title: Broken scale-invariance in time-dependent trapping potentials

abstract:
  The response of a cold atom gas with contact interactions to a smoothly
varying external harmonic confinement in the non-adiabatic regime is studied.
The time variation of the angular frequency is varied such that the system is,
for vanishing or infinitely strong contact interactions, scale invariant. The
time evolution of the system with broken scale invariance (i.e., the time
evolution of the system with finite interaction strength), is contrasted with
that for a scale invariant system, which exhibits Efimovian-like expansion
dynamics that is characterized by log-periodic oscillations with unique period
and amplitude. It is found that the breaking of the scale invariance by the
finiteness of the interactions leads to a time dependence of the oscillation
period and amplitude. It is argued, based on analytical considerations for
atomic gases of arbitrary size and numerical results for two one-dimensional
particles, that the oscillation pe riod approaches that of the scale-invariant
system at large times. The role of the time-dependent contact in the expansion
dynamics is analyzed.


title:
Optical properties of $A$Fe$_\mathbf{2}$As$_\mathbf{2}$ ($A=\,$Ca, Sr,
  and Ba) single crystals

abstract:
  The detailed optical properties have been determined for the iron-based
materials $A$Fe$_2$As$_2$, where $A=\,$Ca, Sr, and Ba, for light polarized in
the iron-arsenic ($a-b$) planes over a wide frequency range, above and below
the magnetic and structural transitions at $T_N =$ 172, 195, and 138 K,
respectively. The real and imaginary parts of the complex conductivity are fit
simultaneously using two Drude terms in combination with a series of
oscillators. Above $T_N$, the free-carrier response consists of a weak, narrow
Drude term, and a strong, broad Drude term, both of which show only a weak
temperature dependence. Below $T_N$ there is a slight decrease of the plasma
frequency but a dramatic drop in the scattering rate for the narrow Drude term,
and for the broad Drude term there is a significant decrease in the plasma
frequency, while the decrease in the scattering rate, albeit significant, is
not as severe. The small values observed for the scattering rates for the
narrow Drude term for $T\ll{T_N}$ may be related to the Dirac cone-like
dispersion of the electronic bands. Below $T_N$ new features emerge in the
optical conductivity that are associated with the reconstruction Fermi surface
and the gapping of bands at $\Delta_1 \simeq$ 45 $-$ 80 meV, and $\Delta_2
\simeq$ 110 $-$ 210 meV. The reduction in the spectral weight associated with
the free carriers is captured by the gap structure, specifically, the spectral
weight from the narrow Drude term appears to be transferred into the low-energy
gap feature, while the missing weight from the broad term shifts to the
high-energy gap.


title:
Dynamical evidence for a strong tidal interaction between the Milky Way
  and its satellite, Leo V

abstract:
  We present a chemodynamical analysis of the Leo~V dwarf galaxy, based on Keck
II DEIMOS spectra of 8 member stars. We find a systemic velocity for the system
of $\langle v_r\rangle = 170.9^{+ 2.1}_{-1.9}$kms$^{-1}$, and barely resolve a
velocity dispersion for the system, with $\sigma_{vr} =
2.3^{+3.2}_{-1.6}$kms$^{-1}$, consistent with previous studies of Leo~V. The
poorly resolved dispersion means we are unable to adequately constrain the dark
matter content of Leo~V. We find an average metallicity for the dwarf of
[Fe/H]$ = -2.48\pm0.21$, and measure a significant spread in the iron abundance
of its member stars, with $-3.1\le$[Fe/H]$\le-1.9$ dex, which cleanly
identifies Leo~V as a dwarf galaxy that has been able to self-enrich its
stellar population through extended star formation. Owing to the tentative
photometric evidence for tidal substructure around Leo~V, we also investigate
whether there is any evidence for tidal stripping or shocking of the system
within its dynamics. We measure a significant velocity gradient across the
system, of $\frac{{\rm d}v}{{\rm d}\chi} = -4.1^{+2.8}_{-2.6}$kms$^{-1}$ per
arcmin (or $\frac{{\rm d}v}{{\rm d}\chi} =
-71.9^{+50.8}_{-45.6}$kms$^{-1}$~kpc$^{-1}$), which points almost directly
toward the Galactic centre. We argue that Leo~V is likely a dwarf on the brink
of dissolution, having just barely survived a past encounter with the centre of
the Milky Way.


title: Tidal disruption events from supermassive black hole binaries

abstract:
  We investigate the pre-disruption gravitational dynamics and post-disruption
hydrodynamics of the tidal disruption of stars by supermassive black hole
(SMBH) binaries. We focus on binaries with relatively low mass primaries
($10^6M_{\odot}$), moderate mass ratios, and separations with reasonably long
gravitational wave inspiral times (tens of Myr). First, we generate a large
ensemble (between 1 and 10 million) of restricted three-body integrations to
quantify the statistical properties of tidal disruptions by circular SMBH
binaries of initially-unbound stars. Compared to the reference case of a
disruption by a single SMBH, the binary potential induces significant variance
into the specific energy and angular momentum of the star at the point of
disruption. Second, we use Newtonian numerical hydrodynamics to study the
detailed evolution of the fallback debris from 120 disruptions randomly
selected from the three-body ensemble (excluding only the most deeply
penetrating encounters). We find that the overall morphology of the debris is
greatly altered by the presence of the second black hole, and the accretion
rate histories display a wide range of behaviors, including order of magnitude
dips and excesses relative to control simulations that include only one black
hole. Complex evolution persists, in some cases, for many orbital periods of
the binary. We find evidence for power in the accretion curves on timescales
related to the binary orbital period, though there is no exact periodicity. We
discuss our results in the context of future wide-field surveys, and comment on
the prospects of identifying and characterizing the subset of events occurring
in nuclei with binary SMBHs.


title:
Low-Redshift Lyman Limit Systems as Diagnostics of Cosmological Inflows
  and Outflows

abstract:
  We use cosmological hydrodynamic simulations with stellar feedback from the
FIRE project to study the physical nature of Lyman limit systems (LLSs) at z<1.
At these low redshifts, LLSs are closely associated with dense gas structures
surrounding galaxies, such as galactic winds, dwarf satellites, and cool
inflows from the intergalactic medium. Our analysis is based on 14 zoom-in
simulations covering the halo mass range M_h~10^9-10^13 Msun at z=0, which we
convolve with the dark matter halo mass function to produce cosmological
statistics. We find that the majority of cosmologically-selected LLSs are
associated with halos in the mass range 10^10 < M_h < 10^12 Msun. The incidence
and HI column density distribution of simulated absorbers with columns 10^16.2
< N_HI < 2x10^20 cm^-2 are consistent with observations. High-velocity outflows
(with radial velocity exceeding the halo circular velocity by a factor >~2)
tend to have higher metallicities ([X/H] ~ -0.5) while very low metallicity
([X/H] < -2) LLSs are typically associated with gas infalling from the
intergalactic medium. However, most LLSs occupy an intermediate region in
metallicity-radial velocity space, for which there is no clear trend between
metallicity and radial kinematics. Metal-enriched inflows arise in the FIRE
simulations as a result of galactic winds that fall back onto galaxies at low
redshift. The overall simulated LLS metallicity distribution has a mean
(standard deviation) [X/H] = -0.9 (0.4) and does not show significant evidence
for bimodality, in contrast to recent observational studies but consistent with
LLSs arising from halos with a broad range of masses and metallicities.


title:
A Tale of Two Twin Higgses: Addressing Little Hierarchy in Natural 2HDM
  Framework

abstract:
  In original twin Higgs model, vacuum misalignment between electroweak and new
physics scales is realized by adding explicit $\mathbb{Z}_2$ breaking term.
Introducing additional twin Higgs could accommodate spontaneous $\mathbb{Z}_2$
breaking, which explains the origin of this misalignment. We introduce a class
of two twin Higgs doublet models with most general scalar potential, and
discuss general conditions which trigger electroweak and $\mathbb{Z}_2$
symmetry breaking. Various scenarios on realising the vacuum misalignment are
systematically discussed in a natural two Higgs double model framework:
explicit $\mathbb{Z}_2$ breaking, radiative $\mathbb{Z}_2$ breaking,
tadpole-induced $\mathbb{Z}_2$ breaking, and quartic-induced $\mathbb{Z}_2$
breaking. We investigate the Higgs mass spectra and the Higgs phenomenology in
these scenarios.


title:
Thermoelectric response of a correlated impurity in the nonequilibrium
  Kondo regime

abstract:
  We study nonequilibrium thermoelectric transport properties of a correlated
impurity connected to two leads for temperatures below the Kondo scale. At
finite bias, for which a current flows across the leads, we investigate the
differential response of the current to a temperature gradient. In particular,
we compare the influence of a bias voltage and of a finite temperature on this
thermoelectric response. This is of interest from a fundamental point of view
to better understand the two different decoherence mechanisms produced by a
bias voltage and by temperature. Our results show that in this respect the
thermoelectric response behaves differently from the electric conductance. In
particular, while the latter displays a similar qualitative behavior as a
function of voltage and temperature, both in theoretical and experimental
investigations, qualitative differences occur in the case of the thermoelectric
response. In order to understand this effect, we analyze the different
contributions in connection to the behavior of the impurity spectral function
versus temperature. Especially in the regime of strong interactions and large
enough bias voltages we obtain a simple picture based on the asymmetric
suppression or enhancement of the split Kondo peaks as a function of the
temperature gradient. Besides the academic interest, these studies could
additionally provide valuable information to assess the applicability of
quantum dot devices as responsive nanoscale temperature sensors.


title: Relaxing the Cosmological Constant: a Proof of Concept

abstract:
  We propose a technically natural scenario whereby an initially large
cosmological constant (c.c.) is relaxed down to the observed value due to the
dynamics of a scalar evolving on a very shallow potential. The model crucially
relies on a sector that violates the null energy condition (NEC) and gets
activated only when the Hubble rate becomes sufficiently small --- of the order
of the present one. As a result of NEC violation, this low-energy universe
evolves into inflation, followed by reheating and the standard Big Bang
cosmology. The symmetries of the theory force the c.c. to be the same before
and after the NEC-violating phase, so that a late-time observer sees an
effective c.c. of the correct magnitude. Importantly, our model allows neither
for eternal inflation nor for a set of possible values of dark energy, the
latter fixed by the parameters of the theory.


title: Zero rest-mass fields and the Newman-Penrose constants on flat space

abstract:
  Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2
propagating on flat space and their corresponding Newman-Penrose (NP) constants
are studied near spatial infinity. The aim of this analysis is to clarify the
correspondence between data for these fields on a spacelike hypersurface and
the value of their corresponding NP constants at future and past null infinity.
To do so, Friedrich's framework of the cylinder at spatial infinity is employed
to show that, expanding the initial data in terms spherical harmonics and
powers of the geodesic spatial distance $\rho$ to spatial infinity, the NP
constants correspond to the data for the second highest possible spherical
harmonic at fixed order in $\rho$. In addition, it is shown that for generic
initial data within the class considered in this article, there is no natural
correspondence between the NP constants at future and past null infinity ---for
both the Maxwell and spin-2 field. However, if the initial data is
time-symmetric then the NP constants at future and past null infinity have the
same information.


title: Cooling a harmonic oscillator by optomechanical modification of its bath

abstract:
  Optomechanical systems show tremendous promise for high sensitivity sensing
of forces and modification of mechanical properties via light. For example,
similar to neutral atoms and trapped ions, laser cooling of mechanical motion
by radiation pressure can take single mechanical modes to their ground state.
Conventional optomechanical cooling is able to introduce additional damping
channel to mechanical motion, while keeping its thermal noise at the same
level, and as a consequence, the effective temperature of the mechanical mode
is lowered. However, the ratio of temperature to quality factor remains roughly
constant, preventing dramatic advances in quantum sensing using this approach.
Here we propose an approach for simultaneously reducing the thermal load on a
mechanical resonator while improving its quality factor. In essence, we use the
optical interaction to dynamically modify the dominant damping mechanism,
providing an optomechanically-induced effect analogous to a phononic band gap.
The mechanical mode of interest is assumed to be weakly coupled to its heat
bath but strongly coupled to a second mechanical mode, which is cooled by
radiation pressure coupling to a red detuned cavity field. We also identify a
realistic optomechanical design that has the potential to realize this novel
cooling scheme.


title: The LPM effect in sequential bremsstrahlung: 4-gluon vertices

abstract:
  The splitting processes of bremsstrahlung and pair production in a medium are
coherent over large distances in the very high energy limit, which leads to a
suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper,
we continue study of the case when the coherence lengths of two consecutive
splitting processes overlap (which is important for understanding corrections
to standard treatments of the LPM effect in QCD), avoiding soft-gluon
approximations. In particular, this paper completes the calculation of the rate
for real double gluon bremsstrahlung from an initial gluon with various
simplifying assumptions (thick media; $\hat q$ approximation; and large $N_c$)
by now including processes involving 4-gluon vertices.


title: Domain walls and gravitational waves in the Standard Model

abstract:
  We study domain walls which can be created in the Standard Model under the
assumption that it is valid up to very high energy scales. We focus on domain
walls interpolating between the physical electroweak vacuum and the global
minimum appearing at very high field strengths. The creation of the network
which ends up in the electroweak vacuum percolating through the Universe is not
as difficult to obtain as one may expect, although it requires certain tuning
of initial conditions. Our numerical simulations confirm that such domain walls
would swiftly decay and thus cannot dominate the Universe. We discuss the
possibility of detection of gravitational waves produced in this scenario. We
have found that for the standard cosmology the energy density of these
gravitational waves is too small to be observed in present and planned
detectors.


title: Postselective quantum interference of distinguishable particles

abstract:
  We show that it is possible for completely distinguishable particles to
interfere postselectively without operating on, or indeed having any knowledge
of, the distinguishing degree of freedom. In particular, we find a family of
three-mode spatial interferometers that, upon inputting, say, a red photon in
port 1 and a green photon in port 2, produce a state such that when vacuum is
detected at one output, the two photons in the other two outputs will pass a
HOM test, despite their frequency degree of freedom remaining untouched. In
doing so we develop a general approach to distinguishability based on the
Schmidt decomposition between particles' "System" and "Label" degrees of
freedom, corresponding to what has been called unitary-unitary duality in
many-body physics. This also gives insight into the relationship between the
first and second quantized pictures, which is useful in bringing other quantum
information concepts across from the former to the latter.


title: Electron Attraction Mediated by Coulomb Repulsion

abstract:
  One of the defining properties of electrons is their mutual Coulombic
repulsion. In solids, however, this basic property may change. A famous example
is that of superconductors, where coupling to lattice vibrations make electrons
attract each other and leads to the formation of bound pairs. But what if all
degrees of freedom are electronic? Is it still possible to make electrons
attractive via their repulsion from other electrons? Such a mechanism, termed
'excitonic', was proposed fifty years ago by W. A. Little, aiming to achieve
stronger and more exotic superconductivity, yet despite many experimental
efforts, direct evidence for such 'excitonic' attraction is still lacking.
Here, we demonstrate this unique attraction by constructing, from the bottom
up, the fundamental building block of this mechanism. Our experiments are based
on quantum devices made from pristine carbon nanotubes, combined with cryogenic
precision manipulation. Using this platform we demonstrate that two electrons
can be made to attract using an independent electronic system as the binding
glue. Owing to its large tunability, our system offers crucial insights into
the underlying physics, such as the dependence of the emergent attraction on
the underlying repulsion and the origin of the pairing energy. We also
demonstrate transport signatures of 'excitonic' pairing. This experimental
demonstration of 'excitonic' pairing paves the way for the design of exotic
states of matter.


title:
Supermodularity in Unweighted Graph Optimization I: Branchings and
  Matchings

abstract:
  The main result of the paper is motivated by the following two, apparently
unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint
branchings theorem, characterize digraphs comprising $k$ disjoint branchings
$B_i$ each having a specified number $\mu _i$ of arcs, (B) as an extension of
Ryser's maximum term rank formula, determine the largest possible matching
number of simple bipartite graphs complying with degree-constraints. The
solutions to these problems and to their generalizations will be obtained from
a new min-max theorem on covering a supermodular function by a simple
degree-constrained bipartite graph. A specific feature of the result is that
its minimum cost extension is already NP-complete. Therefore classic polyhedral
tools themselves definitely cannot be sufficient for solving the problem, even
though they make some good service in our approach.


title: The Exchange Graphs of Weakly Separated Collections

abstract:
  Weakly separated collections arise in the cluster algebra derived from the
Pl\"ucker coordinates on the nonnegative Grassmannian. Oh, Postnikov, and
Speyer studied weakly separated collections over a general Grassmann necklace
$\mathcal{I}$ and proved the connectivity of every exchange graph. Oh and
Speyer later introduced a generalization of exchange graphs that we call
$\mathcal{C}$-constant graphs. They characterized these graphs in the smallest
two cases. We prove an isomorphism between exchange graphs and a certain class
of $\mathcal{C}$-constant graphs. We use this to extend Oh and Speyer's
characterization of these graphs to the smallest four cases, and we present a
conjecture on a bound on the maximal order of these graphs. In addition, we
fully characterize certain classes of these graphs in the special cases of
cycles and trees.


title: Self-avoiding walks adsorbed at a surface and pulled at their mid-point

abstract:
  We consider a self-avoiding walk on the $d$-dimensional hypercubic lattice,
terminally attached to an impenetrable hyperplane at which it can adsorb. When
a force is applied the walk can be pulled off the surface and we consider the
situation where the force is applied at the middle vertex of the walk. We show
that the temperature dependence of the critical force required for desorption
differs from the corresponding value when the force is applied at the end-point
of the walk. This is of interest in single molecule pulling experiments since
it shows that the required force can depend on where the force is applied. We
also briefly consider the situation when the force is applied at other interior
vertices of the walk.


title:
Adjoint Orbits of Matrix Groups over Finite Quotients of Compact
  Discrete Valuation Rings and Representation Zeta Functions

abstract:
  This paper gives methods to describe the adjoint orbits of
$\mathbf{G}(\mathfrak{o}_r)$ on $\mathrm{Lie}(\mathbf{G})(\mathfrak{o}_r)$
where $\mathfrak{o}_r=\mathfrak{o}/\mathfrak{p}^r$ ($r\in\mathbb{N}$) is a
finite quotient of the localization $\mathfrak{o}$ of the ring of integers of a
number field at a prime ideal $\mathfrak{p}$ and $\mathbf{G}$ is a closed
$\mathbb{Z}$-subgroup scheme of $\mathrm{GL}_{n}$ for an $n\in\mathbb{N}$ and
such that the Lie ring $\mathrm{Lie}(\mathbf{G})(\mathfrak{o})$ is quadratic..
The main result is a classification of the adjoint orbits in
$\mathrm{Lie}(\mathbf{G})(\mathfrak{o}_{r+1})$ whose reduction
$\bmod\,\mathfrak{p}^{r}$ contains
$a\in\mathrm{Lie}(\mathbf{G})(\mathfrak{o}_r)$ in terms of the reduction
$\bmod\mathfrak{p}$ of the stabilizer of $a$ for the
$\mathbf{G}(\mathfrak{o}_r)$-adjoint action. As an application, this result is
then used to compute the representation zeta function of the principal
congruence subgroups of $\mathrm{SL}_{3}(\mathfrak{o})$.


title: PFA and guessing models

abstract:
  This paper explores the consistency strength of The Proper Forcing Axiom
($\textsf{PFA}$) and the theory (T) which involves a variation of the
Viale-Wei$\ss$ guessing hull principle. We show that (T) is consistent relative
to a supercompact cardinal. The main result of the paper implies that the
theory "$\sf{AD}$$_\mathbb{R} + \Theta$ is regular" is consistent relative to
(T) and to $\textsf{PFA}$. This improves significantly the previous known best
lower-bound for consistency strength for (T) and $\textsf{PFA}$, which is
roughly "$\sf{AD}$$_\mathbb{R} + \textsf{DC}$".


title: Vladimir Naumovich Gribov: Pieces of biography

abstract:
  The talk presents the main lines of biography of the prominent physicist and
bright personality. Also given is a necessarily brief description of Gribov's
scientific work.


title: Information carrying capacity of a cosmological constant

abstract:
  We analyze the exchange of information in different cosmological backgrounds
when sender and receiver are timelike separated and communicate through
massless fields (without the exchange of light-signals). Remarkably, we show
that the dominance of a cosmological constant makes the amount of recoverable
information imprinted in the field by the sender extremely resilient: it does
not decay in time or with the spatial separation of sender and receiver, and it
actually increases with the rate of expansion of the Universe. This is in stark
contrast with the information carried by conventional light-signals and with
previous results on timelike communication through massless fields in matter
dominated cosmologies.


title:
Supermodularity in Unweighted Graph Opitimization III: Highly-connected
  Digraphs

abstract:
  By generalizing a recent result of Hong, Liu, and Lai on characterizing the
degree-sequences of simple strongly connected directed graphs, a
characterization is provided for degree-sequences of simple $k$-node-connected
digraphs. More generally, we solve the directed node-connectivity augmentation
problem when the augmented digraph is degree-specified and simple. As for
edge-connectivity augmentation, we solve the special case when the
edge-connectivity is to be increased by one and the augmenting digraph must be
simple.


title:
Supermodularity in Unweighted Graph Optimization II: Matroidal Term Rank
  Augmentation

abstract:
  Ryser's max term rank formula with graph theoretic terminology is equivalent
to a characterization of degree sequences of simple bipartite graphs with
matching number at least $\ell$. In a previous paper by the authors, a
generalization was developed for the case when the degrees are constrained by
upper and lower bounds. Here two other extensions of Ryser's theorem are
discussed. The first one is a matroidal model, while the second one settles the
augmentation version. In fact, the two directions shall be integrated into one
single framework.


title:
A near-infrared interferometric survey of debris-disc stars. V. PIONIER
  search for variability

abstract:
  Context: Extended circumstellar emission has been detected within a few 100
milli-arcsec around > 10% of nearby main sequence stars using near-infrared
interferometry. Follow-up observations using other techniques, should they
yield similar results or non-detections, can provide strong constraints on the
origin of the emission. They can also reveal the variability of the phenomenon.
  Aims: We aim to demonstrate the persistence of the phenomenon over time
scales of a few years and to search for variability of our previously detected
excesses.
  Methods: Using VLTI/PIONIER in H band we have carried out multi-epoch
observations of the stars for which a near-infrared excess was previously
detected with the same observing technique and instrument. The detection rates
and distribution of the excesses from our original survey and the follow-up
observations are compared statistically. A search for variability of the
excesses in our time series is carried out based on the level of the broadband
excesses.
  Results: In 12 of 16 follow-up observations, an excess is re-detected with a
significance of > 2 sigma, and in 7 of 16 follow-up observations significant
excess (> 3 sigma) has been re-detected. We statistically demonstrate with very
high confidence that the phenomenon persists for the majority of the systems.
We also present the first detection of potential variability in two sources.
  Conclusions: We conclude that the phenomenon responsible for the excesses
persists over time scales of a few years for the majority of the systems.
However, we also find that variability intrinsic to a target can cause it to
have no significant excess at the time of a specific observation.


title: Hamiltonian Dynamics of Cosmological Quintessence Models

abstract:
  The time-evolution dynamics of two nonlinear cosmological real gas models has
been reexamined in detail with methods from the theory of Hamiltonian dynamical
systems. These examples are FRWL cosmologies, one based on a gas, satisfying
the van der Waals equation and another one based on the virial expansion gas
equation. The cosmological variables used are the expansion rate, given by the
Hubble parameter, and the energy density. The analysis is aided by the
existence of global first integral as well as several special (second)
integrals in each case. In addition, the global first integral can serve as a
Hamiltonian for a canonical Hamiltonian formulation of the evolution equations.
The conserved quantities lead to the existence of stable periodic solutions
(closed orbits) which are models of a cyclic Universe. The second integrals
allow for explicit solutions as functions of time on some special trajectories
and thus for a deeper understanding of the underlying physics. In particular,
it is shown that any possible static equilibrium is reachable only for infinite
time.


title: Many-body localization in infinite chains

abstract:
  We investigate the phase transition between an ergodic and a many-body
localized phase in infinite anisotropic spin-$1/2$ Heisenberg chains with
binary disorder. Starting from the N\'eel state, we analyze the decay of
antiferromagnetic order $m_s(t)$ and the growth of entanglement entropy
$S_{\textrm{ent}}(t)$ during unitary time evolution. Near the phase transition
we find that $m_s(t)$ decays exponentially to its asymptotic value
$m_s(\infty)\neq 0$ in the localized phase while the data are consistent with a
power-law decay at long times in the ergodic phase. In the localized phase,
$m_s(\infty)$ shows an exponential sensitivity on disorder with a critical
exponent $\nu\sim 0.9$. The entanglement entropy in the ergodic phase grows
subballistically, $S_{\textrm{ent}}(t)\sim t^\alpha$, $\alpha\leq 1$, with
$\alpha$ varying continuously as a function of disorder. Exact diagonalizations
for small systems, on the other hand, do not show a clear scaling with system
size and attempts to determine the phase boundary from these data seem to
overestimate the extent of the ergodic phase.

categories: cond-mat.dis-nn cond-mat.quant-gas cond-mat.stat-mech cond-mat.str-el


title: Multipliers of uniform topological algebras

abstract:
  Let $E$ be a complete uniform topological algebra with Arens-Michael normed
factors $\left(E_{\alpha}\right)_{\alpha\in\Lambda}.$ Then $M\left(E\right)
\cong \varprojlim M\left(E_{\alpha}\right)$ within an algebra isomorphism
$\varphi$. If each factor $E_{\alpha}$ is complete, then every multiplier of
$E$ is continuous and $\varphi$ is a topological algebra isomorphism where
$M\left(E\right)$ is endowed with its seminorm topology.


title: Introduction to Cluster Algebras. Chapters 1-3

abstract:
  This is a preliminary draft of Chapters 1-3 of our forthcoming textbook
"Introduction to Cluster Algebras." This installment contains:
  Chapter 1. Total positivity
  Chapter 2. Mutations of quivers and matrices
  Chapter 3. Clusters and seeds


title:
Weak atomic convergence of finite voter models toward Fleming-Viot
  processes

abstract:
  We consider the empirical measures of multi-type voter models with mutation
on large finite sets, and prove their weak atomic convergence in the sense of
Ethier and Kurtz (1994) toward a Fleming-Viot process. Convergence in the weak
atomic topology is strong enough to answer a line of inquiry raised by Aldous
(2013) concerning the distributions of the corresponding entropy processes and
diversity processes for types.


title: Geometric significance of Toeplitz kernels

abstract:
  Let $L^2$ be the Lebesgue space of square-integrable functions on the unit
circle. We show that the injectivity problem for Toeplitz operators is linked
to the existence of geodesics in the Grassmann manifold of $L^2$. We also
investigate this connection in the context of restricted Grassmann manifolds
associated to $p$-Schatten ideals and essentially commuting projections.


title: Embedding-Based Interpolation on the Special Orthogonal Group

abstract:
  We study schemes for interpolating functions that take values in the special
orthogonal group $SO(n)$. Our focus is on interpolation schemes obtained by
embedding $SO(n)$ in a linear space, interpolating in the linear space, and
mapping the result onto $SO(n)$ via the closest point projection. The resulting
interpolants inherit both the order of accuracy and the regularity of the
underlying interpolants on the linear space. The values and derivatives of the
interpolants admit efficient evaluation via either explicit formulas or
iterative algorithms, which we detail for two choices of embeddings: the
embedding of $SO(n)$ in the space of $n \times n$ matrices and, when $n=3$, the
identification of $SO(3)$ with the set of unit quaternions. Along the way, we
point out a connection between these interpolation schemes and geodesic finite
elements. We illustrate the utility of these interpolation schemes by
numerically computing minimum acceleration curves on $SO(n)$, a task which is
handled naturally with $SO(n)$-valued finite elements having $C^1$-continuity.


title:
Pseudo-spectral Maxwell solvers for an accurate modeling of Doppler
  harmonic generation on plasma mirrors with Particle-In-Cell codes

abstract:
  With the advent of PW class lasers, the very large laser intensities
attainable on-target should enable the production of intense high order Doppler
harmonics from relativistic laser-plasma mirrors interactions. At present, the
modeling of these harmonics with Particle-In-Cell (PIC) codes is extremely
challenging as it implies an accurate description of tens of harmonic orders on
a a broad range of angles. In particular, we show here that standard Finite
Difference Time Domain (FDTD) Maxwell solvers used in most PIC codes partly
fail to model Doppler harmonic generation because they induce numerical
dispersion of electromagnetic waves in vacuum which is responsible for a
spurious angular deviation of harmonic beams. This effect was extensively
studied and a simple toy-model based on Snell-Descartes law was developed that
allows us to finely predict the angular deviation of harmonics depending on the
spatio-temporal resolution and the Maxwell solver used in the simulations. Our
model demonstrates that the mitigation of this numerical artifact with FDTD
solvers mandates very high spatio-temporal resolution preventing doing
realistic 3D simulations. We finally show that non dispersive pseudo-spectral
analytical time domain solvers can considerably reduce the spatio-temporal
resolution required to mitigate this spurious deviation and should enable in
the the near future 3D accurate modeling on supercomputers in a realistic
time-to-solution.


title: Proof of a Conjecture of Kleinberg-Sawin-Speyer

abstract:
  In Ellenberg and Gijswijt's groundbreaking work, the authors show that a
subset of $\mathbb{Z}_3^{n}$ with no arithmetic progression of length 3 must be
of size at most $2.755^n$ (no prior upper bound was known of
$(3-\epsilon)^n)$), and provide for any prime $p$ a value $\lambda_p<p$ such
that any subset of $\mathbb{Z}_p^{n}$ with no arithmetic progression of length
3 must be of size at most $\lambda_p^n$.
  Blasiak et al showed that the same bounds apply to tri-coloured sum-free
sets, which are triples $\{(a_i,b_i,c_i):a_i,b_i,c_i\in\mathbb{Z}_p^{n}\}$ with
$a_i+b_j+c_k=0$ if and only if $i=j=k$.
  Building on this work, Kleinberg, Sawin and Speyer gave a description of a
value $\mu_p$ such that no tri-coloured sum-free sets of size $e^{\mu_p n}$
exist in $\mathbb{Z}_p^{n}$, but for any $\epsilon>0$, such sets of size
$e^{(\mu_p-\epsilon) n}$ exist for all sufficiently large $n$. The value of
$\mu_p$ was left open, but a conjecture was stated which would imply that
$e^{\mu_p}=\lambda_p$, i.e. the Ellenberg-Gijswijt bound is correct for the
sum-free set problem.
  The purpose of this note is to close that gap. The conjecture of Kleinberg,
Sawin and Speyer is true, and the Ellenberg-Gijswijt bound is the correct
exponent for the sum-free set problem.


title: A stability version for a theorem of Erd\H{o}s on nonhamiltonian graphs

abstract:
  Let $n, d$ be integers with $1 \leq d \leq \left \lfloor \frac{n-1}{2} \right
\rfloor$, and set $h(n,d):={n-d \choose 2} + d^2$ and $e(n,d):=
\max\{h(n,d),h(n, \left \lfloor \frac{n-1}{2} \right \rfloor)\}$. Because
$h(n,d)$ is quadratic in $d$, there exists a $d_0(n)=(n/6)+O(1)$ such that
$e(n,1)> e(n, 2)> \dots >e(n,d_0)=e(n, d_0+1)=\dots = e(n,\left \lfloor
\frac{n-1}{2} \right \rfloor)$. A theorem by Erd\H{o}s states that for $d\leq
\left \lfloor \frac{n-1}{2} \right \rfloor$, any $n$-vertex nonhamiltonian
graph $G$ with minimum degree $\delta(G) \geq d$ has at most $e(n,d)$ edges,
and for $d > d_0(n)$ the unique sharpness example is simply the graph
$K_n-E(K_{\lceil (n+1)/2\rceil})$. Erd\H{o}s also presented a sharpness example
$H_{n,d}$ for each $1\leq d \leq d_0(n)$. We show that if $d< d_0(n)$ and a
$2$-connected, nonhamiltonian $n$-vertex graph $G$ with $\delta(G) \geq d$ has
more than $e(n,d+1)$ edges, then $G$ is a subgraph of $H_{n,d}$. Note that
$e(n,d) - e(n, d+1) = n - 3d - 2 \geq n/2$ whenever $d< d_0(n)-1$.


title:
Extending the OpenAI Gym for robotics: a toolkit for reinforcement
  learning using ROS and Gazebo

abstract:
  This paper presents an extension of the OpenAI Gym for robotics using the
Robot Operating System (ROS) and the Gazebo simulator. The content discusses
the software architecture proposed and the results obtained by using two
Reinforcement Learning techniques: Q-Learning and Sarsa. Ultimately, the output
of this work presents a benchmarking system for robotics that allows different
techniques and algorithms to be compared using the same virtual conditions.


title: A Scalable Framework for Wireless Distributed Computing

abstract:
  We consider a wireless distributed computing system, in which multiple mobile
users, connected wirelessly through an access point, collaborate to perform a
computation task. In particular, users communicate with each other via the
access point to exchange their locally computed intermediate computation
results, which is known as data shuffling. We propose a scalable framework for
this system, in which the required communication bandwidth for data shuffling
does not increase with the number of users in the network. The key idea is to
utilize a particular repetitive pattern of placing the dataset (thus a
particular repetitive pattern of intermediate computations), in order to
provide coding opportunities at both the users and the access point, which
reduce the required uplink communication bandwidth from users to access point
and the downlink communication bandwidth from access point to users by factors
that grow linearly with the number of users. We also demonstrate that the
proposed dataset placement and coded shuffling schemes are optimal (i.e.,
achieve the minimum required shuffling load) for both a centralized setting and
a decentralized setting, by developing tight information-theoretic lower
bounds.


title:
Decomposition of a complete bipartite multigraph into arbitrary cycle
  sizes

abstract:
  In a graph $G$, let $\mu_G(xy)$ denote the number of edges between $x$ and
$y$ in $G$. Let $\lambda K_{v,u}$ be the graph $(V\cup U,E)$ with $|V|=v$,
$|U|=u$, and \[ \mu_G(xy)=\begin{cases} \lambda &\mbox{if $x\in U$ and $y\in V$
or if $x\in V$ and $y\in U$}\\ 0 &\mbox{otherwise.} \\ \end{cases} \] Let $M$
be a sequence of non-negative integers $m_1,m_2,\ldots,m_n$. An $(M)$-cycle
decomposition of a graph $G$ is a partition of the edge set into cycles of
lengths $m_1,m_2,\ldots,m_n$. In this paper, we establish necessary and
sufficient conditions for the existence of an $(M)$-cycle decomposition of
$\lambda K_{v,u}$.


title:
RETAIN: An Interpretable Predictive Model for Healthcare using Reverse
  Time Attention Mechanism

abstract:
  Accuracy and interpretability are two dominant features of successful
predictive models. Typically, a choice must be made in favor of complex black
box models such as recurrent neural networks (RNN) for accuracy versus less
accurate but more interpretable traditional models such as logistic regression.
This tradeoff poses challenges in medicine where both accuracy and
interpretability are important. We addressed this challenge by developing the
REverse Time AttentIoN model (RETAIN) for application to Electronic Health
Records (EHR) data. RETAIN achieves high accuracy while remaining clinically
interpretable and is based on a two-level neural attention model that detects
influential past visits and significant clinical variables within those visits
(e.g. key diagnoses). RETAIN mimics physician practice by attending the EHR
data in a reverse time order so that recent clinical visits are likely to
receive higher attention. RETAIN was tested on a large health system EHR
dataset with 14 million visits completed by 263K patients over an 8 year period
and demonstrated predictive accuracy and computational scalability comparable
to state-of-the-art methods such as RNN, and ease of interpretability
comparable to traditional models.


title: Supnorm of an eigenfunction of finitely many Hecke operators

abstract:
  Let $\phi$ be a Laplace eigenfunction on a compact hyperbolic surface
attached to an order in a quaternion algebra. Assuming that $\phi$ is an
eigenfunction of Hecke operators at a \emph{fixed finite} collection of primes,
we prove an $L^\infty$-norm bound for $\phi$ that improves upon the trivial
estimate by a power of the logarithm of the eigenvalue. We have constructed an
amplifier whose length depends on the support of the amplifier on Hecke trees.
We have used a method of B\'erard in \cite{Be} to improve the archimedean
amplification.


title:
Space-Filling Curves as a Novel Crystal Structure Representation for
  Machine Learning Models

abstract:
  A fundamental problem in applying machine learning techniques for chemical
problems is to find suitable representations for molecular and crystal
structures. While the structure representations based on atom connectivities
are prevalent for molecules, two-dimensional descriptors are not suitable for
describing molecular crystals. In this work, we introduce the SFC-M family of
feature representations, which are based on Morton space-filling curves, as an
alternative means of representing crystal structures. Latent Semantic Indexing
(LSI) was employed in a novel setting to reduce sparsity of feature
representations. The quality of the SFC-M representations were assessed by
using them in combination with artificial neural networks to predict Density
Functional Theory (DFT) single point, Ewald summed, lattice, and many-body
dispersion energies of 839 organic molecular crystal unit cells from the
Cambridge Structural Database that consist of the elements C, H, N, and O.
Promising initial results suggest that the SFC-M representations merit further
exploration to improve its ability to predict solid-state properties of organic
crystal structures


title:
First Search for Lorentz and CPT Violation in Double Beta Decay with
  EXO-200

abstract:
  This proceedings contribution reports the first experimental search for
Lorentz- and CPT-violating signals specifically studying the effect of the
Standard-Model Extension (SME) oscillation-free momentum-independent neutrino
coupling operator in the double beta decay process. The search has been
performed using an exposure of 100 kg yr of $^{136}$Xe with the EXO-200
detector. No significant evidence of the spectral modification due to isotropic
Lorentz violation was found. A two-sided limit of $-2.65 \times 10^{-5}$ GeV
$<$ $\mathring{a}_{\mathrm{of}}^{(3)}$ $< 7.60 \times 10^{-6}$ GeV (90% C.L.)
is placed on the relevant coefficient within the SME.


title:
Solving a Mixture of Many Random Linear Equations by Tensor
  Decomposition and Alternating Minimization

abstract:
  We consider the problem of solving mixed random linear equations with $k$
components. This is the noiseless setting of mixed linear regression. The goal
is to estimate multiple linear models from mixed samples in the case where the
labels (which sample corresponds to which model) are not observed. We give a
tractable algorithm for the mixed linear equation problem, and show that under
some technical conditions, our algorithm is guaranteed to solve the problem
exactly with sample complexity linear in the dimension, and polynomial in $k$,
the number of components. Previous approaches have required either exponential
dependence on $k$, or super-linear dependence on the dimension. The proposed
algorithm is a combination of tensor decomposition and alternating
minimization. Our analysis involves proving that the initialization provided by
the tensor method allows alternating minimization, which is equivalent to EM in
our setting, to converge to the global optimum at a linear rate.

categories: cs.LG cs.IT math.IT math.ST stat.ML stat.TH


title:
Globular Clusters, Ultracompact Dwarfs, and Dwarf Galaxies in Abell 2744
  at the Redshift of 0.308

abstract:
  We report a photometric study of globular clusters (GCs), ultracompact dwarfs
(UCDs), and dwarf galaxies in the giant merging galaxy cluster Abell 2744 at z
= 0.308. Color-magnitude diagrams of the point sources derived from deep F814W
(restframe r') and F105W (restframe I) images of Abell 2744 in the Hubble Space
Telescope Frontier Field show a rich population of point sources whose colors
are similar to those of typical GCs. These sources are as bright as -14.9 <
M_r' < -11.4 (26.0 < F814W < 29.5) mag, being mostly UCDs and bright GCs in
Abell 2744. The luminosity function (LF) of these sources shows a break at M_r'
~ -12.9 (F814W ~ 28.0) mag, indicating a boundary between UCDs and bright GCs.
The numbers of GCs and UCDs are estimated to be N_GC = 385,000+-24,000, and 147
+- 26, respectively. The clustercentric radial number density profiles of the
UCDs and bright GCs show similar slopes, but these profiles are much steeper
than that of the dwarf galaxies and the mass density profile based on
gravitational lensing analysis. We derive an LF of the red sequence galaxies
for -22.9 < M_r' < -13.9 mag. The faint end of this LF is fit well by a flat
power law with a = -1.14 +- 0.08, showing no faint upturn. These results
support the galaxy-origin scenario for bright UCDs: they are the nuclei of
dwarf galaxies that were stripped when they pass close to the center of massive
galaxies or a galaxy cluster, while some of the faint UCDs are the bright end
of the GCs.


title: The Structured `Low Temperature' Phase of the Retinal Population Code

abstract:
  Recent advances in experimental techniques have allowed the simultaneous
recording of populations of hundreds of neurons, allowing more comprehensive
investigation into the nature of the collective structure of population neural
activity. While recent studies have reported a phase transition in the
parameter space of maximum entropy models describing the neural probability
distributions, the interpretation of these findings has been debated. Here, we
suggest that this phase transition may be evidence of a `structured',
collective state in the neural population. We show that this phase transition
is robust to changes in stimulus ensemble and adaptive state. We find that the
pattern of pairwise correlations between neurons has a strength that is well
within the strongly correlated regime and does not require fine tuning,
suggesting that this state is generic for populations of 100+ neurons. We find
a clear correspondence between the emergence of a phase transition, and the
emergence of attractor-like structure in the inferred energy landscape. A
collective state in the neural population, in which neural activity patterns
naturally form clusters, provides a consistent interpretation for our results.


title: How Einstein Got His Field Equations

abstract:
  We study the pages in Albert Einstein's 1916 landmark paper in the Annalen
der Physik where he derived his field equations for gravity. Einstein made two
heuristic and physically insightful steps. The first was to obtain the field
equations in vacuum in a rather geometric fashion. The second step was
obtaining the field equations in the presence of matter from the field
equations in vacuum. (This transition is an essential principle in physics,
much as the principle of local gauge invariance in quantum field theory.) To
this end, we go over some quick differential geometric background related to
curvilinear coordinates, vectors, tensors, metric tensor, Christoffel symbols,
Riemann curvature tensor, Ricci tensor, and see how Einstein used geometry to
model gravity.


title:
Scattering framework for two particles with isotropic spin-orbit
  coupling applicable to all energies

abstract:
  Previous work developed a K-matrix formalism applicable to positive energies
for the scattering between two $s$-wave interacting particles with two internal
states, isotropic spin-orbit coupling and vanishing center-of-mass momentum [H.
Duan, L. You and B. Gao, Phys. Rev A {\bf{87}}, 052708 (2013)]. This work
extends the formalism to the entire energy regime. Explicit solutions are
obtained for the total angular momentum $J=0$ and $1$ channels. The behavior of
the partial cross sections in the negative energy regime is analyzed in detail.
We find that the leading contributions to the partial cross sections at the
negative energy thresholds are governed by the spin-orbit coupling strength
$k_{\text{so}}$ and the mass ratio. The fact that these contributions are
independent of the two-body scattering length $a_s$ is a direct consequence of
the effective reduction of the dimensionality, and hence of the density of
states, near the scattering thresholds due to the single-particle spin-orbit
coupling terms. The results are analytically continued to the energy regime
where bound states exist. It is shown that our results are consistent with
results obtained by alternative approaches. Our formulation, which can be
regarded as an extension of the standard textbook partial wave decomposition,
can be generalized to two-body systems with other types of spin-orbit coupling,
including cases where the center-of-mass momentum does not vanish.


title: Fast estimation of approximate matrix ranks using spectral densities

abstract:
  In many machine learning and data related applications, it is required to
have the knowledge of approximate ranks of large data matrices at hand. In this
paper, we present two computationally inexpensive techniques to estimate the
approximate ranks of such large matrices. These techniques exploit approximate
spectral densities, popular in physics, which are probability density
distributions that measure the likelihood of finding eigenvalues of the matrix
at a given point on the real line. Integrating the spectral density over an
interval gives the eigenvalue count of the matrix in that interval. Therefore
the rank can be approximated by integrating the spectral density over a
carefully selected interval. Two different approaches are discussed to estimate
the approximate rank, one based on Chebyshev polynomials and the other based on
the Lanczos algorithm. In order to obtain the appropriate interval, it is
necessary to locate a gap between the eigenvalues that correspond to noise and
the relevant eigenvalues that contribute to the matrix rank. A method for
locating this gap and selecting the interval of integration is proposed based
on the plot of the spectral density. Numerical experiments illustrate the
performance of these techniques on matrices from typical applications.


title:
Self-optimizing layered hydrogen evolution catalyst with high
  basal-plane activity

abstract:
  Hydrogen is a promising energy carrier and key agent for many industrial
chemical processes1. One method for generating hydrogen sustainably is via the
hydrogen evolution reaction (HER), in which electrochemical reduction of
protons is mediated by an appropriate catalyst-traditionally, an expensive
platinum-group metal. Scalable production requires catalyst alternatives that
can lower materials or processing costs while retaining the highest possible
activity. Strategies have included dilute alloying of Pt2 or employing less
expensive transition metal alloys, compounds or heterostructures (e.g., NiMo,
metal phosphides, pyrite sulfides, encapsulated metal nanoparticles)3-5.
Recently, low-cost, layered transition-metal dichalcogenides (MX2)6 based on
molybdenum and tungsten have attracted substantial interest as alternative HER
catalysts7-11. These materials have high intrinsic per-site HER activity;
however, a significant challenge is the limited density of active sites, which
are concentrated at the layer edges.8,10,11. Here we use theory to unravel
electronic factors underlying catalytic activity on MX2 surfaces, and leverage
the understanding to report group-5 MX2 (H-TaS2 and H-NbS2) electrocatalysts
whose performance instead derives from highly active basal-plane sites. Beyond
excellent catalytic activity, they are found to exhibit an unusual ability to
optimize their morphology for enhanced charge transfer and accessibility of
active sites as the HER proceeds. This leads to long cycle life and practical
advantages for scalable processing. The resulting performance is comparable to
Pt and exceeds all reported MX2 candidates.


title:
Sufficient conditions for a linear operator on $\mathbb{R}[x]$ to be
  monotone

abstract:
  We demonstrate that being a hyperbolicity preserver does not imply
monotonicity for infinite order differential operators on $\mathbb{R}[x]$,
thereby settling a recent conjecture in the negative. We also give some
sufficient conditions for such operators to be monotone.


title: Periodic approximation of Lyapunov exponents for Banach cocycles

abstract:
  We consider group-valued cocycles over dynamical systems. The base system is
a homeomorphism $f$ of a metric space satisfying a closing property, for
example a hyperbolic dynamical system or a subshift of finite type. The cocycle
$A$ takes values in the group of invertible bounded linear operators on a
Banach space and is H\"older continuous. We prove that upper and lower Lyapunov
exponents of $A$ with respect to an ergodic invariant measure $\mu$ can be
approximated in terms of the norms of the values of $A$ on periodic orbits of
$f$. We also show that these exponents cannot always be approximated by the
exponents of $A$ with respect to measures on periodic orbits. Our arguments
include a result of independent interest on construction and properties of a
Lyapunov norm for infinite dimensional setting. As a corollary, we obtain
estimates of the growth of the norm and of the quasiconformal distortion of the
cocycle in terms of the growth at the periodic points of $f$.


title:
Boundedness, compactness, and invariant norms for Banach cocycles over
  hyperbolic systems

abstract:
  We consider group-valued cocycles over dynamical systems with hyperbolic
behavior. The base system is either a hyperbolic diffeomorphism or a mixing
subshift of finite type. The cocycle $A$ takes values in the group of
invertible bounded linear operators on a Banach space and is H\"older
continuous. We consider the periodic data of $A$, i.e. the set of its return
values along the periodic orbits in the base. We show that if the periodic data
of $A$ is uniformly quasiconformal or bounded or contained in a compact set,
then so is the cocycle. Moreover, in the latter case the cocycle is isometric
with respect to a H\"older continuous family of norms. We also obtain a general
result on existence of a measurable family of norms invariant under a cocycle.


title:
Five-list-coloring graphs on surfaces III. One list of size one and one
  list of size two

abstract:
  Let $G$ be a plane graph with outer cycle $C$ and let $(L(v):v\in V(G))$ be a
family of non-empty sets. By an $L$-coloring of $G$ we mean a (proper) coloring
$\phi$ of $G$ such that $\phi(v)\in L(v)$ for every vertex $v$ of $G$.
Thomassen proved that if $v_1,v_2\in V(C)$ are adjacent, $L(v_1)\ne L(v_2)$,
$|L(v)|\ge3$ for every $v\in V(C)-\{v_1,v_2\}$ and $|L(v)|\ge5$ for every $v\in
V(G)-V(C)$, then $G$ has an $L$-coloring. What happens when $v_1$ and $v_2$ are
not adjacent? Then an $L$-coloring need not exist, but in the first paper of
this series we have shown that it exists if $|L(v_1)|,|L(v_2)|\ge2$. Here we
characterize when an $L$-coloring exists if $|L(v_1)|\ge1$ and $|L(v_2)|\ge2$.
  This result is a lemma toward a more general theorem along the same lines,
which we will use to prove that minimally non-$L$-colorable planar graphs with
two precolored cycles of bounded length are of bounded size. The latter result
has a number of applications which we pursue elsewhere.


title:
On the shift in membrane miscibility transition temperature upon
  addition of short-chain alcohols

abstract:
  I consider the effect of a small concentration of a molecule, such as a
short-chain alcohol, on the miscibility transition temperature of a giant
plasma membrane vesicle. For concentrations sufficiently small such that the
system can be treated as a weak solution, the change in transition temperature
is known to depend upon the extent of the molecule's partition into the
coexisting liquid-disordered and liquid-ordered phases. Preferential
partitioning into the former decreases the miscibility temperature, while
preferential partitioning into the latter causes an increase. The analysis,
combined with calculated values of the partition coefficient of saturated
chains, illuminates the results of recent experiments on the change in
miscibility transition temperatures with changing alcohol chain length, and
makes several testable predictions.


title:
Hybrid excitations due to crystal-field, spin-orbit coupling and
  spin-waves in LiFePO$_4$

abstract:
  We report on the spin waves and crystal field excitations in single crystal
LiFePO$_4$ by inelastic neutron scattering over a wide range of temperatures,
below and above the antiferromagnetic transition of this system. In particular,
we find extra excitations below $T_N=50$ K that are nearly dispersionless and
are most intense around magnetic zone centers. We show that these excitations
correspond to transitions between thermally occupied excited states of
Fe$^{2+}$ due to splitting of the $S=2$ levels that arise from crystal field
and spin-orbit interaction. These excitations are further amplified by the
highly distorted nature of the oxygen octahedron surrounding the iron atoms.
Above $T_N$, magnetic fluctuations are observed up to at least 720~K, with
additional excitation around 4 meV, likely caused by single-ion splittings
through spin-orbit and crystal field interactions. The latter weakens slightly
at 720~K compared to 100~K, which is consistent with calculated cross-sections
using a single-ion model. Our theoretical analysis, using the MF-RPA model,
provides both detailed spectra of the Fe $d-$ shell and estimates of the
average ordered magnetic moment and $T_N$. By applying the MF-RPA model to a
number of existing spin-wave results from other Li$M$PO$_4$ ($M=$ Mn, Co, and
Ni), we are able to obtain reasonable predictions for the moment sizes and
transition temperatures.


title: Coherent hole propagation in an exactly solvable gapless spin liquid

abstract:
  We examine the dynamics of a single hole in the gapless phase of the Kitaev
honeycomb model, focusing on the slow-hole regime where the bare hopping
amplitude $t$ is much less than the Kitaev exchange energy $J$. In this regime,
the hole does not generate gapped flux excitations and is dressed only by the
gapless fermion excitations. Investigating the single-hole spectral function,
we find that the hole propagates coherently with a quasiparticle weight that is
finite but approaches zero as $t/J \to 0$. This conclusion follows from two
approximate treatments, which capture the same physics in complementary ways.
Both treatments use the stationary limit as an exactly solvable starting point
to study the spectral function approximately (i) by employing a variational
approach in terms of a trial state that interpolates between the limits of a
stationary hole and an infinitely fast hole and (ii) by considering a special
point in the gapless phase that corresponds to a simplified one-dimensional
problem.


title: Inference in Probabilistic Logic Programs using Lifted Explanations

abstract:
  In this paper, we consider the problem of lifted inference in the context of
Prism-like probabilistic logic programming languages. Traditional inference in
such languages involves the construction of an explanation graph for the query
and computing probabilities over this graph. When evaluating queries over
probabilistic logic programs with a large number of instances of random
variables, traditional methods treat each instance separately. For many
programs and queries, we observe that explanations can be summarized into
substantially more compact structures, which we call lifted explanation graphs.
In this paper, we define lifted explanation graphs and operations over them. In
contrast to existing lifted inference techniques, our method for constructing
lifted explanations naturally generalizes existing methods for constructing
explanation graphs. To compute probability of query answers, we solve
recurrences generated from the lifted graphs. We show examples where the use of
our technique reduces the asymptotic complexity of inference.


title: Optimally Stopped Optimization

abstract:
  We combine the fields of heuristic optimization and optimal stopping. We
propose a strategy for benchmarking randomized optimization algorithms that
minimizes the expected total cost for obtaining a good solution with an optimal
number of calls to the solver. To do so, rather than letting the objective
function alone define a cost to be minimized, we introduce a further
cost-per-call of the algorithm. We show that this problem can be formulated
using optimal stopping theory. The expected cost is a flexible figure of merit
for benchmarking probabilistic solvers that can be computed when the optimal
solution is not known, and that avoids the biases and arbitrariness that affect
other measures. The optimal stopping formulation of benchmarking directly leads
to a real-time, optimal-utilization strategy for probabilistic optimizers with
practical impact. We apply our formulation to benchmark simulated annealing on
a class of MAX2SAT problems. We also compare the performance of a D-Wave 2X
quantum annealer to the HFS solver, a specialized classical heuristic algorithm
designed for low tree-width graphs. On a set of frustrated-loop instances with
planted solutions defined on up to N = 1098 variables, the D-Wave device is two
orders of magnitude faster than the HFS solver, and, modulo known caveats
related to suboptimal annealing times, exhibits identical scaling with problem
size.


title:
Multiscale modeling of thermomechanical behaviour of three-phase
  nanocomposite

abstract:
  In this work, we developed an improved shear lag model to investigate the
load transfer characteristics of three-phase nanocomposite which is reinforced
with microscale fibers augmented with carbon nanotubes on their circumferential
surfaces. The shear lag model accounts for (i) radial and axial deformations of
different transversely isotropic constituents, (ii) thermomechanical loads on
the representative volume element (RVE), and (iii) staggering effect of
adjacent RVEs. The results from the current newly developed shear lag model are
validated with the finite element simulations and found to be in good
agreement. Our study reveals that the reduction in the maximum value of the
axial stress in the fiber and the interfacial shear stress along its length
become more pronounced in the presence of applied thermomechanical loads on the
staggered RVEs. The existence of shear tractions along the RVE length plays a
significant role in the load transfer characteristics and cannot be ignored.


title: On Nonconvex Decentralized Gradient Descent

abstract:
  Consensus optimization has received considerable attention in recent years. A
number of decentralized algorithms have been proposed for {convex} consensus
optimization. However, to the behaviors or consensus \emph{nonconvex}
optimization, our understanding is more limited.
  When we lose convexity, we cannot hope our algorithms always return global
solutions though they sometimes still do sometimes. Somewhat surprisingly, the
decentralized consensus algorithms, DGD and Prox-DGD, retain most other
properties that are known in the convex setting. In particular, when
diminishing (or constant) step sizes are used, we can prove convergence to a
(or a neighborhood of) consensus stationary solution under some regular
assumptions. It is worth noting that Prox-DGD can handle nonconvex nonsmooth
functions if their proximal operators can be computed. Such functions include
SCAD and $\ell_q$ quasi-norms, $q\in[0,1)$. Similarly, Prox-DGD can take the
constraint to a nonconvex set with an easy projection.
  To establish these properties, we have to introduce a completely different
line of analysis, as well as modify existing proofs that were used the convex
setting.


title: Ultrafast Radiative Heat Transfer

abstract:
  Light absorption in conducting materials produces heating of their conduction
electrons, followed by relaxation into phonons within picoseconds, and
subsequent diffusion into the surrounding media over longer timescales. This
conventional picture of optical heating is supplemented by radiative cooling,
which typically takes place at an even lower pace, only becoming relevant for
structures held in vacuum or under extreme conditions of thermal isolation.
Here we reveal an ultrafast radiative cooling regime between neighboring
plasmon-supporting graphene nanostructures in which noncontact heat transfer
becomes a dominant channel. We predict that >50% of the electronic heat energy
deposited on a graphene disk can be transferred to a neighboring nanoisland
within a femtosecond timescale. This phenomenon is facilitated by the
combination of low electronic heat capacity and large plasmonic field
concentration displayed by doped graphene. Similar effects should take place in
other van der Waals materials, thus opening an unexplored avenue toward
efficient heat management in ultrathin nanostructures.


title:
On Optimal Fronthaul Compression and Decoding Strategies for Uplink
  Cloud Radio Access Networks

abstract:
  This paper investigates the compress-and-forward scheme for an uplink cloud
radio access network (C-RAN) model, where multi-antenna base-stations (BSs) are
connected to a cloud-computing based central processor (CP) via
capacity-limited fronthaul links. The BSs compress the received signals with
Wyner-Ziv coding and send the representation bits to the CP; the CP performs
the decoding of all the users' messages. Under this setup, this paper makes
progress toward the optimal structure of the fronthaul compression and CP
decoding strategies for the compress-and-forward scheme in C-RAN. On the CP
decoding strategy design, this paper shows that under a sum fronthaul capacity
constraint, a generalized successive decoding strategy of the quantization and
user message codewords that allows arbitrary interleaved order at the CP
achieves the same rate region as the optimal joint decoding. Further, it is
shown that a practical strategy of successively decoding the quantization
codewords first, then the user messages, achieves the same maximum sum rate as
joint decoding under individual fronthaul constraints. On the joint
optimization of user transmission and BS quantization strategies, this paper
shows that if the input distributions are assumed to be Gaussian, then under
joint decoding, the optimal quantization scheme for maximizing the achievable
rate region is Gaussian. Moreover, Gaussian input and Gaussian quantization
with joint decoding achieve to within a constant gap of the capacity region of
the Gaussian multiple-input multiple-output (MIMO) uplink C-RAN model. Finally,
this paper addresses the computational aspect of optimizing uplink MIMO C-RAN
by showing that under fixed Gaussian input, the sum rate maximization problem
over the Gaussian quantization noise covariance matrices can be formulated as
convex optimization problems, thereby facilitating its efficient solution.


title: On the asymptotic linearity of reduction number

abstract:
  Let $R$ be a standard graded Noetherian algebra over an infinite field $K$
and $M$ a finitely generated $\mathbb{Z}$-graded $R$-module. Then for any
graded ideal $I\subseteq R_+$ of $R$, we show that there exist integers
$e_1\geq e_2$ such that $r(I^nM)=\rho_I(M)n+e_1$ and $D(I^nM)=\rho_I(M)n+e_2$
for $n\gg0$. Here $r(M)$ and $D(M)$ denote the reduction number of $M$ and the
maximal degree of minimal generators of $M$ respectively, and $\rho_I(M)$ is an
integer determined by both $M$ and $I$. We introduce the notion of generalized
regularity function $\Gamma$ for a standard graded algebra over a Noetherian
ring and prove that $\Gamma(I^nM)$ is also a linear function in $n$ for $n\gg
0$.


title: Hierarchical Scaling in Systems of Natural Cities

abstract:
  Hierarchies can be modeled by a set of exponential functions, from which we
can derive a set of power laws indicative of scaling. The solution to a scaling
relation equation is always a power law. The scaling laws are followed by many
natural and social phenomena such as cities, earthquakes, and rivers. This
paper is devoted to revealing the power law behaviors in systems of natural
cities by reconstructing the hierarchy with cascade structure. The cities of
America, Britain, France, and Germany are taken as examples to make empirical
analyses. The hierarchical scaling relations can be well fitted to the data
points within the scaling ranges of the size and area of the natural cities.
The size-number and area-number scaling exponents are close to 1, and the
allometric scaling exponent is slightly less than 1. The results show that
natural cities follow hierarchical scaling laws and hierarchical conservation
law very well. The hierarchical scaling law proved to be derived from entropy
maximization principle, and this suggests that the evolution of natural cities
is dominated by entropy maximization laws. This study is helpful for scientists
to understand the power law behavior in the development of cities and systems
of cities.


title:
The energy loss effect of incoming gluon from $J/\psi$ production in p-A
  collisions

abstract:
  The energy loss effect of incoming gluon from $J/\psi$ production in p-A (or
d-A) collisions is investigated by means of the E866, RHIC and LHC experimental
data. The gluon mean energy loss per unit path length $dE/dL = 2.18\pm0.14$
GeV/fm is extracted by fitting the E866 experimental data for $J/\psi$
production cross section ratios $R_{W(Fe)/Be}(x_{F})$. The obtained result
indicates that the incoming gluons lose more energy than the incident quarks.
  By comparing the theoretical results with E866, RHIC, and LHC experimental
data, it is found that the nuclear suppression due to the incident gluon
(quark) energy loss reduces (increases) with the increase of the kinematic
variable $x_{F}$ (or $y$). The energy loss effect of incoming gluon plays an
important role on the suppression of $J/\psi$ production in a wide energy range
from $\sqrt{s}=38.7$ GeV to $\sqrt{s}=5.0$ TeV, and the influence of incident
quark energy loss can be ignored for high energy(such as at RHIC and LHC
energy).


title: A Data-Driven Approach for Mapping Multivariate Data to Color

abstract:
  A wide variety of color schemes have been devised for mapping scalar data to
color. Some use the data value to index a color scale. Others assign colors to
different, usually blended disjoint materials, to handle areas where materials
overlap. A number of methods can map low-dimensional data to color, however,
these methods do not scale to higher dimensional data. Likewise, schemes that
take a more artistic approach through color mixing and the like also face
limits when it comes to the number of variables they can encode. We address the
challenge of mapping multivariate data to color and avoid these limitations at
the same time. It is a data driven method, which first gauges the similarity of
the attributes and then arranges them according to the periphery of a convex 2D
color space, such as HSL. The color of a multivariate data sample is then
obtained via generalized barycentric coordinate (GBC) interpolation.


title: Extending Scatterplots to Scalar Fields

abstract:
  Embedding high-dimensional data into a 2D canvas is a popular strategy for
their visualization.


title: Ambiguity appearing on the Hamiltonian formulation of Quantum Mechanics

abstract:
  For the symmetric harmonic oscillator and the symmetric bouncer defined in
2-D, two different Hamiltonian are given describing the same classical
dynamics; however, their quantum dynamics behavior are different.


title: Several properties of $\alpha$-harmonic functions in the unit disk

abstract:
  The aim of this paper is to obtain the Schwarz-Pick type inequality for
$\alpha$-harmonic functions $f$ in the unit disk and get estimates on the
coefficients of $f$. As an application, a Landau type theorem of
$\alpha$-harmonic functions is established.


title: Odds for an enlightened rather than barren future

abstract:
  We are at a stage in our evolution where we do not yet know if we will ever
communicate with intelligent beings that have evolved on other planets, yet we
are intelligent and curious enough to wonder about this. We find ourselves
wondering about this at the very beginning of a long era in which stellar
luminosity warms many planets, and by our best models, continues to provide
equally good opportunities for intelligent life to evolve. By simple Bayesian
reasoning, if, as we believe, intelligent life forms have the same propensity
to evolve later on other planets as we had to evolve on ours, it follows that
they will likely not pass through a similar wondering stage in their evolution.
This suggests that the future holds some kind of interstellar communication
that will serve to inform newly evolved intelligent life forms that they are
not alone before they become curious.

categories: astro-ph.CO astro-ph.GA physics.pop-ph q-bio.PE


title: Topic Sensitive Neural Headline Generation

abstract:
  Neural models have recently been used in text summarization including
headline generation. The model can be trained using a set of document-headline
pairs. However, the model does not explicitly consider topical similarities and
differences of documents. We suggest to categorizing documents into various
topics so that documents within the same topic are similar in content and share
similar summarization patterns. Taking advantage of topic information of
documents, we propose topic sensitive neural headline generation model. Our
model can generate more accurate summaries guided by document topics. We test
our model on LCSTS dataset, and experiments show that our method outperforms
other baselines on each topic and achieves the state-of-art performance.


title:
Reaction time impairments in decision-making networks as a diagnostic
  marker for traumatic brain injuries and neurodegenerative diseases

abstract:
  The presence of diffuse Focal Axonal Swellings (FAS) is a hallmark cellular
feature in many neurodegenerative diseases and traumatic brain injury. Among
other things, the FAS have a significant impact on spike-train encodings that
propagate through the affected neurons, leading to compromised signal
processing on a neuronal network level. This work merges, for the first time,
three fields of study: (i) signal processing in excitatory-inhibitory (EI)
networks of neurons via population codes, (ii) decision-making theory driven by
the production of evidence from stimulus, and (iii) compromised spike-train
propagation through FAS. As such, we demonstrate a mathematical architecture
capable of characterizing compromised decision-making driven by cellular
mechanisms. The computational model also leads to several novel predictions and
diagnostics for understanding injury level and cognitive deficits, including a
key finding that decision-making reaction times, rather than accuracy, are
indicative of network level damage. The results have a number of translational
implications, including that the level of network damage can be characterized
by the reaction times in simple cognitive and motor tests.


title:
Constraints on exotic spin-dependent interactions between electrons from
  helium fine-structure spectroscopy

abstract:
  Agreement between theoretical calculations of atomic structure and
spectroscopic measurements is used to constrain possible contribution of exotic
spin-dependent interactions between electrons to the energy differences between
states in helium-4. In particular, constraints on dipole-dipole interactions
associated with the exchange of pseudoscalar bosons (such as axions or
axion-like particles, ALPs) with masses $10^{-2}~{\rm eV} \lesssim m \lesssim
10^{4}~{\rm eV}$ are improved by a factor of $\sim 100$. The first atomic-scale
constraints on several exotic velocity-dependent dipole-dipole interactions are
established as well.


title: QBism, Bohr, and the quantum omelette tossed by de Ronde

abstract:
  In his recent paper "QBism, FAPP and the Quantum Omelette" [1608.00548v1] de
Ronde makes a variety of questionable claims concerning QBism, Bohr, and the
present author's critical appraisal of QBism [1409.3312v1]. These claims are
examined. Subsequently an outline is presented of what one might see if one
looks into the quantum domain through the window provided by the
quantum-mechanical correlations between outcome-indicating events in the
classical domain.


title: A family of link concordance invariants from perturbed sl(n) homology

abstract:
  We define a family of link concordance invariants $\left\{ s_n
\right\}_{n=2,3, \cdots}$. These link concordance invariants give lower bounds
on the slice genus of a link $L$. We compute the slice genus of positive links.
Moreover, these invariants give lower bounds on the link splitting number of a
link. Especially, this new lower bound determines the splitting number of
positive torus links. This is a generalization of Lobb's knot concordance
invariants $\left\{ s_n \right\}$, obtained from Gornik's spectral sequence.


title: $c\bar{b}$ spectrum and decay properties with coupled channel effects

abstract:
  The mass spectrum of $c\bar{b}$ states has been obtained using the
phenomenological relativistic quark model (RQM) with coupled channel effects.
The Hamiltonian used in the investigation has confinement potential and
confined one gluon exchange potential (COGEP). In the frame work of RQM a study
of M1 and E1 radiative decays of $c\bar{b}$ states has been made. The weak
decay widths in the spectator quark approximation have been estimated. An
overall agreement is obtained with the experimental masses and decay widths.


title:
Non-Orthogonal Multiple Access (NOMA) in Cellular Uplink and Downlink:
  Challenges and Enabling Techniques

abstract:
  By combining the concepts of superposition coding at the transmitter(s) and
successive interference cancellation (SIC) at the receiver(s), non-orthogonal
multiple access (NOMA) has recently emerged as a promising multiple access
technique for 5G wireless technology. In this article, we first discuss the
fundamentals of uplink and downlink NOMA transmissions and outline their key
distinctions (in terms of implementation complexity, detection and decoding at
the SIC receiver(s), incurred intra-cell and inter-cell interferences). Later,
for both downlink and uplink NOMA, we theoretically derive the NOMA dominant
condition for each individual user in a two-user NOMA cluster. NOMA dominant
condition refers to the condition under which the spectral efficiency gains of
NOMA are guaranteed compared to conventional orthogonal multiple access (OMA).
The derived conditions provide direct insights on selecting appropriate users
in two-user NOMA clusters. The conditions are distinct for uplink and downlink
as well as for each individual user. Numerical results show the significance of
the derived conditions for the user selection in uplink/downlink NOMA clusters
and provide a comparison to the random user selection. A brief overview of the
recent research investigations is then provided to highlight the existing
research gaps. Finally, we discuss the potential applications and key
challenges of NOMA transmissions.


title:
Addenda to General Spin Precession and Betatron Oscillation in Storage
  Ring

abstract:
  We give the geralized expression of spin precession of extended bunch
particles having both anomalous magnetic and electric dipole moments in storage
ring in higher order than the previous work and in the presence of ${\bf E}$
field as well as ${\bf B}$ field. These addenda are essential since some
experiments consider the focusing field in the second order of the beam extent
and in the presence of both ${\bf B}$ and ${\bf E}$ fields . It is shown that
some focusing fields with constant magnitude of the velocity considered in many
literatures lead to the violation of self consistency.


title:
Defect-free Perpendicular Diblock Copolymer Films: The Synergistic
  Effect of Surface Topography and Chemistry

abstract:
  We propose a direct self-assembly mechanism towards obtaining defect-free
perpendicular lamellar phases of diblock copolymer (BCP) thin films. In our
numerical study, a thin BCP film having a flat top surface is casted on a
uni-directional corrugated solid substrate. The substrate is treated chemically
and has a weak preference toward one of the two BCP components. Employing
self-consistent field theory (SCFT), we find that there is an enhanced synergy
between two substrate characteristics: its topography (geometrical roughness)
combined with a weak surface preference. This synergy produces the desired
perpendicular lamellar phase with perfect inplane ordering. Defect-free BCP
lamellar phases are reproducible for several random initial states, and are
obtained for a range of substrate roughness and chemical characteristics, even
for a uni-directional multi-mode substrate roughness. Our theoretical study
suggests possible experiments that will explore the interplay between
uni-directional substrate corrugation and chemical surface treatment. It may
lead to viable and economical ways of obtaining BCP films with defect-free
lateral alignment.

categories: cond-mat.soft cond-mat.mtrl-sci cond-mat.stat-mech physics.chem-ph


title: Design of a Trajectory Tracking Controller for a Nanoquadcopter

abstract:
  The primary purpose of this study is to investigate the system modeling of a
nanoquadcopter as well as designing position and trajectory control algorithms,
with the ultimate goal of testing the system both in simulation and on a real
platform.
  The open source nanoquadcopter platform named Crazyflie 2.0 was chosen for
the project. The first phase consisted in the development of a mathematical
model that describes the dynamics of the quadcopter. Secondly, a simulation
environment was created to design two different control architectures: cascaded
PID position tracker and LQT trajectory tracker. Finally, the implementation
phase consisted in testing the controllers on the chosen platform and comparing
their performance in trajectory tracking.
  Our simulations agreed with the experimental results, and further refinement
of the model is proposed as future work through closed-loop model
identification techniques. The results show that the LQT controller performed
better at tracking trajectories, with RMS errors in position up to four times
smaller than those obtained with the PID. LQT control effort was greater, but
eliminated the high control peaks that induced motor saturation in the PID
controller. The LQT controller was also tested using an ultra-wide band two-way
ranging system, and comparisons with the more precise VICON system indicate
that the controller could track a trajectory in both cases despise the
difference in noise levels between the two systems.


title:
Semantics, Specification Logic, and Hoare Logic of Exact Real
  Computation

abstract:
  We propose a simple imperative programming language, ERC, that features
arbitrary real numbers as primitive data type, exactly. Equipped with a
denotational semantics, ERC provides a formal programming language-theoretic
foundation to the algorithmic processing of real numbers. In order to capture
multi-valuedness, which is well-known essential to real number computation, we
use a carefully designed Plotkin powerdomain. This makes our programming
language semantics computable and complete: all and only real functions
computable in computable analysis can be realized in ERC. The base programming
language supports real arithmetic as well as implicit limits; expansions
support additional primitive operations (such as a user-defined exponential
function). By restricting integers to Presburger arithmetic and real coercion
to the `precision' embedding $Z\ni p\mapsto 2^p\in R$, we arrive at a
first-order theory which we prove to be decidable, model-complete, and
expressive for the base programming language. Based on said logic as
specification language for preconditions and postconditions, we extend Hoare
logic to a sound (w.r.t. the denotational semantics) and expressive system for
deriving correct TOTAL correctness predicates. Various examples demonstrate the
practicality and convenience of our language and proof rules.


title:
Melting transition in lipid vesicles functionalised by mobile DNA
  linkers

abstract:
  We study phase behaviours of lipid--bilayer vesicles functionalised by
ligand--receptor complexes made of synthetic DNA by introducing a modelling
framework and a dedicated experimental platform. In particular, we perform
Monte Carlo simulations that combine a coarse grained description of the lipid
bilayer with state of art analytical models for multivalent ligand--receptor
interactions. Using density of state calculations, we derive the partition
function in pairs of vesicles and compute the number of ligand--receptor bonds
as a function of temperature. Numerical results are compared to microscopy and
fluorimetry experiments on Large Unilamellar Vesicles decorated by DNA linkers
carrying complementary overhangs. We find that vesicle aggregation is
suppressed when the total number of linkers falls below a threshold value.
Within the model proposed here, this is due to the higher configurational costs
required to form inter--vesicle bridges as compared to intra-vesicle loops,
which are in turn related to membrane deformability. Our findings and our
numerical/experimental methodologies are applicable to the rational design of
liposomes used as functional materials and drug delivery applications, as well
as to study inter-membrane interactions in living systems, such as cell
adhesion.


title:
Topological obstructions in Lagrangian field theories, with an
  application to 3D Chern-Simons gauge theory

abstract:
  We relate the existence of Noether global conserved currents associated with
locally variational field equations to existence of global solutions for a
local variational problem generating global equations. Both can be
characterized as the vanishing of certain cohomology classes.
  In the case of a 3-dimensional Chern-Simons gauge theory, the variationally
featured cohomological obstruction to the existence of global solutions is
sharp and equivalent to the usual obstruction in terms of the Chern
characteristic class for the flatness of a principal connection.
  We suggest a parallelism between the geometric interpretation of
characteristic classes as obstruction to the existence of flat principal
connections and the interpretation of certain de Rham cohomology classes to be
the obstruction to the existence of global extremals for a local variational
principle.


title:
Geometrically frustrated GdInO$_3$: An exotic system to study negative
  thermal expansion and spin-lattice coupling

abstract:
  In this article, we report negative thermal expansion and spin frustration in
hexagonal GdInO$_{3}$. Rietveld refinement of the XRD patterns reveal that the
negative thermal expansion in the temperature range of 50-100K stems from the
triangular lattice of Gd$^{3+}$ ions. At low temperature, the downward
deviation of the inverse susceptibility ($\chi^{-1}$) vs. $T$ plot from the
Curie-Weiss law indicates spin frustration which inhibits long-range magnetic
ordering down to 2K. Magnetostriction measurements clearly demonstrate a strong
spin-lattice coupling. Low temperature anomalous phonon softening, as obtained
from temperature dependent Raman measurements, also reveals the same. Our
experimental observations are supported by first principles density functional
theory calculations of the electronic and phonon dispersion of GdInO$_3$. The
calculations suggest that the GdInO$_3$ lattice is highly frustrated at low
temperature. Further, the calculated normal mode frequencies of the Gd related
$\Gamma$ point phonons are found to depend on the magnetic structure of the
lattice, suggesting significant magneto-elastic coupling.


title: A Family Group of Two-dimensional Node-Line Semimetals

abstract:
  Using evolutionary algorithm and first-principles calculations, we predict a
family group of two-dimensional node-line semimetals MX (M=Pd, Pt; X=S, Se,
Te), which has zig-zag type mono-layer structure in Pmm2 layer group. Band
structure analysis reveals that node-line features are caused by band inversion
and the inversion exists even in the absence of spin-orbital-coupling. Tests
are carried out to confirm that the node-line loop is protected by crystal
symmetry. This work extends our knowledge of node-line materials to
two-dimensional cases, i.e., a group of metal-group VI compounds sharing the
same lattice structure which has time reversion and crystal-mirror inversion
symmetries.


title: Global Theory to Understand Toroidal Drift Waves in Steep Gradient

abstract:
  Toroidal drift waves with unconventional mode structures and non-ground
eigenstates, which differ from typical ballooning structure mode, are found to
be important recently by large scale global gyrokinetic simulations and
especially become dominant at strong gradient edge plasmas [cf., Xie and Xiao,
Phys. Plasmas, 22, 090703 (2015)]. The global stability and mode structures of
drift wave in this steep edge density and temperature gradients are examined by
both direct numerical solutions of a model two-dimensional eigen equation and
analytical theory employing WKB-ballooning approach. Theory agrees with
numerical solutions quite well. Our results indicate that (i) non-ground
eigenstates and unconventional mode structures generally exist and can be
roughly described by two parameters `quantum number' $l$ and ballooning angle
$\vartheta_k$, (ii) local model can overestimate the growth rate largely, say,
$>50\%$, and (iii) the narrow steep equilibrium profile leads to twisting
(triangle-like) radial mode structures. With velocity space integral,
semi-local theory predicts that the critical jump gradient of the most unstable
ion temperature gradient mode from ground state $l=0$ to non-ground state $l=1$
is $L_T^{-1}R\sim50$. These features can have important consequences to
turbulent transport.


title: Capacity of the Energy Harvesting Gaussian MAC

abstract:
  We consider an energy harvesting multiple access channel (MAC) where the
transmitters are powered by an exogenous stochastic energy harvesting process
and equipped with finite batteries. We characterize the capacity region of this
channel as n-letter mutual information rate and develop inner and outer bounds
that differ by a constant gap. An interesting conclusion that emerges from our
results is that the sum-capacity approaches that of a standard AWGN MAC (with
only an average constraint on the transmitted power), as the number of users in
the MAC becomes large.


title:
Accelerating finite-rate chemical kinetics with coprocessors: comparing
  vectorization methods on GPUs, MICs, and CPUs

abstract:
  Efficient ordinary differential equation solvers for chemical kinetics must
take into account the available thread and instruction-level parallelism of the
underlying hardware, especially on many-core coprocessors, as well as the
numerical efficiency. A stiff Rosenbrock and nonstiff Runge-Kutta solver are
implemented using the single instruction, multiple thread (SIMT) and single
instruction, multiple data (SIMD) paradigms with OpenCL. The performances of
these parallel implementations were measured with three chemical kinetic models
across several multicore and many-core platforms. Two runtime benchmarks were
conducted to clearly determine any performance advantage offered by either
method: evaluating the right-hand-side source terms in parallel, and
integrating a series of constant-pressure homogeneous reactors using the
Rosenbrock and Runge-Kutta solvers. The right-hand-side evaluations with SIMD
parallelism on the host multicore Xeon CPU and many-core Xeon Phi co-processor
performed approximately three times faster than the baseline multithreaded
code. The SIMT model on the host and Phi was 13-35% slower than the baseline
while the SIMT model on the GPU provided approximately the same performance as
the SIMD model on the Phi. The runtimes for both ODE solvers decreased 2.5-2.7x
with the SIMD implementations on the host CPU and 4.7-4.9x with the Xeon Phi
coprocessor compared to the baseline parallel code. The SIMT implementations on
the GPU ran 1.4-1.6 times faster than the baseline multithreaded CPU code;
however, this was significantly slower than the SIMD versions on the host CPU
or the Xeon Phi. The performance difference between the three platforms was
attributed to thread divergence caused by the adaptive step-sizes within the
ODE integrators. Analysis showed that the wider vector width of the GPU incurs
a higher level of divergence than the narrower Sandy Bridge or Xeon Phi.


title: Gribov horizon and Gribov copies effect in lattice Coulomb gauge

abstract:
  Following a recent proposal by Cooper and Zwanziger we investigate via
$SU(2)$ lattice simulations the effect on the Coulomb gauge propagators and on
the Gribov-Zwanziger confinement mechanism of selecting the Gribov copy with
the smallest non-trivial eigenvalue of the Faddeev-Popov operator, i.e.~the one
closest to the Gribov horizon. Although such choice of gauge drives the ghost
propagator towards the prediction of continuum calculations, we find that it
actually overshoots the goal. With increasing computer time, we observe that
Gribov copies with arbitrarily small eigenvalues can be found. For such a
method to work one would therefore need further restrictions on the gauge
condition to isolate the physically relevant copies, since e.g.~the Coulomb
potential $V_C$ defined through the Faddeev-Popov operator becomes otherwise
physically meaningless. Interestingly, the Coulomb potential alternatively
defined through temporal link correlators is only marginally affected by the
smallness of the eigenvalues.


title: Multi-wavelength view of an M2.2 Solar Flare on 26 November 2000

abstract:
  In this paper, we present a study of an M2.2 class solar flare of 26 November
2000 from NOAA AR 9236. The flare was well observed by various ground based
observatories (ARIES, Learmonths Solar Observatory) and space borne instruments
(SOHO, HXRS, GOES) in time interval between 02:30 UT to 04:00 UT. The flare
started with long arc-shape outer flare ribbon. Afterwards the main flare
starts with two main ribbons. Initially the outer ribbons start to expand with
an average speed ($\sim$ 20 km s$^{-1}$) and later it shows contraction. The
flare was associated with partial halo coronal mass ejection (CMEs) which has
average speed of 495 km s$^{-1}$. The SOHO/MDI observations show that the
active region was in quadrupolar magnetic configuration. The flux cancellation
was observed before the flare onset close to flare site. Our analysis indicate
the flare was initiated by the magnetic breakout mechanism.


title:
Zassenhaus Conjecture on torsion units holds for
  $\operatorname{PSL}(2,p)$ with $p$ a Fermat or Mersenne prime

abstract:
  H.J. Zassenhaus conjectured that any unit of finite order in the integral
group ring $\mathbb{Z}G$ of a finite group $G$ is conjugate in the rational
group algebra $\mathbb{Q}G$ to an element of the form $\pm g$ with $g \in G$.
Though known for some series of solvable groups, the conjecture has been proved
only for thirteen non-abelian simple groups. We prove the Zassenhaus Conjecture
for the groups $\operatorname{PSL}(2,p)$, where $p$ is a Fermat or Mersenne
prime. This increases the list of non-abelian simple groups for which the
conjecture is known by probably infinitely many, but at least by 49, groups.
Our result is an easy consequence of known results and our main theorem which
states that the Zassenhaus Conjecture holds for a unit in
$\mathbb{Z}\operatorname{PSL}(2,q)$ of order coprime with $2q$, for some prime
power $q$.


title:
Naturality of the hyperholomorphic sheaf over the cartesian square of a
  manifold of $K3^{[n]}$-type

abstract:
  Let M be a 2n-dimensional smooth and compact moduli space of stable sheaves
on a K3 surface S and U a universal sheaf over S x M. Over M x M there exists a
natural reflexive sheaf E of rank 2n-2, namely the first relative extension
sheaf of the two pullbacks of U to M x S x M. We prove that E is slope-stable
with respect to every Kahler class on M. The sheaf E is known to deform to a
sheaf E' over X x X, for every manifold X deformation equivalent to M, and we
prove that E' is slope-stable with respect to every Kahler class on X. This
triviality of the stability chamber structure combines with a result of S.
Mehrotra and the author to show that the deformed sheaf E' is canonical.
Consequently, the pretriangulated K3 category associated to the pair (X x X,E')
in our earlier work with S. Mehrotra depends only on the isomorphism class of
X.


title: Dynamic Super Efimov Effect

abstract:
  Super Efimov effect is a recently proposed three-body effect characterized by
a double-exponential scaling, which has not been observed experimentally yet.
Here, we present the general dynamic equations determining the cloud size of a
scale invariant quantum gas in a time dependent harmonic trap. We show that a
double-log periodicity as the hallmark of the super Efimov effect emerges when
the trap frequency is decreased with a specially designed time-dependence. We
also demonstrate that this dynamic super Efimov effect can be realized with
realistic choices of parameters in current experiments.