title: Review Based Rating Prediction

abstract:
  Recommendation systems are an important units in today's e-commerce
applications, such as targeted advertising, personalized marketing and
information retrieval. In recent years, the importance of contextual
information has motivated generation of personalized recommendations according
to the available contextual information of users.
  Compared to the traditional systems which mainly utilize users' rating
history, review-based recommendation hopefully provide more relevant results to
users. We introduce a review-based recommendation approach that obtains
contextual information by mining user reviews. The proposed approach relate to
features obtained by analyzing textual reviews using methods developed in
Natural Language Processing (NLP) and information retrieval discipline to
compute a utility function over a given item. An item utility is a measure that
shows how much it is preferred according to user's current context.
  In our system, the context inference is modeled as similarity between the
users reviews history and the item reviews history. As an example application,
we used our method to mine contextual data from customers' reviews of movies
and use it to produce review-based rating prediction. The predicted ratings can
generate recommendations that are item-based and should appear at the
recommended items list in the product page. Our evaluations suggest that our
system can help produce better prediction rating scores in comparison to the
standard prediction methods.


title:
Reduction of some homological conjectures to excellent unique
  factorization domains

abstract:
  In this article, applying the quasi-Gorenstein analogous of the Ulrich's
deformation of certain Gorenstein rings we show that some homological
conjectures, including the Monomial Conjecture, Big Cohen-Macaulay Algebra
Conjecture as well as the Small Cohen-Macaulay Conjecture reduce to the
excellent unique factorization domains. Some other reductions of the Monomial
Conjecture are also proved. We, moreover, show that certain almost complete
intersections adhere the Monomial Conjecture.


title:
Two-dimensional light-front $\phi^4$ theory in a symmetric polynomial
  basis

abstract:
  We study the lowest-mass eigenstates of $\phi^4_{1+1}$ theory with both odd
and even numbers of constituents. The calculation is carried out as a
diagonalization of the light-front Hamiltonian in a Fock-space representation.
In each Fock sector a fully symmetric polynomial basis is used to represent the
Fock wave function. Convergence is investigated with respect to the number of
basis polynomials in each sector and with respect to the number of sectors. The
dependence of the spectrum on the coupling strength is used to estimate the
critical coupling for the positive-mass-squared case. An apparent discrepancy
with equal-time calculations of the critical coupling is resolved by an
appropriate mass renormalization.


title: Open clusters and associations in the Gaia era

abstract:
  Open clusters and associations are groups of young stars, respectively bound
and unbound, that share the same origin and disperse over time into the
galactic field. As such, their formation and evolution are the key to
understand the origin and properties of galactic stellar populations. Moreover,
since their members have about the same age, they are ideal laboratories to
study the properties of young stars and constrain stellar evolution theories.
  In this contribution, I present our current knowledge on open clusters and
associations. I focus on the methods used to derive the statistical properties
(IMF, spatial distribution, IMF) of young stars and briefly discuss how they
depend on the environment. I then describe how open clusters can be used as
probes to investigate the structure, dynamics and chemical composition of the
Milky Way. I conclude by presenting the Gaia mission and discuss how it will
revolutionize this field of research.


title: Phase rotation of muon beams for producing intense low-energy muon beams

abstract:
  Low-energy muon beams are useful for rare decay searches, which provide
access to new physics that cannot be addressed at high-energy colliders.
However, muons are produced within a broad energy spread unmatched to the
low-energy required. In this paper we outline a phase rotation method to
significantly increase the intensity of low-energy muons. The muons are
produced from a short pulsed proton driver, and develop a time-momentum
correlation in a drift space following production. A series of rf cavities is
used to bunch the muons and phase-energy rotate the bunches to a momentum of
around 100 MeV/c. Then another group of rf cavities is used to decelerate the
muon bunches to low-energy. This obtains ~0.1 muon per 8 GeV proton, which is
significantly higher than currently planned Mu2e experiments, and would enable
a next generation of rare decay searches, and other intense muon beam
applications.


title:
Well-posedness of semilinear stochastic wave equations with H\"{o}lder
  continuous coefficients

abstract:
  We prove that semilinear stochastic abstract wave equations, including wave
and plate equations, are well-posed in the strong sense with an
$\alpha$-H\"{o}lder continuous drift coefficient, if $\alpha \in (2/3,1)$. The
uniqueness may fail for the corresponding deterministic PDE and well-posedness
is restored by adding an external random forcing of white noise type. This
shows a kind of regularization by noise for the semilinear wave equation. To
prove the result we introduce an approach based on backward stochastic
differential equations. We also establish regularizing properties of the
transition semigroup associated to the stochastic wave equation by using
control theoretic results.


title: HUME: Human UCCA-Based Evaluation of Machine Translation

abstract:
  Human evaluation of machine translation normally uses sentence-level measures
such as relative ranking or adequacy scales. However, these provide no insight
into possible errors, and do not scale well with sentence length. We argue for
a semantics-based evaluation, which captures what meaning components are
retained in the MT output, thus providing a more fine-grained analysis of
translation quality, and enabling the construction and tuning of
semantics-based MT. We present a novel human semantic evaluation measure, Human
UCCA-based MT Evaluation (HUME), building on the UCCA semantic representation
scheme. HUME covers a wider range of semantic phenomena than previous methods
and does not rely on semantic annotation of the potentially garbled MT output.
We experiment with four language pairs, demonstrating HUME's broad
applicability, and report good inter-annotator agreement rates and correlation
with human adequacy scores.


title:
Beyond Lebesgue and Baire IV: Density topologies and a converse
  Steinhaus-Weil Theorem

abstract:
  The theme here is category-measure duality, in the context of a topological
group. One can often handle the (Baire) category case and the (Lebesgue, or
Haar) measure cases together, by working bi-topologically: switching between
the original topology and a suitable refinement (a density topology). This
prompts a systematic study of such density topologies, and the corresponding
$\sigma$-ideals of negligibles. Such ideas go back to Weil's classic book, and
to Hashimoto's ideal topologies. We make use of group norms, which cast light
on the interplay between the group and measure structures. The Steinhaus-Weil
interior-points theorem (`on $AA^{-1}$') plays a crucial role here; so too does
its converse, the Simmons-Mospan theorem.


title:
A Combined View of Sterile-Neutrino Constraints from CMB and Neutrino
  Oscillation Measurements

abstract:
  We perform a comparative analysis of constraints on sterile neutrinos from
the Planck experiment and from current and future neutrino oscillation
experiments (MINOS, IceCube, SBN). For the first time, we express the Planck
constraints on $N_{\rm eff}$ and $m_{\rm eff}^{\rm sterile}$ from the Cosmic
Microwave Background in the parameter space used by oscillation experiments
using both mass-squared differences and mixing angles. In a model with a single
sterile neutrino species and using standard assumptions, we find that the
Planck data and the oscillation experiments measuring muon-neutrino
disappearance have similar sensitivity.


title: Graphical Mahonian Statistics on Words

abstract:
  Foata and Zeilberger defined the graphical major index, $\mathrm{maj}'_U$,
and the graphical inversion index, $\mathrm{inv}'_U$, for words. These
statistics are a generalization of the classical permutation statistics
$\mathrm{maj}$ and $\mathrm{inv}$ indexed by directed graphs $U$. They showed
that $\mathrm{maj}'_U$ and $\mathrm{inv}'_U$ are equidistributed over all
rearrangement classes if and only if $U$ is bipartitional. In this paper we
strengthen their result by showing that if $\mathrm{maj}'_U$ and
$\mathrm{inv}'_U$ are equidistributed on a single rearrangement class then $U$
is essentially bipartitional. Moreover, we define a graphical sorting index,
$\mathrm{sor}'_U$, which generalizes the sorting index of a permutation. We
then characterize the graphs $U$ for which $\mathrm{sor}'_U$ is equidistributed
with $\mathrm{inv}'_U$ and $\mathrm{maj}'_U$ on a single rearrangement class.


title: Ballpark Learning: Estimating Labels from Rough Group Comparisons

abstract:
  We are interested in estimating individual labels given only coarse,
aggregated signal over the data points. In our setting, we receive sets
("bags") of unlabeled instances with constraints on label proportions. We relax
the unrealistic assumption of known label proportions, made in previous work;
instead, we assume only to have upper and lower bounds, and constraints on bag
differences. We motivate the problem, propose an intuitive formulation and
algorithm, and apply our methods to real-world scenarios. Across several
domains, we show how using only proportion constraints and no labeled examples,
we can achieve surprisingly high accuracy. In particular, we demonstrate how to
predict income level using rough stereotypes and how to perform sentiment
analysis using very little information. We also apply our method to guide
exploratory analysis, recovering geographical differences in twitter dialect.


title:
Stock Market Insider Trading in Continuous Time with Imperfect Dynamic
  Information

abstract:
  This paper studies the equilibrium pricing of asset shares in the presence of
dynamic private information. The market consists of a risk-neutral informed
agent who observes the firm value, noise traders, and competitive market makers
who set share prices using the total order flow as a noisy signal of the
insider's information. I provide a characterization of all optimal strategies,
and prove existence of both Markovian and non Markovian equilibria by deriving
closed form solutions for the optimal order process of the informed trader and
the optimal pricing rule of the market maker. The consideration of non
Markovian equilibrium is relevant since the market maker might decide to
re-weight past information after receiving a new signal. Also, I show that a)
there is a unique Markovian equilibrium price process which allows the insider
to trade undetected, and that b) the presence of an insider increases the
market informational efficiency, in particular for times close to dividend
payment.


title: Dynamic Neural Turing Machine with Soft and Hard Addressing Schemes

abstract:
  We extend neural Turing machine (NTM) model into a dynamic neural Turing
machine (D-NTM) by introducing a trainable memory addressing scheme. This
addressing scheme maintains for each memory cell two separate vectors, content
and address vectors. This allows the D-NTM to learn a wide variety of
location-based addressing strategies including both linear and nonlinear ones.
We implement the D-NTM with both continuous, differentiable and discrete,
non-differentiable read/write mechanisms. We investigate the mechanisms and
effects of learning to read and write into a memory through experiments on
Facebook bAbI tasks using both a feedforward and GRUcontroller. The D-NTM is
evaluated on a set of Facebook bAbI tasks and shown to outperform NTM and LSTM
baselines. We have done extensive analysis of our model and different
variations of NTM on bAbI task. We also provide further experimental results on
sequential pMNIST, Stanford Natural Language Inference, associative recall and
copy tasks.


title: Tunneling in Axion Monodromy

abstract:
  The Coleman formula for vacuum decay and bubble nucleation has been used to
estimate the tunneling rate in models of axion monodromy in recent literature.
However, several of Coleman's original assumptions do not hold for such models.
Here we derive a new estimate with this in mind using a similar Euclidean
procedure. We find that there are significant regions of parameter space for
which the tunneling rate in axion monodromy is not well approximated by the
Coleman formula. However, there is also a regime relevant to large field
inflation in which both estimates parametrically agree. We also briefly comment
on the applications of our results to the relaxion scenario.


title: On stable CMC hypersurfaces with free-boundary in a Euclidean Ball

abstract:
  In this note, we observe that if $B$ is a ball in a Euclidean space with
dimension $n$, $n\geq3$, then a stable CMC hypersurface $\Sigma$ with free
boundary in $B$ satisfies \[ nA\leq L\leq nA\left(
\frac{1+\sqrt{1+4(n+1)H^2}}{2} \right)\,, \] where $L$, $A$ and $H$ denote the
length of $\partial \Sigma$, the area of $\Sigma$ and the mean curvature of
$\Sigma$, respectively. Consequently, if the boundary $\partial \Sigma$ is
embedded then $\Sigma$ must be totally geodesic or starshaped with respect to
the center of the ball. This result is an improvement of a theorem proved by A.
Ros and E. Vergasta \cite{R-V} . In particular, if $n=3$, the only stable CMC
surfaces with free boundary in $B$ are the totally geodesic disks or the
spherical caps. This last result was proved very recently by I. Nunes \cite{N}
using an extended stability result and a modified Hersch type balancing
argument to get a better control on the genus. We don't use that modified
Hersch type argument. However, we use a Nunes type Stability Lemma and a
crucial result due to A. Ros and E. Vergasta.


title:
Koornwinder polynomials and the stationary multi-species asymmetric
  exclusion process with open boundaries

abstract:
  We prove that the normalisation of the stationary state of the multi-species
asymmetric simple exclusion process (mASEP) is a specialisation of a
Koornwinder polynomial. As a corollary we obtain that the normalisation of
mASEP factorises as a product over multiple copies of the two-species ASEP.

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


title:
Circles in the spectrum and the geometry of orbits: a numerical ranges
  approach

abstract:
  We prove that a bounded linear Hilbert space operator has the unit circle in
its essential approximate point spectrum if and only if it admits an orbit
satisfying certain orthogonality and almost-orthogonality relations. This
result is obtained via the study of numerical ranges of operator tuples where
several new results are also obtained. As consequences of our numerical ranges
approach, we derive in particular wide generalizations of Arveson's theorem as
well as show that the weak convergence of operator powers implies the uniform
convergence of their compressions on an infinite-dimensional subspace. Several
related results have been proved as well.


title: Sandwiched R\'enyi Convergence for Quantum Evolutions

abstract:
  We study the speed of convergence of a primitive quantum time evolution
towards its fixed point in the distance of sandwiched R\'enyi divergences. For
each of these distance measures the convergence is typically exponentially fast
and the best exponent is given by a constant (similar to a logarithmic Sobolev
constant) depending only on the generator of the time evolution. We establish
relations between these constants and the logarithmic Sobolev constants as well
as the spectral gap. An important consequence of these relations is the
derivation of mixing time bounds for time evolutions directly from logarithmic
Sobolev inequalities without relying on notions like lp-regularity. We also
derive strong converse bounds for the classical capacity of a quantum time
evolution and apply these to obtain bounds on the classical capacity of some
examples, including stabilizer Hamiltonians under thermal noise.


title:
Thermodynamics of hot quantum scalar field in a (D+1) dimensional curved
  spacetime

abstract:
  We use the brick wall model to calculate the free energy of quantum scalar
field in a curved spacetime (D +1) dimensions. We find the thermodynamics
properties of quantum scalar field in several scenaries: Minkowski spacetime,
Schwarzschild spacetime and BTZ spacetime. For the cases analysed, the
thermodynamical properties of quantum scalar field is exactly with the
reported. It was found that the entropy of the gas is proportional to the
horizon area in a gravity field strong, which is consistent with the
holographic principle.


title: Perturbative approach to covariance matrix of the matter power spectrum

abstract:
  We evaluate the covariance matrix of the matter power spectrum using
perturbation theory up to dominant terms at 1-loop order and compare it to
numerical simulations. We decompose the covariance matrix into the disconnected
(Gaussian) part, trispectrum from the modes outside the survey (beat coupling
or super-sample variance), and trispectrum from the modes inside the survey,
and show how the different components contribute to the overall covariance
matrix. We find the agreement with the simulations is at a 10\% level up to $k
\sim 1 h {\rm Mpc^{-1}}$. We show that all the connected components are
dominated by the large-scale modes ($k<0.1 h {\rm Mpc^{-1}}$), regardless of
the value of the wavevectors $k,\, k'$ of the covariance matrix, suggesting
that one must be careful in applying the jackknife or bootstrap methods to the
covariance matrix. We perform an eigenmode decomposition of the connected part
of the covariance matrix, showing that at higher $k$ it is dominated by a
single eigenmode. The full covariance matrix can be approximated as the
disconnected part only, with the connected part being treated as an external
nuisance parameter with a known scale dependence, and a known prior on its
variance for a given survey volume. Finally, we provide a prescription for how
to evaluate the covariance matrix from small box simulations without the need
to simulate large volumes.


title:
Analysis of a Custom Support Vector Machine for Photometric Redshift
  Estimation and the Inclusion of Galaxy Shape Information

abstract:
  Aims: We present a custom support vector machine classification package for
photometric redshift estimation, including comparisons with other methods. We
also explore the efficacy of including galaxy shape information in redshift
estimation. Support vector machines, a type of machine learning, utilize
optimization theory and supervised learning algorithms to construct predictive
models based on the information content of data in a way that can treat
different input features symmetrically.
  Methods: The custom support vector machine package we have developed is
designated SPIDERz and made available to the community. As test data for
evaluating performance and comparison with other methods, we apply SPIDERz to
four distinct data sets: 1) the publicly available portion of the PHAT-1
catalog based on the GOODS-N field with spectroscopic redshifts in the range $z
< 3.6$, 2) 14365 galaxies from the COSMOS bright survey with photometric band
magnitudes, morphology, and spectroscopic redshifts inside $z < 1.4$, 3) 3048
galaxies from the overlap of COSMOS photometry and morphology with 3D-HST
spectroscopy extending to $z < 3.9$, and 4) 2612 galaxies with five-band
photometric magnitudes and morphology from the All-wavelength Extended Groth
Strip International Survey and $z < 1.57$.
  Results: We find that SPIDER-z achieves results competitive with other
empirical packages on the PHAT-1 data, and performs quite well in estimating
redshifts with the COSMOS and AEGIS data, including in the cases of a large
redshift range ($0 < z < 3.9$). We also determine from analyses with both the
COSMOS and AEGIS data that the inclusion of morphological information does not
have a statistically significant benefit for photometric redshift estimation
with the techniques employed here.


title: Transport of LCLS-II 1.3 Ghz cryomodule to SLAC

abstract:
  In a partnership with SLAC National Accelerator Laboratory (SLAC) and
Jefferson Lab, Fermilab will assemble and test 17 of the 35 total 1.3 GHz
cryomodules for the Linac Coherent Light Source II (LCLS-II) Project. These
include a prototype built and delivered by each Lab. Another two 3.9 GHz
cryomodules will be built, tested and transported by Fermilab to SLAC. Each
assembly will be transported over-the-road from Fermilab or Jefferson Lab using
specific routes to SLAC. The transport system consists of a base frame,
isolation fixture and upper protective truss. The strongback cryomodule lifting
fixture is described along with other supporting equipment used for both
over-the-road transport and local (on-site) transport at Fermilab. Initially,
analysis of fragile components and stability studies will be performed in order
to assess the risk associated with over-the-road transport of a fully assembled
cryomodule.


title:
A Two-Stage Patient-Focused Study Design for Rare Disease Controlled
  Trials

abstract:
  We developed a study design for rare disease clinical trials (RDTs) that
efficiently evaluate treatments, promotes access to new treatments during
treatment development, and optimizes healthcare resource utilization for future
treatment allocation, development, and prioritization. Comprehensive literature
review and focus group discussion were conducted. To address the multifaceted
challenges facing RDTs, four key issues for RDTs must be addressed, which are
1) the opportunity to access the new treatment; 2) assessment of outcomes where
clinically validated outcomes may be lacking; 3) patient heterogeneity; and 4)
duration of the study and number of patients required. Our proposed study
design has two stages. Stage 1 distinguishes patients who respond to the
treatment from those who do not respond to the treatment after assigning them
all to the experimental treatment. Stage 2 evaluates the treatment effect
comparatively among patients responded in Stage 1. In addition to treatment
effect evaluation, our design can greatly benefit rare disease patients and
clinical practice by increasing opportunities to access experimental treatments
and by providing relevant information that can be used for tailoring treatments
to certain subgroups, aiding future research in treatment development, and
improving healthcare resource utilization.


title: The Growth Rate of Tri-Colored Sum-Free Sets

abstract:
  Let $G$ be an abelian group. A tri-colored sum-free set in $G^n$ is a
collection of triples $({\bf a}_i, {\bf b}_i, {\bf c}_i)$ in $G^n$ such that
${\bf a}_i+{\bf b}_j+{\bf c}_k=0$ if and only if $i=j=k$. Fix a prime $q$ and
let $C_q$ be the cyclic group of order $q$. Let $\theta = \min_{\rho>0}
(1+\rho+\cdots + \rho^{q-1}) \rho^{-(q-1)/3}$. Blasiak, Church, Cohn, Grochow,
Naslund, Sawin, and Umans (building on previous work of Croot, Lev and Pach,
and of Ellenberg and Gijswijt) showed that a tri-colored sum-free set in
$C_q^n$ has size at most $3 \theta^n$. Between this paper and a paper of
Pebody, we will show that, for any $\delta > 0$, and $n$ sufficiently large,
there are tri-colored sum-free sets in $C_q^n$ of size $(\theta-\delta)^n$. Our
construction also works when $q$ is not prime.


title: Extending Erd\H{o}s- Beck's theorem to higher dimensions

abstract:
  Erd\H{o}s-Beck theorem states that $n$ points in the plane with at most $n-x$
points collinear define at least $c xn$ lines for some positive constant $c$.
In this paper, we will present two ways to extend this result to higher
dimensions. Our result has application to point-hyperplane incidences and
potential application to the point covering problem.


title:
The Steinhaus-Weil property: its converse, subcontinuity and Solecki
  amenability

abstract:
  The Steinhaus-Weil theorem that concerns us here is the simple, or classical,
`interior-points' property -- that in a Polish topological group a
non-negligible set B has the identity as an interior point of $BB^{-1}$. There
are various converses; the one that mainly concerns us is due to Simmons and
Mospan. Here the group is locally compact, so we have a Haar reference measure
$\eta$. The Simmons-Mospan theorem states that a (regular Borel) measure has
such a Steinhaus-Weil property if and only if it is absolutely continuous with
respect to the Haar measure. In Part I (Propositions 1-7, Theorems 1-4) we
exploit the connection between the interior-points property and a selective
form of infinitesimal invariance afforded by a certain family of selective
reference measures $\sigma$, drawing on Solecki's amenability at 1 (and using
Fuller's notion of subcontinuity). In Part II (Propositions 8, 9, Theorems 5,
6) we develop a number of relatives of the Simmons-Mospan theorem. In Part III
(Theorems 7, 8) we link this with topologies of Weil type. We close in Part IV
with Propositions 12-13 and Theorem B -- concerning the `composite
interior-point' property (of $AB^{-1}$) and the Borell `relative
interior-point' property (relative to the Cameron-Martin space) -- and
complements.


title: Tensor Network Skeletonization

abstract:
  We introduce a new coarse-graining algorithm, tensor network skeletonization,
for the numerical computation of tensor networks. This approach utilizes a
structure-preserving skeletonization procedure to remove short-range
correlations effectively at every scale. This approach is first presented in
the setting of 2D statistical Ising model and is then extended to higher
dimensional tensor networks and disordered systems. When applied to the
Euclidean path integral formulation, this approach also gives rise to new
efficient representations of the ground states for 1D and 2D quantum Ising
models.


title:
Geometric Learning and Topological Inference with Biobotic Networks:
  Convergence Analysis

abstract:
  In this study, we present and analyze a framework for geometric and
topological estimation for mapping of unknown environments. We consider agents
mimicking motion behaviors of cyborg insects, known as biobots, and exploit
coordinate-free local interactions among them to infer geometric and
topological information about the environment, under minimal sensing and
localization constraints. Local interactions are used to create a graphical
representation referred to as the encounter graph. A metric is estimated over
the encounter graph of the agents in order to construct a geometric point cloud
using manifold learning techniques. Topological data analysis (TDA), in
particular persistent homology, is used in order to extract topological
features of the space and a classification method is proposed to infer robust
features of interest (e.g. existence of obstacles). We examine the asymptotic
behavior of the proposed metric in terms of the convergence to the geodesic
distances in the underlying manifold of the domain, and provide stability
analysis results for the topological persistence. The proposed framework and
its convergences and stability analysis are demonstrated through numerical
simulations and experiments.


title: Uniform exponential growth for CAT(0) square complexes

abstract:
  In this paper we start the inquiry into proving uniform exponential growth in
the context of groups acting on CAT(0) cube complexes. We address free group
actions on CAT(0) square complexes and prove a more general statement. This
says that if $F$ is a finite collection of hyperbolic automorphisms of a CAT(0)
square complex $X$, then either there exists a pair of words of length at most
10 in $F$ which freely generate a free semigroup, or all elements of $F$
stabilize a flat (of dimension 1 or 2 in $X$). As a corollary, we obtain a
lower bound for the growth constant, $\sqrt[10]{2}$, which is uniform not just
for a given group acting freely on a given CAT(0) cube complex, but for all
groups which are not virtually abelian and have a free action on a CAT(0)
square complex.


title: Odd decompositions of eulerian graphs

abstract:
  We prove that an eulerian graph $G$ admits a decomposition into $k$ closed
trails of odd length if and only if and it contains at least $k$ pairwise
edge-disjoint odd circuits and $k\equiv |E(G)|\pmod{2}$. We conjecture that a
connected $2d$-regular graph of odd order with $d\ge 1$ admits a decomposition
into $d$ odd closed trails sharing a common vertex and verify the conjecture
for $d\le 3$. The case $d=3$ is crucial for determining the flow number of a
signed eulerian graph which is treated in a separate paper (arXiv:1408.1703v2).
The proof of our conjecture for $d=3$ is surprisingly difficult and calls for
the use of signed graphs as a convenient technical tool.


title: Group orderings, dynamics, and rigidity

abstract:
  Let G be a countable group. We show there is a topological relationship
between the space CO(G) of circular orders on G and the moduli space of actions
of G on the circle; as well as an analogous relationship for spaces of left
orders and actions on the line. In particular, we give a complete
characterization of isolated left and circular orders in terms of strong
rigidity of their induced actions of G on $S^1$ and R.
  As an application of our techniques, we give an explicit construction of
infinitely many nonconjugate isolated points in the spaces CO(F_{2n}) of
circular orders on free groups disproving a conjecture from Baik--Samperton,
and infinitely many nonconjugate isolated points in the space of left orders on
the pure braid group P_3, answering a question of Navas. We also give a
detailed analysis of circular orders on free groups, characterizing isolated
orders.


title:
Understanding and enhancing superconductivity in FeSe/STO by quantum
  size effects

abstract:
  Superconductivity in one-atom-layer iron selenide (FeSe) on a strontium
titanate (STO) substrate is enhanced by almost an order of magnitude with
respect to bulk FeSe. There is recent experimental evidence suggesting that
this enhancement persists in FeSe/STO nano-islands. More specifically, for
sizes $L \sim 10$ nm, the superconducting gap is a highly non-monotonic
function of $L$ with peaks well above the bulk gap value. This is the expected
behavior only for weakly-coupled metallic superconductors such as Al or Sn.
Here we develop a theoretical formalism to describe these experiments based on
three ingredients: Eliashberg theory of superconductivity in the weak coupling
limit, pairing dominated by forward scattering and periodic orbit theory to
model spectral fluctuations. We obtain an explicit analytical expression for
the size dependence of the gap that describes quantitatively the experimental
results with no free parameters. This is a strong suggestion that
superconductivity in FeSe/STO is mediated by STO phonons. We propose that,
since FeSe/STO is still a weakly coupled superconductor, quantum size effects
can be used to further enhance the bulk critical temperature in this interface.


title: Nonlocal problems with singular nonlinearity

abstract:
  We investigate existence and uniqueness of solutions for a class of nonlinear
nonlocal problems involving the fractional $p$-Laplacian operator and singular
nonlinearities.


title:
Molecular Dynamics simulations and Kelvin Probe Force microscopy to
  study of cholesterol-induced electrostatic nanodomains in complex lipid
  mixtures

abstract:
  The molecular arrangement of lipids and proteins within biomembranes and
monolayers gives rise to complex film morphologies as well as regions of
distinct electrical surface potential, topographical and electrostatic
nanoscale domains. To probe these nanodomains in soft matter is a challenging
task both experimentally and theoretically. This work addresses the effects of
cholesterol, lipid composition, lipid charge, and lipid phase on the monolayer
structure and the electrical surface potential distribution. Atomic Force
Microscopy (AFM) was used to resolve topographical nanodomains and Kelvin Probe
Force Microscopy (KPFM) to resolve electrical surface potential of these
nanodomains in lipid monolayers. Model monolayers composed of
dipalmitoylphosphatidylcholine (DPPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine
(DOPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC),
1,2-dioleoyl-sn-glycero-3-[phospho-rac-(3-lysyl(1-glycerol))] (DOPG),
sphingomyelin, and cholesterol were studied. It is shown that cholesterol
changes nanoscale domain formation, affecting both topography and electrical
surface potential. The molecular basis for differences in electrical surface
potential was addressed with atomistic molecular dynamics (MD). MD simulations
qualitatively match the experimental results, with 100s of mV difference in
electrostatic potential between liquid-disordered bilayer (Ld, less cholesterol
and lower chain order) and a liquid-ordered bilayer (Lo, more cholesterol and
higher chain order). Importantly, the difference in electrostatic properties
between Lo and Ld phases suggests a new mechanism by which membrane composition
couples to membrane function.


title:
Sample-to-sample fluctuations of power spectrum of a random motion in a
  periodic Sinai model

abstract:
  The Sinai model of a tracer diffusing in a quenched Brownian potential is a
much studied problem exhibiting a logarithmically slow anomalous diffusion due
to the growth of energy barriers with the system size. However, if the
potential is random but periodic, the regime of anomalous diffusion crosses
over to one of normal diffusion once a tracer has diffused over a few periods
of the system. Here we consider a system in which the potential is given by a
Brownian Bridge on a finite interval $(0,L)$ and then periodically repeated
over the whole real line, and study the power spectrum $S(f)$ of the diffusive
process $x(t)$ in such a potential. We show that for most of realizations of
$x(t)$ in a given realization of the potential, the low-frequency behavior is
$S(f) \sim {\cal A}/f^2$, i.e., the same as for standard Brownian motion, and
the amplitude ${\cal A}$ is a disorder-dependent random variable with a finite
support. Focusing on the statistical properties of this random variable, we
determine the moments of ${\cal A}$ of arbitrary, negative or positive order
$k$, and demonstrate that they exhibit a multi-fractal dependence on $k$, and a
rather unusual dependence on the temperature and on the periodicity $L$, which
are supported by atypical realizations of the periodic disorder. We finally
show that the distribution of ${\cal A}$ has a log-normal left tail, and
exhibits an essential singularity close to the right edge of the support, which
is related to the Lifshitz singularity. Our findings are based both on analytic
results and on extensive numerical simulations of the process $x(t)$.


title: HI absorption spectra for Supernova Remnants in the VGPS survey

abstract:
  The set of supernova remnants (SNR) from Green's SNR catalog which are found
in the VLA Galactic Plane Survey (VGPS) are the objects considered in this
study. For these SNR, we extract and analyse HI absorption spectra in a uniform
way and construct a catalogue of absorption spectra and distance
determinations.


title: Non-abelian Gerbes and Enhanced Leibniz Algebras

abstract:
  We present the most general gauge-invariant action functional for coupled 1-
and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping
eventual contributions that can be added in particular space-time dimensions
only such as higher Chern-Simons terms. After appropriate field redefinitions
it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the
process one sees explicitly how the existence of a gauge invariant functional
enforces that the most general semi-strict Lie 2-algebra describing the bundle
of a non-abelian gerbe gets reduced to a very particular structure, which,
after the field redefinition, can be identified with the one of an enhanced
Leibniz algebra. This is the first step towards a systematic construction of
such functionals for higher gauge theories, with kinetic terms for a tower of
gauge fields up to some highest form degree p, solved here for p = 2.


title:
Towards A Virtual Assistant That Can Be Taught New Tasks In Any Domain
  By Its End-Users

abstract:
  The challenge stated in the title can be divided into two main problems. The
first problem is to reliably mimic the way that users interact with user
interfaces. The second problem is to build an instructible agent, i.e. one that
can be taught to execute tasks expressed as previously unseen natural language
commands. This paper proposes a solution to the second problem, a system we
call Helpa. End-users can teach Helpa arbitrary new tasks whose level of
complexity is similar to the tasks available from today's most popular virtual
assistants. Teaching Helpa does not involve any programming. Instead, users
teach Helpa by providing just one example of a command paired with a
demonstration of how to execute that command. Helpa does not rely on any
pre-existing domain-specific knowledge. It is therefore completely
domain-independent. Our usability study showed that end-users can teach Helpa
many new tasks in less than a minute each, often much less.


title: Local Cohomology and Base Change

abstract:
  Let $X \overset{f}\longrightarrow S$ be a morphism of Noetherian schemes,
with $S$ reduced. For any closed subscheme $Z$ of $X$ finite over $S$, let $j$
denote the open immersion $X\setminus Z \hookrightarrow X$. Koll\'ar asked
whether for any coherent sheaf $\mathcal F$ on $X\setminus Z$ and any index
$r\geq 1$, the sheaf $f_*(R^rj_*\mathcal F)$ is generically free on $S$ and
commutes with base change. We answer this affirmatively, by proving a related
statement about local cohomology: Let $ R$ be Noetherian algebra over a
Noetherian domain $A$, and let $I \subset R$ be an ideal such that $ R/I $ is
finitely generated as an $A$-module. Let $M$ be a finitely generated
$R$-module. Then there exists a non-zero $g \in A$ such that the local
cohomology modules $H^r_I(M) \otimes_A A_g$ are free over $A_g$ and for any
ring map $A\rightarrow L$ factoring through $A_g$, we have $H^r_I(M) \otimes_A
L \cong H^r_{I{\otimes_A}L}(M\otimes_A L)$ for all $r$.


title: Prospects for quantum acoustics with phononic crystal devices

abstract:
  Nanomechanical systems made from phononic crystals can act as highly coherent
microwave-frequency circuits at cryogenic temperatures. However, generating
sufficient coupling between these devices and microwave superconducting quantum
circuits is challenging due to the vastly different length scales of acoustic
and electrical excitations. Here we demonstrate a general recipe for
calculating these interactions and show that large piezoelectric coupling rates
between microwave superconducting circuits containing Josephson junctions and
nanoscale phononic resonances are possible, suggesting a route to phononic
crystal circuits and systems that are nonlinear at the single-phonon level.


title: Maximizing CNN Accelerator Efficiency Through Resource Partitioning

abstract:
  Convolutional neural networks (CNNs) are revolutionizing machine learning,
but they present significant computational challenges. Recently, many
FPGA-based accelerators have been proposed to improve the performance and
efficiency of CNNs. Current approaches construct a single processor that
computes the CNN layers one at a time; the processor is optimized to maximize
the throughput at which the collection of layers is computed. However, this
approach leads to inefficient designs because the same processor structure is
used to compute CNN layers of radically varying dimensions.
  We present a new CNN accelerator paradigm and an accompanying automated
design methodology that partitions the available FPGA resources into multiple
processors, each of which is tailored for a different subset of the CNN
convolutional layers. Using the same FPGA resources as a single large
processor, multiple smaller specialized processors increase computational
efficiency and lead to a higher overall throughput. Our design methodology
achieves 3.8x higher throughput than the state-of-the-art approach on
evaluating the popular AlexNet CNN on a Xilinx Virtex-7 FPGA. For the more
recent SqueezeNet and GoogLeNet, the speedups are 2.2x and 2.0x.


title:
Sensitivities to charged-current nonstandard neutrino interactions at
  DUNE

abstract:
  We investigate the effects of charged-current (CC) nonstandard neutrino
interactions (NSIs) at the source and at the detector in the simulated data for
the planned Deep Underground Neutrino Experiment (DUNE), while neglecting the
neutral-current NSIs at the propagation due to the fact that several solutions
have been proposed to resolve the degeneracies posed by neutral-current NSIs
while no solution exists for the degeneracies due to the CC NSIs. We study the
effects of CC NSIs on the simultaneous measurements of $\theta_{23}$ and
$\delta_{CP}$ in DUNE. The analysis reveals that 3$\sigma $ C.L. measurement of
the correct octant of $\theta_{23}$ in the standard mixing scenario is spoiled
if the CC NSIs are taken into account. Likewise, the CC NSIs can deteriorate
the uncertainty of the $\delta_{CP}$ measurement by a factor of two relative to
that in the standard oscillation scenario. We also show that the source and the
detector CC NSIs can induce a significant amount of fake CP-violation and the
CP-conserving case can be excluded by more than 80\% C.L. in the presence of
fake CP-violation. We further find the potential of DUNE to constrain the
relevant CC NSI parameters from the single parameter fits for both neutrino and
antineutrino appearance and disappearance channels at both the near and far
detectors. The results show that there could be improvement in the current
bounds by at least one order of magnitude at the near and far detector of DUNE
except a few parameters which remain weaker at the far detector.


title:
Eigenvalue estimates for a class of elliptic differential operators in
  divergence form

abstract:
  We compute estimates for eigenvalues of a class of linear second-order
elliptic differential operators in divergence form (with Dirichlet boundary
condition) on a bounded domain in a complete Riemannian manifold. Our estimates
are based upon the Weyl's asymptotic formula. As an application, we find a
lower bound for the mean of the first k eigenvalues of the drifting Laplacian.
In particular, we have extended for this operator a partial solution given by
Cheng and Yang for the generalized conjecture of P\'olya. We also derive a
second-Yang type inequality due to Chen and Cheng, and other two inequalities
which generalize results by Cheng and Yang obtained for a domain in the unit
sphere and for a domain in the projective space.


title:
Unsupervised Learning with Imbalanced Data via Structure Consolidation
  Latent Variable Model

abstract:
  Unsupervised learning on imbalanced data is challenging because, when given
imbalanced data, current model is often dominated by the major category and
ignores the categories with small amount of data. We develop a latent variable
model that can cope with imbalanced data by dividing the latent space into a
shared space and a private space. Based on Gaussian Process Latent Variable
Models, we propose a new kernel formulation that enables the separation of
latent space and derives an efficient variational inference method. The
performance of our model is demonstrated with an imbalanced medical image
dataset.


title: Ward and Nielsen Identities for ABJM Theory in ${\cal N}=1$ Superspace

abstract:
  The structures and the associated gauge algebra of ABJM theory in ${\cal
N}=1$ superspace are reviewed. We derive the Ward identities of the theory in
the class of Lorentz-type gauges at quantum level to justify the
renormalizability of the model. We compute the Nielsen identities for the
two-point functions of the theory with the help of enlarged BRST
transformation. The identities are derived in ABJM theory to ensure the gauge
independence of the physical poles of the Green's functions.


title: Approaching the Standard Quantum Limit of Mechanical Torque Sensing

abstract:
  Mechanical transduction of torque has been key to probing a number of
physical phenomena, such as gravity, the angular momentum of light, the Casimir
effect, magnetism, and quantum oscillations. Following similar trends as mass
and force sensing, mechanical torque sensitivity can be dramatically improved
by scaling down the physical dimensions, and therefore moment of inertia, of a
torsional spring. Yet now, through precision nanofabrication and sub-wavelength
cavity optomechanics, we have reached a point where geometric optimization can
only provide marginal improvements to torque sensitivity. Instead, nanoscale
optomechanical measurements of torque are overwhelmingly hindered by thermal
noise. Here we present cryogenic measurements of a cavity-optomechanical
torsional resonator cooled in a dilution refrigerator to a temperature of 25
mK, corresponding to an average phonon occupation of <n> = 35, that demonstrate
a record-breaking torque sensitivity of 2.9 yNm/Hz^{1/2}. This a 270-fold
improvement over previous optomechanical torque sensors and just over an order
of magnitude from its standard quantum limit. Furthermore, we demonstrate that
mesoscopic test samples, such as micron-scale superconducting disks, can be
integrated with our cryogenic optomechanical torque sensing platform, in
contrast to other cryogenic optomechanical devices, opening the door for
mechanical torque spectroscopy of intrinsically quantum systems.


title:
A Sequence-to-Sequence Model for User Simulation in Spoken Dialogue
  Systems

abstract:
  User simulation is essential for generating enough data to train a
statistical spoken dialogue system. Previous models for user simulation suffer
from several drawbacks, such as the inability to take dialogue history into
account, the need of rigid structure to ensure coherent user behaviour, heavy
dependence on a specific domain, the inability to output several user
intentions during one dialogue turn, or the requirement of a summarized action
space for tractability. This paper introduces a data-driven user simulator
based on an encoder-decoder recurrent neural network. The model takes as input
a sequence of dialogue contexts and outputs a sequence of dialogue acts
corresponding to user intentions. The dialogue contexts include information
about the machine acts and the status of the user goal. We show on the Dialogue
State Tracking Challenge 2 (DSTC2) dataset that the sequence-to-sequence model
outperforms an agenda-based simulator and an n-gram simulator, according to
F-score. Furthermore, we show how this model can be used on the original action
space and thereby models user behaviour with finer granularity.


title: An Operator Theoretic Approach to Nonparametric Mixture Models

abstract:
  When estimating finite mixture models, it is common to make assumptions on
the mixture components, such as parametric assumptions. In this work, we make
no distributional assumptions on the mixture components and instead assume that
observations from the mixture model are grouped, such that observations in the
same group are known to be drawn from the same mixture component. We precisely
characterize the number of observations $n$ per group needed for the mixture
model to be identifiable, as a function of the number $m$ of mixture
components. In addition to our assumption-free analysis, we also study the
settings where the mixture components are either linearly independent or
jointly irreducible. Furthermore, our analysis considers two kinds of
identifiability -- where the mixture model is the simplest one explaining the
data, and where it is the only one. As an application of these results, we
precisely characterize identifiability of multinomial mixture models. Our
analysis relies on an operator-theoretic framework that associates mixture
models in the grouped-sample setting with certain infinite-dimensional tensors.
Based on this framework, we introduce general spectral algorithms for
recovering the mixture components and illustrate their use on a synthetic data
set.


title:
A multilayer perspective for the analysis of urban transportation
  systems

abstract:
  Public urban mobility systems are composed by several transportation modes
connected together. Most studies in urban mobility and planning often ignore
the multi-layer nature of transportation systems considering only aggregated
versions of this complex scenario. In this work we present a model for the
representation of the transportation system of an entire city as a multiplex
network. Using two different perspectives, one in which each line is a layer
and one in which lines of the same transportation mode are grouped together, we
study the interconnected structure of 9 different cities in Europe raging from
small towns to mega-cities like London and Berlin highlighting their
vulnerabilities and possible improvements. Finally, for the city of Zaragoza in
Spain, we also consider data about service schedule and waiting times, which
allow us to create a simple yet realistic model for urban mobility able to
reproduce real-world facts and to test for network improvements.


title: Phase Cascade Bridge Rectifier Array in a 2-D lattice

abstract:
  We report on a novel rectification phenomenon in a 2-D lattice network
consisting of $N\times N$ sites with diode and AC source elements with
controllable phases. A phase cascade configuration is described in which the
current ripple in a load resistor goes to zero in the large $N$ limit,
enhancing the rectification efficiency without requiring any external capacitor
or inductor based filters. The integrated modular configuration is
qualitatively different from conventional rectenna arrays in which the source,
rectifier and filter systems are physically disjoint. Exact analytical results
derived using idealized diodes are compared to a realistic simulation of
commercially available diodes. Our results on nonlinear networks of
source-rectifier arrays are potentially of interest to a fast evolving field of
distributed power networks.


title: Intermittent dipping in a low-mass X-ray Binary

abstract:
  Periodic dips observed in approx. 20% of low-mass X-ray binaries are thought
to arise from obscuration of the neutron star by the outer edge of the
accretion disk. We report the detection with the Rossi X-ray Timing Explorer of
two dipping episodes in Aql X-1, not previously a known dipper. The X-ray
spectrum during the dips exhibited an elevated neutral column density, by a
factor between 1 and almost two orders of magnitude. Dips were not observed in
every cycle of the 18.95-hr orbit, so that the estimated frequency for these
events is 0.10 (+0.07,-0.05)/cycle. This is the first confirmed example of
intermittent dipping in such a system. Assuming that the dips in Aql X-1 occur
because the system inclination is intermediate between the non-dipping and
dipping sources, implies a range of 72-79 deg. for the source. This result
lends support for the presence of a massive (> 2 M_sun) neutron star in Aql
X-1, and further implies that approx. 30 additional LMXBs may have inclinations
within this range, raising the possibility of intermittent dips in those
systems also. Thus, we searched for dips from 24 other bursting systems,
without success. For the system with the largest number of dip phases covered,
4U 1820-303, the nondetection implies a 95% upper limit to the dip frequency of
1.4E-3/cycle.


title: A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions

abstract:
  In this article, we explore the low energy structure of a $U(3)$ gauge theory
over spaces with fuzzy sphere(s) as extra dimensions. In particular, we
determine the equivariant parametrization of the gauge fields, which transform
either invariantly or as vectors under the combined action of $SU(2)$ rotations
of the fuzzy spheres and those $U(3)$ gauge transformations generated by $SU(2)
\subset U(3)$ carrying the spin $1$ irreducible representation of $SU(2)$. The
cases of a single fuzzy sphere $S_F^2$ and a particular direct sum of
concentric fuzzy spheres, $S_F^{2 \, Int}$, covering the monopole bundle
sectors with windings $\pm 1$ are treated in full and the low energy degrees of
freedom for the gauge fields are obtained. Employing the parametrizations of
the fields in the former case, we determine a low energy action by tracing over
the fuzzy sphere and show that the emerging model is abelian Higgs type with
$U(1) \times U(1)$ gauge symmetry and possess vortex solutions on ${\mathbb
R}^2$, which we discuss in some detail. Generalization of our formulation to
the equivariant parametrization of gauge fields in $U(n)$ theories is also
briefly addressed.


title: Multi-class classification: mirror descent approach

abstract:
  We consider the problem of multi-class classification and a stochastic opti-
mization approach to it. We derive risk bounds for stochastic mirror descent
algorithm and provide examples of set geometries that make the use of the
algorithm efficient in terms of error in k.


title:
Existence of a calibrated regime switching local volatility model and
  new fake Brownian motions

abstract:
  By Gyongy's theorem, a local and stochastic volatility (LSV) model is
calibrated to the market prices of all European call options with positive
maturities and strikes if its local volatility function is equal to the ratio
of the Dupire local volatility function over the root conditional mean square
of the stochastic volatility factor given the spot value. This leads to a SDE
nonlinear in the sense of McKean. Particle methods based on a kernel
approximation of the conditional expectation, as presented by Guyon and
Henry-Labord\`ere (2011), provide an efficient calibration procedure even if
some calibration errors may appear when the range of the stochastic volatility
factor is very large. But so far, no global existence result is available for
the SDE nonlinear in the sense of McKean. In the particular case where the
local volatility function is equal to the inverse of the root conditional mean
square of the stochastic volatility factor multiplied by the spot value given
this value and the interest rate is zero, the solution to the SDE is a fake
Brownian motion. When the stochastic volatility factor is a constant (over
time) random variable taking finitely many values and the range of its square
is not too large, we prove existence to the associated Fokker-Planck equation.
Thanks to Figalli (2008), we then deduce existence of a new class of fake
Brownian motions. We then extend these results to the special case of the LSV
model called regime switching local volatility, where the stochastic volatility
factor is a jump process taking finitely many values and with jump intensities
depending on the spot level. Under the same condition on the range of its
square, we prove existence to the associated Fokker-Planck PDE. Finally, we
deduce existence of the calibrated model by extending the results in Figalli
(2008).


title:
A Graph-Algorithmic Approach for the Study of Metastability in Markov
  Chains

abstract:
  Large continuous-time Markov chains with exponentially small transition rates
arise in modeling complex systems in physics, chemistry and biology. We propose
a constructive graph-algorithmic approach to determine the sequence of critical
timescales at which the qualitative behavior of a given Markov chain changes,
and give an effective description of the dynamics on each of them. This
approach is valid for both time-reversible and time-irreversible Markov
processes, with or without symmetry. Central to this approach are two graph
algorithms, Algorithm 1 and Algorithm 2, for obtaining the sequences of the
critical timescales and the hierarchies of Typical Transition Graphs or
T-graphs indicating the most likely transitions in the system {without and
with} symmetry respectively. The sequence of {critical} timescales includes the
subsequence of the reciprocals { of the real parts } of eigenvalues. Under a
certain assumption, we prove sharp asymptotic estimates for eigenvalues
(including prefactors) and show how one can extract them from the output of
Algorithm 1. We discuss the relationship between Algorithms 1 and 2, and
explain how one needs to interpret the output of Algorithm 1 if it is applied
in the case with symmetry instead of Algorithm 2. Finally, we analyze an
example motivated by R. D. Astumian's model of the dynamics of kinesin, a
molecular motor, by means of Algorithm 2.


title: Measurement of many-body chaos using a quantum clock

abstract:
  There has been recent progress in understanding chaotic features in many-body
quantum systems. Motivated by the scrambling of information in black holes, it
has been suggested that the time dependence of out-of-time-ordered (OTO)
correlation functions such as $\langle O_2(t) O_1(0) O_2(t) O_1(0) \rangle $ is
a faithful measure of quantum chaos. Experimentally, these correlators are
challenging to access since they apparently require access to both forward and
backward time evolution with the system Hamiltonian. Here, we propose a
protocol to measure such OTO correlators using an ancilla which controls the
direction of time. Specifically, by coupling the state of ancilla to the system
Hamiltonian of interest, we can emulate the forward and backward time
propagation, where the ancilla plays the role of a 'quantum clock'. Within this
scheme, the continuous evolution of the entire system (the system of interest
and the ancilla) is governed by a time-independent Hamiltonian. Our protocol is
immune to errors that could occur when the direction of time evolution is
externally controlled by a classical switch.

categories: quant-ph cond-mat.mes-hall cond-mat.quant-gas cond-mat.str-el hep-th


title: First-principles dynamics of electrons and phonons

abstract:
  First-principles calculations combining density functional theory and
many-body perturbation theory can provide microscopic insight into the dynamics
of electrons and phonons in materials. We review this theoretical and
computational framework, focusing on perturbative treatments of scattering,
dynamics and transport of coupled electrons and phonons. We discuss application
of these first-principles calculations to electronics, lighting, spectroscopy
and renewable energy.


title: Optimal uncertainty relations in a modified Heisenberg algebra

abstract:
  Various theories that aim at unifying gravity with quantum mechanics suggest
modifications of the Heisenberg algebra for position and momentum. From the
perspective of quantum mechanics, such modifications lead to new uncertainty
relations which are thought (but not proven) to imply the existence of a
minimal observable length. Here we prove this statement in a framework of
sufficient physical and structural assumptions. Moreover, we present a general
method that allows to formulate optimal and state-independent variance-based
uncertainty relations. In addition, instead of variances, we make use of
entropies as a measure of uncertainty and provide uncertainty relations in
terms of min- and Shannon entropies. We compute the corresponding entropic
minimal lengths and find that the minimal length in terms of min-entropy is
exactly one bit.


title: Hyperentanglement purification for two-photon six-qubit quantum systems

abstract:
  Recently, two-photon six-qubit hyperentangled states were produced in
experiment and they can improve the channel capacity of quantum communication
largely. Here we present a scheme for the hyperentanglement purification of
nonlocal two-photon systems in three degrees of freedom (DOFs), including the
polarization, the first-longitudinal-momentum, and the second longitudinal
momentum DOFs. Our hyperentanglement purification protocol (hyper-EPP) is
constructed with two steps resorting to parity-check quantum nondemolition
measurement on the three DOFs and SWAP gates, respectively. With these two
steps, the bit-flip errors in the three DOFs can be corrected efficiently.
Also, we show that using SWAP gates is a universal method for hyper-EPP in the
polarization DOF and multiple longitudinal momentum DOFs. The implementation of
our hyper-EPP is assisted by nitrogen-vacancy centers in optical microcavities,
which could be achieved with current techniques. It is useful for long-distance
high-capacity quantum communication with two-photon six-qubit
hyperentanglement.


title: Conservative Integrators for a Toy Model of Weak Turbulence

abstract:
  Weak turbulence is a phenomenon by which a system generically transfers
energy from low to high wave numbers, while persisting for all finite time. It
has been conjectured by Bourgain that the 2D defocusing nonlinear Schr\"odinger
equation (NLS) on the torus has this dynamic, and several analytical and
numerical studies have worked towards addressing this point.
  In the process of studying the conjecture, Colliander, Keel, Staffilani,
Takaoka, and Tao introduced a "toy model" dynamical system as an approximation
of NLS, which has been subsequently studied numerically. In this work, we
formulate and examine several numerical schemes for integrating this model
equation. The model has two invariants, and our schemes aim to conserve at
least one of them. We prove convergence in some cases, and our numerical
studies show that the schemes compare favorably to others, such as Trapezoidal
Rule and fixed step fourth order Runge-Kutta. The preservation of the
invariants is particularly important in the study of weak turbulence as the
energy transfer tends to occur on long time scales.


title: On Mixed Memberships and Symmetric Nonnegative Matrix Factorizations

abstract:
  The problem of finding overlapping communities in networks has gained much
attention recently. Optimization-based approaches use non-negative matrix
factorization (NMF) or variants, but the global optimum cannot be provably
attained in general. Model-based approaches, such as the popular
mixed-membership stochastic blockmodel or MMSB (Airoldi et al., 2008), use
parameters for each node to specify the overlapping communities, but standard
inference techniques cannot guarantee consistency. We link the two approaches,
by (a) establishing sufficient conditions for the symmetric NMF optimization to
have a unique solution under MMSB, and (b) proposing a computationally
efficient algorithm called GeoNMF that is provably optimal and hence consistent
for a broad parameter regime. We demonstrate its accuracy on both simulated and
real-world datasets.


title: Metadata salad at the Cordoba Observatory

abstract:
  The Plate Archive of the Cordoba Observatory includes 20.000 photographs and
spectra on glass plates dating from 1893 to 1983. This contribution describes
the work performed since the plate archive was transferred to the Observatory
Library in 2011. In 2014 an interdisciplinary team was assembled and a research
grant from the National University of Cordoba was obtained with the objectives
of preserving the glass plates and generate public access for astronomers and
other audiences. The preservation work not only includes practical intervention
to improve conservation conditions for the whole archive, but also a diagnose
of the preservation conditions for the plates and identification of best
practices for cleaning the plates. The access envisioned through digitization
requires not only the scanning of all the plates, but also careful definition
and provision of metadata. In this regard, each institutional level involved
-in this case: archive, library, astronomical observatory and public university
- demands and provides different bibliographic practices, involving multiple
standards of description and coding.


title: A two-sided analogue of the Coxeter complex

abstract:
  For any Coxeter system $(W,S)$ of rank $n$, we introduce an abstract boolean
complex (simplicial poset) of dimension $2n-1$ that contains the Coxeter
complex as a relative subcomplex. Faces are indexed by triples $(I,w,J)$, where
$I$ and $J$ are subsets of the set $S$ of simple generators, and $w$ is a
minimal length representative for the parabolic double coset $W_I w W_J$. There
is exactly one maximal face for each element of the group $W$. The complex is
shellable and thin, which implies the complex is a sphere for the finite
Coxeter groups. In this case, a natural refinement of the $h$-polynomial is
given by the "two-sided" $W$-Eulerian polynomial, i.e., the generating function
for the joint distribution of left and right descents in $W$.


title:
Fractal Dimension Pattern Based Multiresolution Analysis for Rough
  Estimator of Person-Dependent Audio Emotion Recognition

abstract:
  As a general means of expression, audio analysis and recognition has
attracted much attentions for its wide applications in real-life world. Audio
emotion recognition (AER) attempts to understand emotional states of human with
the given utterance signals, and has been studied abroad for its further
development on friendly human-machine interfaces. Distinguish from other
existing works, the person-dependent patterns of audio emotions are conducted,
and fractal dimension features are calculated for acoustic feature extraction.
Furthermore, it is able to efficiently learn intrinsic characteristics of
auditory emotions, while the utterance features are learned from fractal
dimensions of each sub-bands. Experimental results show the proposed method is
able to provide comparative performance for audio emotion recognition.


title: Representations of integers by certain $2k$-ary quadratic forms

abstract:
  Suppose $k$ is a positive integer. In this work, we establish formulas for
for the number of representations of integers by the quadratic forms $$
x_{1}^{2}+\cdots+x_{k}^{2}+l\left(x_{k+1}^{2}+\cdots+x_{2k}^{2}\right) $$ for
$l\in\{2,4\}$.


title: Detecting Algebraic Manipulation in Leaky Storage Systems

abstract:
  Algebraic Manipulation Detection (AMD) Codes detect adversarial noise that is
added to a coded message and stored in a storage that is opaque to the
adversary. We study AMD codes when the storage can leak up to \rho\log|G| bits
of information about the stored codeword, where G is the group in which the
stored codeword lives and \rho is a constant. We propose \rho-AMD codes that
provide protection in this new setting, and define weak and strong \rho-AMD
codes that provide security for a random and an arbitrary message,
respectively. We derive concrete and asymptotic bounds for the efficiency of
these codes featuring a rate upper bound of 1-\rho for the strong codes. We
also define the class of \rho^{LV}-AMD codes that provide protection when
leakage is in the form of a number of codeword components, and give
constructions featuring a strong \rho^{LV}-AMD codes that asymptotically
achieve the rate 1-\rho. We describe applications of \rho-AMD codes to, (i)
robust ramp secret sharing scheme and, (ii) wiretap II channel when the
adversary can eavesdrop a \rho fraction of codeword components and tamper with
all components of the codeword.


title:
An operator theoretical proof for the second-order phase transition in
  the BCS-Bogoliubov model of superconductivity

abstract:
  We first show some properties such as smoothness and monotone decreasingness
of the solution to the BCS-Bogoliubov gap equation for superconductivity.
Moreover we give the behavior of the solution with respect to the temperature
near the transition temperature. On the basis of these results, dealing with
the thermodynamic potential, we then show that the transition from a normal
conducting state to a superconducting state is a second-order phase transition
in the BCS-Bogoliubov model of superconductivity from the viewpoint of operator
theory. Here we have no magnetic field and we need to introduce a cutoff
$\varepsilon>0$, which is sufficiently small and fixed (see Remark
\ref{rmk:varepsilon}). Moreover we obtain the exact and explicit expression for
the gap in the specific heat at constant volume at the transition temperature.

categories: math-ph cond-mat.stat-mech cond-mat.supr-con math.AP math.FA math.MP


title: Reducing overfitting in challenge-based competitions

abstract:
  Over-fitting is a dreaded foe in challenge-based competitions. Because
participants rely on public leaderboards to evaluate and refine their models,
there is always the danger they might over-fit to the holdout data supporting
the leaderboard. The recently published Ladder algorithm aims to address this
problem by preventing the participants from exploiting willingly or
inadvertently minor fluctuations in public leaderboard scores during model
refinement. In this paper, we report a vulnerability of the Ladder that induces
severe over-fitting of the leaderboard when the sample size is small. To
circumvent this attack, we propose a variation of the Ladder that releases a
bootstrapped estimate of the public leaderboard score instead of providing
participants with a direct measure of performance. We also extend the scope of
the Ladder to arbitrary performance metrics by relying on a more broadly
applicable testing procedure based on the Bayesian bootstrap. Our method makes
it possible to use a leaderboard, with the technical and social advantages that
it provides, even in cases where data is scant.


title:
Role of thermal friction in relaxation of turbulent Bose-Einstein
  condensates

abstract:
  In recent experiments, the relaxation dynamics of highly oblate, turbulent
Bose-Einstein condensates (BECs) was investigated by measuring the vortex decay
rates in various sample conditions [Phys. Rev. A $\bf 90$, 063627 (2014)] and,
separately, the thermal friction coefficient $\alpha$ for vortex motion was
measured from the long-time evolution of a corotating vortex pair in a BEC
[Phys. Rev. A $\bf 92$, 051601(R) (2015)]. We present a comparative analysis of
the experimental results, and find that the vortex decay rate $\Gamma$ is
almost linearly proportional to $\alpha$. We perform numerical simulations of
the time evolution of a turbulent BEC using a point-vortex model equipped with
longitudinal friction and vortex-antivortex pair annihilation, and observe that
the linear dependence of $\Gamma$ on $\alpha$ is quantitatively accounted for
in the dissipative point-vortex model. The numerical simulations reveal that
thermal friction in the experiment was too strong to allow for the emergence of
a vortex-clustered state out of decaying turbulence.


title:
Uncertain Loading and Quantifying Maximum Energy Concentration within
  Composite Structures

abstract:
  We introduce a systematic method for identifying the worst case load among
all boundary loads of fixed energy. Here the worst case load is defined to be
the one that delivers the largest fraction of input energy to a prescribed
subdomain of interest. The worst case load is identified with the first
eigenfunction of a suitably defined eigenvalue problem. The first eigenvalue
for this problem is the maximum fraction of boundary energy that can be
delivered to the subdomain. We compute worst case boundary loads and associated
energy contained inside a prescribed subdomain through the numerical solution
of the eigenvalue problem. We apply this computational method to bound the
worst case load associated with an ensemble of random boundary loads given by a
second order random process. Several examples are carried out on heterogeneous
structures to illustrate the method.


title: The far-infrared - radio correlation in dwarf galaxies

abstract:
  The far-infrared - radio correlation connects star formation and magnetic
fields in galaxies, and has been confirmed over a large range of far-infrared
luminosities. Recent investigations indicate that it may even hold in the
regime of local dwarf galaxies, and we explore here the expected behavior in
the regime of star formation surface densities below 0.1 M_sun kpc^{-2}
yr^{-1}. We derive two conditions that can be particularly relevant for
inducing a change in the expected correlation: a critical star formation
surface density to maintain the correlation between star formation rate and the
magnetic field, and a critical star formation surface density below which
cosmic ray diffusion losses dominate over their injection via supernova
explosions. For rotation periods shorter than 1.5x10^7 (H/kpc)^2 yrs, with H
the scale height of the disk, the first correlation will break down before
diffusion losses are relevant, as higher star formation rates are required to
maintain the correlation between star formation rate and magnetic field
strength. For high star formation surface densities Sigma_SFR, we derive a
characteristic scaling of the non-thermal radio to the far-infrared / infrared
emission with Sigma_SFR^{1/3}, corresponding to a scaling of the non-thermal
radio luminosity L_s with the infrared luminosity L_{th} as L_{th}^{4/3}. The
latter is expected to change when the above processes are no longer steadily
maintained. In the regime of long rotation periods, we expect a transition
towards a steeper scaling with Sigma_SFR^{2/3}, implying L_s~L_th^{5/3}, while
the regime of fast rotation is expected to show a considerably enhanced
scatter. These scaling relations explain the increasing thermal fraction of the
radio emission observed within local dwarfs, and can be tested with future
observations by the SKA and its precursor radio telescopes.


title: High-Fidelity Entangled Bell States via Shortcuts to Adiabaticity

abstract:
  We present a couple of protocols based on shortcut to adiabaticity techniques
for rapid generation of robust entangled Bell states in a system of two
two-state systems. Our protocols rely on the so-called transitionless quantum
driving (TQD) algorithm and Lewis-Riesenfeld invariant (LRI) method. Both TQD
and LRI methods result in high fidelity in population transfer.Our study shows
that it is possible to prepare an entangled state in infinitely short time
without losing robustness and efficiency.


title: HEAP: Reliable Assessment of BGP Hijacking Attacks

abstract:
  The detection of BGP prefix hijacking attacks has been the focus of research
for more than a decade. However, state-of-the-art techniques fall short of
detecting more elaborate types of attack. To study such attacks, we devise a
novel formalization of Internet routing, and apply this model to routing
anomalies in order to establish a comprehensive attacker model. We use this
model to precisely classify attacks and to evaluate their impact and
detectability. We analyze the eligibility of attack tactics that suit an
attacker's goals and demonstrate that related work mostly focuses on less
impactful kinds of attacks.
  We further propose, implement and test the Hijacking Event Analysis Program
(HEAP), a new approach to investigate hijacking alarms. Our approachis designed
to seamlessly integrate with previous work in order to reduce the high rates of
false alarms inherent to these techniques. We leverage several unique data
sources that can reliably disprove malicious intent. First, we make use of an
Internet Routing Registry to derive business or organisational relationships
between the parties involved in an event. Second, we use a topology-based
reasoning algorithm to rule out events caused by legitimate operational
practice. Finally, we use Internet-wide network scans to identify
SSL/TLS-enabled hosts, which helps to identify non-malicious events by
comparing public keys prior to and during an event. In our evaluation, we prove
the effectiveness of our approach, and show that day-to-day routing anomalies
are harmless for the most part. More importantly, we use HEAP to assess the
validity of publicly reported alarms. We invite researchers to interface with
HEAP in order to cross-check and narrow down their hijacking alerts.


abstract:
  Edge Detection Methods Based on Differential Phase Congruency of Monogenic
Image Abstract: Edge detection has been widely used in medical image processing
and automatic diagnosis. Some novel edge detection algorithms,based on the
monogenic scale-space, are proposed by detecting points of local extrema in
local amplitude, the local attenuation and modified differential phase
congruency methods. The monogenic scale-space is obtained from a known image by
Poisson and conjugate Poisson filtering. In mathematics, it is the Hardy space
in the upper half-space. The boundary value of the monogenic scale-space
representation is a monogenic image. In the monogenic scale-space, the
definitions involving scale, such as local amplitude,local attenuation, local
phase angle, local phase vector and local frequency (phase derivatives) are
proposed. Using Clifford analysis, the relations between the local attenuation
and the local phase vector are obtained. These study will be improved the
understanding of image analysis in higher dimensional spaces. Experimental
results are shown by using some typical images.


title:
Fully Bayesian Classification with Heavy-tailed Priors for Selection in
  High-dimensional Features with Grouping Structure

abstract:
  Feature selection is demanded in many modern scientific research problems
that use high-dimensional data. A typical example is to find the most useful
genes that are related to a certain disease (eg, cancer) from high-dimensional
gene expressions. The expressions of genes have grouping structures, for
example, a group of co-regulated genes that have similar biological functions
tend to have similar expressions. Many statistical methods have been proposed
to take the grouping structure into consideration in feature selection,
including group LASSO, supervised group LASSO, and regression on group
representatives. In this paper, we propose a fully Bayesian Robit regression
method with heavy-tailed (sparsity) priors (shortened by FBRHT) for selecting
features with grouping structure. The main features of FBRHT include that it
discards more aggressively unrelated features than LASSO, and it can make
feature selection within groups automatically without a pre-specified grouping
structure. In this paper, we use simulated and real datasets to demonstrate
that the predictive power of the sparse feature subsets selected by FBRHT are
comparable with other much larger feature subsets selected by LASSO, group
LASSO, supervised group LASSO, penalized logistic regression and random forest,
and that the succinct feature subsets selected by FBRHT have significantly
better predictive power than the feature subsets of the same size taken from
the top features selected by the aforementioned methods.


title: k-Congruences on semirings

abstract:
  For any semiring, the concept of k-congruences is introduced, criteria for
k-congruences are established, it is proved that there is an
inclusion-preserving bijection between k-congruences and k-ideals, and an
equivalent condition for the existence of a zero is presented with the help of
k-congruences. It is shown that a semiring is k-simple iff it is
k-congruence-simple, and that inclines are k-simple iff they have at most 2
elements. Lemma 2.12(i) in [Glas. Mat. 42(62) (2007) 301] is pointed out being
false.


title:
Scalable ion-photon quantum interface based on integrated diffractive
  mirrors

abstract:
  Quantum networking links quantum processors through remote entanglement for
distributed quantum information processing (QIP) and secure long-range
communication. Trapped ions are a leading QIP platform, having demonstrated
universal small-scale processors and roadmaps for large-scale implementation.
Overall rates of ion-photon entanglement generation, essential for remote
trapped ion entanglement, are limited by coupling efficiency into single mode
fibres5 and scaling to many ions. Here we show a microfabricated trap with
integrated diffractive mirrors that couples 4.1(6)% of the fluorescence from a
$^{174}$Yb$^+$ ion into a single mode fibre, nearly triple the demonstrated
bulk optics efficiency. The integrated optic collects 5.8(8)% of the {\pi}
transition fluorescence, images the ion with sub-wavelength resolution, and
couples 71(5)% of the collected light into the fibre. Our technology is
suitable for entangling multiple ions in parallel and overcomes mode quality
limitations of existing integrated optical interconnects. In addition, the
efficiencies are sufficient for fault tolerant QIP.


title:
Randomized block proximal damped Newton method for composite
  self-concordant minimization

abstract:
  In this paper we consider the composite self-concordant (CSC) minimization
problem, which minimizes the sum of a self-concordant function $f$ and a
(possibly nonsmooth) proper closed convex function $g$. The CSC minimization is
the cornerstone of the path-following interior point methods for solving a
broad class of convex optimization problems. It has also found numerous
applications in machine learning. The proximal damped Newton (PDN) methods have
been well studied in the literature for solving this problem that enjoy a nice
iteration complexity. Given that at each iteration these methods typically
require evaluating or accessing the Hessian of $f$ and also need to solve a
proximal Newton subproblem, the cost per iteration can be prohibitively high
when applied to large-scale problems. Inspired by the recent success of block
coordinate descent methods, we propose a randomized block proximal damped
Newton (RBPDN) method for solving the CSC minimization. Compared to the PDN
methods, the computational cost per iteration of RBPDN is usually significantly
lower. The computational experiment on a class of regularized logistic
regression problems demonstrate that RBPDN is indeed promising in solving
large-scale CSC minimization problems. The convergence of RBPDN is also
analyzed in the paper. In particular, we show that RBPDN is globally convergent
when $g$ is Lipschitz continuous. It is also shown that RBPDN enjoys a local
linear convergence. Moreover, we show that for a class of $g$ including the
case where $g$ is Lipschitz differentiable, RBPDN enjoys a global linear
convergence. As a striking consequence, it shows that the classical damped
Newton methods [22,40] and the PDN [31] for such $g$ are globally linearly
convergent, which was previously unknown in the literature. Moreover, this
result can be used to sharpen the existing iteration complexity of these
methods.

categories: math.OC cs.LG cs.NA math.NA stat.CO stat.ML


title:
Closed-form expressions for projectors onto polyhedral sets in Hilbert
  spaces

abstract:
  We provide formulas for projectors onto a polyhedral set, i.e. the
intersection of a finite number of halfspaces. To this aim we formulate the
problem of finding the projection as a convex optimization problem and we solve
explicitly sufficient and necessary optimality conditions. This approach has
already been successfully applied in deriving formulas for projection onto the
intersection of two halfspaces. We also discuss possible generalizations to
Banach spaces.


title: On homogeneous locally conical spaces

abstract:
  The main result of this article is:
  THEOREM. Every homogeneous locally conical connected separable metric space
that is not a $1$-manifold is strongly $n$-homogeneous for each $n \geq 2$ and
countable dense homogeneous. Furthermore, countable dense homogeneity can be
proven without assuming the space is connected.
  This theorem has the following two consequences.
  COROLLARY 1. If $X$ is a homogeneous compact suspension, then $X$ is an
absolute suspension (i.e., for any two distinct points $p$ and $q$ of $X$,
there is a homeomorphism from $X$ to a suspension that maps $p$ and $q$ to the
suspension points).
  COROLLARY 2. If there exists a locally conical counterexample $X$ to the
Bing-Borsuk Conjecture (i.e., $X$ is a locally conical homogeneous Euclidean
neighborhood retract that is not a manifold), then $X$ is strongly
$n$-homogeneous for all $n \geq 2$ and countable dense homogeneous.


title:
An approximate stationary solution for multi-allele neutral diffusion
  with low mutation rates

abstract:
  We address the problem of determining the stationary distribution of the
multi-allelic, neutral-evolution Wright-Fisher model in the diffusion limit. A
full solution to this problem for an arbitrary K x K mutation rate matrix
involves solving for the stationary solution of a forward Kolmogorov equation
over a (K - 1)-dimensional simplex, and remains intractable. In most practical
situations mutations rates are slow on the scale of the diffusion limit and the
solution is heavily concentrated on the corners and edges of the simplex. In
this paper we present a practical approximate solution for slow mutation rates
in the form of a set of line densities along the edges of the simplex. The
method of solution relies on parameterising the general non-reversible rate
matrix as the sum of a reversible part and a set of (K - 1)(K - 2)/2
independent terms corresponding to fluxes of probability along closed paths
around faces of the simplex. The solution is potentially a first step in
estimat- ing non-reversible evolutionary rate matrices from observed allele
frequency spectra.


title: A Unified Analysis of Linear Quaternion Dynamic Equations on Time Scales

abstract:
  Over the last years, considerable attention has been paid to the role of the
quaternion differential equations (QDEs) which extend the ordinary differential
equations. The theory of QDEs was recently well established and it has wide
applications in physics and life science. This paper establishes a systematic
frame work for the theory of linear quaternion dynamic equations on time scales
(QDETS), which can be applied to wave phenomena modeling, fluid dynamics and
filter design. The algebraic structure of the solutions to the QDETS is
actually a left- or right- module, not a linear vector space. On the
non-commutativity of the quaternion algebra, many concepts and properties of
the classical dynamic equations on time scales (DETS) can not be applied. They
should be redefined accordingly. Using $q$-determinant, a novel definition of
Wronskian is introduced under the framework of quaternions which is different
from the standard one in DETS. Liouville's formula for QDETS is also analyzed.
Upon these, the solutions to the linear QDETS are established. The Putzer's
algorithms to evaluate the fundamental solution matrix for homogeneous QDETS
are presented. Furthermore, the variation of constants formula to solve the
nonhomogeneous QDETs is given. Some concrete examples are provided to
illustrate the feasibility of the proposed algorithms.


title: A note on extended Euclid's algorithm

abstract:
  Starting with the recursive extended Euclid's algorithm, we apply a
systematic approach using matrix notation to transform it into an iterative
algorithm. The partial correctness proof derived from the transformation turns
out to be very elegant, and easy to follow. The paper provides a connection
between recursive and iterative versions of extended Euclid's algorithm.


title:
Precise and diffraction-limited waveguide-to-free-space focusing
  gratings

abstract:
  We present the design and characterization of waveguide grating devices that
couple visible-wavelength light at $\lambda=674$ nm from single-mode, high
index-contrast dielectric waveguides to free-space beams forming micron-scale
diffraction-limited spots a designed distance and angle from the grating. With
a view to application in spatially-selective optical addressing, and in
contrast to previous work on similar devices, deviations from the main Gaussian
lobe up to $25$ microns from the focus and down to the $5\times10^{-6}$ level
in relative intensity are characterized as well; we show that along one
dimension the intensity of these weak sidelobes approaches the limit imposed by
diffraction from the finite field extent in the grating region. Additionally,
we characterize the polarization purity in the focal region, observing at the
center of the focus a low impurity $< 3 \times 10^{-4}$ in relative intensity.
Our approach allows quick, intuitive design of devices with such performance,
which may be applied in trapped-ion quantum information processing and
generally in any systems requiring optical routing to or from objects 10s--100s
of microns from a chip surface, but benefitting from the parallelism and
density of planar-fabricated dielectric integrated optics.


title: Dynamics of Vector Solitons in Bose-Einstein Condensates

abstract:
  We analyze the dynamics of two-component vector solitons, namely
bright-in-dark solitons, via the variational approximation in Bose-Einstein
condensates. The system is described by a vector nonlinear Schr\"odinger
equation appropriate to multi-component Bose-Einstein condensates (BECs). The
variational approximation is based on hyperbolic secant (hyperbolic tangent)
for the bright (dark) component, which leads to a system of coupled ordinary
differential equations for the evolution of the ansatz parameters. We obtain
the oscillation dynamics of two-component dark-bright vector solitons.
Analytical calculations are performed for same-width components in the vector
soliton and numerical calculations extend the results to arbitrary widths. We
calculate the binding energy of the system and find it proportional to the
intercomponent coupling interaction, and numerically demonstrate the break up
or unbinding of a dark-bright soliton. Our calculations explore observable
eigenmodes, namely the internal oscillation eigenmode and the Goldstone
eigenmode. We find analytically that the density of the bright component is
required to be less than the density of the dark component in order to find the
internal oscillation eigenmode of the vector soliton and support the existence
of the dark-bright soliton. This outcome is confirmed by numerical results.
Numerically, we find that the oscillation frequency is amplitude independent.
For dark-bright vector solitons in $^{87}$Rb we find that the oscillation
frequency range is 90 to 405 Hz, and therefore observable in multi-component
BEC experiments.


title:
Distinguishing between $s+id$ and $s+is$ pairing symmetries in multiband
  superconductors through spontaneous magnetization pattern induced by a defect

abstract:
  The symmetry of the pairing state in iron pnictide superconductor
$\mathrm{Ba_{1-x}K_xFe_2As_2}$ is still controversial. At optimal doping ($x
\approx 0.4$), it is very likely $s$-wave, but for $x=1$ there are experimental
and theoretical arguments for both $s$-wave and $d$-wave. Depending on the
choice for $x=1$, intermediate $s+is$ and $s+id$ states have been proposed for
intermediate doping $ 0.4 < x < 1$. In both states, the time reversal symmetry
is broken and a spontaneous magnetization is allowed. In this work we study a
spontaneous magnetization induced by a nonmagnetic defect in the $s+is$ and
$s+id$ states by using a perturbation theory and numerical calculations for the
Ginzburg-Landau free energy functional. We show that the angular dependence of
the magnetization is distinct in these two states due to the difference in
symmetry properties of the order parameters. Our results indicate a possible
way to distinguish between the $s+is$ and $s+id$ pairing symmetries in
multi-band superconductors.


title:
Combining Gradient Boosting Machines with Collective Inference to
  Predict Continuous Values

abstract:
  Gradient boosting of regression trees is a competitive procedure for learning
predictive models of continuous data that fits the data with an additive
non-parametric model. The classic version of gradient boosting assumes that the
data is independent and identically distributed. However, relational data with
interdependent, linked instances is now common and the dependencies in such
data can be exploited to improve predictive performance. Collective inference
is one approach to exploit relational correlation patterns and significantly
reduce classification error. However, much of the work on collective learning
and inference has focused on discrete prediction tasks rather than continuous.
%target values has not got that attention in terms of collective inference. In
this work, we investigate how to combine these two paradigms together to
improve regression in relational domains. Specifically, we propose a boosting
algorithm for learning a collective inference model that predicts a continuous
target variable. In the algorithm, we learn a basic relational model,
collectively infer the target values, and then iteratively learn relational
models to predict the residuals. We evaluate our proposed algorithm on a real
network dataset and show that it outperforms alternative boosting methods.
However, our investigation also revealed that the relational features interact
together to produce better predictions.


title:
Behavior of three modes of decay channels and their self-energies of
  elliptic dielectric microcavity

abstract:
  The Lamb shift (self-energy) of an elliptic dielectric microcavity is
studied. We show that the size of the Lamb shift, which is a small energy shift
due to the system-environment coupling in the quantum regime, is dependent on
the geometry of the boundary conditions. It shows a global transition depending
on the eccentricity of the ellipsis. These transitions can be classified into
three types of decay channels known as whispering-gallery modes,
stable-bouncing-ball modes, and unstable-bouncing-ball modes. These modes are
manifested through the Poincar\'{e} surface of section with the Husimi
distribution function in classical phase space. It is found that the similarity
(measured in Bhattacharyya distance) between the Husimi distributions below
critical lines of two different modes increases as the difference of their
self-energies decreases when the quality factors of the modes are on the same
order of magnitude.


title: The Chiral Potts Spin Glass in d=2 and 3 Dimensions

abstract:
  The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3
spatial dimensions by renormalization-group theory and the global phase
diagrams are calculated in temperature, chirality concentration p, and
chirality-breaking concentration c, with determination of phase chaos and
phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral,
right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to
the ferromagnetic, left- and right-chiral phases show, differently, an unusual,
fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral,
right-chiral, chiral spin-glass) ordered ordered phases, especially in the
multicritical region. The chaotic behavior of the interactions, under scale
change, are determined in the chiral spin-glass phase and on the boundary
between the chiral spin-glass and disordered phases, showing Lyapunov exponents
in magnitudes reversed from the usual ferromagnetic-antiferromagnetic
spin-glass systems. At low temperatures, the boundaries of the left- and
right-chiral phases become thresholded in p and c. In the d=2, the chiral
spin-glass system does not have a spin-glass phase, consistently with the
lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The
left- and right-chirally ordered phases show reentrance in chirality
concentration p.


title: Rigidity of composition operators on the Hardy space $H^p$

abstract:
  Let $\phi$ be an analytic map taking the unit disk $\mathbb{D}$ into itself.
We establish that the class of composition operators $f \mapsto C_\phi(f) = f
\circ \phi$ exhibits a rather strong rigidity of non-compact behaviour on the
Hardy space $H^p$, for $1\le p < \infty$ and $p \neq 2$. Our main result is the
following trichotomy, which states that exactly one of the following
alternatives holds: (i) $C_\phi$ is a compact operator $H^p \to H^p$, (ii)
$C_\phi$ fixes a (linearly isomorphic) copy of $\ell^p$ in $H^p$, but $C_\phi$
does not fix any copies of $\ell^2$ in $H^p$, (iii) $C_\phi$ fixes a copy of
$\ell^2$ in $H^p$. Moreover, in case (iii) the operator $C_\phi$ actually fixes
a copy of $L^p(0,1)$ in $H^p$ provided $p > 1$. We reinterpret these results in
terms of norm-closed ideals of the bounded linear operators on $H^p$, which
contain the compact operators $\mathcal K(H^p)$. In particular, the class of
composition operators on $H^p$ does not reflect the quite complicated lattice
structure of such ideals.


title: Microscopic Description of Diffractive Deuteron Breakup by He-3 Nuclei

abstract:
  A microscopic formalism for describing observed cross sections for deuteron
breakup by three-nucleon nuclei was developed on the basis of the diffraction
nuclear model. A general formula that describes the amplitude for the reaction
d+3He->3He+p+n and which involves only one adjustable parameter was obtained by
using expansions of the integrands involved in terms of a Gaussian basis. This
formula was used to analyze experimental data on the exclusive cross sections
for deuteron breakup by He-3 nuclei at the projectile energy of 89.4 MeV. The
importance of employing, in calculations, a deuteron wave function that has a
correct asymptotic behavior at large nucleon-nucleon distances was
demonstrated.


title:
NUV Star Catalogue from the Lunar-based Ultraviolet Telescope Survey.
  First Release

abstract:
  We present a star catalogue extracted from the Lunar-based Ultraviolet
Telescope (LUT) survey program. LUT's observable sky area is a circular belt
around the Moon's north pole, and the survey program covers a preferred area
for about 2400 deg$^2$ which includes a region of the Galactic plane. The data
is processed with an automatic pipeline which copes with stray light
contamination, artificial sources, cosmic rays, flat field calibration,
photometry and so on. In the first release version, the catalogue provides high
confidence sources which have been cross-identified with Tycho-2 catalogue. All
the sources have signal-to-noise ratio larger than 5, and the corresponding
magnitude limit is typically 14.4 mag, which can be deeper as ~16 mag if the
stray light contamination is in the lowest level. A total number of 86,467
stars are recorded in the catalogue. The full catalogue in electronic form is
available on line.