title: Persistent memories in transient networks

abstract:
  Spatial awareness in mammals is based on an internalized representation of
the environment, encoded by large networks of spiking neurons. While such
representations can last for a long time, the underlying neuronal network is
transient: neuronal cells die every day, synaptic connections appear and
disappear, the networks constantly change their architecture due to various
forms of synaptic and structural plasticity. How can a network with a dynamic
architecture encode a stable map of space? We address this question using a
physiological model of a "flickering" neuronal network and demonstrate that it
can maintain a robust topological representation of space.


title:
Perfect fluid in Lagrangian formulation due to generalized three-form
  field

abstract:
  A Lagrangian formulation of perfect fluid due to a noncanonical three-form
field is investigated. The thermodynamic quantities such as energy density,
pressure and the four velocity are obtained and then analyzed by comparing with
the k-essence scalar field. The nonrelativistic matter due to the generalized
three-form field with the equation of state parameter being zero is realized
while it might not be possible for the k-essence scalar field. We also found
that nonadiabatic pressure perturbations can be possibly generated. The fluid
dynamics of the perfect fluid due to the three-form field corresponds to the
system in which the number of particles is not conserved. We argue that it is
interesting to use this three-form field to represent the dark matter for the
classical interaction theory between dark matter and dark energy.


title: Reflections on a Black Mirror

abstract:
  A black mirror is an accelerated boundary that produces particles in an exact
correspondence to an evaporating black hole. We investigate the spectral
dynamics of the particle creation during the formation process.


title:
Probing CP violation in $e^{+}e^{-}$ production of the Higgs boson and
  toponia

abstract:
  We study the CP violation in the Higgs boson and toponia production process
at the ILC where the toponia are produced near the threshold. With the
approximation that the production vertex of the Higgs boson and toponia is
contact, and neglecting the P-wave toponia, we analytically calculated the
density matrix for the production and decay of the toponia. Under these
assumptions, the production spectrum of the toponia is solely determined by the
spin quantum number, therefore the toponia can be either singlet or triplet. We
find that the production rate of the singlet toponium is highly suppressed, and
behaves just like the production of a P-wave toponia. In the case of the
triplet toponium, three completely independent CP observables, namely azimuthal
angles of lepton and anti-lepton in the toponium rest-frame as well as their
sum, are predicted based on our analytical results, and checked by using the
tree-level event generator. The non-trivial correlations come from the
longitudinal-transverse interferences for the azimuthal angles of leptons, and
the transverse-transverse interference for their sum. These three observables
are well defined at the ILC, where the rest frame of the toponium can be
reconstructed directly. Furthermore, the QCD-strong corrections, which are
important near the threshold region, are also studied with the approximation of
spin-independent QCD-Coulomb potential. While the total cross section is
enhanced, the spin correlations predicted in this paper are not affected.


title: Qualitative evolution in f(R) cosmologies

abstract:
  We investigate the qualitative evolution of (D+1)-dimensional cosmological
models in f(R) gravity for the general case of the function f(R). The analysis
is specified for various examples, including the (D+1)-dimensional
generalization of the Starobinsky model, models with polynomial and exponential
functions. The cosmological dynamics are compared in the Einstein and Jordan
representations of the corresponding scalar-tensor theory. The features of the
cosmological evolution are discussed for Einstein frame potentials taking
negative values in certain regions of the field space.


title:
CLASH-VLT: Strangulation of cluster galaxies in MACSJ0416.1-2403 as seen
  from their chemical enrichment

abstract:
  (abridged) We explore the Frontier Fields cluster MACS J0416.1-2403 at
z=0.3972 with VIMOS/VLT spectroscopy from the CLASH-VLT survey covering a
region which corresponds to almost three virial radii. We measure fluxes of 5
emission lines of 76 cluster members enabling us to unambiguously derive O/H
gas metallicities, and also SFRs from Halpha. For intermediate massses we find
a similar distribution of cluster and field galaxies in the MZR and mass vs.
sSFR diagrams. Bulge-dominated cluster galaxies have on average lower sSFRs and
higher O/Hs compared to their disk-dominated counterparts. We use the location
of galaxies in the projected velocity vs. position phase-space to separate our
cluster sample into a region of objects accreted longer time ago and a region
of recently accreted and infalling galaxies. We find a higher fraction of
accreted metal-rich galaxies (63%) compared to the fraction of 28% of
metal-rich galaxies in the infalling regions. Intermediate mass galaxies
falling into the cluster for the first time are found to be in agreement with
predictions of the fundamental metallicity relation. In contrast, for already
accreted star-forming galaxies of similar masses, we find on average
metallicities higher than predicted by the models. This trend is intensified
for accreted cluster galaxies of the lowest mass bin, that display
metallicities 2-3 times higher than predicted by models with primordial gas
inflow. Environmental effects therefore strongly influence gas regulations and
control gas metallicities of log(M/Msun)<10.2 (Salpeter IMF) cluster galaxies.
We also investigate chemical evolutionary paths of model galaxies with and
without inflow of gas showing that strangulation is needed to explain the
higher metallicities of accreted cluster galaxies. Our results favor a
strangulation scenario in which gas inflow stops for log(M/Msun)<10.2 galaxies
when accreted by the cluster.


title: Universal transport and resonant current from chiral magnetic effect

abstract:
  For relativistic Weyl fermions in 3+1 dimensions, an electric current
proportional to the external magnetic field is predicted. This remarkable
phenomenon is called Chiral Magnetic Effect (CME). Here we show that actual
transports in Weyl semimetals supporting CME cannot be discussed without proper
consideration of the law of electromagnetism. First, even in the absence of an
external magnetic field, CME leads to a material-independent, universal
effective capacitance. Moreover, the induced current by a time-dependent
external magnetic field can be resonantly enhanced reflecting a formation of
electromagnetic standing waves.


title:
Hubble imaging of the ionizing radiation from a star-forming galaxy at
  z=3.2 with fesc>50%

abstract:
  Star-forming galaxies are considered to be the leading candidate sources that
dominate the cosmic reionization at z>7, and the search for analogs at moderate
redshift showing Lyman continuum (LyC) leakage is currently a active line of
research. We have observed a star-forming galaxy at z=3.2 with Hubble/WFC3 in
the F336W filter, corresponding to the 730-890A rest-frame, and detect LyC
emission. This galaxy is very compact and also has large Oxygen ratio
[OIII]5007/[OII]3727 (>=10). No nuclear activity is revealed from
optical/near-infrared spectroscopy and deep multi-band photometry (including
the 6Ms X-ray, Chandra). The measured escape fraction of ionizing radiation
spans the range 50-100\%, depending on the IGM attenuation. The LyC emission is
detected at S/N=10 with m(F336W)=27.57+/-0.11 and it is spatially unresolved,
with effective radius R_e<200pc. Predictions from photoionization and radiative
transfer models are in line with the properties reported here, indicating that
stellar winds and supernova explosions in a nucleated star-forming region can
blow cavities generating density-bounded conditions compatible with optically
thin media. Irrespective to the nature of the ionizing radiation, spectral
signatures of these sources over the entire electromagnetic spectrum are of
central importance for their identification during the epoch of reionization,
when the LyC is unobservable. Intriguingly, the Spitzer/IRAC photometric
signature of intense rest-frame optical emissions ([OIII]+Hbeta) observed
recently at z~7.5-8.5 is similar to what is observed in this galaxy. Only the
James Webb Space Telescope will measure optical line ratios at z>7 allowing a
direct comparison with lower redshift LyC emitters, as reported here.


title:
Massive Warm/Hot Galaxy Coronae as Probed by UV/X-ray Oxygen Absorption
  and Emission: I - Basic Model

abstract:
  We construct an analytic phenomenological model for extended warm/hot gaseous
coronae of $L_*$ galaxies. We consider UV OVI COS-Halos absorption line data in
combination with Milky Way X-ray OVII and OVIII absorption and emission. We fit
these data with a single model representing the COS-Halos galaxies and a
Galactic corona. Our model is multi-phased, with hot and warm gas components,
each with a (turbulent) log-normal distribution of temperatures and densities.
The hot gas, traced by the X-ray absorption and emission, is in hydrostatic
equilibrium in a Milky Way gravitational potential. The median temperature of
the hot gas is $1.5 \times 10^6$~K and the mean hydrogen density is $\sim 5
\times 10^{-5}~{\rm cm^{-3}}$. The warm component as traced by the OVI, is gas
that has cooled out of the high density tail of the hot component. The total
warm/hot gas mass is high and is $1.2 \times 10^{11}~{\rm M_{\odot}}$. The gas
metallicity we require to reproduce the oxygen ion column densities is $0.5$
solar. The warm OVI component has a short cooling time ($\sim 2 \times 10^8$
years), as hinted by observations. The hot component, however, is $\sim 80\%$
of the total gas mass and is relatively long-lived, with $t_{cool} \sim 7
\times 10^{9}$ years. Our model supports suggestions that hot galactic coronae
can contain significant amounts of gas. These reservoirs may enable galaxies to
continue forming stars steadily for long periods of time and account for
"missing baryons" in galaxies in the local universe.


title: Terrestrial planets across space and time

abstract:
  The study of cosmology, galaxy formation and exoplanets has now advanced to a
stage where a cosmic inventory of terrestrial planets may be attempted. By
coupling semi-analytic models of galaxy formation to a recipe that relates the
occurrence of planets to the mass and metallicity of their host stars, we trace
the population of terrestrial planets around both solar-mass (FGK type) and
lower-mass (M dwarf) stars throughout all of cosmic history. We find that the
mean age of terrestrial planets in the local Universe is $7\pm{}1$ Gyr for FGK
hosts and $8\pm{}1$ Gyr for M dwarfs. We estimate that hot Jupiters have
depleted the population of terrestrial planets around FGK stars by no more than
$\approx 10\%$, and that only $\approx 10\%$ of the terrestrial planets at the
current epoch are orbiting stars in a metallicity range for which such planets
have yet to be confirmed. The typical terrestrial planet in the local Universe
is located in a spheroid-dominated galaxy with a total stellar mass comparable
to that of the Milky Way. When looking at the inventory of planets throughout
the whole observable Universe, we argue for a total of $\approx 1\times
10^{19}$ and $\approx 5\times 10^{20}$ terrestrial planets around FGK and M
stars, respectively. Due to light travel time effects, the terrestrial planets
on our past light cone exhibit a mean age of just $1.7\pm 0.2$ Gyr. These
results are discussed in the context of cosmic habitability, the Copernican
principle and searches for extraterrestrial intelligence at cosmological
distances.


title:
The Measurement, Treatment, and Impact of Spectral Covariance and
  Bayesian Priors in Integral-Field Spectroscopy of Exoplanets

abstract:
  The recovery of an exoplanet's atmospheric parameters from its spectrum
requires accurate knowledge of the spectral errors and covariances.
Unfortunately, the complex image processing used in high-contrast
integral-field spectrograph (IFS) observations generally produces spectral
covariances that are poorly understood and often ignored. In this work, we show
how to measure the spectral errors and covariances and include them
self-consistently in parameter retrievals. By combining model exoplanet spectra
with a realistic noise model generated from GPI early science data, we show
that ignoring spectral covariance in high-contrast IFS data can both bias
inferred parameters and lead to unreliable confidence regions on those
parameters. This problem is made worse by the common practice of scaling the
$\chi^2$ per degree of freedom to unity; the input parameters then fall outside
the $95\%$ confidence regions in as many as ${\sim}80\%$ of noise realizations.
The biases we observe can approach the typical levels of precision achieved in
high-contrast spectroscopy. Accounting for realistic priors in fully Bayesian
retrievals can also have a significant impact on the inferred parameters.
Plausible priors on effective temperature and surface gravity can vary by an
order of magnitude across the confidence regions appropriate for objects with
weak age constraints; priors for objects with good age constraints are
dominated by modeling uncertainties. Our methods are directly applicable to
existing high-contrast IFSs including GPI and SPHERE, as well as upcoming
instruments like CHARIS and, ultimately, WFIRST-AFTA.


title:
Bayesian techniques for comparing time-dependent GRMHD simulations to
  variable Event Horizon Telescope observations

abstract:
  The Event Horizon Telescope (EHT) is a millimeter-wavelength,
very-long-baseline interferometry (VLBI) experiment that is capable of
observing black holes with horizon-scale resolution. Early observations have
revealed variable horizon-scale emission in the Galactic Center black hole,
Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general
relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools
that explicitly consider the variability in both the data and the models. We
develop here a Bayesian method to compare time-resolved simulation images to
variable VLBI data, in order to infer model parameters and perform model
comparisons. We use mock EHT data based on GRMHD simulations to explore the
robustness of this Bayesian method and contrast it to approaches that do not
consider the effects of variability. We find that time-independent models lead
to offset values of the inferred parameters with artificially reduced
uncertainties. Moreover, neglecting the variability in the data and the models
often leads to erroneous model selections. We finally apply our method to the
early EHT data on Sgr A*.


title:
CPT, CP, and C transformations of fermions, and their consequences, in
  theories with B-L violation

abstract:
  We consider the transformation properties of fermions under the discrete
symmetries CPT, CP, and C in the presence of B-L violation. We thus generalize
the analysis of the known properties of Majorana neutrinos, probed via
neutrinoless double beta decay, to include the case of Dirac fermions with B-L
violation, which can be probed via neutron-antineutron oscillations. We show
that the resulting CPT phase has implications for the interplay of
neutron-antineutron oscillations with external fields and sources and consider
the differences in the Majorana dynamics of neutrinos and neutrons in the
context of theories with self-conjugate isospin I=0 and I=1/2 fields.


title: Quantum Brownian motion in a Landau level

abstract:
  Motivated by questions about the open-system dynamics of topological quantum
matter, we investigated the quantum Brownian motion of an electron in a
homogeneous magnetic field. When the Fermi length
$l_F=\hbar/(v_Fm_{\text{eff}})$ becomes much longer than the magnetic length
$l_B=(\hbar c/eB)^{1/2}$, then the spatial coordinates $X,Y$ of the electron
cease to commute, $[X,Y]=il_B^2$. As a consequence, localization of the
electron becomes limited by Heisenberg uncertainty, and the linear
bath-electron coupling becomes unconventional. Moreover, because the kinetic
energy of the electron is quenched by the strong magnetic field, the electron
has no energy to give to or take from the bath, and so the usual connection
between frictional forces and dissipation no longer holds. These two features
make quantum Brownian motion topological, in the regime $l_F\gg l_B$, which is
at the verge of current experimental capabilities. We model topological quantum
Brownian motion in terms of an unconventional operator Langevin equation
derived from first principles, and solve this equation with the aim of
characterizing diffusion. While diffusion in the noncommutative plane turns out
to be conventional, with the mean displacement squared being proportional to
$t^\alpha$ and $\alpha=1$, there is an exotic regime for the proportionality
constant in which it is directly proportional to the friction coefficient and
inversely proportional to the square of the magnetic field: in this regime,
friction helps diffusion and the magnetic field suppresses all fluctuations. We
also show that quantum tunneling can be completely suppressed in the
noncommutative plane for suitably designed metastable potential wells, a
feature that might be worth exploiting for storage and protection of quantum
information.


title:
High precision determination of the gluon fusion Higgs boson
  cross-section at the LHC

abstract:
  We present the most precise value for the Higgs boson cross-section in the
gluon-fusion production mode at the LHC. Our result is based on a perturbative
expansion through N$^3$LO in QCD, in an effective theory where the top-quark is
assumed to be infinitely heavy, while all other Standard Model quarks are
massless. We combine this result with QCD corrections to the cross-section
where all finite quark-mass effects are included exactly through NLO. In
addition, electroweak corrections and the first corrections in the inverse mass
of the top-quark are incorporated at three loops. We also investigate the
effects of threshold resummation, both in the traditional QCD framework and
following a SCET approach, which resums a class of $\pi^2$ contributions to all
orders. We assess the uncertainty of the cross-section from missing
higher-order corrections due to both perturbative QCD effects beyond N$^3$LO
and unknown mixed QCD-electroweak effects. In addition, we determine the
sensitivity of the cross-section to the choice of parton distribution function
(PDF) sets and to the parametric uncertainty in the strong coupling constant
and quark masses. For a Higgs mass of $m_H = 125~{\rm GeV}$ and an LHC
center-of-mass energy of $13~{\rm TeV}$, our best prediction for the gluon
fusion cross-section is \[ \sigma = 48.58\,{\rm pb} {}^{+2.22\, {\rm pb}\,
(+4.56\%)}_{-3.27\, {\rm pb}\, (-6.72\%)} \mbox{ (theory)} \pm 1.56 \,{\rm
pb}\, (3.20\%) \mbox{ (PDF+$\alpha_s$)} \]


title:
Neutrino Interactions with Nucleons and Nuclei: Importance for
  Long-Baseline Experiments

abstract:
  This article reviews our present knowledge of neutrino interactions with
nucleons and discusses the interactions with nuclei, the target material of all
presently running and planned long-baseline experiments. I emphasize
descriptions of semi-inclusive reactions and full descriptions of the final
state; the latter are needed to reconstruct the incoming neutrino energy from
final-state observations. I then discuss Monte Carlo generator and more
advanced transport theoretical approaches in connection with experimental
results on various reaction mechanisms. Finally, I describe the effects of
uncertainties in the reconstruction of the incoming neutrino energy on
oscillation parameters. The review argues that the precision era of neutrino
physics also needs precision-era generators.


title: Newton's Theorem of Revolving Orbits in Curved Spacetime

abstract:
  Newton's theorem of revolving orbits states that one can multiply the angular
speed of a Keplerian orbit by a factor $k$ by applying a radial inverse cubed
force proportional to $(1-k^2)$. In this paper we derive an extension of this
theorem in general relativity, valid for the motion of massive particles in any
static, spherically symmetric metrics. We verify the Newtonian limit of this
extension and demonstrate that there is no such generalization for rotating
metrics. Further we also extend the theory to the case of charged particles in
the Einstein-Maxwell and Kaluza-Klein theories.


title: Self-induced neutrino flavor conversion without flavor mixing

abstract:
  Neutrino-neutrino refraction in dense media can cause self-induced flavor
conversion triggered by collective run-away modes of the interacting flavor
oscillators. The growth rates were usually found to be of order a typical
vacuum oscillation frequency $\Delta m^2/2E$. However, even in the simple case
of a $\nu_e$ beam interacting with an opposite-moving $\bar\nu_e$ beam, and
allowing for spatial inhomogeneities, the growth rate of the fastest-growing
Fourier mode is of order $\mu=\sqrt{2} G_{\rm F} n_{\nu}$, a typical
$\nu$--$\nu$ interaction energy. This growth rate is much larger than the
vacuum oscillation frequency and gives rise to flavor conversion on a much
shorter time scale. This phenomenon of "fast flavor conversion" occurs even for
vanishing $\Delta m^2/2E$ and thus does not depend on energy, but only on the
angle distributions. Moreover, it does not require neutrinos to mix or to have
masses, except perhaps for providing seed disturbances. We also construct a
simple homogeneous example consisting of intersecting beams and study a
schematic supernova model proposed by Ray Sawyer, where $\nu_e$ and $\bar\nu_e$
emerge with different zenith-angle distributions, the key ingredient for fast
flavor conversion. What happens in realistic astrophysical scenarios remains to
be understood.


title:
The DBI Action, Higher-derivative Supergravity, and Flattening Inflaton
  Potentials

abstract:
  In string theory compactifications it is common to find an effective
Lagrangian for the scalar fields with a non-canonical kinetic term. We study
the effective action of the scalar position moduli of Type II D$p$-branes. In
many instances the kinetic terms are in fact modified by a term proportional to
the scalar potential itself. This can be linked to the appearance of
higher-dimensional supersymmetric operators correcting the K\"ahler potential.
We identify the supersymmetric dimension-eight operators describing the
$\alpha'$ corrections captured by the D-brane Dirac-Born-Infeld action. Our
analysis then allows an embedding of the D-brane moduli effective action into
an $\mathcal N = 1$ supergravity formulation. The effects of the
potential-dependent kinetic terms may be very important if one of the scalars
is the inflaton, since they lead to a flattening of the scalar potential. We
analyze this flattening effect in detail and compute its impact on the CMB
observables for single-field inflation with monomial potentials.


title:
Numerically validating the completeness of the real solution set of a
  system of polynomial equations

abstract:
  Computing the real solutions to a system of polynomial equations is a
challenging problem, particularly verifying that all solutions have been
computed. We describe an approach that combines numerical algebraic geometry
and sums of squares programming to test whether a given set is "complete" with
respect to the real solution set. Specifically, we test whether the Zariski
closure of that given set is indeed equal to the solution set of the real
radical of the ideal generated by the given polynomials. Examples with finitely
and infinitely many real solutions are provided, along with an example having
polynomial inequalities.


title:
The warm molecular hydrogen of PKS B1718-649: feeding a newly born radio
  AGN

abstract:
  We present new SINFONI VLT observations of molecular hydrogen (H2) in the
central regions (< 2.5 kpc) of the youngest and closest radio source PKS
B1718-649. We study the distribution of the H2 traced by the 1-0 S(1)
ro-vibrational line, revealing a double disk structure with the kinematics of
both disks characterised by rotation. An outer disk (r > 650 pc) is aligned
with other components of the galaxy (atomic hydrogen, stars, dust), while the
inner disk (r< 600 pc) is perpendicular to it and is polar with respect to the
stellar distribution. However, in the innermost 75 pc, the data show the
presence of H2 gas redshifted with respect to the rotating inner disk ($\Delta
v\,$+150 km/s) which may trace gas falling into the super-massive black hole
associated with the central radio source. Along the same line of sight, earlier
observations had shown the presence in the central regions of PKS B1718-649 of
clouds of atomic hydrogen with similar unsettled kinematics. The range of
velocities and mass of these unsettled clouds of HI and H2 suggest they may be
actively contributing in fuelling the central newly-born radio source.


title: IC 751: a new changing-look AGN discovered by NuSTAR

abstract:
  We present the results of five NuSTAR observations of the type 2 active
galactic nucleus (AGN) in IC 751, three of which were performed simultaneously
with XMM-Newton or Swift/XRT. We find that the nuclear X-ray source underwent a
clear transition from a Compton-thick ($N_{\rm\,H}\simeq 2\times
10^{24}\rm\,cm^{-2}$) to a Compton-thin ($N_{\rm\,H}\simeq 4\times
10^{23}\rm\,cm^{-2}$) state on timescales of $\lesssim 3$ months, which makes
IC 751 the first changing-look AGN discovered by NuSTAR. Changes of the
line-of-sight column density at a $\sim2\sigma$ level are also found on a
time-scale of $\sim 48$ hours ($\Delta N_{\rm\,H}\sim 10^{23}\rm\,cm^{-2}$).
From the lack of spectral variability on timescales of $\sim 100$ ks we infer
that the varying absorber is located beyond the emission-weighted average
radius of the broad-line region, and could therefore be related either to the
external part of the broad-line region or a clumpy molecular torus. By adopting
a physical torus X-ray spectral model, we are able to disentangle the column
density of the non-varying absorber ($N_{\rm\,H}\sim 3.8\times
10^{23}\rm\,cm^{-2}$) from that of the varying clouds
[$N_{\rm\,H}\sim(1-150)\times10^{22}\rm\,cm^{-2}$], and to constrain that of
the material responsible for the reprocessed X-ray radiation ($N_{\rm\,H} \sim
6 \times 10^{24}\rm\,cm^{-2}$). We find evidence of significant intrinsic X-ray
variability, with the flux varying by a factor of five on timescales of a few
months in the 2-10 and 10-50 keV band.


title: Direct certification of a class of quantum simulations

abstract:
  One of the main challenges in the field of quantum simulation and computation
is to identify ways to certify the correct functioning of a device when a
classical efficient simulation is not available. Important cases are situations
in which one cannot classically calculate local expectation values of state
preparations efficiently. In this work, we develop weak-membership formulations
of the certification of ground state preparations. We provide a non-interactive
protocol for certifying ground states of frustration-free Hamiltonians based on
simple energy measurements of local Hamiltonian terms. This certification
protocol can be applied to classically intractable analog quantum simulations:
For example, using Feynman-Kitaev Hamiltonians, one can encode universal
quantum computation in such ground states. Moreover, our certification protocol
is applicable to ground states encodings of IQP circuits demonstration of
quantum supremacy. These can be certified efficiently when the error is
polynomially bounded.


title: Holography Inspired Stringy Hadrons

abstract:
  Holography inspired stringy hadrons (HISH) is a set of models that describe
hadrons: mesons, baryons and glueballs as strings in four dimensional space
time. The models are based on a "map" from stringy hadrons of holographic
confining backgrounds. In this note we review the "derivation" of the models.
We start with a brief reminder of the passage from the AdS5xS5 string theory to
certain flavored confining holographic models. We then describe the string
configurations in holographic backgrounds that correspond to a Wilson line,a
meson,a baryon and a glueball. The key ingredients of the four dimensional
picture of hadrons are the "string endpoint mass" and the "baryonic string
vertex". We determine the classical trajectories of the HISH. We review the
current understanding of the quantization of the hadronic strings. We end with
a summary of the comparison of the outcome of the HISH models with the PDG data
about mesons and baryons. We extract the values of the tension, masses and
intercepts from best fits, write down certain predictions for higher excited
hadrons and present attempts to identify glueballs


title:
Are all classical superintegrable systems in two-dimensional space
  linearizable?

abstract:
  Several examples of classical superintegrable systems in two-dimensional spac
are shown to possess hidden symmetries leading to their linearization. They are
those determined 50 years ago in [Phys. Lett. 13, 354 (1965)], and the more
recent Tremblay-Turbiner-Winternitz system [J. Phys. A: Math. Theor. 42, 242001
(2009)].
  We conjecture that all classical superintegrable systems in two-dimensional
space have hidden symmetries that make them linearizable.


title: Sigma Models with Negative Curvature

abstract:
  We construct Higgs Effective Field Theory (HEFT) based on the scalar manifold
H^n, which is a hyperbolic space of constant negative curvature. The Lagrangian
has a non-compact O(n,1) global symmetry group, but it gives a unitary theory
as long as only a compact subgroup of the global symmetry is gauged. Whether
the HEFT manifold has positive or negative curvature can be tested by measuring
the S-parameter, and the cross sections for longitudinal gauge boson and Higgs
boson scattering, since the curvature (including its sign) determines
deviations from Standard Model values.


title: The JCMT Gould Belt Survey: Dense Core Clusters in Orion B

abstract:
  The JCMT Gould Belt Legacy Survey obtained SCUBA-2 observations of dense
cores within three sub-regions of Orion B: LDN 1622, NGC 2023/2024, and NGC
2068/2071, all of which contain clusters of cores. We present an analysis of
the clustering properties of these cores, including the two-point correlation
function and Cartwright's Q parameter. We identify individual clusters of dense
cores across all three regions using a minimal spanning tree technique, and
find that in each cluster, the most massive cores tend to be centrally located.
We also apply the independent M-Sigma technique and find a strong correlation
between core mass and the local surface density of cores. These two lines of
evidence jointly suggest that some amount of mass segregation in clusters has
happened already at the dense core stage.


title: Poisson algebras for non-linear field theories in the Cahiers topos

abstract:
  We develop an approach to construct Poisson algebras for non-linear scalar
field theories that is based on the Cahiers topos model for synthetic
differential geometry. In this framework the solution space of the field
equation carries a natural smooth structure and, following Zuckerman's ideas,
we can endow it with a presymplectic current. We formulate the Hamiltonian
vector field equation in this setting and show that it selects a family of
observables which forms a Poisson algebra. Our approach provides a clean
splitting between geometric and algebraic aspects of the construction of a
Poisson algebra, which are sufficient to guarantee existence, and analytical
aspects that are crucial to analyze its properties.


title:
Quantum perceptron over a field and neural network architecture
  selection in a quantum computer

abstract:
  In this work, we propose a quantum neural network named quantum perceptron
over a field (QPF). Quantum computers are not yet a reality and the models and
algorithms proposed in this work cannot be simulated in actual (or classical)
computers. QPF is a direct generalization of a classical perceptron and solves
some drawbacks found in previous models of quantum perceptrons. We also present
a learning algorithm named Superposition based Architecture Learning algorithm
(SAL) that optimizes the neural network weights and architectures. SAL searches
for the best architecture in a finite set of neural network architectures with
linear time over the number of patterns in the training set. SAL is the first
learning algorithm to determine neural network architectures in polynomial
time. This speedup is obtained by the use of quantum parallelism and a
non-linear quantum operator.


title:
Fast Computation of Shifted Popov Forms of Polynomial Matrices via
  Systems of Modular Polynomial Equations

abstract:
  We give a Las Vegas algorithm which computes the shifted Popov form of an $m
\times m$ nonsingular polynomial matrix of degree $d$ in expected
$\widetilde{\mathcal{O}}(m^\omega d)$ field operations, where $\omega$ is the
exponent of matrix multiplication and $\widetilde{\mathcal{O}}(\cdot)$
indicates that logarithmic factors are omitted. This is the first algorithm in
$\widetilde{\mathcal{O}}(m^\omega d)$ for shifted row reduction with arbitrary
shifts.
  Using partial linearization, we reduce the problem to the case $d \le \lceil
\sigma/m \rceil$ where $\sigma$ is the generic determinant bound, with $\sigma
/ m$ bounded from above by both the average row degree and the average column
degree of the matrix. The cost above becomes $\widetilde{\mathcal{O}}(m^\omega
\lceil \sigma/m \rceil)$, improving upon the cost of the fastest previously
known algorithm for row reduction, which is deterministic.
  Our algorithm first builds a system of modular equations whose solution set
is the row space of the input matrix, and then finds the basis in shifted Popov
form of this set. We give a deterministic algorithm for this second step
supporting arbitrary moduli in $\widetilde{\mathcal{O}}(m^{\omega-1} \sigma)$
field operations, where $m$ is the number of unknowns and $\sigma$ is the sum
of the degrees of the moduli. This extends previous results with the same cost
bound in the specific cases of order basis computation and M-Pad\'e
approximation, in which the moduli are products of known linear factors.


title: Les composantes obscures de l'Univers

abstract:
  This article is the detailed version of a paper on dark matter, dark energy,
and modified gravity, published in the December 2015-January 2016 special issue
of "La Recherche" (in French)

categories: physics.pop-ph astro-ph.CO astro-ph.GA gr-qc hep-ph


title:
Collision strengths and transition probabilities for Co III forbidden
  lines

abstract:
  In this paper we compute the collision strengths and their thermally-averaged
Maxwellian values for electron transitions between the fifteen lowest levels of
doubly-ionised cobalt, Co^{2+}, which give rise to forbidden emission lines in
the visible and infrared region of spectrum. The calculations also include
transition probabilities and predicted relative line emissivities. The data are
particularly useful for analysing the thermodynamic conditions of supernova
ejecta.


title: Dechiralisation lines induced unwinding in confined SmC* liquid crystals

abstract:
  Equilibrium and dynamic behaviors of dechiralisation lines occurring below
SmC* cell boundaries in planar geometry consitute a polemic topic for several
decades. We report new observations in the SmC* phase of the strongly polarized
liquid crystal CFL08. They are compared with vortex motions in superfluids and
type-II superconductors, and we propose a simple heuristic model attempting to
explain the intriguing mismatch between bulk helix pitch and inter-lines
distance. It results from opposite effects of the helix pitch and surface lines
charge value on the equilibrium lines distance. The model assumes that the
lines electric interactions dominate the cell equilibrium state. In particular
the unwinding transition of the bulk helix is provoked by field-induced
displacements of the lines lattices. It permits to relate the lines density and
critical fields to intrinsic energy parameters, and to explain the
pitch-distance mismatch, together with its almost constant value across the
transition. We foresee the helix pitch and unwinding field variations vs.
sample width.


title: Hidden SU(N) Glueball Dark Matter

abstract:
  We investigate the possibility that the dark matter candidate is from a pure
non-abelian gauge theory of the hidden sector, motivated in large part by its
elegance and simplicity. The dark matter is the lightest bound state made of
the confined gauge fields, the hidden glueball. We point out this simple setup
is capable of providing rich and novel phenomena in the dark sector, especially
in the parameter space of large N. They include self-interacting and warm dark
matter scenarios, Bose-Einstein condensation leading to massive dark stars
possibly millions of times heavier than our sun giving rise to gravitational
lensing effects, and indirect detections through higher dimensional operators
as well as interesting collider signatures.


title: Algorithm-Induced Prior for Image Restoration

abstract:
  This paper studies a type of image priors that are constructed implicitly
through the alternating direction method of multiplier (ADMM) algorithm, called
the algorithm-induced prior. Different from classical image priors which are
defined before running the reconstruction algorithm, algorithm-induced priors
are defined by the denoising procedure used to replace one of the two modules
in the ADMM algorithm. Since such prior is not explicitly defined, analyzing
the performance has been difficult in the past.
  Focusing on the class of symmetric smoothing filters, this paper presents an
explicit expression of the prior induced by the ADMM algorithm. The new prior
is reminiscent to the conventional graph Laplacian but with stronger
reconstruction performance. It can also be shown that the overall
reconstruction has an efficient closed-form implementation if the associated
symmetric smoothing filter is low rank. The results are validated with
experiments on image inpainting.


title: Manifolds Containing an Ample P^1-bundle

abstract:
  Sommese has conjectured a classification of smooth projective varieties X
containing, as an ample divisor, a P^d-bundle Y over a smooth variety Z. This
conjecture is known if d>1, if dim(X)<5, or if Z admits a finite morphism to an
Abelian variety. We confirm the conjecture if the Picard rank rho(Z)=1, or if Z
is not uniruled. In general we reduce the conjecture to a conjectural
characterization of projective space: namely that if W is a smooth projective
variety, E is an ample vector bundle on W, and Hom(E, T_W) is non-zero, then W
is isomorphic to P^n.


title:
BMO solvability and the $A_{\infty}$ condition of the elliptic measure
  in uniform domains

abstract:
  We consider the Dirichlet boundary value problem for divergence form elliptic
operators with bounded measurable coefficients. We prove that for uniform
domains with Ahlfors regular boundary, the BMO solvability of such problems is
equivalent to a quantitative absolute continuity of the elliptic measure with
respect to the surface measure, i.e. $\omega_L\in A_{\infty}(\sigma)$. This
generalizes a previous result on Lipschitz domains by Dindos, Kenig and Pipher.


title: Low-frequency electromagnetic field in a Wigner crystal

abstract:
  Long-wave low-frequency oscillations are described in a Wigner crystal by
generalization of the reverse continuum model for the case of electronic
lattice. The internal self-consistent long-wave electromagnetic field is used
to describe the collective motions in the system. The eigenvectors and
eigenvalues of the obtained system of equations are derived. The velocities of
longitudinal and transversal sound waves are found.


title: Robust Covariance Estimation for Approximate Factor Models

abstract:
  In this paper, we study robust covariance estimation under the approximate
factor model with observed factors. We propose a novel framework to first
estimate the initial joint covariance matrix of the observed data and the
factors, and then use it to recover the covariance matrix of the observed data.
We prove that once the initial matrix estimator is good enough to maintain the
element-wise optimal rate, the whole procedure will generate an estimated
covariance with desired properties. For data with only bounded fourth moments,
we propose to use Huber loss minimization to give the initial joint covariance
estimation. This approach is applicable to a much wider range of distributions,
including sub-Gaussian and elliptical distributions. We also present an
asymptotic result for Huber's M-estimator with a diverging parameter. The
conclusions are demonstrated by extensive simulations and real data analysis.


title: Entanglement Entropy of Scattering Particles

abstract:
  We study the entanglement entropy between the two outgoing particles in an
elastic scattering process. It is formulated within an S-matrix formalism using
the partial wave expansion of two-body states, which plays a significant role
in our computation. As a result, we obtain a novel formula that expresses the
entanglement entropy in a high energy scattering by the use of physical
observables, namely the elastic and total cross sections and a physical bound
on the impact parameter range, related to the elastic differential
cross-section.


title:
Concentration of measure without independence: a unified approach via
  the martingale method

abstract:
  The concentration of measure phenomenon may be summarized as follows: a
function of many weakly dependent random variables that is not too sensitive to
any of its individual arguments will tend to take values very close to its
expectation. This phenomenon is most completely understood when the arguments
are mutually independent random variables, and there exist several powerful
complementary methods for proving concentration inequalities, such as the
martingale method, the entropy method, and the method of transportation
inequalities. The setting of dependent arguments is much less well understood.
This chapter focuses on the martingale method for deriving concentration
inequalities without independence assumptions. In particular, we use the
machinery of so-called Wasserstein matrices to show that the Azuma-Hoeffding
concentration inequality for martingales with almost surely bounded
differences, when applied in a sufficiently abstract setting, is powerful
enough to recover and sharpen several known concentration results for
nonproduct measures. Wasserstein matrices provide a natural formalism for
capturing the interplay between the metric and the probabilistic structures,
which is fundamental to the concentration phenomenon.


title:
Enabling Efficient Dynamic Resizing of Large DRAM Caches via A Hardware
  Consistent Hashing Mechanism

abstract:
  Die-stacked DRAM has been proposed for use as a large, high-bandwidth,
last-level cache with hundreds or thousands of megabytes of capacity. Not all
workloads (or phases) can productively utilize this much cache space, however.
Unfortunately, the unused (or under-used) cache continues to consume power due
to leakage in the peripheral circuitry and periodic DRAM refresh. Dynamically
adjusting the available DRAM cache capacity could largely eliminate this energy
overhead. However, the current proposed DRAM cache organization introduces new
challenges for dynamic cache resizing. The organization differs from a
conventional SRAM cache organization because it places entire cache sets and
their tags within a single bank to reduce on-chip area and power overhead.
Hence, resizing a DRAM cache requires remapping sets from the powered-down
banks to active banks.
  In this paper, we propose CRUNCH (Cache Resizing Using Native Consistent
Hashing), a hardware data remapping scheme inspired by consistent hashing, an
algorithm originally proposed to uniformly and dynamically distribute Internet
traffic across a changing population of web servers. CRUNCH provides a
load-balanced remapping of data from the powered-down banks alone to the active
banks, without requiring sets from all banks to be remapped, unlike naive
schemes to achieve load balancing. CRUNCH remaps only sets from the
powered-down banks, so it achieves this load balancing with low bank
power-up/down transition latencies. CRUNCH's combination of good load balancing
and low transition latencies provides a substrate to enable efficient DRAM
cache resizing.


title: An In Silico Model to Simulate the Evolution of Biological Aging

abstract:
  Biological aging is characterized by an age-dependent increase in the
probability of death and by a decrease in the reproductive capacity. Individual
age-dependent rates of survival and reproduction have a strong impact on
population dynamics, and the genetic elements determining survival and
reproduction are under different selective forces throughout an organism
lifespan. Here we develop a highly versatile numerical model of genome
evolution --- both asexual and sexual --- for a population of virtual
individuals with overlapping generations, where the genetic elements affecting
survival and reproduction rate at different life stages are free to evolve due
to mutation and selection. Our model recapitulates several emerging properties
of natural populations, developing longer reproductive lifespan under stable
conditions and shorter survival and reproduction in unstable environments.
Faster aging results as the consequence of the reduced strength of purifying
selection in more unstable populations, which have large portions of the genome
that accumulate detrimental mutations. Unlike sexually reproducing populations
under constant resources, asexually reproducing populations fail to develop an
age-dependent increase in death rates and decrease in reproduction rates,
therefore escaping senescence. Our model provides a powerful in silico
framework to simulate how populations and genomes change in the context of
biological aging and opens a novel analytical opportunity to characterize how
real populations evolve their specific aging dynamics.


title:
Frank-Wolfe Works for Non-Lipschitz Continuous Gradient Objectives:
  Scalable Poisson Phase Retrieval

abstract:
  We study a phase retrieval problem in the Poisson noise model. Motivated by
the PhaseLift approach, we approximate the maximum-likelihood estimator by
solving a convex program with a nuclear norm constraint. While the Frank-Wolfe
algorithm, together with the Lanczos method, can efficiently deal with nuclear
norm constraints, our objective function does not have a Lipschitz continuous
gradient, and hence existing convergence guarantees for the Frank-Wolfe
algorithm do not apply. In this paper, we show that the Frank-Wolfe algorithm
works for the Poisson phase retrieval problem, and has a global convergence
rate of O(1/t), where t is the iteration counter. We provide rigorous
theoretical guarantee and illustrating numerical results.


title: Commuting Contractive Families

abstract:
  A family $f_1,...,f_n$ of operators on a complete metric space $X$ is called
contractive if there exists a positive $\lambda < 1$ such that for any $x,y$ in
$X$ we have $d(f_i(x),f_i(y)) \leq \lambda d(x,y)$ for some $i$. Austin
conjectured that any commuting contractive family of operators has a common
fixed point, and he proved this for the case of two operators. Our aim in this
paper is to show that Austin's conjecture is true for three operators, provided
that $\lambda$ is sufficiently small.


title:
Separated flow operation of the SHARAQ spectrometer for in-flight proton
  decay experiments

abstract:
  New operation mode, "separated flow mode", has been developed for in-flight
proton decay experiments with the SHARAQ spectrometer. In the separated flow
mode, the protons and the heavy-ion products are separated and measured in
coincidence at two different focal planes of SHARAQ. The ion-optical properties
of the new mode were studied by using a proton beam at $246~{\rm MeV}$, and the
momentum vector was properly reconstructed from the parameters measured in the
focal plane of SHARAQ. In the experiment with the $({}^{16}{\rm O},{}^{16}{\rm
F})$ reaction at a beam energy of $247~{\rm MeV/u}$, the outgoing ${}^{15}{\rm
O}+p$ produced by the decay of ${}^{16}{\rm F}$ were measured in coincidence
with SHARAQ. High energy resolutions of $100~{\rm keV}$ (FWHM) and $\sim 2~{\rm
MeV}$ were achieved for the relative energy of $535~{\rm keV}$, and the
${}^{16}{\rm F}$ energy of $3940~{\rm MeV}$, respectively.


title: KPZ and Airy limits of Hall-Littlewood random plane partitions

abstract:
  In this paper we consider a probability distribution on plane partitions,
which arises as a one-parameter generalization of the q^{volume} measure. This
generalization is closely related to the classical multivariate Hall-Littlewood
polynomials, and it was first introduced by Vuletic.
  We prove that as the plane partitions become large (q goes to 1, while the
Hall-Littlewood parameter t is fixed), the scaled bottom slice of the random
plane partition converges to a deterministic limit shape, and that one-point
fluctuations around the limit shape are asymptotically given by the GUE
Tracy-Widom distribution. On the other hand, if t simultaneously converges to
its own critical value of 1, the fluctuations instead converge to the
one-dimensional Kardar-Parisi-Zhang (KPZ) equation with the so-called narrow
wedge initial data.
  The algebraic part of our arguments is closely related to the formalism of
Macdonald processes. The analytic part consists of detailed asymptotic analysis
of the arising Fredholm determinants.


title: $C_0$ Semigroup and Local Spectral Theory

abstract:
  In this paper, we studied some local spectral properties for a Co semigroup
and its generator. Some stabilities results are also established.


title:
Heterogeneous-Reliability Memory: Exploiting Application-Level Memory
  Error Tolerance

abstract:
  This paper summarizes our work on characterizing application memory error
vulnerability to optimize datacenter cost via Heterogeneous-Reliability Memory
(HRM), which was published in DSN 2014, and examines the work's significance
and future potential. Memory devices represent a key component of datacenter
total cost of ownership (TCO), and techniques used to reduce errors that occur
on these devices increase this cost. Existing approaches to providing
reliability for memory devices pessimistically treat all data as equally
vulnerable to memory errors. Our key insight is that there exists a diverse
spectrum of tolerance to memory errors in new data-intensive applications, and
that traditional one-size-fits-all memory reliability techniques are
inefficient in terms of cost. This presents an opportunity to greatly reduce
server hardware cost by provisioning the right amount of memory reliability for
different applications.
  Toward this end, in our DSN 2014 paper, we make three main contributions to
enable highly-reliable servers at low datacenter cost. First, we develop a new
methodology to quantify the tolerance of applications to memory errors. Second,
using our methodology, we perform a case study of three new data-intensive
workloads (an interactive web search application, an in-memory key--value
store, and a graph mining framework) to identify new insights into the nature
of application memory error vulnerability. Third, based on our insights, we
propose several new hardware/software heterogeneous-reliability memory system
designs to lower datacenter cost while achieving high reliability and discuss
their trade-offs. We show that our new techniques can reduce server hardware
cost by 4.7% while achieving 99.90% single server availability.


title:
C-infinity Scaling Asymptotics for the Spectral Function of the
  Laplacian

abstract:
  This article concerns new off-diagonal estimates on the remainder and its
derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian
manifold. As an application, we prove that near any non self-focal point, the
scaling limit of the spectral projector of the Laplacian onto frequency windows
of constant size is a normalized Bessel function depending only on n.

categories: math.AP math-ph math.DG math.FA math.MP math.SP


title:
Limit-order book resiliency after effective market orders: Spread, depth
  and intensity

abstract:
  In order-driven markets, limit-order book (LOB) resiliency is an important
microscopic indicator of market quality when the order book is hit by a
liquidity shock and plays an essential role in the design of optimal submission
strategies of large orders. However, the evolutionary behavior of LOB
resilience around liquidity shocks is not well understood empirically. Using
order flow data sets of Chinese stocks, we quantify and compare the LOB
dynamics characterized by the bid-ask spread, the LOB depth and the order
intensity surrounding effective market orders with different aggressiveness. We
find that traders are more likely to submit effective market orders when the
spreads are relatively low, the same-side depth is high, and the opposite-side
depth is low. Such phenomenon is especially significant when the initial spread
is 1 tick. Although the resiliency patterns show obvious diversity after
different types of market orders, the spread and depth can return to the sample
average within 20 best limit updates. The price resiliency behavior is dominant
after aggressive market orders, while the price continuation behavior is
dominant after less-aggressive market orders. Moreover, the effective market
orders produce asymmetrical stimulus to limit orders when the initial spreads
equal to 1 tick. Under this case, effective buy market orders attract more buy
limit orders and effective sell market orders attract more sell limit orders.
The resiliency behavior of spread and depth is linked to limit order intensity.


title:
Lower semicontinuity of mass under $C^0$ convergence and Huisken's
  isoperimetric mass

abstract:
  Given a sequence of asymptotically flat 3-manifolds of nonnegative scalar
curvature with outermost minimal boundary, converging in the pointed $C^0$
Cheeger--Gromov sense to an asymptotically flat limit space, we show that the
total mass of the limit is bounded above by the liminf of the total masses of
the sequence. In other words, total mass is lower semicontinuous under such
convergence. In order to prove this, we use Huisken's isoperimetric mass
concept, together with a modified weak mean curvature flow argument. We include
a brief discussion of Huisken's work before explaining our extension of that
work. The results are all specific to three dimensions.


title: Well-quasi-ordering H-contraction-free graphs

abstract:
  A well-quasi-order is an order which contains no infinite decreasing sequence
and no infinite collection of incomparable elements. In this paper, we consider
graph classes defined by excluding one graph as contraction. More precisely, we
give a complete characterization of graphs H such that the class of
H-contraction-free graphs is well-quasi-ordered by the contraction relation.
This result is the contraction analogue on the previous dichotomy theorems of
Damsaschke [Induced subgraphs and well-quasi-ordering, Journal of Graph Theory,
14(4):427-435, 1990] on the induced subgraph relation, Ding [Subgraphs and
well-quasi-ordering, Journal of Graph Theory, 16(5):489-502, 1992] on the
subgraph relation, and B{\l}asiok et al. [Induced minors and
well-quasi-ordering, ArXiv e-prints, 1510.07135, 2015] on the induced minor
relation.


title: Learning Data Triage: Linear Decoding Works for Compressive MRI

abstract:
  The standard approach to compressive sampling considers recovering an unknown
deterministic signal with certain known structure, and designing the
sub-sampling pattern and recovery algorithm based on the known structure. This
approach requires looking for a good representation that reveals the signal
structure, and solving a non-smooth convex minimization problem (e.g., basis
pursuit). In this paper, another approach is considered: We learn a good
sub-sampling pattern based on available training signals, without knowing the
signal structure in advance, and reconstruct an accordingly sub-sampled signal
by computationally much cheaper linear reconstruction. We provide a theoretical
guarantee on the recovery error, and show via experiments on real-world MRI
data the effectiveness of the proposed compressive MRI scheme.


title: Formation of caustics in k-essence and Horndeski theory

abstract:
  We study propagation of waves and appearance of caustics in k-essence and
galileon theories. First we show that previously known solutions for travelling
waves in k-essence and galileon models correspond to very specific fine-tuned
initial conditions. On the contrary, as we demonstrate by the method of
characteristics, generic initial conditions leads to a wave in k-essence which
ends up with formation of caustics. Finally, we find that any wave solution in
pure k-essence is also a solution for a galileon theory with the same k-essence
term. Thus in the Horndeski theory with a k-essence term formation of caustics
is generic. We discuss physical consequences of the caustics formation and
possible ways to cure the problem.


title: Fluoride microresonators for mid-IR applications

abstract:
  We study crystalline fluoride microresonators for mid-infrared applications.
Whispering gallery mode resonators were fabricated with BaF$_2$, CaF$_2$ and
MgF$_2$ crystals. The quality factors were measured at wavelengths of 1.56
{\mu}m and 4.58 {\mu}m. The impacts of fabrication technique, impurities,
multiphonon absorption and surface water are investigated. It is found that
MgF2 resonators have room temperature Q factor of $8.3\times 10^6$ at
wavelength of 4.58 {\mu}m, limited by multiphonon absorption.


title:
Resolved gas kinematics in a sample of low-redshift high star-formation
  rate galaxies

abstract:
  We have used integral field spectroscopy of a sample of six nearby
(z~0.01-0.04) high star-formation rate (SFR~10-40 solar masses per year)
galaxies to investigate the relationship between local velocity dispersion and
star formation rate on sub-galactic scales. The low redshift mitigates, to some
extent, the effect of beam smearing which artificially inflates the measured
dispersion as it combines regions with different line-of-sight velocities into
a single spatial pixel. We compare the parametric maps of the velocity
dispersion with the Halpha flux (a proxy for local star-formation rate), and
the velocity gradient (a proxy for the local effect of beam smearing). We find,
even for these very nearby galaxies, the Halpha velocity dispersion correlates
more strongly with velocity gradient than with Halpha flux - implying that beam
smearing is still having a significant effect on the velocity dispersion
measurements. We obtain a first-order non parametric correction for the
unweighted and flux weighted mean velocity dispersion by fitting a 2D linear
regression model to the spaxel-by-spaxel data where the velocity gradient and
the Halpha flux are the independent variables and the velocity dispersion is
the dependent variable; and then extrapolating to zero velocity gradient. The
corrected velocity dispersions are a factor of ~1.3-4.5 and ~1.3-2.7 lower than
the uncorrected flux-weighted and unweighted mean line-of-sight velocity
dispersion values, respectively. These corrections are larger than has been
previously cited using disc models of the velocity and velocity dispersion
field to correct for beam smearing. The corrected flux-weighted velocity
dispersion values are sigma_m~20-50 km/s.


title: A canonical torsion theory for pro-p Iwahori-Hecke modules

abstract:
  Let $\mathfrak F$ be a locally compact nonarchimedean field with residue
characteristic $p$ and $G$ the group of $\mathfrak{F}$-rational points of a
connected split reductive group over $\mathfrak{F}$. We define a torsion pair
in the category Mod$(H)$ of modules over the pro-$p$-Iwahori Hecke $k$-algebra
$H$ of $G$, where $k$ is an arbitrary field. We prove that, under a certain
hypothesis, the torsionfree class embeds fully faithfully into the category
Mod${}^I(G)$ of smooth $k$-representations of $G$ generated by their
pro-$p$-Iwahori fixed vectors.
  If the characteristic of $k$ is different from $p$ then this hypothesis is
always satisfied and the torsionfree class is the whole category Mod$(H)$.
  If $k$ contains the residue field of $\mathfrak F$ then we study the case $G
= \mathbf{SL_2}(\mathfrak F)$. We show that our hypothesis is satisfied, and we
describe explicitly the torsionfree and the torsion classes. If $\mathfrak
F\neq \mathbb Q_p$ and $p\neq 2$, then an $H$-module is in the torsion class if
and only if it is a union of supersingular finite length submodules; it lies in
the torsionfree class if and only if it does not contain any nonzero
supersingular finite length module. If $\mathfrak{F} = \mathbb{Q}_p$, the
torsionfree class is the whole category Mod$(H)$, and we give a new proof of
the fact that Mod$(H)$ is equivalent to Mod${}^I(G)$. These results are based
on the computation of the $H$-module structure of certain natural cohomology
spaces for the pro-$p$-Iwahori subgroup $I$ of $G$.


title: Towards a topological fingerprint of music

abstract:
  Can music be represented as a meaningful geometric and topological object? In
this paper, we propose a strategy to describe some music features as a
polyhedral surface obtained by a simplicial interpretation of the
\textit{Tonnetz}. The \textit{Tonnetz} is a graph largely used in computational
musicology to describe the harmonic relationships of notes in equal tuning. In
particular, we use persistent homology in order to describe the
\textit{persistent} properties of music encoded in the aforementioned model.
Both the relevance and the characteristics of this approach are discussed by
analyzing some paradigmatic compositional styles. Eventually, the task of
automatic music style classification is addressed by computing the hierarchical
clustering of the topological fingerprints associated with some collections of
compositions.


title: Drifting Asteroid Fragments Around WD 1145+017

abstract:
  We have obtained extensive photometric observations of the polluted white
dwarf WD 1145+017 which has been reported to be transited by at least one, and
perhaps several, large asteroids (or, planetesimals) with dust emission. We
have carried out 53 observation sessions on 37 nights, totaling 192 hours, of
this 17th magnitude star with small to modest size telescopes covering the
interval 2015 November 1 to 2016 January 21. In all, we have detected some 237
significant dips in flux. Periodograms of the data reveal a significant
periodicity of 4.5004 hours that is consistent with the dominant ("A") period
detected with K2. The folded light curve at this period shows there is an
hour-long depression in flux with a mean depth of nearly 10%. This depression
is comprised of a series of shorter and sometimes deeper dips that do not
always occur at exactly the same orbital phase, and which would be unresolvable
with K2. In fact, we find numerous dips in flux at other orbital phases. Nearly
all of the dips associated with this activity appear to drift systematically in
phase with respect to the "A" period by about 2.5 minutes per day with a
dispersion of ~0.5 min/d, corresponding to a mean drift period of 4.4928 hours.
In all, we can track approximately 15 of these drifting features. There is no
detection of the "B"-"F" periods found with K2, but if they remain at the K2
levels we would not expect to have seen them. We explain the drifting motion as
that of smaller bodies (`fragments') that break off from the asteroid and go
into a slightly smaller orbit than that of the asteroid. If our interpretation
is correct, we can use the drift rate to determine the mass of the asteroid.
Under that scenario, we find that the mass of the asteroid is M_a ~ = 10^23
grams, or about 1/10th the mass of Ceres, with an uncertainty of about a factor
of 2.


title: Perturbative BV theories with Segal-like gluing

abstract:
  This is a survey of our program of perturbative quantization of gauge
theories on manifolds with boundary compatible with cutting/pasting and with
gauge symmetry treated by means of a cohomological resolution
(Batalin-Vilkovisky) formalism. We also give two explicit quantum examples --
abelian BF theory and the Poisson sigma model. This exposition is based on a
talk by P.M. at the ICMP 2015 in Santiago de Chile.


title:
Neumann Boundary Controllability of the Gear--Grimshaw System With
  Critical Size Restrictions on the Spacial Domain

abstract:
  In this paper we study the boundary controllability of the Gear-Grimshaw
system posed on a finite domain $(0,L)$, with Neumann boundary conditions:
\begin{equation} \label{abs} \begin{cases} u_t + uu_x+u_{xxx} + a v_{xxx} +
a_1vv_x+a_2 (uv)_x =0, & \text{in} \,\, (0,L)\times (0,T), c v_t +rv_x
+vv_x+abu_{xxx} +v_{xxx}+a_2buu_x+a_1b(uv)_x =0, & \text{in} \,\, (0,L)\times
(0,T), u_{xx}(0,t)=h_0(t),\,\,u_x(L,t)=h_1(t),\,\,u_{xx}(L,t)=h_2(t), &
\text{in} \,\, (0,T),
v_{xx}(0,t)=g_0(t),\,\,v_x(L,t)=g_1(t),\,\,v_{xx}(L,t)=g_2(t), & \text{in} \,\,
(0,T), u(x,0)= u^0(x), \quad v(x,0)= v^0(x), & \text{in} \,\, (0,L).\nonumber
\end{cases} \end{equation} We first prove that the corresponding linearized
system around the origin is exactly controllable in $(L^2(0,L))^2$ when
$h_2(t)=g_2(t)=0$. In this case, the exact controllability property is derived
for any $L>0$ with control functions $h_0, g_0\in H^{-\frac{1}{3}}(0,T)$ and
$h_1, g_1\in L^2(0,T)$. If we change the position of the controls and consider
$h_0(t)=h_2(t)=0$ (resp. $g_0(t)=g_2(t)=0)$ we obtain the result with control
functions $g_0, g_2\in H^{-\frac{1}{3}}(0,T)$ and $h_1, g_1\in L^2(0,T)$ if and
only if the length $L$ of the spatial domain $(0,L)$ belongs to a countable
set. In all cases the regularity of the controls are sharp in time. If only one
control act in the boundary condition, $h_0(t)=g_0(t)=h_2(t)=g_2(t)=0$ and
$g_1(t)=0$ (resp. $h_1(t)=0$), the linearized system is proved to be exactly
controllable for small values of the length $L$ and large time of control $T$.
Finally, the nonlinear system is shown to be locally exactly controllable via
the contraction mapping principle, if the associated linearized systems are
exactly controllable.


title: Representation of real numbers by the alternating Cantor series

abstract:
  The article is devoted to the alternating Cantor series.
  It is proved that any real number belonging to $[a_0-1;a_0]$, where
$a_0=\sum^{\infty} _{k=1} {\frac{d_{2k}-1}{d_1d_2...d_{2k}}} $, has no more
than two representations by the series and only numbers from countable subset
of real numbers have two representations. Geometry of the representation,
properties of cylinders sets and semicylinders, simplest metric problems are
investigated. Some applications of the series in fractal theory and relation
between positive and alternating Cantor series are described. A shift operator
and its some applications, set of incomplete sums are studied. Necessary and
sufficient conditions for representations of rational numbers by the
alternating Cantor series are formulated.


title: The Eddy Current-LLG Equations-Part I: FEM-BEM Coupling

abstract:
  We analyse a numerical method for the coupled system of the eddy current
equations in $\mathbb{R}^3$ with the Landau-Lifshitz-Gilbert equation in a
bounded domain. The unbounded domain is discretised by means of
finite-element/boundary-element coupling. Even though the considered problem is
strongly nonlinear, the numerical approach is constructed such that only two
linear systems per time step have to be solved. In this first part of the
paper, we prove unconditional weak convergence (of a subsequence) of the
finite-element solutions towards a weak solution. A priori error estimates will
be presented in the second part.


title:
The Eddy Current--LLG Equations: FEM-BEM Coupling and A Priori Error
  Estimates

abstract:
  We analyze a numerical method for the coupled system of the eddy current
equations in $\mathbb{R}^3$ with the Landau-Lifshitz-Gilbert equation in a
bounded domain. The unbounded domain is discretized by means of
finite-element/boundary-element coupling. Even though the considered problem is
strongly nonlinear, the numerical approach is constructed such that only two
linear systems per time step have to be solved. We prove unconditional weak
convergence (of a subsequence) of the finite-element solutions towards a weak
solution. We establish a priori error estimates if a sufficiently smooth strong
solution exists. Numerical experiments underlining the theoretical results are
presented.


title: Implicit Asymptotic Preserving Method for Linear Transport Equations

abstract:
  The computation of the radiative transfer equation is expensive mainly due to
two stiff terms: the transport term and the collision operator. The stiffness
in the former comes from the fact that particles (such as photons) travels at
the speed of light, while that in the latter is due to the strong scattering in
the diffusive regime. We study the fully implicit scheme for this equation to
account for the stiffness. The main challenge in the implicit treatment is the
coupling between the spacial and velocity coordinates that requires the large
size of the to-be-inverted matrix, which is also ill-conditioned and not
necessarily symmetric. Our main idea is to utilize the spectral structure of
the ill-conditioned matrix to construct a pre-conditioner, which, along with an
exquisite split of the spatial and angular dependence, significantly improve
the condition number and allows matrix-free treatment. We also design a fast
solver to compute this pre-conditioner explicitly in advance. Meanwhile, we
reformulate the system via an even-odd parity, which results in a symmetric and
positive definite matrix that can be inverted using conjugate gradient method.
This idea can also be implemented to the original non-symmetric system whose
inversion is solved by GMRES. A qualitative comparison with the conventional
methods, including Krylov iterative method pre-conditioned with diffusive
synthetic acceleration and asymptotic preserving scheme via even-odd
decomposition, is also discussed.


title:
A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the
  Vlasov-Poisson Equation

abstract:
  Numerical solutions to the Vlasov-Poisson system of equations have important
applications to both plasma physics and cosmology. In this paper, we present a
new Particle-in-Cell (PIC) method for solving this system that is 4th-order
accurate in both space and time. Our method is a high-order extension of one
presented previously [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput.,
33 (2011), pp. 3509--3537]. It treats all of the stages of the standard PIC
update - charge deposition, force interpolation, the field solve, and the
particle push - with 4th-order accuracy, and includes a 6th-order accurate
phase-space remapping step for controlling particle noise. We demonstrate the
convergence of our method on a series of one- and two- dimensional
electrostatic plasma test problems, comparing its accuracy to that of a
2nd-order method. As expected, the 4th-order method can achieve comparable
accuracy to the 2nd-order method with many fewer resolution elements.


title: Gysin functors and the Grothendieck-Witt category, Part I

abstract:
  We define the Grothendieck-Witt category over a fixed ground ring. In order
to study the structure of this category, we introduce the general theory of
Gysin functors and their associated categories of correspondences. The latter
generalizes the familiar construction of the Burnside category over a finite
group. We prove various results about the structure of these correspondence
categories, and we prove a "recognition theorem" loosely saying that these
correspondence categories naturally show up in situations where one has both a
symmetric monoidal structure and transfers. Returning to the Grothendieck-Witt
category, a few examples are worked out.


title:
Combining ConvNets with Hand-Crafted Features for Action Recognition
  Based on an HMM-SVM Classifier

abstract:
  This paper proposes a new framework for RGB-D-based action recognition that
takes advantages of hand-designed features from skeleton data and deeply
learned features from depth maps, and exploits effectively both the local and
global temporal information. Specifically, depth and skeleton data are firstly
augmented for deep learning and making the recognition insensitive to view
variance. Secondly, depth sequences are segmented using the hand-crafted
features based on skeleton joints motion histogram to exploit the local
temporal information. All training se gments are clustered using an Infinite
Gaussian Mixture Model (IGMM) through Bayesian estimation and labelled for
training Convolutional Neural Networks (ConvNets) on the depth maps. Thus, a
depth sequence can be reliably encoded into a sequence of segment labels.
Finally, the sequence of labels is fed into a joint Hidden Markov Model and
Support Vector Machine (HMM-SVM) classifier to explore the global temporal
information for final recognition.


title:
Effect of atomic-scale defects and dopants on phosphorene electronic
  structure and quantum transport properties

abstract:
  By means of a multi-scale first-principles approach, a description of the
local electronic structure of two-dimensional and narrow phosphorene sheets
with various types of modifications is presented. First, a rational argument
based on the geometry of the pristine and modified P network, and supported by
the Wannier functions formalism is introduced to describe a hybridization model
of the P atomic orbitals. {\it Ab initio} calculations show that
non-isoelectronic foreign atoms form quasi-bound states at varying energy
levels and create different polarization states depending on the number of
valence electrons between P and the doping atom. The quantum transport
properties of modified phosphorene ribbons are further described with great
accuracy. The distortions on the electronic bands induced by the external
species lead to strong backscattering effects on the propagating charge
carriers. Depending on the energy of the charge-carrier and the type of doping,
the conduction may range from the diffusive to the localized regime.
Interstitial defects at vacant sites lead to homogeneous transport fingerprints
across different types of doping atoms. We suggest that the relatively low
values of charge mobility reported in experimental measurements may have their
origin in the presence of defects.


title:
Effect of Pressure Broadening on Molecular Absorption Cross Sections in
  Exoplanetary Atmospheres

abstract:
  Spectroscopic observations of exoplanets are leading to unprecedented
constraints on their atmospheric compositions. However, molecular abundances
derived from spectra are degenerate with the absorption cross sections which
form critical input data in atmospheric models. Therefore, it is important to
quantify the uncertainties in molecular cross sections to reliably estimate the
uncertainties in derived molecular abundances. However, converting line lists
into cross sections via line broadening involves a series of prescriptions for
which the uncertainties are not well understood. We investigate and quantify
the effects of various factors involved in line broadening in exoplanetary
atmospheres - the profile evaluation width, pressure versus thermal broadening,
broadening agent, spectral resolution, and completeness of broadening
parameters - on molecular absorption cross sections. We use H$_2$O as a case
study as it has the most complete absorption line data. For low resolution
spectra (R$\lesssim$100) for representative temperatures and pressures (T
$\sim$ 500K-3000K, P$\lesssim$1 atm) of H$_2$-rich exoplanetary atmospheres we
find the median difference in cross sections ($\delta$) introduced by various
aspects of pressure broadening to be $\lesssim$1\%. For medium resolutions
(R$\lesssim$5000), including those attainable with JWST, we find that $\delta$
can be up to 40\%. For high resolutions (R$\sim$10$^5$) $\delta$ can be
$\gtrsim$100\%, reaching $\gtrsim$1000\% for low temperatures (T$\lesssim$500K)
and high pressures (P$\gtrsim$1 atm). The effect is higher still for self
broadening. We generate a homogeneous database of absorption cross sections of
molecules of relevance to exoplanetary atmospheres for which high temperature
line lists are available, particularly H$_2$O, CO, CH$_4$, CO$_2$, HCN, and
NH$_3$.


title: Zeta-polynomials for modular form periods

abstract:
  Answering problems of Manin, we use the critical $L$-values of even weight
$k\geq 4$ newforms $f\in S_k(\Gamma_0(N))$ to define zeta-polynomials $Z_f(s)$
which satisfy the functional equation $Z_f(s)=\pm Z_f(1-s)$, and which obey the
Riemann Hypothesis: if $Z_f(\rho)=0$, then $\operatorname{Re}(\rho)=1/2$. The
zeros of the $Z_f(s)$ on the critical line in $t$-aspect are distributed in a
manner which is somewhat analogous to those of classical zeta-functions. These
polynomials are assembled using (signed) Stirling numbers and "weighted
moments" of critical values $L$-values. In analogy with Ehrhart polynomials
which keep track of integer points in polytopes, the $Z_f(s)$ keep track of
arithmetic information. Assuming the Bloch--Kato Tamagawa Number Conjecture,
they encode the arithmetic of a combinatorial arithmetic-geometric object which
we call the "Bloch-Kato complex" for $f$. Loosely speaking, these are graded
sums of weighted moments of orders of \v{S}afarevi\v{c}-Tate groups associated
to the Tate twists of the modular motives.


title: Are Elephants Bigger than Butterflies? Reasoning about Sizes of Objects

abstract:
  Human vision greatly benefits from the information about sizes of objects.
The role of size in several visual reasoning tasks has been thoroughly explored
in human perception and cognition. However, the impact of the information about
sizes of objects is yet to be determined in AI. We postulate that this is
mainly attributed to the lack of a comprehensive repository of size
information. In this paper, we introduce a method to automatically infer object
sizes, leveraging visual and textual information from web. By maximizing the
joint likelihood of textual and visual observations, our method learns reliable
relative size estimates, with no explicit human supervision. We introduce the
relative size dataset and show that our method outperforms competitive textual
and visual baselines in reasoning about size comparisons.


title:
Electric gating induced bandgaps and enhanced Seebeck effect in zigzag
  bilayer graphene ribbons

abstract:
  We theoretically investigate effect of a transverse electric field generated
by side gates and a vertical electric field generated by top, back gates on
energy bands and transport properties of zigzag bilayer graphene ribbons
(Bernal stacking). Using atomistic Tight Binding calculations and Green
function formalism we demonstrate that bandgap is opened when either field is
applied and even enlarged under simultaneous influence of the two fields.
Interestingly, although vertical electric fields are widely used to control
bandgap in bilayer graphene, here we show that transverse fields exhibit more
positive effect in terms of modulating a larger range of bandgap and retaining
good electrical conductance. Seebeck effect is also demonstrated to be enhanced
strongly about 13 times for a zigzag bilayer graphene ribbons with 16 chain
lines. These results may motivate new designs of devices made of bilayer
graphene ribbons using electric gates.


title:
Efficient polarization insensitive complex wavefront control using
  Huygens' metasurfaces based on dielectric resonant meta-atoms

abstract:
  Subwavelength-thin metasurfaces have shown great promises for the control of
optical wavefronts, thus opening new pathways for the development of efficient
flat optics. In particular, Huygens' metasurfaces based on all-dielectric
resonant meta-atoms have already shown a huge potential for practical
applications with their polarization insensitivity and high transmittance
efficiency. Here, we experimentally demonstrate a polarization insensitive
holographic Huygens' metasurface based on dielectric resonant meta-atoms
capable of complex wavefront control at telecom wavelengths. Our metasurface
produces a hologram image in the far-field with 82% transmittance efficiency
and 40% imaging efficiency. Such efficient complex wavefront control shows that
Huygens' metasurfaces based on resonant dielectric meta-atoms are a big step
towards practical applications of metasurfaces in wavefront design related
technologies, including computer-generated holograms, ultra-thin optics,
security and data storage devices.


title: Rotation invariant ultradistributions

abstract:
  We prove that an ultradistribution is rotation invariant if and only if it
coincides with its spherical mean. For it, we study the problem of spherical
representations of ultradistributions on $\mathbb{R}^{n}$. Our results apply to
both the quasianalytic and the non-quasianalytic case.


title:
On weighted mixed-norm Sobolev estimates for some basic parabolic
  equations

abstract:
  Novel global weighted parabolic Sobolev estimates, weighted mixed-norm
estimates and a.e. convergence results of singular integrals for evolution
equations are obtained. Our results include the classical heat equation, the
harmonic oscillator evolution equation $$\partial_tu=\Delta u-|x|^2u+f,$$ and
their corresponding Cauchy problems. We also show weighted mixed-norm estimates
for solutions to degenerate parabolic extension problems arising in connection
with the fractional space-time nonlocal equations $(\partial_t-\Delta)^su=f$
and $(\partial_t-\Delta+|x|^2)^su=f$, for $0<s<1$.


title:
A Hubble Space Telescope Survey for Novae in M87. I. Light and Color
  Curves, Spatial Distributions and the Nova Rate

abstract:
  The Hubble Space Telescope has imaged the central part of M87 over a 10 week
span, leading to the discovery of 32 classical novae and nine fainter, likely
very slow and/or symbiotic novae. In this first in a series of papers we
present the M87 nova finder charts, and the light and color curves of the
novae. We demonstrate that the rise and decline times, and the colors of M87
novae are uncorrelated with each other and with position in the galaxy. The
spatial distribution of the M87 novae follows the light of the galaxy,
suggesting that novae accreted by M87 during cannibalistic episodes are
well-mixed. Conservatively using only the 32 brightest classical novae we
derive a nova rate for M87: $363_{-45}^{+33}$ novae/yr. We also derive the
luminosity-specific classical nova rate for this galaxy, which is
$7.88_{-2.6}^{+2.3} /yr/ 10^{10}L_\odot,_{K}$. Both rates are 3-4 times higher
higher than those reported for M87 in the past, and similarly higher than those
reported for all other galaxies. We suggest that most previous ground-based
surveys for novae in external galaxies, including M87, miss most faint, fast
novae, and almost all slow novae near the centers of galaxies.


title: The DRAGON simulations: globular cluster evolution with a million stars

abstract:
  Introducing the DRAGON simulation project, we present direct $N$-body
simulations of four massive globular clusters (GCs) with $10^6$ stars and 5$\%$
primordial binaries at a high level of accuracy and realism. The GC evolution
is computed with NBODY6++GPU and follows the dynamical and stellar evolution of
individual stars and binaries, kicks of neutron stars and black holes, and the
effect of a tidal field. We investigate the evolution of the luminous (stellar)
and dark (faint stars and stellar remnants) GC components and create mock
observations of the simulations (i.e. photometry, color-magnitude diagrams,
surface brightness and velocity dispersion profiles). By connecting internal
processes to observable features we highlight the formation of a long-lived
'dark' nuclear subsystem made of black holes (BHs), which results in a
two-component structure. The inner core is dominated by the BH subsystem and
experiences a core collapse phase within the first Gyr. It can be detected in
the stellar (luminous) line-of-sight velocity dispersion profiles. The outer
extended core - commonly observed in the (luminous) surface brightness profiles
- shows no collapse features and is continuously expanding. We demonstrate how
a King (1966) model fit to observed clusters might help identify the presence
of post core-collapse BH subsystems. For global observables like core and
half-mass radii the direct simulations agree well with Monte-Carlo models.
Variations in the initial mass function can result in significantly different
GC properties (e.g. density distributions) driven by varying amounts of early
mass loss and the number of forming BHs.


title: Noncommutative reproducing kernel Hilbert spaces

abstract:
  The theory of positive kernels and associated reproducing kernel Hilbert
spaces, especially in the setting of holomorphic functions, has been an
important tool for the last several decades in a number of areas of complex
analysis and operator theory. An interesting generalization of holomorphic
functions, namely free noncommutative functions (e.g., functions of
square-matrix arguments of arbitrary size satisfying additional natural
compatibility conditions), is now an active area of research, with motivation
and applications from a variety of areas (e.g., noncommutative functional
calculus, free probability, and optimization theory in linear systems
engineering). The purpose of this article is to develop a theory of positive
kernels and associated reproducing kernel Hilbert spaces for the setting of
free noncommutative function theory.


title:
Optimality and Rate-Compatibility for Erasure-Coded Packet Transmissions
  when Fading Channel Diversity Increases with Packet Length

abstract:
  A message composed of packets is transmitted using erasure and channel coding
over a fading channel with no feedback. For this scenario, the paper explores
the trade-off between the redundancies allocated to the packet-level erasure
code and the channel code, along with an objective of a low probability of
failure to recover the message.
  To this end, we consider a fading model that we term proportional-diversity
block fading (PD block fading). For a fixed overall code rate and transmit
power, we formulate an optimization problem to numerically find the optimal
channel-coding rate (and thus the optimal erasure-coding rate) that minimizes
the probability of failure for various approximations of the problem.
  Furthermore, an interpretation of the results from an incremental redundancy
point of view shows how rate-compatibility affects the possible trajectories of
the failure probability as a function of the overall code rate. Our numerical
results suggest that an optimal, rateless, hybrid coding scheme for a
single-user wireless system over the PD block-fading channel should have the
rate of the erasure code approach one.


title:
Interpolation and transfer-function realization for the noncommutative
  Schur-Agler class

abstract:
  The Schur-Agler class consists of functions over a domain satisfying an
appropriate von Neumann inequality. Originally defined over the polydisk, the
idea has been extended to general domains in multivariable complex Euclidean
space with matrix polynomial defining function as well as to certain
multivariable noncommutative-operator domains with a noncommutative
linear-pencil defining function. Still more recently there has emerged a free
noncommutative function theory (functions of noncommuting matrix variables
respecting direct sums and similaritytransformations). The purpose of the
present paper is to extend the Schur-Agler-class theory to the free
noncommutative functionsetting. This includes the positive-kernel-decomposition
characterization of the class, transfer-function realization and Pick
interpolation theory. A special class of defining functions is identified for
which the associated Schur-Agler class coincides with the
contractive-multiplier class on an associated noncommutative reproducing kernel
Hilbert space; in this case, solution of the Pick interpolation problem is in
terms of the complete positivity of an associated Pick matrix which is
explicitly determined from the interpolation data.


title: Simple Online and Realtime Tracking

abstract:
  This paper explores a pragmatic approach to multiple object tracking where
the main focus is to associate objects efficiently for online and realtime
applications. To this end, detection quality is identified as a key factor
influencing tracking performance, where changing the detector can improve
tracking by up to 18.9%. Despite only using a rudimentary combination of
familiar techniques such as the Kalman Filter and Hungarian algorithm for the
tracking components, this approach achieves an accuracy comparable to
state-of-the-art online trackers. Furthermore, due to the simplicity of our
tracking method, the tracker updates at a rate of 260 Hz which is over 20x
faster than other state-of-the-art trackers.


title:
Inhomogeneous generalization of multispecies totally asymmetric zero
  range process

abstract:
  The $n$-species totally asymmetric zero range process ($n$-TAZRP) on
one-dimensional periodic chain studied recently by the authors is a continuous
time Markov process where arbitrary number of particles can occupy the same
sites and hop to the adjacent sites only in one direction with a priority
constraint according to their species. In this paper we introduce an
$n$-parameter generalization of the $n$-TAZRP having inhomogeneous transition
rate. The steady state probability is obtained in a matrix product form and
also by an algorithm related to combinatorial $R$.

categories: math-ph cond-mat.stat-mech math.MP math.QA nlin.SI


title:
Operator Positivstellens\"atze for noncommutative polynomials positive
  on matrix convex sets

abstract:
  This article studies algebraic certificates of positivity for noncommutative
(nc) operator-valued polynomials on matrix convex sets, such as the solution
set $D_L$, called a free Hilbert spectrahedron, of the linear operator
inequality (LOI) $L(X)=A_0\otimes I+\sum_{j=1}^g A_{j}\otimes X_j\succeq 0,$
where $A_j$ are self-adjoint linear operators on a separable Hilbert space,
$X_j$ matrices and $I$ is an identity matrix. If $A_j$ are matrices, then
$L(X)\succeq 0$ is called a linear matrix inequality (LMI) and $D_L$ a free
spectrahedron. For monic LMIs, i.e., $A_0=I$, and nc matrix-valued polynomials
the certificates of positivity were established by Helton, Klep and McCollough
in a series of articles with the use of the theory of complete positivity from
operator algebras and classical separation arguments from real algebraic
geometry. Since the full strength of the theory of complete positivity is not
restricted to finite dimensions, but works well also in the
infinite-dimensional setting, we use it to tackle our problems. First we extend
the characterization of the inclusion $D_{L_1}\subseteq D_{L_2}$ from monic
LMIs to monic LOIs. As a corollary one obtains the description of a polar dual
of a free Hilbert spectrahedron $D_L$ and its projection, called a free Hilbert
spectrahedrop. Using this characterization in a separation argument, we obtain
a certificate for multivariate matrix-valued nc polynomials $F$ positive
semidefinite on a free Hilbert spectrahedron defined by a monic LOI. Replacing
the separation argument by an operator Fej\'er-Riesz theorem enables us to
extend this certificate, in the univariate case, to operator-valued polynomials
$F$. Finally, focusing on the algebraic description of the equality
$D_{L_1}=D_{L_2}$, we remove the assumption of boundedness from the description
in the LMIs case by an extended analysis. However, the description does not
extend to LOIs.


title: User Access Mode Selection in Fog Computing Based Radio Access Networks

abstract:
  Fog computing based radio access network is a promising paradigm for the
fifth generation wireless communication system to provide high spectral and
energy efficiency. With the help of the new designed fog computing based access
points (F-APs), the user-centric objectives can be achieved through the
adaptive technique and will relieve the load of fronthaul and alleviate the
burden of base band unit pool. In this paper, we derive the coverage
probability and ergodic rate for both F-AP users and device-to-device users by
taking into account the different nodes locations, cache sizes as well as user
access modes. Particularly, the stochastic geometry tool is used to derive
expressions for above performance metrics. Simulation results validate the
accuracy of our analysis and we obtain interesting trade-offs that depend on
the effect of the cache size, user node density, and the quality of service
constrains on the different performance metrics.


title: Distance-Sensitive Planar Point Location

abstract:
  Let $\mathcal{S}$ be a connected planar polygonal subdivision with $n$ edges
that we want to preprocess for point-location queries, and where we are given
the probability $\gamma_i$ that the query point lies in a polygon $P_i$ of
$\mathcal{S}$. We show how to preprocess $\mathcal{S}$ such that the query time
for a point~$p\in P_i$ depends on~$\gamma_i$ and, in addition, on the distance
from $p$ to the boundary of~$P_i$---the further away from the boundary, the
faster the query. More precisely, we show that a point-location query can be
answered in time $O\left(\min \left(\log n, 1 + \log
\frac{\mathrm{area}(P_i)}{\gamma_i \Delta_{p}^2}\right)\right)$, where
$\Delta_{p}$ is the shortest Euclidean distance of the query point~$p$ to the
boundary of $P_i$. Our structure uses $O(n)$ space and $O(n \log n)$
preprocessing time. It is based on a decomposition of the regions of
$\mathcal{S}$ into convex quadrilaterals and triangles with the following
property: for any point $p\in P_i$, the quadrilateral or triangle
containing~$p$ has area $\Omega(\Delta_{p}^2)$. For the special case where
$\mathcal{S}$ is a subdivision of the unit square and
$\gamma_i=\mathrm{area}(P_i)$, we present a simpler solution that achieves a
query time of $O\left(\min \left(\log n, \log
\frac{1}{\Delta_{p}^2}\right)\right)$. The latter solution can be extended to
convex subdivisions in three dimensions.


title: Exotic t-structures for two-block Springer fibers

abstract:
  We study the exotic t-structure on the derived category of coherent sheaves
on two-block Springer fibre (i.e. for a nilpotent matrix of type (m+n,n) in
type A). The exotic t-structure has been defined by Bezrukavnikov and Mirkovic
for Springer theoretic varieties in order to study representations of Lie
algebras in positive characteristic. Using work of Cautis and Kamnitzer, we
construct functors indexed by affine tangles, between categories of coherent
sheaves on different two-block Springer fibres (i.e. for different values of
n). After checking some exactness properties of these functors, we describe the
irreducible objects in the heart of the exotic t-structure, and enumerate them
by crossingless (m,m+2n) matchings. We compute the Ext's between the
irreducible objects, and show that the resulting algebras are an annular
variant of Khovanov's arc algebras. In subsequent work we will make a link with
annular Khovanov homology, and use these results to give a positive
characteristic analogue of some categorification results using two-block
parabolic category O (by Bernstein-Frenkel-Khovanov, Brundan, Stroppel, et al).


title:
Small-sample testing inference in symmetric and log-symmetric linear
  regression models

abstract:
  This paper deals with the issue of testing hypothesis in symmetric and
log-symmetric linear regression models in small and moderate-sized samples. We
focus on four tests, namely the Wald, likelihood ratio, score, and gradient
tests. These tests rely on asymptotic results and are unreliable when the
sample size is not large enough to guarantee a good agreement between the exact
distribution of the test statistic and the corresponding chi-squared asymptotic
distribution. Bartlett and Bartlett-type corrections typically attenuate the
size distortion of the tests. These corrections are available in the literature
for the likelihood ratio and score tests in symmetric linear regression models.
Here, we derive a Bartlett-type correction for the gradient test. We show that
the corrections are also valid for the log-symmetric linear regression models.
We numerically compare the various tests, and bootstrapped tests, through
simulations. Our results suggest that the corrected and bootstrapped tests
exhibit type I probability error closer to the chosen nominal level with
virtually no power loss. The analytically corrected tests, including the
Bartlett-corrected gradient test derived in this paper, perform as well as the
bootstrapped tests with the advantage of not requiring
computationally-intensive calculations. We present two real data applications
to illustrate the usefulness of the modified tests.
  Keywords: Symmetric regression models; Bartlett correction; Bartlett-type
correction; Bootstrap; Log-symmetric regression models; gradient statistic;
score statistic; likelihood ratio statistic; Wald statistic.