title: On a Tur\'an problem in weakly quasirandom 3-uniform hypergraphs

abstract:
  Extremal problems for $3$-uniform hypergraphs are known to be very difficult
and despite considerable effort the progress has been slow. We suggest a more
systematic study of extremal problems in the context of quasirandom
hypergraphs. We say that a $3$-uniform hypergraph $H=(V,E)$ is weakly
$(d,\eta)$-quasirandom if for any subset $U\subseteq V$ the number of
hyperedges of $H$ contained in $U$ is in the interval
$d\binom{|U|}{3}\pm\eta|V|^3$. We show that for any $\varepsilon>0$ there
exists $\eta>0$ such that every sufficiently large weakly
$(1/4+\varepsilon,\eta)$-quasirandom hypergraph contains four vertices spanning
at least three hyperedges. This was conjectured by Erd\H{o}s and S\'os and it
is known that the density $1/4$ is best possible.
  Recently, a computer assisted proof of this result based on the flag-algebra
method was established by Glebov, Kr\'al', and Volec. In contrast to their work
our proof presented here is based on the regularity method of hypergraphs and
requires no heavy computations. In addition we obtain an ordered version of
this result. The method of our proof allows us to study extremal problems of
this type in a more systematic way and we discuss a few extensions and open
problems here.


title: Discrepancy and Eigenvalues of Cayley Graphs

abstract:
  We consider quasirandom properties for Cayley graphs of finite abelian
groups. We show that having uniform edge-distribution (i.e., small discrepancy)
and having large eigenvalue gap are equivalent properties for such Cayley
graphs, even if they are sparse. This positively answers a question of Chung
and Graham ["Sparse quasi-random graphs", Combinatorica 22 (2002), no. 2,
217-244] for the particular case of Cayley graphs of abelian groups, while in
general the answer is negative.


title: Geometric models of twisted differential K-theory I

abstract:
  This is the first in a series of papers constructing geometric models of
twisted differential K-theory. In this paper we construct a model of even
twisted differential K-theory when the underlying topological twist represents
a torsion class. By differential twists we will mean smooth U(1)-gerbes with
connection, and we use twisted vector bundles with connection as cocycles. The
model we construct satisfies the axioms of Kahle and Valentino, including
functoriality, naturality of twists, and the hexagon diagram. This paper
confirms a long-standing hypothetical idea that twisted vector bundles with
connection define twisted differential K-theory.


title: On Efficient Distributed Construction of Near Optimal Routing Schemes

abstract:
  Given a distributed network represented by a weighted undirected graph
$G=(V,E)$ on $n$ vertices, and a parameter $k$, we devise a distributed
algorithm that computes a routing scheme in $(n^{1/2+1/k}+D)\cdot n^{o(1)}$
rounds, where $D$ is the hop-diameter of the network. The running time matches
the lower bound of $\tilde{\Omega}(n^{1/2}+D)$ rounds (which holds for any
scheme with polynomial stretch), up to lower order terms. The routing tables
are of size $\tilde{O}(n^{1/k})$, the labels are of size $O(k\log^2n)$, and
every packet is routed on a path suffering stretch at most $4k-5+o(1)$. Our
construction nearly matches the state-of-the-art for routing schemes built in a
centralized sequential manner. The previous best algorithms for building
routing tables in a distributed small messages model were by \cite[STOC
2013]{LP13} and \cite[PODC 2015]{LP15}. The former has similar properties but
suffers from substantially larger routing tables of size $O(n^{1/2+1/k})$,
while the latter has sub-optimal running time of
$\tilde{O}(\min\{(nD)^{1/2}\cdot n^{1/k},n^{2/3+2/(3k)}+D\})$.


title:
A Source-Channel Separation Theorem with Application to the Source
  Broadcast Problem

abstract:
  A converse method is developed for the source broadcast problem.
Specifically, it is shown that the separation architecture is optimal for a
variant of the source broadcast problem and the associated source-channel
separation theorem can be leveraged, via a reduction argument, to establish a
necessary condition for the original problem, which unifies several existing
results in the literature. Somewhat surprisingly, this method, albeit based on
the source-channel separation theorem, can be used to prove the optimality of
non-separation based schemes and determine the performance limits in certain
scenarios where the separation architecture is suboptimal.


title: On Unification of Gravity and Gauge Interactions

abstract:
  Considering a higher dimensional Lorentz group as the tangent symmetry, we
unify gravity and gauge interactions in a natural way. The spin connection of
the gauged Lorentz group is then responsible for both gravity and gauge fields,
and the action for the gauged fields becomes part of the spin curvature
squared. The realistic group which unifies all known particles and interactions
is the $SO(1,13)$ Lorentz group whose gauge part leads to $SO(10)$ grand
unified theory and contains double the number of required fermions in the
fundamental spinor representation. Mirror fermions could acquire mass utilizing
a mechanism employed for topological superconductors. Family unification could
be achieved by considering the $SO(1,21)$ Lorentz group.


title:
Report on the Third Workshop on Sustainable Software for Science:
  Practice and Experiences (WSSSPE3)

abstract:
  This report records and discusses the Third Workshop on Sustainable Software
for Science: Practice and Experiences (WSSSPE3). The report includes a
description of the keynote presentation of the workshop, which served as an
overview of sustainable scientific software. It also summarizes a set of
lightning talks in which speakers highlighted to-the-point lessons and
challenges pertaining to sustaining scientific software. The final and main
contribution of the report is a summary of the discussions, future steps, and
future organization for a set of self-organized working groups on topics
including developing pathways to funding scientific software; constructing
useful common metrics for crediting software stakeholders; identifying
principles for sustainable software engineering design; reaching out to
research software organizations around the world; and building communities for
software sustainability. For each group, we include a point of contact and a
landing page that can be used by those who want to join that group's future
activities. The main challenge left by the workshop is to see if the groups
will execute these activities that they have scheduled, and how the WSSSPE
community can encourage this to happen.


title: The Cayley isomorphism property for Cayley maps

abstract:
  In this paper we study finite groups which have Cayley isomorphism property
with respect to Cayley maps, CIM-groups for a brief. We show that the structure
of the CIM-groups is very restricted. It is described in Theorem~\ref{111015a}
where a short list of possible candidates for CIM-groups is given.
Theorem~\ref{111015c} provides concrete examples of infinite series of
CIM-groups.


title:
Global existence of solutions for an $m$-component reaction--diffusion
  system with a tridiagonal 2-Toeplitz diffusion matrix and polynomially
  growing reaction terms

abstract:
  This paper is concerned with the local and global existence of solutions for
a generalized $m$-component reaction--diffusion system with a tridiagonal
$2$--Toeplitz diffusion matrix and polynomial growth. We derive the eigenvalues
and eigenvectors and determine the parabolicity conditions in order to
diagonalize the proposed system. We, then,determine the invariant regions and
utilize a Lyapunov functional to establish the global existence of solutions
for the proposed system. A numerical example is used to illustrate and confirm
the findings of the study.


title:
Some remarks on the extremal function for uniformly two-path dense
  hypergraphs

abstract:
  We investigate extremal problems for hypergraphs satisfying the following
density condition. A $3$-uniform hypergraph $H=(V, E)$ is $(d, \eta,P_2)$-dense
if for any two subsets of pairs $P$, $Q\subseteq V\times V$ the number of pairs
$((x,y),(x,z))\in P\times Q$ with $\{x,y,z\}\in E$ is at least
$d|\mathcal{K}_{P_2}(P,Q)|-\eta|V|^3,$ where $\mathcal{K}_{P_2}(P,Q)$ denotes
the set of pairs in $P\times Q$ of the form $((x,y),(x,z))$. For a given
$3$-uniform hypergraph $F$ we are interested in the infimum $d\geq 0$ such that
for sufficiently small $\eta$ every sufficiently large $(d, \eta,P_2)$-dense
hypergraph $H$ contains a copy of $F$ and this infimum will be denoted by
$\pi_{P_2}(F)$. We present a few results for the case when $F=K_k^{(3)}$ is a
complete three uniform hypergraph on $k$ vertices. It will be shown that
$\pi_{P_2}(K_{2^r}^{(3)})\leq \frac{r-2}{r-1}$, which is sharp for $r=2,3,4$,
where the lower bound for $r=4$ is based on a result of Chung and Graham
[Edge-colored complete graphs with precisely colored subgraphs, Combinatorica 3
(3-4), 315-324].


title:
Line arrangements and configurations of points with an unusual geometric
  property

abstract:
  The SHGH conjecture proposes a solution to the question of how many
conditions a general union of fat points imposes on the complete linear system
of curves in $\mathbb P^2$ of fixed degree $d$, and it is known to be true in
many cases. We propose a new problem, namely to understand the number of
conditions imposed by a general union of fat points on the incomplete linear
system defined by the condition of passing through a given finite set of points
$Z$ (not general). Motivated by work of Di Gennaro-Ilardi-Vall\`es and
Faenzi-Vall\`es, we give a careful analysis for the case where there is a
single general fat point, which has multiplicity $d-1$. There is an expected
number of conditions imposed by this fat point, and we study those $Z$ for
which this expected value is not achieved. We show, for instance, that if $Z$
is in linear general position then such unexpected curves do not exist. We give
criteria for the occurrence of such unexpected curves and describe the range of
values of $d$ for which they occur. Unexpected curves have a very particular
structure, which we describe, and they are often unique for a given set of
points. In particular, we give a criterion for when they are irreducible, and
we exhibit examples both where they are reducible and where they are
irreducible. Furthermore, we relate properties of $Z$ to properties of the
arrangement of lines dual to the points of $Z$. In particular, we obtain a new
interpretation of the splitting type of a line arrangement. Finally, we use our
results to establish a Lefschetz-like criterion for Terao's conjecture on the
freeness of line arrangements.


title: Classical theorems in the Implicational Propositional Calculus

abstract:
  For formulas of the Implicational Propositional Calculus (IPC) that are
theorems of the classical Propositional Calculus (PC) we show that PC proofs
yield IPC proofs. As a consequence, completeness of PC yields completeness of
IPC.


title: On the structure of dense graphs with fixed clique number

abstract:
  We study structural properties of graphs with fixed clique number and high
minimum degree. In particular, we show that there exists a function
$L=L(r,\varepsilon)$, such that every $K_r$-free graph $G$ on $n$ vertices with
minimum degree at least $(\frac{2r-5}{2r-3}+\varepsilon)n$ is homomorphic to a
$K_r$-free graph on at most $L$ vertices. It is known that the required minimum
degree condition is approximately best possible for this result.
  For $r=3$ this result was obtained by \L uczak [On the structure of
triangle-free graphs of large minimum degree, Combinatorica 26 (2006), no. 4,
489-493] and, more recently, Goddard and Lyle [Dense graphs with small clique
number, J. Graph Theory 66 (2011), no. 4, 319-331] deduced the general case
from \L uczak's result. \L uczak's proof was based on an application of
Szemer\'edi's regularity lemma and, as a consequence, it only gave rise to a
tower-type bound on $L(3,\varepsilon)$. The proof presented here replaces the
application of the regularity lemma by a probabilistic argument, which yields a
bound for $L(r,\varepsilon)$ that is doubly exponential in poly($\varepsilon$).


title:
Photon-activated electron hopping in a single-electron trap enhanced by
  Josephson radiation

abstract:
  Using a Josephson junction interferometer (DC SQUID) as a microwave source
for irradiating a single-electron trap, both devices fabricated on the same
chip, we study the process of photon-assisted tunneling as an effective
mechanism of single photon detection. High sensitivity down to a very small
oscillation amplitude $v_{\rm J} \sim$ 10 nV$\ll E_{\rm act} \lesssim hf_{\rm
J}$ and down to low photon absorption rates $\Gamma_{\rm ph} \sim$ (1--50)Hz,
as well as a clear threshold type of operation with an activation energy
$E_{\rm act} \sim$ 400 $\mu$eV, are demonstrated for the trap with respect to
the microwave photons of frequency $f_{\rm J} \sim$ (100--200)GHz. Tunable
generation is demonstrated with respect to the power and frequency of the
microwave signal produced by the SQUID source biased within the subgap voltage
range. A much weaker effect is observed at the higher junction voltages along
the quasiparticle branch of the $I-V$ curve; this response mostly appears due
to the recombination phonons.


title: Observable currents in lattice field theories

abstract:
  Observable currents are spacetime local objects that induce physical
observables when integrated on an auxiliary codimension one surface. Since the
resulting observables are independent of local deformations of the integration
surface, the currents themselves carry most of the information about the
induced physical observables. I introduce observable currents in a
multisymplectic framework for Lagrangian field theory over discrete spacetime.
One family of examples is composed by Noether currents. A much larger family of
examples is composed by currents, spacetime local objects, that encode the
symplectic product between two arbitrary vectors tangent to the space of
solutions. A weak version of observable currents, which in general are
nonlocal, is also introduced. Weak observable currents can be used to separate
points in the space of physically distinct solutions. It is shown that a large
class of weak observable currents can be "improved" to become local. A Poisson
bracket gives the space of observable currents the structure of a Lie algebra.
Peierls bracket for bulk observables gives an algebra homomorphism mapping
equivalence classes of bulk observables to weak observable currents. The study
covers scalar fields, nonlinear sigma models and gauge theories (including
gauge theory formulations of general relativity) on the lattice. Even when this
paper is entirely classical, this study is relevant for quantum field theory
because a quantization of the framework leads to a spin foam model formulation
of lattice field theory.


title:
On the connection between dissipative particle dynamics and the
  It\^o-Stratonovich dilemma

abstract:
  Dissipative Particle Dynamics (DPD) is a popular simulation model for
investigating hydrodynamic behavior of systems with non-negligible equilibrium
thermal fluctuations. DPD employs soft core repulsive interactions between the
system particles, thus allowing them to overlap. This supposedly permits
relatively large integration time steps, which is an important feature for
simulations on large temporal scales. In practice, however, an increase in the
integration time step leads to increasingly larger systematic errors in the
sampling statistics. Here, we demonstrate that the prime origin of these
systematic errors is the multiplicative nature of the thermal noise term in
Langevin's equation, i.e., the fact that it depends on the instantaneous
coordinates of the particles. This lead to an ambiguity in the interpretation
of the stochastic differential Langevin equation, known as the
It\^o-Stratonovich dilemma. Based on insights from previous studies of the
dilemma, we propose a novel algorithm for DPD simulations exhibiting almost an
order of magnitude improvement in accuracy, and nearly twice the efficiency of
commonly used DPD Langevin thermostats.


title: Preconditioned iterative methods for eigenvalue counts

abstract:
  We describe preconditioned iterative methods for estimating the number of
eigenvalues of a Hermitian matrix within a given interval. Such estimation is
useful in a number of applications.In particular, it can be used to develop an
efficient spectrum-slicing strategy to compute many eigenpairs of a Hermitian
matrix. Our method is based on the Lanczos- and Arnoldi-type of iterations. We
show that with a properly defined preconditioner, only a few iterations may be
needed to obtain a good estimate of the number of eigenvalues within a
prescribed interval. We also demonstrate that the number of iterations required
by the proposed preconditioned schemes is independent of the size and condition
number of the matrix. The efficiency of the methods is illustrated on several
problems arising from density functional theory based electronic structure
calculations.


title: Yang-Mills Theories at High-Energy Accelerators

abstract:
  I'll begin with a brief review of the triumph of Yang-Mills theory at
particle accelerators, a development that began some years after their historic
paper. This story reached a culmination, or at least local extremum, with the
discovery at the Large Hadron Collider of a Higgs-like scalar boson in 2012.
The talk then proceeds to a slightly more technical level, discussing how we
derive predictions from the gauge field theories of the Standard Model and its
extensions for use at high energy accelerators.


title:
Controllability analysis and control synthesis for the ribosome flow
  model

abstract:
  The ribosomal density along the coding region of the mRNA molecule affect
various fundamental intracellular phenomena including: protein production
rates, organismal fitness, ribosomal drop off, and co-translational protein
folding. Thus, regulating translation in order to obtain a desired ribosomal
profile along the mRNA molecule is an important biological problem. We study
this problem using a model for mRNA translation, called the ribosome flow model
(RFM). In the RFM, the mRNA molecule is modeled as chain of n sites. The n
state-variables describe the ribosomal density profile along the mRNA molecule,
whereas the transition rates from each site to the next are controlled by n+1
positive constants. To study the problem of controlling the density profile, we
consider some or all of the transition rates as time-varying controls. We
consider the following problem: given an initial and a desired ribosomal
density profile, determine the time-varying values of the transition rates that
steer the RFM to this density profile, if they exist. Specifically, we consider
two control problems. In the first, all transition rates can be regulated and
the goal is to steer the ribosomal density profile and the protein production
rate from a given initial value to a desired value. In the second, a single
transition rate is controlled and the goal is to steer the production rate to a
desired value. In the first case, we show that the system is controllable, i.e.
the control is powerful enough to steer the RFM to any desired value, and we
provide closed-form expressions for constant control functions (or transition
rates) asymptotically steering the RFM to the desired value. For the second
problem, we show that the production rate can be steered to any desired value
in a feasible region determined by the other, constant transition rates. We
discuss some of the biological implications of these results.


title: Supergravity backgrounds and symmetry superalgebras

abstract:
  We consider the bosonic sectors of supergravity theories in ten and eleven
dimensions which correspond to the low energy limits of string theories and
M-theory. The solutions of supergravity field equations are known as
supergravity backgrounds and the number of preserved supersymmetries in those
backgrounds are determined by Killing spinors. We provide some examples of
supergravity backgrounds which preserve different fractions of supersymmetry.
An important invariant for the characterization of supergravity backgrounds is
their Killing superalgebras which are constructed out of Killing vectors and
Killing spinors of the background. After constructing Killing superalgebras of
some special supergravity backgrounds, we discuss about the possibilities of
the extensions of these superalgebras to include the higher degree hidden
symmetries of the background.


title: Testing the isotropy of the Hubble expansion

abstract:
  We have used the Union2.1 SNIa compilation to search for possible Hubble
expansion anisotropies, dividing the sky in 9 solid angles containing roughly
the same number of SNIa, as well as in the two Galactic hemispheres. We
identified only one sky region, containing 82 SNIa (~15% of total sample with
$z>0.02$), that indeed appears to share a significantly different Hubble
expansion than the rest of the sample. However, this behavior appears to be
attributed to the joint "erratic" behavior of only three SNIa and not to an
anisotropic expansion. We also find that the northern and southern galactic
hemispheres have different cosmological parameter solutions but still not
significant enough to assert the detection of a Hubble expansion anisotropy. We
conclude that even a few outliers can have such an effect as to induce
artificial indications of anisotropies, when the number of analysed SNIa is
relatively small.


title: R\'enyi Divergence Variational Inference

abstract:
  This paper introduces the variational R\'enyi bound (VR) that extends
traditional variational inference to R\'enyi's alpha-divergences. This new
family of variational methods unifies a number of existing approaches, and
enables a smooth interpolation from the evidence lower-bound to the log
(marginal) likelihood that is controlled by the value of alpha that
parametrises the divergence. The reparameterization trick, Monte Carlo
approximation and stochastic optimisation methods are deployed to obtain a
tractable and unified framework for optimisation. We further consider negative
alpha values and propose a novel variational inference method as a new special
case in the proposed framework. Experiments on Bayesian neural networks and
variational auto-encoders demonstrate the wide applicability of the VR bound.


title: Universality for a class of random band matrices

abstract:
  We prove the universality for the eigenvalue gap statistics in the bulk of
the spectrum for band matrices, in the regime where the band width is
comparable with the dimension of the matrix, $W\sim N$. All previous results
concerning universality of non-Gaussian random matrices are for mean-field
models. By relying on a new mean-field reduction technique, we deduce
universality from quantum unique ergodicity for band matrices.


title:
All-electron self-consistent GW in the Matsubara-time domain:
  implementation and benchmarks of semiconductors and insulators

abstract:
  The GW approximation is a well-known method to improve electronic structure
predictions calculated within density functional theory. In this work, we have
implemented a computationally efficient GW approach that calculates central
properties within the Matsubara-time domain using the modified version of Elk,
the full-potential linearized augmented plane wave (FP-LAPW) package.
Continuous-pole expansion (CPE), a recently proposed analytic continuation
method, has been incorporated and compared to the widely used Pade
approximation. Full crystal symmetry has been employed for computational
speedup. We have applied our approach to 18 well-studied
semiconductors/insulators that cover a wide range of band gaps computed at the
levels of single-shot G0W0, partially self-consistent GW0, and fully
self-consistent GW (scGW). Our calculations show that G0W0 leads to band gaps
that agree well with experiment for the case of simple s-p electron systems,
whereas scGW is required for improving the band gaps in 3-d electron systems.
In addition, GW0 almost always predicts larger band gap values compared to
scGW, likely due to the substantial underestimation of screening effects. Both
the CPE method and Pade approximation lead to similar band gaps for most
systems except strontium titantate, suggesting further investigation into the
latter approximation is necessary for strongly correlated systems. Our computed
band gaps serve as important benchmarks for the accuracy of the Matsubara-time
GW approach.


title:
Time-evolution of quantum systems via a complex nonlinear Riccati
  equation II. Dissipative systems

abstract:
  In our former contribution [Ann. Phys. 360 (2015) 44], we have shown the
sensitivity to the choice of initial conditions in the evolution of Gaussian
wave packets via the nonlinear Riccati equation. The formalism developed in the
previous work is extended to effective approaches for the description of
dissipative quantum systems. By means of simple examples we show the effects of
the environment on the quantum uncertainties, correlation function, quantum
energy contribution and tunneling currents. We prove that the environmental
parameter $\gamma$ is strongly related with the sensitivity to the choice of
initial conditions.


title: Inequalities for exponential sums

abstract:
  Inequalities for exponential sums are studied. Our results improve an old
result of G. Halasz and a recent result of G. Kos. We prove several other
essentially sharp related results in this paper.


title: A class of random Cantor sets

abstract:
  In this paper we study a class of random Cantor sets. We determine their
almost sure Hausdorff, packing, box, and Assouad dimensions. From a topological
point of view, we also compute their typical dimensions in the sense of Baire
category. For the natural random measures on these random Cantor sets, we
consider their almost sure lower and upper local dimensions. In the end we
study the hitting probabilities of a special subclass of these random Cantor
sets.


title: An alternate Cayley-Dickson product

abstract:
  Although the Cayley-Dickson algebras are twisted group algebras, little
attention has been paid to the nature of the Cayley-Dickson twist. One reason
is that the twist appears to be highly chaotic and there are other interesting
things about the algebras to focus attention upon. However, if one uses a
doubling product for the algebras different from yet equivalent to the ones
commonly used and if one uses a numbering of the basis vectors different from
the standard basis a quite beautiful and highly periodic twist emerges. This
leads easily to a simple closed form formula for the product of any two basis
vectors of a Cayley-Dickson algebra.


title: Endomorphism algebras for a class of negative Calabi-Yau categories

abstract:
  We consider an orbit category of the bounded derived category of a path
algebra of type A_n which can be viewed as a -(m+1)-cluster category, for m >=
1. In particular, we give a characterisation of those maximal m-rigid objects
whose endomorphism algebras are connected, and then use it to explicitly study
these algebras. Specifically, we give a full description of them in terms of
quivers and relations, and relate them with (higher) cluster-tilted algebras of
type A. As a by-product, we introduce a larger class of algebras, called
'tiling algebras'.


title:
Kac--Moody groups and automorphic forms in low dimensional supergravity
  theories

abstract:
  Kac--Moody groups $G$ over $\mathbb{R}$ have been conjectured to occur as
symmetry groups of supergravity theories dimensionally reduced to dimensions
less than 3, and their integral forms $G(\mathbb{Z})$ conjecturally encode
quantized symmetries. In this review paper, we briefly introduce the
conjectural symmetries of Kac--Moody groups in supergravity as well as the
known evidence for these conjectures. We describe constructions of Kac--Moody
groups over $\R$ and $\Z$ using certain choices of fundamental modules that are
considered to have physical relevance. Eisenstein series on certain finite
dimensional algebraic groups are known to encode quantum corrections in the low
energy limit of superstring theories. We describe briefly how the construction
of Eisenstein series extends to Kac--Moody groups. The constant terms of
Eisenstein series on $E_9$, $E_{10}$ and $E_{11}$ are predicted to encode
perturbative string theory corrections.


title: A Remark on Bifurcation of Fredholm Maps

abstract:
  We modify an argument for multiparameter bifurcation of Fredholm maps by
Fitzpatrick and Pejsachowicz to strengthen results on the topology of the
bifurcation set. Furthermore, we discuss an application to families of
differential equations parameterised by Grassmannians.


title: Large-gap quantum spin Hall state in functionalized dumbbell stanene

abstract:
  Two-dimensional dumbbell (DB) stanene has been proposed as a promising
candidate material for realizing quantum spin Hall effect (QSHE) by Tang et al
[P. Tang, P. Chen, W. Cao, H. Huang, S. Cahangirov, L. Xian, Y. Xu, S. C.
Zhang, W. Duan, A. Rubio. Phys. Rev. B, 90, 121408 (2014)]. However, the small
bulk-gap limits its possible applications at room temperature. Based on
first-principles calculations, we predict that its band gap can be enhanced to
148 meV under methyl-functionalization, which can be further tuned by applying
lattice strain. The QSHE is confirmed by s-px,y band inversion, topological
invariant Z2 = 1, and helical gapless edge within bulk band gap. Notably, the
characteristic properties of edge states, such as the large Fermi velocity and
Dirac cone, can be modulated by edge modification. The effects of substrates on
topological properties are explored when it is grown on various substrates,
like SiC, h-BN, and Bi2Te3 sheets. These findings provide significant guidance
for future fabrication and realistic applications of QSHE based on stanene in
spintronics.


title: Quantum storage based on controllable frequency comb

abstract:
  We suggest an all-optical scheme for the storage, retrieval and processing of
a single-photon wave packet through its off-resonant Raman interaction with a
series of coherent control beams. These control beams, each with distinct
carrier frequency, are distributed along the way of single-photon propagation,
thus effectively forming a gradient absorption structure which can be
controlled in various ways to achieve different single-photon processing
functionalities. Such a controllable frequency comb is a hybrid of Raman,
gradient echo memory (GEM) and atomic frequency comb (AFC) methods, therefore
demonstrates many of their advantages all together in one.


title: Charge-Tunable Indium Gallium Nitride Quantum Dots

abstract:
  III-Nitride quantum dots have emerged as a new chip-scale system for quantum
information science, which combines electrical and optical interfaces on a
semiconductor chip that is compatible with non-cryogenic operating
temperatures. Yet most work has been limited to optical excitations. To enable
single-spin based quantum optical and quantum information research, we
demonstrate here quantized charging in optically active, site-controlled
III-Nitride quantum dots. Single-electron charging was confirmed by the voltage
dependence of the energy, dipole moment, fine structures and polarization
properties of the exciton states in the quantum dots. The fundamental energy
structures of the quantum dots were identified, including neutral and charged
excitons, fine structures of excitons, and A and B excitons. The results lay
the ground for coherent control of single charges in III-Nitride QDs, opening a
door to III-Nitride based spintronics and spin-qubit quantum information
processing.


title:
Critical exponent $\eta$ in 2D $O(N)$-symmetric $\varphi^4$-model up to
  6~loops

abstract:
  Critical exponent $\eta$ (Fisher exponent) in $O(N)$-symmetric
$\varphi^4$-model was calculated using renormalization group approach in the
space of fixed dimension $D=2$ up to 6~loops. The calculation of the
renormalization constants was performed with the use of $R'$-operation and
specific values for diagrams were calculated in Feynman representation using
sector decomposition method. Presented approach allows easy automation and
generalization for the case of complex symmetries. Also a summation of the
perturbation series was obtained by Borel transformation with conformal
mapping. The contribution of the 6-th term of the series led to the increase of
the Fisher exponent in $O(1)$ model up to $8\%$.


title: Site-controlled InGaN/GaN single-photon-emitting diode

abstract:
  We report single-photon emission from electrically driven site-controlled
InGaN/GaN quantum dots, fabricated from a planar light-emitting diode structure
containing a single InGaN quantum well using a top-down approach. The location,
dimension, and height of each single-photon-emitting diode are controlled
lithographically, providing great flexibility for chip-scale integration.


title: Epstein zeta-functions, subconvexity, and the purity conjecture

abstract:
  Subconvexity bounds are proved for general Epstein zeta functions of k-ary
quadratic forms. This is related to sup-norm bounds for Eisenstein series on
GL(k), and the exact sup-norm exponent is determined to be (k-2)/8 for k >= 2.
In particular, if $k$ is odd, this exponent is not in Z/4, which shows that
Sarnak's purity conjecture does not hold for Eisenstein series.


title: Convex shapes and harmonic caps

abstract:
  Any planar shape $P\subset \mathbb{C}$ can be embedded isometrically as part
of the boundary surface $S$ of a convex subset of $\mathbb{R}^3$ such that
$\partial P$ supports the positive curvature of $S$. The complement $Q = S
\setminus P$ is the associated {\em cap}. We study the cap construction when
the curvature is harmonic measure on the boundary of
$(\hat{\mathbb{C}}\setminus P, \infty)$. Of particular interest is the case
when $P$ is a filled polynomial Julia set and the curvature is proportional to
the measure of maximal entropy.


title:
Path integral Monte Carlo determination of the fourth-order virial
  coefficient for unitary two-component Fermi gas with zero-range interactions

abstract:
  The unitary equal-mass Fermi gas with zero-range interactions constitutes a
paradigmatic model system that is relevant to atomic, condensed matter,
nuclear, particle, and astro physics. This work determines the fourth-order
virial coefficient $b_4$ of such a strongly-interacting Fermi gas using a
customized \textit{ab initio} path integral Monte Carlo (PIMC) algorithm. In
contrast to earlier theoretical results, which disagreed on the sign and
magnitude of $b_4$, our $b_4$ agrees within error bars with the experimentally
determined value, thereby resolving an ongoing literature debate. Utilizing a
trap regulator, our PIMC approach determines the fourth-order virial
coefficient by directly sampling the partition function. An on-the-fly
anti-symmetrization avoids the Thomas collapse and, combined with the use of
the exact two-body zero-range propagator, establishes an efficient general
means to treat small Fermi systems with zero-range interactions.


title: Perfect dyadic operators: weighted T(1) theorem and two weight estimates

abstract:
  Perfect dyadic operators were first introduced in \cite{AHMTT}, where a local
$T(b)$ theorem was proved for such operators. In \cite{AY} it was shown that
for every singular integral operator $T$ with locally bounded kernel on
$\mathbb{R}^n \times \mathbb{R}^n$ there exists a perfect dyadic operator
$\mathbb{T}$ such that $T -\mathbb{T}$ is bounded on $L^p (dx)$ for all
$1<p<\infty$.
  In this paper we show a decomposition of perfect dyadic operators on real
line into four well known operators: two selfadjoint operators, paraproduct and
its adjoint. Based on this decomposition we prove a sharp weighted version of
the $T(1)$ theorem for such operators, which implies $A_2$ conjecture for such
operators with constant which only depends on $\|T(1)\|_{BMO^d}$,
$\|T^*(1)\|_{BMO^d}$ and the constant in testing conditions for $T$. Moreover,
the constant depends on these parameters at most linearly. In this paper we
also obtain sufficient conditions for the two weight boundedness for a perfect
dyadic operator and simplify these conditions under additional assumptions that
weights are in the Muckenhoupt class $A_\infty^d$.


title: The Diffusion Geometry of Fibre Bundles: Horizontal Diffusion Maps

abstract:
  Kernel-based non-linear dimensionality reduction methods, such as Local
Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise
distances or similarity scores, with which one can construct and study a
weighted graph associated with the dataset. When each individual data object
carries additional structural details, however, the correspondence relations
between these structures provide extra information that can be leveraged for
studying the dataset using the graph. Based on this observation, we generalize
Diffusion Maps (DM) in manifold learning and introduce the framework of
Horizontal Diffusion Maps (HDM). We model a dataset with pairwise structural
correspondences as a fibre bundle equipped with a connection. We demonstrate
the advantage of incorporating such additional information and study the
asymptotic behavior of HDM on general fibre bundles. In a broader context, HDM
reveals the sub-Riemannian structure of high-dimensional datasets, and provides
a nonparametric learning framework for datasets with structural
correspondences.


title:
Entanglement concentration for concatenated Greenberger-Horne-Zeiglinger
  state with feasible linear optics

abstract:
  The concatenated Greenberger-Horne-Zeiglinger (C-GHZ) state which is a new
type of logic-qubit entanglement has attracted a lot of attentions recently. We
present a feasible entanglement concentration protocol (ECP) for logic-qubit
entanglement. This ECP is based on the linear optics, and it does not know the
initial coefficients of the less-entangled C-GHZ state. This protocol can be
extended to arbitrary C-GHZ state. This protocol may be useful in future
quantum information processing tasks.


title: Scalable Text Mining with Sparse Generative Models

abstract:
  The information age has brought a deluge of data. Much of this is in text
form, insurmountable in scope for humans and incomprehensible in structure for
computers. Text mining is an expanding field of research that seeks to utilize
the information contained in vast document collections. General data mining
methods based on machine learning face challenges with the scale of text data,
posing a need for scalable text mining methods.
  This thesis proposes a solution to scalable text mining: generative models
combined with sparse computation. A unifying formalization for generative text
models is defined, bringing together research traditions that have used
formally equivalent models, but ignored parallel developments. This framework
allows the use of methods developed in different processing tasks such as
retrieval and classification, yielding effective solutions across different
text mining tasks. Sparse computation using inverted indices is proposed for
inference on probabilistic models. This reduces the computational complexity of
the common text mining operations according to sparsity, yielding probabilistic
models with the scalability of modern search engines.
  The proposed combination provides sparse generative models: a solution for
text mining that is general, effective, and scalable. Extensive experimentation
on text classification and ranked retrieval datasets are conducted, showing
that the proposed solution matches or outperforms the leading task-specific
methods in effectiveness, with a order of magnitude decrease in classification
times for Wikipedia article categorization with a million classes. The
developed methods were further applied in two 2014 Kaggle data mining prize
competitions with over a hundred competing teams, earning first and second
places.


title:
Introduction to the Special Issue on Sounding Rockets and
  Instrumentation

abstract:
  Rocket technology, originally developed for military applications, has
provided a low-cost observing platform to carry critical and rapid-response
scientific investigations for over 70 years. Even with the development of
launch vehicles that could put satellites into orbit, high altitude sounding
rockets have remained relevant. In addition to science observations, sounding
rockets provide a unique technology test platform and a valuable training
ground for scientists and engineers. Most importantly, sounding rockets remain
the only way to explore the tenuous regions of the Earth's atmosphere (the
upper stratosphere, mesosphere, and lower ionosphere/thermosphere) above
balloon altitudes ($\sim$40 km) and below satellite orbits ($\sim$160 km). They
can lift remote sensing telescope payloads with masses up to 400 kg to
altitudes of 350 km providing observing times of up to 6 minutes above the
blocking influence of Earth's atmosphere. Though a number of sounding rocket
research programs exist around the world, this article focuses on the NASA
Sounding Rocket Program, and particularly on the astrophysical and solar
sounding rocket payloads.


title:
ERBlox: Combining Matching Dependencies with Machine Learning for Entity
  Resolution

abstract:
  Entity resolution (ER), an important and common data cleaning problem, is
about detecting data duplicate representations for the same external entities,
and merging them into single representations. Relatively recently, declarative
rules called "matching dependencies" (MDs) have been proposed for specifying
similarity conditions under which attribute values in database records are
merged. In this work we show the process and the benefits of integrating four
components of ER: (a) Building a classifier for duplicate/non-duplicate record
pairs built using machine learning (ML) techniques; (b) Use of MDs for
supporting the blocking phase of ML; (c) Record merging on the basis of the
classifier results; and (d) The use of the declarative language "LogiQL" -an
extended form of Datalog supported by the "LogicBlox" platform- for all
activities related to data processing, and the specification and enforcement of
MDs.


title:
Photon flux and bunching noise from measurement of the shot noise
  variance

abstract:
  We report the experimental observation of photon bunching noise through shot
noise measurements made on a pseudo-thermal state of light using balanced
detection. A full theory describing the measurement is developed, and in
agreement with theory it is found that the shot noise variance in the balanced
signal reproduces the time series of the flux of the primary incoherent beam.
Moreover, when the average power of the pseudo-thermal light is varied, the
balanced detection is seen to track this change. A comparison of direct
detection and balanced detection of the thermal field, shows that the balanced
detection performs at least as well the direct detection and under some
conditions appears to outperform the direct detection. There is not necessarily
a contradiction with quantum field theory which predicts that at best the
performance of the balanced detection should be equal to the direct detection,
because the direct detection process is subject to nonlinearity that has not
been excluded by measurements (even though any tests we performed suggest such
effects are small). This is the first time that the bunching noise effect of
high occupation number chaotic light via the shot noise of the field has
successfully been measured, to the point of using it to infer the flux of the
field. The findings may be relevant to radio receiver design, specifically from
the viewpoint of sensitivity improvement.

categories: physics.ins-det astro-ph.IM physics.optics quant-ph


title:
Adelic Cartier divisors with base conditions and the
  Bonnesen-Diskant-type inequalities

abstract:
  In this paper, we introduce positivity notions for pairs of adelic R-Cartier
divisors and R-base conditions, and study fundamental properties of the
arithmetic volumes defined for such pairs. We show that the Gateaux derivatives
of the arithmetic volume function at big pairs along the directions of adelic
R-Cartier divisors are given by suitable arithmetic positive intersection
numbers. As a corollary, we obtain an Arakelov theoretic analogue of the
Bonnesen-Diskant inequality in convex geometry.


title:
Low-power continuous-wave four-wave mixing wavelength conversion in
  AlGaAs-nanowaveguide microresonators

abstract:
  We experimentally demonstrate enhanced wavelength conversion in a Q=7500
deeply etched AlGaAs-nanowaveguide microresonator via degenerate
continuous-wave four-wave mixing with a pump power of 24 mW. The maximum
conversion efficiency is -43 dB and accounts for 12 dB enhancement compared to
that of a straight nanowaveguide. The experimental results and theoretical
predictions agree very well and show optimized conversion efficiency of -15 dB.
This work represents a step toward realizing a fully integrated optical devices
for generating new optical frequencies.


title: Stratified Bayesian Optimization

abstract:
  We consider derivative-free black-box global optimization of expensive noisy
functions, when most of the randomness in the objective is produced by a few
influential scalar random inputs. We present a new Bayesian global optimization
algorithm, called Stratified Bayesian Optimization (SBO), which uses this
strong dependence to improve performance. Our algorithm is similar in spirit to
stratification, a technique from simulation, which uses strong dependence on a
categorical representation of the random input to reduce variance. We
demonstrate in numerical experiments that SBO outperforms state-of-the-art
Bayesian optimization benchmarks that do not leverage this dependence.


title:
Dynamic Selection of Virtual Machines for Application Servers in Cloud
  Environments

abstract:
  Autoscaling is a hallmark of cloud computing as it allows flexible
just-in-time allocation and release of computational resources in response to
dynamic and often unpredictable workloads. This is especially important for web
applications whose workload is time dependent and prone to flash crowds. Most
of them follow the 3-tier architectural pattern, and are divided into
presentation, application/domain and data layers. In this work we focus on the
application layer. Reactive autoscaling policies of the type "Instantiate a new
Virtual Machine (VM) when the average server CPU utilisation reaches X%" have
been used successfully since the dawn of cloud computing. But which VM type is
the most suitable for the specific application at the moment remains an open
question. In this work, we propose an approach for dynamic VM type selection.
It uses a combination of online machine learning techniques, works in real time
and adapts to changes in the users' workload patterns, application changes as
well as middleware upgrades and reconfigurations. We have developed a
prototype, which we tested with the CloudStone benchmark deployed on AWS EC2.
Results show that our method quickly adapts to workload changes and reduces the
total cost compared to the industry standard approach.


title:
Interaction of microwave photons with nanostructured magnetic
  metasurfaces

abstract:
  A theoretical formalism for the description of the interaction of microwave
photons with a thin (compared to the photon wavelength) magnetic metasurface
comprised of dipolarly interacting nano-scale magnetic elements is developed. A
scattering matrix describing the processes of photon transmission and
reflection at the metasurface boundary is derived. As an example of the use of
the developed formalism, it is demonstrated, that the introduction of a
magnetic metasurface inside a microstrip electromagnetic waveguide
quantitatively changes the dispersion relation of the fundamental waveguide
mode, opening a non-propagation frequency band gap in the waveguide spectrum.
The frequency position and the width of the band gap are dependent on the
waveguide thickness, and can be controlled dynamically by switching the
magnetic ground state of the metasurface. For sufficiently thin waveguides the
position of the band gap is shifted from the resonance absorption frequency of
the metasurface. In such a case, the magnetic metasurface inside a waveguide
works as an efficient reflector, as the energy absorption in the metasurface is
small, and most of the electromagnetic energy inside the non-propagation band
gap is reflected.


title:
A Dirichlet problem for nonlocal degenerate elliptic operators with
  internal nonlinearity

abstract:
  We study a Dirichlet problem in the entire space for some nonlocal degenerate
elliptic operators with internal nonlinearities. With very mild assumptions on
the boundary datum, we prove existence and uniqueness of the solution in the
viscosity sense. If we further assume uniform ellipticity then the solution is
shown to be classical, and even smooth if both the operator and the boundary
datum are smooth.


title: Realizable classes and embedding problems

abstract:
  Let $K$ be a number field with ring of integers $\mathcal{O}_K$ and let $G$
be a finite group. Given a $G$-Galois $K$-algebra $K_h$, let $\mathcal{O}_h$
denote its ring of integers. If $K_h/K$ is tame, then a classical theorem of E.
Noether implies that $\mathcal{O}_h$ is locally free over $\mathcal{O}_KG$ and
hence defines a class in the locally free class group of $\mathcal{O}_KG$. For
$G$ abelian, by combining the work of J. Brinkhuis and L. McCulloh, we prove
that the structure of the collection of all such classes is related to the
study of embedding problems.


title:
Eye-CU: Sleep Pose Classification for Healthcare using Multimodal
  Multiview Data

abstract:
  Manual analysis of body poses of bed-ridden patients requires staff to
continuously track and record patient poses. Two limitations in the
dissemination of pose-related therapies are scarce human resources and
unreliable automated systems. This work addresses these issues by introducing a
new method and a new system for robust automated classification of sleep poses
in an Intensive Care Unit (ICU) environment. The new method,
coupled-constrained Least-Squares (cc-LS), uses multimodal and multiview (MM)
data and finds the set of modality trust values that minimizes the difference
between expected and estimated labels. The new system, Eye-CU, is an affordable
multi-sensor modular system for unobtrusive data collection and analysis in
healthcare. Experimental results indicate that the performance of cc-LS matches
the performance of existing methods in ideal scenarios. This method outperforms
the latest techniques in challenging scenarios by 13% for those with poor
illumination and by 70% for those with both poor illumination and occlusions.
Results also show that a reduced Eye-CU configuration can classify poses
without pressure information with only a slight drop in its performance.


title:
Electronic structures of transition metal dipnictides $XPn_2$ ($X$=Ta,
  Nb; $Pn$=P, As, Sb)

abstract:
  The electronic structures and topological properties of transition metal
dipnictides $XPn_2$ ($X$=Ta, Nb; $Pn$=P, As, Sb) have been systematically
studied using first-principles calculations. In addition to small bulk Fermi
surfaces, the band anticrossing features near the Fermi level can be identified
from band structures without spin-orbit coupling, leading to nodal lines in all
these compounds. Inclusion of spin-orbit coupling gaps out these nodal lines
leaving only a pair of disentangled electron/hole bands crossing the Fermi
level. Therefore, the low energy physics can be in general captured by the
corresponding two band model with several isolated small Fermi pockets.
Detailed analysis of the Fermi surfaces suggests that the arsenides and
NbSb$_2$ are nearly compensated semimetals while the phosphorides and TaSb$_2$
are not. Based on the calculated band parities, the electron and hole bands are
found to be weakly topological non-trivial giving rise to surface states. As an
example, we presented the surface-direction-dependent band structure of the
surfaces states in TaSb$_2$.


title: Control of Directional Errors in Fixed Sequence Multiple Testing

abstract:
  In this paper, we consider the problem of simultaneously testing many
two-sided hypotheses when rejections of null hypotheses are accompanied by
claims of the direction of the alternative. The fundamental goal is to
construct methods that control the mixed directional familywise error rate,
which is the probability of making any type 1 or type 3 (directional) error. In
particular, attention is focused on cases where the hypotheses are ordered as
$H_1 , \ldots, H_n$, so that $H_{i+1}$ is tested only if $H_1 , \ldots, H_i$
have all been previously rejected. In this situation, one can control the usual
familywise error rate under arbitrary dependence by the basic procedure which
tests each hypothesis at level $\alpha$, and no other multiplicity adjustment
is needed. However, we show that this is far too liberal if one also accounts
for directional errors. But, by imposing certain dependence assumptions on the
test statistics, one can retain the basic procedure. Through a simulation study
and a clinical trial example, we numerically illustrate good performance of the
proposed procedures compared to the existing mdFWER controlling procedures. The
proposed procedures are also implemented in the R-package FixSeqMTP.


title: Inverting the Rational Sweep Map

abstract:
  We present a simple algorithm for inverting the sweep map on rational
$(m,n)$-Dyck paths for a co-prime pair $(m,n)$ of positive integers. This work
is inspired by Thomas-Williams work on the modular sweep map. A simple proof of
the validity of our algorithm is included.


title:
Linear recurrence relations in $Q$-systems via lattice points in
  polyhedra

abstract:
  We prove that the sequence of the characters of the Kirillov-Reshetikhin (KR)
modules $W_{m}^{(a)}, m\in \mathbb{Z}_{m\geq 0}$ associated to a node $a$ of
the Dynkin diagram of a complex simple Lie algebra $\mathfrak{g}$ satisfies a
linear recurrence relation except for some cases in types $E_7$ and $E_8$. To
this end we use the $Q$-system and the existing lattice point summation formula
for the decomposition of KR modules, known as domino removal rules when
$\mathfrak{g}$ is of classical type. As an application, we show how to reduce
some unproven lattice point summation formulas in exceptional types to finite
problems in linear algebra and also give a new proof of them in type $G_2$,
which is the only completely proven case when KR modules have an irreducible
summand with multiplicity greater than 1. We also apply the recurrence to prove
that the function $\dim W_{m}^{(a)}$ is a quasipolynomial in $m$ and establish
its properties. We conjecture that there exists a rational polytope such that
its Ehrhart quasipolynomial in $m$ is $\dim W_{m}^{(a)}$ and the lattice points
of its $m$-th dilate carry the same crystal structure as the crystal associated
with $W_{m}^{(a)}$.


title:
Economic and Technological Complexity: A Model Study of Indicators of
  Knowledge-based Innovation Systems

abstract:
  The Economic Complexity Index (ECI; Hidalgo & Hausmann, 2009) measures the
complexity of national economies in terms of product groups. Analogously to
ECI, a Patent Complexity Index (PatCI) can be developed on the basis of a
matrix of nations versus patent classes. Using linear algebra, the three
dimensions: countries, product groups, and patent classes can be combined into
a measure of "Triple Helix" complexity (THCI) including the trilateral
interaction terms between knowledge production, wealth generation, and
(national) control. THCI can be expected to capture the extent of systems
integration between the global dynamics of markets (ECI) and technologies
(PatCI) in each national system of innovation. We measure ECI, PatCI, and THCI
during the period 2000-2014 for the 34 OECD member states, the BRICS countries,
and a group of emerging and affiliated economies (Argentina, Hong Kong,
Indonesia, Malaysia, Romania, and Singapore). The three complexity indicators
are correlated between themselves; but the correlations with GDP per capita are
virtually absent. Of the world's major economies, Japan scores highest on all
three indicators, while China has been increasingly successful in combining
economic and technological complexity. We could not reproduce the correlation
between ECI and average income that has been central to the argument about the
fruitfulness of the economic complexity approach.


title:
Effect of relativistic acceleration on localized two-mode Gaussian
  quantum states

abstract:
  We study how an arbitrary Gaussian state of two localized wave packets,
prepared in an inertial frame of reference, is described by a pair of uniformly
accelerated observers. We explicitly compute the resulting state for
arbitrarily chosen proper accelerations of the observers and independently
tuned distance between them. To do so, we introduce a generalized Rindler frame
of reference and analytically derive the corresponding state transformation as
a Gaussian channel. Our approach provides several new insights into the
phenomenon of vacuum entanglement such as the highly non-trivial effect of
spatial separation between the observers including sudden death of
entanglement. We also calculate the fidelity of the two-mode channel for
non-vacuum Gaussian states and obtain bounds on classical and quantum
capacities of a single-mode channel. Our framework can be directly applied to
any continuous variable quantum information protocol in which the effects of
acceleration or gravity cannot be neglected.


title: Solving Ridge Regression using Sketched Preconditioned SVRG

abstract:
  We develop a novel preconditioning method for ridge regression, based on
recent linear sketching methods. By equipping Stochastic Variance Reduced
Gradient (SVRG) with this preconditioning process, we obtain a significant
speed-up relative to fast stochastic methods such as SVRG, SDCA and SAG.


title:
Studying topological structure in the epoch of reionization with
  3D-Minkowski functionals of 21cm line fluctuations

abstract:
  The brightness temperature of the redshifted 21cm line brings rich
information on the Inter Galactic Medium (IGM) from the Cosmic Dawn and Epoch
of Reionization (EoR). While the power spectrum is a useful tool to
statistically investigate the 21cm signal, the 21cm brightness temperature
field is highly non-Gaussian, and the power spectrum is inadequate to
characterize the non-Gaussianity. The Minkowski Functionals (MFs) are promising
tools to extract non-gaussian features of the 21cm signal and give topological
information such as morphology of ionized bubbles. In this work, we study the
21cm line signal in detail with MFs. To promote understanding of basic features
of the 21cm signal, we calculate the MFs of not only the hydrogen neutral
fraction but the matter density and spin temperature, which contribute to the
brightness temperature fluctuations. We find that the structure of the
brightness temperature depends mainly on the ionized fraction and the spin
temperature at late and early stages of the EoR, respectively. Further, we
investigate the redshift evolution of the MFs at $7 < z < 20$. Then, we find
that, after the onset of reionization, the MFs reflect mainly the ionized
bubble property. In addition, the MFs are sensitive to model parameters which
are related to the topology of ionized bubbles and we consider the possibility
of constraining the parameters by the future 21cm signal observations.


title: Prony's method in several variables

abstract:
  The paper gives an extension of Prony's method to the multivariate case which
is based on the relationship between polynomial interpolation, normal forms
modulo ideals and H--bases.


title:
Three-dimensional chiral skyrmions with attractive interparticle
  interactions

abstract:
  We introduce a new class of isolated three-dimensional skyrmion that can
occur within the cone phase of chiral magnetic materials. These novel solitonic
states consist of an axisymmetric core separated from the host phase by an
asymmetric shell. These skyrmions attract one another. We derive regular
solutions for isolated skyrmions arising in the cone phase of cubic helimagnets
and investigate their bound states.


title: The Square-Shoulder-Asakura-Oosawa model

abstract:
  A new model for a colloidal size-asymmetric binary mixture is proposed: The
Square-Shoulder-Asakura-Oosawa. This belongs to the larger class of
non-additive hard-spheres models and has the property that its effective pair
formulation is exact whenever the solvent particle fits inside the interstitial
region of three touching solute particles. Therefore one can study its
properties from the equivalent one-component effective problem. Some remarks on
the phase diagram of this new model are also addressed.

categories: cond-mat.soft cond-mat.mes-hall cond-mat.mtrl-sci physics.chem-ph physics.class-ph


title: Hyperparameter optimization with approximate gradient

abstract:
  Most models in machine learning contain at least one hyperparameter to
control for model complexity. Choosing an appropriate set of hyperparameters is
both crucial in terms of model accuracy and computationally challenging. In
this work we propose an algorithm for the optimization of continuous
hyperparameters using inexact gradient information. An advantage of this method
is that hyperparameters can be updated before model parameters have fully
converged. We also give sufficient conditions for the global convergence of
this method, based on regularity conditions of the involved functions and
summability of errors. Finally, we validate the empirical performance of this
method on the estimation of regularization constants of L2-regularized logistic
regression and kernel Ridge regression. Empirical benchmarks indicate that our
approach is highly competitive with respect to state of the art methods.


title: Analytic Bethe-Salpeter Description of the Lightest Pseudoscalar Mesons

abstract:
  Within the Bethe-Salpeter formalism for instantaneous interactions, we
describe, along a totally analytic route, the lightest pseudoscalar mesons by
quark-antiquark bound states which show at least three indispensable general
features, namely, the (almost) masslessness required for pions and kaons to be
interpretable as (pseudo) Goldstone bosons, the suitable asymptotic behaviour
in the limit of large spacelike relative momenta as determined by the
relationship between quark mass function and Bethe-Salpeter amplitudes, and a
pointwise behaviour for finite spacelike relative momenta suited for
guaranteeing colour confinement.


title:
An efficient method for the computation of the Feigenbaum constants to
  high precision

abstract:
  We propose a new practical algorithm for computing the Feigenbaum constants
{\alpha} and {\delta}, having significantly lower time and space complexity
than previously used methods. The algorithm builds upon well-known linear
algebra techniques, and is easily parallelizable. An implementation of it has
been developed and used to determine both constants to 10,000 decimal places.


title: NED: An Inter-Graph Node Metric Based On Edit Distance

abstract:
  Node similarity is a fundamental problem in graph analytics. However, node
similarity between nodes in different graphs (inter-graph nodes) has not
received a lot of attention yet. The inter-graph node similarity is important
in learning a new graph based on the knowledge of an existing graph (transfer
learning on graphs) and has applications in biological, communication, and
social networks. In this paper, we propose a novel distance function for
measuring inter-graph node similarity with edit distance, called NED. In NED,
two nodes are compared according to their local neighborhood structures which
are represented as unordered k-adjacent trees, without relying on labels or
other assumptions. Since the computation problem of tree edit distance on
unordered trees is NP-Complete, we propose a modified tree edit distance,
called TED*, for comparing neighborhood trees. TED* is a metric distance, as
the original tree edit distance, but more importantly, TED* is polynomially
computable. As a metric distance, NED admits efficient indexing, provides
interpretable results, and shows to perform better than existing approaches on
a number of data analysis tasks, including graph de-anonymization. Finally, the
efficiency and effectiveness of NED are empirically demonstrated using
real-world graphs.


title: FARGO3D: A new GPU-oriented MHD code

abstract:
  We present the FARGO3D code, recently publicly released. It is a
magnetohydrodynamics code developed with special emphasis on protoplanetary
disks physics and planet-disk interactions, and parallelized with MPI. The
hydrodynamics algorithms are based on finite difference upwind, dimensionally
split methods. The magnetohydrodynamics algorithms consist of the constrained
transport method to preserve the divergence-free property of the magnetic field
to machine accuracy, coupled to a method of characteristics for the evaluation
of electromotive forces and Lorentz forces. Orbital advection is implemented,
and an N-body solver is included to simulate planets or stars interacting with
the gas. We present our implementation in detail and present a number of widely
known tests for comparison purposes. One strength of FARGO3D is that it can run
on both "Graphical Processing Units" (GPUs) or "Central Processing unit"
(CPUs), achieving large speed up with respect to CPU cores. We describe our
implementation choices, which allow a user with no prior knowledge of GPU
programming to develop new routines for the CPU, and have them translated
automatically for the GPU.


title: Difference sets are not multiplicatively closed

abstract:
  We prove that for any finite set A of real numbers its difference set D:=A-A
has large product set and quotient set, namely, |DD|, |D/D| \gg |D|^{1+c},
where c>0 is an absolute constant. A similar result takes place in the prime
field F_p for sufficiently small D. It gives, in particular, that
multiplicative subgroups of size less than p^{4/5-\eps} cannot be represented
in the form A-A for any A from F_p.


title:
A note on the Brawley-Carlitz theorem on irreducibility of composed
  products of polynomials over finite fields

abstract:
  We give a new proof of the Brawley-Carlitz theorem on irreducibility of the
composed products of irreducible polynomials. Our proof shows that
associativity of the binary operation for the composed product is not
necessary. We then investigate binary operations defined by polynomial
functions, and give a sufficient condition in terms of degrees for the
requirement in the Brawley-Carlitz theorem.


title:
On the circuit complexity of the standard and the Karatsuba methods of
  multiplying integers

abstract:
  We provide accurate upper bounds on the Boolean circuit complexity of the
standard and the Karatsuba methods of integer multiplication


title:
Analysis of the observed and intrinsic durations of gamma-ray bursts
  with known redshift

abstract:
  The duration distribution of 408 GRBs with measured both duration $T_{90}$
and redshift $z$ is examined. Mixtures of a number of distributions (standard
normal, skew-normal, sinh-arcsinh, and alpha-skew-normal) are fitted to the
observed and intrinsic durations using the maximum log-likelihood method. The
best fit is chosen via the Akaike information critetion. The aim of this work
is to assess the presence of the presumed intermediate GRB class, and to
provide a phenomenological model more appropriate than the common mixture of
standard Gaussians. While $\log T^{obs}_{90}$ are well described by a truly
trimodal fit, after moving to the rest frame the statistically most significant
fit is unimodal. To trace the source of this discrepancy, 334 GRBs observed
only by $Swift$/BAT are examined in the same way. In the observer frame, this
results in a number of statistically plausible descriptions, being uni- and
bimodal, and with the number of components ranging from one to three. After
moving to the rest frame, no unambiguous conclusions may be put forward. It is
concluded that the size of the sample is not big enough to infer reliably GRB
properties based on a univariate statistical reasoning only.


title:
Storage and conversion of quantum-statistical properties of light in the
  resonant quantum memory on tripod atomic configuration

abstract:
  We have considered theoretically the feasibility of the broadband quantum
memory based on the resonant tripod-type atomic configuration. In this case,
the writing of a signal field is carried out simultaneously into two channels,
and characterized by an excitation of two spin waves of the atomic ensemble.
With simultaneous read out from both channels quantum properties of the
original signal are mapped on the retrieval pulse no worse than in the case of
memory based on Lambda-type atomic configuration. At the same time new
possibilities are opened up for manipulation of quantum states associated with
sequential reading out (and/or sequential writing) of signal pulses. For
example, the pulse in squeezed state is converted into two partially entangled
pulses with partially squeezed quadratures. Alternatively, two independent
signal pulses with orthogonal squeezed quadratures can be converted into two
entangled pulses.


title:
Hexagonal phase stabilization and magnetic orders of multiferroic
  Lu$_{1-x}$Sc$_x$FeO$_3$

abstract:
  Hexagonal LuFeO$_3$ has drawn a lot of research attention due to its
contentious room-temperature multiferroicity. Due to the unstability of
hexagonal phase in the bulk form, most experimental studies focused on
LuFeO$_3$ thin films which can be stabilized by strain using proper substrates.
Here we report on the hexagonal phase stabilization, magnetism, and
magnetoelectric coupling of bulk LuFeO$_3$ by partial Sc-substitution of Lu.
First, our first-principles calculations show that the hexagonal structure can
be stabilized by partial Sc substitution, while the multiferroic properties
including the noncollinear magnetic order and geometric ferroelectricity remain
robustly unaffected. Therefore, Lu$_{1-x}$Sc$_x$FeO$_3$ can act as a platform
to check the multiferroicity of LuFeO$_3$ and related materials in the bulk
form. Second, the magnetic characterizations on bulk Lu$_{1-x}$Sc$_x$FeO$_3$
demonstrate a magnetic anomaly (probable antiferromagnetic ordering) above room
temperature, $\sim425-445$ K, followed by magnetic transitions in low
temperatures ($\sim167-172$ K). In addition, a magnetoelectric response is
observed in the low temperature region. Our study provides useful information
on the multiferroic physics of hexagonal $R$FeO$_3$ and related systems.


title:
On the Degrees-of-Freedom of the Large-Scale Interfering Two-Way Relay
  Network

abstract:
  Achievable degrees-of-freedom (DoF) of the large-scale interfering two-way
relay network is investigated. The network consists of $K$ pairs of
communication nodes (CNs) and $N$ relay nodes (RNs). It is assumed that $K\ll
N$ and each pair of CNs communicates with each other through one of the $N$
relay nodes without a direct link between them. Interference among RNs is also
considered. Assuming local channel state information (CSI) at each RN, a
distributed and opportunistic RN selection technique is proposed for the
following three promising relaying protocols: amplify--forward,
decode--forward, and compute--forward. As a main result, the asymptotically
achievable DoF is characterized as $N$ increases for the three relaying
protocols. In particular, a sufficient condition on $N$ required to achieve the
certain DoF of the network is analyzed. Through extensive simulations, it is
shown that the proposed RN selection techniques outperform conventional schemes
in terms of achievable rate even in practical communication scenarios. Note
that the proposed technique operates with a distributed manner and requires
only local CSI, leading to easy implementation for practical wireless systems.


title: A Diffusion Kernel LMS algorithm for nonlinear adaptive networks

abstract:
  This work presents a distributed algorithm for nonlinear adaptive learning.
In particular, a set of nodes obtain measurements, sequentially one per time
step, which are related via a nonlinear function; their goal is to collectively
minimize a cost function by employing a diffusion based Kernel Least Mean
Squares (KLMS). The algorithm follows the Adapt Then Combine mode of
cooperation. Moreover, the theoretical properties of the algorithm are studied
and it is proved that under certain assumptions the algorithm suffers a no
regret bound. Finally, comparative experiments verify that the proposed scheme
outperforms other variants of the LMS.


title: Liquid Crystal Elastomer Strips as Soft Crawlers

abstract:
  In this paper, we speculate on a possible application of Liquid Crystal
Elastomers to the field of soft robotics. In particular, we study a concept for
limbless locomotion that is amenable to miniaturisation. For this purpose, we
formulate and solve the evolution equations for a strip of nematic elastomer,
subject to directional frictional interactions with a flat solid substrate, and
cyclically actuated by a spatially uniform, time-periodic stimulus (e.g.,
temperature change). The presence of frictional forces that are sensitive to
the direction of sliding transforms reciprocal, 'breathing-like' deformations
into directed forward motion. We derive formulas quantifying this motion in the
case of distributed friction, by solving a differential inclusion for the
displacement field. The simpler case of concentrated frictional interactions at
the two ends of the strip is also solved, in order to provide a benchmark to
compare the continuously distributed case with a finite-dimensional benchmark.
We also provide explicit formulas for the axial force along the crawler body.


title: Thermal unfolding of myoglobin in the Landau-Ginzburg-Wilson approach

abstract:
  The Landau-Ginzburg-Wilson paradigm is applied to model the low-temperature
crystallographic C$\alpha$ backbone structure of sperm whale myoglobin. The
Glauber protocol is employed to simulate its response to an increase in ambient
temperature. The myoglobin is found to unfold from its native state by a
succession of $\alpha$-helical intermediates, fully in line with the observed
folding and unfolding patterns in denaturation experiments. In particular, a
molten globule intermediate is identified with experimentally correct
attributes. A detailed, experimentally testable contact map is constructed to
characterise the specifics of the unfolding pathway, including the formation of
long range interactions. The results reveal how the unfolding process of a
protein is driven by the interplay between, and a successive melting of, its
modular secondary structure components.

categories: q-bio.BM cond-mat.soft nlin.PS physics.bio-ph


title: All-spherical telescope with extremely wide field of view

abstract:
  An all-spherical catadioptic telescope with the angular field of view of
several tens of degrees in diameter and spherical focal surface is proposed for
the monitoring of large sky areas. We provide a few examples of such a system
with the apertures up to 800 mm and the field of view $30^\circ$ and $40^\circ$
in diameter. The curvature of the focal surface is repaid by high performance
of the telescope. In particular, the diameter of a circle, that includes 80% of
energy in the polychromatic image of a star, is in the range $1.4'' - 1.9''$
across the field of $30^\circ$ size and $2.2'' - 2.9''$ for the field of
$40^\circ$ size. Some ways of working with curved focal surfaces are discussed.


title:
Cosmetic surgery and the $SL(2,\mathbb{C})$ Casson invariant for
  two-bridge knots

abstract:
  We consider the cosmetic surgery problem for two-bridge knots in the
3-sphere. It is seen that all the two-bridge knots at most 9 crossings other
than $9_{27} = S(49,19)=C[2,2,-2,2,2,-2]$ admits no purely cosmetic surgery
pairs. Then we show that any two-bridge knot of the Conway form
$[2x,2,-2x,2x,2,-2x]$ with $x \ge 1$ admits no cosmetic surgery pairs yielding
homology 3-spheres, where $9_{27}$ appears for $x=1$. Our advantage to prove
this is using the $SL(2,\mathbb{C})$ Casson invariant.


title:
On the Fano variety of linear spaces contained in two odd-dimensional
  quadrics

abstract:
  In this paper we describe the geometry of the 2m-dimensional Fano manifold G
parametrizing (m-1)-planes in a smooth complete intersection Z of two quadric
hypersurfaces in the complex projective space P^{2m+2}, for m>0. We show that
there are exactly 2^{2m+2} distinct isomorphisms in codimension one between G
and the blow-up of P^{2m} at 2m+3 general points, parametrized by the 2^{2m+2}
distinct m-planes contained in Z, and describe these rational maps explicitly.
We also describe the cones of nef, movable and effective divisors of G, as well
as their dual cones of curves. Finally, we determine the automorphism group of
G. These results generalize to arbitrary even dimension the classical
description of quartic del Pezzo surfaces (m=1).


title:
Supervised and Semi-Supervised Text Categorization using LSTM for Region
  Embeddings

abstract:
  One-hot CNN (convolutional neural network) has been shown to be effective for
text categorization (Johnson & Zhang, 2015). We view it as a special case of a
general framework which jointly trains a linear model with a non-linear feature
generator consisting of `text region embedding + pooling'. Under this
framework, we explore a more sophisticated region embedding method using Long
Short-Term Memory (LSTM). LSTM can embed text regions of variable (and possibly
large) sizes, whereas the region size needs to be fixed in a CNN. We seek
effective and efficient use of LSTM for this purpose in the supervised and
semi-supervised settings. The best results were obtained by combining region
embeddings in the form of LSTM and convolution layers trained on unlabeled
data. The results indicate that on this task, embeddings of text regions, which
can convey complex concepts, are more useful than embeddings of single words in
isolation. We report performances exceeding the previous best results on four
benchmark datasets.


title:
On separability of the functional space with the open-point and
  bi-point-open topologies

abstract:
  In this paper we study the property of separability of functional space with
the open-point and bi-point-open topologies.


title: Monodromy and K-theory of Schubert curves via generalized jeu de taquin

abstract:
  We establish a combinatorial connection between the real geometry and the
$K$-theory of complex Schubert curves $S(\lambda_\bullet)$, which are
one-dimensional Schubert problems defined with respect to flags osculating the
rational normal curve. In a previous paper, the second author showed that the
real geometry of these curves is described by the orbits of a map $\omega$ on
skew tableaux, defined as the commutator of jeu de taquin rectification and
promotion. In particular, the real locus of the Schubert curve is naturally a
covering space of $\mathbb{RP}^1$, with $\omega$ as the monodromy operator.
  We provide a local algorithm for computing $\omega$ without rectifying the
skew tableau, and show that certain steps in our algorithm are in bijective
correspondence with Pechenik and Yong's genomic tableaux, which enumerate the
$K$-theoretic Littlewood-Richardson coefficient associated to the Schubert
curve. We then give purely combinatorial proofs of several numerical results
involving the $K$-theory and real geometry of $S(\lambda_\bullet)$.


title: One-Generator Quasi-Abelian Codes Revisited

abstract:
  The class of 1-generator quasi-abelian codes over finite fields is revisited.
Alternative and explicit characterization and enumeration of such codes are
given. An algorithm to find all 1-generator quasi-abelian codes is provided.
Two 1-generator quasi-abelian codes whose minimum distances are improved from
Grassl's online table are presented.


title:
Find an Optimal Path in Static System and Dynamical System within
  Polynomial Runtime

abstract:
  We study an ancient problem that in a static or dynamical system, sought an
optimal path, which the context always means within an extremal condition. In
fact, through those discussions about this theme, we established a universal
essential calculated model to serve for these complex systems. Meanwhile we
utilize the sample space to character the system. These contents in this paper
would involve in several major areas including the geometry, probability, graph
algorithms and some prior approaches, which stands the ultimately subtle linear
algorithm to solve this class problem. Along with our progress, our discussion
would demonstrate more general meaning and robust character, which provides
clear ideas or notion to support our concrete applications, who work in a more
popular complex system.


title:
General parametrization of axisymmetric black holes in metric theories
  of gravity

abstract:
  Following previous work of ours in spherical symmetry, we here propose a new
parametric framework to describe the spacetime of axisymmetric black holes in
generic metric theories of gravity. In this case, the metric components are
functions of both the radial and the polar angular coordinates, forcing a
double expansion to obtain a generic axisymmetric metric expression. In
particular, we use a continued-fraction expansion in terms of a compactified
radial coordinate to express the radial dependence, while we exploit a Taylor
expansion in terms of the cosine of the polar angle for the polar dependence.
These choices lead to a superior convergence in the radial direction and to an
exact limit on the equatorial plane. As a validation of our approach, we build
parametrized representations of Kerr, rotating dilaton, and
Einstein-dilaton-Gauss-Bonnet black holes. The match is already very good at
lowest order in the expansion and improves as new orders are added. We expect a
similar behavior for any stationary and axisymmetric black-hole metric.


title:
Bounded negativity, Harbourne constants and transversal arrangements of
  curves

abstract:
  The Bounded Negativity Conjecture predicts that for every complex projective
surface $X$ there exists a number $b(X)$ such that $C^2\geq -b(X)$ holds for
all reduced curves $C\subset X$. For birational surfaces $f:Y\to X$ there have
been introduced certain invariants (Harbourne constants) relating to the effect
the numbers $b(X)$, $b(Y)$ and the complexity of the map $f$. These invariants
have been studied previously when $f$ is the blowup of all singular points of
an arrangement of lines in ${\mathbb P}^2$, of conics and of cubics. In the
present note we extend these considerations to blowups of ${\mathbb P}^2$ at
singular points of arrangements of curves of arbitrary degree $d$. We also
considerably generalize and modify the approach witnessed so far and study
transversal arrangements of sufficiently positive curves on arbitrary surfaces
with the non-negative Kodaira dimension.


title: New Physics at 1 TeV?

abstract:
  If decays of a heavy particle S are responsible for the diphoton excess with
invariant mass 750 GeV observed at the 13 TeV LHC run, it can be easily
accomodated in the Standard Model. Two scenarios are considered: production in
gluon fusion through a loop of heavy isosinglet quark(s) and production in
photon fusion through a loop of heavy isosinglet leptons. In the second case
many heavy leptons are needed or/and they should have large electric charges in
order to reproduce experimental data on $\sigma(pp \to SX) \cdot \mathrm{Br}(S
\to \gamma \gamma)$.


title:
Local structure of singular profiles for a Derivative Nonlinear
  Schr\"odinger Equation

abstract:
  The Derivative Nonlinear Schr\"odinger equation is an $L^2$-critical
nonlinear dispersive equation model for Alfv\'en waves in space plasmas. Recent
numerical studies on an $L^2$-supercritical extension of this equation provide
evidence of finite time singularities. Near the singular point, the solution is
described by a universal profile that solves a nonlinear elliptic eigenvalue
problem depending only on the strength of the nonlinearity. In the present
work, we describe the deformation of the profile and its parameters near
criticality, combining asymptotic analysis and numerical simulations.


title:
Some properties of Hamiltonian homeomorphisms on closed aspherical
  surfaces

abstract:
  On closed symplectically aspherical manifolds, Schwarz proved a classical
result that the action function of a nontrivial Hamiltonian diffeomorphism is
not constant by using Floer homology. In this article, we generalize Schwarz's
theorem to the $C^0$-case on closed aspherical surfaces. Our methods involve
the theory of transverse foliations for dynamical systems of surfaces inspired
by Le Calvez and its recent progresses. As an application, we prove that the
contractible fixed points set (and consequently the fixed points set) of a
nontrivial Hamiltonian homeomorphism is not connected. Furthermore, we obtain
that the growth of the action width of a Hamiltonian homeomorphism increases at
least linearly, and that the group of Hamiltonian homeomorphisms of
$\mathbb{T}^2$ and the group of area preserving homeomorphisms isotopic to the
identity of $\Sigma_g$ ($g>1$) are torsion free, where $\Sigma_g$ is a closed
orientated surface with genus $g$. Finally, we will show how the $C^1$-Zimmer's
conjecture on surfaces deduces from $C^0$-Schwarz's theorem.


title: Disentangled Representations in Neural Models

abstract:
  Representation learning is the foundation for the recent success of neural
network models. However, the distributed representations generated by neural
networks are far from ideal. Due to their highly entangled nature, they are di
cult to reuse and interpret, and they do a poor job of capturing the sparsity
which is present in real- world transformations. In this paper, I describe
methods for learning disentangled representations in the two domains of
graphics and computation. These methods allow neural methods to learn
representations which are easy to interpret and reuse, yet they incur little or
no penalty to performance. In the Graphics section, I demonstrate the ability
of these methods to infer the generating parameters of images and rerender
those images under novel conditions. In the Computation section, I describe a
model which is able to factorize a multitask learning problem into subtasks and
which experiences no catastrophic forgetting. Together these techniques provide
the tools to design a wide range of models that learn disentangled
representations and better model the factors of variation in the real world.


title:
The benefit of a 1-bit jump-start, and the necessity of stochastic
  encoding, in jamming channels

abstract:
  We consider the problem of communicating a message $m$ in the presence of a
malicious jamming adversary (Calvin), who can erase an arbitrary set of up to
$pn$ bits, out of $n$ transmitted bits $(x_1,\ldots,x_n)$. The capacity of such
a channel when Calvin is exactly causal, i.e. Calvin's decision of whether or
not to erase bit $x_i$ depends on his observations $(x_1,\ldots,x_i)$ was
recently characterized to be $1-2p$. In this work we show two (perhaps)
surprising phenomena. Firstly, we demonstrate via a novel code construction
that if Calvin is delayed by even a single bit, i.e. Calvin's decision of
whether or not to erase bit $x_i$ depends only on $(x_1,\ldots,x_{i-1})$ (and
is independent of the "current bit" $x_i$) then the capacity increases to $1-p$
when the encoder is allowed to be stochastic. Secondly, we show via a novel
jamming strategy for Calvin that, in the single-bit-delay setting, if the
encoding is deterministic (i.e. the transmitted codeword is a deterministic
function of the message $m$) then no rate asymptotically larger than $1-2p$ is
possible with vanishing probability of error, hence stochastic encoding (using
private randomness at the encoder) is essential to achieve the capacity of
$1-p$ against a one-bit-delayed Calvin.


title:
How close can we approach the event horizon of the Kerr black hole from
  the detection of the gravitational quasinormal modes?

abstract:
  Using the WKB method, we show that the peak location ($r_{\rm peak}$) of the
potential, which determines the quasinormal mode frequency of the Kerr black
hole, obeys an accurate empirical relation as a function of the specific
angular momentum $a$ and the gravitational mass $M$. If the quasinormal mode
with $a/M \sim 1$ is observed by gravitational wave detectors, we can confirm
the black-hole space-time around the event horizon, $r_{\rm peak}=r_+
+O(\sqrt{1-q})$ where $r_+$ is the event horizon radius. While if the
quasinormal mode is different from that of general relativity, we are forced to
seek the true theory of gravity and/or face to the existence of the naked
singularity.


title: Network Inference by Learned Node-Specific Degree Prior

abstract:
  We propose a novel method for network inference from partially observed edges
using a node-specific degree prior. The degree prior is derived from observed
edges in the network to be inferred, and its hyper-parameters are determined by
cross validation. Then we formulate network inference as a matrix completion
problem regularized by our degree prior. Our theoretical analysis indicates
that this prior favors a network following the learned degree distribution, and
may lead to improved network recovery error bound than previous work.
Experimental results on both simulated and real biological networks demonstrate
the superior performance of our method in various settings.


title: Monitoring Temporal Properties using Interval Analysis

abstract:
  Verification of temporal logic properties plays a crucial role in proving the
desired behaviors of continuous systems. In this paper, we propose an interval
method that verifies the properties described by a bounded signal temporal
logic. We relax the problem so that if the verification process cannot succeed
at the prescribed precision, it outputs an inconclusive result. The problem is
solved by an efficient and rigorous monitoring algorithm. This algorithm
performs a forward simulation of a continuous-time dynamical system, detects a
set of time intervals in which the atomic propositions hold, and validates the
property by propagating the time intervals. In each step, the continuous state
at a certain time is enclosed by an interval vector that is proven to contain a
unique solution. We experimentally demonstrate the utility of the proposed
method in formal analysis of nonlinear and complex continuous systems.


title:
ALMA Cycle 1 Observations of the HH46/47 Molecular Outflow: Structure,
  Entrainment and Core Impact

abstract:
  We present ALMA Cycle 1 observations of the HH46/47 molecular outflow using
combined 12m array and ACA observations. The improved angular resolution and
sensitivity of our multi-line maps reveal structures that help us study the
entrainment process in much more detail and allow us to obtain more precise
estimates of outflow properties than previous observations. We use 13CO(1-0)
and C18O(1-0) emission to correct for the 12CO(1-0) optical depth to accurately
estimate the outflow mass, momentum and kinetic energy. This correction
increases the estimates of the mass, momentum and kinetic energy by factors of
about 9, 5 and 2, respectively, with respect to estimates assuming optically
thin emission. The new 13CO and C18O data also allow us to trace denser and
slower outflow material than that traced by the 12CO maps, and they reveal an
outflow cavity wall at very low velocities (as low as 0.2km/s with respect to
the cores central velocity). Adding with the slower material traced only by
13CO and C18O, there is another factor of 3 increase in the mass estimate and
50% increase in the momentum estimate. The estimated outflow properties
indicate that the outflow is capable of dispersing the parent core within the
typical lifetime of the embedded phase of a low-mass protostar, and that it is
responsible for a core-to-star efficiency of 1/4 to 1/3. We find that the
outflow cavity wall is composed of multiple shells associated with a series of
jet bow-shock events. Within about 3000AU of the protostar the 13CO and C18O
emission trace a circumstellar envelope with both rotation and infall motions,
which we compare with a simple analytic model. The CS(2-1) emission reveals
tentative evidence of a slowly-moving rotating outflow, which we suggest is
entrained not only poloidally but also toroidally by a disk wind that is
launched from relatively large radii from the source.


title:
Ensemble Robustness and Generalization of Stochastic Deep Learning
  Algorithms

abstract:
  The question why deep learning algorithms generalize so well has attracted
increasing research interest. However, most of the well-established approaches,
such as hypothesis capacity, stability or sparseness, have not provided
complete explanations (Zhang et al., 2016; Kawaguchi et al., 2017). In this
work, we focus on the robustness approach (Xu & Mannor, 2012), i.e., if the
error of a hypothesis will not change much due to perturbations of its training
examples, then it will also generalize well. As most deep learning algorithms
are stochastic (e.g., Stochastic Gradient Descent, Dropout, and
Bayes-by-backprop), we revisit the robustness arguments of Xu & Mannor, and
introduce a new approach, ensemble robustness, that concerns the robustness of
a population of hypotheses. Through the lens of ensemble robustness, we reveal
that a stochastic learning algorithm can generalize well as long as its
sensitiveness to adversarial perturbations is bounded in average over training
examples. Moreover, an algorithm may be sensitive to some adversarial examples
(Goodfellow et al., 2015) but still generalize well. To support our claims, we
provide extensive simulations for different deep learning algorithms and
different network architectures exhibiting a strong correlation between
ensemble robustness and the ability to generalize.


title:
Lower Bounds for Interactive Function Computation via Wyner Common
  Information

abstract:
  The question of how much communication is required between collaborating
parties to compute a function of their data is of fundamental importance in the
fields of theoretical computer science and information theory. In this work,
the focus is on coming up with lower bounds on this. The information cost of a
protocol is the amount of information the protocol reveals to Alice and Bob
about each others inputs, and the information complexity of a function is the
infimum of information costs over all valid protocols. For the amortized case,
it is known that the optimal rate for the computation is equal to the
information complexity. Exactly computing this information complexity is not
straight forward however. In this work we lower bound information complexity
for independent inputs in terms of the Wyner common information of a certain
pair of random variables. We show a structural property for the optimal
auxiliary random variable of Wyner common information and exploit this to
exactly compute the Wyner common information in certain cases. The lower bound
obtained through this technique is shown to be tight for a non-trivial example
- equality (EQ) for the ternary alphabet. We also give an example to show that
the lower bound may, in general, not be tight.


title: An Information-Theoretic Foundation for the Weighted Updating Model

abstract:
  Weighted Updating generalizes Bayesian updating, allowing for biased beliefs
by weighting the likelihood function and prior distribution with positive real
exponents. I provide a rigorous foundation for the model by showing that
transforming a distribution by exponential weighting (and normalizing)
systematically affects the information entropy of the resulting distribution.
For weights greater than one the resulting distribution has less information
entropy than the original distribution, and vice versa. The entropy of a
distribution measures how informative a decision maker is treating the
underlying observation(s), so this result suggests a useful interpretation of
the weights. For example, a weight greater than one on a likelihood function
models an individual who is treating the associated observation(s) as being
more informative than a perfect Bayesian would.


title:
On the Correct Estimate of the Probability of False Detection of the
  Matched Filter in Weak-Signal Detection Problems

abstract:
  The detection reliability of weak signals is a critical issue in many
astronomical contexts and may have severe consequences for determining number
counts and luminosity functions, but also for optimising the use of telescope
time in follow-up observations. Because of its optimal properties, one of the
most popular and widely-used detection technique is the matched filter (MF).
This is a linear filter designed to maximise the detectability of a signal of
known structure that is buried in additive Gaussian random noise. In this work
we show that in the very common situation where the number and position of the
searched signals within a data sequence (e.g. an emission line in a spectrum)
or an image (e.g. a point-source in an interferometric map) are unknown, this
technique, when applied in its standard form, may severely underestimate the
probability of false detection. This is because the correct use of the MF
relies upon a-priori knowledge of the position of the signal of interest. In
the absence of this information, the statistical significance of features that
are actually noise is overestimated and detections claimed that are actually
spurious. For this reason, we present an alternative method of computing the
probability of false detection that is based on the probability density
function (PDF) of the peaks of a random field. It is able to provide a correct
estimate of the probability of false detection for the one-, two- and
three-dimensional case. We apply this technique to a real two-dimensional
interferometric map obtained with ALMA.