\to 0\quad \mbox{in}\ L^2
\mbox{as}\ t\downarrow 0. \] Second, we prove that, for $0<t\ll 1$, $x\leqslant
-\frac 1t -1$, \[ S(t,x) \sim - \frac 12 \|Q\|_{L^1} |x|^{-3/2}, \] and related
bounds for the derivatives of $S(t)$ of any order. We also prove
$\int_{\mathbb{R}} S(t,x)\,dx=0$.


title: Inhomogeneous Anisotropic Cosmology

abstract:
  In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the
topology of the universe determines its ultimate fate. If the Weak Energy
Condition is satisfied, open and flat universes must expand forever, while
closed cosmologies can recollapse to a Big Crunch. A similar statement holds
for homogeneous but anisotropic (Bianchi) universes. Here, we prove that
$arbitrarily$ inhomogeneous and anisotropic cosmologies with "flat" (including
toroidal) and "open" (including compact hyperbolic) spatial topology that are
initially expanding must continue to expand forever at least in some region at
a rate bounded from below by a positive number, despite the presence of
arbitrarily large density fluctuations and/or the formation of black holes.
Because the set of 3-manifold topologies is countable, a single integer
determines the ultimate fate of the universe, and, in a specific sense, most
3-manifolds are "flat" or "open". Our result has important implications for
inflation: if there is a positive cosmological constant (or suitable
inflationary potential) and initial conditions for the inflaton, cosmologies
with "flat" or "open" topology must expand forever in some region at least as
fast as de Sitter space, and are therefore very likely to begin inflationary
expansion eventually, regardless of the scale of the inflationary energy or the
spectrum and amplitude of initial inhomogeneities and gravitational waves. Our
result is also significant for numerical general relativity, which often makes
use of periodic (toroidal) boundary conditions.


title: Tops as Building Blocks for G2 Manifolds

abstract:
  A large number of examples of compact $G_2$ manifolds, relevant to
supersymmetric compactifications of M-Theory to four dimensions, can be
constructed by forming a twisted connected sum of two appropriate building
blocks times a circle. These building blocks, which are appropriate $K3$-fibred
threefolds, are shown to have a natural and elegant construction in terms of
tops, which parallels the construction of Calabi-Yau manifolds via reflexive
polytopes.


title: A strong maximum principle for nonlinear nonlocal diffusion equations

abstract:
  This is a study of a class of nonlocal nonlinear diffusion equations. We
present a strong maximum principle for nonlocal time-dependent Dirichlet
problems. Results are for bounded functions of space, rather than
(semi)-continuous functions. Solutions that attain interior global extrema must
be identically trivial. However, depending on the nonlinearity, trivial
solutions may not be constant in space; they may have an infinite number of
discontinuities, for example. We give examples of nonconstant trivial solutions
for different nonlinearities. For porous medium-type equations, these functions
do not solve the associated classical differential equations, even those in
weak form. We also show that these problems are globally wellposed for
Lipschitz, nonnegative diffusion coefficients.


title: Astrophysical flows near $f(T)$ gravity black holes

abstract:
  In this paper, we study the accretion process for fluids flowing near a black
hole in the context of $f(T)$ teleparallel gravity. Specifically, by performing
a dynamical analysis by a Hamiltonian system, we are able to find the sonic
points. After that, we consider different isothermal test fluids in order to
study the accretion process when they are falling onto the black hole. We found
that these flows can be classified according to the equation of state and the
black hole features. Results are compared in $f(T)$ and $f(R)$ gravity.


title:
Constraining the subgrid physics in simulations of isolated dwarf
  galaxies

abstract:
  Simulating dwarf galaxy halos in a reionizing Universe puts severe
constraints on the sub-grid model employed in the simulations. Using the same
sub-grid model that works for simulations without a UV-background (UVB) results
in gas poor galaxies that stop forming stars very early on, except for halos
with high masses. This is in strong disagreement with observed galaxies, which
are gas rich and star forming down to a much lower mass range. To resolve this
discrepancy, we ran a large suite of isolated dwarf galaxy simulations to
explore a wide variety of sub-grid models and parameters, including timing and
strength of the UVB, strength of the stellar feedback, and metallicity
dependent Pop III feedback. We compared these simulations to observed dwarf
galaxies by means of the baryonic Tully-Fisher relation (BTFR), which links the
baryonic content of a galaxy to the observationally determined strength of its
gravitational potential. We found that the results are robust to changes in the
UVB. The strength of the stellar feedback shifts the results on the BTFR, but
does not help to form gas rich galaxies at late redshifts. Only by including
Pop III feedback are we able to produce galaxies that lie on the observational
BTFR and that have neutral gas and ongoing star formation at redshift zero.


title:
Correcting inconsistencies in the conventional superfluid path integral
  scheme

abstract:
  In this paper we show how to redress a shortcoming of the path integral
scheme for fermionic superfluids and superconductors. This approach is built
around a simultaneous calculation of electrodynamics and thermodynamics. An
important sum rule, the compressibility sum rule, fails to be satisfied in the
usual calculation of the electromagnetic and thermodynamic response at the
Gaussian fluctuation level. Here we present a path integral scheme to address
this inconsistency. Specifically, at the leading order we argue that the
superconducting gap should be calculated using a different saddle point
condition modified by the presence of an external vector potential. This leads
to the well known gauge-invariant BCS electrodynamic response and is associated
with the usual (mean field) expression for thermodynamics. In this way the
compressibility sum rule is satisfied at the BCS level. Moreover, this scheme
can be readily extended to address arbitrary higher order fluctuation theories.
At any level this approach will lead to a gauge invariant and compressibility
sum rule consistent treatment of electrodynamics and thermodynamics.


title: Cold Dark Matter Substructures in Early-Type Galaxy Halos

abstract:
  We present initial results from the "Ponos" zoom-in numerical simulations of
dark matter substructures in massive ellipticals. Two very highly resolved dark
matter halos with $M_{\rm vir}=1.2\times 10^{13}$ $M_{\odot}$ and $M_{\rm
vir}=6.5\times 10^{12}$ $M_{\odot}$ and different ("violent" vs. "quiescent")
assembly histories have been simulated down to $z=0$ in a $\Lambda$CDM
cosmology with a total of 921,651,914 and 408,377,544 particles, respectively.
Within the virial radius, the total mass fraction in self-bound $M_{\rm
sub}>10^6$ $M_{\odot}$ subhalos at the present epoch is 15% for the violent
host and 16.5% for the quiescent one. At $z=0.7$, these fractions increase to
19 and 33%, respectively, as more recently accreted satellites are less prone
to tidal destruction. In projection, the average fraction of surface mass
density in substructure at a distance of $R/R_{\rm vir}=0.02$ ($\sim 5-10$ kpc)
from the two halo centers ranges from 0.6% to $\gtrsim 2$%, significantly
higher than measured in simulations of Milky Way-sized halos. The contribution
of subhalos with $M_{\rm sub} < 10^9$ $M_{\odot}$ to the projected mass
fraction is between one fifth and one third of the total, with the smallest
share found in the quiescent host. We assess the impact of baryonic effects via
twin, lower-resolution hydrodynamical simulations that include
metallicity-dependent gas cooling, star formation, and a
delayed-radiative-cooling scheme for supernova feedback. Baryonic contraction
produces a super-isothermal total density profile and increases the number of
massive subhalos in the inner regions of the main host. The host density
profiles and projected subhalo mass fractions appear to be broadly consistent
with observations of gravitational lenses.


title:
Can Star-Disk Collisions Explain the Missing Red Giants Problem in the
  Galactic Center?

abstract:
  Observations have revealed a relative paucity of red giant (RG) stars within
the central 0.5pc in the Galactic Center (GC). Motivated by this finding we
investigate the hypothesis that collisions of stars with a fragmenting
accretion disk are responsible for the observed dearth of evolved stars. We use
3-dimensional hydrodynamic simulations to model a star with radius $10
R_{\odot}$ and mass $1 M_{\odot}$, representative of the missing population of
RGs, colliding with high density clumps. We find that multiple collisions with
clumps of column density $\gtrsim10^{8}\, {\rm g\,cm^{-2}}$ can strip a
substantial fraction of the star's envelope and in principle render it
invisible to observations. Simulations confirm that repeated impacts are
particularly efficient in driving mass loss as partially stripped RGs expand
and have increased cross sections for subsequent collisions. Because the
envelope is unbound on account of the kinetic energy of the star, any
significant amount of stripping of the RG population in the GC should be
mirrored by a systematic decay of their orbits and possibly by their enhanced
rotational velocity. To be viable, this scenario requires that the total mass
of the fragmenting disk has been several orders of magnitude higher than that
of the early type stars which now form the stellar disk in the GC.


title:
The featureless and non-variable optical spectral energy distribution of
  AXP 4U 0142+61

abstract:
  We present GTC-10.4m spectroscopy and multi-band photometry of the faint (r
~26) optical counterpart of the anomalous X-ray pulsar 4U 0142+61. The 5000 -
9000 Angs spectrum -- the first obtained for a magnetar -- is featureless,
allowing us to set an equivalent width upper limit EW < 25 Angs to the presence
of emission lines in the Halfa region. Multi-band photometry in the g, r, i, z
SDSS bands obtained at different epochs over 12 years shows no significant
variability from minutes-to-years time scales. The photometry has been
calibrated, for the first time, against the SDSS itself, resulting in solid
upper limits to variability ranging from ~0.2 mag in i (over 12 years) to 0.05
mag in z (over 1.5 years). The shape of the optical + near-infrared (literature
values) spectral energy distribution is not well constrained due to the high
extinction along the line of sight. Using a Markov Chain Monte Carlo analysis
we find that it can be described by a power-law with a spectral index
beta=-0.7+-0.5 and E_(B-V)=1.5+-0.4. We also discuss on the implications of
adding hard X-ray flux values from literature to the spectral fitting.


title: New N = 2 dualities

abstract:
  We consider N = 2 superconformal field theory with following properties: a)
Coulomb branch operators have fractional scaling dimensions, b) there are exact
marginal deformations . The weakly coupled gauge theory descriptions are found
by decomposing 3d mirror into different components, and different
decompositions correspond to different duality frames. The gauge theory is
formed by gauging Argyres-Douglas matter, and we write down all duality frames
for several classes with infinite sequence of theories.


title: Witten Index for Noncompact Dynamics

abstract:
  Among gauged dynamics motivated by string theory, we find many with gapless
asymptotic directions. Although the natural boundary condition for ground
states is $L^2$, one often turns on chemical potentials or supersymmetric mass
terms to regulate the infrared issues, instead, and computes the twisted
partition function. We point out how this procedure generically fails to
capture physical $L^2$ Witten index with often misleading results. We also
explore how, nevertheless, the Witten index is sometimes intricately embedded
in such twisted partition functions. For $d=1$ theories with gapless continuum
sector from gauge multiplets, such as non-primitive quivers and pure
Yang-Mills, a further subtlety exists, leading to fractional expressions. Quite
unexpectedly, however, the integral $L^2$ Witten index can be extracted
directly and easily from the twisted partition function of such theories. This
phenomenon is tied to the notion of the rational invariant that appears
naturally in the wall-crossing formulae, and offers a general mechanism of
reading off Witten index directly from the twisted partition function. Along
the way, we correct early numerical results for some of $\mathcal N=4,8,16$
pure Yang-Mills quantum mechanics, and count threshold bound states for general
gauge groups beyond $SU(N)$.


title: G11.2-0.3: The Young Remnant of a Stripped-Envelope Supernova

abstract:
  We present results of a 400-ks Chandra observation of the young shell
supernova remnant (SNR) G11.2-0.3, containing a pulsar and pulsar-wind nebula
(PWN). We measure a mean expansion rate for the shell since 2000 of
0.0277+/-0.0018% per yr, implying an age between 1400 and 2400 yr, and making
G11.2-0.3 one of the youngest core-collapse SNRs in the Galaxy. However, we
find very high absorption ($A_V \sim 16^m \pm 2^m$), confirming near-IR
determinations and ruling out a claimed association with the possible
historical SN of 386 CE. The PWN shows strong jets and a faint torus within a
larger, more diffuse region of radio emission and nonthermal X-rays. Central
soft thermal X-ray emission is anticorrelated with the PWN; that, and more
detailed morphological evidence, indicates that the reverse shock has already
reheated all ejecta and compressed the PWN. The pulsar characteristic
energy-loss timescale is well in excess of the remnant age, and we suggest that
the bright jets have been produced since the recompression. The relatively
pronounced shell and diffuse hard X-ray emission in the interior, enhanced at
the inner edge of the shell, indicate that the immediate circumstellar medium
into which G11.2-0.3 is expanding was quite anisotropic. We propose a possible
origin for G11.2-0.3 in a stripped-envelope progenitor that had lost almost all
its envelope mass, in an anisotropic wind or due to binary interaction, leaving
a compact core whose fast winds swept previously lost mass into a dense
irregular shell, and which exploded as a Type cIIb or Ibc supernova.


title:
Peering through the Dust: NuSTAR Observations of Two FIRST-2MASS Red
  Quasars

abstract:
  Some reddened quasars appear to be transitional objects in the merger-induced
black hole growth/galaxy evolution paradigm, where a heavily obscured nucleus
starts to be unveiled by powerful quasar winds evacuating the surrounding
cocoon of dust and gas. Hard X-ray observations are able to peer through this
gas and dust, revealing the properties of circumnuclear obscuration. Here, we
present NuSTAR and XMM-Newton/Chandra observations of FIRST-2MASS selected red
quasars F2M 0830+3759 and F2M 1227+3214. We find that though F2M 0830+3759 is
moderately obscured ($N_{\rm H,Z} = 2.1\pm0.2 \times10^{22}$ cm$^{-2}$) and F2M
1227+3214 is mildly absorbed ($N_{\rm H,Z} = 3.4^{+0.8}_{-0.7}\times10^{21}$
cm$^{-2}$) along the line-of-sight, heavier global obscuration may be present
in both sources, with $N_{\rm H,S} = 3.7^{+4.1}_{-2.6} \times 10^{23}$
cm$^{-2}$ and $< 5.5\times10^{23}$ cm$^{-2}$, for F2M 0830+3759 and F2M
1227+3214, respectively. F2M 0830+3759 also has an excess of soft X-ray
emission below 1 keV which is well accommodated by a model where 7% of the
intrinsic AGN X-ray emission is scattered into the line-of-sight. While F2M
1227+3214 has a dust-to-gas ratio ($E(B-V)$/$N_{\rm H}$) consistent with the
Galactic value, the $E(B-V)$/$N_{\rm H}$ value for F2M 0830+3759 is lower than
the Galactic standard, consistent with the paradigm that the dust resides on
galactic scales while the X-ray reprocessing gas originates within the
dust-sublimation zone of the broad-line-region. The X-ray and 6.1$\mu$m
luminosities of these red quasars are consistent with the empirical relations
derived for high-luminosity, unobscured quasars, extending the parameter space
of obscured AGN previously observed by NuSTAR to higher luminosities.


title:
Diffuse Low-Ionization Gas in the Galactic Halo Casts Doubts on $z\simeq
  0.03$ WHIM Detections

abstract:
  In this Letter we demonstrate that the two claims of $z\simeq 0.03$ OVII
K$\alpha$ absorption lines from Warm Hot Intergalactic Medium (WHIM) along the
lines of sight to the blazars H~2356-309 (Buote et al., 2009; Fang et al.,
2010) and Mkn~501 (Ren, Fang \& Buote, 2014) are likely misidentifications of
the $z=0$ OII K$\beta$ line produced by a diffuse Low-Ionization Metal Medium
in the Galaxy's Interstellar and Circum-Galactic mediums. We perform detailed
modeling of all the available high signal-to-noise Chandra LETG and XMM-Newton
RGS spectra of H 2356-309 and Mkn 501 and demonstrate that the $z\simeq 0.03$
WHIM absorption along these two sightlines is statistically not required. Our
results, however, do not rule out a small contribution from the $z\simeq 0.03$
OVII K$\alpha$ absorber along the line of sight to H~2356-309. In our model the
temperature of the putative $z = 0.031$ WHIM filament is T$= 3\times 10^5$ K
and the OVII column density is N$_{OV II} \le 4\times 10^{15}$ cm$^{-2}$,
twenty times smaller than the OVII column density previously reported, and now
more consistent with the expectations from cosmological hydrodynamical
simulations.


title: Unsupervised Transductive Domain Adaptation

abstract:
  Supervised learning with large scale labeled datasets and deep layered models
has made a paradigm shift in diverse areas in learning and recognition.
However, this approach still suffers generalization issues under the presence
of a domain shift between the training and the test data distribution. In this
regard, unsupervised domain adaptation algorithms have been proposed to
directly address the domain shift problem. In this paper, we approach the
problem from a transductive perspective. We incorporate the domain shift and
the transductive target inference into our framework by jointly solving for an
asymmetric similarity metric and the optimal transductive target label
assignment. We also show that our model can easily be extended for deep feature
learning in order to learn features which are discriminative in the target
domain. Our experiments show that the proposed method significantly outperforms
state-of-the-art algorithms in both object recognition and digit classification
experiments by a large margin.


title: Two worlds collide: Interacting shells in AdS spacetime and chaos

abstract:
  We study the simplest two-body problem in asymptotically anti-de Sitter
spacetime: two, infinitely thin, concentric spherical shells of matter. We
include only gravitational interaction between the two shells, but we show that
the dynamics of this system is highly nontrivial. We observe prompt collapse to
a black hole, delayed collapse and even perpetual oscillatory motion, depending
on the initial location of the shells (or their energy content). The system
exhibits critical behavior, and we show strong hints that it is also chaotic.


title: Duality between erasures and defects

abstract:
  We investigate the duality of the binary erasure channel (BEC) and the binary
defect channel (BDC). This duality holds for channel capacities, capacity
achieving schemes, minimum distances, and upper bounds on the probability of
failure to retrieve the original message. In addition, the relations between
BEC, BDC, binary erasure quantization (BEQ), and write-once memory (WOM) are
described. From these relations we claim that the capacity of the BDC can be
achieved by Reed-Muller (RM) codes under maximum a posterior (MAP) decoding.
Also, polar codes with a successive cancellation encoder achieve the capacity
of the BDC.
  Inspired by the duality between the BEC and the BDC, we introduce locally
rewritable codes (LWC) for resistive memories, which are the counterparts of
locally repairable codes (LRC) for distributed storage systems. The proposed
LWC can improve endurance limit and power efficiency of resistive memories.


title: Dominating Sets in Intersection Graphs of Finite Groups

abstract:
  Let $G$ be a group. The intersection graph $\Gamma(G)$ of $G$ is an
undirected graph without loops and multiple edges defined as follows: the
vertex set is the set of all proper non-trivial subgroups of $G$, and there is
an edge between two distinct vertices $H$ and $K$ if and only if $H\cap K \neq
1$ where $1$ denotes the trivial subgroup of $G$. In this paper we studied the
dominating sets in intersection graphs of finite groups. It turns out a subset
of the vertex set is a dominating set if and only if the union of the
corresponding subgroups contains the union of all minimal subgroups. We
classified abelian groups by their domination number and find upper bounds for
some specific classes of groups. Subgroup intersection is related with Burnside
rings. We introduce the notion of intersection graph of a $G$-set (somewhat
generalizing the ordinary definition of intersection graph of a group) and
establish a general upper bound for the domination number of $\Gamma(G)$ in
terms of subgroups satisfying a certain property in Burnside ring. Intersection
graph of $G$ is the $1$-skeleton of the simplicial complex whose faces are the
sets of proper subgroups which intersect non-trivially. We call this simplicial
complex intersection complex of $G$ and show that it shares the same homotopy
type with the order complex of proper non-trivial subgroups of $G$. We also
prove that if domination number of $\Gamma(G)$ is $1$, then intersection
complex of $G$ is contractible.


title:
Excitation spectra of a Bose-Einstein condensate with an angular
  spin-orbit coupling

abstract:
  A theoretical model of a Bose-Einstein condensate with angular spin-orbit
coupling has recently been proposed and it has been established that a
half-skyrmion represents the ground state in a certain regime of spin-orbit
coupling and interaction. Here we investigate low-lying excitations of this
phase by using the Bogoliubov method and numerical simulations of the
time-dependent Gross-Pitaevskii equation. We find that a sudden shift of the
trap bottom results in a complex two-dimensional motion of the system's center
of mass that is markedly different from the response of a competing phase, and
comprises two dominant frequencies. Moreover, the breathing mode frequency of
the half-skyrmion is set by both the spin-orbit coupling and the interaction
strength, while in the competing state it takes a universal value. Effects of
interactions are especially pronounced at the transition between the two
phases.


title:
Efficient classical simulation of matchgate circuits with generalized
  inputs and measurements

abstract:
  Matchgates are a restricted set of two-qubit gates known to be classically
simulable under particular conditions. Specifically, if a circuit consists only
of nearest-neighbour matchgates, an efficient classical simulation is possible
if either (i) the input is a computational basis state and the simulation
requires computing probabilities of multi-qubit outcomes (including also
adaptive measurements), or (ii) if the input is an arbitrary product state, but
the output of the circuit consists of a single qubit. In this paper we extend
these results to show that matchgates are classically simulable even in the
most general combination of these settings, namely, if the inputs are arbitrary
product states, if the measurements are over arbitrarily many output qubits,
and if adaptive measurements are allowed. This remains true even for arbitrary
single-qubit measurements, albeit only in a weaker notion of classical
simulation. These results make for an interesting contrast with other
restricted models of computation, such as Clifford circuits or (bosonic) linear
optics, where the complexity of simulation varies greatly under similar
modifications.


title: Homonym Population Protocols

abstract:
  The population protocol model was introduced by Angluin \emph{et al.} as a
model of passively mobile anonymous finite-state agents. This model computes a
predicate on the multiset of their inputs via interactions by pairs. The
original population protocol model has been proved to compute only semi-linear
predicates and has been recently extended in various ways. In the community
protocol model by Guerraoui and Ruppert, agents have unique identifiers but may
only store a finite number of the identifiers they already heard about. The
community protocol model provides the power of a Turing machine with a $O(n\log
n)$ space. We consider variations on the two above models and we obtain a whole
landscape that covers and extends already known results. Namely, by considering
the case of homonyms, that is to say the case when several agents may share the
same identifier, we provide a hierarchy that goes from the case of no
identifier (population protocol model) to the case of unique identifiers
(community protocol model). We obtain in particular that any Turing Machine on
space $O(\log^{O(1)} n)$ can be simulated with at least $O(\log^{O(1)} n)$
identifiers, a result filling a gap left open in all previous studies. Our
results also extend and revisit in particular the hierarchy provided by
Chatzigiannakis \emph{et al.} on population protocols carrying Turing Machines
on limited space, solving the problem of the gap left by this work between
per-agent space $o(\log \log n)$ (proved to be equivalent to population
protocols) and $O(\log n)$ (proved to be equivalent to Turing machines).


title: Mathematical modelling of fractional order circuits

abstract:
  In this work a classical derivation of fractional order circuits models is
presented. Generalized constitutive equations in terms of fractional
Riemann-Liouville derivatives are introduced in the Maxwell's equations. Next
the Kirchhoff voltage law is applied in a RCL circuit configuration. A
fractional differential equation model is obtained with Caputo derivatives.
Thus standard initial conditions apply.


title: Weakly Hamiltonian actions

abstract:
  In this paper we generalize constructions of non-commutative integrable
systems to the context of weakly Hamiltonian actions on Poisson manifolds. In
particular we prove that abelian weakly Hamiltonian actions on symplectic
manifolds split into Hamiltonian and non-Hamiltonian factors, and explore
generalizations in the Poisson setting.


title:
Using full configuration interaction quantum Monte Carlo in a seniority
  zero space to investigate the correlation energy equivalence of pair coupled
  cluster doubles and doubly occupied configuration interaction

abstract:
  Over the past few years pair coupled cluster doubles (pCCD) has shown promise
for the description of strong correlation. This promise is related to its
apparent ability to match results from doubly occupied configuration
interaction (DOCI), even though the latter method has exponential computational
cost. Here, by modifying the full configuration interaction quantum Monte Carlo
(FCIQMC) algorithm to sample only the seniority zero sector of Hilbert space,
we show that the DOCI and pCCD energies are in agreement for a variety of 2D
Hubbard models, including for systems well out of reach for conventional
configuration interaction algorithms. Our calculations are aided by the sign
problem being much reduced in the seniority zero space compared with the full
space. We present evidence for this, and then discuss the sign problem in terms
of the wave function of the system which appears to have a simplified sign
structure.


title: Toward a consistent evolution of the quark-gluon plasma and heavy quarks

abstract:
  Heavy-quark observables in ultrarelativistic heavy-ion collisions, like the
nuclear modification factor and the elliptic flow, give insight into the
mechanisms of high-momentum suppression and low-momentum thermalization of
heavy quarks. Here, we present a global study of these two observables within a
coupled approach of the heavy-quark propagation in a realistic fluid dynamical
medium, MC@sHQ+EPOS2, and compare to experimental data from RHIC and LHC
experiments. The heavy quarks scatter elastically and inelastically with the
quasiparticles of the quark-gluon plasma (QGP), which are represented
consistently with the underlying equation of state. We examine two scenarios:
first, we interpret the lattice QCD equation of state as a sum of partonic and
hadronic contributions, and second, as a gas of massive partonic
quasiparticles. It is observed that independent of their momentum the energy
loss of heavy quarks depends strongly on how the lattice QCD equation of state
is translated into degrees of freedom of the QGP.


title:
On the rate and on the gravitational wave emission of short and long
  GRBs

abstract:
  On the ground of the large number of gamma-ray bursts (GRBs) detected with
cosmological redshift, we classified GRBs in seven subclasses, all with binary
progenitors originating gravitational waves (GWs). Each binary is composed by
combinations of carbon-oxygen cores (CO$_{\rm core}$), neutron stars (NSs),
black holes (BHs) and white dwarfs (WDs). The long bursts, traditionally
assumed to originate from a BH with an ultra-relativistic jetted emission, not
emitting GWs, have been subclassified as (I) X-ray flashes (XRFs), (II)
binary-driven hypernovae (BdHNe), and (III) BH-supernovae (BH-SNe). They are
framed within the induced gravitational collapse (IGC) paradigm with progenitor
a CO$_{\rm core}$-NS/BH binary. The supernova (SN) explosion of the CO$_{\rm
core}$ triggers an accretion process onto the NS/BH. If the accretion does not
lead the NS to its critical mass, an XRF occurs, while when the BH is present
or formed by accretion, a BdHN occurs. When the binaries are not disrupted,
XRFs lead to NS-NS and BdHNe lead to NS-BH. The short bursts, originating in
NS-NS, are subclassified as (IV) short gamma-ray flashes (S-GRFs) and (V) short
GRBs (S-GRBs), the latter when a BH is formed. There are (VI) ultra-short GRBs
(U-GRBs) and (VII) gamma-ray flashes (GRFs), respectively formed in NS-BH and
NS-WD. We use the occurrence rate and GW emission of these subclasses to assess
their detectability by Advanced LIGO-Virgo, eLISA, and resonant bars. We
discuss the consequences of our results in view of the announcement of the
LIGO-Virgo Collaboration of the source GW 170817 as being originated by a
NS-NS.


title:
Superconductor Digital Electronics: Scalability and Energy Efficiency
  Issues

abstract:
  Superconductor digital electronics using Josephson junctions as ultrafast
switches and magnetic-flux encoding of information was proposed over 30 years
ago as a sub-terahertz clock frequency alternative to semiconductor electronics
based on complementary metal-oxide-semiconductor (CMOS) transistors. Recently,
interest in developing superconductor electronics has been renewed due to a
search for energy saving solutions in applications related to high-performance
computing. The current state of superconductor electronics and fabrication
processes are reviewed in order to evaluate whether this electronics is
scalable to a very large scale integration (VLSI) required to achieve
computation complexities comparable to CMOS processors. A fully planarized
process at MIT Lincoln Laboratory, perhaps the most advanced process developed
so far for superconductor electronics, is used as an example. The process has
nine superconducting layers: eight Nb wiring layers with the minimum feature
size of 350 nm, and a thin superconducting layer for making compact
high-kinetic-inductance bias inductors. All circuit layers are fully planarized
using chemical mechanical planarization (CMP) of SiO2 interlayer dielectric.
The physical limitations imposed on the circuit density by Josephson junctions,
circuit inductors, shunt and bias resistors, etc., are discussed. Energy
dissipation in superconducting circuits is also reviewed in order to estimate
whether this technology, which requires cryogenic refrigeration, can be energy
efficient. Fabrication process development required for increasing the density
of superconductor digital circuits by a factor of ten and achieving densities
above 10^7 Josephson junctions per cm^2 is described.


title:
On maximal tail probability of sums of nonnegative, independent and
  identically distributed random variables

abstract:
  We consider the problem of finding the optimal upper bound for the tail
probability of a sum of $k$ nonnegative, independent and identically
distributed random variables with given mean $x$. For $k=1$ the answer is given
by Markov's inequality and for $k=2$ the solution was found by Hoeffding and
Shrikhande in 1955. We solve the problem for $k=3$ as well as for general $k$
and $x\leq1/(2k-1)$ by showing that it follows from the fractional version of
an extremal graph theory problem of Erd\H{o}s on matchings in hypergraphs.


title: Invisible $K_L$ decays in the SM extensions

abstract:
  In the Standard Model (SM) the branching ratio for the decay $K_L \to \nu
\bar{\nu}$ into two neutrinos is helicity suppressed and predicted to be very
small $ \leq O(10^{-17})$. We consider two natural extensions of the SM, such
as two-Higgs-doublet model (2HDM) and the $\nu$MSM with additional singlet
scalar, those main features is that they can lead to an enhanced $Br(K_L \to
invisible)$. In the 2HDM the smallness of the neutrino mass is explained due to
the smallness of the second Higgs doublet vacuum expectation value. Moreover,
the $\nu$MSM extension with additional singlet field can explain the $(g - 2)$
muon anomaly. The considered models demonstrate that the $K_L \to invisible $
decay is a clean probe of new physics scales well above 100 TeV, that is
complementary to rare $K \to \pi+invisible$ decay, and provide a strong
motivation for its sensitive search in a near future low-energy experiment.


title: Ising Spin Glasses and Renormalization Group Theory: the Binder cumulant

abstract:
  Numerical data on scaling of the normalized Binder cumulant and the
normalized correlation length are shown for the Thermodynamic limit regime,
first for canonical Ising ferromagnet models and then for a range of Ising spin
glass models. A fundamental Renormalization Group Theory rule linking the
critical exponents for the two observables is well obeyed in the Ising models,
but not for the Ising spin glasses in dimensions three and four. We conclude
that there is a violation of a standard Josephson hyperscaling rule in Ising
spin glasses.


title: Enumeration of colored Dyck paths via partial Bell polynomials

abstract:
  We consider a class of lattice paths with certain restrictions on their
ascents and down steps and use them as building blocks to construct various
families of Dyck paths. We let every building block $P_j$ take on $c_j$ colors
and count all of the resulting colored Dyck paths of a given semilength. Our
approach is to prove a recurrence relation of convolution type, which yields a
representation in terms of partial Bell polynomials that simplifies the
handling of different colorings. This allows us to recover multiple known
formulas for Dyck paths and related lattice paths in an unified manner.


title: Knowledge Transfer with Medical Language Embeddings

abstract:
  Identifying relationships between concepts is a key aspect of scientific
knowledge synthesis. Finding these links often requires a researcher to
laboriously search through scien- tific papers and databases, as the size of
these resources grows ever larger. In this paper we describe how distributional
semantics can be used to unify structured knowledge graphs with unstructured
text to predict new relationships between medical concepts, using a
probabilistic generative model. Our approach is also designed to ameliorate
data sparsity and scarcity issues in the medical domain, which make language
modelling more challenging. Specifically, we integrate the medical relational
database (SemMedDB) with text from electronic health records (EHRs) to perform
knowledge graph completion. We further demonstrate the ability of our model to
predict relationships between tokens not appearing in the relational database.


title: Learning Privately from Multiparty Data

abstract:
  Learning a classifier from private data collected by multiple parties is an
important problem that has many potential applications. How can we build an
accurate and differentially private global classifier by combining
locally-trained classifiers from different parties, without access to any
party's private data? We propose to transfer the `knowledge' of the local
classifier ensemble by first creating labeled data from auxiliary unlabeled
data, and then train a global $\epsilon$-differentially private classifier. We
show that majority voting is too sensitive and therefore propose a new risk
weighted by class probabilities estimated from the ensemble. Relative to a
non-private solution, our private solution has a generalization error bounded
by $O(\epsilon^{-2}M^{-2})$ where $M$ is the number of parties. This allows
strong privacy without performance loss when $M$ is large, such as in
crowdsensing applications. We demonstrate the performance of our method with
realistic tasks of activity recognition, network intrusion detection, and
malicious URL detection.


title:
Proof that the real part of all non-trivial zeros of Riemann zeta
  function is 1/2

abstract:
  This article proves the Riemann hypothesis, which states that all non-trivial
zeros of the zeta function have a real part equal to 1/2. We inspect in detail
the integral form of the (symmetrized) completed zeta function, which is a
product between the zeta and gamma functions. It is known that two integral
lines, expressing the completed zeta function, rotated from the real axis in
the opposite directions, can be shifted without affecting the completed zeta
function owing to the residue theorem. The completed zeta function is regular
in the region of the complex plane under consideration. For convenience in the
subsequent singularity analysis of the above integral, we first deform and
shift the integral contours. We then investigate the singularities of the
composite elements (caused by polynomial integrals in opposite directions),
which appear only in the case for which the distance between the contours and
the origin of the coordinates approaches zero. The real part of the zeros of
the zeta function is determined to be 1/2 along a symmetry line from the
singularity removal condition. (In the other points, the singularities are
adequately cancelled as a whole to lead to a finite value.)


title: A new Composition-Diamond lemma for associative conformal algebras

abstract:
  Let $C(B,N)$ be the free associative conformal algebra generated by a set $B$
with a bounded locality $N$. Let $S$ be a subset of $C(B,N)$. A
Composition-Diamond lemma for associative conformal algebras is firstly
established by Bokut, Fong, and Ke in 2004 \cite{BFK04} which claims that if
(i) $S$ is a Gr\"obner-Shirshov basis in $C(B,N)$, then (ii) the set of
$S$-irreducible words is a linear basis of the quotient conformal algebra
$C(B,N|S)$, but not conversely. In this paper, by introducing some new
definitions of normal $S$-words, compositions and compositions to be trivial,
we give a new Composition-Diamond lemma for associative conformal algebras
which makes the conditions (i) and (ii) equivalent. We show that for each ideal
$I$ of $C(B,N)$, $I$ has a unique reduced Gr\"obner-Shirshov basis. As
applications, we show that Loop Virasoro Lie conformal algebra and Loop
Heisenberg-Virasoro Lie conformal algebra are embeddable into their universal
enveloping associative conformal algebras.


title: On the Success of Mishandling Euclid's Lemma

abstract:
  We examine Euclid's lemma that if $p$ is a prime number such that $p | ab$,
then $p$ divides at least one of $a$ or $b$. Specifically, we consider the
common misapplication of this lemma to numbers that are not prime, as is often
made by undergraduate students. We show that a randomly chosen implication of
the form $r |ab \Rightarrow r|a \text{ or } r|b$ is almost surely false in a
probabilistic sense, and we quantify this with a corresponding asymptotic
formula.


title: Endless love: On the termination of a playground number game

abstract:
  A simple and popular childhood game, `LOVES' or the `Love Calculator',
involves an iterated rule applied to a string of digits and gives rise to
surprisingly rich behaviour. Traditionally, players' names are used to set the
initial conditions for an instance of the game: its behaviour for an exhaustive
set of pairings of popular UK childrens' names, and for more general initial
conditions, is examined. Convergence to a fixed outcome (the desired result) is
not guaranteed, even for some plausible first name pairings. No pairs of top-50
common first names exhibit non-convergence, suggesting that it is rare in the
playground; however, including surnames makes non-convergence more likely due
to higher letter counts (for example, `Reese Witherspoon LOVES Calvin Harris').
Different game keywords (including from different languages) are also
considered. An estimate for non-convergence propensity is derived: if the sum
$m$ of digits in a string of length $w$ obeys $m > 18/(3/2)^{w-4}$, convergence
is less likely. Pairs of top UK names with pairs of `O's and several `L's (for
example, Chloe and Joseph, or Brooke and Scarlett) often attain high scores.
When considering individual names playing with a range of partners, those with
no `LOVES' letters score lowest, and names with intermediate (not simply the
highest) letter counts often perform best, with Connor and Evie averaging the
highest scores when played with other UK top names.


title: Old Techniques for New Join Algorithms: A Case Study in RDF Processing

abstract:
  Recently there has been significant interest around designing specialized RDF
engines, as traditional query processing mechanisms incur orders of magnitude
performance gaps on many RDF workloads. At the same time researchers have
released new worst-case optimal join algorithms which can be asymptotically
better than the join algorithms in traditional engines. In this paper we apply
worst-case optimal join algorithms to a standard RDF workload, the LUBM
benchmark, for the first time. We do so using two worst-case optimal engines:
(1) LogicBlox, a commercial database engine, and (2) EmptyHeaded, our prototype
research engine with enhanced worst-case optimal join algorithms. We show that
without any added optimizations both LogicBlox and EmptyHeaded outperform two
state-of-the-art specialized RDF engines, RDF-3X and TripleBit, by up to 6x on
cyclic join queries-the queries where traditional optimizers are suboptimal. On
the remaining, less complex queries in the LUBM benchmark, we show that three
classic query optimization techniques enable EmptyHeaded to compete with RDF
engines, even when there is no asymptotic advantage to the worst-case optimal
approach. We validate that our design has merit as EmptyHeaded outperforms
MonetDB by three orders of magnitude and LogicBlox by two orders of magnitude,
while remaining within an order of magnitude of RDF-3X and TripleBit.


title:
Non-local gravity and comparison with observational datasets. II.
  Updated results and Bayesian model comparison with $\Lambda$CDM

abstract:
  We present a comprehensive and updated comparison with cosmological
observations of two non-local modifications of gravity previously introduced by
our group, the so called RR and RT models. We implement the background
evolution and the cosmological perturbations of the models in a modified
Boltzmann code, using CLASS. We then test the non-local models against the {\em
Planck} 2015 TT, TE, EE and Cosmic Microwave Background (CMB) lensing data,
isotropic and anisotropic Baryonic Acoustic Oscillations (BAO) data, JLA
supernovae, $H_0$ measurements and growth rate data, and we perform Bayesian
parameter estimation. We then compare the RR, RT and $\Lambda$CDM models, using
the Savage-Dickey method. We find that the RT model and $\Lambda$CDM perform
equally well, while the performance of the RR model with respect to
$\Lambda$CDM depends on whether or not we include a prior on $H_0$ based on
local measurements.


title: Common probability patterns arise from simple invariances

abstract:
  Shift and stretch invariance lead to the exponential-Boltzmann probability
distribution. Rotational invariance generates the Gaussian distribution.
Particular scaling relations transform the canonical exponential and Gaussian
patterns into the variety of commonly observed patterns. The scaling relations
themselves arise from the fundamental invariances of shift, stretch, and
rotation, plus a few additional invariances. Prior work described the three
fundamental invariances as a consequence of the equilibrium canonical ensemble
of statistical mechanics or the Jaynesian maximization of information entropy.
By contrast, I emphasize the primacy and sufficiency of invariance alone to
explain the commonly observed patterns. Primary invariance naturally creates
the array of commonly observed scaling relations and associated probability
patterns, whereas the classical approaches derived from statistical mechanics
or information theory require special assumptions to derive commonly observed
scales.

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