title:
Topological superconducting phases from inversion symmetry breaking
  order in spin-orbit-coupled systems

abstract:
  We analyze the superconducting instabilities in the vicinity of the
quantum-critical point of an inversion symmetry breaking order. We first show
that the fluctuations of the inversion symmetry breaking order lead to two
degenerate superconducting (SC) instabilities, one in the $s$-wave channel, and
the other in a time-reversal invariant odd-parity pairing channel (the simplest
case being the same as the of $^3$He-B phase). Remarkably, we find that unlike
many well-known examples, the selection of the pairing symmetry of the
condensate is independent of the momentum-space structure of the collective
mode that mediates the pairing interaction. We found that this degeneracy is a
result of the existence of a conserved fermionic helicity, $\chi$, and the two
degenerate channels correspond to even and odd combinations of SC order
parameters with $\chi=\pm1$. As a result, the system has an enlarged symmetry
$U(1)\times U(1)$, with each $U(1)\times U(1)$ corresponding to one value of
the helicity $\chi$. Because of the enlarged symmetry, this system admits
exotic topological defects such as a fractional quantum vortex, which we show
has a Majorana zero mode bound at its core. We discuss how the enlarged
symmetry can be lifted by small perturbations, such as the Coulomb interaction
or Fermi surface splitting in the presence of broken inversion symmetry, and we
show that the resulting superconducting state can be topological or trivial
depending on parameters. The $U(1)\times U(1)$ symmetry is restored at the
phase boundary between the topological and trivial SC states, and allows for a
transition between topologically distinct SC phases without the vanishing of
the order parameter. We present a global phase diagram of the superconducting
states and discuss possible experimental implications.


title:
ISM excitation and metallicity of star-forming galaxies at z~3.3 from
  near-IR spectroscopy

abstract:
  We study the relationship between stellar mass, star formation rate
(SFR),ionization state, and gas-phase metallicity for a sample of 41 normal
star-forming galaxies at $3 \lesssim z \lesssim 3.7$. The gas-phase oxygen
abundance, ionization parameter, and electron density of ionized gas are
derived from rest-frame optical strong emission lines measured on near-infrared
spectra obtained with Keck/MOSFIRE. We remove the effect of these strong
emission lines in the broad-band fluxes to compute stellar masses via spectral
energy distribution fitting, while the SFR is derived from the dust-corrected
ultraviolet luminosity. The ionization parameter is weakly correlated with the
specific SFR, but otherwise the ionization parameter and electron density do
not correlate with other global galaxy properties such as stellar mass, SFR,
and metallicity. The mass-metallicity relation (MZR) at $z\simeq3.3$ shows
lower metallicity by $\simeq 0.7$ dex than that at $z=0$ at the same stellar
mass. Our sample shows an offset by $\simeq 0.3$ dex from the locally defined
mass-metallicity-SFR relation, indicating that simply extrapolating such
relation to higher redshift may predict an incorrect evolution of MZR.
Furthermore, within the uncertainties we find no SFR-metallicity correlation,
suggesting a less important role of SFR in controlling the metallicity at high
redshift. We finally investigate the redshift evolution of the MZR by using the
model by Lilly et al. (2013), finding that the observed evolution from $z=0$ to
$z\simeq3.3$ can be accounted for by the model assuming a weak redshift
evolution of the star formation efficiency.


title:
Improving the modelling of redshift-space distortions - II. A pairwise
  velocity model covering large and small scales

abstract:
  We develop a model for the redshift-space correlation function, valid for
both dark matter particles and halos on scales $>5\,h^{-1}$Mpc. In its simplest
formulation, the model requires the knowledge of the first three moments of the
line-of-sight pairwise velocity distribution plus two well-defined
dimensionless parameters. The model is obtained by extending the
Gaussian-Gaussianity prescription for the velocity distribution, developed in a
previous paper, to a more general concept allowing for local skewness, which is
required to match simulations. We compare the model with the well known
Gaussian streaming model and the more recent Edgeworth streaming model. Using
N-body simulations as a reference, we show that our model gives a precise
description of the redshift-space clustering over a wider range of scales. We
do not discuss the theoretical prescription for the evaluation of the velocity
moments, leaving this topic to further investigation.


title: Disk-fed giant planet formation

abstract:
  Massive giant planets, such as the ones being discovered by direct imaging
surveys, likely experience the majority of their growth through a
circumplanetary disc. We argue that the entropy of accreted material is
determined by boundary layer processes, unlike the "cold-" or "hot-start"
hypotheses usually invoked in the core accretion and direct collapse scenarios.
A simple planetary evolution model illustrates how a wide range of radius and
luminosity tracks become possible, depending on details of the accretion
process. Specifically, the proto-planet evolves towards "hot-start" tracks if
the scale-height of the boundary layer is $\gtrsim0.24$, a value not much
larger than the scale-height of the circumplanetary disc. Understanding the
luminosity and radii of young giant planets will thus require detailed models
of circumplanetary accretion.


title:
Closing the Wedge: Search Strategies for Extended Higgs Sectors with
  Heavy Flavor Final States

abstract:
  We consider search strategies for an extended Higgs sector at the
high-luminosity LHC14 utilizing multi-top final states. In the framework of a
Two Higgs Doublet Model, the purely top final states ($t\bar t, \, 4t$) are
important channels for heavy Higgs bosons with masses in the wedge above
$2\,m_t$ and at low values of $\tan\beta$, while a $2 b 2t$ final state is most
relevant at moderate values of $\tan \beta$. We find, in the $t\bar t H$
channel, with $H \rightarrow t \bar t$, that both single and 3 lepton final
states can provide statistically significant constraints at low values of $\tan
\beta$ for $m_A$ as high as $\sim 750$ GeV. When systematics on the $t \bar t$
background are taken into account, however, the 3 lepton final state is more
powerful, though the precise constraint depends fairly sensitively on lepton
fake rates. We also find that neither $2b2t$ nor $t \bar t$ final states
provide constraints on additional heavy Higgs bosons with couplings to tops
smaller than the top Yukawa due to expected systematic uncertainties in the $t
\bar t$ background.


title:
Radio-loud Narrow Line Seyfert 1 under a different perspective: a
  revised black hole mass estimate from optical spectropolarimetry

abstract:
  Several studies indicate that radio-loud (RL) Active Galactic Nuclei (AGN)
are produced only by the most massive black holes (BH), $M_{\rm BH} \sim
10^8$-$10^{10} M_\odot$. This idea has been challenged by the discovery of RL
Narrow Line Seyfert 1 (RL NLSy1), having estimated masses of $M_{\rm
BH}$$\sim$$10^6$-$10^7$ M$_\odot$. However, these low $M_{\rm BH}$ estimates
might be due to projection effects. Spectropolarimetry allows us to test this
possibility by looking at RL NLSy1s under a different perspective, i.e., from
the viewing angle of the scattering material. We here report the results of a
pilot study of VLT spectropolarimetric observations of the RL NLSy1 PKS
2004-447. Its polarization properties are remarkably well reproduced by models
in which the scattering occurs in an equatorial structure surrounding its broad
line region, seen close to face-on. In particular, we detect a polarized
H$\alpha$ line with a width of $\sim$ 9,000 km s$^{-1}$, $\sim 6$ times broader
than the width seen in direct light. This corresponds to a revised estimate of
$M_{\rm BH}$$\sim$$6\times10^8$ M$_\odot$, well within the typical range of RL
AGN. The double-peaked polarized broad H$\alpha$ profile of the target suggests
that the rare combination of the orientation effects and a broad line region
dominated by the rotation might account for this class of objects, casting
doubts on the virial estimates of BH mass for type-I AGN.


title:
Vortex matter freezing in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ samples with
  a very dense distribution of columnar defects

abstract:
  We show that the dynamical freezing of vortex structures nucleated at diluted
densities in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ samples with a dense
distribution of columnar defects, $B \sim 10^{-2} B_{\Phi}$ with
$B_{\Phi}=5$\,kG, results in configurations with liquid-like correlations. We
propose a freezing model considering a relaxation dynamics dominated by
double-kink excitations driven by the local stresses obtained directly from
experimental images. With this model we estimate the relaxation barrier and the
freezing temperature. We argue that the low-field frozen vortex structures
nucleated in a dense distribution of columnar defects thus correspond to an
out-of-equilibrium non-entangled liquid with strongly reduced mobility rather
than to a snapshot of a metastable state with divergent activation barriers as
for instance expected for the Bose-glass phase at equilibrium.


title:
Electron contribution to the muon anomalous magnetic moment at four
  loops

abstract:
  We present results for the QED contributions to the anomalous magnetic moment
of the muon containing closed electron loops. The main focus is on perturbative
corrections at four-loop order where the external photon couples to the
external muon. Furthermore, all four-loop contributions involving
simultaneously a closed electron and tau loop are computed. In combination with
our recent results on the light-by-light-type corrections (see Ref.
\cite{Kurz:2015bia}) the complete four-loop electron-loop contribution to the
anomalous magnetic moment of the muon has been obtained with an independent
calculation. Our calculation is based on an asymptotic expansion in the ratio
of the electron and the muon mass and shows the importance of higher order
terms in this ratio. We perform a detailed comparison with results available in
the literature and find good numerical agreement.
  As a by-product we present analytic results for the on-shell muon mass and
wave function renormalization constants at three-loop order including massive
closed electron and tau loops, which we also calculated using the method of
asymptotic expansion.


title: Finite-size scaling in a 2D disordered electron gas with spectral nodes

abstract:
  We study the DC conductivity of a weakly disordered 2D electron gas with two
bands and spectral nodes, employing the field theoretical version of the
Kubo--Greenwood conductivity formula. Disorder scattering is treated within the
standard perturbation theory by summing up ladder and maximally crossed
diagrams. The emergent gapless (diffusion) modes determine the behavior of the
conductivity on large scales. We find a finite conductivity with an
intermediate logarithmic finite-size scaling towards smaller conductivities but
do not obtain the logarithmically divergence of the weak-localization approach.
Our results agree with the experimentally observed logarithmic scaling of the
conductivity in graphene with the formation of a plateau near $e^2/\pi h$.


title: Riley's Conjecture on SL(2,R) Representations of 2-Bridge Knots

abstract:
  We prove Riley's conjecture on the number of parabolic SL(2,R)
representations of 2-bridge knot groups.


title:
Revisiting the Sanders-Freiman-Ruzsa Theorem in $\mathbb{F}_p^n$ and its
  Application to Non-malleable Codes

abstract:
  Non-malleable codes (NMCs) protect sensitive data against degrees of
corruption that prohibit error detection, ensuring instead that a corrupted
codeword decodes correctly or to something that bears little relation to the
original message. The split-state model, in which codewords consist of two
blocks, considers adversaries who tamper with either block arbitrarily but
independently of the other. The simplest construction in this model, due to
Aggarwal, Dodis, and Lovett (STOC'14), was shown to give NMCs sending k-bit
messages to $O(k^7)$-bit codewords. It is conjectured, however, that the
construction allows linear-length codewords. Towards resolving this conjecture,
we show that the construction allows for code-length $O(k^5)$. This is achieved
by analysing a special case of Sanders's Bogolyubov-Ruzsa theorem for general
Abelian groups. Closely following the excellent exposition of this result for
the group $\mathbb{F}_2^n$ by Lovett, we expose its dependence on $p$ for the
group $\mathbb{F}_p^n$, where $p$ is a prime.


title: Halpha Kinematics of S4G Spiral Galaxies - III. Inner rotation curves

abstract:
  We present a detailed study of the shape of the innermost part of the
rotation curves of a sample of 29 nearby spiral galaxies, based on high angular
and spectral resolution kinematic Halpha Fabry-Perot observations. In
particular, we quantify the steepness of the rotation curve by measuring its
slope dRvc(0). We explore the relationship between the inner slope and several
galaxy parameters, such as stellar mass, maximum rotational velocity, central
surface brightness ({\mu}0), bar strength and bulge-to-total ratio. Even with
our limited dynamical range, we find a trend for low-mass galaxies to exhibit
shallower rotation curve inner slopes than high-mass galaxies, whereas steep
inner slopes are found exclusively in high-mass galaxies. This trend may arise
from the relationship between the total stellar mass and the mass of the bulge,
which are correlated among them. We find a correlation between the inner slope
of the rotation curve and the morphological T-type, complementary to the
scaling relation between dRvc(0) and {\mu}0 previously reported in the
literature. Although we find that the inner slope increases with the Fourier
amplitude A2 and decreases with the bar torque Qb, this may arise from the
presence of the bulge implicit in both A2 and Qb. As previously noted in the
literature, the more compact the mass in the central parts of a galaxy (more
concretely, the presence of a bulge), the steeper the inner slopes. We conclude
that the baryonic matter dominates the dynamics in the central parts of our
sample galaxies.


title:
UV contribution and power dependence on $\Lambda_\mathrm{QCD}$ of Adler
  function

abstract:
  We formulate a way to separate UV and IR contributions to the Adler function
and discuss how $\Lambda_\mathrm{QCD}^2/Q^2$ dependence is encoded in the UV
contribution within perturbative QCD.


title: A Uniform Catalog of Molecular Clouds in the Milky Way

abstract:
  The all-Galaxy CO survey of Dame, Hartmann, & Thaddeus (2001) is by far the
most uniform, large-scale Galactic CO survey. Using a dendrogram-based
decomposition of this survey, we present a catalog of 1064 massive molecular
clouds throughout the Galactic plane. This catalog contains $2.5 \times 10^8$
solar masses, or $25^{+10.7}_{-5.8} \%$ of the Milky Way's estimated H$_2$
mass. We track clouds in some spiral arms through multiple quadrants. The power
index of Larson's first law, the size-linewidth relation, is consistent with
0.5 in all regions - possibly due to an observational bias - but clouds in the
inner Galaxy systematically have significantly (~ 30%) higher linewidths at a
given size, indicating that their linewidths are set in part by Galactic
environment. The mass functions of clouds in the inner Galaxy versus the outer
Galaxy are both qualitatively and quantitatively distinct. The inner Galaxy
mass spectrum is best described by a truncated power-law with a power index of
$\gamma=-1.6\pm0.1$ and an upper truncation mass $M_0 = (1.0 \pm 0.2) \times
10^7 M_\odot$, while the outer Galaxy mass spectrum is better described by a
non-truncating power law with $\gamma=-2.2\pm0.1$ and an upper mass $M_0 = (1.5
\pm 0.5) \times 10^6 M_\odot$, indicating that the inner Galaxy is able to form
and host substantially more massive GMCs than the outer Galaxy. Additionally,
we have simulated how the Milky Way would appear in CO from extragalactic
perspectives, for comparison with CO maps of other galaxies.


title: Autocratic strategies for alternating games

abstract:
  Repeated games have a long tradition in the behavioral sciences and
evolutionary biology. Recently, strategies were discovered that permit an
unprecedented level of control over repeated interactions by enabling a player
to unilaterally enforce linear constraints on payoffs. Here, we extend this
theory of "zero-determinant" (or, more generally, "autocratic") strategies to
alternating games, which are often biologically more relevant than traditional
synchronous games. Alternating games naturally result in asymmetries between
players because the first move matters or because players might not move with
equal probabilities. In a strictly-alternating game with two players, $X$ and
$Y$, we give conditions for the existence of autocratic strategies for player
$X$ when (i) $X$ moves first and (ii) $Y$ moves first. Furthermore, we show
that autocratic strategies exist even for (iii) games with randomly-alternating
moves. Particularly important categories of autocratic strategies are
extortionate and generous strategies, which enforce unfavorable and favorable
outcomes for the opponent, respectively. We illustrate these strategies using
the continuous Donation Game, in which a player pays a cost to provide a
benefit to the opponent according to a continuous cooperative investment level.
Asymmetries due to alternating moves could easily arise from dominance
hierarchies, and we show that they can endow subordinate players with more
autocratic strategies than dominant players.


title:
Kaluza-Klein graviton phenomenology for warped compactifications, and
  the 750 GeV diphoton excess

abstract:
  A generic prediction of scenarios with extra dimensions accessible in
TeV-scale collisions is the existence of Kaluza-Klein excitations of the
graviton. For a broad class of strongly-warped scenarios one expects to
initially find an isolated resonance, whose phenomenology in the simplest cases
is described by a simplified model with two parameters, its mass, and a
constant $\Lambda$ with units of mass parameterizing its coupling to the
Standard Model stress tensor. These parameters are in turn determined by the
geometrical configuration of the warped compactification. We explore the
possibility that the 750 GeV excess recently seen in 13 TeV data at ATLAS and
CMS could be such a warped Kaluza-Klein graviton, and find a best-fit value
$\Lambda\approx 60$ TeV. We find that while there is some tension between this
interpretation and data from 8 TeV and from the dilepton channel at 13 TeV, it
is not strongly excluded. However, in the simplest scenarios of this kind, such
a signal should soon become apparent in both diphoton and dilepton channels.


title:
Comments on "On Clock Synchronization Algorithms for Wireless Sensor
  Networks Under Unknown Delay"

abstract:
  The generalization of the maximum-likelihood-like estimator for clock skew by
Leng and Wu in the above paper is erroneous because the correlation of the
noise components in the model is not taken into account in the derivation of
the maximum likelihood estimator, its performance bound, and the optimal
selection of the gap between two subtracting time stamps. This comment
investigates the issue of noise correlation in the model and provides the range
of the gap for which the maximum likelihood estimator and its performance bound
are valid and corrects the optimal selection of the gap based on the provided
range.


title:
The Mathematical Basics and the Results of the Theory of physical
  structures

abstract:
  The theory of Physical Structures (TPS) was put forward by Professor Yu.I.
Kulakov for the sake of classifying the laws of Physics. The history of the
development of that theory is given in his monograph [1]. A physical structure
is a geometry of one or two sets whose metric function assigns a number to
every pair of points. Its phenomenological symmetry, under Kulakov, means that
for every collection of some finite number of points all of their reciprocal
distances are functionally related. Such geometries are endowed with a group
symmetry under Klein, which is equivalent to the phenomenological symmetry, and
many of them have an essential physical interpretation. That is why they are to
be defined precisely and explored as purely mathematical objects. In this
monograph we treat the mathematical basics of the TPS and present the results
of attempts at classification that have been obtained by now. We hope that the
monograph will be of interest for research workers and teachers, senior and
post graduate students, as well as to all those interested in algebra, geometry
and theoretical physics who would like to use the TPS in their research
projects or could want to contribute to the development of its mathematical
apparatus.


title:
Proof of some divisibility results on sums involving binomial
  coefficients

abstract:
  By using the Rodriguez-Villegas-Mortenson supercongruences, we prove four
supercongruences on sums involving binomial coefficients, which were originally
conjectured by Sun. We also confirm a related conjecture of Guo on
integer-valued polynomials.


title: Spanning Trees and Mahler Measure

abstract:
  The complexity of a finite connected graph is its number of spanning trees;
for a non-connected graph it is the product of complexities of its connected
components. If $G$ is an infinite graph with cofinite free ${\mathbb
Z}^d$-symmetry, then the logarithmic Mahler measure $m(\Delta)$ of its
Laplacian polynomial $\Delta$ is the exponential growth rate of the complexity
of finite quotients of $G$. It is bounded below by $m(\Delta({\mathbb G}_d))$,
where ${\mathbb G}_d$ is the grid graph of dimension $d$. The growth rates
$m(\Delta({\mathbb G}_d))$ are asymptotic to $\log 2d$ as $d$ tends to
infinity. If $m(\Delta(G))\ne 0$, then $m(\Delta(G)) \ge \log 2$. An
application to determinant growth rates of families of alternating links
arising from planar graphs is given.


title:
Global wellposedness for a class of
  reaction-advection-anisotropic-diffusion systems

abstract:
  We prove existence and uniqueness of global solutions for a class of
reaction-advection-anisotropic-diffusion systems whose reaction terms have a
"triangular structure". We thus extend previous results to the case of
time-space dependent anisotropic diffusions and with time-space dependent
advection terms. The corresponding models are in particular relevant for
transport processes inside porous media and in situations in which additional
migration occurs. The proofs are based on optimal $L^p$-maximal regularity
results for the general time-dependent linear operator dual to the one involved
in the considered systems. As an application, we prove global well-posedness
for a prototypical class of chemically reacting systems with mass-action
kinetics, involving networks of reactions of the type $C_1+\ldots+C_{P-1}
\rightleftharpoons C_{P} $. Finally, we analyze how a classical a priori
$L^2$-estimate of the solutions, which holds with this kind of nonlinear
reactive terms, extends to our general anisotropic-advection framework. It does
extend with the same assumptions for isotropic diffusions and is replaced by an
$L^{(N+1)/N}$-estimate in the general situation.


title:
Piezoelectric softening in ferroelectrics: ferroelectric versus
  antiferroelectric PbZr$_{1-x}$Ti$_{x}$O$_{3}$

abstract:
  The traditional derivation of the elastic anomalies associated with
ferroelectric (FE) phase transitions in the framework of the Landau theory is
combined with the piezoelectric constitutive relations instead of being
explicitly carried out with a definite expression of the FE part of the free
energy. In this manner it is shown that the softening within the FE phase is of
electrostrictive and hence piezoelectric origin. Such a piezoelectric softening
may be canceled by the better known piezoelectric stiffening, when the
piezoelectric charges formed during the vibration are accompanied by the
depolarization field, as for example in Brillouin scattering experiments. As
experimental validation, we present new measurements on Zr-rich PZT, where the
FE phase transforms into antiferroelectric on cooling or doping with La, and a
comparison of existing measurements made on FE PZT with low frequency and
Brillouin scattering experiments.


title:
Primary frequency regulation with load-side participation: stability and
  optimality

abstract:
  We present a method to design distributed generation and demand control
schemes for primary frequency regulation in power networks that guarantee
asymptotic stability and ensure fairness of allocation. We impose a passivity
condition on net power supply variables and provide explicit steady state
conditions on a general class of generation and demand control dynamics that
ensure convergence of solutions to equilibria that solve an appropriately
constructed network optimization problem. We also show that the inclusion of
controllable demand results in a drop in steady state frequency deviations. We
discuss how various classes of dynamics used in recent studies fit within our
framework and show that this allows for less conservative stability and
optimality conditions. We illustrate our results with simulations on the IEEE
68 bus system and observe that both static and dynamic demand response schemes
that fit within our framework offer improved transient and steady state
behavior compared with control of generation alone. The dynamic scheme is also
seen to enhance the robustness of the system to time-delays.


title: The algebra of Kleene stars of the plane and polylogarithms

abstract:
  We extend the definition and study the algebraic properties of the
polylogarithm Li(T), where T is rational series over the alphabet X = {x 0, x
1} belonging to suitable subalgebras of rational series.


title: Large superconformal near-horizons from M-theory

abstract:
  We report on a classification of supersymmetric solutions to 11D supergravity
with $SO(2,2) \times SO(3)$ isometry, which are AdS/CFT dual to 2D CFTs with
$\mathcal{N} = (0,4)$ supersymmetry. We recover the Maldacena, Strominger,
Witten (MSW) near-horizon with small superconformal symmetry and identify a
class of $AdS_3 \times S^2 \times S^2 \times CY_2$ geometries with emergent
large superconformal symmetry. This exhausts known compact geometries.
Compactification of M-theory on $CY_2$ results in a vacuum of 7D supergravity
with large superconformal symmetry, providing a candidate near-horizon for an
extremal black hole and a potential new setting to address microstates.


title: Large deviations for infectious diseases models

abstract:
  We establish large deviation estimates for Poisson driven models of
infectious disease, and apply those estimates to the time of exit from the
basin of attraction of an endemic equilibrium. We apply our results to the
classical SIRS model.


title: A Baryonic Effect on the Merger Timescale of Galaxy Clusters

abstract:
  Accurate estimation of the merger timescale of galaxy clusters is important
to understand the cluster merger process and further the formation and
evolution of the large-scale structure of the universe. In this paper, we
explore a baryonic effect on the merger timescale of galaxy clusters by using
hydrodynamical simulations. We find that the baryons play an important role in
accelerating the merger process. The merger timescale decreases with increasing
the gas fraction of galaxy clusters. For example, the merger timescale is
shortened by a factor of up to 3 for merging clusters with gas fractions 0.15,
compared with the timescale obtained with zero gas fractions. The baryonic
effect is significant for a wide range of merger parameters and especially more
significant for nearly head-on mergers and high merging velocities. The
baryonic effect on the merger timescale of galaxy clusters is expected to have
impacts on the structure formation in the universe, such as the cluster mass
function and massive substructures in galaxy clusters, and a bias of "no-gas"
may exist in the results obtained from the dark matter-only cosmological
simulations.


title: Renormalization Group Circuits for Gapless States

abstract:
  We show that a large class of gapless states are renormalization group fixed
points in the sense that they can be grown scale by scale using local
unitaries. This class of examples includes some theories with dynamical
exponent different from one, but does not include conformal field theories. The
key property of the states we consider is that the ground state wavefunction is
related to the statistical weight of a local statistical model. We give several
examples of our construction in the context of Ising magnetism.


title:
Massive pulsating stars observed by BRITE-Constellation. I. The triple
  system Beta Centauri (Agena)

abstract:
  This paper aims to precisely determine the masses and detect pulsation modes
in the two massive components of Beta Cen with BRITE-Constellation photometry.
In addition, seismic models for the components are considered and the effects
of fast rotation are discussed. This is done to test the limitations of seismic
modeling for this very difficult case. A simultaneous fit of visual and
spectroscopic orbits is used to self-consistently derive the orbital
parameters, and subsequently the masses, of the components. The derived masses
are equal to 12.02 +/- 0.13 and 10.58 +/- 0.18 M_Sun. The parameters of the
wider, A - B system, presently approaching periastron passage, are constrained.
Analysis of the combined blue- and red-filter BRITE-Constellation photometric
data of the system revealed the presence of 19 periodic terms, of which eight
are likely g modes, nine are p modes, and the remaining two are combination
terms. It cannot be excluded that one or two low-frequency terms are rotational
frequencies. It is possible that both components of Beta Cen are Beta Cep/SPB
hybrids. An attempt to use the apparent changes of frequency to distinguish
which modes originate in which component did not succeed, but there is
potential for using this method when more BRITE data become available. Agena
seems to be one of very few rapidly rotating massive objects with rich p- and
g-mode spectra, and precisely known masses. It can therefore be used to gain a
better understanding of the excitation of pulsations in relatively rapidly
rotating stars and their seismic modeling. Finally, this case illustrates the
potential of BRITE-Constellation data for the detection of rich-frequency
spectra of small-amplitude modes in massive pulsating stars.


title:
Observation of nonlinear thermal optical dynamics in a chalcogenide
  nanobeam cavity

abstract:
  We present a theoretical and experimental analysis of nonlinear thermo-optic
effects in suspended chalcogenide glass nanobeam cavities. We measure the power
dependent resonance peaks and characterise the dynamic nonlinear thermo-optic
response of the cavity under modulated light input. Several distinct nonlinear
characteristics are identified, including a modified spectral response
containing periodic fringes, a critical wavelength jump and saturated time
delay for modulation frequency faster than the thermal characteristic time. We
reveal that the coupling to a parasitic Fabry-Perot cavity enables isolated
thermal equilibrium states resulting in the discontinuous thermo-optic critical
point.


title: On some Variational Problems set on domains tending to infinity

abstract:
  Let $\Omega_\ell = \ell\omega_1 \times \omega_2$ where $\omega_1 \subset
\R^p$ and $\omega_2 \subset \R^{n-p}$ are assumed to be open and bounded. We
consider the following minimization problem: $$E_{\Omega_\ell}(u_\ell) =
\min_{u\in W_0^{1,q}(\Omega_\ell)}E_{\Omega_\ell}(u)$$ where
$E_{\Omega_\ell}(u) = \int_{\Omega_\ell}F(\grad u)-fu$, $F$ is a convex
function and $f\in L^{q'}(\omega_2)$. We are interested in studying the
asymptotic behavior of the solution $u_\ell$ as $\ell$ tends to infinity.


title:
Dynamical formation signatures of black hole binaries in the first
  detected mergers by LIGO

abstract:
  The dynamical formation of stellar-mass black hole-black hole binaries has
long been a promising source of gravitational waves for the Laser
Interferometer Gravitational-Wave Observatory (LIGO). Mass segregation,
gravitational focusing, and multibody dynamical interactions naturally increase
the interaction rate between the most massive black holes in dense stellar
systems, eventually leading them to merge. We find that dynamical interactions,
particularly three-body binary formation, enhance the merger rate of black hole
binaries with total mass M_tot roughly as ~M_tot^beta, with beta >~ 4. We find
that this relation holds mostly independently of the initial mass function, but
the exact value depends on the degree of mass segregation. The detection rate
of such massive black hole binaries is only further enhanced by LIGO's greater
sensitivity to massive black hole binaries with M_tot <~ 80 solar masses. We
find that for power-law BH mass functions dN/dM ~ M^-alpha with alpha <~ 2,
LIGO is most likely to detect black hole binaries with a mass twice that of the
maximum initial black hole mass and a mass ratio near one. Repeated mergers of
black holes inside the cluster result in about ~5% of mergers being observed
between two and three times the maximum initial black hole mass. Using these
relations, one may be able to invert the observed distribution to the initial
mass function with multiple detections of merging black hole binaries.


title: PyCFTBoot: A flexible interface for the conformal bootstrap

abstract:
  We introduce PyCFTBoot, a wrapper designed to reduce the barrier to entry in
conformal bootstrap calculations that require semidefinite programming.
Symengine and SDPB are used for the most intensive symbolic and numerical steps
respectively. After reviewing the built-in algorithms for conformal blocks, we
explain how to use the code through a number of examples that verify past
results. As an application, we show that the multi-correlator bootstrap still
appears to single out the Wilson-Fisher fixed points as special theories in
dimensions between 3 and 4 despite the recent proof that they violate
unitarity.


title: Born-Oppenheimer Approximation for a Singular System

abstract:
  We discuss a simple singular system in one dimension, two heavy particles
interacting with a light particle via an attractive contact interaction. It is
natural to apply Born-Oppenheimer approximation to this problem. We present a
detailed discussion of this approach, the advantage of this simple model is
that one can estimate the error terms self-consistently. Moreover, a Fock space
approach to this problem is presented where a systematic expansion can be
proposed to get higher order corrections. A slight modification of the same
problem in which the light particle is relativistic is discussed in a later
section. Here, the second quantized description is more challenging but with
some care one can recover the first order term as well as introducing a more
systematic approach to higher orders.


title: Subleading Effects and the Field Range in Axion Inflation

abstract:
  An attractive candidate for the inflaton is an axion slowly rolling down a
flat potential protected by a perturbative shift symmetry. Realisations of this
idea within large field, natural and monomial inflation have been disfavoured
by observations and are difficult to embed in string theory. We show that
subleading, but significant non-perturbative corrections can superimpose sharp
cliffs and gentle plateaus into the potential, whose overall effect is to
enhance the number of e-folds of inflation. Sufficient e-folds are therefore
achieved for smaller field ranges compared to the potential without such
corrections. Thus, both single-field natural and monomial inflation in UV
complete theories like string theory, can be restored into the favour of
current observations, with distinctive signatures. Tensor modes result
un-observably small, but there is a large negative running of the spectral
index. Remarkably, natural inflation can be achieved with a single field whose
axion decay constant is sub-Planckian.


title: Mode-coupling effects in anisotropic flow in heavy-ion collisions

abstract:
  Higher-order anisotropic flows in heavy-ion collisions are affected by
nonlinear mode coupling effects. It has been suggested that the associated
nonlinear hydrodynamic response coefficients probe the transport properties and
are largely insensitive to the spectrum of initial density fluctuations of the
medium created in these collisions. To test this suggestion, we explore
nonlinear mode coupling effects in event-by-event viscous fluid dynamics, using
two different models for the fluctuating initial density profiles, and compare
the nonlinear coupling coefficients between the initial eccentricity vectors
before hydrodynamic expansion and the final flow vectors after the expansion.
For several mode coupling coefficients we find significant sensitivity to the
initial fluctuation spectrum. They all exhibit strong sensitivity to the
specific shear viscosity at freeze-out, but only weak dependence on the shear
viscosity during hydrodynamic evolution.


title: Finiteness of irreducible holomorphic eta quotients of a given level

abstract:
  We show that for any positive integer $N$, there are only finitely many
holomorphic eta quotients of level $N$, none of which is a product of two
holomorphic eta quotients other than 1 and itself. This result is an analog of
Zagier's conjecture/ Mersmann's theorem which states that: Of any given weight,
there are only finitely many irreducible holomorphic eta quotients, none of
which is an integral rescaling of another eta quotient. We construct such eta
quotients for all cubefree levels. In particular, our construction demonstrates
the existence of irreducible holomorphic eta quotients of arbitrarily large
weights.


title: Asymptotic *-moments of some random Vandermonde matrices

abstract:
  Appropriately normalized square random Vandermonde matrices based on
independent random variables with uniform distribution on the unit circle are
studied. It is shown that as the matrix sizes increases without bound, with
respect to the expectation of the trace there is an asymptotic *-distribution,
equal to that of a C[0,1]-valued R-diagonal element.


title:
Are the hosts of VLBI selected radio-AGN different to those of
  radio-loud AGN?

abstract:
  Recent studies have found that radio-AGN selected by radio-loudness show
little difference in terms of their host galaxy properties when compared to
non-AGN galaxies of similar stellar mass and redshift. Using new 1.4~GHz VLBI
observations of the COSMOS field we find that approximately 49$\pm8$\% of
high-mass (M $>$ 10$^{10.5}$ M$_{\odot}$), high luminosity (L$_{1.4}$ $>$
10$^{24}$ W~Hz$^{-1}$) radio-AGN possess a VLBI detected counterpart. These
objects show no discernible bias towards specific stellar masses, redshifts or
host properties other than what is shown by the radio-AGN population in
general. Radio-AGN that are detected in VLBI observations are not special, but
form a representative sample of the radio-loud AGN population.


title:
Tunnel barrier design in donor nanostructures defined by hydrogen-resist
  lithography

abstract:
  A four-terminal donor quantum dot (QD) is used to characterize potential
barriers between degenerately doped nanoscale contacts. The QD is fabricated by
hydrogen-resist lithography on Si(001) in combination with $n$-type doping by
phosphine. The four contacts have different separations ($d$ = 9, 12, 16 and 29
nm) to the central 6 nm $\times$ 6 nm QD island, leading to different tunnel
and capacitive coupling. Cryogenic transport measurements in the
Coulomb-blockade (CB) regime are used to characterize these tunnel barriers. We
find that field enhancement near the apex of narrow dopant leads is an
important effect that influences both barrier breakdown and the magnitude of
the tunnel current in the CB transport regime. From CB-spectroscopy
measurements, we extract the mutual capacitances between the QD and the four
contacts, which scale inversely with the contact separation $d$. The
capacitances are in excellent agreement with numerical values calculated from
the pattern geometry in the hydrogen resist. We show that by engineering the
source-drain tunnel barriers to be asymmetric, we obtain a much simpler
excited-state spectrum of the QD, which can be directly linked to the orbital
single-particle spectrum.


title: A Precessing Ferromagnetic Needle Magnetometer

abstract:
  A ferromagnetic needle is predicted to precess about the magnetic field axis
at a Larmor frequency $\Omega$ under conditions where its intrinsic spin
dominates over its rotational angular momentum, $N\hbar \gg I\Omega$ ($I$ is
the moment of inertia of the needle about the precession axis and $N$ is the
number of polarized spins in the needle). In this regime the needle behaves as
a gyroscope with spin $N\hbar$ maintained along the easy axis of the needle by
the crystalline and shape anisotropy. A precessing ferromagnetic needle is a
correlated system of $N$ spins which can be used to measure magnetic fields for
long times. In principle, by taking advantage of rapid averaging of quantum
uncertainty, the sensitivity of a precessing needle magnetometer can far
surpass that of magnetometers based on spin precession of atoms in the gas
phase. Under conditions where noise from coupling to the environment is
subdominant, the scaling with measurement time $t$ of the quantum- and
detection-limited magnetometric sensitivity is $t^{-3/2}$. The phenomenon of
ferromagnetic needle precession may be of particular interest for precision
measurements testing fundamental physics.


title:
Forces for Structural Optimizations in Correlated Materials within
  DFT+Embedded DMFT Functional Approach

abstract:
  We implemented the derivative of the free energy functional with respect to
the atom displacements, so called force, within the combination of Density
Functional Theory and the Embedded Dynamical Mean Field Theory. We show that in
combination with the numerically exact quantum Monte Carlo (MC) impurity
solver, the MC noise cancels to a great extend, so that the method can be used
very efficiently for structural optimization of correlated electron materials.
As an application of the method, we show how strengthening of the fluctuating
moment in FeSe superconductor leads to a substantial increase of the anion
height, and consequently to a very large effective mass, and also strong
orbital differentiation.


title: Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"

abstract:
  We present a relativistic formulation of the quantum Hall effect on Haldane
sphere. An explicit form of the pseudopotential is derived for the relativistic
quantum Hall effect with/without mass term. We clarify particular features of
the relativistic quantum Hall states with the use of the exact diagonalization
study of the pseudopotential Hamiltonian. Physical effects of the mass term to
the relativistic quantum Hall states are investigated in detail. The mass term
acts as an interpolating parameter between the relativistic and
non-relativistic quantum Hall effects. It is pointed out that the mass term
unevenly affects the many-body physics of the positive and negative Landau
levels as a manifestation of the "parity anomaly". In particular, we explicitly
demonstrate the instability of the Laughlin state of the positive first
relativistic Landau level with the reduction of the charge gap.


title: The Riesz transform of codimension smaller than one and the Wolff energy

abstract:
  Fix $d\geq 2$, and $s\in (d-1,d)$. We characterize the non-negative locally
finite non-atomic Borel measures $\mu$ in $\mathbb{R}^d$ for which the
associated $s$-Riesz transform is bounded in $L^2(\mu)$ in terms of the Wolff
energy. This extends the range of $s$ in which the Mateu-Prat-Verdera
characterization of measures with bounded $s$-Riesz transform is known.
  As an application, we give a metric characterization of the removable sets
for locally Lipschitz continuous solutions of the fractional Laplacian operator
$(-\Delta)^{\alpha/2}$, $\alpha\in (1,2)$, in terms of a well-known capacity
from non-linear potential theory. This result contrasts sharply with
removability results for Lipschitz harmonic functions.


title:
Parameterizing Region Covariance: An Efficient Way To Apply Sparse Codes
  On Second Order Statistics

abstract:
  Sparse representations have been successfully applied to signal processing,
computer vision and machine learning. Currently there is a trend to learn
sparse models directly on structure data, such as region covariance. However,
such methods when combined with region covariance often require complex
computation. We present an approach to transform a structured sparse model
learning problem to a traditional vectorized sparse modeling problem by
constructing a Euclidean space representation for region covariance matrices.
Our new representation has multiple advantages. Experiments on several vision
tasks demonstrate competitive performance with the state-of-the-art methods.


title: Poor starting points in machine learning

abstract:
  Poor (even random) starting points for learning/training/optimization are
common in machine learning. In many settings, the method of Robbins and Monro
(online stochastic gradient descent) is known to be optimal for good starting
points, but may not be optimal for poor starting points -- indeed, for poor
starting points Nesterov acceleration can help during the initial iterations,
even though Nesterov methods not designed for stochastic approximation could
hurt during later iterations. The common practice of training with nontrivial
minibatches enhances the advantage of Nesterov acceleration.


title: ASASSN-14li: A Model Tidal Disruption Event

abstract:
  ASASSN-14li is a recently-discovered tidal disruption event with an
exceptionally rich data-set: spectra and lightcurves in soft X-rays, UV,
optical, and radio. To understand its emission properties in all these bands,
we have extended our model for post-tidal disruption accretion and photon
production to estimate both soft X-ray radiation produced by the prompt
accretion phase and synchrotron emission associated with the bow shock driven
through an external medium by the unbound tidal debris, as well as optical and
UV light. We find that fiducial values of the stellar mass ($1 M_\odot$) and
black hole mass ($10^{6.5} M_{\odot}$) yield: quantitative agreement with the
optical/UV luminosity, lightcurve, and color temperature; approximate agreement
with the somewhat uncertain soft X-ray spectrum and lightcurve; and
quantitative agreement with the radio luminosity, spectrum and lightcurve.
Equipartition analysis of the radio data implies that the radio-emitting region
expands with a constant speed, and its magnitude is comparable to the speed
expected for the unbound stellar ejecta. Both facts provide strong support to
our model. We find that the disruption event took place in mid-September 2014.
Two independent parameters, the magnitude and logarithmic radial gradient of
the ambient gas density near the black hole, must be fit to the data to explain
the radio emission; their inferred values are comparable to those found near
both Sgr A* and the TDE candidate Swift J1644.


title: Finiteness of simple holomorphic eta quotients of a given weight

abstract:
  We provide a simplified proof of Zagier's conjecture / Mersmann's theorem
which states that of any particular weight, there are only finitely many
holomorphic eta quotients, none of which is an integral rescaling of another
eta quotient or a product of two holomorphic eta quotients other than 1 and
itself.


title: On the relation between continuous and combinatorial

abstract:
  Axiomatic Cohesion proposes that the contrast between cohesion and
non-cohesion may be expressed by means of a geometric morphism $p :\mathcal{E}
\to \mathcal {S}$ (between toposes) with certain special properties that allow
to effectively use the intuition that the objects of $\mathcal{E}$ are `spaces'
and those of $\mathcal{S}$ are `sets'. Such geometric morphisms are called
(pre-)cohesive. We may also say that $\mathcal{E}$ is pre-cohesive (over
$\mathcal{S}$). In this case, the topos $\mathcal{E}$ determines an
$\mathcal{S}$-enriched `homotopy' category. The purpose of the present paper is
to study certain aspects of this homotopy theory. We introduce weakly Kan
objects in a pre-cohesive topos, which are analogous to Kan complexes in the
topos of simplicial sets. Also, given a geometric morphism $g:\mathcal{F}
\to\mathcal{E}$ between pre-cohesive toposes $\mathcal{F}$ and $\mathcal{E}$
(over the same base), we define what it means for $g$ to preserve pieces. We
prove that if $g$ preserves pieces then it induces an adjunction between the
homotopy categories determined by $\mathcal{F}$ and $\mathcal{E}$, and that the
direct image $g_*:\mathcal{F}\to \mathcal{E}$ preserves weakly Kan objects.
These and other results support the intuition that the inverse image of $g$ is
`geometric realization'. In particular, since Kan complexes are weakly Kan in
the pre-cohesive topos of simplicial sets, the result relating $g$ and weakly
Kan objects is analogous to the fact that the singular complex of a space is a
Kan complex.


title: A Hamiltonian Perturbation Theory for the Nonlinear Vlasov Equation

abstract:
  The nonlinear Vlasov equation contains the full nonlinear dynamics and
collective effects of a given Hamiltonian system. The linearized approximation
is not valid for a variety of interesting systems, nor is it simple to extend
to higher order. It is also well-known that the linearized approximation to the
Vlasov equation is invalid for long times, due to its inability to correctly
capture fine phase space structures. We derive a perturbation theory for the
Vlasov equation based on the underlying Hamiltonian structure of the phase
space evolution. We obtain an explicit perturbation series for a dressed
Hamiltonian applicable to arbitrary systems whose dynamics can be described by
the nonlinear Vlasov equation.

categories: physics.plasm-ph math-ph math.MP physics.class-ph


title:
Model Waveform Accuracy Requirements for the Allen $\chi^2$
  Discriminator

abstract:
  This paper derives accuracy standards for model gravitational waveforms
required to ensure proper use of the Allen $\chi^2$ discriminator in
gravitational wave (GW) data analysis. These standards are different from
previously established requirements for detection and waveform parameter
measurement based on signal-to-noise optimization. We present convenient
formulae for evaluating and interpreting the contribution of model errors to
measured values of this $\chi^2$ statistic. The new accuracy standards derived
here are needed to ensure the reliability of measured values of the Allen
$\chi^2$ statistic, both in their traditional role as vetoes and in their
current role as elements in evaluating the significance of candidate
detections.


title:
Minkowski and Special Relativity: Does His Spacetime Geometry Explain
  Space Contraction?

abstract:
  For over a century Minkowskian spacetime has dominated discussions of space
contraction and time dilation within special relativity. Brown and Pooley have
called into question both the assumptions of Minkowski and the effects his
presumed spacetime has upon objects in motion. But while they reject Minkowski,
Brown and Pooley do not fill in the missing causal connection between velocity
and space contraction and time dilation. To supply this causal connection
between object and observer in relative motion we should be focusing on energy
difference rather than velocity difference. When different inertial observers
at different relative velocities measure the same rod (or clock), each observer
registers a different amount of kinetic energy for the object. Following the
consequences of this permits a new understanding of relativistic space
contraction and time dilation.


title:
Binarized Neural Networks: Training Deep Neural Networks with Weights
  and Activations Constrained to +1 or -1

abstract:
  We introduce a method to train Binarized Neural Networks (BNNs) - neural
networks with binary weights and activations at run-time. At training-time the
binary weights and activations are used for computing the parameters gradients.
During the forward pass, BNNs drastically reduce memory size and accesses, and
replace most arithmetic operations with bit-wise operations, which is expected
to substantially improve power-efficiency. To validate the effectiveness of
BNNs we conduct two sets of experiments on the Torch7 and Theano frameworks. On
both, BNNs achieved nearly state-of-the-art results over the MNIST, CIFAR-10
and SVHN datasets. Last but not least, we wrote a binary matrix multiplication
GPU kernel with which it is possible to run our MNIST BNN 7 times faster than
with an unoptimized GPU kernel, without suffering any loss in classification
accuracy. The code for training and running our BNNs is available on-line.


title:
Minimum Distances of the QC-LDPC Codes in IEEE 802 Communication
  Standards

abstract:
  This work applies earlier results on Quasi-Cyclic (QC) LDPC codes to the
codes specified in six separate IEEE 802 standards, specifying wireless
communications from 54 MHz to 60 GHz. First, we examine the weight matrices
specified to upper bound the codes' minimum distance independent of block
length. Next, we search for the minimum distance achieved for the parity check
matrices selected at each block length. Finally, solutions to the computational
challenges encountered are addressed.


title: Hierarchical Tree Algorithm for Collisional N-body Simulations on GRAPE

abstract:
  We present an implementation of the hierarchical tree algorithm on the
individual timestep algorithm (the Hermite scheme) for collisional $N$-body
simulations, running on GRAPE-9 system, a special-purpose hardware accelerator
for gravitational many-body simulations. Such combination of the tree algorithm
and the individual timestep algorithm was not easy on the previous GRAPE system
mainly because its memory addressing scheme was limited only to sequential
access to a full set of particle data. The present GRAPE-9 system has an
indirect memory addressing unit and a particle memory large enough to store all
particles data and also tree nodes data. The indirect memory addressing unit
stores interaction lists for the tree algorithm, which is constructed on host
computer, and, according to the interaction lists, force pipelines calculate
only the interactions necessary. In our implementation, the interaction
calculations are significantly reduced compared to direct $N^2$ summation in
the original Hermite scheme. For example, we can archive about a factor 30 of
speedup (equivalent to about 17 teraflops) against the Hermite scheme for a
simulation of $N=10^6$ system, using hardware of a peak speed of 0.6 teraflops
for the Hermite scheme.


title:
Effect of Pauli principle on the deformed QRPA calculations and its
  consequence in the $\beta$-decay calculations of deformed even-even nuclei

abstract:
  In this work, we take into consideration of Pauli Exclusion Principle(PEP) in
the quasi-particle random phase approximation (QRPA) calculations for the
deformed systems by replacing the traditional Quasi-Boson Approximation(QBA)
with the renormalized one. With this new formalism, the parametrization of QRPA
calculations has been changed and the collapse of QRPA solutions could be avoid
for realistic $g_{pp}$ values. We further find that the necessity of
renormalization parameter of particle-particle residual interaction $g_{pp}$ in
QRPA calculations is due to the exclusion of PEP. So with the inclusion of PEP,
we could easily extend the deformed QRPA calculations to the less explored
region where lack of experimental data prevent effective parametrization of
$g_{pp}$ for QRPA methods. With this theoretical improvement, we give
predictions of weak decay rates for even-even isotopes in the rare earth region
and the results are then compared with existing calculations.


title:
Joint Data Detection and Phase Noise Mitigation for Light Field Video
  Transmission in MIMO-OFDM Systems

abstract:
  Previous studies in the literature for video transmission over wireless
communication systems focused on combating the effects of additive channel
noise and fading channels without taking the impairments in the physical layer
such as phase noise (PHN) into account. Oscillator phase noise impairs the
performance of multi-input multi-output- orthogonal frequency division
multiplexing (MIMO-OFDM) systems in providing high data rates for video
applications and may lead to decoding failure. In this paper, we propose a
light field (LF) video transmission system in wireless channels, and analyze
joint data detection and phase mitigation in MIMO-OFDM systems for LF video
transmission. The signal model and rate-distortion (RD) model for LF video
transmission in the presence of multiple PHNs are discussed. Moreover, we
propose an iterative algorithm based on the extended Kalman filter for joint
data detection and PHN tracking. Numerical results show that the proposed
detector can significantly improve the average bit-error rate (BER) and
peak-to-noise ratio (PSNR) performance for LF video transmission compared to
existing algorithms. Moreover, the BER and PSNR performance of the proposed
system is closer to that of the ideal case of perfect PHN estimation. Finally,
it is demonstrated that the proposed system model and algorithm are well suited
for LF video transmission in wireless channels.


title: Holomorphic eta quotients of weight 1/2

abstract:
  We give a short proof of Zagier's conjecture / Mersmann's theorem which
states that each holomorphic eta quotient of weight 1/2 is an integral
rescaling of some eta quotient from Zagier's list of fourteen primitive
holomorphic eta quotients. In particular, given any holomorphic eta quotient
$f$ of weight 1/2, this result enables us to provide a closed-form expression
for the coefficient of qn in the $q$-series expansion of $f$, for all $n$. We
also demonstrate another application of the above theorem in extending the
levels of the simple (resp. irreducible) holomorphic eta quotients.


title: An equivariant index for proper actions II: properties and applications

abstract:
  In the first part of this series, we defined an equivariant index without
assuming the group acting or the orbit space of the action to be compact. This
allowed us to generalise an index of deformed Dirac operators, defined for
compact groups by Braverman. In this paper, we investigate properties and
applications of this index. We prove that it has an induction property that can
be used to deduce various other properties of the index. In the case of compact
orbit spaces, we show how it is related to the analytic assembly map from the
Baum-Connes conjecture, and an index used by Mathai and Zhang. We use the index
to define a notion of K-homological Dirac induction, and show that, under
conditions, it satisfies the quantisation commutes with reduction principle.


title: Dirichlet's problem with entire data posed on an ellipsoidal cylinder

abstract:
  We consider the Dirichlet problem in an ellipsoidal cylinder when the data
function is entire. Under an additional assumption that the order of the data
function is less than one, we show that there is a solution that extends as an
entire harmonic function.


title: An Exact Efficiency Formula for Holographic Heat Engines

abstract:
  Further consideration is given to the efficiency of black hole heat engines
that perform mechanical work via the pdV terms present in the First Law of
extended gravitational thermodynamics. It is noted that when the engine cycle
is a rectangle with sides parallel to the (p,V) axes, the efficiency can be
written simply in terms of the mass of the black hole evaluated at the corners.
Since an arbitrary cycle can be approximated to any desired accuracy by a
tiling of rectangles, a general geometrical algorithm for computing the
efficiency follows. A simple generalization of the algorithm renders it
applicable to more general classes of heat engine, beyond the black hole
context.


title:
Caution on emergent continuous symmetry: a Monte Carlo investigation of
  transverse-field frustrated Ising model on triangle and honeycomb lattices

abstract:
  Continuous symmetries are believed to emerge at many quantum critical points
in frustrated magnets. In this work, we study two candidates of this paradigm:
the transverse-field frustrated Ising model (TFFIM) on the triangle and the
honeycomb lattices. The former is the prototypical example of this paradigm,
and the latter has recently been proposed as another realization. Our
large-scale Monte Carlo simulation confirms that the quantum phase transition
(QPT) in the triangle lattice TFFIM indeed hosts an emergent O(2) symmetry, but
that in the honeycomb lattice TFFIM is a first-order QPT and does not have an
emergent continuous symmetry. Furthermore, our analysis of the order parameter
histogram reveals that such different behavior originates from the irrelevance
and relevance of anisotropic terms near the QPT in the low-energy effective
theory of the two models. The comparison between theoretical analysis and
numerical simulation in this work paves the way for scrutinizing investigation
of emergent continuous symmetry at classical and quantum phase transitions.


title: Co-Designing a Scalable Quantum Computer with Trapped Atomic Ions

abstract:
  The first generation of quantum computers are on the horizon, fabricated from
quantum hardware platforms that may soon be able to tackle certain tasks that
cannot be performed or modelled with conventional computers. These quantum
devices will not likely be universal or fully programmable, but special-purpose
processors whose hardware will be tightly co-designed with particular target
applications. Trapped atomic ions are a leading platform for first generation
quantum computers, but are also fundamentally scalable to more powerful general
purpose devices in future generations. This is because trapped ion qubits are
atomic clock standards that can be made identical to a part in 10^15, and their
quantum circuit connectivity can be reconfigured through the use of external
fields, without modifying the arrangement or architecture of the qubits
themselves. In this article we show how a modular quantum computer of any size
can be engineered from ion crystals, and how the wiring between ion trap qubits
can be tailored to a variety of applications and quantum computing protocols.


title: Combinatorial Scoring of Phylogenetic Networks

abstract:
  Construction of phylogenetic trees and networks for extant species from their
characters represents one of the key problems in phylogenomics. While solution
to this problem is not always uniquely defined and there exist multiple methods
for tree/network construction, it becomes important to measure how well the
constructed networks capture the given character relationship across the
species.
  In the current study, we propose a novel method for measuring the specificity
of a given phylogenetic network in terms of the total number of distributions
of character states at the leaves that the network may impose. While for binary
phylogenetic trees, this number has an exact formula and depends only on the
number of leaves and character states but not on the tree topology, the
situation is much more complicated for non-binary trees or networks.
Nevertheless, we develop an algorithm for combinatorial enumeration of such
distributions, which is applicable for arbitrary trees and networks under some
reasonable assumptions.


title: Collaborative filtering via sparse Markov random fields

abstract:
  Recommender systems play a central role in providing individualized access to
information and services. This paper focuses on collaborative filtering, an
approach that exploits the shared structure among mind-liked users and similar
items. In particular, we focus on a formal probabilistic framework known as
Markov random fields (MRF). We address the open problem of structure learning
and introduce a sparsity-inducing algorithm to automatically estimate the
interaction structures between users and between items. Item-item and user-user
correlation networks are obtained as a by-product. Large-scale experiments on
movie recommendation and date matching datasets demonstrate the power of the
proposed method.


title: Periodicity of the Cayley-Dickson twists

abstract:
  Regarding the Cayley-Dickson algebras as twisted group algebras, this paper
reveals some basic periodic properties of these twists.


title:
Integral right triangle and rhombus pairs with a common area and a
  common perimeter

abstract:
  We prove that there are infinitely many integral right triangle and
$\theta$-integral rhombus pairs with a common area and a common perimeter by
the theory of elliptic curves.


title: Online Active Linear Regression via Thresholding

abstract:
  We consider the problem of online active learning to collect data for
regression modeling. Specifically, we consider a decision maker with a limited
experimentation budget who must efficiently learn an underlying linear
population model. Our main contribution is a novel threshold-based algorithm
for selection of most informative observations; we characterize its performance
and fundamental lower bounds. We extend the algorithm and its guarantees to
sparse linear regression in high-dimensional settings. Simulations suggest the
algorithm is remarkably robust: it provides significant benefits over passive
random sampling in real-world datasets that exhibit high nonlinearity and high
dimensionality --- significantly reducing both the mean and variance of the
squared error.


title: Dynamical degrees of Hurwitz correspondences

abstract:
  Let $\phi$ be a post-critically finite branched covering of a two-sphere. By
work of Koch, the Thurston pullback map induced by $\phi$ on Teichm\"{u}ller
space descends to a multi-valued self-map --- a Hurwitz correspondence
$\mathcal{H}_{\phi}$ --- of the moduli space $\mathcal{M}_{0,P}$. We study the
dynamics of Hurwitz correspondences via numerical invariants called dynamical
degrees. We show that the sequence of dynamical degrees of $\mathcal{H}_{\phi}$
is always non-increasing, and the behavior of this sequence is constrained by
the behavior of $\phi$ at and near points of its post-critical set.


title:
Refined Multiscale Fuzzy Entropy based on Standard Deviation for
  Biomedical Signal Analysis

abstract:
  Multiscale entropy (MSE) has been a prevalent algorithm to quantify the
complexity of fluctuations in the local mean value of biomedical time series.
Recent developments in the field have tried to improve the MSE by reducing its
variability in large scale factors. On the other hand, there has been recent
interest in using other statistical moments than the mean, i.e. variance, in
the coarse-graining step of the MSE. Building on these trends, here we
introduce the so-called refined composite multiscale fuzzy entropy based on the
standard deviation (RCMFE{\sigma}) to quantify the dynamical properties of
spread over multiple time scales. We demonstrate the dependency of the
RCMFE{\sigma}, in comparison with other multiscale approaches, on several
straightforward signal processing concepts using a set of synthetic signals. We
also investigate the complementarity of using the standard deviation instead of
the mean in the coarse-graining process using magnetoencephalograms in
Alzheimer disease and publicly available electroencephalograms recorded from
focal and non-focal areas in epilepsy. Our results indicate that RCMFE{\sigma}
offers complementary information to that revealed by classical coarse-graining
approaches and that it has superior performance to distinguish different types
of physiological activity.


title:
Relativistic Tearing and Drift-kink Instabilities in Two-fluid
  Simulations

abstract:
  The stability of current sheets in collisionless relativistic pair plasma was
studied via two-dimensional two-fluid relativistic magnetohydrodynamic
simulations with vanishing internal friction between fluids. In particular, we
investigated the linear growth of the tearing and drift-kink modes in the
current sheets both with and without the guide field and obtained the growth
rates which are very similar to what has been found in the corresponding PIC
simulations. This suggests that the two-fluid simulations can be useful in
studying the large-scale dynamics of astrophysical relativistic plasmas in
problems involving magnetic reconnection.


title:
Charge storage in oxygen deficient phases of TiO$_2$: defect Physics
  without defects

abstract:
  Defects in semiconductors can exhibit multiple charge states, which can be
used for charge storage applications. Here we consider such charge storage in a
series of oxygen deficient phases of TiO$_2$, known as Magn\'eli phases. These
Ti$_n$O$_{2n-1}$ Magn\'eli phases present well-defined crystalline structures,
i. e., their deviation from stoichiometry is accommodated by changes in space
group as opposed to point defects. We show that these phases exhibit
intermediate bands with the same electronic quadruple donor transitions akin to
interstitial Ti defect levels in TiO$_2$-rutile. Thus, the Magn\'eli phases
behave as if they contained a very large pseudo-defect density: $\frac{1}{2}$
per formula unit Ti$_n$O$_{2n-1}$. Depending on the Fermi Energy the whole
material will become charged. These crystals are natural charge storage
materials with a storage capacity that rivals the best known supercapacitors.


title: Toward Optimal Feature Selection in Naive Bayes for Text Categorization

abstract:
  Automated feature selection is important for text categorization to reduce
the feature size and to speed up the learning process of classifiers. In this
paper, we present a novel and efficient feature selection framework based on
the Information Theory, which aims to rank the features with their
discriminative capacity for classification. We first revisit two information
measures: Kullback-Leibler divergence and Jeffreys divergence for binary
hypothesis testing, and analyze their asymptotic properties relating to type I
and type II errors of a Bayesian classifier. We then introduce a new divergence
measure, called Jeffreys-Multi-Hypothesis (JMH) divergence, to measure
multi-distribution divergence for multi-class classification. Based on the
JMH-divergence, we develop two efficient feature selection methods, termed
maximum discrimination ($MD$) and $MD-\chi^2$ methods, for text categorization.
The promising results of extensive experiments demonstrate the effectiveness of
the proposed approaches.


title:
Supplementary difference sets related to a certain class of complex
  spherical 2-codes

abstract:
  In this paper, we study skew-symmetric $2$-$\{v;r,k;\lambda\}$ supplementary
difference sets related to a certain class of complex spherical 2-codes. A
classification of such supplementary difference sets is complete for $v \le
51$.


title: Compliance-Aware Bandits

abstract:
  Motivated by clinical trials, we study bandits with observable
non-compliance. At each step, the learner chooses an arm, after, instead of
observing only the reward, it also observes the action that took place. We show
that such noncompliance can be helpful or hurtful to the learner in general.
Unfortunately, naively incorporating compliance information into bandit
algorithms loses guarantees on sublinear regret. We present hybrid algorithms
that maintain regret bounds up to a multiplicative factor and can incorporate
compliance information. Simulations based on real data from the International
Stoke Trial show the practical potential of these algorithms.


title:
Corrigendum to "On the equivariant $K$-theory of the nilpotent cone in
  the general linear group," published in Represent. Theory 8 (2004)

abstract:
  In the paper [P. Achar, "On the equivariant $K$-theory of the nilpotent cone
in the general linear group," Represent. Theory 8 (2004), 180-211], the author
gave a combinatorial algorithm for computing the Lusztig-Vogan bijection for
$GL(n,\mathbb{C})$. However, that paper failed to mention one easy case that
may sometimes arise, making the description of the algorithm incomplete. This
note fills in that gap.


title:
On Stepwise Control of Directional Errors under Independence and Some
  Dependence

abstract:
  In this paper, the problem of error control of stepwise multiple testing
procedures is considered. For two-sided hypotheses, control of both type 1 and
type 3 (or directional) errors is required, and thus mixed directional
familywise error rate control and mixed directional false discovery rate
control are each considered by incorporating both types of errors in the error
rate. Mixed directional familywise error rate control of stepwise methods in
multiple testing has proven to be a challenging problem, as demonstrated in
Shaffer (1980). By an appropriate formulation of the problem, some new stepwise
procedures are developed that control type 1 and directional errors under
independence and various dependencies.


title:
Non-Affine Displacements and the Non-Linear Response of a Strained
  Amorphous Solid

abstract:
  We demonstrate that irreversible structural reorganization is not necessary
for the observation of yield behaviour in an amorphous solid. While the
majority of solids strained to their yield point do indeed undergo an
irreversible reorganization, we find a significant fraction of solids exhibit
yield via a reversible strain. We also demonstrate that large instantaneous
strains in excess of the yield stress can result in complete stress relaxation,
a result of the large non-affine motions driven by the applied strain. The
empirical similarity of the dependence of the ratio of stress over strain on
the non-affine mean squared displacement with that for the shear modulus
obtained from quiescent liquid at non-zero temperature supports the proposition
that rigidity depends on the size of the sampled configurational space only,
and is insensitive as to how this space is sampled.


title:
High-Cadence, High-Contrast Imaging for Exoplanet Mapping: Observations
  of the HR 8799 Planets with VLT/SPHERE Satellite Spot-Corrected Relative
  Photometry

abstract:
  Time-resolved photometry is an important new probe of the physics of
condensate clouds in extrasolar planets and brown dwarfs. Extreme adaptive
optics systems can directly image planets, but precise brightness measurements
are challenging. We present VLT/SPHERE high-contrast, time-resolved broad
H-band near-infrared photometry for four exoplanets in the HR 8799 system,
sampling changes from night to night over five nights with relatively short
integrations. The photospheres of these four planets are often modeled by
patchy clouds and may show large-amplitude rotational brightness modulations.
Our observations provide high-quality images of the system. We present a
detailed performance analysis of different data analysis approaches to
accurately measure the relative brightnesses of the four exoplanets. We explore
the information in satellite spots and demonstrate their use as a proxy for
image quality. While the brightness variations of the satellite spots are
strongly correlated, we also identify a second-order anti-correlation pattern
between the different spots. Our study finds that PCA-based KLIP reduction with
satellite spot-modulated artificial planet-injection based photometry (SMAP)
leads to a significant (~3x) gain in photometric accuracy over standard
aperture-based photometry and reaches 0.1 mag per point accuracy for our
dataset, the signal-to-noise of which is limited by small field rotation.
Relative planet-to-planet photometry can be compared be- tween nights, enabling
observations spanning multiple nights to probe variability. Recent high-quality
relative H-band photometry of the b-c planet pair agree to about 1%.


title:
Mean Square Stability Analysis of Stochastic Continuous-time Linear
  Networked Systems

abstract:
  In this technical note, we study the mean square stability-based analysis of
stochastic continuous-time linear networked systems. The stochastic uncertainty
is assumed to enter multiplicatively in system dynamics through input and
output channels of the plant. Necessary and sufficient conditions for mean
square exponential stability are expressed in terms of the input-output
property of deterministic or nominal system dynamics captured by the {\it mean
square} system norm and variance of channel uncertainty. The stability results
can also be interpreted as a small gain theorem for continuous-time stochastic
systems. Linear Matrix Inequalities (LMI)-based optimization formulation is
provided for the computation of mean square system norm for stability analysis.
For a special case of single input channel uncertainty, we also prove a
fundamental limitation result that arises in the mean square exponential
stabilization of the continuous-time linear system. Overall, the contributions
in this work generalize the existing results on stability analysis from
discrete-time linear systems to continuous-time linear systems with
multiplicative uncertainty. Simulation results are presented for WSCC $9$ bus
power system to demonstrate the application of the developed framework.


title: Quantum Circuit Model for a Uniformly Accelerated Mirror

abstract:
  We develop a quantum circuit model describing unitary interactions between
quantum fields and a uniformly accelerated object, and apply it to a
semi-transparent mirror which uniformly accelerates in the Minkowski vacuum.
The reflection coefficient $R_{\omega}$ of the mirror varies between 0 and 1,
representing a generalization of the perfect mirror ($R_{\omega}=1$) discussed
extensively in the literature. Our method is non-perturbative, not requiring
$R_{\omega} \sim 0$. We use the circuit model to calculate the radiation from
an eternally accelerated mirror and obtain a finite particle flux along the
past horizon provided an appropriate low frequency regularization is
introduced. More importantly, it is straightforward to see from our formalism
that the radiation is squeezed. The squeezing is closely related to cutting the
correlation across the horizon, which therefore may have important implications
to the formation of a black hole firewall.


title: Sharp Weighted Convolution Inequalities and Some Applications

abstract:
  In this paper, the index groups for which the weighted Young's inequalities
hold in both continuous case and discrete case are characterized. As
applications, the index groups for the product inequalities on modulation
spaces are characterized, we also obtain the weakest conditions for the
boundedness of bilinear Fourier multipliers on modulation spaces in some sense.
For the fractional integral operator, the sharp conditions for the boundedness
of power weighted Lp-Lq estimates in both continuous case and discrete case are
obtained. By a quite different approach from others, our theorems optimize some
previous results which are committed to finding sharp conditions for some
classical convolution inequalities.


title: Impact of integrity attacks on real-time pricing in smart grids

abstract:
  Modern information and communication technologies used by smart grids are
subject to cybersecurity threats. This paper studies the impact of integrity
attacks on real-time pricing (RTP), a key feature of smart grids that uses such
technologies to improve system efficiency. Recent studies have shown that RTP
creates a closed loop formed by the mutually dependent real-time price signals
and price-taking demand. Such a closed loop can be exploited by an adversary
whose objective is to destabilize the pricing system. Specifically, small
malicious modifications to the price signals can be iteratively amplified by
the closed loop, causing inefficiency and even severe failures such as
blackouts. This paper adopts a control-theoretic approach to deriving the
fundamental conditions of RTP stability under two broad classes of integrity
attacks, namely, the scaling and delay attacks. We show that the RTP system is
at risk of being destabilized only if the adversary can compromise the price
signals advertised to smart meters by reducing their values in the scaling
attack, or by providing old prices to over half of all consumers in the delay
attack. The results provide useful guidelines for system operators to analyze
the impact of various attack parameters on system stability, so that they may
take adequate measures to secure RTP systems.


title:
A model for risk assessment of a large earthquake with application to
  Chilean data

abstract:
  We study the asymptotic distribution for the occurrence time of the next
large earthquake, by knowing the last large seismic event occurred a long time
ago. We prove that, under reasonable conditions, such a distribution is
asymptotically exponential with a rate depending on the asymptotic slope of the
cumulative intensity function corresponding to a non-homogeneous Poisson
process. Moreover, as it is not possible to obtain an empirical cumulative
distribution function for the waiting time of the next large earthquake, a
random cumulative function based on existing data is stated. We demonstrate
that analogous results to the theorems of Glivenko-Cantelli and Kolmogorov are
satisfied by this random cumulative function. We conduct a simulation study for
detecting in what scenario the approximate distribution of the studied elapsed
time performs well. Finally, a real-world data analysis is carried out to
illustrate the potential applications of our proposal.


title:
A Feature-Based Prediction Model of Algorithm Selection for Constrained
  Continuous Optimisation

abstract:
  With this paper, we contribute to the growing research area of feature-based
analysis of bio-inspired computing. In this research area, problem instances
are classified according to different features of the underlying problem in
terms of their difficulty of being solved by a particular algorithm. We
investigate the impact of different sets of evolved instances for building
prediction models in the area of algorithm selection. Building on the work of
Poursoltan and Neumann [11,10], we consider how evolved instances can be used
to predict the best performing algorithm for constrained continuous
optimisation from a set of bio-inspired computing methods, namely high
performing variants of differential evolution, particle swarm optimization, and
evolution strategies. Our experimental results show that instances evolved with
a multi-objective approach in combination with random instances of the
underlying problem allow to build a model that accurately predicts the best
performing algorithm for a wide range of problem instances.


title: Efficient Reassembling of Graphs, Part 2: The Balanced Case

abstract:
  The reassembling of a simple connected graph G = (V,E) is an abstraction of a
problem arising in earlier studies of network analysis. The reassembling
process has a simple formulation (there are several equivalent formulations)
relative to a binary tree B (reassembling tree), with root node at the top and
$n$ leaf nodes at the bottom, where every cross-section corresponds to a
partition of V such that:
  - the bottom (or first) cross-section (all the leaves) is the finest
partition of V with n one-vertex blocks,
  - the top (or last) cross-section (the root) is the coarsest partition with a
single block, the entire set V,
  - a node (or block) in an intermediate cross-section (or partition) is the
result of merging its two children nodes (or blocks) in the cross-section (or
partition) below it.
  The maximum edge-boundary degree encountered during the reassembling process
is what we call the alpha-measure of the reassembling, and the sum of all
edge-boundary degrees is its beta-measure. The alpha-optimization (resp.
beta-optimization) of the reassembling of G is to determine a reassembling tree
B that minimizes its alpha-measure (resp. beta-measure).
  There are different forms of reassembling. In an earlier report, we studied
linear reassembling, which is the case when the height of B is (n-1). In this
report, we study balanced reassembling, when B has height [log n].
  The two main results in this report are the NP-hardness of alpha-optimization
and beta-optimization of balanced reassembling. The first result is obtained by
a sequence of polynomial-time reductions from minimum bisection of graphs
(known to be NP-hard), and the second by a sequence of polynomial-time
reductions from clique cover of graphs (known to be NP-hard).


title:
Semi-External Memory Sparse Matrix Multiplication for Billion-Node
  Graphs

abstract:
  Sparse matrix multiplication is traditionally performed in memory and scales
to large matrices using the distributed memory of multiple nodes. In contrast,
we scale sparse matrix multiplication beyond memory capacity by implementing
sparse matrix dense matrix multiplication (SpMM) in a semi-external memory
(SEM) fashion; i.e., we keep the sparse matrix on commodity SSDs and dense
matrices in memory. Our SEM-SpMM incorporates many in-memory optimizations for
large power-law graphs. It outperforms the in-memory implementations of
Trilinos and Intel MKL and scales to billion-node graphs, far beyond the
limitations of memory. Furthermore, on a single large parallel machine, our
SEM-SpMM operates as fast as the distributed implementations of Trilinos using
five times as much processing power. We also run our implementation in memory
(IM-SpMM) to quantify the overhead of keeping data on SSDs. SEM-SpMM achieves
almost 100% performance of IM-SpMM on graphs when the dense matrix has more
than four columns; it achieves at least 65% performance of IM-SpMM on all
inputs. We apply our SpMM to three important data analysis tasks--PageRank,
eigensolving, and non-negative matrix factorization--and show that our SEM
implementations significantly advance the state of the art.


title:
The Role of Typicality in Object Classification: Improving The
  Generalization Capacity of Convolutional Neural Networks

abstract:
  Deep artificial neural networks have made remarkable progress in different
tasks in the field of computer vision. However, the empirical analysis of these
models and investigation of their failure cases has received attention
recently. In this work, we show that deep learning models cannot generalize to
atypical images that are substantially different from training images. This is
in contrast to the superior generalization ability of the visual system in the
human brain. We focus on Convolutional Neural Networks (CNN) as the
state-of-the-art models in object recognition and classification; investigate
this problem in more detail, and hypothesize that training CNN models suffer
from unstructured loss minimization. We propose computational models to improve
the generalization capacity of CNNs by considering how typical a training image
looks like. By conducting an extensive set of experiments we show that
involving a typicality measure can improve the classification results on a new
set of images by a large margin. More importantly, this significant improvement
is achieved without fine-tuning the CNN model on the target image set.


title: High order steady-state diffusion approximation of the Erlang-C system

abstract:
  In this paper we introduce a new diffusion approximation for the steady-state
customer count of the Erlang-C system. Unlike previous diffusion
approximations, which use the steady-state distribution of a diffusion process
with a constant diffusion coefficient, our approximation uses the steady-state
distribution of a diffusion process with a \textit{state-dependent} diffusion
coefficient. We show, both analytically and numerically, that our new
approximation is an order of magnitude better than its counterpart. To obtain
the analytical results, we use Stein's to show that a variant of the
Wasserstein distance between the normalized customer count distribution and our
approximation vanishes at a rate of $1/R$, where $R$ is the offered load to the
system. In contrast, the previous approximation only achieved a rate of $1/R$.
We hope our results motivate others to consider diffusion approximations with
state-dependent diffusion coefficients.


title: Value Iteration Networks

abstract:
  We introduce the value iteration network (VIN): a fully differentiable neural
network with a `planning module' embedded within. VINs can learn to plan, and
are suitable for predicting outcomes that involve planning-based reasoning,
such as policies for reinforcement learning. Key to our approach is a novel
differentiable approximation of the value-iteration algorithm, which can be
represented as a convolutional neural network, and trained end-to-end using
standard backpropagation. We evaluate VIN based policies on discrete and
continuous path-planning domains, and on a natural-language based search task.
We show that by learning an explicit planning computation, VIN policies
generalize better to new, unseen domains.


title: Data-Driven Evaluation of Building Demand Response Capacity

abstract:
  Before a building can participate in a demand response program, its facility
managers must characterize the site's ability to reduce load. Today, this is
often done through manual audit processes and prototypical control strategies.
In this paper, we propose a new approach to estimate a building's demand
response capacity using detailed data from various sensors installed in a
building. We derive a formula for a probabilistic measure that characterizes
various tradeoffs between the available demand response capacity and the
confidence level associated with that curtailment under the constraints of
building occupant comfort level (or utility). Then, we develop a data-driven
framework to associate observed or projected building energy consumption with a
particular set of rules learned from a large sensor dataset. We apply this
methodology using testbeds in two buildings in Singapore: a unique net-zero
energy building and a modern commercial office building. Our experimental
results identify key control parameters and provide insight into the available
demand response strategies at each site.


title:
Boundary blow-up solutions of elliptic equations involving regional
  fractional Laplacian

abstract:
  In this paper, we study existence of boundary blow-up solutions for elliptic
equations involving regional fractional Laplacian. We also discuss the
optimality of our results.


title: Dynamics of a membrane interacting with an active wall

abstract:
  Active motions of a biological membrane can be induced by non-thermal
fluctuations that occur in the outer environment of the membrane. We discuss
the dynamics of a membrane interacting hydrodynamically with an active wall
that exerts random velocities on the ambient fluid. Solving the hydrodynamic
equations of a bound membrane, we first derive a dynamic equation for the
membrane fluctuation amplitude in the presence of different types of walls.
Membrane two-point correlation functions are calculated for three different
cases; (i) a static wall, (ii) an active wall, and (iii) an active wall with an
intrinsic time scale. We focus on the mean squared displacement (MSD) of a
tagged membrane describing the Brownian motion of a membrane segment. For the
static wall case, there are two asymptotic regimes of MSD ($\sim t^{2/3}$ and
$\sim t^{1/3}$) when the hydrodynamic decay rate changes monotonically. In the
case of an active wall, the MSD grows linearly in time ($\sim t$) in the early
stage, which is unusual for a membrane segment. This linear-growth region of
the MSD is further extended when the active wall has a finite intrinsic time
scale.


title: Characterization of Some Properties on Weighted Modulation Spaces

abstract:
  In this paper, some properties on weighted modulation and Wiener amalgam
spaces are characterized by the corresponding properties on weighted Lebesgue
spaces. As applications, sharp conditions for product inequalities, convolution
inequalities and embedding on weighted modulation and Wiener amalgam spaces are
obtained. These applications improve and extend many known results.


title: Gravitational wave astronomy: the current status

abstract:
  In the centenary year of Einstein's General Theory of Relativity, this paper
reviews the current status of gravitational wave astronomy across a spectrum
which stretches from attohertz to kilohertz frequencies. Sect. 1 of this paper
reviews the historical development of gravitational wave astronomy from
Einstein's first prediction to our current understanding the spectrum. It is
shown that detection of signals in the audio frequency spectrum can be expected
very soon, and that a north-south pair of next generation detectors would
provide large scientific benefits. Sect. 2 reviews the theory of gravitational
waves and the principles of detection using laser interferometry. The state of
the art Advanced LIGO detectors are then described. These detectors have a high
chance of detecting the first events in the near future. Sect. 3 reviews the
KAGRA detector currently under development in Japan, which will be the first
laser interferometer detector to use cryogenic test masses. Sect. 4 of this
paper reviews gravitational wave detection in the nanohertz frequency band
using the technique of pulsar timing. Sect. 5 reviews the status of
gravitational wave detection in the attohertz frequency band, detectable in the
polarisation of the cosmic microwave background, and discusses the prospects
for detection of primordial waves from the big bang. The techniques described
in sects. 1-5 have already placed significant limits on the strength of
gravitational wave sources. Sects. 6 and 7 review ambitious plans for future
space based gravitational wave detectors in the millihertz frequency band.
Sect. 6 presents a roadmap for development of space based gravitational wave
detectors by China while sect. 7 discusses a key enabling technology for space
interferometry known as time delay interferometry.


title:
Expected constraints on models of the epoch of reionization with the
  variance and skewness in redshifted 21cm-line fluctuations

abstract:
  Redshifted 21cm-line signal from neutral hydrogens in the intergalactic
medium (IGM) gives a direct probe of the epoch of reionization (EoR). In this
paper, we investigate the potential of the variance and skewness of the
probability distribution function of the 21cm brightness temperature for
constraining EoR models. These statistical quantities are simple, easy to
calculate from the observed visibility and thus suitable for the early
exploration of the EoR with ongoing telescopes such as the Murchison Widefield
Array (MWA) and LOw Frequency ARray (LOFAR). We show, by performing Fisher
analysis, that the variance and skewness at $z=7-9$ are complementary to each
other to constrain the EoR model parameters such as the minimum virial
temperature of halos which host luminous objects, ionizing efficiency and mean
free path of ionizing photons in the IGM. Quantitatively, the constraining
power highly depends on the quality of the foreground subtraction and
calibration. We give a best case estimate of the constraints on the parameters,
neglecting the systematics other than the thermal noise.


title: The Influence of Initial Conditions during Dissipative Collapse

abstract:
  Starting off with two distinct initially static stellar cores (i) Florides
interior (constant density, vanishing radial pressure) and (ii) Wyman interior
(constant density, nonvanishing radial pressure), we explore the dynamics of
these two models once hydrostatic equilibrium is lost. We show that although
the time of formation of horizon, evolution of the mass and proper radius are
independent of the chosen initially static configurations, there is a
significant difference in the temperature profiles of the radiating bodies as
the collapse proceeds.


title:
The detection of quasinormal mode with $a/M \sim 0.95$ would prove a
  sphere $99\%$ soaking in the ergoregion of the Kerr space-time

abstract:
  Recent numerical relativity simulations of mergers of binary black holes
suggest that the maximum final value of $a/M$ is $\sim 0.95$ for the
coalescence of two equal mass black holes with aligned spins of the same
magnitude $a/M=0.994$ which is close to the upper limit $a/M=0.998$ of
accretion spin-up shown by Thorne. Using the WKB method, we suggest that if
quasinormal modes with $a/M \sim 0.95$ are detected by the second generation
gravitational wave detectors, we could confirm the strong gravity space-time
based on Einstein's general relativity up to $1.33M$ which is only $\sim 1.014$
times the event horizon radius and within the ergoregion. One more message
about black hole geometry is expected here. If the quasinormal mode is
different from that of general relativity, we need to find the true theory of
gravity which deviates from general relativity only near the black hole
horizon.


title:
Topological quantum phase transitions in a Majorana chain with spatial
  modulation

abstract:
  We numerically study the quantum phase transitions and the stability of
Majorana zero modes in a generalized Kitaev model in one dimension when the
chemical potential is periodically modulating in space. By using the exact
diagonalization method for open boundary condition, we investigate the
ground-state phases in terms of the non-local properties such as the
entanglement spectrum (ES) and the string correlation functions. When we vary
the phase of the modulation, the number of the Majorana zero modes changes,
which manifests itself in the degeneracy of the lowest level of the ES. Next,
we study the quantum phase transitions driven by the change in the amplitude of
the modulation. In particular, for certain values of the wave number and the
phase of the modulation, we observe a quantum phase transition from one
topological phase into another where the string correlation function oscillates
in space. We also show a case where the degeneracy of the ES does not change
even for large enough amplitude of the modulation. Finally, we characterize the
phases of the system with periodic boundary condition by the topological
invariant, which reflects the number of the zero-energy excitations.