title: Incremental $2$-Edge-Connectivity in Directed Graphs

abstract:
  In this paper, we initiate the study of the dynamic maintenance of
$2$-edge-connectivity relationships in directed graphs. We present an algorithm
that can update the $2$-edge-connected blocks of a directed graph with $n$
vertices through a sequence of $m$ edge insertions in a total of $O(mn)$ time.
After each insertion, we can answer the following queries in asymptotically
optimal time: (i) Test in constant time if two query vertices $v$ and $w$ are
$2$-edge-connected. Moreover, if $v$ and $w$ are not $2$-edge-connected, we can
produce in constant time a "witness" of this property, by exhibiting an edge
that is contained in all paths from $v$ to $w$ or in all paths from $w$ to $v$.
(ii) Report in $O(n)$ time all the $2$-edge-connected blocks of $G$. To the
best of our knowledge, this is the first dynamic algorithm for $2$-connectivity
problems on directed graphs, and it matches the best known bounds for simpler
problems, such as incremental transitive closure.


title:
Covariant and background independent functional RG flow for the
  effective average action

abstract:
  We extend our prescription for the construction of a covariant and
background-independent effective action for scalar quantum field theories to
the case where momentum modes below a certain scale are suppressed by the
presence of an infrared regulator. The key step is an appropriate choice of the
infrared cutoff for which the Ward identity, capturing the information from
single-field dependence of the ultraviolet action, continues to be exactly
solvable, and therefore, in addition to covariance, manifest background
independence of the effective action is guaranteed at any scale. A practical
consequence is that in this framework one can adopt truncations dependent on
the single total field. Furthermore we discuss the necessary and sufficient
conditions for the preservation of symmetries along the renormalization group
flow.


title: Additivity of the rho map on the topological structure group

abstract:
  Let M be an orientable topological manifold of dimension m, m greater or
equal to 5, with fundamental group $\Gamma$. Let S(M) be the topological
structure set, endowed with the group structure induced by its identification
with Ranicki's algebraic structure set. We prove that the (rationalized) rho
map $\rho_\Gamma: S(M)\rightarrow K_{m+1} (D^*_\Gamma)\otimes \mathbb{Q}$ is a
homomorphism of abelian groups.


title: Koopman Theory for Partial Differential Equations

abstract:
  We consider the application of Koopman theory to nonlinear partial
differential equations. We demonstrate that the observables chosen for
constructing the Koopman operator are critical for enabling an accurate
approximation to the nonlinear dynamics. If such observables can be found, then
the dynamic mode decomposition algorithm can be enacted to compute a
finite-dimensional approximation of the Koopman operator, including its
eigenfunctions, eigenvalues and Koopman modes. Judiciously chosen observables
lead to physically interpretable spatio-temporal features of the complex system
under consideration and provide a connection to manifold learning methods. We
demonstrate the impact of observable selection, including kernel methods, and
construction of the Koopman operator on two canonical, nonlinear PDEs: Burgers'
equation and the nonlinear Schr\"odinger equation. These examples serve to
highlight the most pressing and critical challenge of Koopman theory: a
principled way to select appropriate observables.


title:
Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N)
  Models

abstract:
  We use the conformal bootstrap approach to explore $5D$ CFTs with $O(N)$
global symmetry, which contain $N$ scalars $\phi_i$ transforming as $O(N)$
vector. Specifically, we study multiple four-point correlators of the leading
$O(N)$ vector $\phi_i$ and the $O(N)$ singlet $\sigma$. The crossing symmetry
of the four-point functions and the unitarity condition provide nontrivial
constraints on the scaling dimensions ($\Delta_\phi$, $\Delta_\sigma$) of
$\phi_i$ and $\sigma$. With reasonable assumptions on the gaps between scaling
dimensions of $\phi_i$ ($\sigma$) and the next $O(N)$ vector (singlet) scalar,
we are able to isolate the scaling dimensions $(\Delta_\phi$, $\Delta_\sigma)$
in small islands. In particular, for large $N=500$, the isolated region is
highly consistent with the result obtained from large $N$ expansion.
  We also study the interacting $O(N)$ CFTs for $1\leqslant N\leqslant100$.
Isolated regions on $(\Delta_\phi,\Delta_\sigma)$ plane are obtained using
conformal bootstrap program with lower order of derivatives $\Lambda$; however,
they disappear after increasing $\Lambda$. We think these islands are
corresponding to interacting but nonunitary $O(N)$ CFTs. Our results provide a
lower bound on the critical value $N_c>100$, below which the interacting $O(N)$
CFTs turn into nonunitary. The critical value is unexpectedly large comparing
with previous estimations.


title:
Effective Connectivity-Based Neural Decoding: A Causal
  Interaction-Driven Approach

abstract:
  We propose a geometric model-free causality measurebased on multivariate
delay embedding that can efficiently detect linear and nonlinear causal
interactions between time series with no prior information. We then exploit the
proposed causal interaction measure in real MEG data analysis. The results are
used to construct effective connectivity maps of brain activity to decode
different categories of visual stimuli. Moreover, we discovered that the
MEG-based effective connectivity maps as a response to structured images
exhibit more geometric patterns, as disclosed by analyzing the evolution of
toplogical structures of the underlying networks using persistent homology.
Extensive simulation and experimental result have been carried out to
substantiate the capabilities of the proposed approach.


title: Spherical spectral synthesis

abstract:
  In this paper we make an attempt to extend L. Schwartz's classical result on
spectral synthesis to several dimensions. Due to counterexamples of D. I.
Gurevich this is impossible for translation invariant varieties. Our idea is to
replace translations by proper euclidean motions in higher dimensions. For this
purpose we introduce the basic concepts of spectral analysis and synthesis in
the non-commutative setting based on Gelfand pairs, where "translation
invariance" will be replaced by invariance with respect to a compact group of
automorphisms. The role of exponential functions will be played by spherical
functions. As an application we obtain the extension of L. Schwartz's
fundamental result.


title:
Robust ergodicity and tracking in antithetic integral control of
  stochastic biochemical reaction networks

abstract:
  Controlling stochastic reactions networks is a challenging problem with
important implications in various fields such as systems and synthetic biology.
Various regulation motifs have been discovered or posited over the recent
years, the most recent one being the so-called Antithetic Integral Control
(AIC) motif in Briat et al. (Cell Systems, 2016). Several favorable properties
for the AIC motif have been demonstrated for classes of reaction networks that
satisfy certain irreducibility, ergodicity and output controllability
conditions. Here we address the problem of verifying these conditions for large
sets of reaction networks with fixed topology using two different approaches.
The first one is quantitative and relies on the notion of interval matrices
while the second one is qualitative and is based on sign properties of
matrices. The obtained results lie in the same spirit as those obtained in
Briat et al. (Cell Systems, 2016) where properties of reaction networks are
independently characterized in terms of control theoretic concepts, linear
programming conditions and graph theoretic conditions.


title: Orbifold autoequivalent exceptional unimodal singularities

abstract:
  We prove that different expressions of the same exceptional unimodal
singularity are orbifold equivalent. As in our previous paper, the matrix
factorizations proving these orbifold equivalences depend again on certain
parameters satisfying some equations whose solutions are permuted by Galois
groups.


title: On the edge capacitated Steiner tree problem

abstract:
  Given a graph G = (V,E) with a root r in V, positive capacities {c(e)|e in
E}, and non-negative lengths {l(e)|e in E}, the minimum-length (rooted) edge
capacitated Steiner tree problem is to find a tree in G of minimum total
length, rooted at r, spanning a given subset T of vertices, and such that, for
each e in E, there are at most c(e) paths, linking r to vertices in T, that
contain e. We study the complexity and approximability of the problem,
considering several relevant parameters such as the number of terminals, the
edge lengths and the minimum and maximum edge capacities. For all but one
combinations of assumptions regarding these parameters, we settle the question,
giving a complete characterization that separates tractable cases from hard
ones. The only remaining open case is proved to be equivalent to a
long-standing open problem. We also prove close relations between our problem
and classical Steiner tree as well as vertex-disjoint paths problems.


title: Graphical modelling of multivariate spatial point processes

abstract:
  This paper proposes a novel graphical model, termed the spatial dependence
graph model, which captures the global dependence structure of different events
that occur randomly in space. In the spatial dependence graph model, the edge
set is identified by using the conditional partial spectral coherence. Thereby,
nodes are related to the components of a multivariate spatial point process and
edges express orthogonality relation between the single components. This paper
introduces an efficient approach towards pattern analysis of highly structured
and high dimensional spatial point processes. Unlike all previous methods, our
new model permits the simultaneous analysis of all multivariate conditional
interrelations. The potential of our new technique to investigate multivariate
structural relations is illustrated using data on forest stands in Lansing
Woods as well as monthly data on crimes committed in the City of London.


title:
Distinguishing number and distinguishing index of graphs from primary
  subgraphs

abstract:
  The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the
least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$
labels that is preserved only by a trivial automorphism. Let $G$ be a connected
graph constructed from pairwise disjoint connected graphs $G_1,\ldots ,G_k$ by
selecting a vertex of $G_1$, a vertex of $G_2$, and identify these two
vertices. Then continue in this manner inductively. We say that $G$ is obtained
by point-attaching from $G_1, \ldots ,G_k$ and that $G_i$'s are the primary
subgraphs of $G$. In this paper, we consider some particular cases of these
graphs that are of importance in chemistry and study their distinguishing
number and index.


title:
A construction of commuting systems of integrable symplectic birational
  maps

abstract:
  We give a construction of completely integrable $(2m)$-dimensional
Hamiltonian systems with cubic Hamilton functions. The construction depends on
a constant skew-Hamiltonian matrix $A$, that is, a matrix satisfying $A^{\rm
T}J=JA$, where $J$ is a non-degenerate skew-symmetric matrix defining the
standard symplectic structure on the phase space $\mathbb R^{2m}$. Applying to
any such system the so called Kahan-Hirota-Kimura discretization scheme, we
arrive at a birational $(2m)$-dimensional map. We show that this map is
symplectic with respect to a symplectic structure that is a perturbation of the
standard symplectic structure on $\mathbb R^{2m}$, and possesses $m$
independent integrals of motion, which are perturbations of the original
Hamilton functions and are in involution with respect to the invariant
symplectic structure. Thus, this map is completely integrable in the
Liouville-Arnold sense. Moreover, under a suitable normalization of the
original $m$-tuples of commuting vector fields, their Kahan-Hirota-Kimura
discretizations also commute and share the invariant symplectic structure and
the $m$ integrals of motion.


title: An Actor-Critic Algorithm for Sequence Prediction

abstract:
  We present an approach to training neural networks to generate sequences
using actor-critic methods from reinforcement learning (RL). Current
log-likelihood training methods are limited by the discrepancy between their
training and testing modes, as models must generate tokens conditioned on their
previous guesses rather than the ground-truth tokens. We address this problem
by introducing a \textit{critic} network that is trained to predict the value
of an output token, given the policy of an \textit{actor} network. This results
in a training procedure that is much closer to the test phase, and allows us to
directly optimize for a task-specific score such as BLEU. Crucially, since we
leverage these techniques in the supervised learning setting rather than the
traditional RL setting, we condition the critic network on the ground-truth
output. We show that our method leads to improved performance on both a
synthetic task, and for German-English machine translation. Our analysis paves
the way for such methods to be applied in natural language generation tasks,
such as machine translation, caption generation, and dialogue modelling.


title: On Wireless Energy and Information Transfer in Relay Networks

abstract:
  This paper investigates the outage probability and the throughput of relay
networks with wireless information and energy transfer where the relays harvest
energy from the transmitted radio-frequency signal of the source. Considering
different power consumption models, we derive the outage probability for both
adaptive and non-adaptive power allocations at the relay. With a total energy
consumption constraint at the source, we provide closed-form expressions for
the optimal time sharing and power allocation between the source energy and
information transfer signals as well as the optimal relay positioning such that
the outage probability is minimized. Finally, we extend our analysis to
multi-relay networks. We show that with perfect channel state information (CSI)
available at the relays and $N$ relays the opportunistic relaying scheme
achieves diversity order of $\frac{N+1}{2}$. Also, we analyze the opportunistic
relaying with partial CSI where either the source-relay or the
relay-destination CSI is provided at its corresponding transmit terminal, and
prove that the relay selection based on the source-relay CSI outperforms the
relay selection based on the relay-destination CSI, in terms of outage
probability. The analytical and simulation results demonstrate the efficiency
of wireless energy and information transfer systems in different conditions.


title: The triple-zero Painlev\'e I transcendent

abstract:
  We offer elementary proofs for fundamental properties of the unique
triple-zero solution to the first Painlev\'e equation.


title: Pion mean fields and heavy baryons

abstract:
  We show that the masses of the lowest-lying heavy baryons can be very well
described in a pion mean-field approach. We consider a heavy baryon as a system
consisting of the $N_c-1$ light quarks that induce the pion mean field, and a
heavy quark as a static color source under the influence of this mean field. In
this approach we derive a number of \textit{model-independent} relations and
calculate the heavy baryon masses using those of the lowest-lying light baryons
as input. The results are in remarkable agreement with the experimental data.
In addition, the mass of the $\Omega_b^*$ baryon is predicted.


title:
Non-perturbative determination of improvement coefficients using
  coordinate space correlators in $N_f=2+1$ lattice QCD

abstract:
  We determine quark mass dependent order $a$ improvement terms of the form
$b_Jam$ for non-singlet scalar, pseudoscalar, vector and axialvector currents
using correlators in coordinate space on a set of CLS ensembles. These have
been generated employing non-perturbatively improved Wilson Fermions and the
tree-level L\"uscher-Weisz gauge action at $\beta = 3.4, 3.46, 3.55$ and $3.7$,
corresponding to lattice spacings ranging from $a \approx 0.085$ fm down to
$0.05$ fm. In the $N_f=2+1$ flavour theory two types of improvement
coefficients exist: $b_J$, proportional to non-singlet quark mass combinations,
and $\bar{b}_J$ (or $\tilde{b}_J$), proportional to the trace of the quark mass
matrix. Combining our non-perturbative determinations with perturbative
results, we quote Pad\'e approximants parameterizing the $b_J$ improvement
coefficients within the above window of lattice spacings. We also give
preliminary results for $\tilde{b}_J$ at $\beta=3.4$.


title:
Super-giant magnetoresistance at room-temperature in copper nanowires
  due to magnetic field modulation of potential barrier heights at
  nanowire-contact interfaces

abstract:
  We have observed a super-giant (~10,000,000%) negative magnetoresistance at
39 mT field in Cu nanowires contacted with Au contact pads. In these nanowires,
potential barriers form at the two Cu/Au interfaces because of Cu oxidation
that results in an ultrathin copper oxide layer forming between Cu and Au.
Current flows when electrons tunnel through, and/or thermionically emit over,
these barriers. A magnetic field applied transverse to the direction of current
flow along the wire deflects electrons toward one edge of the wire because of
the Lorentz force, causing electron accumulation at that edge and depletion at
the other. This lowers the potential barrier at the accumulated edge and raises
it at the depleted edge, causing a super-giant magnetoresistance at room
temperature.


title: Search for Lorentz Violation using Short-Range Tests of Gravity

abstract:
  Experimental tests of the newtonian inverse square law at short range, one at
Indiana University and the other at the Huazhong University of Science and
Technology, have been used to set limits on Lorentz violation in the pure
gravity sector of the nonminimal Standard-Model Extension. In the
nonrelativistic limit, the constraints derived for the 14 independent SME
coefficients for Lorentz violation acting simultaneously are of order $10^{-9}$
m$^{2}$.


title:
Coupled-Channel $D\pi$, $D\eta$ and $D_{s}\bar{K}$ Scattering from
  Lattice QCD

abstract:
  We present the first lattice QCD study of coupled-channel $D\pi$, $D\eta$ and
$D_{s}\bar{K}$ scattering in isospin-1/2 in three partial waves. Using
distillation, we compute matrices of correlation functions with bases of
operators capable of resolving both meson and meson-meson contributions to the
spectrum. These correlation matrices are analysed using a variational approach
to extract the finite-volume energy eigenstates. Utilising L\"uscher's method
and its extensions, we constrain scattering amplitudes in $S$, $P$ and $D$-wave
as a function of energy. By analytically continuing the scattering amplitudes
to complex energies, we investigate the $S$-matrix singularities. Working at
$m_\pi \approx 391$ MeV, we find a pole corresponding to a $J^{P} = 0^{+}$
near-threshold bound state with a large coupling to $D\pi$. We also find a
deeply bound $J^{P} = 1^{-}$ state, and evidence for a $J^{P} = 2^{+}$ narrow
resonance coupled predominantly to $D\pi$. Elastic $D\pi$ scattering in the
isospin-$3/2$ channel is studied and we find a weakly repulsive interaction in
$S$-wave.


title: Active region fine structure observed at 0.08 arcsec resolution

abstract:
  The various mechanisms of magneto-convective energy transport determines the
structure of sunspots and active regions. We characterise the appearance of
light bridges and other fine-structure details and elaborate on their
magneto-convective nature. We present speckle-reconstructed images taken with
the broad-band imager at the 1.5 m GREGOR telescope in the 486nm and 589nm
bands. We estimate the spatial resolution from the noise characteristics of the
image bursts and obtain 0.08" at 589nm. We describe structure details in
individual best images as well as the temporal evolution of selected features.
We find branched dark lanes extending along thin (~1") light bridges in
sunspots at various heliocentric angles. In thick (~2") light bridges the
branches are disconnected from the central lane and have a Y shape with a
bright grain toward the umbra. The images reveal that light bridges exist on
varying intensity levels and that their small-scale features evolve on
timescales of minutes. Faint light bridges show dark lanes outlined by the
surrounding bright features. Dark lanes are very common and are also found in
the boundary of pores. They have a characteristic width of 0.1" or smaller.
Intergranular dark lanes of that width are seen in active region granulation.
While central dark lanes in thin light bridges are elevated and associated with
an density increase above upflows, the dark lane branches correspond to
locations of downflows and are depressed relative to the adjacent bright
plasma. Thick light bridges with central dark lanes show no projection effect.
They have a flat elevated plateau that falls off steeply at the umbral
boundary. There, Y-shaped filaments form as they do in the inner penumbra. This
indicates the presence of inclined magnetic fields, meaning that the umbral
magnetic field is wrapped around the convective light bridge.


title: Compact objects in pure Lovelock theory

abstract:
  For static fluid interiors of compact objects in pure Lovelock gravity
(involving ony one $N$th order term in the equation) we establish similarity in
solutions for the critical odd and even $d=2N+1, 2N+2$ dimensions. It turns out
that in critical odd $d=2N+1$ dimensions, there can exist no bound distribution
with a finite radius, while in critical even $d=2N+2$ dimensions, all solutions
have similar behavior. For exhibition of similarity we would compare star
solutions for $N =1, 2$ in $d=4$ Einstein and $d=6$ in Gauss-Bonnet theory
respectively. We also obtain the pure Lovelock analogue of the Finch-Skea
model.


title:
An improved algorithm based on finite difference schemes for fractional
  boundary value problems with non-smooth solution

abstract:
  In this paper, an efficient algorithm is presented by the extrapolation
technique to improve the accuracy of finite difference schemes for solving the
fractional boundary value problems with non-smooth solution. Two popular finite
difference schemes, the weighted shifted Gr\"{u}nwald difference (WSGD) scheme
and the fractional centered difference (FCD) scheme, are revisited and the
error estimate of the schemes is provided in maximum norm. Based on the
analysis of leading singularity of exact solution for the underlying problem,
it is demonstrated that, with the use of the proposed algorithm, the improved
WSGD and FCD schemes can recover the second-order accuracy for non-smooth
solution. Several numerical examples are given to validate our theoretical
prediction. It is shown that both accuracy and convergence rate of numerical
solutions can be significantly improved by using the proposed algorithm.


title:
Statistical mechanics for complex systems: On the structure of
  $q$-triplets

abstract:
  A plethora of natural, artificial and social complex systems exists which
violate the basic hypothesis (e.g., ergodicity) of Boltzmann-Gibbs (BG)
statistical mechanics. Many of such cases can be satisfactorily handled by
introducing nonadditive entropic functionals, such as $S_q\equiv
k\frac{1-\sum_{i=1}^W p_i^q}{q-1} \; \Bigl(q \in {\cal R}; \, \sum_{i=1}^W
p_i=1 \Bigr)$, with $S_1=S_{BG}\equiv -k\sum_{i=1}^W p_i \ln p_i$. Each class
of such systems can be characterized by a set of values $\{q\}$, directly
corresponding to its various physical/dynamical/geometrical properties. A most
important subset is usually referred to as the $q$-triplet, namely
$(q_{sensitivity}, q_{relaxation}, q_{stationary\,state})$, defined in the body
of this paper. In the BG limit we have
$q_{sensitivity}=q_{relaxation}=q_{stationary\,state}=1$. For a given class of
complex systems, the set $\{q\}$ contains only a few independent values of $q$,
all the others being functions of those few. An illustration of this structure
was given in 2005 [Tsallis, Gell-Mann and Sato, Proc. Natl. Acad. Sc. USA {\bf
102}, 15377; TGS]. This illustration enabled a satisfactory analysis of the
Voyager 1 data on the solar wind. But the general form of these structures
still is an open question. This is so, for instance, for the challenging
$q$-triplet associated with the edge of chaos of the logistic map. We introduce
here a transformation which sensibly generalizes the TGS one, and which might
constitute an important step towards the general solution.


title:
A second-order difference scheme for the time fractional substantial
  diffusion equation

abstract:
  In this work, a second-order approximation of the fractional substantial
derivative is presented by considering a modified shifted substantial
Gr\"{u}nwald formula and its asymptotic expansion. Moreover, the proposed
approximation is applied to a fractional diffusion equation with fractional
substantial derivative in time. With the use of the fourth-order compact scheme
in space, we give a fully discrete Gr\"{u}nwald-Letnikov-formula-based compact
difference scheme and prove its stability and convergence by the energy method
under smooth assumptions. In addition, the problem with nonsmooth solution is
also discussed, and an improved algorithm is proposed to deal with the
singularity of the fractional substantial derivative. Numerical examples show
the reliability and efficiency of the scheme.


title: Inverse Optimization of Convex Risk Functions

abstract:
  The theory of convex risk functions has now been well established as the
basis for identifying the families of risk functions that should be used in
risk averse optimization problems. Despite its theoretical appeal, the
implementation of a convex risk function remains difficult, as there is little
guidance regarding how a convex risk function should be chosen so that it also
well represents one's own risk preferences. In this paper, we address this
issue through the lens of inverse optimization. Specifically, given solution
data from some (forward) risk-averse optimization problems we develop an
inverse optimization framework that generates a risk function that renders the
solutions optimal for the forward problems. The framework incorporates the
well-known properties of convex risk functions, namely, monotonicity,
convexity, translation invariance, and law invariance, as the general
information about candidate risk functions, and also the feedbacks from
individuals, which include an initial estimate of the risk function and
pairwise comparisons among random losses, as the more specific information. Our
framework is particularly novel in that unlike classical inverse optimization,
no parametric assumption is made about the risk function, i.e. it is
non-parametric. We show how the resulting inverse optimization problems can be
reformulated as convex programs and are polynomially solvable if the
corresponding forward problems are polynomially solvable. We illustrate the
imputed risk functions in a portfolio selection problem and demonstrate their
practical value using real-life data.


title:
Vortices, skyrmions, and chirality waves in frustrated Mott insulators
  with a quenched periodic array of impurities

abstract:
  Finite-${\mathbf Q}$ magnetic instabilities are rather common in frustrated
magnets. When the magnetic susceptibility is maximized at multiple-${\mathbf
Q}$ vectors related through lattice symmetry operations, exotic magnetic
orderings such as vortex and skyrmion crystals may follow. Here we show that a
periodic array of nonmagnetic impurities, which can be realized through charge
density wave ordering, leads to a rich phase diagram featuring a plethora of
chiral magnetic phases, especially when there is a simple relation between the
reciprocal vectors of the impurity superlattice and the magnetic ${\mathbf
Q}$-vectors. We also investigate the effect of changing the impurity
concentration or disturbing the impurity array with small quenched randomness.
Alternative realizations of impurity superlattices are briefly discussed.


title:
Evidence for percolation diffusion of cations and material recovery in
  disordered pyrochlore from accelerated molecular dynamics simulations

abstract:
  We used classical and accelerated molecular dynamics simulations to
characterize vacancy-mediated diffusion of cations in Gd$_2$Ti$_2$O$_7$
pyrochlore as a function of the disorder on the microsecond timescale. We find
that cation vacancy diffusion is slow in materials with low levels of disorder.
However, higher levels of disorder allow for fast cation diffusion, which is
then also accompanied by fast antisite annihilation and ordering of the
cations. The cation diffusivity is therefore not constant, but decreases as the
material reorders. The results suggest that fast cation diffusion is triggered
by the existence of a percolation network of antisites. This is in marked
contrast with oxygen diffusion, which showed a smooth increase of the ionic
diffusivity with increasing disorder in the same compound. The increase of the
cation diffusivity with disorder is also contrary to observations from other
complex oxides and disordered media models, suggesting a fundamentally
different relation between disorder and mass transport. These results highlight
the dynamic interplay between fast cation diffusion and the recovery of
disorder and have important implications for understanding radiation damage
evolution, sintering and aging, as well as diffusion in disorder oxides more
generally.


title:
On a $L^\infty$ functional derivative estimate relating to the Cauchy
  problem for scalar semi-linear parabolic partial differential equations with
  general continuous nonlinearity

abstract:
  In this paper, we consider a $L^\infty$ functional derivative estimate for
the first spatial derivative of bounded classical solutions $u:\mathbb{R}\times
[0,T]\to\mathbb{R}$ to the Cauchy problem for scalar semi-linear parabolic
partial differential equations with a continuous nonlinearity
$f:\mathbb{R}\to\mathbb{R}$ and initial data $u_0:\mathbb{R}\to\mathbb{R}$, of
the form, \[ \sup_{x\in\mathbb{R}}|u_x (x , t)| \leq \mathcal{F}_t (f,u_0,u) \
\ \ \forall t\in [0,T] . \] Here $\mathcal{F}_t:\mathcal{A}_t\to\mathbb{R}$ is
a functional as defined in \textsection 1. We establish that the functional
derivative estimate is non-trivially sharp, by constructing a sequence
$(f_n,0,u^{(n)})$, where for each $n\in\mathbb{N}$, $u^{(n)}:\mathbb{R}\times
[0,T]\to\mathbb{R}$ is a solution to the Cauchy problem with zero initial data
and nonlinearity $f_n:\mathbb{R}\to\mathbb{R}$, and for which
$\sup_{x\in\mathbb{R}} |u_x^{(n)}(x,T)| \geq \alpha >0$, with \[
\lim_{n\to\infty} \left( \inf_{t\in [0,T]} \left(
\sup_{x\in\mathbb{R}}|u_x^{(n)}(\cdot , t)| - \mathcal{F}_t (f_n , 0 , u^{(n)})
\right) \right) = 0 . \]


title:
Analytical comparison of the first- and second-order resonances for
  implementation of the dynamical Casimir effect in nonstationary circuit QED

abstract:
  We investigate analytically and numerically the nonstationary circuit QED
setup in which $N$ independent qubits interact with a single mode of the
Electromagnetic field confined in a resonator. We consider the harmonic time
modulation of some parameter (atomic transition frequency or the atom-field
coupling strength) and derive the unitary dynamics up to the second order in
the modulation depth for $N=1$ and $N\gg 1$. It is shown that all the resonant
phenomena that occur for modulation frequencies $\sim 2\omega _{0}$ (where
$\omega _{0}$ is the cavity frequency) also occur for the halved frequencies.
However, in the latter case the associated transition rates are significantly
smaller and the modulation of the coupling strength is less effective. The
transition rates are evaluated explicitly and the prospects of employing the
second-order resonances in the phenomena related to the dynamical Casimir
effect are examined.


title:
Finite difference schemes for multi-term time-fractional mixed
  diffusion-wave equations

abstract:
  The multi-term time-fractional mixed diffusion-wave equations (TFMDWEs) are
considered and the numerical method with its error analysis is presented in
this paper. First, a $L2$ approximation is proved with first order accuracy to
the Caputo fractional derivative of order $\beta \in (1,2).$ Then the
approximation is applied to solve a one-dimensional TFMDWE and an implicit,
compact difference scheme is constructed. Next, a rigorous error analysis of
the proposed scheme is carried out by employing the energy method, and it is
proved to be convergent with first order accuracy in time and fourth order in
space, respectively. In addition, some results for the distributed order and
two-dimensional extensions are also reported in this work. Subsequently, a
practical fast solver with linearithmic complexity is provided with partial
diagonalization technique. Finally, several numerical examples are given to
demonstrate the accuracy and efficiency of proposed schemes.


title: Revenue Gaps for Static and Dynamic Posted Pricing of Homogeneous Goods

abstract:
  We consider the problem of maximizing the expected revenue from selling $k$
homogeneous goods to $n$ unit-demand buyers who arrive sequentially with
independent and identically distributed valuations. In this setting the optimal
posted prices are dynamic in the sense that they depend on the remaining
numbers of goods and buyers. We investigate how much revenue is lost when a
single static price is used instead for all buyers and goods, and prove upper
bounds on the ratio between the maximum revenue from dynamic prices and that
from static prices. These bounds are tight for all values of $k$ and $n$ and
vary depending on a regularity property of the underlying distribution. For
general distributions we obtain a ratio of $2-k/n$, for regular distributions a
ratio that increases in $n$ and is bounded from above by $1/(1-k^k/(e^{k}k!))$,
which is roughly $1/(1-1/(\sqrt{2\pi k}))$. The lower bounds hold for the
revenue gap between dynamic and static prices. The upper bounds are obtained
via an ex-ante relaxation of the revenue maximization problem, as a consequence
the tight bounds of $2-k/n$ in the general case and of $1/(1-1/(\sqrt{2\pi
k}))$ in the regular case apply also to the potentially larger revenue gap
between the optimal incentive-compatible mechanism and the optimal static
price. Our results imply that for regular distributions the benefit of dynamic
prices vanishes while for non-regular distributions dynamic prices may achieve
up to twice the revenue of static prices.


title: Transverse momentum correlations of quarks in recursive jet models

abstract:
  In the symmetric string fragmentation recipe adopted by PYTHIA for jet
simulations, the transverse momenta of successive quarks are uncorrelated. This
is a simplification but has no theoretical reason. Transverse momentum
correlations are naturally expected, for instance, in a covariant
multiperipheral model of quark hadronization. We propose a simple recipe of
string fragmentation which lead to such correlations. The definition of the jet
axis and its relation with the primordial transverse momentum of the quark is
also discussed.


title:
Reconstructing the Universe Evolution from Loop Quantum Cosmology Scalar
  Fields

abstract:
  We extend the scalar-tensor reconstruction techniques for classical cosmology
frameworks, in the context of loop quantum cosmology. After presenting in some
detail how the equations are generalized in the loop quantum cosmology case, we
discuss which new features and limitations does the quantum framework brings
along, and we use various illustrative examples in order to demonstrate how the
method works. As we show the energy density has two different classes of
solutions, and one of these yields the correct classical limit while the second
captures the quantum phenomena. We study in detail the scalar tensor
reconstruction method for both these solutions. Also we discuss some scenarios
for which the Hubble rate becomes unbounded at finite time, which corresponds
for example in a case that a Big Rip occurs. As we show this issue is
non-trivial and we discuss how this case should be treated in a consistent way.
Finally, we investigate how the classical stability conditions for the
scalar-tensor solutions are generalized in the loop quantum framework.


title: Model-Independent Price Bounds for Catastrophic Mortality Bonds

abstract:
  In this paper, we are concerned with the valuation of Catastrophic Mortality
Bonds and, in particular, we examine the case of the Swiss Re Mortality Bond
2003 as a primary example of this class of assets. This bond was the first
Catastrophic Mortality Bond to be launched in the market and encapsulates the
behaviour of a well-defined mortality index to generate payoffs for
bondholders. Pricing these type of bonds is a challenging task and no closed
form solution exists in the literature. In our approach, we express the payoff
of such a bond in terms of the payoff of an Asian put option and present a new
approach to derive model-independent bounds exploiting comonotonic theory as
illustrated in \cite{prime1}, \cite{2} and \cite{Simon} for the pricing of
Asian options. We carry out Monte Carlo simulations to estimate the bond price
and illustrate the quality of the bounds.


title: Uniqueness of the approximative trace

abstract:
  We study the approximative trace for individual elements in the Sobolev space
$W^{1,p}(\Omega)$ for $1\le p\le\infty$. This notion of a trace was introduced
for $p=2$ in [AtE11] in the setting of general open sets
$\Omega\subset\mathbb{R}^d$. The approximative trace exhibits a curious
nonuniqueness phenomenon. We provide a detailed analysis of this phenomenon
based on methods of geometric measure theory and are able to give very weak
geometric conditions that are sufficient for the uniqueness of the
approximative trace. In particular, we prove that the approximative trace is
unique on open sets with continuous boundary and on arbitrary connected domains
in $\mathbb{R}^2$. Furthermore, we provide an example which shows that the
uniqueness of the approximative trace depends on $p$. These results answer
several open questions.


title: Deep nets for local manifold learning

abstract:
  The problem of extending a function $f$ defined on a training data
$\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a
tubular neighborhood of this manifold is considered in this paper. For
$\mathbb{X}$ embedded in a high dimensional ambient Euclidean space
$\mathbb{R}^D$, a deep learning algorithm is developed for finding a local
coordinate system for the manifold {\bf without eigen--decomposition}, which
reduces the problem to the classical problem of function approximation on a low
dimensional cube. Deep nets (or multilayered neural networks) are proposed to
accomplish this approximation scheme by using the training data. Our methods do
not involve such optimization techniques as back--propagation, while assuring
optimal (a priori) error bounds on the output in terms of the number of
derivatives of the target function. In addition, these methods are universal,
in that they do not require a prior knowledge of the smoothness of the target
function, but adjust the accuracy of approximation locally and automatically,
depending only upon the local smoothness of the target function. Our ideas are
easily extended to solve both the pre--image problem and the out--of--sample
extension problem, with a priori bounds on the growth of the function thus
extended.


title:
Enhanced collectivity of gamma vibration in neutron-rich Dy isotopes
  with N=108 - 110

abstract:
  Background: The $\gamma$ vibrational mode of excitation is an acknowledged
collective mode in deformed nuclei. The collectivity depends on the details of
the shell structure around the Fermi levels, in particular the presence of the
orbitals that have the enhanced transition matrix elements of the non-axial
quadrupole excitation. Quite recently, a sudden decrease in the excitation
energy of the $\gamma$ vibration was observed at RIKEN RIBF for the
neutron-rich Dy isotopes at $N=106$. Purpose: In the present work, by studying
systematically the microscopic structure of the $\gamma$ vibration in the
neutron-rich Dy isotopes with $N=98-114$, we try to understand the mechanism of
the observed softening. Methods: The low-frequency modes of excitation in the
neutron-rich rare-earth nuclei are described based on nuclear
density-functional theory. We employ the Skyrme energy-density functionals
(EDF) in the Hartree-Fock-Bogoliubov calculation for the ground states and in
the Quasiparticle Random-Phase Approximation (QRPA) for the excitations.
Results: The lowering of the excitation energy around $N=106$ is reproduced
well by employing the SkM* and SLy4 functionals. We find the similar isotopic
dependence of the excitation energy in the neutron-rich Er and Yb isotopes as
well. Conclusions: The microscopic framework of the Skyrme-EDF based QRPA
describes well the isotopic dependence of the energy of the $\gamma$ vibration
in the well-deformed neutron-rich rare-earth nuclei. The strong collectivity at
$N=108-110$ is expected as the Fermi level of neutrons lies just among the
orbitals that play an important role in generating the collectivity around
$N=106$.


title:
A Lefschetz theorem for overconvergent isocrystals with Frobenius
  structure

abstract:
  We show a Lefschetz theorem for irreducible overconvergent $F$-isocrystals on
smooth varieties defined over a finite field. We derive several consequences
from it.


title: Gravity Sector of the SME

abstract:
  In this talk, the gravity sector of the effective field theory description of
local Lorentz violation is discussed, including minimal and nonminimal
curvature couplings. Also, recent experimental and observational analyses
including solar-system ephemeris and short-range gravity tests are reviewed.


title:
The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric
  Surface

abstract:
  Let $\xi$ be a stable Chern character on $\mathbb{P}^1 \times \mathbb{P}^1$,
and let $M(\xi)$ be the moduli space of Gieseker semistable sheaves on
$\mathbb{P}^1 \times \mathbb{P}^1$ with Chern character $\xi$. In this paper,
we provide an approach to computing the effective cone of $M(\xi)$ after
showing that it is a Mori dream space for all $\xi$. We find Brill-Noether
divisors spanning extremal rays of the effective cone using resolutions of the
general elements of $M(\xi)$ which are found using the machinery of exceptional
bundles. We use this approach to provide many examples of extremal rays in
these effective cones. In particular, we completely compute the effective cone
of the first fifteen Hilbert schemes of points on $\mathbb{P}^1 \times
\mathbb{P}^1$.


title:
Thermalization rates in the one dimensional Hubbard model with
  next-to-nearest neighbor hopping

abstract:
  We consider a fermionic Hubbard chain with an additional next-to-nearest
neighbor hopping term. We study the thermalization rates of the quasi-momentum
distribution function within a quantum Boltzmann equation approach. We find
that the thermalization rates are proportional to the square of the
next-to-nearest neighbor hopping: Even weak next-to-nearest neighbor hopping in
addition to nearest neighbor hopping leads to thermalization in a two-particle
scattering quantum Boltzmann equation in one dimension. We also investigate the
temperature dependence of the thermalization rates, which away from half
filling become exponentially small for small temperature of the final
thermalized distribution.


title: Investigation of the $\eta'N$ system using the linear sigma model

abstract:
  In this paper, we investigate the $\eta'N$ system using the three-flavor
linear sigma model including the effect of flavor SU(3) symmetry breaking. The
$\eta'N$ bound state is also found in the case including flavor symmetry
breaking and coupling with the $\eta N$ and $\pi N$ channels. The $\eta'N$
interaction becomes more attractive with the inclusion of flavor symmetry
breaking, which causes mixing between the singlet and octet scalar mesons. The
existence of such a bound state would have some impact on the $\eta'$-nucleus
system, which is of interest from both theoretical and experimental viewpoints.


title: Higher Order and Secondary Hochschild Cohomology

abstract:
  In this note we give a generalization for the higher order Hochschild
cohomology and show that the secondary Hochschild cohomology is a particular
case of this new construction.


title:
Accuracy in Measuring the Neutron Star Mass in Gravitational Wave
  Parameter Estimation for Black Hole-Neutron Star Binaries

abstract:
  Recently, two gravitational wave (GW) signals, named as GW150914 and
GW151226, have been detected by the two LIGO detectors. Although both signals
were identified as originating from merging black hole (BH) binaries, GWs from
systems containing neutron stars (NSs) are also expected to be detected in the
near future by the Advanced detector network. In this work, we assess the
accuracy in measuring the NS mass ($M_{ns}$) for the GWs from BH-NS binaries
adopting the Advanced LIGO sensitivity with a signal-to-noise ratio of 10. By
using the Fisher matrix method, we calculate the measurement errors ($\sigma$)
in $M_{ns}$ assuming the NS mass of $1 \leq M_{ns}/M_{\odot} \leq 2$ and low
mass BHs with the range of $4 \leq M_{bh}/M_{\odot} \leq 10$. We used the
TaylorF2 waveform model where the spins are aligned with the orbital angular
momentum, but here we only consider the BH spins. We find that the fractional
errors ($\sigma/M_{ns} \times 100$) are in the range of $10\% - 50\%$ in our
mass region for a given dimensionless BH spin as $\chi_{bh} = 0$. The errors
tend to increase as the BH spin increases, and this tendency is stronger for
higher NS masses (or higher total masses). In particular, for the highest mass
NSs ($M_{ns}=2~M_{\odot}$), the errors $\sigma$ can be larger than the true
value of $M_{ns}$ if the dimensionless BH spin exceeds $\sim 0.6$.


title:
Multiparty Quantum Private Comparsion with Individually Dishonest Third
  Parties for Strangers

abstract:
  This study explores a new security problem existing in various
state-of-the-art quantum private comparison (QPC) protocols, where a malicious
third-party (TP) announces fake comparison (or intermediate) results. In this
case, the participants could eventually be led to a wrong direction and the QPC
will become fraudulent. In order to resolve this problem, a new level of
trustworthiness for TP is defined and a new QPC protocol is proposed, where a
second TP is introduced to monitor the first one. Once a TP announces a fake
comparison (or intermediate) result, participants can detect the fraud
immediately. Besides, due to the introduction of the second TP, the proposed
protocol allows strangers to compare their secrets privately, whereas the
state-of-the-art QPCs require the involved clients to know each other before
running the protocol.


title:
Energy distribution and local fluctuations in strongly coupled open
  quantum systems: The extended resonant level model

abstract:
  We study the energy distribution in the extended resonant level model at
equilibrium. Previous investigations [Phys. Rev. B {\bf 89}, 161306 (2014),
Phys. Rev. B {\bf 93}, 115318 (2016)] have found, for a resonant electronic
level interacting with a thermal free electron wide-band bath, that the
expectation value for the energy of the interacting subsystem can be correctly
calculated by considering a symmetric splitting of the interaction Hamiltonian
between the subsystem and the bath. However, the general implications of this
approach were questioned [Phys. Rev. B {\bf 92}, 235440 (2015)]. Here we show
that already at equilibrium, such splitting fails to describe the energy
fluctuations, as measured here by the second and third central moments (namely
width and skewness) of the energy distribution. Furthermore, we find that when
the wide-band approximation does not hold, no splitting of the system-bath
interaction can describe the system thermodynamics. We conclude that in general
no proper division subsystem of the Hamiltonian of the composite system can
account for the energy distribution of the subsystem. This also implies that
the thermodynamic effects due to local changes in the subsystem cannot in
general be described by such splitting.


title:
The Impact of Learning Assistants on Inequities in Physics Student
  Outcomes

abstract:
  This study investigates how Learning Assistants (LAs) and related course
features are associated with inequities in student learning in introductory
university physics courses. 2,868 physics students' paired pre- and post-test
scores on concept inventories from 67 classes in 16 LA Alliance member
institutions are examined in this investigation. The concept inventories
included the Force Concept Inventory, Force and Motion Conceptual Evaluation,
and the Conceptual Survey of Electricity and Magnetism. Our analyses include a
multiple linear regression model that examines the impact of student (e.g.
gender and race) and course level variables (e.g. presence of LAs and Concept
Inventory used) on student learning outcomes (Cohen's d effect size) across
classroom contexts. The presence of LAs was found to either remove or invert
the traditional learning gaps between students from dominant and non-dominant
populations. Significant differences in student performance were also found
across the concept inventories.


title: Canceling effects in higher-order Hardy-Sobolev inequalities

abstract:
  A classical first-order Hardy-Sobolev inequality in Euclidean domains,
involving weighted norms depending on powers of the distance function from
their boundary, is known to hold for every, but one, value of the power. We
show that, by contrast, the missing power is admissible in a suitable
counterpart for higher-order Sobolev norms. Our result complements and extends
contributions by Castro and Wang [CW], and Castro, D\'avila and Wang [CDW1,
CDW2], where a surprising canceling phenomenon underling the relevant
inequalities was discovered in the special case of functions with derivatives
in $L^1$.


title:
Study of Excited $\Xi_c$ States Decaying into $\Xi_c^0$ and $\Xi_c^+$
  Baryons

abstract:
  Using a data sample of 980 ${\rm fb}^{-1}$ of $e^+e^-$ annihilation data
taken with the Belle detector operating at the KEKB asymmetric-energy $e^+e^-$
collider, we report the results of a study of excited $\Xi_c$ states that
decay, via the emission of photons and/or charged pions, into $\Xi_c^0$ or
$\Xi_c^+$ ground state charmed-strange baryons. We present new measurements of
the masses of all members of the $\Xi_c^{\prime}$, $\Xi_c(2645)$,
$\Xi_c(2790)$, $\Xi_c(2815)$, and $\Xi_c(2980)$ isodoublets, measurements of
the intrinsic widths of those that decay strongly, and evidence of previously
unknown transitions.


title: Observability transition in real networks

abstract:
  We consider the observability model in networks with arbitrary topologies. We
introduce a system of coupled nonlinear equations, valid under the locally
tree-like ansatz, to describe the size of the largest observable cluster as a
function of the fraction of directly observable nodes present in the network.
We perform a systematic analysis on 95 real-world graphs and compare our
theoretical predictions with numerical simulations of the observability model.
Our method provides almost perfect predictions in the majority of the cases,
even for networks with very large values of the clustering coefficient.
Potential applications of our theory include the development of efficient and
scalable algorithms for real-time surveillance of social networks, and
monitoring of technological networks.


title:
No Signatures of Black-Hole Spin in the X-ray Spectrum of the Seyfert 1
  Galaxy Fairall 9

abstract:
  Fairall 9 is one of several type 1 active galactic nuclei for which it has
been claimed that the angular momentum (or spin) of the supermassive black hole
can be robustly measured, using the Fe K$\alpha$ emission line and
Compton-reflection continuum in the X-ray spectrum. The method rests upon the
interpretation of the Fe K$\alpha$ line profile and associated
Compton-reflection continuum in terms of relativistic broadening in the strong
gravity regime in the innermost regions of an accretion disc, within a few
gravitational radii of the black hole. Here, we re-examine a Suzaku X-ray
spectrum of Fairall 9 and show that a face-on toroidal X-ray reprocessor model
involving only nonrelativistic and mundane physics provides an excellent fit to
the data. The Fe K$\alpha$ line emission and Compton reflection continuum are
calculated self-consistently, the iron abundance is solar, and an equatorial
column density of $\sim 10^{24} \ \rm cm^{-2}$ is inferred. In this scenario,
neither the Fe K$\alpha$ line, nor the Compton-reflection continuum provide any
information on the black-hole spin. Whereas previous analyses have assumed an
infinite column density for the distant-matter reprocessor, the shape of the
reflection spectrum from matter with a finite column density eliminates the
need for a relativistically broadened Fe K$\alpha$ line. We find a 90 per cent
confidence range in the Fe K$\alpha$ line FWHM of $1895$-$6205 \ \rm km \
s^{-1}$, corresponding to a distance of $\sim 3100$ to $33,380$ gravitational
radii from the black hole, or $0.015$-$0.49$ pc for a black-hole mass of $\sim
1-3 \times 10^{8} \ M_{\odot}$.


title: Reflection Positive Doubles

abstract:
  Here we introduce reflection positive doubles, a general framework for
reflection positivity, covering a wide variety of systems in statistical
physics and quantum field theory. These systems may be bosonic, fermionic, or
parafermionic in nature. Within the framework of reflection positive doubles,
we give necessary and sufficient conditions for reflection positivity. We use a
reflection-invariant cone to implement our construction. Our characterization
allows for a direct interpretation in terms of coupling constants, making it
easy to check in concrete situations. We illustrate our methods with numerous
examples.

categories: math-ph hep-th math.FA math.MP math.OA quant-ph


title: Homological mirror symmetry for local Calabi-Yau manifolds via SYZ

abstract:
  This is a write-up of the author's talk in the conference "Algebraic Geometry
in East Asia 2016" held at the University of Tokyo in January 2016. We give a
survey on a series of papers of the author and his collaborators Daniel
Pomerleano and Kazushi Ueda where we show how Strominger-Yau-Zaslow (SYZ)
transforms can be applied to understand the geometry of Kontsevich's
homological mirror symmetry (HMS) conjecture for certain local Calabi-Yau
manifolds.


title:
Computing the unique CANDECOMP/PARAFAC decomposition of unbalanced
  tensors by homotopy method

abstract:
  The Candecomp/Parafac (CP) decomposition of the tensor whose maximal
dimension is greater than its rank is considered. We derive the upper bound of
rank under which the generic uniqueness of CP decomposition is guaranteed. The
bound only depends on the dimension of the tensor and the proof is
constructive. Under these conditions, an algorithm applying homotopy
continuation method is developed for computing the CP decomposition of tensors.


title:
Exploiting Symmetry and/or Manhattan Properties for 3D Object Structure
  Estimation from Single and Multiple Images

abstract:
  Many man-made objects have intrinsic symmetries and Manhattan structure. By
assuming an orthographic projection model, this paper addresses the estimation
of 3D structures and camera projection using symmetry and/or Manhattan
structure cues, which occur when the input is single- or multiple-image from
the same category, e.g., multiple different cars. Specifically, analysis on the
single image case implies that Manhattan alone is sufficient to recover the
camera projection, and then the 3D structure can be reconstructed uniquely
exploiting symmetry. However, Manhattan structure can be difficult to observe
from a single image due to occlusion. To this end, we extend to the
multiple-image case which can also exploit symmetry but does not require
Manhattan axes. We propose a novel rigid structure from motion method,
exploiting symmetry and using multiple images from the same category as input.
Experimental results on the Pascal3D+ dataset show that our method
significantly outperforms baseline methods.


title:
A No-Go Theorem for Derandomized Parallel Repetition: Beyond
  Feige-Kilian

abstract:
  In this work we show a barrier towards proving a randomness-efficient
parallel repetition, a promising avenue for achieving many tight
inapproximability results. Feige and Kilian (STOC'95) proved an impossibility
result for randomness-efficient parallel repetition for two prover games with
small degree, i.e., when each prover has only few possibilities for the
question of the other prover. In recent years, there have been indications that
randomness-efficient parallel repetition (also called derandomized parallel
repetition) might be possible for games with large degree, circumventing the
impossibility result of Feige and Kilian. In particular, Dinur and Meir
(CCC'11) construct games with large degree whose repetition can be derandomized
using a theorem of Impagliazzo, Kabanets and Wigderson (SICOMP'12). However,
obtaining derandomized parallel repetition theorems that would yield optimal
inapproximability results has remained elusive.
  This paper presents an explanation for the current impasse in progress, by
proving a limitation on derandomized parallel repetition. We formalize two
properties which we call "fortification-friendliness" and "yields robust
embeddings." We show that any proof of derandomized parallel repetition
achieving almost-linear blow-up cannot both (a) be fortification-friendly and
(b) yield robust embeddings. Unlike Feige and Kilian, we do not require the
small degree assumption.
  Given that virtually all existing proofs of parallel repetition, including
the derandomized parallel repetition result of Dinur and Meir, share these two
properties, our no-go theorem highlights a major barrier to achieving
almost-linear derandomized parallel repetition.


title:
Stimulated emission of Cooper pairs in a high-temperature cuprate
  superconductor

abstract:
  The concept of stimulated emission of bosons has played an important role in
modern science and technology, and constitutes the working principle for
lasers. In a stimulated emission process, an incoming photon enhances the
probability that an excited atomic state will transition to a lower energy
state and generate a second photon of the same energy. It is expected, but not
experimentally shown, that stimulated emission contributes significantly to the
zero resistance current in a superconductor by enhancing the probability that
scattered Cooper pairs will return to the macroscopically occupied condensate
instead of entering any other state. Here, we use time- and angle-resolved
photoemission spectroscopy to study the initial rise of the non-equilibrium
quasiparticle population in a Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ cuprate
superconductor induced by an ultrashort laser pulse. Our finding reveals
significantly slower buildup of quasiparticles in the superconducting state
than in the normal state. The slower buildup only occurs when the pump pulse is
too weak to deplete the superconducting condensate, and for cuts inside the
Fermi arc region. We propose this is a manifestation of stimulated
recombination of broken Cooper pairs, and signals an important momentum space
dichotomy in the formation of Cooper pairs inside and outside the Fermi arc
region.


title: The 2-Ranking Numbers of Graphs

abstract:
  In a graph whose vertices are assigned integer ranks, a path is well-ranked
if the endpoints have distinct ranks or some interior point has a higher rank
than the endpoints. A ranking is an assignment of ranks such that all
nontrivial paths are well-ranked. A $k$-ranking is a relaxation in which all
nontrivial paths of length at most $k$ are well-ranked. The $k$-ranking number
of a graph $G$ is the minimum $t$ such that there is a $k$-ranking of $G$ using
ranks in $\{1,\ldots,t\}$.
  We prove that the $2$-ranking number of the $n$-dimensional hypercube $Q_n$
is $n+1$. As a corollary, we improve the bounds on the star chromatic number of
products of cycles when each cycle has length divisible by $4$. For $m\le n$,
we show that the $2$-ranking number of $K_m \mathop\square K_n$ is
$\Omega(n\log m)$ and $O(nm^{\log_2(3)-1})$ with an asymptotic result when $m$
is constant and an exact result when $m!$ divides $n$. We prove that every
subcubic graph has $2$-ranking number at most $7$, and we also prove the
existence of a graph with maximum degree $k$ and $2$-ranking number
$\Omega(k^2/\log(k))$.


title: Uniqueness of static photon surfaces: Perturbative approach

abstract:
  A photon surface $S$ is defined as a three-dimensional timelike hypersurface
such that any null geodesic initially tangent to $S$ continues to be included
in $S$, like $r=3M$ of the Schwarzschild spacetime. Using analytic solutions to
static perturbations of a Schwarzschild spacetime, we examine whether a
nonspherical spacetime can possess a distorted static photon surface. It is
shown that if the region outside of $r=3M$ is vacuum, no distorted photon
surface can be present. Therefore, we establish the perturbative uniqueness for
an asymptotically flat vacuum spacetime with a static photon surface. It is
also pointed out that if matter is present in the outside region, there is a
possibility that a distorted photon surface could form.


title:
Improved critical eigenfunction restriction estimates on Riemannian
  manifolds with constant negative curvature

abstract:
  We show that one can obtain logarithmic improvements of $L^2$ geodesic
restriction estimates for eigenfunctions on 3-dimensional compact Riemannian
manifolds with constant negative curvature. We obtain a
$(\log\lambda)^{-\frac12}$ gain for the $L^2$-restriction bounds, which
improves the corresponding bounds of Burq, G\'erard and Tzvetkov, Hu, Chen and
Sogge. We achieve this by adapting the approaches developed by Chen and Sogge,
Blair and Sogge, Xi and the author. We derive an explicit formula for the wave
kernel on 3D hyperbolic space, which improves the kernel estimates from the
Hadamard parametrix in Chen and Sogge. We prove detailed oscillatory integral
estimates with fold singularities by Phong and Stein and use the Poincar\'e
half-space model to establish bounds for various derivatives of the distance
function restricted to geodesic segments on the universal cover $\mathbb{H}^3$.


title: Metric spaces with complexity of the smallest infinite ordinal number

abstract:
  In this paper, we are concerned with the study on metric spaces with
complexity of the smallest infinite ordinal number. We give equivalent
formulations of the definition of metric spaces with complexity of the smallest
infinite ordinal number and prove that the exact complexity of the finite
product of wreath product is the smallest infinite ordinal number.
Consequently, we obtain the complexity of (ZwrZ)wrZ is w+1.


title:
Standing waves for the Chern-Simons-Schrodinger equation with critical
  exponential growth

abstract:
  In this paper, by combing the variational methods and Trudinger-Moser
inequality, we study the existence and multiplicity of the positive standing
wave for the following Chern-Simons-Schr\"odinger equation \begin{equation}
-\Delta u+u
+\lambda\left(\int_{0}^{\infty}\frac{h(s)}{s}u^{2}(s)ds+\frac{h^{2}(\vert
x\vert)}{\vert x\vert^{2}}\right)u=f(x,u)+\epsilon k(x)\quad\quad
\text{in}\,\,\mathbb{R}^2, \\ \end{equation} where
$h(s)=\int_{0}^{s}\frac{l}{2}u^{2}(l)dl$, $\lambda>0$ and the nonlinearity
$f:\mathbb{R}^2\times \mathbb{R}\rightarrow \mathbb{R}$ behaves like
$\text{exp}(\alpha\vert u\vert^{2})$ as $\vert u\vert\rightarrow \infty$. For
the case $\epsilon=0$, we can get a mountain-pass type solution.


title: Some cosmological solutions in Einstein-Chern-Simons gravity

abstract:
  In this paper we find new solutions for the so called Einstein-Chern-Simons
Friedmann-Robertson-Walker field equations studied in refs. (Phys. Rev. D 84
(2011) 063506, Eur. Phys. J. C 74 (2014) 3087). We consider three cases:(i) in
the first case we find some solutions of the five-dimensional ChS-FRW field
equations when the $h^a$ field is a perfect fluid that obeys a barotropic
equation of state; (ii) in the second case we study the solutions, for the
cases $\gamma =1/2,\ 3/4$, when the $h^a$ field is a five dimensional
politropic fluid that obeys the equation $P^{(h)}=\omega ^{(h)}\rho ^{(h)\gamma
}$; (iii) in the third case we find the scale factor and the state parameter
$\omega (t)$ when the $h^a$ field is a variable modified Chaplygin gas.
  We consider also a space-time metric which contains as a subspace to the
usual four-dimensional FRW and then we study the same three cases considered in
the five-dimensional, namely when (i) the $h^a$ field is a perfect fluid, (ii)
the $h^a$ field is a five dimensional politropic fluid and (iii) the $h^a$
field is a variable modified Chaplygin gas.


title:
The tunneling radiation of a black hole with a $f(R)$ global monopole
  under generalized uncertainty principle

abstract:
  The Parikh-Kraus-Wilczeck tunneling radiation of black hole involving a
$f(R)$ global monopole is considered based on the generalized uncertainty
principle. The influences from global monopole, $f(R)$ gravity and the
corrections to the uncertainty appear in the expression of black hole entropy
difference. It is found that the global monopole and the revision of general
relativity both hinder the black hole from emitting the photons. The two parts
as corrections to the uncertainty make the entropy difference of this kind of
black hole larger or smaller respectively.


title:
Emergence of Sparsely Synchronized Rhythms and Their Responses to
  External Stimuli in An Inhomogeneous Small-World Complex Neuronal Network

abstract:
  We consider an inhomogeneous small-world network (SWN) composed of inhibitory
short-range (SR) and long-range (LR) interneurons. By varying the fraction of
LR interneurons $p_{long}$, we investigate the effect of network architecture
on emergence of sparsely synchronized rhythms, and make comparison with that in
the Watts-Strogatz SWN. Although SR and LR interneurons have the same average
in- and out-degrees, their betweenness centralities (characterizing the
potentiality in controlling communication between other interneurons) are
distinctly different. Hence, in view of the betweenness, SWNs we consider are
inhomogeneous, unlike the "canonical" Watts-Strogatz SWN with nearly same
betweenness centralities. As $p_{long}$ is increased, the average path length
becomes shorter, and the load of communication traffic is less concentrated on
LR interneurons, which leads to better efficiency of global communication
between interneurons. Eventually, when passing a critical value
$p_{long}^{(c)}$ $(\simeq 0.16)$, sparsely synchronized rhythms are found to
emerge. We also consider two cases of external time-periodic stimuli applied to
sub-groups of LR and SR interneurons, respectively. Dynamical responses (such
as synchronization suppression and enhancement) to these two cases of stimuli
are studied and discussed in relation to the betweenness centralities of
stimulated interneurons, representing the effectiveness for transfer of
stimulation effect in the whole network.


title: Impact of Baryonic Physics on Intrinsic Alignments

abstract:
  We explore the effects of specific assumptions in the subgrid models of star
formation and stellar and AGN feedback on intrinsic alignments of galaxies in
cosmological simulations of "MassiveBlack-II" family. Using smaller volume
simulations, we explored the parameter space of the subgrid star formation and
feedback model and found remarkable robustness of the observable statistical
measures to the details of subgrid physics. The one observational probe most
sensitive to modeling details is the distribution of misalignment angles. We
hypothesize that the amount of angular momentum carried away by the galactic
wind is the primary physical quantity that controls the orientation of the
stellar distribution. Our results are also consistent with a similar study by
the EAGLE simulation team.


title: A unified treatment for Lp Brunn-Minkowski type inequalities

abstract:
  A unified approach used to generalize classical Brunn-Minkowski type
inequalities to Lp Brunn-Minkowski type inequalities, called the Lp
transference principle, is refined in this paper. As illustrations of the
effectiveness and practicability of this method, several new Lp Brunn-Minkowski
type inequalities concerning the mixed volume, moment of inertia,
quermassintegral, projection body and capacity are established.


title:
Observation of an anisotropic Dirac cone reshaping and ferrimagnetic
  spin polarization in an organic conductor

abstract:
  The Coulomb interaction among massless Dirac fermions in graphene is
unscreened around the isotropic Dirac points, causing a logarithmic velocity
renormalization and a cone reshaping. In less symmetric Dirac materials
possessing anisotropic cones with tilted axes, the Coulomb interaction can
provide still more exotic phenomena which have not been experimentally unveiled
yet. Here, using site-selective nuclear magnetic resonance, we find a
non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent
ferrimagnetism in tilted Dirac cones that appear on the verge of charge
ordering in an organic compound. Our theoretical analyses based on the
renormalization-group approach and the Hubbard model show that these
observations are the direct consequences of the long-range and short-range
parts of the Coulomb interaction, respectively. The cone reshaping and the
bandwidth renormalization, as well as the novel magnetism revealed here, can be
ubiquitous and vital for many Dirac materials.


title: Boundaries, spectral triples and K-homology

abstract:
  This paper extends the notion of a spectral triple to a relative spectral
triple, an unbounded analogue of a relative Fredholm module for an ideal
$J\triangleleft A$. Examples include manifolds with boundary, manifolds with
conical singularities, dimension drop algebras, $\theta$-deformations and
Cuntz-Pimsner algebras of vector bundles.
  The bounded transform of a relative spectral triple is a relative Fredholm
module, making the image of a relative spectral triple under the boundary
mapping in $K$-homology easy to compute. We introduce an additional operator
called a Clifford normal with which a relative spectral triple can be doubled
into a spectral triple.
  The Clifford normal also provides a boundary Hilbert space, a representation
of the quotient algebra, a boundary Dirac operator and an analogue of the
Calderon projection. In the examples this data does assemble to give a boundary
spectral triple, though we can not prove this in general.
  When we do obtain a boundary spectral triple, we provide sufficient
conditions for the boundary triple to represent the $K$-homological boundary.
Thus we abstract the proof of Baum-Douglas-Taylor's "boundary of Dirac is Dirac
on the boundary" theorem into the realm of non-commutative geometry.


title: A Study of Projections of 2-Bouquet Graphs

abstract:
  We extend the concepts of trivializing and knotting numbers for knots to
spatial graphs and 2-bouquet graphs, in particular. Furthermore, we calculate
the trivializing and knotting numbers for projections and pseudodiagrams of
2-bouquet spatial graphs based on the number of precrossings and the placement
of the precrossings in the pseudodiagram of the spatial graph.


title:
Broken rotational symmetry on the Fermi surface of a high-T$_\mathrm{c}$
  superconductor

abstract:
  Broken fourfold rotational (C$_4$) symmetry is observed in the experimental
properties of several classes of unconventional superconductors. It has been
proposed that this symmetry breaking is important for superconducting pairing
in these materials, but in the high superconducting transition temperature
(high-T$_{\mathrm{c}}$) cuprates this broken symmetry has never been observed
on the Fermi surface. We have measured a pronounced anisotropy in the angle
dependence of the interlayer magnetoresistance of the underdoped
high-T$_{\mathrm{c}}$) superconductor YBa$_2$Cu$_3$O$_{6.58}$, directly
revealing broken C$_4$ symmetry on the Fermi surface. Moreover, we demonstrate
that this Fermi surface has C$_2$ symmetry of the type produced by a uniaxial
or anisotropic density-wave phase. This establishes the central role of C$_4$
symmetry breaking in the Fermi surface reconstruction of
YBa$_2$Cu$_3$O$_{6+\delta}$, and suggests a striking degree of universality
among unconventional superconductors.


title:
Multi-resonant piezoelectric shunting induced by digital controllers for
  subwavelength elastic wave attenuation in smart metamaterial

abstract:
  Instead of analog electronic circuits and components, digital controllers
that are capable of active multi-resonant piezoelectric shunting are applied to
elastic metamaterials integrated with piezoelectric patches. Giving thanks to
the introduced digital control technique, shunting strategies with transfer
functions that can hardly be realized with analog circuits is possible now. As
an example, the "pole-zero" method is developed to design single- or
multi-resonant bandgaps by adjusting poles and zeros in the transfer function
of piezoelectric shunting directly. Large simultaneous attenuations in up to
three frequency bands at deep subwavelength scale (with the normalized
frequency as low as 0.077) are achieved. The underlying physical mechanism is
attributed to the negative group velocity of flexural wave within bandgaps. As
digital controllers can be readily adapted via wireless broadcasting, the
bandgaps can be tuned easily instead of tuning the electric components in
analog shunting circuits one by one manually. The theoretical results are well
verified experimentally with the measured vibration transmission properties
where large insulations of up to 20dB in low-frequency ranges are observed.


title: Aspects of infinite dimensional $\ell$-super Galilean conformal algebra

abstract:
  In this work we construct a infinite dimensional $\ell$-super Galilean
conformal algebra, which is a generalization of the $\ell=1$ algebra found in
the literature. We give a classification of central extensions, the vector
field representation, the coadjoint representation and the operator product
expansion of the infinite dimensional $\ell$-super Galilean conformal algebra,
keeping possible applications in physics and mathematics in mind.


title:
Effects of entrance channel on fusion probability in hot fusion
  reactions

abstract:
  Within the framework of the dinuclear system (DNS) model, the fusion
reactions leading to the compound nuclei 274Hs and 286Cn are investigated. The
fusion probability as a function of DNS excitation energy is studied. The
calculated results are in good agreement with the available experimental data.
The obtained results show that the fusion probabilities are obviously enhanced
for the reactions located at high place in potential energy surface, although
these reactions may have small values of mass asymmetry. It is found that the
enhancement is due to the large potential energy of the initial DNS.


title: Efficient quantum circuits for dense and non-unitary operators

abstract:
  Circulant matrices are an important family of operators, which have a wide
range of applications in science and engineering related fields. They are in
general non-sparse and non-unitary. In this paper, we present efficient quantum
circuits to implement circulant operators using fewer resources and with lower
complexity than existing methods. Moreover, our quantum circuits can be readily
extended to the implementation of Toeplitz, Hankel, and block circulant
matrices. Efficient quantum algorithms to implement the inverses and products
of circulant operators are also provided.


title: Generalized Controlled Quantum Secure Communication using GHZ-like state

abstract:
  We present a novel scheme for controlled quantum secure communication (CQSC)
using GHZ-like state. In this scheme, a trusted controller assists the users
for achieving secure transmission of data between them. The dense coding
technique is exploited to increase the qubit efficiency and we show that the
proposed scheme is immune against common eavesdropping attacks. We show how the
method can be generalized to include N controllers using sets of GHZ-like
states shared among the controllers and users. In this process entanglement
swapping and single particle measurements are performed by the controllers to
relax their controls and the users get entangled in Bell states.


title:
Very Strong Superconducting Proximity Effects in PbS Semiconductor
  Nanowires

abstract:
  We report the fabrication of strongly coupled nanohybrid superconducting
junctions using PbS semiconductor nanowires and Pb0.5In0.5 superconducting
electrodes. The maximum supercurrent in the junction reaches up to ~15 \mu A at
0.3 K, which is the highest value ever observed in semiconductor-nanowire-based
superconducting junctions. The observation of microwave-induced constant
voltage steps confirms the existence of genuine Josephson coupling through the
nanowire. Monotonic suppression of the critical current under an external
magnetic field is also in good agreement with the narrow junction model. The
temperature-dependent stochastic distribution of the switching current exhibits
a crossover from phase diffusion to a thermal activation process as the
temperature decreases. These strongly coupled nanohybrid superconducting
junctions would be advantageous to the development of gate-tunable
superconducting quantum information devices.


title:
Spectrum in the presence of brane-localized mass on torus extra
  dimensions

abstract:
  The lightest mass eigenvalue of a six-dimensional theory compactified on a
torus is numerically evaluated in the presence of the brane-localized mass
term. The dependence on the cutoff scale $\Lambda$ is non-negligible even when
$\Lambda$ is two orders of magnitude above the compactification scale, which
indicates that the mass eigenvalue is sensitive to the size of the brane, in
contrast to five-dimensional theories. We obtain an approximate expression of
the lightest mass in the thin brane limit, which well fits the numerical
calculations, and clarifies its dependence on the torus moduli parameter
$\tau$. We find that the lightest mass is typically much lighter than the
compactification scale by an order of magnitude even in the limit of a large
brane mass.


title: Higher dimensional Schwarz's surfaces and Scherk's surfaces

abstract:
  Higher dimensional generalizations of Schwarz's $P$-surface, Schwarz's
$D$-surface and Scherk's second surface are constructed as complete embedded
periodic minimal hy- persurfaces in $\mathbb R^n$.


title:
An all-optical buffer based on temporal cavity solitons operating at 10
  Gb/s

abstract:
  We demonstrate the operation of an all-optical buffer based on temporal
cavity solitons stored in a nonlinear passive fiber ring resonator. Unwanted
acoustic interactions between neighboring solitons are suppressed by modulating
the phase of the external laser driving the cavity. A new locking scheme is
presented that allows the buffer to operate with an arbitrarily large number of
cavity solitons in the loop. Experimentally, we are able to demonstrate the
storage of 4536 bits of data, written all-optically into the fiber ring at 10
Gb/s, for 1 minute.


title:
A Unified Multi-scale Deep Convolutional Neural Network for Fast Object
  Detection

abstract:
  A unified deep neural network, denoted the multi-scale CNN (MS-CNN), is
proposed for fast multi-scale object detection. The MS-CNN consists of a
proposal sub-network and a detection sub-network. In the proposal sub-network,
detection is performed at multiple output layers, so that receptive fields
match objects of different scales. These complementary scale-specific detectors
are combined to produce a strong multi-scale object detector. The unified
network is learned end-to-end, by optimizing a multi-task loss. Feature
upsampling by deconvolution is also explored, as an alternative to input
upsampling, to reduce the memory and computation costs. State-of-the-art object
detection performance, at up to 15 fps, is reported on datasets, such as KITTI
and Caltech, containing a substantial number of small objects.


title: Low growth equational complexity

abstract:
  The equational complexity function
$\beta_\mathscr{V}:\mathbb{N}\to\mathbb{N}$ of an equational class of algebras
$\mathscr{V}$ bounds the size of equation required to determine membership of
$n$-element algebras in $\mathscr{V}$. Known examples of finitely generated
varieties $\mathscr{V}$ with unbounded equational complexity have growth in
$\Omega(n^c)$, usually for $c\geq \frac{1}{2}$. We show that much slower growth
is possible, exhibiting $O(\log_2^3(n))$ growth amongst varieties of
semilattice ordered inverse semigroups and additive idempotent semirings. We
also examine a quasivariety analogue of equational complexity, and show that a
finite group has polylogarithmic quasi-equational complexity function, bounded
if and only if all Sylow subgroups are abelian.


title: Alexander $r$-tuples and Bier complexes

abstract:
  Alexander $r$-tuples are introduced as a common generalization of pairs of
Alexander dual complexes (Alexander $2$-tuples) and $r$-unavoidable complexes
of Blagojevi\'{c}, Frick and Ziegler. The associated "Bier complexes" include
both the Bier spheres and "optimal multiple chessboard complexes" as
interesting, special cases. Our main result is Theorem 4.3 saying that (1) the
$r$-fold deleted join of Alexander $r$-tuple is a pure complex homotopy
equivalent to a wedge of spheres, and (2) the $r$-fold deleted join of a
collectively unavoidable $r$-tuple is $(n-r-1)$-connected. We also give a
complete classification (Theorem 5.1 and Corollary 5.2) of Alexander $r$-tuples
and Bier complexes.


title: Coherence Disparity in Broadcast and Multiple Access Channels

abstract:
  Individual links in a wireless network may experience unequal fading
coherence times due to differences in mobility or scattering environment, a
practical scenario where the fundamental limits of communication have been
mostly unknown. This paper studies broadcast and multiple access channels where
multiple receivers experience unequal fading block lengths, and channel state
information (CSI) is not available at the transmitter(s), or for free at any
receiver. In other words, the cost of acquiring CSI at the receiver is fully
accounted for in the degrees of freedom. In the broadcast channel, the method
of product superposition is employed to find the achievable degrees of freedom.
We start with unequal coherence intervals with integer ratios. As long as the
coherence time is at least twice the number of transmit and receive antennas,
these degrees of freedom meet the upper bound in four cases: when the
transmitter has fewer antennas than the receivers, when all receivers have the
same number of antennas, when the coherence time of one receiver is much
shorter than all others, or when all receivers have identical block fading
intervals. The degrees of freedom region of the broadcast under identical
coherence times was also previously unknown and is settled by the results of
this paper. The disparity of coherence times leads to gains that are distinct
from those arising from other techniques such as spatial multiplexing or
multi-user diversity; this class of gains is denoted coherence diversity. The
inner bounds are further extended to the case of multiple receivers
experiencing fading block lengths of arbitrary ratio or alignment. Also, in the
multiple access channel with unequal coherence times, achievable and outer
bounds on the degrees of freedom are obtained.


title: Coupling of symmetric operators and the third Green identity

abstract:
  The principal aim of this paper is to derive an abstract form of the third
Green identity associated with a proper extension $T$ of a symmetric operator
$S$ in a Hilbert space $\mathfrak H$, employing the technique of quasi boundary
triples for $T$. The general results are illustrated with couplings of
Schr\"{o}dinger operators on Lipschitz domains on smooth, boundaryless
Riemannian manifolds.


title: Large-Scale Video Search with Efficient Temporal Voting Structure

abstract:
  In this work, we propose a fast content-based video querying system for
large-scale video search. The proposed system is distinguished from similar
works with two major contributions. First contribution is superiority of joint
usage of repeated content representation and efficient hashing mechanisms.
Repeated content representation is utilized with a simple yet robust feature,
which is based on edge energy of frames. Each of the representation is
converted into hash code with Hamming Embedding method for further queries.
Second contribution is novel queue-based voting scheme that leads to modest
memory requirements with gradual memory allocation capability, contrary to
complete brute-force temporal voting schemes. This aspect enables us to make
queries on large video databases conveniently, even on commodity computers with
limited memory capacity. Our results show that the system can respond to video
queries on a large video database with fast query times, high recall rate and
very low memory and disk requirements.


title:
A novel superconducting-velocity--tunable quasiparticle state and spin
  relaxation in GaAs (100) quantum wells in proximity to $s$-wave
  superconductor

abstract:
  We present a novel quasiparticle state driven by a supercurrent in GaAs (100)
quantum wells in proximity to an $s$-wave superconductor, which can be tuned by
the superconducting velocity. Rich features such as the suppressed Cooper
pairings, large quasiparticle density and non-monotonically tunable momentum
current can be realized by varying the superconducting velocity. In the
degenerate regime, the quasiparticle Fermi surface is composed by two arcs,
referred to as Fermi arcs, which are contributed by the electron- and hole-like
branches. The D'yakonov-Perel' spin relaxation is explored, and intriguing
physics is revealed when the Fermi arc emerges. Specifically, when the order
parameter tends to zero, it is found that the branch-mixing scattering is
forbidden in the quasi-electron band. When the condensation process associated
with the annihilation of the quasi-electron and quasi-hole is {\em slow}, this
indicates that the electron- and hole-like Fermi arcs in the quasi-electron
band are independent. The open structure of the Fermi arc leads to the nonzero
angular-average of the effective magnetic field due to the spin-orbit coupling,
which acts as an effective Zeeman field. This Zeeman field leads to the spin
oscillations even in the strong scattering regime. Moreover, in the strong
scattering regime, we show that the open structure of the Fermi arc also leads
to the insensitiveness of the spin relaxation to the momentum scattering, in
contrast to the conventional motional narrowing situation. Nevertheless, with a
{\em finite} order parameter, the branch-mixing scattering can be triggered,
opening the inter-branch spin relaxation channel, which is dominant in the
strong scattering regime. In contrast to the situation with an extremely small
order parameter,....(omitted due to the limit of space)


title:
Remarkable Hydrogen Storage on Beryllium Oxide Clusters: First
  Principles Calculations

abstract:
  Since the current transportation sector is the largest consumer of oil, and
subsequently responsible for major air pollutants, it is inevitable to use
alternative renewable sources of energies for vehicular applications. The
hydrogen energy seems to be a promising candidate. To explore the possibility
of achieving a solid-state high-capacity storage of hydrogen for onboard
applications, we have performed first principles density functional theoretical
calculations of hydrogen storage properties of beryllium oxide clusters
(BeO)$_{n}$ (n=2 -- 8). We observed that polar BeO bond is responsible for
H$_{2}$ adsorption. The problem of cohesion of beryllium atoms does not arise,
as they are an integral part of BeO clusters. The (BeO)$_{n}$ (n=2 -- 8)
adsorbs 8--12 H$_{2}$ molecules with an adsorption energy in the desirable
range of reversible hydrogen storage. The gravimetric density of H$_{2}$
adsorbed on BeO clusters meets the ultimate 7.5 wt% limit, recommended for
onboard practical applications.
  In conclusion, beryllium oxide clusters exhibit a remarkable solid-state
hydrogen storage.


title:
Performance of Lattice Coset Codes on Universal Software Radio
  Peripherals

abstract:
  We consider an experimental setup of three USRPs that implement a wiretap
channel, two USRPs are the legitimate players Alice and Bob, while the third
USRP is the eavesdropper, whose position we vary to evaluate information
leakage. The experimented channels are close to slow fading channels, and coset
coding of lattice constellations is used for transmission, allowing to
introduce controlled randomness at the transmitter. Simulation and measurement
results show to which extent coset coding can provide confidentiality, as a
function of Eve's position, and the amount of randomness used.


title: Normality of different orders for Cantor series expansions

abstract:
  Let $S \subseteq \mathbb{N}$ have the property that for each $k \in S$ the
set $(S - k) \cap \mathbb{N} \setminus S$ has asymptotic density $0$. We prove
that there exists a basic sequence $Q$ where the set of numbers $Q$-normal of
all orders in $S$ but not $Q$-normal of all orders not in $S$ has full
Hausdorff dimension. If the function $k \mapsto 1_S(k)$ is computable, then
there exist computable examples. For example, there exists a computable basic
sequence $Q$ where the set of numbers normal of all even orders and not normal
of all odd orders has full Hausdorff dimension. This is in strong constrast to
the $b$-ary expansions where any real number that is normal of order $k$ must
also be normal of all orders between $1$ and $k-1$.
  Additionally, all numbers we construct satisfy the unusual condition that
block frequencies sampled along non-trivial arithmetic progressions don't
converge to the expected value. This is also in strong contrast to the case of
the $b$-ary expansions, but more similar to the case of the continued fraction
expansion. As a corollary, the set of $Q$-normal numbers that are not normal
when sampled along any non-trivial arithmetic progression has full Hausdorff
dimension.


title:
The totally nonnegative part of the finite Toda lattice via a reducible
  rational curve

abstract:
  A totally nonnegative matrix is a real-valued matrix whose minors are all
nonnegative. In this paper, we concern with the totally nonnegative structure
of the finite Toda lattice, a classical integrable system, which is expressed
as a differential equation of square matrices. The Toda flow naturally
translates into a (multiplicative) linear flow on the (generalized) Jacobi
variety associated with some reducible rational curve $X$. This correspondence
provides an algebro-geometric characterization of the totally positive part of
the Toda equation. We prove that the totally nonnegative part of the finite
Toda lattice is isomorphic to a connected component of
$\mathrm{Jac}(X)_{\mathbb{R}}$, the real part of the generalized Jacobi variety
$\mathrm{Jac}(X)$, as semi-algebraic varieties.


title:
Lyman-alpha radiation hydrodynamics of galactic winds before cosmic
  reionization

abstract:
  The dynamical impact of Lyman-alpha (Ly{\alpha}) radiation pressure on galaxy
formation depends on the rate and duration of momentum transfer between
Ly{\alpha} photons and neutral hydrogen gas. Although photon trapping has the
potential to multiply the effective force, ionizing radiation from stellar
sources may relieve the Ly{\alpha} pressure before appreciably affecting the
kinematics of the host galaxy or efficiently coupling Ly{\alpha} photons to the
outflow. We present self-consistent Ly{\alpha} radiation-hydrodynamics
simulations of high-$z$ galaxy environments by coupling the Cosmic Ly{\alpha}
Transfer code (COLT) with spherically symmetric Lagrangian frame hydrodynamics.
The accurate but computationally expensive Monte-Carlo radiative transfer
calculations are feasible under the one-dimensional approximation. The initial
starburst drives an expanding shell of gas from the centre and in certain cases
Ly{\alpha} feedback significantly enhances the shell velocity. Radiative
feedback alone is capable of ejecting baryons into the intergalactic medium
(IGM) for protogalaxies with a virial mass of $M_{\rm vir} \lesssim 10^8~{\rm
M}_\odot$. We compare the Ly{\alpha} signatures of Population III stars with
$10^5$ K blackbody emission to that of direct collapse black holes with a
nonthermal Compton-thick spectrum and find substantial differences if the
Ly{\alpha} spectra are shaped by gas pushed by Ly{\alpha} radiation-driven
winds. For both sources, the flux emerging from the galaxy is reprocessed by
the IGM such that the observed Ly{\alpha} luminosity is reduced significantly
and the time-averaged velocity offset of the Ly{\alpha} peak is shifted
redward.


title: Decays of $B$, $B_s$ and $B_c$ to $D$-wave heavy-light mesons

abstract:
  We study the weak decays of $\bar{B}_{(s)}$ and $B_c$ into $D$-wave
heavy-light mesons, including $J^P=2^-$ ($D_{(s)2},D'_{(s)2},B_{(s)2},
B'_{(s)2}$) and $3^-$~($D^*_{(s)3}, B^*_{(s)3}$) states. The weak decay
hadronic matrix elements are achieved based on the instantaneous Bethe-Salpeter
method. The branching ratios for $\bar{B}$ decays are $\mathcal{B}[\bar{B}\to
D_{2}e\bar{\nu}_e] = 1.1^{-0.3}_{+0.3} \times 10^{-3}$, $\mathcal{B}[\bar{B}\to
D'_2e\bar{\nu}_e]=4.1^{-0.8}_{+0.9} \times 10^{-4}$, and
$\mathcal{B}[\bar{B}\to D^*_3e\bar{\nu}_e]=1.0^{-0.2}_{+0.2} \times 10^{-3}$,
respectively. For semi-electronic decays of $\bar B_s$ to $D_{s2}$, $D'_{s2}$,
and $D^*_{s3}$, the corresponding branching ratios are $1.7^{-0.5}_{+0.5}\times
10^{-3}$, $5.2^{-1.5}_{+1.6}\times 10^{-4}$, and $1.5^{-0.4}_{+0.4}\times
10^{-3}$, respectively. The branching ratios of semi-electronic decays of $B_c$
to $D$-wave $D$ mesons are in the order of $10^{-5}$. We also achieved the
forward-backward asymmetry, angular spectra, and lepton momentum spectra. In
particular the distribution of decay widths for $2^-$ states $D_2$ and $D'_2$
varying along with mixing angle are presented.


title:
High sensitivity photonic time-stretch electro-optic sampling of
  terahertz pulses

abstract:
  Single-shot recording of terahertz electric signals has recently become
possible at high repetition rates, by using the photonic time-stretch
electro-optic sampling (EOS) technique. However the moderate sensitivity of
time-stretch EOS is still a strong limit for a range of applications. Here we
present a variant enabling to increase the sensitivity of photonic time-stretch
for free-propagating THz signals. A key point is to integrate the idea
presented in Ref. [Ahmed et al., Rev. Sci. Instrum. 85, 013114 (2014)], for
upgrading classical time-stretch systems. The method is tested using the high
repetition rate terahertz coherent synchrotron radiation source (CSR) of the
SOLEIL synchrotron radiation facility. The signal-to-noise ratio of our
terahertz digitizer could thus be straightforwardly improved by a factor
$\approx 6.5$, leading to a noise-equivalent input electric field below
$1.25$~V/cm inside the electro-optic crystal, over the 0-300~GHz band (i.e,
2.3~$\mu$V/cm/$\sqrt{\text{Hz}}$). The sensitivity is scalable with respect to
the available laser power, potentially enabling further sensitivity
improvements when needed.


title: A Topological Representation for Taking Cities as a Coherent Whole

abstract:
  A city is a whole, as are all cities in a country. Within a whole, individual
cities possess different degrees of wholeness, defined by Christopher Alexander
as a life-giving order or simply a living structure. To characterize the
wholeness and in particular to advocate for wholeness as an effective design
principle, this paper develops a geographic representation that views cities as
a whole. This geographic representation is topology-oriented, so fundamentally
differs from existing geometry-based geographic representations. With the
topological representation, all cities are abstracted as individual points and
put into different hierarchical levels, according to their sizes and based on
head/tail breaks - a classification scheme and visualization tool for data with
a heavy tailed distribution. These points of different hierarchical levels are
respectively used to create Thiessen polygons. Based on polygon-polygon
relationships, we set up a complex network. In this network, small polygons
point to adjacent large polygons at the same hierarchical level and contained
polygons point to containing polygons across two consecutive hierarchical
levels. We computed the degrees of wholeness for individual cities, and
subsequently found that the degrees of wholeness possess both properties of
differentiation and adaptation. To demonstrate, we developed four case studies
of all China and UK natural cities, as well as Beijing and London natural
cities, using massive amounts of street nodes and Tweet locations. The
topological representation and the kind of topological analysis in general can
be applied to any design or pattern, such as carpets, Baroque architecture and
artifacts, and fractals in order to assess their beauty, echoing the
introductory quote from Christopher Alexander.
  Keywords: Wholeness, natural cities, head/tail breaks, complex networks,
scaling hierarchy, urban design