title:
Improved Bounds on the Epidemic Threshold of Exact SIS Models on Complex
  Networks

abstract:
  The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary
network, without making approximations, is a $2^n$-state Markov chain with a
unique absorbing state (the all-healthy state). This makes analysis of the SIS
model and, in particular, determining the threshold of epidemic spread quite
challenging. It has been shown that the exact marginal probabilities of
infection can be upper bounded by an $n$-dimensional linear time-invariant
system, a consequence of which is that the Markov chain is "fast-mixing" when
the LTI system is stable, i.e. when
$\frac{\beta}{\delta}<\frac{1}{\lambda_{\max}(A)}$ (where $\beta$ is the
infection rate per link, $\delta$ is the recovery rate, and $\lambda_{\max}(A)$
is the largest eigenvalue of the network's adjacency matrix). This well-known
threshold has been recently shown not to be tight in several cases, such as in
a star network. In this paper, We provide tighter upper bounds on the exact
marginal probabilities of infection, by also taking pairwise infection
probabilities into account. Based on this improved bound, we derive tighter
eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing
time) of the chain. We demonstrate the improvement of the threshold condition
by comparing the new bound with the known one on various networks and epidemic
parameters.


title:
On a 1D nonlocal transport equation with nonlocal velocity and
  subcritical or supercritical diffusion

abstract:
  We study a 1D transport equation with nonlocal velocity with subcritical or
supercritical dissipation. For all data in the weighted Sobolev space
$H^{k}(w_{\lambda,\kappa}) \cap L^{\infty},$ with $k=\max(0,3/2-\alpha)$ and
$w_{\lambda, \kappa}$ is a given family of Muckenhoupt weights. We prove a
global existence result in the subcritical case $\alpha \in (1,2)$. We also
prove a local existence theorem for large data in $H^{2}(w_{\lambda,
\kappa})\cap L^{\infty}$ in the supercritical case $\alpha \in (0,1)$. The
proofs are based on the use of the weighted Littlewood-Paley theory,
interpolation along with some new commutator estimates.


title:
Cooperative Planning for Coupled Multi-Agent Systems under Timed
  Temporal Specifications

abstract:
  This paper presents a fully automated procedure for controller synthesis for
multi-agent systems under coupled constraints. Each agent has dynamics
consisting of two terms: the first one models the coupled constraints and the
other one is an additional control input. We aim to design these inputs so that
each agent meets an individual high-level specification given as a Metric
Interval Temporal Logic (MITL). First, a decentralized abstraction that
provides a time and space discretization of the multi-agent system is designed.
Second, by utilizing this abstraction and techniques from formal veri-
fication, we provide an algorithm that computes the individual runs which
provably satisfy the high-level tasks. The overall approach is demonstrated in
a simulation example.


title:
Charge-sensitive front-end electronics with operational amplifiers for
  CdZnTe detectors

abstract:
  Cadmium zinc telluride (CdZnTe, CZT) radiation detectors are suitable for a
variety of applications, due to their high spatial resolution and spectroscopic
energy performance at room temperature. However, state-of-the-art detector
systems require high-performance readout electronics. Though an
application-specific integrated circuit (ASIC) is an adequate solution for the
readout, requirements of high dynamic range and high throughput are not
available in any commercial circuit. Consequently, the present study develops
the analog front-end electronics with operational amplifiers for an 8x8
pixelated CZT detector. For this purpose, we modeled an electrical equivalent
circuit of the CZT detector with the associated charge-sensitive amplifier
(CSA). Based on a detailed network analysis, the circuit design is completed by
numerical values for various features such as ballistic deficit,
charge-to-voltage gain, rise time, and noise level. A verification of the
performance is carried out by synthetic detector signals and a pixel detector.
The experimental results with the pixel detector assembly and a 22Na
radioactive source emphasize the depth dependence of the measured energy. After
pulse processing with depth correction based on the fit of the weighting
potential, the energy resolution is 2.2% (FWHM) for the 511 keV photopeak.


title:
Topology-Guided Path Integral Approach for Stochastic Optimal Control in
  Cluttered Environment

abstract:
  This paper addresses planning and control of robot motion under uncertainty
that is formulated as a continuous-time, continuous-space stochastic optimal
control problem, by developing a topology-guided path integral control method.
The path integral control framework, which forms the backbone of the proposed
method, re-writes the Hamilton-Jacobi-Bellman equation as a statistical
inference problem; the resulting inference problem is solved by a sampling
procedure that computes the distribution of controlled trajectories around the
trajectory by the passive dynamics. For motion control of robots in a highly
cluttered environment, however, this sampling can easily be trapped in a local
minimum unless the sample size is very large, since the global optimality of
local minima depends on the degree of uncertainty. Thus, a homology-embedded
sampling-based planner that identifies many (potentially) local-minimum
trajectories in different homology classes is developed to aid the sampling
process. In combination with a receding-horizon fashion of the optimal control
the proposed method produces a dynamically feasible and collision-free motion
plans without being trapped in a local minimum. Numerical examples on a
synthetic toy problem and on quadrotor control in a complex obstacle field
demonstrate the validity of the proposed method.


title: Counterintuitive Behaviors in Configuration Mixing

abstract:
  By starting with a simple configurations of 2 neutrons in a single j shell we
hare able to learn the effects of high lying configurations on physical
properties such as nuclear magnetic g factors. Some counterintuitive results
are found when both high lying spin orbit partners are allowed to admix with
the basic configuration.


title:
Regularization and decimation pseudolikelihood approaches to statistical
  inference in $XY$-spin models

abstract:
  We implement a pseudolikelyhood approach with l2-regularization as well as
the recently introduced pseudolikelihood with decimation procedure to the
inverse problem in continuous spin models on arbitrary networks, with
arbitrarily disordered couplings. Performances of the approaches are tested
against data produced by Monte Carlo numerical simulations and compared also
from previously studied fully-connected mean-field-based inference techniques.
The results clearly show that the best network reconstruction is obtained
through the decimation scheme, that also allows to dwell the inference down to
lower temperature regimes. Possible applications to phasor models for light
propagation in random media are proposed and discussed.


title: $\delta$-exceedance records and random adaptive walks

abstract:
  We study a modified record process where the $k$'th record in a series of
independent and identically distributed random variables is defined recursively
through the condition $Y_k > Y_{k-1} - \delta_{k-1}$ with a deterministic
sequence $\delta_k > 0$ called the handicap. For constant $\delta_k \equiv
\delta$ and exponentially distributed random variables it has been shown in
previous work that the process displays a phase transition as a function of
$\delta$ between a normal phase where the mean record value increases
indefinitely and a stationary phase where the mean record value remains bounded
and a finite fraction of all entries are records (Park \textit{et al} 2015 {\it
Phys. Rev.} E \textbf{91} 042707). Here we explore the behavior for general
probability distributions and decreasing and increasing sequences $\delta_k$,
focusing in particular on the case when $\delta_k$ matches the typical spacing
between subsequent records in the underlying simple record process without
handicap. We find that a continuous phase transition occurs only in the
exponential case, but a novel kind of first order transition emerges when
$\delta_k$ is increasing. The problem is partly motivated by the dynamics of
evolutionary adaptation in biological fitness landscapes, where $\delta_k$
corresponds to the change of the deterministic fitness component after $k$
mutational steps. The results for the record process are used to compute the
mean number of steps that a population performs in such a landscape before
being trapped at a local fitness maximum.


title: Eta invariants and the hypoelliptic Laplacian

abstract:
  The purpose of this paper is to give a new proof of results of Moscovici and
Stanton on the orbital integrals associated with eta invariants on compact
locally symmetric spaces. Moscovici and Stanton used methods of harmonic
analysis on reductive groups. Here, we combine our approach to orbital
integrals using the hypoelliptic Laplacian, with the introduction of a rotation
on certain Clifford algebras. Probabilistic methods play an important role in
establishing key estimates. In particular, we construct the proper It{\^o}
calculus associated with certain hypoelliptic diffusions.


title: Liftability of singularities and their Frobenius morphism modulo $p^2$

abstract:
  We investigate the $W_2(k)$-liftability of singular schemes. We prove
constructibility of the locus of $W_2(k)$-liftable schemes in a flat family $X
\to S$. Moreover, we construct an explicit $W_2(k)$-lifting of a Frobenius
split scheme $X$ over a perfect field $k$, reproving Bhatt's existential
result. Furthermore, we study existence of liftings of the Frobenius morphism.
In particular, we prove that in dimension $n \geq 4$ ordinary double points do
not admit a $W_2(k)$-lifting compatible with Frobenius, and that canonical
surface singularities are Frobenius liftable. Combined with Bhatt's results,
the latter result implies that the crystalline cohomology groups over $k$ of
surfaces with canonical singularities are not finite dimensional. As a
corollary of our results, we provide a thorough comparison between the notions
of $W_2(k)$-liftability, Frobenius liftability and classical $F$-singularity
types.


title: Kazhdan-Lusztig Theory of super type D and quantum symmetric pairs

abstract:
  We reformulate the Kazhdan-Lusztig theory for the BGG category $\mathcal{O}$
of Lie algebras of type D via the theory of canonical bases arising from
quantum symmetric pairs initiated by Weiqiang Wang and the author. This is
further applied to formulate and establish for the first time the
Kazhdan-Lusztig theory for the BGG category $\mathcal{O}$ of the
ortho-symplectic Lie superalgebra $\mathfrak{osp}(2m|2n)$.


title: One-Shot Generalization in Deep Generative Models

abstract:
  Humans have an impressive ability to reason about new concepts and
experiences from just a single example. In particular, humans have an ability
for one-shot generalization: an ability to encounter a new concept, understand
its structure, and then be able to generate compelling alternative variations
of the concept. We develop machine learning systems with this important
capacity by developing new deep generative models, models that combine the
representational power of deep learning with the inferential power of Bayesian
reasoning. We develop a class of sequential generative models that are built on
the principles of feedback and attention. These two characteristics lead to
generative models that are among the state-of-the art in density estimation and
image generation. We demonstrate the one-shot generalization ability of our
models using three tasks: unconditional sampling, generating new exemplars of a
given concept, and generating new exemplars of a family of concepts. In all
cases our models are able to generate compelling and diverse samples---having
seen new examples just once---providing an important class of general-purpose
models for one-shot machine learning.


title: A Hamiltonian version of a result of Gromoll and Grove

abstract:
  The theorem that if all geodesics of a Riemannian two-sphere are closed they
are also simple closed is generalized to real Hamiltonian structures on
$\mathbb{R}P^3$. For reversible Finsler $2$-spheres all of whose geodesics are
closed this implies that the lengths of all geodesics coincide.


title: Improved nonlinear plasmonic slot waveguide: a full study

abstract:
  We present a full study of an improved nonlinear plasmonic slot waveguides
(NPSWs) in which buffer linear dielectric layers are added between the Kerr
type nonlinear dielectric core and the two semi-infinite metal regions. For TM
polarized waves, the inclusion of these supplementary layers have two
consequences. First, they reduced the overall losses. Secondly, they modify the
types of solutions that propagate in the NPSWs adding new profiles enlarging
the possibilities offered by these nonlinear waveguides. Our structure also
provides longer propagation length due to the decrease of the losses compared
to the simple nonlinear slot waveguide and exhibits, for well-chosen refractive
index or thickness of the buffer layer, a spatial transition of its main modes
that can be controlled by the power. We provide a full phase diagram of the TM
wave operating regimes of these improved NPSWs. The stability of the main TM
modes is then demonstrated numerically using the FDTD. We also demonstrate the
existence of TE waves for both linear and nonlinear cases (for some
configurations) in which the maximum intensity is located in the middle of the
waveguide. This kind of structures could be fabricated and characterized
experimentally due to the realistic parameters chosen to model them.


title:
Bridging coupled wires and lattice Hamiltonian for two-component bosonic
  quantum Hall states

abstract:
  We investigate a model of hard-core bosons with correlated hopping on the
honeycomb lattice in an external magnetic field by means of a coupled-wire
approach. It has been numerically shown that this model exhibits at half
filling the bosonic integer quantum Hall (BIQH) state, which is a
symmetry-protected topological phase protected by the $U(1)$ particle
conservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015)]. By
combining the bosonization approach and a coupled-wire construction, we
analytically confirm this finding and show that it even holds in the strongly
anisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQH
phase against tunneling that break the separate particle conservations on
different sublattices down to a global particle conservation. We further argue
that a phase transition between two different BIQH phases is in a deconfined
quantum critical point described by two copies of the (2+1)-dimensional $O(4)$
nonlinear sigma model with the topological $\theta$ term at $\theta=\pi$.
Finally we predict a possible fractional quantum Hall state, the Halperin (221)
state, at 1/6 filling.


title:
Domain decomposition algorithms for the two dimensional nonlinear
  Schr{\"o}dinger equation and simulation of Bose-Einstein condensates

abstract:
  In this paper, we apply the optimized Schwarz method to the two dimensional
nonlinear Schr{\"o}dinger equation and extend this method to the simulation of
Bose-Einstein condensates (Gross-Pitaevskii equation). We propose an extended
version of the Schwartz method by introducing a preconditioned algorithm. The
two algorithms are studied numerically. The experiments show that the
preconditioned algorithm improves the convergence rate and reduces the
computation time. In addition, the classical Robin condition and a newly
constructed absorbing condition are used as transmission conditions.


title: Copositive matrices with circulant zero support set

abstract:
  Let $n \geq 5$ and let $u^1,\dots,u^n$ be nonnegative real $n$-vectors such
that the indices of their positive elements form the sets
$\{1,2,\dots,n-2\},\{2,3,\dots,n-1\},\dots,\{n,1,\dots,n-3\}$, respectively.
Here each index set is obtained from the previous one by a circular shift. The
set of copositive forms which vanish on the vectors $u^1,\dots,u^n$ is a face
of the copositive cone ${\cal C}^n$. We give an explicit semi-definite
description of this face and of its subface consisting of positive
semi-definite forms, and study their properties. If the vectors $u^1,\dots,u^n$
and their positive multiples exhaust the zero set of an exceptional copositive
form belonging to this face, then we say it has minimal circulant zero support
set, and otherwise non-minimal circulant zero support set. We show that forms
with non-minimal circulant zero support set are always extremal, and forms with
minimal circulant zero support sets can be extremal only if $n$ is odd. We
construct explicit examples of extremal forms with non-minimal circulant zero
support set for any order $n \geq 5$, and examples of extremal forms with
minimal circulant zero support set for any odd order $n \geq 5$. The set of all
forms with non-minimal circulant zero support set, i.e., defined by different
collections $u^1,\dots,u^n$ of zeros, is a submanifold of codimension $2n$, the
set of all forms with minimal circulant zero support set a submanifold of
codimension $n$.


title:
An optimal single-electron charge qubit for solid-state double quantum
  dots

abstract:
  We report on an optimal single-electron charge qubit for a solid-state double
quantum dot (DQD) system and analyse its dynamics under a time-dependent linear
detuning, using GPU accelerated numerical solutions to the time-dependent
Schr\"odinger equation. The optimal qubit is found to have basis states defined
as the symmetric and antisymmetric linear combinations of the lowest energy
bonding and anti-bonding states of the DQD at zero bias. In contrast to charge
qubits defined by the two localised ground states of the uncoupled DQD, this
choice of the basis causes the resulting dynamics to have a maximal overlap
with an idealised two-state model. Our optimal qubit basis states are not
localised to a single quantum dot and, as such, initialising the qubit requires
a particular sequence of gate pulses to take the system from an initial
fiducial state of the DQD to the logical $0$ or $1$. We determine this sequence
using pulses that incorporate the expected experimental finite rise times. We
also show how to perform arbitrary single qubit operations on the Bloch sphere
using spin-echo type pulsing, allowing us to obtain any qubit state with at
most two single pulses. Measurement of the optimal qubits is achieved by
determining the probability of finding the electron in one of the dots.


title:
Correspondence of $F(R)$ Gravity Singularities in Jordan and Einstein
  Frames

abstract:
  We study the finite time singularity correspondence between the Jordan and
Einstein frames for various $F(R)$ gravity theories. Particularly we
investigate the ordinary pure $F(R)$ gravity case and the unimodular $F(R)$
gravity cases, in the absence of any matter fluids. In the ordinary $F(R)$
gravity cases, by using specific illustrative examples, we show that it is
possible to have various correspondences of finite time singularities, and in
some cases it is possible a singular cosmology in one frame might be
non-singular in the other frame. In the unimodular $F(R)$ gravity case, the
unimodular constraint is affected from the conformal transformation, so this
has an effect on the metric we choose. Moreover, we study the Einstein frame
counterpart theory of the unimodular $F(R)$ gravity case, and we investigate
the correspondences of the singularities in the two theories by considering
specific illustrative examples. Finally, a brief dynamical system analysis is
performed for the vacuum unimodular $F(R)$ gravity and we demonstrate how the
dynamical system behaves near the future Big Rip singularity.


title: Analytic current-vortex sheets in incompressible magnetohydrodynamics

abstract:
  In this paper, we address the problem of current-vortex sheets in ideal
incompressible magnetohydrodynamics. More precisely, we prove a local-in-time
existence and uniqueness result for analytic initial data using a
Cauchy-Kowalevskaya theorem.


title:
Global solutions to the electrodynamic two-body problem on a straight
  line

abstract:
  The classical electrodynamic two-body problem has been a long standing open
problem in mathematics. For motion constrained to the straight line, the
interaction is similar to that of the two-body problem of classical
gravitation. The additional complication is the presence of unbounded
state-dependent delays in the Coulomb forces due to the finiteness of the speed
of light. This circumstance renders the notion of local solutions meaningless,
and therefore, straight-forward ODE techniques can not be applied. Here, we
study the time-symmetric case, i.e., the Fokker-Schwarzschild-Tetrode (FST)
equations, comprising both advanced and retarded delays. We extend the
technique developed in \cite{DirkGuenter}, where existence of FST solutions was
proven on the half-line, to ensure global existence -- a result that had been
obtained by Bauer \cite{Bauer} in 1997. Due to the novel technique, the
presented proof is shorter and more transparent but also relies on the idea to
employ asymptotic data to characterize solutions.


title:
Dominating sequences under atomic changes with applications in
  Sierpi\'{n}ski and interval graphs

abstract:
  A sequence $S=(v_1,\ldots,v_k)$ of distinct vertices of a graph $G$ is called
a legal sequence if $N[v_i] \setminus \cup_{j=1}^{i-1}N[v_j]\not=\emptyset$ for
any $i$. The maximum length of a legal (dominating) sequence in $G$ is called
the Grundy domination number $\gamma_{gr}(G)$ of a graph $G$. It is known that
the problem of determining the Grundy domination number is NP-complete in
general, while efficient algorithm exist for trees and some other classes of
graphs. In this paper we find an efficient algorithm for the Grundy domination
number of an interval graph. We also show the exact value of the Grundy
domination number of an arbitrary Sierpi\'{n}ski graph $S_p^n$, and present
algorithms to construct the corresponding sequence. These results are obtained
by using the main result of the paper, which are sharp bounds for the Grundy
domination number of a vertex- and edge-removed graph. That is, given a graph
$G$, $e\in E(G)$, and $u\in V(G)$, we prove that $\gamma_{gr}(G)-1\le
\gamma_{gr}(G-e) \le \gamma_{gr}(G)+1$ and $\gamma_{gr}(G)-2\le
\gamma_{gr}(G-u) \le \gamma_{gr}(G)$. For each of the bounds there exist
graphs, in which all three possibilities occur for different edges,
respectively vertices.


title:
An Algorithm for Solving Quadratic Optimization Problems with Nonlinear
  Equality Constraints

abstract:
  The classical method to solve a quadratic optimization problem with nonlinear
equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality
conditions using Newton's method. This approach however is usually
computationally demanding, especially for large-scale problems. This paper
presents a new computationally efficient algorithm for solving quadratic
optimization problems with nonlinear equality constraints. It is proven that
the proposed algorithm converges locally to a solution of the KKT optimality
conditions. Two relevant application problems, fitting of ellipses and state
reference generation for electrical machines, are presented to demonstrate the
effectiveness of the proposed algorithm.


title: Recurrent Dropout without Memory Loss

abstract:
  This paper presents a novel approach to recurrent neural network (RNN)
regularization. Differently from the widely adopted dropout method, which is
applied to \textit{forward} connections of feed-forward architectures or RNNs,
we propose to drop neurons directly in \textit{recurrent} connections in a way
that does not cause loss of long-term memory. Our approach is as easy to
implement and apply as the regular feed-forward dropout and we demonstrate its
effectiveness for Long Short-Term Memory network, the most popular type of RNN
cells. Our experiments on NLP benchmarks show consistent improvements even when
combined with conventional feed-forward dropout.


title: New Bounds for the Snake-in-the-Box Problem

abstract:
  The Snake-in-the-Box problem is that of finding a longest induced path in an
$n$-dimensional hypercube. We prove new lower bounds for the values $n\in
\{11,12,13\}$. The Coil-in-the-Box problem is that of finding a longest induced
cycle in an $n$-dimensional hypercube. We prove new lower bounds for the values
$n\in \{12,13\}$.


title: Constraints on low-mass WIMPs from the EDELWEISS-III dark matter search

abstract:
  We present the results of a search for elastic scattering from galactic dark
matter in the form of Weakly Interacting Massive Particles (WIMPs) in the 4-30
GeV/$c^2$ mass range. We make use of a 582 kg-day fiducial exposure from an
array of 800 g Germanium bolometers equipped with a set of interleaved
electrodes with full surface coverage. We searched specifically for $\sim
2.5-20$ keV nuclear recoils inside the detector fiducial volume. As an
illustration the number of observed events in the search for 5 (resp. 20)
GeV/$c^2$ WIMPs are 9 (resp. 4), compared to an expected background of 6.1
(resp. 1.4). A 90% CL limit of $4.3\times 10^{-40}$ cm$^2$ (resp. $9.4\times
10^{-44}$ cm$^2$) is set on the spin-independent WIMP-nucleon scattering
cross-section for 5 (resp. 20) GeV/$c^2$ WIMPs. This result represents a
41-fold improvement with respect to the previous EDELWEISS-II low-mass WIMP
search for 7 GeV/$c^2$ WIMPs. The derived constraint is in tension with hints
of WIMP signals from some recent experiments, thus confirming results obtained
with different detection techniques.


title: Some Existence Results on Cantor Sets

abstract:
  The existence of two different Cantor sets, one of them contained in the set
of Liouville numbers and the other one inside the set of Diophantine numbers,
is proved. Finally, a necessary and sufficient condition for the existence of a
Cantor set contained in a subset of the real line is given.


title:
A tuple of multiplication operators defined by twisted holomorphic
  proper maps

abstract:
  This paper mainly concerns the von Neumann algebras induced by a tuple of
multiplication operators on Bergman spaces which arise essentially from
holomorphic proper maps over higher dimensional domains. We study the
structures and abelian properties of the related von Neumann algebras, and in
interesting cases they turns out to be tightly related to a Riemann manifold.
There is a close interplay between operator theory, geometry and complex
analysis. Many examples are presented.


title:
Soft X-ray absorption excess in gamma-ray burst afterglow spectra:
  Absorption by turbulent ISM

abstract:
  Two-thirds of long duration gamma-ray bursts (GRBs) show soft X-ray
absorption in excess of the Milky Way. The column densities of metals inferred
from UV and optical spectra differ from those derived from soft X-ray spectra,
at times by an order of magnitude, with the latter being higher. The origin of
the soft X-ray absorption excess observed in GRB X-ray afterglow spectra
remains a heavily debated issue, which has resulted in numerous investigations
on the effect of hot material both internal and external to the GRB host galaxy
on our X-ray afterglow observations. Nevertheless, all models proposed so far
have either only been able to account for a subset of our observations (i.e. at
z > 2), or they have required fairly extreme conditions to be present within
the absorbing material. In this paper, we investigate the absorption of the GRB
afterglow by a collisionally ionised and turbulent interstellar medium (ISM).
We find that a dense (3 per cubic centimeters) collisionally ionised ISM could
produce UV/optical and soft X-ray absorbing column densities that differ by a
factor of 10, however the UV/optical and soft X-ray absorbing column densities
for such sightlines and are 2-3 orders of magnitude lower in comparison to the
GRB afterglow spectra. For those GRBs with a larger soft X-ray excess of up to
an order of magnitude, the contribution in absorption from a turbulent ISM as
considered here would ease the required conditions of additional absorbing
components, such as the GRB circumburst medium and intergalactic medium.


title:
Potential Methods for Extending Galvin and J\'onsson's Characterization
  of Distributive Sublattices of Free Lattices

abstract:
  In 1959, F.Galvin and B.Jonsson characterized distributive sublattices of
free lattices in their paper. In this paper, I will create new proofs to a
portion of Galvin and J\'onsson's results. Based on these new proofs, I will
explore possible generalizations of F.Galvin and B.J\'onsson's work by defining
\emph{spanning pairs} and proving partial results which may help with analysing
finite width sublattices of free lattices; and by making some new observations
on finitely generated lattices over semidistributive varieties.
  The work done in this paper may assist in attacking the following
long-standing open problem: Which countable lattices are isomorphic to a
sublattice of a free lattice?


title:
Secular resonances between bodies on close orbits: a case study of the
  Himalia prograde group of jovian irregular satellites

abstract:
  The gravitational interaction between two objects on similar orbits can
effect noticeable changes in the orbital evolution even if the ratio of their
masses to that of the central body is vanishingly small. Christou (2005)
observed an occasional resonant lock in the differential node $\Delta \Omega$
between two members in the Himalia irregular satellite group of Jupiter in the
$N$-body simulations (corresponding mass ratio $\sim 10^{-9}$). Using a
semianalytical approach, we have reproduced this phenomenon. We also
demonstrate the existence of two additional types of resonance, involving angle
differences $\Delta\omega$ and $\Delta (\Omega+\varpi)$ between two group
members. These resonances cause secular oscillations in eccentricity and/or
inclination on timescales $\sim$ 1 Myr. We locate these resonances in $(a,e,i)$
space and analyse their topological structure. In subsequent $N$-body
simulations, we confirm these three resonances and find a fourth one involving
$\Delta \varpi$. In addition, we study the occurrence rates and the stability
of the four resonances from a statistical perspective by integrating 1000 test
particles for 100 Myr. We find $\sim 10-30$ librators for each of the
resonances. Particularly, the nodal resonance found by Christou is the most
stable: 2 particles are observed to stay in libration for the entire
integration.


title: Classification of special curves in the space of cubic polynomials

abstract:
  We describe all special curves in the parameter space of complex cubic
polynomials, that is all algebraic irreducible curves containing infinitely
many post-critically finite polynomials. This solves in a strong form a
conjecture by Baker and DeMarco for cubic polynomials.
  We also prove that an irreducible component of the algebraic curve consisting
of those cubic polynomials that admit an orbit of any given period and given
multiplier is special if and only if the multiplier is 0.


title:
Quantum Memory and Optical Transistor Based on Electromagnetically
  Induced Transparency in Optical Cavities

abstract:
  We theoretically studied the implementation of a quantum memory and an
optical transistor in a system composed by a single atom trapped inside a high
finesse cavity. In order to store and map the quantum state of an input pulse
onto internal states of the single atom (quantum memory) we employ the
electromagnetically induced transparency (EIT) phenomenon (which can work out
as an optical transistor) where the information can be transferred to the dark
state of the atom modelled by a three-level system in a {\Lambda}-type
configuration. In our model we consider a suitable temporal shape for the
control field that ensures the adiabaticity of the storage process and
retrieval of the probe pulse. The dynamic of the field inside the cavity was
obtained by master equation approach, while the outside field was calculated by
input-output formalism. We have analysed two different setups: i) two-sided and
ii) single-sided cavities. While the first setup is the most appropriate and
commonly used to observe cavity-EIT in the transmission spectrum, thus the best
configuration for the optical transistor, the maximum quantum memory efficiency
can not reach reasonable values, being limited to 50% for symmetric cavities.
On the other hand, with single-sided cavity the quantum memory efficiency
increases considerably and can reach values close to 100% in the strong
atom-field coupling regime. However this specific setup is not favourable to
observe the cavity-EIT effect in the transmission spectrum and then it is not
appropriate to control the transmission of light pulses.


title: RankSynd a PRNG Based on Rank Metric

abstract:
  In this paper, we consider a pseudo-random generator based on the difficulty
of the syndrome decoding problem for rank metric codes. We also study the
resistance of this problem against a quantum computer. Our results show that
with rank metric it is possible to obtain fast PRNG with small public data,
without considering additional structure for public matrices like
quasi-cyclicity for Hamming distance.


title: Monotone semiflows with respect to high-rank cones on a Banach space

abstract:
  We consider semiflows in general Banach spaces motivated by monotone cyclic
feedback systems or differential equations with integer-valued Lyapunov
functionals. These semiflows enjoy strong monotonicity properties with respect
to cones of high ranks, which imply order-related structures on the
$\omega$-limit sets of precompact semi-orbits. We show that for a
pseudo-ordered precompact semi-orbit the $\omega$-limit set $\Omega$ is either
ordered, or is contained in the set of equilibria, or possesses a certain
ordered homoclinic property. In particular, we show that if $\Omega$ contains
no equilibrium, then $\Omega$ itself is ordered and hence the dynamics of the
semiflow on $\Omega$ is topologically conjugate to a compact flow on
$\mathbb{R}^k$ with $k$ being the rank. We also establish a
Poincar\'{e}-Bendixson type Theorem in the case where $k=2$. All our results
are established without the smoothness condition on the semiflow, allowing
applications to such cellular or physiological feedback systems with piecewise
linear vector fields and to such infinite dimensional systems where the
$C^1$-Closing Lemma or smooth manifold theory has not been developed.


title:
Theory on the Structure and Coloring of Maximal Planar Graphs
  (1)Recursion Formulae of Chromatic Polynomial and Four-Color Conjecture

abstract:
  In this paper, two recursion formulae of chromatic polynomial of a maximal
planar graph G are obtained. Moreover, the application of these formulaes to
the proof of Four-Color Conjecture is investigated. By using these formulae,
the proof of Four-Color Conjecture boils down to the study on a special class
of graphs, viz., 4-chromatic-funnel pseudo uniquely-4-colorable maximal planar
graphs.


title: An Inequality

abstract:
  In this paper we prove that the weighted linear combination of products of
the k-subsets of an n-set of positive real numbers with weight being the
harmonic mean of their reciprocal sets is less than or equal to uniformly
weighted sum of products of the k-subsets with weight being the harmonic mean
of the whole reciprocal set.


title:
On Optimal Policies in Full-Duplex Wireless Powered Communication
  Networks

abstract:
  The optimal resource allocation scheme in a full-duplex Wireless Powered
Communication Network (WPCN) composed of one Access Point (AP) and two wireless
devices is analyzed and derived. AP operates in a full-duplex mode and is able
to broadcast wireless energy signals in downlink and receive information data
in uplink simultaneously. On the other hand, each wireless device is assumed to
be equipped with Radio-Frequency (RF) energy harvesting circuitry which gathers
the energy sent by AP and stores it in a finite capacity battery. The harvested
energy is then used for performing uplink data transmission tasks. In the
literature, the main focus so far has been on slot-oriented optimization. In
this context, all the harvested RF energy in a given slot is also consumed in
the same slot. However, this approach leads to sub-optimal solutions because it
does not take into account the Channel State Information (CSI) variations over
future slots. Differently from most of the prior works, in this paper we focus
on the long-term weighted throughput maximization problem. This approach
significantly increases the complexity of the optimization problem since it
requires to consider both CSI variations over future slots and the evolution of
the batteries when deciding the optimal resource allocation. We formulate the
problem using the Markov Decision Process (MDP) theory and show how to solve
it. Our numerical results emphasize the superiority of our proposed full-duplex
WPCN compared to the half-duplex WPCN and reveal interesting insights about the
effects of perfect as well as imperfect self-interference cancellation
techniques on the network performance.


title:
Characterizations of variational source conditions, converse results,
  and maxisets of spectral regularization methods

abstract:
  We describe a general strategy for the verification of variational source
condition by formulating two sufficient criteria describing the smoothness of
the solution and the degree of ill-posedness of the forward operator in terms
of a family of subspaces. For linear deterministic inverse problems we show
that variational source conditions are necessary and sufficient for convergence
rates slower than the square root of the noise level. A similar result is shown
for linear inverse problems with white noise. If the forward operator can be
written in terms of the functional calculus of a Laplace-Beltrami operator,
variational source conditions can be characterized by Besov spaces. This is
discussed for a number of prominent inverse problems.


title: The chromatic number of finite type-graphs

abstract:
  By a finite type-graph we mean a graph whose set of vertices is the set of
all $k$-subsets of $[n]=\{1,2,\ldots, n\}$ for some integers $n\ge k\ge 1$, and
in which two such sets are adjacent if and only if they realise a certain order
type specified in advance. Examples of such graphs have been investigated in a
great variety of contexts in the literature with particular attention being
paid to their chromatic number. In recent joint work with Tomasz {\L}uczak, two
of the authors embarked on a systematic study of the chromatic numbers of such
type-graphs, formulated a general conjecture determining this number up to a
multiplicative factor, and proved various results of this kind. In this article
we fully prove this conjecture.


title:
Initial State Independent Equilibration at the Breakdown of the
  Eigenstate Thermalization Hypothesis

abstract:
  This work aims at understanding the interplay between the Eigenstate
Thermalization Hypothesis (ETH), initial state independent equilibration and
quantum chaos in systems that do not have a direct classical counterpart. It is
based on numerical investigations of asymmetric Heisenberg spin ladders with
varied interaction strengths between the legs, i.e., along the rungs. The
relaxation of the energy difference between the legs is investigated. Two
different parameters, both intended to quantify the degree of accordance with
the ETH, are computed. Both indicate violation of the ETH at large interaction
strengths but at different thresholds. Indeed the energy difference is found
not to relax independently of its initial value above some critical interaction
strength which coincides with one of the thresholds. At the same point the
level statistics shift from Poisson-type to Wigner-type. Hence the system may
be considered to become integrable again in the strong interaction limit.


title:
Decoherence of Topological Qubit in Linear and Circular Motions:
  Decoherence Impedance, Anti-Unruh and Information Backflow

abstract:
  In this paper, we consider the decoherence patterns of a topological qubit
made of two Majorana zero modes in the generic linear and circular motions in
the Minkowski spacetime. We show that the reduced dynamics is exact without
Markov approximation. Our results imply that the acceleration will cause
thermalization as expected by Unruh effect. However, for the short-time scale,
we find the rate of decoherence is anti-correlated with the acceleration, as
kind of decoherence impedance. This is in fact related to the "anti-Unruh"
phenomenon previously found by studying the transition probability of
Unruh-DeWitt detector. We also obtain the information backflow by some time
modulations of coupling constant or acceleration, which is a characteristic of
the underlying non-Markovian reduced dynamics. Moreover, by exploiting the
nonlocal nature of the topological qubit, we find that some incoherent
accelerations of the constituent Majorana zero modes can preserve the coherence
instead of thermalizing it.


title:
The environment of the gamma-ray emitting SNR G338.3-0.0: a hadronic
  interpretation for HESS J1640-465

abstract:
  The supernova remnant (SNR) G338.3-0.0 spatially correlates with HESS
J1640-465, which is considered the most luminous gamma-ray source associated
with a SNR in our Galaxy. The X-ray pulsar PSR J1640-4631 has been recently
discovered within the SNR shell, which could favor a leptonic origin for the
detected very-high energy (VHE) emission. In spite of this, the origin of the
VHE radiation from HESS J1640-465 has not been unambiguously clarified so far.
Indeed, a hadronic explanation cannot be ruled out by current observations. On
the basis of atomic (HI) and molecular (12^CO) archival data, we determine, for
the first time, the total ambient density of protons in the region of the
G338.3-0.0/HESS J1640-465 system, a critical parameter for understanding the
emission mechanisms at very high energies. The value obtained is in the 100-130
cm^-3 range. Besides this, we developed a new hadronic model to describe the
spectral energy distribution (SED) of the HESS J1640-465 source, which includes
the latest total gamma-ray cross-section for proton-proton collisions available
in the literature. By using the assessed ambient proton density, we found that
the total energy in accelerated protons required to fit the data is
5.4^{+4.7}_{-2.3} x 10^49 erg and 1.6^{+1.4}_{-0.7} x 10^50 erg for a source
distance of 8.5 and 13 kpc, respectively. The case where the source distance is
8.5 kpc agrees with the typical scenario in which the energy released is on the
order of 10^51 erg and ~10% of that energy is transferred to the accelerated
protons, whereas the case corresponding to a source distance of 13 kpc requires
either a higher value of the energy released in the explosion or a larger
energy fraction to accelerate protons.


title:
How two-dimensional brick layer J-aggregates differ from linear ones:
  excitonic properties and line broadening mechanisms

abstract:
  We study the excitonic coupling and homogeneous spectral line width of brick
layer J-aggregate films. We begin by analysing the structural information
revealed by the two-exciton states probed in two-dimensional spectra. Our first
main result is that the relation between the excitonic couplings and the
spectral shift in a two-dimensional structure is different (larger shift for
the same nearest neighbour coupling) from that in a one-dimensional structure,
which leads to an estimation of dipolar coupling in two-dimensional lattices.
We next investigate the mechanisms of homogeneous broadening - population
relaxation and pure dephasing - and evaluate their relative importance in
linear and two-dimensional aggregates. Our second main result is that pure
dephasing dominates the line width in two-dimensional systems up to a crossover
temperature, which explains the linear temperature dependence of the
homogeneous line width. This is directly related to the decreased density of
states at the band edge when compared with linear aggregates, thus reducing the
contribution of population relaxation to dephasing. Pump-probe experiments are
suggested to directly measure the lifetime of the bright state and can
therefore support the proposed model.


title: Cellularity of hermitian K-theory and Witt theory

abstract:
  Hermitian K-theory and Witt-theory are cellular in the sense of stable
motivic homotopy theory over any base scheme without points of characteristic
two.


title:
Auger recombination in self-assembled quantum dots: Quenching and
  broadening of the charged exciton transition

abstract:
  In quantum dots (QDs) the Auger recombination is a non-radiative process,
where the electron-hole recombination energy is transferred to an additional
carrier. It has been studied mostly in colloidal QDs, where the Auger
recombination time is in the ps range and efficiently quenches the light
emission. In self-assembled QDs, on the other hand, the influence of Auger
recombination on the optical properties is in general neglected, assuming that
it is masked by other processes such as spin and charge fluctuations. Here, we
use time-resolved resonance fluorescence to analyze the Auger recombination and
its influence on the optical properties of a single self-assembled QD. From
excitation-power dependent measurements, we find a long Auger recombination
time of about 500 ns and a quenching of the trion transition by about 80
percent. Furthermore, we observe a broadening of the trion transition linewidth
by up to a factor of two. With a model based on rate equations, we are able to
identify the interplay between tunneling and Auger rate as the underlying
mechanism for the reduced intensity and the broadening of the linewidth. This
demonstrates that self-assembled QDs can serve as an ideal model system to
study how the charge recapture process, given by the band-structure surrounding
the confined carriers, influences the Auger process. Our findings are not only
relevant for improving the emission properties of colloidal QD-based emitters
and dyes, which have recently entered the consumer market. They are also of
interest for more visionary applications, such as quantum information
technologies, based on self-assembled quantum dots.


title: Analytical approach to a bosonic ladder subject to a magnetic field

abstract:
  We examine a bosonic two-leg ladder model subject to a magnetic flux, and
especially focus on a regime where the lower energy band has two minima. By
using a low-energy field theory approach, we study several issues discussed in
the system: the existence of local patterns in density and current,
chiral-current reversal, and the effect of a nearest-neighbor interaction along
the rung direction. In our formalism, the local patterns are interpreted as a
result of breaking of discrete symmetry. The chiral-current reversal occurs
through a competition between a current component determined at a commensurate
vortex density causing an enlargement of the unit cell, and another component,
which is proportional to the magnetic field doping from the corresponding
commensurate flux. The nearest-neighbor interaction along the rung direction
available with the technique on a synthetic dimension is shown to favor a
population-imbalance solution in an experimentally relevant regime.


title:
Can banks default overnight? Modeling endogenous contagion on O/N
  interbank market

abstract:
  We propose a new model of the liquidity driven banking system focusing on
overnight interbank loans. This significant branch of the interbank market is
commonly neglected in the banking system modeling and systemic risk analysis.
We construct a model where banks are allowed to use both the interbank and the
securities markets to manage their liquidity demand and supply as driven by
prudential requirements in a volatile environment. The network of interbank
loans is dynamic and simulated every day. We show how only the intrasystem cash
fluctuations, without any external shocks, may lead to systemic defaults, what
may be a symptom of the self-organized criticality of the system. We also
analyze the impact of different prudential regulations and market conditions on
the interbank market resilience. We confirm that central bank's asset purchase
programs, limiting the declines in government bond prices, can successfully
stabilize bank's liquidity demand. The model can be used to analyze the
interbank market impact of macroprudential tools.


title: Robust Structural Identification via Polyhedral Template Matching

abstract:
  Successful scientific applications of large-scale molecular dynamics often
rely on automated methods for identifying the local crystalline structure of
condensed phases. Many existing methods for structural identification, such as
Common Neighbour Analysis, rely on interatomic distances (or thresholds
thereof) to classify atomic structure. As a consequence they are sensitive to
strain and thermal displacements, and preprocessing such as quenching or
temporal averaging of the atomic positions is necessary to provide reliable
identifications. We propose a new method, Polyhedral Template Matching (PTM),
which classifies structures according to the topology of the local atomic
environment, without any ambiguity in the classification, and with greater
reliability than e.g. Common Neighbour Analysis in the presence of thermal
fluctuations. We demonstrate that the method can reliably be used to identify
structures even in simulations near the melting point, and that it can identify
the most common ordered alloy structures as well. In addition, the method makes
it easy to identify the local lattice orientation in polycrystalline samples,
and to calculate the local strain tensor. An implementation is made available
under a Free and Open Source Software license.


title: Profiles for voltage-activated currents are multiphasic, not curvilinear

abstract:
  Data for voltage-activation of a potassium channel (Matulef et al. Proc Natl
Acad Sci USA 110: 17886-17891. 2013) were, as conventionally done, fitted by
the authors by a Boltzmann function, i.e. by a curvilinear profile. Reanalysis
of the data reveals however that this interpretation must be rejected in favor
of a multiphasic profile, a series of straight lines separated by discontinuous
transitions, quite often in the form of noncontiguities (jumps). In contrast to
the generally very poor fits to the Boltzmann profiles, the fits to multiphasic
profiles are very good. (For the four replicates, the average deviations from
the Boltzmann curves were 10- to 100-fold larger than the deviations from the
multiphasic profiles.) The difference in the median values was statistically
highly significant, P<0.001 in most cases. For the mean values the deviations
from the Boltzmann curve were 20-fold larger than the deviations from the
multiphasic profile, and the difference in the median values was also highly
significant. The curvilinear interpretation must be rejected also because of
the uneven distribution of the points around the Boltzmann curves. The combined
probability for the four replicates that this uneven distribution is due to
chance is less than 0.002.
  In addition to activation of ion channels, a wide variety of biological as
well as non-biological processes and phenomena involving binding, pH,
folding/unfolding and effect of chain length can be well represented by
multiphasic profiles (Nissen 2015a,b. Posted on arXiv.org with Paper ID arXiv:
1511.06601 and 1512.02561).


title:
Suppressing the Unusual: towards Robust CNNs using Symmetric Activation
  Functions

abstract:
  Many deep Convolutional Neural Networks (CNN) make incorrect predictions on
adversarial samples obtained by imperceptible perturbations of clean samples.
We hypothesize that this is caused by a failure to suppress unusual signals
within network layers. As remedy we propose the use of Symmetric Activation
Functions (SAF) in non-linear signal transducer units. These units suppress
signals of exceptional magnitude. We prove that SAF networks can perform
classification tasks to arbitrary precision in a simplified situation. In
practice, rather than use SAFs alone, we add them into CNNs to improve their
robustness. The modified CNNs can be easily trained using popular strategies
with the moderate training load. Our experiments on MNIST and CIFAR-10 show
that the modified CNNs perform similarly to plain ones on clean samples, and
are remarkably more robust against adversarial and nonsense samples.


title: Left-right asymmetry and 750 GeV diphoton excess

abstract:
  We propose the left-right models based on SU(3)_C\otimes SU(M)_L \otimes
SU(N)_R \otimes U(1)_X gauge symmetry for (M,N)=(3,3), (2,3), and (3,2) that
address the 750 GeV diphoton excess recently reported by the LHC. The fermion
contents are minimally introduced, and the generation number must match the
fundamental color number to cancel anomalies and ensure QCD asymptotic freedom.
The diphoton excess arises from the field that breaks the left-right symmetry
spontaneously in the first model, while for the last models it emerges as an
explicit violation of the left-right symmetry. The neutrino masses,
flavor-changing neutral currents, and new boson searches are also discussed.


title: Non-dissipative effects in nonequilibrium systems

abstract:
  Studying the role of activity parameters and the nature of time-symmetric
path-variables constitutes an important part of nonequilibrium physics, so we
argue. The relevant variables are residence times and the undirected traffic
between different states. Parameters are the reactivities, escape rates and
accessibilities and how those possibly depend on the imposed driving. All those
count in the frenetic contribution to statistical forces, response and
fluctuations, operational even in the stationary distribution when far enough
from equilibrium. As these time-symmetric aspects can vary independently from
the entropy production we call the resulting effects non-dissipative, ranking
among features of nonequilibrium that have traditionally not been much included
in statistical mechanics until recently. Those effects can be linked to
localization such as in negative differential conductivity, in jamming or
glassy behavior or in the slowing down of thermalization. Activities may decide
the direction of physical currents away from equilibrium, and the nature of the
stationary distribution, including its population inversion, is not as in
equilibrium decided by energy-entropy content. The ubiquity of non-dissipative
effects and of that frenetic contribution in theoretical considerations invites
a more operational understanding and statistical forces outside equilibrium
appear to provide such a frenometry.


title: Mean-field theory of atomic self-organization in optical cavities

abstract:
  Photons mediate long-range optomechanical forces between atoms in high
finesse resonators, which can induce the formation of ordered spatial patterns.
When a transverse laser drives the atoms, the system undergoes a second order
phase transition, that separates a uniform spatial density from a Bragg grating
maximizing scattering into the cavity and is controlled by the laser intensity.
Starting from a Fokker-Planck equation describing the semiclassical dynamics of
the $N$-atom distribution function, we systematically develop a mean-field
model and analyse its predictions for the equilibrium and out-of-equilibrium
dynamics. The validity of the mean-field model is tested by comparison with the
numerical simulations of the $N$-body Fokker-Planck equation and by means of a
BBGKY hierarchy. The mean-field theory predictions well reproduce several
results of the $N$-body Fokker-Planck equation for sufficiently short times,
and are in good agreement with existing theoretical approaches based on
field-theoretical models. Mean-field, on the other hand, predicts
thermalization time scales which are at least one order of magnitude shorter
than the ones predicted by the $N$-body dynamics. We attribute this discrepancy
to the fact that the mean-field ansatz discards the effects of the long-range
incoherent forces due to cavity losses.


title: Stability of stagnation via an expanding accretion shock wave

abstract:
  Stagnation of a cold plasma streaming to the center or axis of symmetry via
an expanding accretion shock wave is ubiquitous in inertial confinement fusion
(ICF) and high-energy-density plasma physics, the examples ranging from plasma
flows in x-ray-generating Z pinches [Y. Maron et al., Phys. Rev. Lett. 111,
035001 (2013)] to the experiments in support of the recently suggested concept
of impact ignition in ICF [H. Azechi et al., Phys. Rev. Lett. 102, 235002
(2009); M. Murakami et al., Nucl. Fusion 54, 054007 (2014)]. Some experimental
evidence indicates that stagnation via an expanding shock wave is stable, but
its stability has never been studied theoretically. We present such analysis
for the stagnation that does not involve a rarefaction wave behind the
expanding shock front and is described by the classic ideal-gas Noh solution in
spherical and cylindrical geometry. In either case the stagnated flow has been
demonstrated to be stable, initial perturbations exhibiting a power-law,
oscillatory or monotonic, decay with time for all the eigenmodes. This
conclusion has been supported by our simulations done both on a Cartesian grid
and on a curvilinear grid in spherical coordinates. Dispersion equation
determining the eigenvalues of the problem and explicit formulas for the
eigenfunction profiles corresponding to these eigenvalues are presented, making
it possible to use the theory for hydro code verification in two and three
dimensions.


title: Crossing symmetry and Higher spin towers

abstract:
  We consider higher spin operators in weakly coupled gauge conformal field
theories. Crossing symmetry of mixed scalar correlators relates different
higher spin towers and we study the consequences for the spectrum and structure
constants of higher spin operators of different twists. Constraints are
obtained to all loops in perturbation theory. The large spin contributions to
the structure constants can be resummed into a theory-dependent prefactor times
a universal factor, whose structure of poles agrees with the one that would be
obtained from a Witten diagram supergravity computation, although only crossing
symmetry is assumed. Finally, our results provide an all loop expression for
the double null limit of mixed correlators, which is in perfect agreement with
the correlator/Wilson loop correspondence.


title: A calculus for the moduli space of curves

abstract:
  This article accompanies my lecture at the 2015 AMS summer institute in
algebraic geometry in Salt Lake City. I survey the recent advances in the study
of tautological classes on the moduli spaces of curves. After discussing the
Faber-Zagier relations on the moduli spaces of nonsingular curves and the kappa
rings of the moduli spaces of curves of compact type, I present Pixton's
proposal for a complete calculus of tautological classes on the moduli spaces
of stable curves. Several open questions are discussed. An effort has been made
to condense a great deal of mathematics into as few pages as possible with the
hope that the reader will follow through to the end.


title: Feature Selection as a Multiagent Coordination Problem

abstract:
  Datasets with hundreds to tens of thousands features is the new norm. Feature
selection constitutes a central problem in machine learning, where the aim is
to derive a representative set of features from which to construct a
classification (or prediction) model for a specific task. Our experimental
study involves microarray gene expression datasets, these are high-dimensional
and noisy datasets that contain genetic data typically used for distinguishing
between benign or malicious tissues or classifying different types of cancer.
In this paper, we formulate feature selection as a multiagent coordination
problem and propose a novel feature selection method using multiagent
reinforcement learning. The central idea of the proposed approach is to
"assign" a reinforcement learning agent to each feature where each agent learns
to control a single feature, we refer to this approach as MARL. Applying this
to microarray datasets creates an enormous multiagent coordination problem
between thousands of learning agents. To address the scalability challenge we
apply a form of reward shaping called CLEAN rewards. We compare in total nine
feature selection methods, including state-of-the-art methods, and show that
the proposed method using CLEAN rewards can significantly scale-up, thus
outperforming the rest of learning-based methods. We further show that a hybrid
variant of MARL achieves the best overall performance.


title:
Molecular dynamics simulation of nanoindentation on nanocomposite
  pearlite

abstract:
  We carry out molecular dynamics simulations of nanoindentation to investigate
the effect of cementite size and temperature on the deformation behavior of
nanocomposite pearlite composed of alternating ferrite and cementite layers. We
find that, instead of the coherent transmission, dislocation propagates by
forming a widespread plastic deformation in cementite layer. We also show that
increasing temperature enhances the distribution of plastic strain in the
ferrite layer, which reduces the stress acting on the cementite layer. Hence,
thickening cementite layer or increasing temperature reduces the likelihood of
dislocation propagation through the cementite layer. Our finding sheds a light
on the mechanism of dislocation blocking by cementite layer in the pearlite.


title:
2D Discrete Fourier Transform with Simultaneous Edge Artifact Removal
  for Real-Time Applications

abstract:
  Two-Dimensional (2D) Discrete Fourier Transform (DFT) is a basic and
computationally intensive algorithm, with a vast variety of applications. 2D
images are, in general, non-periodic, but are assumed to be periodic while
calculating their DFTs. This leads to cross-shaped artifacts in the frequency
domain due to spectral leakage. These artifacts can have critical consequences
if the DFTs are being used for further processing. In this paper we present a
novel FPGA-based design to calculate high-throughput 2D DFTs with simultaneous
edge artifact removal. Standard approaches for removing these artifacts using
apodization functions or mirroring, either involve removing critical
frequencies or a surge in computation by increasing image size. We use a
periodic-plus-smooth decomposition based artifact removal algorithm optimized
for FPGA implementation, while still achieving real-time ($\ge$23 frames per
second) performance for a 512$\times$512 size image stream. Our optimization
approach leads to a significant decrease in external memory utilization thereby
avoiding memory conflicts and simplifies the design. We have tested our design
on a PXIe based Xilinx Kintex 7 FPGA system communicating with a host PC which
gives us the advantage to further expand the design for industrial
applications.


title:
Periods of the motivic fundamental groupoid of
  $\boldsymbol{\mathbb{P}^{1} \diagdown \lbrace 0, \mu_{N}, \infty \rbrace}$

abstract:
  In this thesis, following F. Brown's point of view, we look at the Hopf
algebra structure of motivic cyclotomic multiple zeta values, which are motivic
periods of the fundamental groupoid of $\mathbb{P}^{1} \diagdown \lbrace 0,
\mu_{N}, \infty \rbrace $. By application of a surjective \textit{period} map
(which, under Grothendieck's period conjecture, is an isomorphism), we deduce
results (such as generating families, identities, etc.) on cyclotomic multiple
zeta values, which are complex numbers. The coaction of this Hopf algebra
(explicitly given by a combinatorial formula from A. Goncharov and F. Brown's
works) is the dual of the action of a so-called \textit{motivic} Galois group
on these specific motivic periods. This entire study was actually motivated by
the hope of a Galois theory for periods, which should extend the usual Galois
theory for algebraic numbers.


title:
Continuous-wave and Transient Characteristics of Phosphorene Microwave
  Transistors

abstract:
  Few-layer phosphorene MOSFETs with 0.3-um-long gate and 15-nm-thick Al2O3
gate insulator was found to exhibit a forward-current cutoff frequency of 2 GHz
and a maximum oscillation frequency of 8 GHz after de-embedding for the
parasitic capacitance associated mainly with the relatively large probe pads.
The gate lag and drain lag of the transistor was found to be on the order of 1
us or less, which is consistent with the lack of hysteresis, carrier freeze-out
or persistent photoconductivity in DC characteristics. These results confirm
that the phosphorene MOSFET can be a viable microwave transistor for both
small-signal and large-signal applications.


title:
Comparing Convolutional Neural Networks to Traditional Models for Slot
  Filling

abstract:
  We address relation classification in the context of slot filling, the task
of finding and evaluating fillers like "Steve Jobs" for the slot X in "X
founded Apple". We propose a convolutional neural network which splits the
input sentence into three parts according to the relation arguments and compare
it to state-of-the-art and traditional approaches of relation classification.
Finally, we combine different methods and show that the combination is better
than individual approaches. We also analyze the effect of genre differences on
performance.


title: A Landau-de Gennes theory for hard colloidal rods: defects and tactoids

abstract:
  We construct a phenomenological Landau-de Gennes theory for hard colloidal
rods by performing an order parameter expansion of the chemical-potential
dependent grand potential. By fitting the coefficients to known results of
Onsager theory, we are not only able to describe the isotropic-nematic phase
transition as function of density, including the well-known density jump, but
also the isotropic-nematic planar interface. The resulting theory is applied in
calculations of the isotropic core size in a radial hedgehog defect, the
density dependence of linear defects of hard rods in square confinement, and
the formation of a nematic droplet in an isotropic background.


title:
Polarization preservation of partially coherent Hermite-Gaussian beams
  for multiple-degrees-of-freedom free-space communication

abstract:
  Multiple-degrees-of-freedom free-space communication combining polarization
and high-order spatial modes promises high-capacity communication channel.
While high-order spatial modes have been widely exploited for dense coding and
high-dimensional quantum information processing, the properties of polarization
preservation of high-order spatial beams propagating in turbulent atmosphere
have not been comprehensively investigated yet. Here we focus on the properties
of polarization preservation of partially coherent Hermite-Gaussian beams
propagating along different atmospheric turbulence paths. The analytical
expressions for the polarization of partially coherent Hermite-Gaussian beams
propagating through atmospheric turbulence along different paths have been
derived. It is shown that the larger the coherence length is, and the larger
the beam order m, n are, the less the polarization is changed. We find that the
evolution properties of the polarization in slant-down paths through turbulent
atmosphere are similar to the case in free space if the condition zenith angle
{\xi}<{\pi}/4 is satisfied. While at a long propagation distance, evolution
properties of polarization in horizontal paths of turbulent atmosphere differs
much from that in free space and in slant paths. The results may allow one to
choose the optimal propagation path in terms of specific applications, which is
helpful for future experimental implementation of multiple-degrees-of-freedom
free-space communication.


title:
Recent Results from SPLASH: Chemical Abundances and Kinematics of
  Andromeda's Stellar Halo

abstract:
  Large scale surveys of Andromeda's resolved stellar populations have
revolutionized our view of this galaxy over the past decade. The combination of
large-scale, contiguous photometric surveys and pointed spectroscopic surveys
has been particularly powerful for discovering substructure and disentangling
the structural components of Andromeda. The SPLASH (Spectroscopic and
Photometric Landscape of Andromeda's Stellar Halo) survey consists of broad-
and narrow-band imaging and spectroscopy of red giant branch stars in lines of
sight ranging in distance from 2 kpc to more than 200 kpc from Andromeda's
center. The SPLASH data reveal a power-law surface brightness profile extending
to at least two-thirds of Andromeda's virial radius (Gilbert et al. 2012), a
metallicity gradient extending to at least 100 kpc from Andromeda's center
(Gilbert et al. 2014), and evidence of a significant population of heated disk
stars in Andromeda's inner halo (Dorman et al. 2013). We are also using the
velocity distribution of halo stars to measure the tangential motion of
Andromeda (Beaton et al., in prep).


title:
Dimension transformation formula for conformal maps into the complement
  of an SLE curve

abstract:
  We prove a formula relating the Hausdorff dimension of a deterministic Borel
subset of $\mathbb R$ and the Hausdorff dimension of its image under a
conformal map from the upper half-plane to a complementary connected component
of an SLE$_\kappa$ curve for $\kappa \not =4$. Our proof is based on the
relationship between SLE and Liouville quantum gravity together with the
one-dimensional KPZ formula of Rhodes-Vargas (2011) and the KPZ formula of
Gwynne-Holden-Miller (2015). As an intermediate step we prove a KPZ formula
which relates the Euclidean dimension of a subset of an SLE$_\kappa$ curve for
$\kappa \in (0,4)\cup(4,8)$ and the dimension of the same set with respect to
the $\gamma$-quantum natural parameterization of the curve induced by an
independent Gaussian free field, $\gamma = \sqrt \kappa \wedge
(4/\sqrt\kappa)$.


title: A (Basis for a) Philosophy of a Theory of Fuzzy Computation

abstract:
  Vagueness is a linguistic phenomenon as well as a property of physical
objects. Fuzzy set theory is a mathematical model of vagueness that has been
used to define vague models of computation. The prominent model of vague
computation is the fuzzy Turing machine. This conceptual computing device gives
an idea of what computing under vagueness means, nevertheless, it is not the
most natural model. Based on the properties of this and other models of vague
computing, it is aimed to formulate a basis for a philosophy of a theory of
fuzzy computation.


title:
Accelerating Data Regeneration for Distributed Storage Systems with
  Heterogeneous Link Capacities

abstract:
  Distributed storage systems provide large-scale reliable data storage
services by spreading redundancy across a large group of storage nodes. In such
a large system, node failures take place on a regular basis. When a storage
node breaks down, a replacement node is expected to regenerate the redundant
data as soon as possible in order to maintain the same level of redundancy.
Previous results have been mainly focused on the minimization of network
traffic in regeneration. However, in practical networks, where link capacities
vary in a wide range, minimizing network traffic does not always yield the
minimum regeneration time. In this paper, we investigate two approaches to the
problem of minimizing regeneration time in networks with heterogeneous link
capacities. The first approach is to download different amounts of repair data
from the helping nodes according to the link capacities. The second approach
generalizes the conventional star-structured regeneration topology to
tree-structured topologies so that we can utilize the links between helping
nodes with bypassing low-capacity links. Simulation results show that the
flexible tree-structured regeneration scheme that combines the advantages of
both approaches can achieve a substantial reduction in the regeneration time.


title:
Robust coupling of DPG and BEM for a singularly perturbed transmission
  problem

abstract:
  We consider a transmission problem consisting of a singularly perturbed
reaction diffusion equation on a bounded domain and the Laplacian in the
exterior, connected through standard transmission conditions. We establish a
DPG scheme coupled with Galerkin boundary elements for its discretization, and
prove its robustness for the field variables in so-called balanced norms. Our
coupling scheme is the one from [F\"uhrer, Heuer, Karkulik: On the coupling of
DPG and BEM, arXiv:1508.00630], adapted to the singularly perturbed case by
using the scheme from [Heuer, Karkulik: A robust DPG method for singularly
perturbed reaction diffusion problems, arXiv:1509.07560]. Essential feature of
our method is that optimal test functions have to be computed only locally. We
report on various numerical experiments in two dimensions.


title: Non-Markovianity in atom-surface dispersion forces

abstract:
  We discuss the failure of the Markov approximation in the description of
atom-surface fluctuation-induced interactions, both at equilibrium
(Casimir-Polder forces) and out-of-equilibrium (quantum friction). Using
general theoretical arguments, we show that the Markov approximation can lead
to erroneous predictions of such phenomena with regard to both strength and
functional dependencies on system parameters. Our findings highlight the
importance of non-Markovian effects in dispersion interactions. In particular,
we show that the long-time power-law tails of temporal correlations, and the
corresponding low-frequency behavior, of two-time dipole correlations,
neglected in the Markovian limit, dramatically affect the prediction of the
force.


title:
Fifty Years of Pulsar Candidate Selection: From simple filters to a new
  principled real-time classification approach

abstract:
  Improving survey specifications are causing an exponential rise in pulsar
candidate numbers and data volumes. We study the candidate filters used to
mitigate these problems during the past fifty years. We find that some existing
methods such as applying constraints on the total number of candidates
collected per observation, may have detrimental effects on the success of
pulsar searches. Those methods immune to such effects are found to be
ill-equipped to deal with the problems associated with increasing data volumes
and candidate numbers, motivating the development of new approaches. We
therefore present a new method designed for on-line operation. It selects
promising candidates using a purpose-built tree-based machine learning
classifier, the Gaussian Hellinger Very Fast Decision Tree (GH-VFDT), and a new
set of features for describing candidates. The features have been chosen so as
to i) maximise the separation between candidates arising from noise and those
of probable astrophysical origin, and ii) be as survey-independent as possible.
Using these features our new approach can process millions of candidates in
seconds (~1 million every 15 seconds), with high levels of pulsar recall
(90%+). This technique is therefore applicable to the large volumes of data
expected to be produced by the Square Kilometre Array (SKA). Use of this
approach has assisted in the discovery of 20 new pulsars in data obtained
during the LOFAR Tied-Array All-Sky Survey (LOTAAS).


title:
A sharp counterexample to local existence of low regularity solutions to
  Einstein's equations in wave coordinates

abstract:
  We are concerned with how regular initial data have to be to ensure local
existence for Einstein's equations in wave coordinates. Klainerman-Rodnianski
and Smith-Tataru showed that there in general is local existence for data in
Sobolev spaces H^s with regularity s>2. We give an example of data in Sobolev
spaces with regularity s=2 for which there is no local solution in this space.


title: Stability and Robustness of RBF Interpolation

abstract:
  We consider how some methods of uniform and nonuniform interpolation by
translates of radial basis functions -- specifically the so-called general
multiquadrics -- perform in the presence of certain types of noise. These
techniques provide some new avenues for interpolation on bounded domains that
is different from the existing literature by using fast Fourier transform
methods to approximate cardinal functions associated with the RBF.


title: Stringy origin of 4d black hole microstates

abstract:
  We derive a precise dictionary between micro-state geometries and open string
condensates for a large class of excitations of four dimensional BPS black
holes realised in terms of D3-branes intersecting on a six-torus. The complete
multipole expansion of the supergravity solutions at weak coupling is extracted
from string amplitudes involving one massless closed string and multiple open
strings insertions on disks with mixed boundary conditions.


title: Indifference to symmetry in Hrushovski's ab initio construction

abstract:
  Denote Hrushovski's non-collapsed ab initio construction for an $n$-ary
relation by $\mathcal{M}_{\not\sim}$ and the analogous construction for a
symmetric $n$-ary relation by $\mathcal{M}_{\sim}$. We show that
$\mathcal{M}_{\not\sim}$ is isomorphic to a proper reduct of
$\mathcal{M}_{\sim}$ and vice versa, and that the combinatorial pregeometries
associated with both structures are isomorphic.


title: Coalescence of Euclidean geodesics on the Poisson-Delaunay triangulation

abstract:
  Let us consider Euclidean first-passage percolation on the Poisson-Delaunay
triangulation. We prove almost sure coalescence of any two semi-infinite
geodesics with the same asymptotic direction. The proof is based on an adapted
Burton-Keane argument and makes use of the concentration property for
shortest-path lengths in the considered graphs. Moreover, by considering the
specific example of the relative neighborhood graph, we illustrate that our
approach extends to further well-known graphs in computational geometry. As an
application, we show that the expected number of semi-infinite geodesics
starting at a given vertex and leaving a disk of a certain radius grows at most
sublinearly in the radius.


title:
Resonance effects in the Raman scattering of mono- and few layers
  MoSe$_2$

abstract:
  Using resonant Raman scattering spectroscopy with 25 different laser lines,
we describe the Raman scattering spectra of mono- and multi-layers
2H-molybdenum diselenide (MoSe$_2$) as well as the different resonances
affecting the most pronounced features. For high-energy phonons, both A- and E-
symmetry type phonons present resonances with A and B excitons of MoSe$_2$
together with a marked increase of intensity when exciting at higher energy,
close to the C exciton energy. We observe symmetry dependent exciton-phonon
coupling affecting mainly the low-energy rigid layer phonon modes. The shear
mode for multilayer displays a pronounced resonance with the C exciton while
the breathing mode has an intensity that grows with the excitation laser
energy, indicating a resonance with electronic excitations at energies higher
than that of the C exciton.


title:
SUSY partners of the truncated oscillator, Painlev\'e transcendents and
  B\"acklund transformations

abstract:
  In this work the supersymmetric technique is applied to the truncated
oscillator to generate Hamiltonians ruled by second and third-order polynomial
Heisenberg algebras, which are connected to the Painlev\'e IV and Painlev\'e V
equations respectively. The aforementioned connection is exploited to produce
particular solutions to both non-linear differential equations and the
B\"acklund transformations relating them.


title:
New parametrization of the deuteron wave function and calculations of
  the tensor polarization

abstract:
  The coefficients of new analytical forms for the deuteron wave function in
coordinate space for NijmI, NijmII, Nijm93, Reid93 and Argonne v18 potentials
have been numerically calculated. The obtained wave functions do not contain
any superfluous knots. The designed parameters of the deuteron are in good
agreement with the experimental and theoretical data. The new parameterization
of the deuteron wave function in momentum space is obtained. The tensor
polarization t20 calculated based on the wave functions is proportionate to the
earlier published results.


title:
Coexistence of topological Dirac fermions in the surface and
  three-dimensional Dirac cone state in the bulk of ZrTe$_{5}$ single crystal

abstract:
  Although, the long-standing debate on the resistivity anomaly in ZrTe$_{5}$
somewhat comes to an end, the exact topological nature of the electronic band
structure remains elusive till today. Theoretical calculations predicted that
bulk ZrTe$_{5}$ to be either a weak or a strong three-dimensional (3D)
topological insulator. However, the angle resolved photoemission spectroscopy
and transport measurements clearly demonstrate 3D Dirac cone state with a small
mass gap between the valence band and conduction band in the bulk. From the
magnetization and magneto-transport measurements on ZrTe$_{5}$ single crystal,
we have detected both the signature of helical spin texture from topological
surface state and chiral anomaly associated with the 3D Dirac cone state in the
bulk. This implies that ZrTe$_{5}$ is a novel 3D topological insulator having
massless Dirac fermionic excitation in its bulk gap state. Whereas, no 3D
topological insulator known in material science holds linear band dispersion in
its insulating bulk. Apart from the band topology, it is also apparent from the
resistivity and Hall measurements that the anomalous peak in the resistivity
can be shifted to a much lower temperature ($T$$<$2 K) by controlling impurity
and defects.


title:
Laser Pulse Driven THz Generation via Resonant Transition Radiation in
  Inhomogeneous Plasmas

abstract:
  An intense, short laser pulse propagating across a plasma boundary
ponderomotively drives THz radiation. Full format PIC simulations and
theoretical analysis are conducted to investigate the properties of this
radiation. Simulation results show the THz emission originates in regions of
varying density and covers a broad spectrum with maximum frequency close to the
maximum plasma frequency. In the case of a sharp vacuum-plasma boundary, the
radiation is generated symmetrically at the plasma entrance and exit, and its
properties are independent of plasma density when the density exceeds a
characteristic value determined by the product of the plasma frequency and the
laser pulse duration. For a diffuse vacuum-plasma boundary, the emission from
the plasma entrance and exit is asymmetric: increasing and decreasing density
ramps enhance and diminish the radiated energy respectively. Enhancements by
factors of 50 are found and simulations show that a 1.66 J, 50 fs driver pulse
can generate ~400 \mu J of THz radiation in a 1.2 mm increasing density ramp.
We present a model that attributes this effect to a plasma resonance process in
the density ramp. The results from the model match those of the simulations for
ramp lengths less than 600 \mu m. For longer ramps for which simulations are
too time consuming the model shows that the amount of radiation reaches a
maximum at a ramp length determined by collisional absorption.


title: Mechanism of the fcc-hcp Phase Transformation in Solid Ar

abstract:
  We present an atomistic description of the {\it fcc}--to--{\it hcp}
transformation mechanism in solid argon (Ar) obtained from transition path
sampling molecular dynamics simulation. The phase transition pathways collected
during the sampling for an 8000--particle system reveal three transition types
according to the lattice deformation and relaxation details. In all three
transition types, we see a critical accumulation of defects and uniform growth
of a less ordered transition state, followed by a homogeneous growth of an
ordered phase. Stacking disorder is discussed to describe the transition
process and the cooperative motions of atoms in \{111\} planes. We investigate
the nucleation with larger system. In a system of 18000--particles, the
collective movements of atoms required for this transition are facilitated by
the formation and growth of stacking faults. However the enthalpy barrier is
still far beyond the thermal fluctuation. The high barrier explains previous
experimental observations of the inaccessibility of the bulk transition at low
pressure and its sluggishness even at extremely high pressure. The transition
mechanism in bulk Ar is different from Ar nanoclusters as the orthorhombic
intermediate structure proposed for the latter is not observed in any of our
simulations.


title: Unramified Euler sums and Hoffman $\star$ basis

abstract:
  When looking at how periods of
$\pi_{1}^{\mathfrak{m}}(\mathbb{P}^{1}\diagdown \lbrace 0, 1, \infty \rbrace
)$, i.e. multiple zeta values, embeds into periods of
$\pi_{1}^{\mathfrak{m}}(\mathbb{P}^{1}\diagdown \lbrace 0, \pm 1, \infty
\rbrace )$, i.e. Euler sums, an explicit criteria via the coaction $\Delta$
acting on their motivic versions comes out. In this paper, adopting this Galois
descent approach, we present a new basis for the space $\mathcal{H}^{1}$ of
motivic multiple zeta values via motivic Euler sums. Up to an analytic
conjecture, we also prove that the motivic Hoffman star basis $\zeta^{\star,
\mathfrak{m}} (2^{a_{1}},3,\cdots,3, 2^{a_{p}}, 3, 2^{b})$ is a basis of
$\mathcal{H}^{1}$. Under a general motivic identity that we conjecture, these
bases are identical. Other examples of unramified ES with alternating patterns
of even and odds are also provided.


title:
Gaps, rings, and non-axisymmetric structures in protoplanetary disks -
  Emission from large grains

abstract:
  Dust grains with sizes around (sub)mm are expected to couple only weakly to
the gas motion in regions beyond 10 au of circumstellar disks. In this work, we
investigate the influence of the spatial distribution of such grains on the
(sub)mm appearance of magnetized protoplanetary disks. We perform non-ideal
global 3D magneto-hydrodynamic stratified disk simulations including particles
of different sizes (50 micron to 1 cm), using a Lagrangian particle solver. We
calculate the spatial dust temperature distribution, including the dynamically
coupled submicron-sized dust grains, and derive ideal continuum re-emission
maps of the disk through radiative transfer simulations. Finally, we
investigate the feasibility to observe specific structures in the thermal
re-emission maps with the Atacama Large Millimeter/submillimeter Array (ALMA).
The pressure bump close to the outer edge of the dead-zone leads to particle
trapping in ring structures. More specifically, vortices in the disk
concentrate the dust and create an inhomogeneous distribution of the solid
material in the azimuthal direction. The large-scale disk perturbations are
preserved in the (sub)mm re-emission maps. The observable structures are very
similar to those expected to result from planet-disk interaction. The larger
dust particles increase the brightness contrast between gap and ring
structures. We find that rings, gaps and the dust accumulation in the vortex
could be traced with ALMA down to a scale of a few astronomical units in
circumstellar disks located in nearby star-forming regions. Finally, we present
a brief comparison of these structures with those recently found with ALMA in
the young circumstellar disks of HL Tau and Oph IRS 48.


title: Linear embedding of free energy minimization

abstract:
  Exact free energy minimization is a convex optimization problem that is
usually approximated with stochastic sampling methods. Deterministic
approximations have been less successful because many desirable properties have
been difficult to attain. Such properties include the preservation of
convexity, lower bounds on free energy, and applicability to systems without
subsystem structure. We satisfy all of these properties by embedding free
energy minimization into a linear program over energy-resolved expectation
values. Numerical results on small systems are encouraging, but a lack of size
consistency necessitates further development for large systems.


title:
Strength of weak layers in cascading failures on multiplex networks:
  case of the international trade network

abstract:
  Many real-world complex systems across natural, social, and economical
domains consist of manifold layers to form multiplex networks. The multiple
network layers give rise to nonlinear effect for the emergent dynamics of
systems. Especially, weak layers that can potentially play significant role in
amplifying the vulnerability of multiplex networks might be shadowed in the
aggregated single-layer network framework which indiscriminately accumulates
all layers. Here we present a simple model of cascading failure on multiplex
networks of weight-heterogeneous layers. By simulating the model on the
multiplex network of international trades, we found that the multiplex model
produces more catastrophic cascading failures which are the result of emergent
collective effect of coupling layers, rather than the simple sum thereof.
Therefore risks can be systematically underestimated in single-layer network
analyses because the impact of weak layers can be overlooked. We anticipate
that our simple theoretical study can contribute to further investigation and
design of optimal risk-averse real-world complex systems.


title: Fractal symmetries: Ungauging the cubic code

abstract:
  Gauging is a ubiquitous tool in many-body physics. It allows one to construct
highly entangled topological phases of matter from relatively simple phases and
to relate certain characteristics of the two. Here we develop a gauging
procedure for general submanifold symmetries of Pauli Hamiltonians, including
symmetries of fractal type. We show a relation between the pre- and
post-gauging models and use this to construct short-range entangled phases with
fractal-like symmetries, one of which is mapped to the cubic code by the
gauging.


title: On the effect of randomness on planted 3-coloring models

abstract:
  We present the hosted coloring framework for studying algorithmic and
hardness results for the $k$-coloring problem. There is a class ${\cal H}$ of
host graphs. One selects a graph $H\in{\cal H}$ and plants in it a balanced
$k$-coloring (by partitioning the vertex set into $k$ roughly equal parts, and
removing all edges within each part). The resulting graph $G$ is given as input
to a polynomial time algorithm that needs to $k$-color $G$ (any legal
$k$-coloring would do -- the algorithm is not required to recover the planted
$k$-coloring). Earlier planted models correspond to the case that ${\cal H}$ is
the class of all $n$-vertex $d$-regular graphs, a member $H\in{\cal H}$ is
chosen at random, and then a balanced $k$-coloring is planted at random. Blum
and Spencer [1995] designed algorithms for this model when $d=n^{\delta}$ (for
$0<\delta\le1$), and Alon and Kahale [1997] managed to do so even when $d$ is a
sufficiently large constant.
  The new aspect in our framework is that it need not involve randomness. In
one model within the framework (with $k=3$) $H$ is a $d$ regular spectral
expander (meaning that except for the largest eigenvalue of its adjacency
matrix, every other eigenvalue has absolute value much smaller than $d$) chosen
by an adversary, and the planted 3-coloring is random. We show that the
3-coloring algorithm of Alon and Kahale [1997] can be modified to apply to this
case. In another model $H$ is a random $d$-regular graph but the planted
balanced $3$-coloring is chosen by an adversary, after seeing $H$. We show that
for a certain range of average degrees somewhat below $\sqrt{n}$, finding a
3-coloring is NP-hard. Together these results (and other results that we have)
help clarify which aspects of randomness in the planted coloring model are the
key to successful 3-coloring algorithms.


title: Redshift-space distortions around voids

abstract:
  We have derived estimators for the linear growth rate of density fluctuations
using the cross-correlation function of voids and haloes in redshift space,
both directly and in Fourier form. In linear theory, this cross-correlation
contains only monopole and quadrupole terms. At scales greater than the void
radius, linear theory is a good match to voids traced out by haloes in N-body
simulations; small-scale random velocities are unimportant at these radii, only
tending to cause small and often negligible elongation of the redshift-space
cross-correlation function near its origin. By extracting the monopole and
quadrupole from the cross-correlation function, we measure the linear growth
rate without prior knowledge of the void profile or velocity dispersion. We
recover the linear growth parameter $\beta$ to 9% precision from an effective
volume of 3(Gpc/h)^3 using voids with radius greater than 25Mpc/h. Smaller
voids are predominantly sub-voids, which may be more sensitive to the random
velocity dispersion; they introduce noise and do not help to improve the
measurement. Adding velocity dispersion as a free parameter allows us to use
information at radii as small as half of the void radius. The precision on
$\beta$ is reduced to approximately 5%. Contrary to the simple redshift-space
distortion pattern in overdensities, voids show diverse shapes in redshift
space, and can appear either elongated or flattened along the line of sight.
This can be explained by the competing amplitudes of the local density
contrast, plus the radial velocity profile and its gradient, with the latter
two factors being determined by the cumulative density profile of voids. The
distortion pattern is therefore determined solely by the void profile and is
different for void-in-cloud and void-in-void. This diversity of redshift-space
void morphology complicates measurements of the Alcock-Paczynski effect using
voids.


title: Negativity in the Generalized Valence Bond Solid State

abstract:
  Using a graphical presentation of the spin $S$ one dimensional Valence Bond
Solid (VBS) state, based on the representation theory of the $SU(2)$
Lie-algebra of spins, we compute the spectrum of a mixed state reduced density
matrix. This mixed state of two blocks of spins $A$ and $B$ is obtained by
tracing out the spins outside $A$ and $B$, in the pure VBS state density
matrix. We find in particular that the negativity of the mixed state is
non-zero only for adjacent subsystems. The method introduced here can be
generalized to the computation of entanglement properties in Levin-Wen models,
that possess a similar algebraic structure to the VBS state in the groundstate.

categories: quant-ph cond-mat.str-el math-ph math.MP


title: Acoustic Scattering from Corners, Edges and Circular Cones

abstract:
  Consider the time-harmonic acoustic scattering from a bounded penetrable
obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed
to possess a circular conic point or an edge point on the boundary in three
dimensions and a planar corner point in two dimensions. The opening angles of
cones and edges are allowed to be any number in $(0,2\pi)\backslash\{\pi\}$. We
prove that such an obstacle scatters any incoming wave non-trivially (i.e., the
far field patterns cannot vanish identically), leading to the absence of real
non-scattering wavenumbers. Local and global uniqueness results for the inverse
problem of recovering the shape of a penetrable scatterers are also obtained
using a single incoming wave. Our approach relies on the singularity analysis
of the inhomogeneous Laplace equation in a cone.


title:
Clumpy wind accretion in supergiant neutron star high mass X-ray
  binaries

abstract:
  The accretion of the stellar wind material by a compact object represents the
main mechanism powering the X-ray emission in classical supergiant high mass
X-ray binaries and supergiant fast X-ray transients. In this work we present
the first attempt to simulate the accretion process of a fast and dense massive
star wind onto a neutron star, taking into account the effects of the
centrifugal and magnetic inhibition of accretion ("gating") due to the spin and
magnetic field of the compact object. We made use of a radiative hydrodynamical
code to model the non-stationary radiatively driven wind of an O-B supergiant
star and then place a neutron star characterized by a fixed magnetic field and
spin period at a certain distance from the massive companion. Our calculations
follow, as a function of time (on a total time scale of several hours), the
transition of the system through all different accretion regimes that are
triggered by the intrinsic variations in the density and velocity of the
non-stationary wind. The X-ray luminosity released by the system is computed at
each time step by taking into account the relevant physical processes occurring
in the different accretion regimes. Synthetic lightcurves are derived and
qualitatively compared with those observed from classical supergiant high mass
X-ray binaries and supergiant fast X-ray transients. Although a number of
simplifications are assumed in these calculations, we show that taking into
account the effects of the centrifugal and magnetic inhibition of accretion
significantly reduces the average X-ray luminosity expected for any neutron
star wind-fed binary. The present model calculations suggest that long spin
periods and stronger magnetic fields are favoured in order to reproduce the
peculiar behavior of supergiant fast X-ray transients in the X-ray domain.


title:
Computational Analysis of Sparsity-Exploiting Moment Relaxations of the
  OPF Problem

abstract:
  With the potential to find global solutions, significant research interest
has focused on convex relaxations of the non-convex OPF problem. Recently,
"moment-based" relaxations from the Lasserre hierarchy for polynomial
optimization have been shown capable of globally solving a broad class of OPF
problems. Global solution of many large-scale test cases is accomplished by
exploiting sparsity and selectively applying the computationally intensive
higher-order relaxation constraints. Previous work describes an iterative
algorithm that indicates the buses for which the higher-order constraints
should be enforced. In order to speed computation of the moment relaxations,
this paper provides a study of the key parameter in this algorithm as applied
to relaxations from both the original Lasserre hierarchy and a recent complex
extension of the Lasserre hierarchy.