title: Ultimate Precision of Adaptive Noise Estimation

abstract:
  We consider the estimation of noise parameters in a quantum channel, assuming
the most general strategy allowed by quantum mechanics. This is based on the
exploitation of unlimited entanglement and arbitrary quantum operations, so
that the channel inputs may be interactively updated. In this general scenario
we draw a novel connection between quantum metrology and teleportation. In
fact, for any teleportation-covariant channel (e.g., Pauli, erasure, or
Gaussian channel), we find that adaptive noise estimation cannot beat the
standard quantum limit, with the quantum Fisher information being determined by
the channel's Choi matrix. As an example, we establish the ultimate precision
for estimating excess noise in a thermal-loss channel which is crucial for
quantum cryptography. Because our general methodology applies to any functional
which is monotonic under trace-preserving maps, it can be applied to simplify
other adaptive protocols, including those for quantum channel discrimination.
Setting the ultimate limits for noise estimation and discrimination paves the
way for exploring the boundaries of quantum sensing, imaging and tomography.


title: Thermally induced magnon accumulation in two-sublattice magnets

abstract:
  We present a temperature dependent study of the thermal excitation of
magnonic spin currents in two-sublattice magnetic materials. Using atomistic
spin model simulations, we study the local magnetization profiles in the
vicinity of a temperature step in antiferromagnets, as well as in ferrimagnets.
It is shown that the strength of the excitation of the spin currents in these
systems scales with the derivative of the magnetization with respect to the
temperature.


title:
Cu nuclear magnetic resonance study of charge and spin stripe order in
  La$_{1.875}$Ba$_{0.125}$CuO$_4$

abstract:
  We present a Cu nuclear magnetic/quadrupole resonance study of the charge
stripe ordered phase of LBCO, with detection of previously unobserved
('wiped-out') signal. We show that spin-spin and spin-lattice relaxation rates
are strongly enhanced in the charge ordered phase, explaining the apparent
signal decrease in earlier investigations. The enhancement is caused by
magnetic, rather than charge fluctuations, conclusively confirming the
long-suspected assumption that spin fluctuations are responsible for the
wipeout effect. Observation of the full Cu signal enables insight into the spin
and charge dynamics of the stripe-ordered phase, and measurements in external
magnetic fields provide information on the nature and suppression of spin
fluctuations associated with charge order. We find glassy spin dynamics, in
agreement with previous work, and incommensurate static charge order with
charge modulation amplitude similar to other cuprate compounds, suggesting that
the amplitude of charge stripes is universal in the cuprates.


title:
Dynamical Gauge Effects and Holographic Scaling of Non-Equilibrium
  Motion in a Disordered and Dissipative Atomic Gas

abstract:
  We present a table-top realization of a non-equilibrium quantum system
described by a dynamical gauge field propagating on an effectively curved space
and time manifold. The system is formed by neutral atoms interacting with both
a conservative disordered optical field and a dissipative pumping field. In the
presence of a sufficiently dark state, we demonstrate non-equilibrium behavior
reminiscent of the information paradox in black hole physics. At a well-defined
transition point, the analog of gauge-boson mass is seen to vanish, inducing
scale-invariant behavior as a Higgs-like mechanism is removed. The subsequent
scaling behavior can be understood using the holographic principle with a
tunable analog of the Planck length derived from the scaling of disorder. These
effects suggest a range of new phenomena in weakly dissipative quantum systems,
including the presence of analog forms of emergent gravitation.


title:
Motion of solitons in one-dimensional spin-orbit-coupled Bose-Einstein
  condensates

abstract:
  Solitons play a fundamental role in dynamics of nonlinear excitations. Here
we explore the motion of solitons in one-dimensional uniform Bose-Einstein
condensates subjected to a spin-orbit coupling (SOC). We demonstrate that the
spin dynamics of solitons is governed by a nonlinear Bloch equation. The spin
dynamics influences the orbital motion of the solitons leading to the
spin-orbit effects in the dynamics of the macroscopic quantum objects
(mean-field solitons). The latter perform oscillations with a frequency
determined by the SOC, Raman coupling, and intrinsic nonlinearity. These
findings reveal unique features of solitons affected by the SOC, which is
confirmed by analytical considerations and numerical simulations of the
underlying Gross-Pitaevskii equations.


title: A conformal block Farey tail

abstract:
  We investigate the constraints of crossing symmetry on CFT correlation
functions. Four point conformal blocks are naturally viewed as functions on the
upper-half plane, on which crossing symmetry acts by PSL(2,Z) modular
transformations. This allows us to construct a unique, crossing symmetric
function out of a given conformal block by averaging over PSL(2,Z). In some two
dimensional CFTs the correlation functions are precisely equal to the modular
average of the contributions of a finite number of light states. For example,
in the two dimensional Ising and tri-critical Ising model CFTs, the correlation
functions of identical operators are equal to the PSL(2,Z) average of the
Virasoro vacuum block; this determines the 3 point function coefficients
uniquely in terms of the central charge. The sum over PSL(2,Z) in CFT2 has a
natural AdS3 interpretation as a sum over semi-classical saddle points, which
describe particles propagating along rational tangles in the bulk. We
demonstrate this explicitly for the correlation function of certain heavy
operators, where we compute holographically the semi-classical conformal block
with a heavy internal operator.


title: Planar harmonic and monogenic polynomials of type A

abstract:
  Harmonic polynomials of type A are polynomials annihilated by the Dunkl
Laplacian associated to the symmetric group acting as a reflection group on
$\mathbb{R}^{N}$. The Dunkl operators are denoted by $T_{j}$ for $1\leq j\leq
N$, and the Laplacian $\Delta_{\kappa}=\sum_{j=1}^{N}T_{j}^{2}$. This paper
finds the homogeneous harmonic polynomials annihilated by all $T_{j}$ for
$j>2$. The structure constants with respect to the Gaussian and sphere inner
products are computed. These harmonic polynomials are used to produce monogenic
polynomials, those annihilated by a Dirac-type operator.


title: Thermodynamics of anisotropic branes

abstract:
  We study the thermodynamics of flavor D7-branes embedded in an anisotropic
black brane solution of type IIB supergravity. The flavor branes undergo a
phase transition between a `Minkowski embedding', in which they lie outside of
the horizon, and a `black hole embedding', in which they fall into the horizon.
This transition depends on the black hole temperature, its degree of
anisotropy, and the mass of the flavor degrees of freedom. It happens either at
a critical temperature or at a critical anisotropy. A general lesson we learn
from this analysis is that the anisotropy, in this particular realization,
induces similar effects as the temperature. In particular, increasing the
anisotropy bends the branes more and more into the horizon. Moreover, we
observe that the transition becomes smoother for higher anisotropies.


title: Strongness of companion bases for cluster-tilted algebras of finite type

abstract:
  For every cluster-tilted algebra of simply-laced Dynkin type we provide a
companion basis which is strong, i.e. gives the set of dimension vectors of the
finitely generated indecomposable modules for the cluster-tilted algebra. This
shows in particular that every companion basis of a cluster-tilted algebra of
simply-laced Dynkin type is strong. Thus we give a proof of Parsons's
conjecture.


title:
Secret key capacity of the thermal-loss channel: Improving the lower
  bound

abstract:
  We consider the secret key capacity of the thermal loss channel, which is
modeled by a beam splitter mixing an input signal mode with an environmental
thermal mode. This capacity is the maximum value of secret bits that two remote
parties can generate by means of the most general adaptive protocols assisted
by unlimited and two-way classical communication. To date, only upper and lower
bounds are known. The present work improves the lower bound by resorting to
Gaussian protocols based on suitable trusted-noise detectors.


title: Metrological measures of non-classical correlations

abstract:
  Non-classical correlations denote the ways in which quantum systems can be
correlated beyond what is possible in classical physics. They include but are
not limited to entanglement: non-entangled states can also exhibit forms of
non-classical correlations. We here review the literature on metrological
measures of non-classical correlations and show how they relate to increased
probe sensitivity in quantum metrology protocols such as interferometric
parameter estimation and state discrimination.


title:
The Effect of Class Imbalance and Order on Crowdsourced Relevance
  Judgments

abstract:
  In this paper we study the effect on crowd worker efficiency and
effectiveness of the dominance of one class in the data they process. We aim at
understanding if there is any positive or negative bias in workers seeing many
negative examples in the identification of positive labels. To test our
hypothesis, we design an experiment where crowd workers are asked to judge the
relevance of documents presented in different orders. Our findings indicate
that there is a significant improvement in the quality of relevance judgements
when presenting relevant results before the non-relevant ones.


title:
The New Phase due to Symmetry Protected Piecewise Berry Phases; Enhanced
  Pumping and Non-reciprocity in Trimer Lattices

abstract:
  Finding new phase is a fundamental task in physics. Landau's theory explained
the deep connection between symmetry breaking and phase transition commonly
occurring in magnetic, superconducting and super uid systems. The discovery of
the quantum Hall effect led to Z topological phases which could be different
for same symmetry and are characterized by the discrete values of the Berry
phases. By studying 1D trimer lattices we report new phases characterized by
Berry phases which are piecewise continuous rather than discrete numbers. The
phase transition occurs at the discontinuity point. With time-dependent
changes, trimer lattices also give a 2D phases characterized by very specific
2D Berry phases of half period. These Berry phases change smoothly within a
phase while change discontinuously at the transition point. We further
demonstrate the existence of adiabatic pumping for each phase and gain assisted
enhanced pumping. The non-reciprocity of the pumping process makes the system a
good optical diode.


title:
Asymptotic stability of strong contact discontinuity for full
  compressible Navier-Stokes equations with initial boundary value problem

abstract:
  This paper is concerned with Dirichlet problem $u(0,t)=0$,
$\theta(0,t)=\theta_-$ for one-dimensional full compressible Navier-Stokes
equations in the half space $\R_+=(0,+\infty)$. Because the boundary decay rate
is hard to control, stability of contact discontinuity result is very
difficult. In this paper, we raise the decay rate and establish that for a
certain class of large perturbation, the asymptotic stability result is contact
discontinuity. Also, we ask the strength of contact discontinuity not small.
The proofs are given by the elementary energy method.


title:
Distributed sampled-data control of nonholonomic multi-robot systems
  with proximity networks

abstract:
  This paper considers the distributed sampled-data control problem of a group
of mobile robots connected via distance-induced proximity networks. A dwell
time is assumed in order to avoid chattering in the neighbor relations that may
be caused by abrupt changes of positions when updating information from
neighbors. Distributed sampled-data control laws are designed based on nearest
neighbour rules, which in conjunction with continuous-time dynamics results in
hybrid closed-loop systems. For uniformly and independently initial states, a
sufficient condition is provided to guarantee synchronization for the system
without leaders. In order to steer all robots to move with the desired
orientation and speed, we then introduce a number of leaders into the system,
and quantitatively establish the proportion of leaders needed to track either
constant or time-varying signals. All these conditions depend only on the
neighborhood radius, the maximum initial moving speed and the dwell time,
without assuming a prior properties of the neighbor graphs as are used in most
of the existing literature.


title:
Tauberian theorems for general iterations of operators: applications to
  zero-sum stochastic games

abstract:
  This paper proves several Tauberian theorems for general iterations of
operators, and provides two applications to zero-sum stochastic games where the
total payoff is a weighted sum of the stage payoffs. The first application is
to provide conditions under which the existence of the asymptotic value implies
the convergence of the values of the weighted game, as players get more and
more patient. The second application concerns stochastic games with finite
state space and action sets. This paper builds a simple class of asymptotically
optimal strategies in the weighted game, that at each stage play optimally in a
discounted game with a discount factor corresponding to the relative weight of
the current stage.


title:
Transverse Thermoelectric Response as a Probe for Existence of
  Quasiparticles

abstract:
  The electrical Hall conductivities of any anisotropic interacting system with
reflection symmetry obey sigma_{xy} = - sigma_{yx}. In contrast, we show that
the analogous relation between the transverse thermoelectric Peltier
coefficients, alpha_{xy}= - alpha_{yx}, does not generally hold in the same
system. This fact may be traced to interaction contributions to the heat
current operator and the mixed nature of the thermoelectric response functions.
Remarkably, however, it appears that emergence of quasiparticles at low
temperatures forces alpha_{xy} = - alpha_{yx}. This suggests that
quasiparticle-free groundstates (so-called non-Fermi liquids) may be detected
by examining the relationship between alpha_{xy} and alpha_{yx} in the presence
of reflection symmetry and microscopic anisotropy. These conclusions are based
on the following results: (i) The relation between the Peltier coefficients is
exact for elastically scattered noninteracting particles; (ii) It holds
approximately within Boltzmann theory for interacting particles when elastic
scattering dominates over inelastic processes. In a disordered Fermi liquid the
latter lead to deviations that vanish as T^3. (iii) We calculate the
thermoelectric response in a model of weakly-coupled spin-gapped Luttinger
liquids and obtain strong breakdown of antisymmetry between the off-diagonal
components of alpha. We also find that the Nernst signal in this model is
enhanced by interactions and can change sign as function of magnetic field and
temperature.


title: On Z/3-Godeaux surfaces

abstract:
  We prove that Godeaux--Reid surfaces with torsion group Z/3 have topological
fundamental group Z/3. For this purpose, we describe degenerations to stable
KSBA surfaces with one 1/4(1,1) singularity, whose minimal resolution are
elliptic fibrations with two multiplicity 3 fibres and one I_4 singular fibre.
We study special such degenerations which have an involution, describing the
corresponding Campedelli double plane construction. We also find some stable
rational degenerations, some of which have more singularities, and one of which
has a single 1/9(1,2) singularity, the minimal possible index for such a
surface. Finally, we do the analogous study for the Godeaux surfaces with
torsion Z/4.


title: The environment of radio sources in the VLA-COSMOS Survey field

abstract:
  This work studies the correlation among environmental density and radio AGN
presence up to $z = 2$. Using data from the photometric COSMOS survey and its
radio 1.4 GHz follow-up (VLA-COSMOS), a sample of radio AGNs has been defined.
The environment was studied using the richness distributions inside a
parallelepiped with base side of 1 Mpc and height proportional to the
photometric redshift precision. Radio AGNs are found to be always located in
environments significantly richer than those around galaxies with no radio
emission. Moreover, a distinction based on radio AGN power shows that the
significance of the environmental effect is only maintained for low-power radio
sources. The results of this work show that denser environments play a
significant role in enhancing the probability that a galaxy hosts a radio AGN
and, in particular, low-power ones.


title: Robustness of DC Power Networks under Weight Control

abstract:
  We study, possibly distributed, robust weight control policies for DC power
networks that change link susceptances, or weights in response to balanced
disturbances to the supply-demand vector. The margin of robustness for a given
control policy is defined as the radius of the largest $l_1$ ball in the space
of balanced disturbances under which the link flows can be asymptotically
contained within their specified limits. For centralized control policies, the
control design as well as margin of robustness are obtained from solution to an
non-convex weight control problem. We establish relationship between feasible
sets for DC power flow and associated network flow, which is used to establish
an upper bound on the margin of robustness in terms of the min cut capacity.
This bound is proven to be tight if the network is tree-like, or if the lower
bound of the operation range of weight control is zero. An explicit expression
for the flow-weight Jacobian is derived and is used to devise a projected
sub-gradient algorithm to solve the relaxed weight control problem. An exact
multi-level programming approach to solve the weight control problem for
reducible networks, based on recursive application of equivalent bilevel
formulation for relevant class of non-convex network optimization problems, is
also proposed. The lower level problem in each recursion corresponds to
replacing a sub-network by a (virtual) link with equivalent weight and
capacities. The equivalent capacity function for tree-reducible networks is
shown to possess a strong quasi-concavity property, facilitating easy solution
to the weight control problem. Robustness analysis for natural decentralized
control policies that decrease weights on overloaded links, and increase
weights on underloaded links with increasing flows is provided for parallel
networks. Illustrative simulation results for a benchmark IEEE network are
included.


title:
Phase transitions in definite total spin states of two-component Fermi
  gases

abstract:
  Second-order phase transitions have no latent heat and are characterized by a
change in symmetry. In addition to the conventional symmetric and
anti-symmetric states under permutations of bosons and fermions, mathematical
group-representation theory allows for non-Abelian permutation symmetry. Such
symmetry can be hidden in states with defined total spins of spinor gases,
which can be formed in optical cavities. The present work shows that the
symmetry reveals itself in spin-independent or coordinate-independent
properties of these gases, namely as non-Abelian entropy in thermodynamic
properties. In weakly interacting Fermi gases, two phases appear associated
with fermionic and non-Abelian symmetry under permutations of particle states,
respectively. The second-order transitions between the phases are characterized
by discontinuities in specific heat. Unlike other phase transitions, the
present ones are not caused by interactions and can appear even in ideal gases.
Similar effects in Bose gases and strong interactions are discussed.

categories: cond-mat.quant-gas cond-mat.stat-mech physics.atom-ph quant-ph


title:
Geometry and a natural symplectic structure of phase tropical
  hypersurfaces

abstract:
  First, we define phase tropical hypersurfaces in terms of a degeneration data
of smooth complex algebraic hypersurfaces in $(\mathbb{C}^*)^n$. Next, we prove
that complex hyperplanes are diffeomorphic to their degeneration called phase
tropical hyperplanes. More generally, using Mikhalkin's decomposition into
pairs-of-pants of smooth algebraic hypersurfaces, we show that phase tropical
hypersurfaces with smooth tropicalization, possess naturally a smooth
differentiable structure. Moreover, we prove that phase tropical hypersurfaces
possess a natural symplectic structure.


title: Feedback and Timing in a Crowdsourcing Game

abstract:
  The present research examines two problems inherent to the creation of
crowdsourcing games: how to give feedback when the right answer is not always
known by the game and how much time to give players without sacrificing data
quality. Taken together, the present research provides an important first step
in considering how to create fun, challenging crowdsourcing games that generate
quality data.


title:
Experimental radiative lifetimes for highly excited states and
  calculated oscillator strengths for lines of astrophysical interest in singly
  ionized cobalt (Co II)

abstract:
  This work reports new experimental radiative lifetimes and calculated
oscillator strengths for transitions of astrophysical interest in singly
ionized cobalt. More precisely, nineteen radiative lifetimes in Co+ have been
measured with the time-resolved laser-induced fluorescence technique using one-
and two-step excitations. Out of these, seven belonging to the high lying
3d$^7$($^4$F)4d configuration in the energy range 90697 - 93738 cm$^{-1}$ are
new, and the other twelve from th3d$^7$($^4$F)F)4p configuration with energies
between 45972 and 49328 cm$^{-1}$1 are compared with previous measurements. In
addition, a relativistic Hartree-Fock model including core-polarization effects
has been employed to compute transition rates. Supported by the good agreement
between theory and experiment for the lifetimes, new reliable transition
probabilities and oscillator strengths have been deduced for 5080 Co II
transitions in the spectral range 114 - 8744 nm.


title: Linear orbits of alternating forms on real vector spaces

abstract:
  In this note we complete the calculation of the number of $GL(\mathbb
R^n)$-orbits on $\Lambda^k(\mathbb R^n)^*$, by treating the cases $(n,k)=
(7,4)$ and $(8,5)$ not covered in the literature. We also calculate the number
of of non-degenerate and stable orbits, as they are of special interest to
multisymplectic and special geometry.


title:
Observational Confirmation of a Link Between Common Envelope Binary
  Interaction and Planetary Nebula Shaping

abstract:
  A current issue in the study of planetary nebulae with close binary central
stars is the extent to which the binaries affect the shaping of the nebulae.
Recent studies have begun to show a high coincidence rate between nebulae with
large-scale axial or point symmetries and close binary stars. In addition,
combined binary-star and spatio-kinematic modeling of the nebulae have
demonstrated that all of the systems studied to date appear to have their
central binary axis aligned with the primary axis of the nebula. Here we add
two more systems to the list, the central stars and nebulae of NGC 6337 and Sp
1. We show both systems to be low inclination, with their binary axis nearly
aligned with our line-of-sight. Their inclinations match published values for
the inclinations of their surrounding nebulae. Including these two systems with
the existing sample statistically demonstrates a direct link between the
central binary and the nebular morphology. In addition to the systems'
inclinations we give ranges for other orbital parameters from binary modeling,
including updated orbital periods for the binary central stars of NGC 6337 and
Sp 1.


title: Bayes Factors via Savage-Dickey Supermodels

abstract:
  We outline a new method to compute the Bayes Factor for model selection which
bypasses the Bayesian Evidence. Our method combines multiple models into a
single, nested, Supermodel using one or more hyperparameters. Since the models
are now nested the Bayes Factors between the models can be efficiently computed
using the Savage-Dickey Density Ratio (SDDR). In this way model selection
becomes a problem of parameter estimation. We consider two ways of constructing
the supermodel in detail: one based on combined models, and a second based on
combined likelihoods. We report on these two approaches for a Gaussian linear
model for which the Bayesian evidence can be calculated analytically and a toy
nonlinear problem. Unlike the combined model approach, where a standard Monte
Carlo Markov Chain (MCMC) struggles, the combined-likelihood approach fares
much better in providing a reliable estimate of the log-Bayes Factor. This
scheme potentially opens the way to computationally efficient ways to compute
Bayes Factors in high dimensions that exploit the good scaling properties of
MCMC, as compared to methods such as nested sampling that fail for high
dimensions.


title: Memory Erasure using Time Multiplexed Potentials

abstract:
  We study the thermodynamics of a Brownian particle under the influence of a
time multiplexed harmonic potential of finite width. The memory storage
mechanism and the erasure protocol realized by time multiplexed potentials are
utilized to experimentally realize erasure with work close to the Landauer's
bound. We quantify the work done on the system with respect to the duty-ratio
of time multiplexing, which also provides a handle to approach reversible
erasures. A Langevin dynamics based simulation model is developed for the
proposed memory bit and the erasure protocol, which guides the experimental
realization. The study also provides insights into transport at the micro
scale.


title: Axial Vector $Z'$ and Anomaly Cancellation

abstract:
  Whilst the prospect of new $Z'$ gauge bosons with only axial couplings to the
Standard Model (SM) fermions is widely discussed, examples of anomaly-free
renormalisable models are lacking in the literature. We look to remedy this by
constructing several motivated examples. Specifically, we consider axial
vectors which couple universally to all SM fermions, as well as those which are
generation-specific, leptophilic, and leptophobic. Anomaly cancellation
typically requires the presence of new coloured and charged chiral fermions,
and we argue that in a large class of models masses of these new states are
expected to be comparable to that of the axial vector. Finally, an axial vector
mediator could provide a portal between SM and hidden sector states, and we
also consider the possibility that the axial vector couples to dark matter. If
the dark matter relic density is set due to freeze-out via the axial vector,
this strongly constrains the parameter space.


title:
Oscillation estimates of eigenfunctions via the combinatorics of
  noncrossing partitions

abstract:
  We study oscillations in the eigenfunctions for a fractional Schr\"odinger
operator on the real line. An argument in the spirit of Courant's nodal domain
theorem applies to an associated local problem in the upper half plane and
provides a bound on the number of nodal domains for the extensions of the
eigenfunctions. Using the combinatorial properties of noncrossing partitions,
we turn the nodal domain bound into an estimate for the number of sign changes
in the eigenfunctions. We discuss applications in the periodic setting and the
Steklov problem on planar domains.


title: Modeling the cryosphere with FEniCS

abstract:
  This manuscript is a collection of problems and solutions related to modeling
the cryosphere using the finite element software FEniCS. Included is an
introduction to the finite element method; solutions to a variety of problems
in one, two, and three dimensions; an overview of popular stabilization
techniques for numerically-unstable problems; and an introduction to the
governing equations of ice-sheet dynamics with associated FEniCS
implementations. The software developed for this project, Cryospheric Problem
Solver (CSLVR), is fully open-source and has been designed with the goal of
simplifying many common tasks associated with modeling the cryosphere. CSLVR
possesses the ability to download popular geological and geographical data,
easily convert between geographical projections, develop sophisticated two- or
three-dimensional finite-element meshes, convert data between many popular
formats, and produce production-quality images of data. Scripts are presented
which model the flow of ice using geometry defined by mathematical functions
and observed Antarctic and Greenland ice-sheets data. A new way of solving the
internal energy distribution of ice to match observed intra-ice water contents
within temperate regions is thoroughly explained.


title:
Online Learning for Sparse PCA in High Dimensions: Exact Dynamics and
  Phase Transitions

abstract:
  We study the dynamics of an online algorithm for learning a sparse leading
eigenvector from samples generated from a spiked covariance model. This
algorithm combines the classical Oja's method for online PCA with an
element-wise nonlinearity at each iteration to promote sparsity. In the
high-dimensional limit, the joint empirical measure of the underlying sparse
eigenvector and its estimate provided by the algorithm is shown to converge
weakly to a deterministic, measure-valued process. This scaling limit is
characterized as the unique solution of a nonlinear PDE, and it provides exact
information regarding the asymptotic performance of the algorithm. For example,
performance metrics such as the cosine similarity and the misclassification
rate in sparse support recovery can be obtained by examining the limiting
dynamics. A steady-state analysis of the nonlinear PDE also reveals an
interesting phase transition phenomenon. Although our analysis is asymptotic in
nature, numerical simulations show that the theoretical predictions are
accurate for moderate signal dimensions.


title:
Surface single-molecule dynamics controlled by entropy at low
  temperatures

abstract:
  Configuration transitions of individual molecules and atoms on surfaces are
traditionally described with energy barriers and attempt rates using an
Arrhenius law. This approach yields consistent energy barrier values, but also
attempt rates orders of magnitude below expected oscillation frequencies of
particles in the meta-stable state. Moreover, even for identical systems, the
measurements can yield values differing from each other by orders of magnitude.
Using low temperature scanning tunnelling microscopy (STM) to measure an
individual dibutyl-sulfide molecule (DBS) on Au(111), we show that we can avoid
these apparent inconsistencies if we account for the relative position of tip
apex and molecule with accuracy of a fraction of the molecule size. Altering
the tip position on that scale modifies the transition's barrier and attempt
rate in a highly correlated fashion, which on account of the relation between
the latter and entropy results in a single-molecular enthalpy-entropy
compensation. By appropriately positioning the tip apex the STM tip can be used
to select the operating point on the compensation line and modify the
transition rates. The results highlight the need to consider entropy in
transition rates of a single molecule, even at temperatures where entropy
effects are usually neglected.


title: Energy Transparency for Deeply Embedded Programs

abstract:
  Energy transparency is a concept that makes a program's energy consumption
visible, from hardware up to software, through the different system layers.
Such transparency can enable energy optimizations at each layer and between
layers, and help both programmers and operating systems make energy-aware
decisions. In this paper, we focus on deeply embedded devices, typically used
for Internet of Things (IoT) applications, and demonstrate how to enable energy
transparency through existing Static Resource Analysis (SRA) techniques and a
new target-agnostic profiling technique, without hardware energy measurements.
Our novel mapping technique enables software energy consumption estimations at
a higher level than the Instruction Set Architecture (ISA), namely the LLVM
Intermediate Representation (IR) level, and therefore introduces energy
transparency directly to the LLVM optimizer. We apply our energy estimation
techniques to a comprehensive set of benchmarks, including single- and also
multi-threaded embedded programs from two commonly used concurrency patterns,
task farms and pipelines. Using SRA, our LLVM IR results demonstrate a high
accuracy with a deviation in the range of 1% from the ISA SRA. Our profiling
technique captures the actual energy consumption at the LLVM IR level with an
average error of 3%.


title:
Corrective Control to Handle Forecast Uncertainty: A Chance Constrained
  Optimal Power Flow

abstract:
  Higher shares of electricity generation from renewable energy sources and
market liberalization is increasing uncertainty in power systems operation. At
the same time, operation is becoming more flexible with improved control
systems and new technology such as phase shifting transformers (PSTs) and high
voltage direct current connections (HVDC). Previous studies have shown that the
use of corrective control in response to outages contributes to a reduction in
operating cost, while maintaining N-1 security. In this work, we propose a
method to extend the use of corrective control of PSTs and HVDCs to react to
uncertainty. We characterize the uncertainty as continuous random variables,
and define the corrective control actions through affine control policies. This
allows us to efficiently model control reactions to a large number of
uncertainty sources. The control policies are then included in a chance
constrained optimal power flow formulation, which guarantees that the system
constraints are enforced with a desired probability. By applying an analytical
reformulation of the chance constraints, we obtain a second-order cone problem
for which we develop an efficient solution algorithm. In a case study for the
IEEE 118 bus system, we show that corrective control for uncertainty leads to a
decrease in operational cost, while maintaining system security. Further, we
demonstrate the scalability of the method by solving the problem for the IEEE
300 bus and the Polish system test cases.


title:
Einstein's $R^{\hat{0} \hat{0}}$ equation for non-relativistic sources
  derived from Einstein's inertial motion and the Newtonian law for relative
  acceleration

abstract:
  With Einstein's inertial motion (free-falling and non-rotating relative to
gyroscopes), geodesics for non-relativistic particles can intersect repeatedly,
allowing one to compute the space-time curvature $R^{\hat{0} \hat{0}}$ exactly.
Einstein's $R^{\hat{0} \hat{0}}$ for strong gravitational fields and for
relativistic source-matter is identical with the Newtonian expression for the
relative radial acceleration of neighboring free-falling test-particles,
spherically averaged.--- Einstein's field equations follow from Newtonian
experiments, local Lorentz-covariance, and energy-momentum conservation
combined with the Bianchi identity.


title: Conformal covariance and the split property

abstract:
  We show that for a conformal local net of observables on the circle, the
split property is automatic. Both full conformal covariance (i.e.
diffeomorphism covariance) and the circle-setting play essential roles in this
fact, while by previously constructed examples it was already known that even
on the circle, M\"obius covariance does not imply the split property.
  On the other hand, here we also provide an example of a local conformal net
living on the two-dimensional Minkowski space, which - although being
diffeomorphism covariant - does not have the split property.


title:
Pilot Contamination Attack Detection by Key-Confirmation in Secure MIMO
  Systems

abstract:
  Many security techniques working at the physical layer need a correct channel
state information (CSI) at the transmitter, especially when devices are
equipped with multiple antennas. Therefore such techniques are vulnerable to
pilot contamination attacks (PCAs) by which an attacker aims at inducing false
CSI. In this paper we provide a solution to some PCA methods, by letting two
legitimate parties to compare their channel estimates. The comparison is made
in order to minimize the information leakage on the channel to a possible
attacker. By reasonable assumptions on both the channel knowledge by the
attacker and the correlation properties of the attacker and legitimate channels
we show the validity of our solution. An accurate analysis of possible attacks
and countermeasures is provided, together with a numerical evaluation of the
attainable secrecy outage probability when our solution is used in conjunction
with beamforming for secret communications.


title:
Sequential Linear Quadratic Optimal Control for Nonlinear Switched
  Systems

abstract:
  In this contribution, we introduce an efficient method for solving the
optimal control problem for an unconstrained nonlinear switched system with an
arbitrary cost function. We assume that the sequence of the switching modes are
given but the switching time in between consecutive modes remains to be
optimized. The proposed method uses a two-stage approach as introduced by Xu
and Antsaklis (2004) where the original optimal control problem is transcribed
into an equivalent problem parametrized by the switching times and the optimal
control policy is obtained based on the solution of a two-point boundary value
differential equation. The main contribution of this paper is to use a
Sequential Linear Quadratic approach to synthesize the optimal controller
instead of solving a boundary value problem. The proposed method is numerically
more efficient and scales very well to the high dimensional problems. In order
to evaluate its performance, we use two numerical examples as benchmarks to
compare against the baseline algorithm. In the third numerical example, we
apply the proposed algorithm to the Center of Mass control problem in a
quadruped robot locomotion task.


title: Localization and Fractionalization in a Chain of Rotating Atomic Gases

abstract:
  We describe the phase diagram and thermodynamic properties of a chain of
axially-tunnel-coupled fractional quantum Hall systems realized by rotating a
series of optical dipole traps about their center. We demonstrate not only a
experimentally feasible pathway to a state describable as a Mott-insulator of
composite bosons, but also describe the nature of the coherent states at higher
tunnel coupling strength, and identify a series of new superfluid phases with
rich behavior. The phase diagram directly reveals not only characteristic
features of the few-body systems, including the effective mass of composite
particle- and hole-like excitations and their interactions, but emergent
properties of the chain also reveal a fundamental mapping between the adiabatic
dynamics of two dimensional systems governed by particle braiding and the
hydrostatic response of the gas in the conducting phases.


title: Discrete Variational Autoencoders

abstract:
  Probabilistic models with discrete latent variables naturally capture
datasets composed of discrete classes. However, they are difficult to train
efficiently, since backpropagation through discrete variables is generally not
possible. We present a novel method to train a class of probabilistic models
with discrete latent variables using the variational autoencoder framework,
including backpropagation through the discrete latent variables. The associated
class of probabilistic models comprises an undirected discrete component and a
directed hierarchical continuous component. The discrete component captures the
distribution over the disconnected smooth manifolds induced by the continuous
component. As a result, this class of models efficiently learns both the class
of objects in an image, and their specific realization in pixels, from
unsupervised data, and outperforms state-of-the-art methods on the
permutation-invariant MNIST, Omniglot, and Caltech-101 Silhouettes datasets.


title: Chemical abundances for A-and F-type supergiant stars

abstract:
  We present the stellar parameters and elemental abundances of a set of
A--F-type supergiant stars HD\,45674, HD\,180028, HD\,194951 and HD\,224893
using high resolution ($R$\,$\sim$\,42,000) spectra taken from ELODIE library.
We present the first results of the abundance analysis for HD\,45674 and
HD\,224893. We reaffirm the abundances for HD\,180028 and HD\,194951 studied
previously by Luck (2014) respectively. Alpha-elements indicates that objects
belong to the thin disc population. From their abundances and its location on
the Hertzsprung-Russell diagram seems point out that HD\,45675, HD\,194951 and
HD\,224893 are in the post-first dredge-up (post-1DUP) phase and they are
moving in the red-blue loop region. HD~180028, on the contary, shows typical
abundances of the population I but its evolutionary status could not be
satisfactorily defined.


title: Deconstructing Odorant Identity via Primacy in Dual Networks

abstract:
  In the olfactory system, odor percepts retain their identity despite
substantial variations in concentration, timing, and background. We propose a
novel strategy for encoding intensity-invariant stimuli identity that is based
on representing relative rather than absolute values of the stimulus features.
Because, in this scheme, stimulus identity depends on relative amplitudes of
stimulus features, identity becomes invariant with respect to variations in
intensity and monotonous non-linearities of neuronal responses. In the
olfactory system, stimulus identity can be represented by the identities of the
p strongest responding odorant receptor types out of a species dependent
complement. We show that this information is sufficient to recover sparse
stimuli (odorants) via elastic net loss minimization. Such a minimization has
to be performed under constraints imposed by the relationships between stimulus
features. We map this problem onto the dual problem of minimizing a functional
of Lagrange multipliers. The dual problem, in turn, can be solved by a neural
network whose Lyapunov function represents the dual Lagrangian. We thus propose
that networks in the piriform cortex compute odorant identity and implement
dual computations with the sparse activities of individual neurons representing
the Lagrange multipliers.


title:
First NuSTAR observations of the BL Lac - type blazar PKS~2155-304:
  constraints on the jet content and distribution of radiating particles

abstract:
  We report the first hard X-ray observations with NuSTAR of the BL Lac type
blazar PKS 2155-304, augmented with soft X-ray data from XMM-Newton and
gamma-ray data from the Fermi Large Area Telescope, obtained in April 2013 when
the source was in a very low flux state. A joint NuSTAR and XMM spectrum,
covering the energy range 0.5 - 60 keV, is best described by a model consisting
of a log-parabola component with curvature beta = 0.3(+0.2,-0.1) and a (local)
photon index 3.04 +/- 0.15 at photon energy of 2 keV, and a hard power-law tail
with photon index 2.2 +/- 0.4. The hard X-ray tail can be smoothly joined to
the quasi-simultaneous gamma-ray spectrum by a synchrotron self-Compton
component produced by an electron distribution with index p = 2.2. Assuming
that the power-law electron distribution extends down to the minimum electron
Lorentz factor gamma_min = 1 and that there is one proton per electron, an
unrealistically high total jet power L_p of roughly 10^47 erg/s is inferred.
This can be reduced by two orders of magnitude either by considering a
significant presence of electron-positron pairs with lepton-to-proton ratio of
at least 30, or by introducing an additional, low-energy break in the electron
energy distribution at the electron Lorentz factor gamma_br1 of roughly 100. In
either case, the jet composition is expected to be strongly matter-dominated.


title:
A comprehensive search for stellar bowshock nebulae in the Milky Way: a
  catalog of 709 mid-infrared selected candidates

abstract:
  We identify 709 arc-shaped mid-infrared nebula in 24 micron Spitzer Space
Telescope or 22 micron Wide Field Infrared Explorer surveys of the Galactic
Plane as probable dusty interstellar bowshocks powered by early-type stars.
About 20% are visible at 8 microns or shorter mid-infrared wavelengths as well.
The vast majority (660) have no previous identification in the literature.
These extended infrared sources are strongly concentrated near Galactic
mid-Plane with an angular scale height of ~0.6 degrees. All host a
symmetrically placed star implicated as the source of a stellar wind sweeping
up interstellar material. These are candidate "runaway" stars potentially
having high velocities in the reference frame of the local medium. Among the
286 objects with measured proper motions, we find an unambiguous excess having
velocity vectors aligned with the infrared morphology --- kinematic evidence
that many of these are "runaway" stars with large peculiar motions responsible
for the bowshock signature. We discuss a population of "in-situ" bowshocks (103
objects) that face giant HII regions where the relative motions between the
star and ISM may be caused by bulk outflows from an overpressured bubble. We
also identify 58 objects that face 8 micron bright-rimmed clouds and apparently
constitute a sub-class of in-situ bowshocks where the stellar wind interacts
with a photo-evaporative flow from an eroding molecular cloud interface (i.e.,
"PEF bowshocks"). Orientations of the arcuate nebulae exhibit a correlation
over small angular scales, indicating that external influences such as HII
regions are responsible for producing some bowshock nebulae. However, the vast
majority of this sample appear to be isolated (499 objects) from obvious
external influences.


title: On the Determination of Star Bodies from Their Half-Sections

abstract:
  We obtain explicit inversion formulas for the Radon-like transform that
assigns to a function on the unit sphere the integrals of that function over
hemispheres lying in lower dimensional central cross-sections. The results are
applied to determination of star bodies from the volumes of their central
half-sections.


title: A couple of real hyperbolic disc bundles over surfaces

abstract:
  Applying the techniques developed in [AGG], we construct new real hyperbolic
manifolds whose underlying topology is that of a disc bundle over a closed
orientable surface. By the Gromov-Lawson-Thurston conjecture [GLT], such
bundles $M\to S$ should satisfy the inequality $|eM/\chi S|\leqslant1$, where
$eM$ stands for the Euler number of the bundle and $\chi S$, for the Euler
characteristic of the surface. In this paper, we construct new examples that
provide a maximal value of $|eM/\chi S|=\frac35$ among all known examples. The
former maximum, belonging to Feng Luo [Luo], was $|eM/\chi S|=\frac12$.


title: Nuclear Physics and Astrophysics of Neutrino Oscillations

abstract:
  For a long time very little experimental information was available about
neutrino properties, even though a minute neutrino mass has intriguing
cosmological and astrophysical implications. This situation has changed in
recent decades: intense experimental activity to measure many neutrino
properties took place. Some of these developments and their implications for
astrophysics and cosmology are briefly reviewed with a particular emphasis on
neutrino magnetic moments and collective neutrino oscillations


title: Breaking the Bandwidth Barrier: Geometrical Adaptive Entropy Estimation

abstract:
  Estimators of information theoretic measures such as entropy and mutual
information are a basic workhorse for many downstream applications in modern
data science. State of the art approaches have been either geometric (nearest
neighbor (NN) based) or kernel based (with a globally chosen bandwidth). In
this paper, we combine both these approaches to design new estimators of
entropy and mutual information that outperform state of the art methods. Our
estimator uses local bandwidth choices of $k$-NN distances with a finite $k$,
independent of the sample size. Such a local and data dependent choice improves
performance in practice, but the bandwidth is vanishing at a fast rate, leading
to a non-vanishing bias. We show that the asymptotic bias of the proposed
estimator is universal; it is independent of the underlying distribution.
Hence, it can be pre-computed and subtracted from the estimate. As a byproduct,
we obtain a unified way of obtaining both kernel and NN estimators. The
corresponding theoretical contribution relating the asymptotic geometry of
nearest neighbors to order statistics is of independent mathematical interest.


title: A lower bound on the spectrum of unimodular networks

abstract:
  Unimodular networks are a generalization of finite graphs in a stochastic
sense. We prove a lower bound to the spectral radius of the adjacency operator
and of the Markov operator of an unimodular network in terms of its average
degree. This allows to prove an Alon-Boppana type bound for the largest
eigenvalues in absolute value of large, connected, bounded degree graphs, which
generalizes the Alon-Boppana theorem for regular graphs.
  A key step is establishing a lower bound to the spectral radius of a
unimodular tree in terms of its average degree. Similarly, we provide a lower
bound on the volume growth rate of an unimodular tree in terms of its average
degree.


title: Enumerating cycles in the graph of overlapping permutations

abstract:
  The graph of overlapping permutations is a directed graph that is an analogue
to the De Bruijn graph. It consists of vertices that are permutations of length
$n$ and edges that are permutations of length $n+1$ in which an edge $a_1\cdots
a_{n+1}$ would connect the standardization of $a_1\cdots a_n$ to the
standardization of $a_2\cdots a_{n+1}$. We examine properties of this graph to
determine where directed cycles can exist, to count the number of directed
$2$-cycles within the graph, and to enumerate the vertices that are contained
within closed walks and directed cycles of more general lengths.


title:
Quasi-stability and Exponential Attractors for A Non-Gradient
  System---Applications to Piston-Theoretic Plates with Internal Damping

abstract:
  We consider a nonlinear (Berger or Von Karman) clamped plate model with a
{\em piston-theoretic} right hand side---which include non-dissipative,
non-conservative lower order terms. The model arises in aeroelasticity when a
panel is immersed in a high velocity linear potential flow; in this case the
effect of the flow can be captured by a dynamic pressure term written in terms
of the material derivative of the plate's displacement. The effect of
fully-supported internal damping is studied for both Berger and von Karman
dynamics. The non-dissipative nature of the dynamics preclude the use of strong
tools such as backward-in-time smallness of velocities and finiteness of the
dissipation integral. Modern quasi-stability techniques are utilized to show
the existence of compact global attractors and generalized fractal exponential
attractors. Specific results depending on the size of the damping parameter and
the nonlinearity in force. For the Berger plate, in the presence of large
damping, the existence of a proper global attractor (whose fractal dimension is
finite in the state space) is shown via a decomposition of the nonlinear
dynamics. This leads to the construction of a compact set upon which
quasi-stability theory can be implemented. Numerical investigations for
appropriate 1-D models are presented which explore and support the abstract
results presented herein.


title:
Explicit symplectic approximation of nonseparable Hamiltonians:
  algorithm and long time performance

abstract:
  Explicit symplectic integrators have been important tools for accurate and
efficient approximations of mechanical systems with separable Hamiltonians. For
the first time, the article proposes for arbitrary Hamiltonians similar
integrators, which are explicit, of any even order, symplectic in an extended
phase space, and with pleasant long time properties. They are based on a
mechanical restraint that binds two copies of phase space together. Using
backward error analysis, KAM theory, and additional multiscale analysis, an
error bound of $\mathcal{O}(T\delta^l \omega)$ is established for integrable
systems, where $T$, $\delta$, $l$ and $\omega$ are respectively the (long)
simulation time, step size, integrator order, and some binding constant. For
non-integrable systems with positive Lyapunov exponents, such an error bound is
generally impossible, but satisfactory statistical behaviors were observed in a
numerical experiment with a nonlinear Schr\"{o}dinger equation.

categories: math.NA math.DS physics.class-ph physics.comp-ph


title:
Unsupervised cryo-EM data clustering through adaptively constrained
  K-means algorithm

abstract:
  In single-particle cryo-electron microscopy (cryo-EM), K-means clustering
algorithm is widely used in unsupervised 2D classification of projection images
of biological macromolecules. 3D ab initio reconstruction requires accurate
unsupervised classification in order to separate molecular projections of
distinct orientations. Due to background noise in single-particle images and
uncertainty of molecular orientations, traditional K-means clustering algorithm
may classify images into wrong classes and produce classes with a large
variation in membership. Overcoming these limitations requires further
development on clustering algorithms for cryo-EM data analysis. We propose a
novel unsupervised data clustering method building upon the traditional K-means
algorithm. By introducing an adaptive constraint term in the objective
function, our algorithm not only avoids a large variation in class sizes but
also produces more accurate data clustering. Applications of this approach to
both simulated and experimental cryo-EM data demonstrate that our algorithm is
a significantly improved alterative to the traditional K-means algorithm in
single-particle cryo-EM analysis.


title:
Automated Segmentation of Retinal Layers from Optical Coherent
  Tomography Images Using Geodesic Distance

abstract:
  Optical coherence tomography (OCT) is a non-invasive imaging technique that
can produce images of the eye at the microscopic level. OCT image segmentation
to localise retinal layer boundaries is a fundamental procedure for diagnosing
and monitoring the progression of retinal and optical nerve disorders. In this
paper, we introduce a novel and accurate geodesic distance method (GDM) for OCT
segmentation of both healthy and pathological images in either two- or
three-dimensional spaces. The method uses a weighted geodesic distance by an
exponential function, taking into account both horizontal and vertical
intensity variations. The weighted geodesic distance is efficiently calculated
from an Eikonal equation via the fast sweeping method. The segmentation is then
realised by solving an ordinary differential equation with the geodesic
distance. The results of the GDM are compared with manually segmented retinal
layer boundaries/surfaces. Extensive experiments demonstrate that the proposed
GDM is robust to complex retinal structures with large curvatures and
irregularities and it outperforms the parametric active contour algorithm as
well as the graph theoretic based approaches for delineating the retinal layers
in both healthy and pathological images.


title:
A Trip to the Cataclysmic Binary Zoo: Detailed Follow-Up of 35
  Recently-Discovered Systems

abstract:
  We report follow-up studies of 35 recently-discovered cataclysmic variables
(CVs), 32 of which were found in large, automated synoptic sky surveys. The
objects were selected for observational tractability. For 34 of the objects we
present mean spectra and spectroscopic orbital periods, and for one more we
give an eclipse-based period. Thirty-two of the period determinations are new,
and three of these refine published estimates based on superhump periods. The
remaining three of our determinations confirm previously published periods.
Twenty of the stars are confirmed or suspected dwarf novae with periods shorter
than 3 hours, but we also find three apparent polars (AM Her stars), and six
systems with P > 5 h, five of which have secondary stars visible in their
spectra, from which we estimate distances when possible. The orbital period
distribution of this sample is very similar to that of previously discovered
CVs.


title:
A Galerkin BEM for high-frequency scattering problems based on frequency
  dependent changes of variables

abstract:
  In this paper we develop a class of efficient Galerkin boundary element
methods for the solution of two-dimensional exterior single-scattering
problems. Our approach is based upon construction of Galerkin approximation
spaces confined to the asymptotic behaviour of the solution through a certain
direct sum of appropriate function spaces weighted by the oscillations in the
incident field of radiation. Specifically, the function spaces in the
illuminated/shadow regions and the shadow boundaries are simply algebraic
polynomials whereas those in the transition regions are generated utilizing
novel, yet simple, \emph{frequency dependent changes of variables perfectly
matched with the boundary layers of the amplitude} in these regions. While, on
the one hand, we rigorously verify for smooth convex obstacles that these
methods require only an $\mathcal{O}\left( k^{\epsilon} \right)$ increase in
the number of degrees of freedom to maintain any given accuracy independent of
frequency, and on the other hand, remaining in the realm of smooth obstacles
they are applicable in more general single-scattering configurations. The most
distinctive property of our algorithms is their \emph{remarkable success} in
approximating the solution in the shadow region when compared with the
algorithms available in the literature.


title: Magnonic Interferometric Switch for Multi-Valued Logic Circuits

abstract:
  We investigated a possible use of the magnonic interferometric switches in
multi-valued logic circuits. The switch is a three-terminal device consisting
of two spin channels where input, control, and output signals are spin waves.
Signal modulation is achieved via the interference between the source and gate
spin waves. We report experimental data on a micrometer scale prototype based
on Y3Fe2(FeO4)3 structure. The output characteristics are measured at different
angles of the bias magnetic field. The On/Off ratio of the prototype exceeds 36
dB at room temperature. Experimental data is complemented by the theoretical
analysis and the results of micro magnetic simulations showing spin wave
propagation in a micrometer size magnetic junction. We also present the results
of numerical modeling illustrating the operation of a nanometer-size switch
consisting of just 20 spins in the source-drain channel. The utilization of
spin wave interference as a switching mechanism makes it possible to build
nanometer-scale logic gates, and minimize energy per operation, which is
limited only by the noise margin. The utilization of phase in addition to
amplitude for information encoding offers an innovative route towards
multi-state logic circuits. We describe possible implementation of the
three-value logic circuits based on the magnonic interferometric switches. The
advantages and shortcomings inherent in interferometric switches are also
discussed.


title:
Measurement of the Yb I $^1S_0 - ^1P_1$ transition frequency at 399 nm
  using an optical frequency comb

abstract:
  We determine the frequency of the Yb I $^1S_0 - ^1P_1$ transition at 399 nm
using an optical frequency comb. Although this transition was measured
previously using an optical transfer cavity [D. Das et al., Phys. Rev. A 72,
032506 (2005)], recent work has uncovered significant errors in that method. We
compare our result of 751 526 533.49 $\pm$ 0.33 MHz for the Yb-174 isotope with
those from the literature and discuss observed differences. We verify the
correctness of our method by measuring the frequencies of well-known
transitions in Rb and Cs, and by demonstrating proper control of systematic
errors in both laser metrology and atomic spectroscopy. We also demonstrate the
effect of quantum interference due to hyperfine structure in a divalent atomic
system and present isotope shift measurements for all stable isotopes.


title: Loop expansion and the bosonic representation of loop quantum gravity

abstract:
  We introduce a new loop expansion that provides a resolution of the identity
in the Hilbert space of loop quantum gravity on a fixed graph. We work in the
bosonic representation obtained by the canonical quantization of the spinorial
formalism. The resolution of the identity gives a tool for implementing the
projection of states in the full bosonic representation onto the space of
solutions to the Gauss and area matching constraints of loop quantum gravity.
This procedure is particularly efficient in the semiclassical regime, leading
to explicit expressions for the loop expansions of coherent, heat kernel and
squeezed states.


title: Heat Kernel Renormalization on Manifolds with Boundary

abstract:
  In the monograph Renormalization and Effective Field Theory, Costello made
two major advances towards the mathematical formulation of quantum field
theory. Firstly, he developed an inductive position space renormalization
procedure for constructing effective field theories that is based on heat
kernel regularization of the propagator. Secondly, he gave a rigorous
formulation of quantum gauge theory within effective field theory that makes
use of the BV formalism. In this work, we extend Costello's inductive
renormalization procedure from manifolds without boundary to a class of
manifolds with boundary. In addition, we reorganize the presentation of the
preexisting material, filling in details and strengthening the results.


title:
Systems of quasi-variational inequalities related to the switching
  problem

abstract:
  We prove the existence of weak solution for a system of quasi-variational
inequalities related to a switching problem with dynamic driven by operator
associated with a semi-Dirichlet form and with measure data. We give a
stochastic representation of solutions in terms of solutions of a system of
reflected BSDEs with oblique reflection. As a by-product, we prove the
existence of an optimal strategy in the switching problem and show regularity
of the payoff function.


title: Stellar nuclei and inner polar disks in lenticular galaxies

abstract:
  I analyze statistics of the stellar population properties for stellar nuclei
and bulges of nearby lenticular galaxies in different environments by using
panoramic spectral data of the integral-field spectrograph SAURON retrieved
from the open archive of Isaac Newton Group. I estimate also the fraction of
nearby lenticular galaxies having inner polar gaseous disks by exploring the
volume-limited sample of early-type galaxies of the ATLAS-3D survey. By
inspecting the two-dimensional velocity fields of the stellar and gaseous
components with running tilted-ring technique, I have found 7 new cases of the
inner polar disks. Together with those, the frequency of inner polar disks in
nearby S0 galaxies reaches 10% that is much higher than the frequency of
large-scale polar rings. Interestingly, the properties of the nuclear stellar
populations in the inner polar ring hosts are statistically the same as those
in the whole S0 sample implying similar histories of multiple gas accretion
events from various directions.


title:
Entanglement Entropy in the $\sigma$-Model with the de Sitter Target
  Space

abstract:
  We derive the formula of the entanglement entropy between the left and right
oscillating modes of the $\sigma$-model with the de Sitter target space. To
this end, we study the theory in the \emph{cosmological gauge} in which the
non-vanishing components of the metric on the two-dimensional base space are
functions of the expansion parameter of the de Sitter space. The model is
embedded in the causal north pole diamond of the Penrose diagram. We argue that
the cosmological gauge is natural to the $\sigma$-model as it is compatible
with the canonical quantization relations. In this gauge, we obtain a new
general solution to the equations of motion in terms of time-independent
oscillating modes. The constraint structure is adequate for quantization in the
Gupta-Bleuler formalism. We construct the space of states as a one-parameter
family of Hilbert spaces and give the Bargmann-Fock and Jordan-Schwinger
representations of it. Also, we give a simple description of the physical
subspace as an infinite product of $\mathcal{D}^{+}_{\frac{1}{2}}$ in the
positive discreet series irreducible representations of the $SU(1,1)$ group. We
construct the map generated by the Hamiltonian between states at two different
values of time and show how it produces the entanglement of left and right
excitations. Next, we derive the formula of the entanglement entropy of the
reduced density matrix for the ground state acted upon by the Hamiltonian map.
Finally, we determine the asymptotic form of the entanglement entropy of a
single mode bi-oscillator in the limit of large values of time.


title: Fundamental Limitation on Cooling under Classical Noise

abstract:
  We prove a general theorem that the action of arbitrary classical noise or
random unitary channels can not increase the maximum population of any
eigenstate of an open quantum system, assuming initial system-environment
factorization. Such factorization is the conventional starting point for
descriptions of open system dynamics. In particular, our theorem implies that a
system can not be ideally cooled down unless it is initially prepared as a pure
state. The resultant inequality rigorously constrains the possibility of
cooling the system solely through temporal manipulation, i.e., dynamical
control over the system Hamiltonian without resorting to measurement based
cooling methods.


title: Quantum lattice gas algorithmic representation of gauge field theory

abstract:
  Presented is a quantum lattice gas algorithm to efficiently model a system of
Dirac particles interacting through an intermediary gauge field. The algorithm
uses a fixed qubit array to represent both the spacetime and the particles
contained in the spacetime. Despite being a lattice based algorithm, Lorentz
invariance is preserved down to the grid scale, with the continuum Dirac
Hamiltonian generating the local unitary evolution even at that scale: there is
nonlinear scaling between the smallest observable time and that time measured
in the quantum field theory limit, a kind of time dilation effect that emerges
on small scales but has no effect on large scales. The quantum lattice gas
algorithm correctly accounts for the anticommutative braiding of
indistinguishable fermions---it does not suffer the Fermi-sign problem. It
provides a highly convergent numerical simulation for strongly-correlated
fermions equal to a covariant path integral, presented here for the case when a
Dirac particle's Compton wavelength is large compared to the grid scale of the
qubit array.


title: Fitted Learning: Models with Awareness of their Limits

abstract:
  Though deep learning has pushed the boundaries of classification forward, in
recent years hints of the limits of standard classification have begun to
emerge. Problems such as fooling, adding new classes over time, and the need to
retrain learning models only for small changes to the original problem all
point to a potential shortcoming in the classic classification regime, where a
comprehensive a priori knowledge of the possible classes or concepts is
critical. Without such knowledge, classifiers misjudge the limits of their
knowledge and overgeneralization therefore becomes a serious obstacle to
consistent performance. In response to these challenges, this paper extends the
classic regime by reframing classification instead with the assumption that
concepts present in the training set are only a sample of the hypothetical
final set of concepts. To bring learning models into this new paradigm, a novel
elaboration of standard architectures called the competitive overcomplete
output layer (COOL) neural network is introduced. Experiments demonstrate the
effectiveness of COOL by applying it to fooling, separable concept learning,
one-class neural networks, and standard classification benchmarks. The results
suggest that, unlike conventional classifiers, the amount of generalization in
COOL networks can be tuned to match the problem.


title:
Optimal ALOHA-like Random Access with Heterogeneous QoS Guarantees for
  Multi-Packet Reception Aided Visible Light Communications

abstract:
  There is a paucity of random access protocols designed for alleviating
collisions in visible light communication (VLC) systems, where carrier sensing
is hard to be achieved due to the directionality of light. To resolve the
problem of collisions, we adopt the successive interference cancellation (SIC)
algorithm to enable the coordinator to simultaneously communicate with multiple
devices, which is referred to as the multi-packet reception (MPR) capability.
However, the MPR capability could be fully utilized only when random access
algorithms are properly designed. Considering the characteristics of the SIC
aided random access VLC system, we propose a novel effective capacity
(EC)-based ALOHA-like distributed random access algorithm for MPR-aided uplink
VLC systems having heterogeneous quality-of-service (QoS) guarantees. Firstly,
we model the VLC network as a conflict graph and derive the EC for each device.
Then, we formulate the VLC QoS-guaranteed random access problem as a saturation
throughput maximization problem subject to multiple statistical QoS
constraints. Finally, the resultant non-concave optimization problem (OP) is
solved by a memetic search algorithm relying on invasive weed optimization and
differential evolution (IWO-DE). We demonstrate that our derived EC expression
matches the Monte Carlo simulation results accurately, and the performance of
our proposed algorithms is competitive.


title: Learning to learn with backpropagation of Hebbian plasticity

abstract:
  Hebbian plasticity is a powerful principle that allows biological brains to
learn from their lifetime experience. By contrast, artificial neural networks
trained with backpropagation generally have fixed connection weights that do
not change once training is complete. While recent methods can endow neural
networks with long-term memories, Hebbian plasticity is currently not amenable
to gradient descent. Here we derive analytical expressions for activity
gradients in neural networks with Hebbian plastic connections. Using these
expressions, we can use backpropagation to train not just the baseline weights
of the connections, but also their plasticity. As a result, the networks "learn
how to learn" in order to solve the problem at hand: the trained networks
automatically perform fast learning of unpredictable environmental features
during their lifetime, expanding the range of solvable problems. We test the
algorithm on various on-line learning tasks, including pattern completion,
one-shot learning, and reversal learning. The algorithm successfully learns how
to learn the relevant associations from one-shot instruction, and fine-tunes
the temporal dynamics of plasticity to allow for continual learning in response
to changing environmental parameters. We conclude that backpropagation of
Hebbian plasticity offers a powerful model for lifelong learning.


title:
Quantum lattice gas model of spin-2 Bose-Einstein condensates and
  closed-form analytical continuation of nonlinear interactions in spin-2
  superfluids

abstract:
  Presented is an unitary operator splitting method for handling the
spin-density interaction in spinor Bose-Einstein condensates. The zero
temperature behavior of a spinor BEC is given by mean field theory, where the
Hamiltonian includes a nonlinear hyperfine spin interaction. This hyperfine
interaction has a diagonal probability-density term (leading to the usual
Gross-Pitaevskii type equation of motion) but also has a nondiagonal
spin-density term. Since the F=2 spinor BEC (spin-2 BEC) has a non-Abelian
superfluid phase (nonperturbative cyclic phase in the strong spin-density
coupling regime), an infinite-order expansion of the quantum evolution operator
is needed for quantum simulation applications. An infinite-order expansion,
obtained by analytical continuation and expressed in analytically closed form,
for the spin-2 BEC is presented.


title: Decomposition of radiation energy into work and heat

abstract:
  We investigate energy transfer by the radiation from a cavity quantum
electrodynamics (QED) system in the context of quantum thermodynamics. We
propose a method of decomposing it into work and heat within the framework of
quantum master equations. We find that the work and heat correspond
respectively to the coherent and incoherent parts of the radiation. In the
derivation of the method, it is crucial to investigate the dynamics of the
system that receives the radiation from the cavity.


title: Cohomological invariants of genus three hyperelliptic curves

abstract:
  We compute the cohomological invariants with coefficients in
$\mathbb{Z}/p\mathbb{Z}$ of the stack $\mathscr{H}_3$ of hyperelliptic curves
of genus $3$ over an algebraically closed field.


title: A millisecond pulsar candidate in a 21-hr orbit: 3FGL J0212.1+5320

abstract:
  We present the discovery of a variable optical counterpart to the
unidentified gamma-ray source 3FGL J0212.1+5320, and argue this is a new
compact binary millisecond pulsar (MSP) candidate. We show 3FGL J0212.1+5320
hosts a semi-detached binary with a 0.86955$\pm$0.00015 d orbital period and a
F6-type companion star at an estimated distance of D=1.1$\pm$0.2 kpc, with a
radial velocity curve semi-amplitude K$_2$=214.1$\pm$5.0 km s$^{-1}$ and a
projected rotational velocity of Vsin(i)=73.2$\pm$1.6 km s$^{-1}$. We find a
hard X-ray source at the same location with a 0.5$-$10 keV luminosity
L$_\mathrm{X}$=2.6$\times$10$^{32}$ (D/1.1 kpc)$^2$ erg s$^{-1}$, which
strengthens the MSP identification. Our results imply a mass ratio
q=M$_2$/M$_1$=0.26$^{+0.02}_{-0.03}$ if the companion star fills its Roche
lobe, and q$\gtrsim$0.26 in any case. This classifies 3FGL J0212.1+5320 as a
"redback" binary MSP; if its MSP nature is confirmed, this will be the
brightest compact binary MSP in the optical band (r'$\simeq$14.3 mag) and will
have the longest orbital period among Galactic field systems (nearly 21 hr).
Based on the light curve peak-to-peak amplitude ($\Delta$r=0.19 mag), we
further suggest that the orbital inclination is high and the putative pulsar
mass is close to canonical (M$_1$$\simeq$1.3$-$1.6 M$_\odot$). Finally, we
discuss the lack of heating signatures and asymmetric optical light curves in
the context of other redback MSPs.


title:
Optimization methods for frame conditioning and application to graph
  Laplacian scaling

abstract:
  A frame is scalable if each of its vectors can be rescaled in such a way that
the resulting set becomes a Parseval frame. In this paper, we consider four
different optimization problems for determining if a frame is scalable. We
offer some algorithms to solve these problems. We then apply and extend our
methods to the problem of reweighing (finite) graph so as to minimize the
condition number of the resulting Laplacian.


title:
From Physical to Cyber: Escalating Protection for Personalized Auto
  Insurance

abstract:
  Nowadays, auto insurance companies set personalized insurance rate based on
data gathered directly from their customers' cars. In this paper, we show such
a personalized insurance mechanism -- wildly adopted by many auto insurance
companies -- is vulnerable to exploit. In particular, we demonstrate that an
adversary can leverage off-the-shelf hardware to manipulate the data to the
device that collects drivers' habits for insurance rate customization and
obtain a fraudulent insurance discount. In response to this type of attack, we
also propose a defense mechanism that escalates the protection for insurers'
data collection. The main idea of this mechanism is to augment the insurer's
data collection device with the ability to gather unforgeable data acquired
from the physical world, and then leverage these data to identify manipulated
data points. Our defense mechanism leveraged a statistical model built on
unmanipulated data and is robust to manipulation methods that are not foreseen
previously. We have implemented this defense mechanism as a proof-of-concept
prototype and tested its effectiveness in the real world. Our evaluation shows
that our defense mechanism exhibits a false positive rate of 0.032 and a false
negative rate of 0.013.


title: Explicit Schoen surfaces

abstract:
  We give an explicit construction for the $4$-dimensional family of Schoen
surfaces by computing equations for their canonical images, which are
$40$-nodal complete intersections of a quadric and the Igusa quartic in
$\mathbb P^4$. We then study a particularly interesting example, with $240$
automorphisms and maximal Picard number.


title: Latent Dependency Forest Models

abstract:
  Probabilistic modeling is one of the foundations of modern machine learning
and artificial intelligence. In this paper, we propose a novel type of
probabilistic models named latent dependency forest models (LDFMs). A LDFM
models the dependencies between random variables with a forest structure that
can change dynamically based on the variable values. It is therefore capable of
modeling context-specific independence. We parameterize a LDFM using a
first-order non-projective dependency grammar. Learning LDFMs from data can be
formulated purely as a parameter learning problem, and hence the difficult
problem of model structure learning is circumvented. Our experimental results
show that LDFMs are competitive with existing probabilistic models.


title: The unrelaxed dynamical structure of the galaxy cluster Abell 85

abstract:
  For the first time, we explore the dynamics of the central region of a galaxy
cluster within $r_{500}\sim 600h^{-1}$~kpc from its center by combining optical
and X-ray spectroscopy. We use (1) the caustic technique that identifies the
cluster substructures and their galaxy members with optical spectroscopic data,
and (2) the X-ray redshift fitting procedure that estimates the redshift
distribution of the intracluster medium (ICM). We use the spatial and redshift
distributions of the galaxies and of the X-ray emitting gas to associate the
optical substructures to the X-ray regions. When we apply this approach to
Abell 85 (A85), a complex dynamical structure of A85 emerges from our analysis:
a galaxy group, with redshift $z=0.0509 \pm 0.0021$ is passing through the
cluster center along the line of sight dragging part of the ICM present in the
cluster core; two additional groups, at redshift $z=0.0547 \pm 0.0022$ and
$z=0.0570 \pm 0.0020$, are going through the cluster in opposite directions,
almost perpendicularly to the line of sight, and have substantially perturbed
the dynamics of the ICM. An additional group in the outskirts of A85, at
redshift $z=0.0561 \pm 0.0023$, is associated to a secondary peak of the X-ray
emission, at redshift $z=0.0583^{+0.0039}_{-0.0047}$. Although our analysis and
results on A85 need to be confirmed by high-resolution spectroscopy, they
demonstrate how our new approach can be a powerful tool to constrain the
formation history of galaxy clusters by unveiling their central and surrounding
structures.


title:
Robinson Stability of Parametric Constraint Systems via Variational
  Analysis

abstract:
  This paper investigates a well-posedness property of parametric constraint
systems named here Robinson stability. Based on advanced tools of variational
analysis and generalized differentiation, we derive first-order and
second-order conditions for this property under minimal constraint
qualifications and establish relationships of Robinson stability with other
well-posedness properties in variational analysis and optimization. The results
obtained are applied to robust Lipschitzian stability of parametric variational
systems.


title:
Evaluation of bipartite entanglement between two optical multi-mode
  systems using mode translation symmetry

abstract:
  Optical multi-mode systems provide large scale Hilbert spaces that can be
accessed and controlled using single photon sources, linear optics and photon
detection. Here, we consider the bipartite entanglement generated by coherently
distributing $M$ photons in $M$ modes to two separate locations, where linear
optics and photon detection is used to verify the non-classical correlations
between the two $M$-mode systems. We show that the entangled state is symmetric
under mode shift operations performed in the two systems and use this symmetry
to derive correlations between photon number distributions detected after a
discrete Fourier transform (DFT) of the modes. The experimentally observable
correlations can be explained by a simple and intuitive rule that relates the
sum of the output mode indices to the eigenvalue of the input state under the
mode shift operation. Since the photon number operators after the DFT do not
commute with the initial photon number operators, entanglement is necessary to
achieve strong correlations in both the initial mode photon numbers and the
photon numbers observed after the DFT. We can therefore derive entanglement
witnesses based on the experimentally observable correlations in both photon
number distributions, providing a practical criterion for the evaluation of
large scale entanglement in optical multi-mode systems. Our method thus
demonstrates how non-classical signatures in large scale optical quantum
circuits can be accessed experimentally by choosing an appropriate combination
of modes in which to detect the photon number distributions that characterize
the quantum coherences of the state.


title: Slices of Parameter Space of Cubic Polynomials

abstract:
  In this paper, we study slices of the parameter space of cubic polynomials,
up to affine conjugacy, given by a fixed value of the multiplier at a
non-repelling fixed point. In particular, we study the location of the $main\,
cubioid$ in this parameter space. The $main\, cubioid$ is the set of affine
conjugacy classes of complex cubic polynomials that have certain dynamical
properties generalizing those of polynomials $z^2+c$ for $c$ in the filled main
cardioid.


title: Nodal Variational Principle for Excited States

abstract:
  It is proven that the exact excited-state wave function and energy may be
obtained by minimizing the energy expectation value of trial wave functions
that are constrained only to have the correct nodes of the state of interest.
This excited-state nodal minimum principle has the advantage that it requires
neither minimization with the constraint of wave-function orthogonality to all
lower eigenstates nor the antisymmetry of the trial wave functions. It is also
found that the minimization over the entire space can be partitioned into
several interconnected minimizations within the individual nodal regions, and
the exact excited-state energy may be obtained by a minimization in just one or
several of these nodal regions. For the proofs of the theorem, it is observed
that the many-electron eigenfunction (excited state as well as ground state),
restricted to a nodal region, is equivalent to a ground-state wave function of
one electron in a higher-dimensional space; and, alternatively, an explicit
excited-state energy variational expression is utilized by generalizing the
Jacobi method of multiplicative variation. In corollaries, error functions are
constructed for cases for which the nodes are not necessarily exact. The exact
nodes minimize the energy error functions with respect to nodal variations.
Simple numerical illustrations of the error functions are presented.


title: Spin accumulation in disordered topological insulator thin films

abstract:
  Topological insulator (TI) thin films differ from the more commonly studied
semi-infinite bulk TIs in that the former possesses both top and bottom
surfaces where the surface states localized at different surfaces can couple to
one another due to the finite thickness of the film. In the presence of an
in-plane mangnetization TI thin films display two distinct phases depending on
which of the inter-surface coupling or the magnetization is stronger. In this
work, we consider a TI thin film system with an in-plane magnetization and
calculate numerically the resulting spin accumulation on both surfaces of the
film due to an in-plane electric field to linear order. We describe a numerical
scheme for performing the Kubo calculation calculation in which we include
impurity scattering and vertex corrections. We find that the sums of the spin
accumulation over the two surfaces in the in-plane direction perpendicular to
the magnetization, and in the out of plane direction, are antisymmetric in
Fermi energy about the charge neutrality point and are non-vanishing only when
the symmetry between the top and bottom TI surfaces is broken. The impurity
scattering, in general, diminishes the magnitude of the spin accumulation and
can also change the sign of the spin accumulation at some Fermi energies where
the accumulation is small.


title:
Determination of Pedestrian Flow Performance Based on Video Tracking and
  Microscopic Simulations

abstract:
  One of the objectives of understanding pedestrian behavior is to predict the
effect of proposed changes in the design or evaluation of pedestrian
facilities. We want to know the impact to the user of the facilities, as the
design of the facilities change. That impact was traditionally evaluated by
level of service standards. Another design criterion to measure the impact of
design change is measured by the pedestrian flow performance index. This paper
describes the determination of pedestrian flow performance based video tracking
or any microscopic pedestrian simulation models. Most of pedestrian researches
have been done on a macroscopic level, which is an aggregation of all
pedestrian movement in pedestrian areas into flow, average speed and area
module. Macroscopic level, however, does not consider the interaction between
pedestrians. It is also not well suited for prediction of pedestrian flow
performance in pedestrian areas or in buildings with some obstruction, that
reduces the effective width of the walkways. On the other hand, the microscopic
level has a more general usage and considers detail in the design. More
efficient pedestrian flow can even be reached with less space. Those results
have rejected the linearity assumption of space and flow in the macroscopic
level.


title: On minimality of two-bridge knots

abstract:
  A knot is called minimal if its knot group admits epimorphisms onto the knot
groups of only the trivial knot and itself. In this paper, we determine which
two-bridge knot $\mathfrak{b}(p,q)$ is minimal where $q \leq 6$ or $p \leq
100$.


title:
Supermassive black holes formed by direct collapse of inflationary
  perturbations

abstract:
  We propose a mechanism of producing a new type of primordial perturbations
that collapse to primordial black holes whose mass can be as large as necessary
for them to grow to the supermassive black holes observed at high redshifts,
without contradicting COBE/FIRAS upper limits on cosmic microwave background
(CMB) spectral distortions. In our model, the observable Universe consists of
two kinds of many small patches which experienced different expansion histories
during inflation. Primordial perturbations large enough to form primordial
black holes are realized on patches that experienced more Hubble expansion than
the others. By making these patches the minor component, the rarity of
supermassive black holes can be explained. On the other hand, most regions of
the Universe experienced the standard history and, hence, only have standard
almost-scale-invariant adiabatic perturbations confirmed by observations of CMB
or large-scale structures of the Universe. Thus, our mechanism can evade the
constraint from the nondetection of the CMB distortion set by the COBE/FIRAS
measurement. Our model predicts the existence of supermassive black holes even
at redshifts much higher than those observed. Hence, our model can be tested by
future observations peeking into the higher-redshift Universe.


title:
A Unified Hamiltonian Solution to Maxwell-Schrodinger Equations for
  Modeling Electromagnetic Field-Particle Interaction

abstract:
  A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger
equation for modeling the interaction between classical electromagnetic (EM)
fields and particles. Based on the Hamiltonian of electromagnetics and quantum
mechanics, a unified Maxwell-Schrodinger system is derived by the variational
principle. The coupled system is well-posed and symplectic, which ensures
energy conserving property during the time evolution. However, due to the
disparity of wavelengths of EM waves and that of electron waves, a numerical
implementation of the finite-difference time-domain (FDTD) method to the
multiscale coupled system is extremely challenging. To overcome this
difficulty, a reduced eigenmode expansion technique is first applied to
represent the wave function of the particle. Then, a set of ordinary
differential equations (ODEs) governing the time evolution of the
slowly-varying expansion coefficients are derived to replace the original
Schrodinger equation. Finally, Maxwell's equations represented by the vector
potential with a Coulomb gauge, together with the ODEs, are solved
self-consistently. For numerical examples, the interaction between EM fields
and a particle is investigated for both the closed, open and inhomogeneous
electromagnetic systems. The proposed approach not only captures the Rabi
oscillation phenomenon in the closed cavity but also captures the effects of
radiative decay and shift in the open free space. After comparing with the
existing theoretical approximate models, it is found that the approximate
models break down in certain cases where a rigorous self-consistent approach is
needed. This work is helpful for the EM simulation of emerging nanodevices or
next-generation quantum electrodynamic systems.

categories: physics.optics math.NA math.SG physics.comp-ph quant-ph


title:
Demixing Sines and Spikes: Robust Spectral Super-resolution in the
  Presence of Outliers

abstract:
  We consider the problem of super-resolving the line spectrum of a
multisinusoidal signal from a finite number of samples, some of which may be
completely corrupted. Measurements of this form can be modeled as an additive
mixture of a sinusoidal and a sparse component. We propose to demix the two
components and super-resolve the spectrum of the multisinusoidal signal by
solving a convex program. Our main theoretical result is that-- up to
logarithmic factors-- this approach is guaranteed to be successful with high
probability for a number of spectral lines that is linear in the number of
measurements, even if a constant fraction of the data are outliers. The result
holds under the assumption that the phases of the sinusoidal and sparse
components are random and the line spectrum satisfies a minimum-separation
condition. We show that the method can be implemented via semidefinite
programming and explain how to adapt it in the presence of dense perturbations,
as well as exploring its connection to atomic-norm denoising. In addition, we
propose a fast greedy demixing method which provides good empirical results
when coupled with a local nonconvex-optimization step.


title:
Investigating Magnetic Activity in the Galactic Centre by Global MHD
  Simulation

abstract:
  By performing a global magnetohydrodynamical (MHD) simulation for the Milky
Way with an axisymmetric gravitational potential, we propose that spatially
dependent amplification of magnetic fields possibly explains the observed
noncircular motion of the gas in the Galactic centre (GC) region. The radial
distribution of the rotation frequency in the bulge region is not monotonic in
general. The amplification of the magnetic field is enhanced in regions with
stronger differential rotation, because magnetorotational instability and
field-line stretching are more effective. The strength of the amplified
magnetic field reaches >~ 0.5 mG, and radial flows of the gas are excited by
the inhomogeneous transport of angular momentum through turbulent magnetic
field that is amplified in a spatially dependent manner. As a result, the
simulated position-velocity diagram exhibits a time-dependent asymmetric
parallelogram-shape owing to the intermittency of the magnetic turbulence; the
present model provides a viable alternative to the bar-potential-driven model
for the parallelogram shape of the central molecular zone. In addition, Parker
instability (magnetic buoyancy) creates vertical magnetic structure, which
would correspond to observed molecular loops, and frequently excited vertical
flows. Furthermore, the time-averaged net gas flow is directed outward, whereas
the flows are highly time dependent, which would contribute to the outflow from
the bulge.


title:
Clustering Multiple Sclerosis Medication Sequence Data with Mixture
  Markov Chain Analysis with covariates using Multiple Simplex Constrained
  Optimization Routine (MSiCOR)

abstract:
  Multiple sclerosis (MS) is an autoimmune disease of the central nervous
system that causes neurodegeneration. While disease-modifying therapies (DMTs)
reduce inflammatory disease activity and delay worsening disability in MS,
there are significantly varying treatment responses across people with MS
(pwMS). pwMS often receive serial monotherapies of DMTs. Here, we propose a
novel method to cluster pwMS according to the sequence of DMT prescriptions and
associated clinical features (covariates). This is achieved via a mixture
Markov chain analysis with covariates, where the sequence of prescribed DMTs
for each patient is modeled as a Markov chain. Given the computational
challenges to maximize the mixture likelihood on the constrained parameter
space, we develop a pattern search-based global optimization technique which
can optimize any objective function on a collection of simplexes and shown to
outperform other related global optimization techniques. In simulation
experiments, the proposed method is shown to outperform the
Expectation-Maximization (EM) algorithm based method for clustering sequence
data without covariates. Based on the analysis, we divided MS patients into 3
clusters: inferon-beta dominated, multi-DMTs, and natalizumab dominated.
Further cluster-specific summaries of relevant covariates indicate patient
differences among the clusters. This method may guide the DMT prescription
sequence based on clinical features.


title: On Singer's conjecture for the fifth algebraic transfer

abstract:
  Let $P_k:= \mathbb{F}_2[x_1,x_2,\ldots ,x_k]$ be the polynomial algebra in
$k$ variables with the degree of each $x_i$ being $1,$ regarded as a module
over the mod-$2$ Steenrod algebra $\mathcal{A},$ and let $GL_k$ be the general
linear group over the prime field $\mathbb{F}_2$ which acts naturally on $P_k$.
We study the hit problem, set up by Frank Peterson, of finding a minimal set of
generators for the polynomial algebra $P_k$ as a module over the mod-2 Steenrod
algebra, $\mathcal{A}$. These results are used to study the Singer algebraic
transfer which is a homomorphism from the homology of the mod-$2$ Steenrod
algebra, $\mbox{Tor}^{\mathcal{A}}_{k, k+n}(\mathbb{F}_2, \mathbb{F}_2),$ to
the subspace of $\mathbb{F}_2\otimes_{\mathcal{A}}P_k$ consisting of all the
$GL_k$-invariant classes of degree $n.$ In this paper, we explicitly compute
the hit problem for $k = 5$ and the degree $7.2^s-5$ with $s$ an arbitrary
positive integer. Using this result, we show that Singer's conjecture for the
algebraic transfer is true in the case $k=5$ and the above degree.


title:
Characterizations and Effective Computation of Supremal Relatively
  Observable Sublanguages

abstract:
  Recently we proposed relative observability for supervisory control of
discrete-event systems under partial observation. Relative observability is
closed under set unions and hence there exists the supremal relatively
observable sublanguage of a given language. In this paper we present a new
characterization of relative observability, based on which an operator on
languages is proposed whose largest fixpoint is the supremal relatively
observable sublanguage. Iteratively applying this operator yields a monotone
sequence of languages; exploiting the linguistic concept of support based on
Nerode equivalence, we prove for regular languages that the sequence converges
finitely to the supremal relatively observable sublanguage, and the operator is
effectively computable. Moreover, for the purpose of control, we propose a
second operator that in the regular case computes the supremal relatively
observable and controllable sublanguage. The computational effectiveness of the
operator is demonstrated on a case study.