title:
A Unified Computational and Statistical Framework for Nonconvex Low-Rank
  Matrix Estimation

abstract:
  We propose a unified framework for estimating low-rank matrices through
nonconvex optimization based on gradient descent algorithm. Our framework is
quite general and can be applied to both noisy and noiseless observations. In
the general case with noisy observations, we show that our algorithm is
guaranteed to linearly converge to the unknown low-rank matrix up to minimax
optimal statistical error, provided an appropriate initial estimator. While in
the generic noiseless setting, our algorithm converges to the unknown low-rank
matrix at a linear rate and enables exact recovery with optimal sample
complexity. In addition, we develop a new initialization algorithm to provide a
desired initial estimator, which outperforms existing initialization algorithms
for nonconvex low-rank matrix estimation. We illustrate the superiority of our
framework through three examples: matrix regression, matrix completion, and
one-bit matrix completion. We also corroborate our theory through extensive
experiments on synthetic data.


title:
On the computation of harmonic maps by unconstrained algorithms based on
  totally geodesic embeddings

abstract:
  In this paper, we present an algorithm for the computation of harmonic maps,
and respectively, of the harmonic map heat flow between two closed Riemannian
manifolds. Our approach is based on the totally geodesic embedding of the
target manifold into $\mathbb{R}^N$ . Since embeddings of Riemannian manifolds
into Euclidean spaces can easily be made totally geodesic by extending the
Riemannian metric in a certain way into some tubular neighbourhood, the here
presented approach is quite general. Totally geodesic embeddings allow to
reformulate the harmonic map heat flow in a neighbourhood of the embedded
target manifold. This reformulation has the advantage that the problem becomes
unconstrained: Instead of assuming a priori that the solution to the flow maps
into the target manifold this fact becomes a property of the solution to the
extended flow for special initial data. The solution space to the reformulated
problem therefore exists of maps which are also allowed to map into the ambient
space of the target manifold. This simplifies the discretization of the
problem. Based on this observation, we here propose algorithms for the
computation of the harmonic map heat flow and of harmonic maps. In contrast to
previous schemes, our algorithm does not make use of projections onto the
target manifold, discrete tangential deformations, geodesic finite elements or
of Lagrange multipliers. We prove error estimates in the stationary case and
present some numerical tests at the end of the paper.


title:
Spaces of harmonic maps of the projective plane to the four-dimensional
  sphere

abstract:
  The spaces of harmonic maps of the projective plane to the four-dimensional
sphere are investigated in this paper by means of twistor lifts. It is shown
that such spaces are empty in case of even harmonic degree. In case of harmonic
degree less than 6 it was shown that such spaces are path-connected and an
explicit parameterization of the canonical representatives was found. In
addition, the last section summarizes known results for harmonic maps of the
two-dimensional sphere to the four-dimensional sphere of harmonic degree less
than 6.


title: The Group Law for Edwards Curves

abstract:
  This article gives an elementary computational proof of the group law for
Edwards elliptic curves following Bernstein, Lange, et al., Edwards, and
Friedl. The associative law is expressed as a polynomial identity over the
integers that is directly checked by polynomial division. No preliminaries such
as intersection numbers, B\'ezout's theorem, projective geometry, divisors, or
Riemann Roch are required. The proofs have been designed to facilitate the
formal verification of elliptic curve cryptography.


title:
Effects of interedge scattering on the Wigner crystallization in
  graphene nanoribbons

abstract:
  We investigate the effects of coupling between the two zigzag edges of
graphene nanoribbons on the Wigner crystallization of electrons and holes using
a combination of tight-binding, mean field Hubbard and many-body configuration
interaction methods. We show that the thickness of the nanoribbon plays a
crucial role in the formation of Wigner crystal. For ribbon widths smaller than
16 \mbox{\AA}, increased kinetic energy overcomes the long-range Coulomb
repulsion and suppresses the Wigner crystallization. For wider ribbons up to 38
\mbox{\AA} wide, strong Wigner localization is observed for even number of
electrons, revealing an even-odd effect also found in Coulomb blockade addition
spectrum. Interedge correlations are found to be strong enough to allow
simultaneous crystallization on both edges, although an applied electric field
can decouple the two edges. Finally, we show that Wigner crystallization can
also occurs for holes, albeit weaker than for electrons.


title:
Mitigating the Influence of the Boundary on PDE-based Covariance
  Operators

abstract:
  Gaussian random fields over infinite-dimensional Hilbert spaces require the
definition of appropriate covariance operators. The use of elliptic PDE
operators to construct covariance operators allows to build on fast PDE solvers
for manipulations with the resulting covariance and precision operators.
However, PDE operators require a choice of boundary conditions, and this choice
can have a strong and usually undesired influence on the Gaussian random field.
We propose two techniques that allow to ameliorate these boundary effects for
large-scale problems. The first approach combines the elliptic PDE operator
with a Robin boundary condition, where a varying Robin coefficient is computed
from an optimization problem. The second approach normalizes the pointwise
variance by rescaling the covariance operator. These approaches can be used
individually or can be combined. We study properties of these approaches, and
discuss their computational complexity. The performance of our approaches is
studied for random fields defined over simple and complex two- and
three-dimensional domains.


title: Charged Rotating AdS Black Holes with Chern-Simons coupling

abstract:
  We obtain a perturbative solution for rotating charged black holes in
5-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological
constant. We start from a small undeformed Kerr-AdS solution and use the
electric charge as a perturbative parameter to build up black holes with
equal-magnitude angular momenta up to forth order. These black hole solutions
are described by three parameters, the charge, horizon radius and horizon
angular velocity. We determine the physical quantities of these black holes and
study their dependence on the parameters of black holes and arbitrary
Chern-Simons coefficient. In particular, for values of CS coupling constant
beyond its supergravity amount, due to a rotational instability,
counterrotating black holes arise. Also the rotating solutions appear to have
vanishing angular momenta and do not manifest uniquely by their global charges.


title:
Charged rotating black holes in Einstein--Maxwell--Chern-Simons theory
  with a negative cosmological constant

abstract:
  We consider rotating black hole solutions in five-dimensional
Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and
a generic value of the Chern-Simons coupling constant $\lambda$. Using both
analytical and numerical techniques, we focus on cohomogeneity-1
configurations, with two equal-magnitude angular momenta, which approach at
infinity a globally AdS background. We find that the generic solutions share a
number of basic properties with the known Cvetic, L\"u and Pope black holes
which have $\lambda=1$. New features occur as well, for example, when the
Chern-Simons coupling constant exceeds a critical value, the solutions are no
longer uniquely determined by their global charges. Moreover, the black holes
possess radial excitations which can be labelled by the node number of the
magnetic gauge potential function. Solutions with small values of $\lambda$
possess other distinct features. For instance, the extremal black holes there
form two disconnected branches, while not all near-horizon solutions are
associated with global solutions.


title: On-shell recursion relations for generic integrands

abstract:
  The quantum effects encapsulated in loop corrections are crucial in quantum
field theory for a wide variety of formal and phenomenological applications. In
this article we propose and check a definition of the so-called single cut
contributions needed to complete on-shell recursion relations for the integrand
of scattering amplitudes in generic power-counting renormalisable theories at
conjecturally any loop order. Our proposal meshes well with standard
dimensional regularisation and applies in particular directly to much of the
standard model of particle physics. Apart from a diagrammatic construction, at
one loop order we provide a direct cross-check for box coefficients.
Interestingly, at one loop our proposal can be related to a specific subset of
all double unitarity cuts as well as tree-level poles by iterated recursion. We
focus in particular on demonstrating the method in rational-term one-loop
examples in pure Yang-Mills theory. For the finite amplitudes we present
all-order arguments. First steps toward gravity integrands are taken.


title: Statistical mechanics approach to lattice field theory

abstract:
  The mean spherical approximation (MSA) is a closure relation for pair
correlation functions (two-point functions) in statistical physics. It can be
applied to a wide range of systems, is computationally fairly inexpensive, and
when properly applied and interpreted lead to rather good results.
  In this paper we promote its applicability to euclidean quantum field
theories formulated on a lattice, by demonstrating how it can be used to locate
the critical lines of a class of multi-component bosonic models. The MSA has
the potential to handle models lacking a positive definite integration measure,
which therefore are difficult to investigate by Monte-Carlo simulations.


title: Knotted optical vortices in exact solutions to Maxwell's equations

abstract:
  We construct a family of exact solutions to Maxwell's equations in which the
points of zero intensity form knotted lines topologically equivalent to a given
but arbitrary algebraic link. These lines of zero intensity, more commonly
referred to as optical vortices, and their topology are preserved as time
evolves and the fields have finite energy. To derive explicit expressions for
these new electromagnetic fields that satisfy the nullness property, we make
use of the Bateman variables for the Hopf field as well as complex polynomials
in two variables whose zero sets give rise to algebraic links. The class of
algebraic links includes not only all torus knots and links thereof, but also
more intricate cable knots. While the unknot has been considered before, the
solutions presented here show that more general knotted structures can also
arise as optical vortices in exact solutions to Maxwell's equations.


title:
Two-dimensional lattice solitons in polariton condensates with
  spin-orbit coupling

abstract:
  We study two-dimensional fundamental and vortex solitons in polariton
condensates with spin-orbit coupling and Zeeman splitting evolving in square
arrays of microcavity pillars. Due to repulsive excitonic nonlinearity such
states are encountered in finite gaps in the spectrum of the periodic array.
Spin-orbit coupling between two polarization components stemming from TE-TM
energy splitting of the cavity photons acting together with Zeeman splitting
lifts the degeneracy between vortex solitons with opposite topological charges
and makes their density profiles different for a fixed energy. This results in
formation of four distinct families of vortex solitons with topological charges
m=+-1, all of which can be stable. At the same time, only two stable families
of fundamental gap solitons characterized by domination of different
polarization components are encountered.


title:
Internet of Things Applications: Animal Monitoring with Unmanned Aerial
  Vehicle

abstract:
  In animal monitoring applications, both animal detection and their movement
prediction are major tasks. While a variety of animal monitoring strategies
exist, most of them rely on mounting devices. However, in real world, it is
difficult to find these animals and install mounting devices. In this paper, we
propose an animal monitoring application by utilizing wireless sensor networks
(WSNs) and unmanned aerial vehicle (UAV). The objective of the application is
to detect locations of endangered species in large-scale wildlife areas and
monitor movement of animals without any attached devices. In this application,
sensors deployed throughout the observation area are responsible for gathering
animal information. The UAV flies above the observation area and collects the
information from sensors. To achieve the information efficiently, we propose a
path planning approach for the UAV based on a Markov decision process (MDP)
model. The UAV receives a certain amount of reward from an area if some animals
are detected at that location. We solve the MDP using Q-learning such that the
UAV prefers going to those areas that animals are detected before. Meanwhile,
the UAV explores other areas as well to cover the entire network and detects
changes in the animal positions. We first define the mathematical model
underlying the animal monitoring problem in terms of the value of information
(VoI) and rewards. We propose a network model including clusters of sensor
nodes and a single UAV that acts as a mobile sink and visits the clusters.
Then, one MDP-based path planning approach is designed to maximize the VoI
while reducing message delays. The effectiveness of the proposed approach is
evaluated using two real-world movement datasets of zebras and leopard.
Simulation results show that our approach outperforms greedy, random heuristics
and the path planning based on the traveling salesman problem.


title:
Modeling shift-variant X-ray focal spot blur for high-resolution
  flat-panel cone-beam CT

abstract:
  Flat-panel cone-beam CT (CBCT) has been applied clinically in a number of
high-resolution applications. Increasing geometric magnification can
potentially improve resolution, but also increases blur due to an extended
x-ray focal-spot. We present a shift-variant focal-spot blur model and
incorporate it into a model-based iterative-reconstruction algorithm. We apply
this algorithm to simulation and CBCT test-bench data. In a trabecular bone
simulation study, we find traditional reconstruction approaches without a blur
model exhibit shift-variant resolution properties that depend greatly on the
acquisition protocol (e.g. short vs. full scans) and the anode angles of the
rays used to reconstruct a particular region. For physical CBCT experiments
focal spot blur was characterized and a spatial resolution phantom was scanned
and reconstructed. In both experiments image quality using the shift-variant
model was significantly improved over approaches that modeled no blur or only a
shift-invariant blur, suggesting a potential means to overcome traditional CBCT
spatial resolution and system design limitations.


title:
Scalable Designs for Quasiparticle-Poisoning-Protected Topological
  Quantum Computation with Majorana Zero Modes

abstract:
  We present designs for scalable quantum computers composed of qubits encoded
in aggregates of four or more Majorana zero modes, realized at the ends of
topological superconducting wire segments that are assembled into
superconducting islands with significant charging energy. Quantum information
can be manipulated according to a measurement-only protocol, which is
facilitated by tunable couplings between Majorana zero modes and nearby
semiconductor quantum dots. Our proposed architecture designs have the
following principal virtues: (1) the magnetic field can be aligned in the
direction of all of the topological superconducting wires since they are all
parallel; (2) topological $T$-junctions are not used, obviating possible
difficulties in their fabrication and utilization; (3) quasiparticle poisoning
is abated by the charging energy; (4) Clifford operations are executed by a
relatively standard measurement: detection of corrections to quantum dot
energy, charge, or differential capacitance induced by quantum fluctuations;
(5) it is compatible with strategies for producing good approximate magic
states.


title: Phase tropical hypersurfaces

abstract:
  We prove that a generic smooth complex hypersurface in the complex torus is
homeomorphic to the corresponding phase tropical hypersurface.


title: Congruence Property in Orbifold Theory

abstract:
  Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of
CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the
kernel of the representation of the modular group on twisted conformal blocks
associated to $V$ and $G$ is a congruence subgroup. In particular, the
$q$-character of each irreducible twisted module is a modular function on the
same congruence subgroup. In the case $V$ is the Frenkel-Lepowsky-Meurman's
moonshine vertex operator algebra and $G$ is the monster simple group, the
generalized McKay-Thompson series associated to any commuting pair in the
monster group is a modular function.


title: Short cycles in digraphs and the Caccetta-H\"{a}ggkvist conjecture

abstract:
  In the theory of digraphs, the study of cycles is a subject of great
importance and has given birth to a number of deep questions such as the
Behzad-Chartrand-Wall conjecture (1970) and its generalization, the
Caccetta-H\"{a}ggkvist conjecture (1978). Despite a lot of interest and
efforts, the progress on these remains slow and mostly restricted to the
solution of some special cases. In this note, we prove these conjectures for
digraphs with girth is at least as large as their minimum out-degree and
without short even cycles. More generally, we prove that if a digraph has
sufficiently large girth and does not contain closed walks of certain lengths,
then the conjectures hold. The proof makes use of some of the known results on
the Caccetta-H\"{a}ggkvist conjecture, properties of direct products of
digraphs and a construction that multiplies the girth of a digraph.


title:
A New M Dwarf Debris Disk Candidate in a Young Moving Group Discovered
  with Disk Detective

abstract:
  We used the Disk Detective citizen science project and the BANYAN II Bayesian
analysis tool to identify a new candidate member of a nearby young association
with infrared excess. WISE J080822.18-644357.3, an M5.5-type debris disk system
with significant excess at both 12 and 22 $\mu$m, is a likely member ($\sim
90\%$ BANYAN II probability) of the $\sim 45$ Myr-old Carina association. Since
this would be the oldest M dwarf debris disk detected in a moving group, this
discovery could be an important constraint on our understanding of M dwarf
debris disk evolution.


title:
Simple Lyapunov spectrum for certain linear cocycles over partially
  hyperbolic maps

abstract:
  Criteria for the simplicity of the Lyapunov spectra of linear cocycles have
been found by Furstenberg, Guivarc'h-Raugi, Gol'dsheid-Margulis and, more
recently, Bonatti-Viana and Avila-Viana. In all the cases, the authors consider
cocycles over hyperbolic systems, such as shift maps or Axiom A
diffeomorphisms.
  In this paper we propose to extend such criteria to situations where the base
map is just partially hyperbolic. This raises several new issues concerning,
among others, the recurrence of the holonomy maps and the (lack of) continuity
of the Rokhlin disintegrations of $u$-states.
  Our main results are stated for certain partially hyperbolic skew-products
whose iterates have bounded derivatives along center leaves. They allow us, in
particular, to exhibit non-trivial examples of stable simplicity in the
partially hyperbolic setting.


title: Swelling, Structure, and Phase Stability of Compressible Microgels

abstract:
  Microgels are soft colloidal particles that, when dispersed in a solvent,
swell and deswell in response to changes in environmental conditions, such as
temperature, concentration, and $p$H. Using Monte Carlo simulation, we model
bulk suspensions of microgels that interact via Hertzian elastic interparticle
forces and can expand or contract via trial moves that allow particles to
change size in accordance with the Flory-Rehner free energy of cross-linked
polymer gels. We monitor the influence of particle compressibility, size
fluctuations, and concentration on bulk structural and thermal properties by
computing particle swelling ratios, radial distribution functions, static
structure factors, osmotic pressures, and freezing densities. For microgels in
the nanoscale size range, particle compressibility and associated size
fluctuations suppress crystallization, shifting the freezing transition to a
higher density than for the hard-sphere fluid. As densities increase beyond
close packing, microgels progressively deswell, while their intrinsic size
distribution grows increasingly polydisperse.


title:
Bounding the average gate fidelity of composite channels using the
  unitarity

abstract:
  There is currently a significant need for robust and efficient methods for
characterizing quantum devices. While there has been significant progress in
this direction, there remains a crucial need to precisely determine the
strength and type of errors on individual gate operations, in order to assess
and improve control as well as reliably bound the total error in a quantum
circuit given some partial information about the errors on the components. In
this work, we first provide an optimal bound on the total fidelity of a circuit
in terms of component fidelities, which can be efficiently experimentally
estimated via randomized benchmarking. We then derive a tighter bound that
applies under additional information about the coherence of the error, namely,
the unitarity, which can also be efficiently estimated via a related
experimental protocol. This improved bound smoothly interpolates between the
worst-case quadratic and best-case linear scalings for composite error
channels. As an application we show how our analysis substantially improves the
achievable precision on estimates of the error rates of individual gates under
interleaved randomized benchmarking, enabling greater precision for current
experimental methods to assess and tune-up control over quantum gate
operations.


title: Anisotropic Contrast Optical Microscope

abstract:
  An optical microscope is described that reveals contrast in the Mueller
matrix images of a thin, transparent or semi-transparent specimen located
within an anisotropic object plane (anisotropic filter). The specimen changes
the anisotropy of the filter and thereby produces contrast within the Mueller
matrix images. Here we use an anisotropic filter composed of a
semi-transparent, nanostructured thin film with sub-wavelength thickness placed
within the object plane. The sample is illuminated as in common optical
microscopy but the light is modulated in its polarization using combinations of
linear polarizers and phase plate (compensator) to control and analyze the
state of polarization. Direct generalized ellipsometry data analysis approaches
permit extraction of fundamental Mueller matrix object plane images dispensing
with the need of Fourier expansion methods. Generalized ellipsometry model
approaches are used for quantitative image analyses. We demonstrate the
anisotropic contrast optical microscope by measuring lithographically defined
micro-patterned anisotropic filters, and we quantify the adsorption of an
organic self-assembled monolayer film onto the anisotropic filter. In our
current instrument we estimate the limit of detection for organic volumetric
mass within the object plane of $\approx$ 49 fg within $\approx$
7$\times$7~$\mu$m$^2$ object surface area. Compared to a quartz crystal
microbalance with dissipation instrumentation, where contemporary limits
require a total load of $\approx$ 500~pg for detection, the instrumentation
demonstrated here improves sensitivity to a total mass required for detection
by 4 orders of magnitude. We present further applications to detection of
nanoparticles, to novel approaches for imaging chromatography, and to new
contrast modalities for observations on living cells.


title:
Alignment dependent ultrafast electron-nuclear dynamics in high-order
  harmonic generation

abstract:
  We investigated the high-order harmonic generation (HHG) process of diatomic
molecular ion $\mathrm{H}_2^+$ in non-Born-Oppenheimer approximations. The
corresponding three-dimensional time-dependent Schr\"odinger equation is solved
with arbitrary alignment angles. It is found that the nuclear motion can lead
to spectral modulation of HHG. Redshifts are unique in molecular HHG which
decrease with the increase of alignment angles of the molecules and are
sensitive to the initial vibrational states. It can be used to extract the
ultrafast electron-nuclear dynamics and image molecular structure.


title: Cosmic Censorship in Quantum Einstein Gravity

abstract:
  We study the quantum gravity modification of the Kuroda-Papapetrou model
induced by the running of the Newton's constant at high energy in Quantum
Einstein Gravity. We argue that although the antiscreening character of the
gravitational interaction favours the formation of a naked singularity, quantum
gravity effects turn the classical singularity into a "whimper" singularity
which remains naked for a finite amount of advanced time.


title:
Triplet Cooper pairs induced in diffusive s-wave superconductors
  interfaced with strongly spin-polarized magnetic insulators or half-metallic
  ferromagnets

abstract:
  Interfacing superconductors with strongly spin-polarized magnetic materials
opens the possibility to discover new spintronic devices in which spin-triplet
Cooper pairs play a key role. Motivated by the recent derivation of
spin-polarized quasiclassical boundary conditions capable of describing such a
scenario in the diffusive limit, we consider the emergent physics in hybrid
structures comprised of a conventional s-wave superconductor (e.g. Nb, Al) and
either strongly spin-polarized ferromagnetic insulators (e.g. EuO, GdN) or
halfmetallic ferromagnets (e.g. CrO2, LCMO). In contrast to most previous
works, we focus on how the superconductor itself is influenced by the proximity
effect, and how the generated triplet Cooper pairs manifest themselves in the
self-consistently computed density of states (DOS) and the superconducting
critical temperature Tc. We provide a comprehensive treatment of how the
superconductor and its properties are affected by the triplet pairs,
demonstrating that our theory can reproduce the recent observation of an
unusually large zero-energy peak in a superconductor interfaced with a
half-metal, which even exceeds the normal-state DOS. We also discuss the recent
observation of a large superconducting spin-valve effect with a Tc change ~1K
in superconductor/half-metal structures, in which case our results indicate
that the experiment cannot be explained fully by a long-ranged triplet
proximity effect.


title: Nearest Neighbor: The Low-Mass Milky Way Satellite Tucana III

abstract:
  We present Magellan/IMACS spectroscopy of the recently discovered Milky Way
satellite Tucana III (Tuc III). We identify 26 member stars in Tuc III, from
which we measure a mean radial velocity of v_hel = -102.3 +/- 0.4 (stat.) +/-
2.0 (sys.) km/s, a velocity dispersion of 0.1^+0.7_-0.1 km/s, and a mean
metallicity of [Fe/H] = -2.42^+0.07_-0.08. The upper limit on the velocity
dispersion is sigma < 1.5 km/s at 95.5% confidence, and the corresponding upper
limit on the mass within the half-light radius of Tuc III is 9.0 x 10^4 Msun.
We cannot rule out mass-to-light ratios as large as 240 Msun/Lsun for Tuc III,
but much lower mass-to-light ratios that would leave the system
baryon-dominated are also allowed. We measure an upper limit on the metallicity
spread of the stars in Tuc III of 0.19 dex at 95.5% confidence. Tuc III has a
smaller metallicity dispersion and likely a smaller velocity dispersion than
any known dwarf galaxy, but a larger size and lower surface brightness than any
known globular cluster. Its metallicity is also much lower than those of the
clusters with similar luminosity. We therefore tentatively suggest that Tuc III
is the tidally-stripped remnant of a dark matter-dominated dwarf galaxy, but
additional precise velocity and metallicity measurements will be necessary for
a definitive classification. If Tuc III is indeed a dwarf galaxy, it is one of
the closest external galaxies to the Sun. Because of its proximity, the most
luminous stars in Tuc III are quite bright, including one star at V=15.7 that
is the brightest known member star of an ultra-faint satellite.


title: Flares in Gamma Ray Bursts: Disc Fragmentation and Evolution

abstract:
  Flaring activity following gamma-ray bursts (GRBs), observed in both long and
short GRBs, signals a long-term activity of the central engine. However, its
production mechanism has remained elusive. Here we develop a quantitative model
of the idea proposed by Perna et al. of a disc whose outer regions fragment due
to the onset of gravitational instability. The self-gravitating clumps migrate
through the disc and begin to evolve viscously when tidal and shearing torques
break them apart. Our model consists of two ingredients: theoretical bolometric
flare lightcurves whose shape (width, skewness) is largely insensitive to the
model parameters, and a spectral correction to match the bandpass of the
available observations, that is calibrated using the observed spectra of the
flares. This simple model reproduces, with excellent agreement, the empirical
statistical properties of the flares as measured by their width-to-arrival time
ratio and skewness (ratio between decay and rise time). We present model fits
to the observed lightcurves of two well-monitored flares, of GRB 060418 and of
GRB 060904B. To the best of our knowledge, this is the first quantitative model
able to reproduce the flare lightcurves and explain their global statistical
properties.


title: Supernova enrichment of planetary systems in low-mass star clusters

abstract:
  The presence and abundance of short lived radioisotopes (SLRs) $^{26}$Al and
$^{60}$Fe in chondritic meteorites implies that the Sun formed in the vicinity
of one or more massive stars that exploded as supernovae (SNe). Massive stars
are more likely to form in massive star clusters ($>$1000 M$_{\odot}$) than
lower mass clusters. However, photoevaporation of protoplanetary discs from
massive stars and dynamical interactions with passing stars can inhibit planet
formation in clusters with radii of $\sim$1 pc. We investigate whether low-mass
(50 - 200 M$_{\odot}$) star clusters containing one or two massive stars are a
more likely avenue for early Solar system enrichment as they are more
dynamically quiescent.
  We analyse $N$-body simulations of the evolution of these low-mass clusters
and find that a similar fraction of stars experience supernova enrichment than
in high mass clusters, despite their lower densities. This is due to two-body
relaxation, which causes a significant expansion before the first supernova
even in clusters with relatively low (100 stars pc$^{-3}$) initial densities.
However, because of the high number of low mass clusters containing one or two
massive stars, the absolute number of enriched stars is the same, if not higher
than for more populous clusters. Our results show that direct enrichment of
protoplanetary discs from supernovae occurs as frequently in low mass clusters
containing one or two massive stars (>20 M$_{\odot}$) as in more populous star
clusters (1000 M$_\odot$). This relaxes the constraints on the direct
enrichment scenario and therefore the birth environment of the Solar System.

categories: astro-ph.EP astro-ph.GA astro-ph.SR physics.geo-ph


title:
Clumpy galaxies seen in H-alpha: inflated observed clump properties due
  to limited spatial resolution and sensitivity

abstract:
  High-resolution simulations of star-forming massive galactic discs have shown
that clumps form with a characteristic baryonic mass in the range
$10^7-10^8~M_{\odot}$, with a small tail exceeding $10^9~M_{\odot}$ produced by
clump-clump mergers. This is in contrast with the observed kpc-size clumps with
masses up to $10^{10}~M_{\odot}$ in high-redshift star-forming galaxies. In
this paper we show that the comparison between simulated and observed
star-forming clumps is hindered by limited observational spatial resolution and
sensitivity. We post-process high-resolution hydrodynamical simulations of
clumpy discs using accurate radiative transfer to model the effect of ionizing
radiation from young stars and to compute H$\alpha$ emission maps. By comparing
the intrinsic clump size and mass distributions with those inferred from
convolving the H$\alpha$ maps with different gaussian apertures, we mimick the
typical resolution used in observations. We found that with 100 pc resolution,
mock observations can recover the intrinsic clump radii and stellar masses, in
agreement with those found by lensing observations. Instead, using a 1 kpc
resolution smears out individual clumps, resulting in their apparent merging.
This causes significant overestimations of the clump radii and, therefore,
masses derived using methods that use their observed sizes. We show that
limited sensitivity can also force observations to significantly overestimate
the clump masses. We conclude that a significant fraction of giant clumps
detected in the observations may result from artificially inflated radii and
masses, and that $\approx 100$ pc spatial resolution is required to capture
correctly the physical characteristics of star-forming clumps if they are
coherent structures produced by disc fragmentation.


title:
Testing cosmic-ray acceleration with radio relics: a high-resolution
  study using MHD and tracers

abstract:
  Weak shocks in the intracluster medium may accelerate cosmic-ray protons and
cosmic-ray electrons differently depending on the angle between the upstream
magnetic field and the shock normal. In this work, we investigate how shock
obliquity affects the production of cosmic rays in high-resolution simulations
of galaxy clusters. For this purpose, we performed a magneto-hydrodynamical
simulation of a galaxy cluster using the mesh refinement code \enzo. We use
Lagrangian tracers to follow the properties of the thermal gas, the cosmic rays
and the magnetic fields over time. We tested a number of different acceleration
scenarios by varying the obliquity-dependent acceleration efficiencies of
protons and electrons, and by examining the resulting hadronic $\gamma$-ray and
radio emission. We find that the radio emission does not change significantly
if only quasi-perpendicular shocks are able to accelerate cosmic-ray electrons.
Our analysis suggests that radio emitting electrons found in relics have been
typically shocked many times before $z=0$. On the other hand, the hadronic
$\gamma$-ray emission from clusters is found to decrease significantly if only
quasi-parallel shocks are allowed to accelerate cosmic-ray protons. This might
reduce the tension with the low upper limits on $\gamma$-ray emission from
clusters set by the \textit{Fermi}-satellite.


title:
On the direct correlation between gamma-rays and PeV neutrinos from
  blazars

abstract:
  We study the frequently used assumption in multi-messenger astrophysics that
the gamma-ray and neutrino fluxes are directly connected because they are
assumed to be produced by the same photohadronic production chain. An
interesting candidate source for this test is the flat-spectrum radio quasar
PKS B1424-418, which recently called attention of a potential correlation
between an IceCube PeV-neutrino event and its burst phase. We simulate both the
multi-waveband photon and the neutrino emission from this source using a
self-consistent radiation model. We demonstrate that a simple hadronic model
cannot adequately describe the spectral energy distribution for this source,
but a lepto-hadronic model with sub-dominant hadronic component can reproduce
the multi-waveband photon spectrum observed during various activity phases of
the blazar. As a conclusion, up to about 0.3 neutrino events may coincide with
the burst, which implies that the leptonic contribution dominates in the
relevant energy band. We also demonstrate that the time-wise correlation
between the neutrino event and burst phase is weak.


title: Binary star influence on post-main-sequence multi-planet stability

abstract:
  Nearly every star known to host planets will become a white dwarf, and nearly
100 planet-hosts are now known to be accompanied by binary stellar companions.
Here, we determine how a binary companion triggers instability in otherwise
unconditionally stable single-star two-planet systems during the giant branch
and white dwarf phases of the planet host. We perform about 700 full-lifetime
(14 Gyr) simulations with A0 and F0 primary stars and secondary K2 companions,
and identify the critical binary distance within which instability is triggered
at any point during stellar evolution. We estimate this distance to be about
seven times the outer planet separation, for circular binaries. Our results
help characterize the fates of planetary systems, and in particular which ones
might yield architectures that are conducive to generating observable heavy
metal pollution in white dwarf atmospheres.


title: Averaged Null Energy Condition from Causality

abstract:
  Unitary, Lorentz-invariant quantum field theories in flat spacetime obey
microcausality: commutators vanish at spacelike separation. For interacting
theories in more than two dimensions, we show that this implies that the
averaged null energy, $\int du T_{uu}$, must be positive. This non-local
operator appears in the operator product expansion of local operators in the
lightcone limit, and therefore contributes to $n$-point functions. We derive a
sum rule that isolates this contribution and is manifestly positive. The
argument also applies to certain higher spin operators other than the stress
tensor, generating an infinite family of new constraints of the form $\int du
X_{uuu\cdots u} \geq 0$. These lead to new inequalities for the coupling
constants of spinning operators in conformal field theory, which include as
special cases (but are generally stronger than) the existing constraints from
the lightcone bootstrap, deep inelastic scattering, conformal collider methods,
and relative entropy. We also comment on the relation to the recent derivation
of the averaged null energy condition from relative entropy, and suggest a more
general connection between causality and information-theoretic inequalities in
QFT.


title:
Gravitational wave sources in the era of multi-frequency gravitational
  wave astronomy

abstract:
  The focus of this Chapter is on describing the prospective sources of the
gravitational wave universe accessible to present and future observations, from
kHz, to mHz down to nano-Hz frequencies. The multi-frequency gravitational wave
universe gives a deep view into the cosmos, inaccessible otherwise. It has as
main actors core-collapsing massive stars, neutron stars, coalescing compact
object binaries of different flavours and stellar origin, coalescing massive
black hole binaries, extreme mass ratio inspirals, and possibly the very early
universe itself. Here, we highlight the science aims and describe the
gravitational wave signals expected from the sources and the information
gathered in it. We show that the observation of gravitational wave sources will
play a transformative role in our understanding of the processes ruling the
formation and evolution of stars and black holes, galaxy clustering and
evolution, the nature of the strong forces in neutron star interiors, and the
most mysterious interaction of Nature: gravity. The discovery, by the LIGO
Scientific Collaboration and Virgo Collaboration, of the first source of
gravitational waves from the cosmos GW150914, and the superb technological
achievement of the space mission LISA Pathfinder herald the beginning of the
new phase of exploration of the universe.


title:
Star Formation in Intermediate Redshift 0.2 < z < 0.7 Brightest Cluster
  Galaxies

abstract:
  We present a multi-wavelength photometric and spectroscopic study of 42
Brightest Cluster Galaxies (BCGs) in two samples of galaxy clusters chosen for
a gravitational lensing study. The study's initial sample combines 25 BCGs from
the Cluster Lensing and Supernova Survey with Hubble (CLASH) sample and 37 BCGs
from the Sloan Giant Arcs Survey (SGAS) with a total redshift range of 0.2 < z
< 0.7. Using archival GALEX, Hubble Space Telescope, Wide-field Infrared Survey
Explorer, Herschel, and Very Large Array data we determine the BCGs' stellar
mass, radio power, and star formation rates. The radio power is higher than
expected if due to star formation, consistent with the BCGs being active
galactic nucleus (AGN)-powered radio sources. This suggests that the AGN and
star formation are both fueled by cold gas in the host galaxy. The specific
star formation rate (sSFR) is low and constant with redshift. The mean sSFR is
9.42 * 10^-12 yr^-1, which corresponds to a mass doubling time of 105 billion
years. These findings are consistent with models for hierarchical formation of
BCGs, which suggest that star formation is no longer a significant channel for
galaxy growth for z < 1. Instead, stellar growth (of the order of a factor of
at least two) during this period is expected to occur mainly via minor dry
mergers


title:
N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal
  deformations

abstract:
  We continue to investigate the $\mathcal{N}=1$ deformations of
four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) labeled
by a nilpotent element of the flavor symmetry. This triggers a renormalization
group (RG) flow to an $\mathcal{N}=1$ SCFT. We systematically analyze all
possible deformations of this type for certain classes of $\mathcal{N}=2$
SCFTs: conformal SQCDs, generalized Argyres-Douglas theories and the $E_6$
SCFT. We find a number of examples where the amount of supersymmetry gets
enhanced to $\mathcal{N}=2$ at the end point of the RG flow. Most notably, we
find that the $SU(N)$ and $Sp(N)$ conformal SQCDs can be deformed to flow to
the Argyres-Douglas (AD) theories of type $(A_1, D_{2N-1})$ and $(A_1, D_{2N})$
respectively. This RG flow therefore allows us to compute the full
superconformal index of the $(A_1,D_N)$ class of AD theories. Moreover, we find
an infrared duality between $\mathcal{N}=1$ theories where the fixed point is
described by an $\mathcal{N}=2$ AD theory. We observe that the classes of
examples that exhibit supersymmetry enhancement saturate certain bounds for the
central charges implied by the associated two-dimensional chiral algebra.


title:
Unveiling the first black holes with JWST: multi-wavelength spectral
  predictions

abstract:
  Growing the supermassive black holes (~10^9 Msun) that power the detected
luminous, highest redshift quasars (z > 6) from light seeds - the remnants of
the first stars - within ~ 1 Gyr of the Big Bang poses a timing challenge for
growth models. The formation of massive black hole seeds via direct collapse
with initial masses ~ 10^4 - 10^5 Msun alleviates this problem. Physical
conditions required to form these massive direct collapse black hole (DCBH)
seeds are available in the early universe. These viable DCBH formation sites,
satellite halos of star-forming galaxies, merge and acquire a stellar
component. These produce a new, transient class of objects at high redshift,
Obese Black hole Galaxies (OBGs), where the luminosity produced by accretion
onto the black hole outshines the stellar component. Therefore, the OBG stage
offers a unique way to discriminate between light and massive initial seeds. We
predict the multi-wavelength energy output of OBGs and growing Pop III remnants
at a fiducial redshift (z = 9), exploring both standard and slim disk accretion
onto the growing central black hole for high and low metallicities of the
associated stellar population. With our computed templates, we derive the
selection criteria for OBGs, that comprise a pre-selection that eliminates blue
sources; followed by color-color cuts ([F_{070W} - F_{220W}] > 0; -0.3 <
[F_{200W} - F_{444W}] < 0.3) and when available, a high ratio of X-ray flux to
rest-frame optical flux (F_X/F_{444W} >> 1) (Abridged).


title:
Large Molecular Gas Reservoirs in Ancestors of Milky Way-Mass Galaxies 9
  Billion Years Ago

abstract:
  The gas accretion and star-formation histories of galaxies like the Milky Way
remain an outstanding problem in astrophysics. Observations show that 8 billion
years ago, the progenitors to Milky Way-mass galaxies were forming stars 30
times faster than today and predicted to be rich in molecular gas, in contrast
with low present-day gas fractions ($<$10%). Here we show detections of
molecular gas from the CO(J=3-2) emission (rest-frame 345.8 GHz) in galaxies at
redshifts z=1.2-1.3, selected to have the stellar mass and star-formation rate
of the progenitors of today's Milky Way-mass galaxies. The CO emission reveals
large molecular gas masses, comparable to or exceeding the galaxy stellar
masses, and implying most of the baryons are in cold gas, not stars. The
galaxies' total luminosities from star formation and CO luminosities yield long
gas-consumption timescales. Compared to local spiral galaxies, the
star-formation efficiency, estimated from the ratio of total IR luminosity to
CO emission,} has remained nearly constant since redshift z=1.2, despite the
order of magnitude decrease in gas fraction, consistent with results for other
galaxies at this epoch. Therefore the physical processes that determine the
rate at which gas cools to form stars in distant galaxies appear to be similar
to that in local galaxies.


title: $\lambda$-deformations of left-right asymmetric CFTs

abstract:
  We compute the all-loop anomalous dimensions of current and primary field
operators in deformed current algebra theories based on a general semi-simple
group, but with different (large) levels for the left and right sectors. These
theories, unlike their equal level counterparts, possess a new non-trivial
fixed point in the IR. By computing the exact in $\lambda$ two- and three-point
functions for these operators we deduce their OPEs and their equal-time
commutators. Using these we argue on the nature of the CFT at the IR fixed
point. The associated to the currents Poisson brackets are a two-parameter
deformation of the canonical structure of the isotropic PCM.


title:
Hi-C-constrained physical models of human chromosomes recover
  functionally-related properties of genome organization

abstract:
  Combining genome-wide structural models with phenomenological data is at the
forefront of efforts to understand the organizational principles regulating the
human genome. Here, we use chromosome-chromosome contact data as
knowledge-based constraints for large-scale three-dimensional models of the
human diploid genome. The resulting models remain minimally entangled and
acquire several functional features that are observed in vivo and that were
never used as input for the model. We find, for instance, that gene-rich,
active regions are drawn towards the nuclear center, while gene poor and
lamina-associated domains are pushed to the periphery. These and other
properties persist upon adding local contact constraints, suggesting their
compatibility with non-local constraints for the genome organization. The
results show that suitable combinations of data analysis and physical modelling
can expose the unexpectedly rich functionally-related properties implicit in
chromosome-chromosome contact data. Specific directions are suggested for
further developments based on combining experimental data analysis and genomic
structural modelling.


title:
HI 21-cm absorption survey of quasar-galaxy pairs: Distribution of cold
  gas around z<0.4 galaxies

abstract:
  We present the results from our survey of HI 21-cm absorption, using GMRT,
VLA and WSRT, in a sample of 55 z<0.4 galaxies towards radio sources with
impact parameters (b) in the range ~0-35 kpc. In our primary sample (defined
for statistical analyses) of 40 quasar-galaxy-pairs (QGPs), probed by 45
sightlines, we have found seven HI 21-cm absorption detections, two of which
are reported here for the first time. Combining our primary sample with
measurements having similar optical depth sensitivity ($\int\tau dv$ <= 0.3
km/s) from the literature, we find a weak anti-correlation (rank correlation
coefficient = -0.20 at 2.42sigma level) between $\int\tau dv$ and b, consistent
with previous literature results. The covering factor of HI 21-cm absorbers
(C_21) is estimated to be 0.24 (+0.12/-0.08) at b <= 15 kpc and 0.06
(+0.09/-0.04) at b = 15-35 kpc. $\int\tau dv$ and C_21 show similar declining
trend with radial distance along the galaxy's major axis and distances scaled
with the effective HI radius. There is also tentative indication that most of
the HI 21-cm absorbers could be co-planar with the extended HI discs. No
significant dependence of $\int\tau dv$ and C_21 on galaxy luminosity, stellar
mass, colour and star formation rate is found, though the HI 21-cm absorbing
gas cross-section may be larger for the luminous galaxies. The higher detection
rate (by a factor of ~4) of HI 21-cm absorption in z<1 DLAs compared to the
QGPs indicates towards small covering factor and patchy distribution of cold
gas clouds around low-z galaxies.


title: Konishi Form Factor at Three Loop in ${\cal N}=4$ SYM

abstract:
  We present the first results on the third order corrections to on-shell form
factor (FF) of the Konishi operator in ${\cal N}=4$ supersymmetric Yang-Mills
theory using Feynman diagrammatic approach in modified dimensional reduction
($\overline {DR}$) scheme. We show that it satisfies KG equation in $\overline
{DR}$ scheme while the result obtained in four dimensional helicity (FDH)
scheme needs to be suitably modified not only to satisfy the KG equation but
also to get the correct ultraviolet (UV) anomalous dimensions. We find that the
cusp, soft and collinear anomalous dimensions obtained to third order are same
as those of the FF of the half-BPS operator confirming the universality of the
infrared (IR) structures of on-shell form factors. In addition, the highest
transcendental terms of the FF of Konishi operator are identical to those of
half-BPS operator indicating the probable existence of deeper structure of the
on-shell FF. We also confirm the UV anomalous dimensions of Konishi operator up
to third order providing a consistency check on the both UV and universal IR
structures in ${\cal N}=4$.


title: Tales of 1001 Gluons

abstract:
  These lectures are centred around tree-level scattering amplitudes in pure
Yang-Mills theories, the most prominent example is given by the tree-level
gluon amplitudes of QCD. I will discuss several ways of computing these
amplitudes, illustrating in this way recent developments in perturbative
quantum field theory. Topics covered in these lectures include colour
decomposition, spinor and twistor methods, off- and on-shell recursion, MHV
amplitudes and MHV expansion, the Grassmannian and the amplituhedron, the
scattering equations and the CHY representation. At the end of these lectures
there will be an outlook on the relation between pure Yang-Mills amplitudes and
scattering amplitudes in perturbative quantum gravity.


title: Can we reconcile the TA excess and hotspot with Auger observations?

abstract:
  The Telescope Array (TA) shows a 20$^{\circ}$ hotspot as well as an excess of
UHECRs above 50~EeV when compared with the Auger spectrum. We consider the
possibility that both the TA excess and hotspot are due to a dominant source in
the Northern sky. We carry out detailed simulations of UHECR propagation in
both the intergalactic medium and the Galaxy, using different values for the
intergalactic magnetic field. We consider two general classes of sources:
transients and steady, adopting a mixed UHECR composition that is consistent
with the one found by Auger. The spatial location of the sources is draw
randomly. We generate Auger-like and TA-like data sets from which we determine
the spectrum, the sky maps and the level of anisotropy. We find that, while
steady sources are favored over transients, it is unlikely to account for all
the currently available observational data. While we reproduce fairly well the
Auger spectrum for the vast majority of the simulated data sets, most of the
simulated data sets with a spectrum compatible with that of TA (at most a few
percent depending on density model tested) show a much stronger anisotropy than
the one observed. We find that the rare cases in which both the spectrum and
the anisotropy are consistent require a steady source within $\sim 10$ Mpc, to
account for the flux excess, and a strong extragalactic magnetic field $\sim
10$ nG, to reduce the excessive anisotropy.


title: Runaway Relaxion Monodromy

abstract:
  We examine the relaxion mechanism in string theory. An essential feature is
that an axion winds over $N \gg 1$ fundamental periods. In string theory
realizations via axion monodromy, this winding number corresponds to a physical
charge carried by branes or fluxes. We show that this monodromy charge
backreacts on the compact space, ruining the structure of the relaxion action.
In particular, the barriers generated by strong gauge dynamics have height
$\propto e^{-N}$, so the relaxion does not stop when the Higgs acquires a vev.
Backreaction of monodromy charge can therefore spoil the relaxion mechanism. We
comment on the limitations of technical naturalness arguments in this context.


title: Cosmic Growth and Expansion Conjoined

abstract:
  Cosmological measurements of both the expansion history and growth history
have matured, and the two together provide an important test of general
relativity. We consider their joint evolutionary track, showing that this has
advantages in distinguishing cosmologies relative to considering them
individually or at isolated redshifts. In particular, the joint comparison
relaxes the shape degeneracy that makes $f\sigma_8(z)$ curves difficult to
separate from the overall growth amplitude. The conjoined method further helps
visualization of which combinations of redshift ranges provide the clearest
discrimination. We examine standard dark energy cosmologies, modified gravity,
and "stuttering" growth, each showing distinct signatures.


title: Hot methanol from the inner region of the HH 212 protostellar system

abstract:
  The mechanisms leading to the formation of disks around young stellar objects
(YSOs) and to the launching of the associated jets are crucial to the
understanding of the earliest stages of star and planet formation. HH 212 is a
privileged laboratory to study a pristine jet-disk system. Therefore we
investigate the innermost region ($<100$ AU) around the HH 212-MM1 protostar
through ALMA band\,7 observations of methanol. The 8 GHz bandwidth spectrum
towards the peak of the continuum emission of the HH 212 system reveals at
least 19 transitions of methanol. Several of these lines (among which several
vibrationally excited lines in the v$_{\rm t}=1,2$ states) have upper energies
above 500 K. They originate from a compact ($<135$ AU in diameter), hot ($\sim
295$ K) region elongated along the direction of the SiO jet. We performed a fit
in the $uv$ plane of various velocity channels of the strongest high-excitation
lines. The blue- and red-shifted velocity centroids are shifted roughly
symmetrically on either side of the jet axis, indicating that the line-of-sight
velocity beyond 0.7 km s$^{-1}$ from systemic is dominated by rotational
motions. The velocity increases moving away from the protostar further
indicating that the emission of methanol is not associated with a Keplerian
disk or rotating-infalling cavity, and it is more likely associated with
outflowing gas. We speculate that CH$_3$OH traces a disk wind gas accelerated
at the base. The launching region would be at a radius of a few astronomical
units from the YSO.


title: Type II supernovae Early Light Curves

abstract:
  Observations of type II supernova early light, from breakout until
recombination, can be used to constrain the explosion energy and progenitor
properties. Currently available for this purpose are purely analytic models,
which are accurate only to within an order of magnitude, and detailed numerical
simulations, which are more accurate but are applied to any event separately.
In this paper we derive an analytic model that is calibrated by numerical
simulations. This model is much more accurate than previous analytic models,
yet it is as simple to use. To derive the model we analyze simulated light
curves from numerical explosion of $124$ red supergiant progenitors, calculated
using the stellar evolution code MESA. We find that although the structure of
the progenitors we consider varies, the resulting light curves can be described
rather well based only on the explosion energy, ejecta mass and progenitor
radius. Our calibrated analytic model, which is based on these three
parameters, reproduces the bolometric luminosity within $25\%-35\%$ accuracy
and the observed temperature within $15\%$ accuracy (compared to previous
analytic models which are indeed found to be accurate only to within an order
of magnitude). We also consider deviations of the early time spectrum from
blackbody, and find that the Rayleigh-Jeans regime is slightly shallower
(roughly $L_\nu \propto \nu^{1.4}$). This modified spectrum affects the
optical/near-UV light curve mostly during the first day when the typical
observed temperature is $\gg 10^4 ~^\circ$K. We use our results to study the
optical and near-UV early light curves from first light until recombination and
briefly discuss what can be learned from current and future observations. Light
curves generated using our calibrated model can be downloaded at
http://www.astro.tau.ac.il/~tomersh/.


title:
Two-dimensional multi-component photometric decomposition of CALIFA
  galaxies

abstract:
  We present a two-dimensional multi-component photometric decomposition of 404
galaxies from the CALIFA Data Release 3. They represent all possible galaxies
with no clear signs of interaction and not strongly inclined in the final
CALIFA data release. Galaxies are modelled in the g, r, and i SDSS images
including, when appropriate, a nuclear point source, bulge, bar, and an
exponential or broken disc component. We use a human-supervised approach to
determine the optimal number of structures to be included in the fit. The
dataset, including the photometric parameters of the CALIFA sample, is released
together with statistical errors and a visual analysis of the quality of each
fit. The analysis of the photometric components reveals a clear segregation of
the structural composition of galaxies with stellar mass. At high masses
(log(Mstar/Msun)>11), the galaxy population is dominated by galaxies modelled
with a single Sersic or a bulge+disc with a bulge-to-total (B/T) luminosity
ratio B/T>0.2. At intermediate masses (9.5<log(Mstar/Msun)<11), galaxies
described with bulge+disc but B/T < 0.2 are preponderant, whereas, at the low
mass end (log(Mstar/Msun)<9.5), the prevailing population is constituted by
galaxies modelled with either pure discs or nuclear point sources+discs (i.e.,
no discernible bulge). We obtain that 57% of the volume corrected sample of
disc galaxies in the CALIFA sample host a bar. This bar fraction shows a
significant drop with increasing galaxy mass in the range
9.5<log(Mstar/Msun)<11.5. The analyses of the extended multi-component radial
profile result in a volume-corrected distribution of 62%, 28%, and 10% for the
so-called Type I, Type II, and Type III disc profiles, respectively. These
fractions are in discordance with previous findings. We argue that the
different methodologies used to detect the breaks are the main cause for these
differences.


title: Energy imbalance market call options and the valuation of storage

abstract:
  The use of energy storage to balance electric grids is increasing and, with
it, the importance of operational optimisation from the twin viewpoints of cost
and system stability. In this paper we assess the real option value of
balancing reserve provided by an energy-limited storage unit. The contractual
arrangement is a series of American-style call options in an energy imbalance
market (EIM), physically covered and delivered by the store, and purchased by
the power system operator. We take the EIM price as a general regular
one-dimensional diffusion and impose natural economic conditions on the option
parameters. In this framework we derive the operational strategy of the storage
operator by solving two timing problems: when to purchase energy to load the
store (to provide physical cover for the option) and when to sell the option to
the system operator. We give necessary and sufficient conditions for the
finiteness and positivity of the value function -- the total discounted cash
flows generated by operation of the storage unit. We also provide a
straightforward procedure for the numerical evaluation of the optimal
operational strategy (EIM prices at which power should be purchased) and the
value function. This is illustrated with an operational and economic analysis
using data from the German Amprion EIM.


title:
Stochastic Optics: A Scattering Mitigation Framework for Radio
  Interferometric Imaging

abstract:
  Just as turbulence in the Earth's atmosphere can severely limit the angular
resolution of optical telescopes, turbulence in the ionized interstellar medium
fundamentally limits the resolution of radio telescopes. We present a
scattering mitigation framework for radio imaging with very long baseline
interferometry (VLBI) that partially overcomes this limitation. Our framework,
"stochastic optics," derives from a simplification of strong interstellar
scattering to separate small-scale ("diffractive") effects from large-scale
("refractive") effects, thereby separating deterministic and random
contributions to the scattering. Stochastic optics extends traditional
synthesis imaging by simultaneously reconstructing an unscattered image and its
refractive perturbations. Its advantages over direct imaging come from
utilizing the many deterministic properties of the scattering -- such as the
time-averaged "blurring," polarization independence, and the deterministic
evolution in frequency and time -- while still accounting for the stochastic
image distortions on large scales. These distortions are identified in the
image reconstructions through regularization by their time-averaged power
spectrum. Using synthetic data, we show that this framework effectively removes
the blurring from diffractive scattering while reducing the spurious image
features from refractive scattering. Stochastic optics can provide significant
improvements over existing scattering mitigation strategies and is especially
promising for imaging the Galactic Center supermassive black hole, Sagittarius
A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.


title: Looking for dark matter trails in colliding galaxy clusters

abstract:
  If dark matter interacts, even weakly, via non-gravitational forces,
simulations predict that it will be preferentially scattered towards the
trailing edge of the halo during collisions between galaxy clusters. This will
temporarily create a non-symmetric mass profile, with a trailing over-density
along the direction of motion. To test this hypothesis, we fit (and subtract)
symmetric halos to the weak gravitational data of 72 merging galaxy clusters
observed with the Hubble Space Telescope. We convert the shear directly into
excess {\kappa} and project in to a one dimensional profile. We generate
numerical simulations and find that the one dimensional profile is well
described with simple Gaussian approximations. We detect the weak lensing
signal of trailing gas at a 4{\sigma} confidence, finding a mean gas fraction
of Mgas/Mdm = 0.13 +/- 0.035. We find no evidence for scattered dark matter
particles with a estimated scattering fraction of f = 0.03 +/- 0.05. Finally we
find that if we can reduce the statistical error on the positional estimate of
a single dark matter halo to <2.5", then we will be able to detect a scattering
fraction of 10% at the 3{\sigma} level with current surveys. This poten- tially
interesting new method can provide an important independent test for other
complimentary studies of the self-interaction cross-section of dark matter.


title:
Unstable normal modes of low T/W dynamical instabilities in
  differentially rotating stars

abstract:
  We investigate the nature of low T/W dynamical instabilities in
differentially rotating stars by means of linear perturbation. Here, T and W
represent rotational kinetic energy and the gravitational binding energy of the
star. This is the first attempt to investigate low T/W dynamical instabilities
as a complete set of the eigenvalue problem. Our equilibrium configuration has
"constant" specific angular momentum distribution, which potentially contains a
singular solution in the perturbed enthalpy at corotation radius in linear
perturbation. We find the unstable normal modes of differentially rotating
stars by solving the eigenvalue problem along the equatorial plane of the star,
imposing the regularity condition on the center and the vanished enthalpy at
the oscillating equatorial surface. We find that the existing pulsation modes
become unstable due to the existence of the corotation radius inside the star.
The feature of the unstable mode eigenfrequency and its eigenfunction in the
linear analysis roughly agrees with that in three-dimensional hydrodynamical
simulations in Newtonian gravity. Therefore, our normal mode analysis in the
equatorial motion proves valid to find the unstable equilibrium stars
efficiently. Moreover, the nature of the eigenfunction that oscillates between
corotation and the surface radius for unstable stars requires reinterpretation
of the pulsation modes in differentially rotating stars.


title:
OpenMP, OpenMP/MPI, and CUDA/MPI C programs for solving the
  time-dependent dipolar Gross-Pitaevskii equation

abstract:
  We present new versions of the previously published C and CUDA programs for
solving the dipolar Gross-Pitaevskii equation in one, two, and three spatial
dimensions, which calculate stationary and non-stationary solutions by
propagation in imaginary or real time. Presented programs are improved and
parallelized versions of previous programs, divided into three packages
according to the type of parallelization. First package contains improved and
threaded version of sequential C programs using OpenMP. Second package
additionally parallelizes three-dimensional variants of the OpenMP programs
using MPI, allowing them to be run on distributed-memory systems. Finally,
previous three-dimensional CUDA-parallelized programs are further parallelized
using MPI, similarly as the OpenMP programs. We also present speedup test
results obtained using new versions of programs in comparison with the previous
sequential C and parallel CUDA programs. The improvements to the sequential
version yield a speedup of 1.1 to 1.9, depending on the program. OpenMP
parallelization yields further speedup of 2 to 12 on a 16-core workstation,
while OpenMP/MPI version demonstrates a speedup of 11.5 to 16.5 on a computer
cluster with 32 nodes used. CUDA/MPI version shows a speedup of 9 to 10 on a
computer cluster with 32 nodes.

categories: cond-mat.quant-gas cs.MS nlin.PS physics.comp-ph


title: Cosmology with a light ghost

abstract:
  We study the creation and evolution of cosmological perturbations in
renormalizable quadratic gravity with a Weyl term. We adopt a prescription that
implies the stability of the vacuum at the price of introducing a massive
spin-two ghost state, leading to the loss of unitarity. The theory may still be
predictive regardless the interpretation of non-unitary processes provided that
their rate is negligible compared to the Universe expansion rate. This implies
that the ghost is effectively stable. In such a setup, there are two scalar
degrees of freedom excited during inflation. The first one is the usual
curvature perturbation whose power spectrum appears to coincide with that of
single-field inflation. The second one is a scalar component of the ghost
encoded in the shift vector of the metric in the uniform inflaton gauge. The
amplitudes of primordial tensor and vector perturbations are strongly
suppressed. After inflation the ghost field starts to oscillate and its energy
density shortly becomes dominant in the Universe. For all ghost masses allowed
by laboratory constraints ghosts should have "overclosed" the Universe at
temperatures higher than that of primordial nucleosynthesis. Thus, the model
with the light Weyl ghost is ruled out.


title:
Self-similar real trees defined as fixed-points and their geometric
  properties

abstract:
  We consider fixed-point equations for probability measures charging measured
compact metric spaces that naturally yield continuum random trees. On the one
hand, we study the existence/uniqueness of the fixed-points and the convergence
of the corresponding iterative schemes. On the other hand, we study the
geometric properties of the random measured real trees that are fixed-points,
in particular their fractal properties. We obtain bounds on the Minkowski and
Hausdorff dimension, that are proved tight in a number of applications,
including the very classical continuum random tree, but also for the dual trees
of random recursive triangulations of the disk introduced by Curien and Le Gall
[Ann Probab, vol. 39, 2011]. The method happens to be especially efficient to
treat cases for which the mass measure on the real tree induced by natural
encodings only provides weak estimates on the Hausdorff dimension.


title:
Vector magnetic field measurements along a cooled stereo-imaged coronal
  loop

abstract:
  The variation of the vector magnetic field along structures in the solar
corona remains unmeasured. Using a unique combination of spectropolarimetry and
stereoscopy, we infer and compare the vector magnetic field structure and
three-dimensional morphology of an individuated coronal loop structure
undergoing a thermal instability. We analyze spectropolarimetric data of the He
I 10830 {\AA} triplet ($1s2s{\ }^{3}S_{1} - 1s2p{\ }^{3}P_{2,1,0}$) obtained at
the Dunn Solar Telescope with the Facility Infrared Spectropolarimeter on 19
September 2011. Cool coronal loops are identified by their prominent drainage
signatures in the He I data (redshifts up to 185 km sec$^{-1}$). Extinction of
EUV background radiation along these loops is observed by both the Atmospheric
Imaging Assembly onboard the Solar Dynamics Observatory and the Extreme
Ultraviolet Imager onboard spacecraft A of the Solar Terrestrial Relations
Observatory, and is used to stereoscopically triangulate the loop geometry up
to heights of 70 Mm ($0.1$ $R_{sun}$) above the solar surface. The He I
polarized spectra along this loop exhibit signatures indicative of atomic-level
polarization as well as magnetic signatures through the Hanle and Zeeman
effects. Spectropolarimetric inversions indicate that the magnetic field is
generally oriented along the coronal loop axis, and provide the height
dependence of the magnetic field intensity. The technique we demonstrate is a
powerful one that may help better understand the thermodynamics of coronal fine
structure magnetism.


title: Matrix Thermalization

abstract:
  Matrix quantum mechanics offers an attractive environment for discussing
gravitational holography, in which both sides of the holographic duality are
well-defined. Similarly to higher-dimensional implementations of holography,
collapsing shell solutions in the gravitational bulk correspond in this setting
to thermalization processes in the dual quantum mechanical theory. We construct
an explicit, fully nonlinear supergravity solution describing a generic
collapsing dilaton shell, specify the holographic renormalization prescriptions
necessary for computing the relevant boundary observables, and apply them to
evaluating thermalizing two-point correlation functions in the dual matrix
theory.


title: Limits of Femtosecond Fiber Amplification by Parabolic Pre-Shaping

abstract:
  We explore parabolic pre-shaping as a means of generating and amplifying
ultrashort pulses. We develop a theoretical framework for modeling the
technique and use its conclusions to design a femtosecond fiber amplifier.
Starting from 9 ps pulses, we obtain 4.3 $\mu$J, nearly transform-limited
pulses 275 fs in duration, simultaneously achieving over 40 dB gain and 33-fold
compression. Finally, we show that this amplification scheme is limited by
Raman scattering, and outline a method by which the pulse duration and energy
may be further improved and tailored for a given application.


title:
Bounding averages rigorously using semidefinite programming: mean
  moments of the Lorenz system

abstract:
  We describe methods for proving bounds on infinite-time averages in
differential dynamical systems. The methods rely on the construction of
nonnegative polynomials with certain properties, similarly to the way nonlinear
stability can be proved using Lyapunov functions. Nonnegativity is enforced by
requiring the polynomials to be sums of squares, a condition which is then
formulated as a semidefinite program (SDP) that can be solved computationally.
Although such computations are subject to numerical error, we demonstrate two
ways to obtain rigorous results: using interval arithmetic to control the error
of an approximate SDP solution, and finding exact analytical solutions to
relatively small SDPs. Previous formulations are extended to allow for bounds
depending analytically on parametric variables. These methods are illustrated
using the Lorenz equations, a system with three state variables $(x,y,z)$ and
three parameters $(\beta,\sigma,r)$. Bounds are reported for infinite-time
averages of all eighteen moments $x^ly^mz^n$ up to quartic degree that are
symmetric under $(x,y)\mapsto(-x,-y)$. These bounds apply to all solutions
regardless of stability, including chaotic trajectories, periodic orbits, and
equilibrium points. The analytical approach yields two novel bounds that are
sharp: the mean of $z^3$ can be no larger than its value of $(r-1)^3$ at the
nonzero equilibria, and the mean of $xy^3$ must be nonnegative. The interval
arithmetic approach is applied at the standard chaotic parameters to bound
eleven average moments that all appear to be maximized on the shortest periodic
orbit. Our best upper bound on each such average exceeds its value on the
maximizing orbit by less than 1%. Many bounds reported here are much tighter
than would be possible without computer assistance.


title:
Absorption of Direct Factors With Respect to the Minimal Faithful
  Permutation Degree of a Finite Group

abstract:
  The minimal faithful permutation degree $\mu(G)$ of a finite group $G$ is the
least nonnegative integer $n$ such that $G$ embeds in the symmetric group
$\Sym(n)$. We prove that if $H$ is a group then $\mu(G)=\mu(G\times H)$ for
some group $G$ then $H$ embeds in $A\times Q^k$ for some abelian group of odd
order, some generalised quaternion $2$-group and some nonnegative integer $k$.
As a consequence, $\mu(G^{n+1})=\mu(G^n)$ for some nonnegative integer $n$ if
and only if $G$ is trivial.


title:
Observation of semi-localized dispersive states in the strongly
  correlated electron-doped ferromagnet Eu$_{1-x}$Gd$_{x}$O

abstract:
  Chemical substitution plays a key role in controlling the electronic and
magnetic properties of complex materials. For instance, in EuO, carrier doping
can induce a spin-polarized metallic state, colossal magnetoresistance, and
significantly enhance the Curie temperature. Here, we employ a combination of
molecular-beam epitaxy, angle-resolved photoemission spectroscopy, and an
effective model calculation to investigate and understand how semi-localized
states evolve in lightly electron doped Eu$_{1-x}$Gd$_{x}$O above the
ferromagnetic Curie temperature. Our studies reveal a characteristic length
scale for the spatial extent of the donor wavefunctions which remains constant
as a function of doping, consistent with recent tunneling studies of doped EuO.
Our work sheds light on the nature of the semiconductor-to-metal transition in
Eu$_{1-x}$Gd$_{x}$O and should be generally applicable for doped complex
oxides.


title: The software package SpectralSequences

abstract:
  We describe the computer algebra software package SpectralSequences for the
computer algebra system Macaulay2. This package implements many data types,
objects and algorithms which pertain to, among other things, filtered
complexes, spectral sequence pages and maps therein. We illustrate some of the
syntax and capabilities of SpectralSequences by way of several examples.


title: Random Holographic "Large Worlds" with Emergent Dimensions

abstract:
  I propose a random network model governed by a Gaussian weight corresponding
to Ising link antiferromagnetism as a model for emergent quantum space-time. In
this model, discrete space is fundamental, not a regularization, its spectral
dimension $d_s$ is not a model input but is, rather, completely determined by
the antiferromagnetic coupling constant. Perturbative terms suppressing
triangles and favouring squares lead to locally Euclidean ground states that
are Ricci flat "large worlds" with power-law extension. I then consider the
quenched graphs of lowest energy for $d_s=2$ and $d_s=3$ and I show how
quenching leads to the spontaneous emergence of embedding spaces of Hausdorff
dimension $d_H=4$ and $d_H=5$, respectively. One of the additional, spontaneous
dimensions can be interpreted as time, causality being an emergent property
that arises in the large $N$ limit (with $N$ the number of vertices). For
$d_s=2$, the quenched graphs constitute a discrete version of a
5D-space-filling surface with a number of fundamental degrees of freedom
scaling like $N^{2/5}$, a graph version of the holographic principle. These
holographic degrees of freedom can be identified with the squares of the
quenched graphs, which, being these triangle-free, are the fundamental area (or
loop) quanta.


title: Quadratic sequences of powers and Mohanty's Conjecture

abstract:
  We prove under the Bombieri-Lang conjecture for surfaces that there is an
absolute bound on the length of sequences of integer squares with constant
second differences, for sequences which are not formed by the squares of
integers in arithmetic progression. This answers a question proposed in 2010 by
J. Browkin and J. Brzezinski, and independently by E. Gonzalez-Jimenez and X.
Xarles.
  We also show that under the Bombieri-Lang conjecture for surfaces, for every
$k\geq 3$ there is an absolute bound on the length of sequences formed by
$k$-th powers with constant second differences. This gives a conditional result
on one of Mohanty's conjectures on arithmetic progressions in Mordell's
elliptic curves $y^2=x^3+b$. Moreover, we obtain an unconditional result
regarding infinite families of such arithmetic progressions. We also study the
case of hyperelliptic curves of the form $y^2=x^k+b$.
  These results are proved by unconditionally finding all curves of genus $0$
or $1$ on certain surfaces of general type. Moreover, we prove the
unconditional analogues of these arithmetic results for function fields by
finding all the curves of low genus on these surfaces.


title: Hydrodynamic Overview at Hot Quarks 2016

abstract:
  This presents an overview of relativistic hydrodynamic modeling in heavy-ion
collisions prepared for Hot Quarks 2016, at South Padre Island, TX, USA. The
influence of the initial state and viscosity on various experimental
observables are discussed. Specific problems that arise in the hydrodynamical
modeling at the Beam Energy Scan are briefly discussed.


title:
Tracing the Hercules stream with Gaia and LAMOST: new evidence for a
  fast bar in the Milky Way

abstract:
  The length and pattern speed of the Milky Way bar are still controversial.
Photometric and spectroscopic surveys of the inner Galaxy, as well as gas
kinematics, favour a long and slowly rotating bar, with corotation around a
Galactocentric radius of 6 kpc. On the other hand, the existence of the
Hercules stream in local velocity space favours a short and fast bar with
corotation around 4 kpc. This follows from the fact that the Hercules stream
looks like a typical signature of the outer Lindblad resonance of the bar. As
we showed recently, reconciling this local stream with a slow bar would need to
find a yet unknown alternative explanation, based for instance on the effect of
spiral arms. Here, by combining the TGAS catalogue of the Gaia DR1 with LAMOST
radial velocities, we show that the position of Hercules in velocity space as a
function of radius in the outer Galaxy indeed varies exactly as predicted by
fast bar models with a pattern speed no less than 1.8 times the circular
frequency at the Sun's position.


title: Secondary Upsilon invariants of knots

abstract:
  The knot invariant Upsilon, defined by Ozsvath, Stipsicz, and Szabo, induces
a homomorphism from the smooth knot concordance group to the group of piecewise
linear functions on the interval [0,2]. Here we define a set of related
secondary invariants, each of which assigns to a knot a piecewise linear
function on [0,2]. These secondary invariants provide bounds on the genus and
concordance genus of knots. Examples of knots for which Upsilon vanishes but
which are detected by these secondary invariants are presented.


title: A variant of Bombieri-Vinogradov theorem with explicit constants

abstract:
  In this paper we improve the result of Akbary and Hambrook by a factor of log
x by obtaining a better version of Vaughan's inequality and using the explicit
variant of an inequality connected to the M\"obius function, derived by
Helfgott in his work on ternary Goldbach conjecture.


title: Spin and hyperelliptic structures of log twisted differentials

abstract:
  Using stable log maps, we introduce log twisted differentials extending the
notion of abelian differentials to the Deligne-Mumford boundary of stable
curves. The moduli stack of log twisted differentials provides a
compactification of the strata of abelian differentials. The open strata can
have up to three connected components, due to spin and hyperelliptic
structures. We prove that the spin parity can be distinguished on the boundary
of the log compactification. Moreover, combining the techniques of log geometry
and admissible covers, we introduce log twisted hyperelliptic differentials,
and prove that their moduli stack provides a toroidal compactification of the
hyperelliptic loci in the open strata.


title: A $L^{2}$ to $L^{\infty}$ approach for the Landau Equation

abstract:
  Consider the Landau equation with Coulomb potential in a periodic box. We
develop a new $L^{2}\rightarrow L^{\infty }$ framework to construct global
unique solutions near Maxwellian with small $L^{\infty }\ $norm. The first step
is to establish global $L^{2}$ estimates with strong velocity weight and time
decay, under the assumption of $L^{\infty }$ bound, which is further controlled
by such $L^{2}$ estimates via De Giorgi's method \cite{golse2016harnack} and
\cite{mouhot2015holder}. The second step is to employ estimates in $S_{p}$
spaces to control velocity derivatives to ensure uniqueness, which is based on
Holder estimates via De Giorgi's method \cite{golse2016harnack},
\cite{golse2015holder}, and \cite{mouhot2015holder}.


title: Link Prediction in evolving networks based on the popularity of nodes

abstract:
  Link prediction aims to uncover the underlying relationship behind networks,
which could be utilized to predict the missing edges or identify the spurious
edges, and attracts much attention from various fields. The key issue of link
prediction is to estimate the likelihood of two nodes in networks. Most current
approaches of link prediction base on static structural analysis and ignore the
temporal aspects of evolving networks. Unlike previous work, in this paper, we
propose a popularity based structural perturbation method (PBSPM) that
characterizes the similarity of an edge not only from existing connections of
networks, but also from the popularity of its two endpoints, since popular
nodes have much more probability to form links between themselves. By taking
popularity of nodes into account, PBSPM could suppress nodes that have high
importance, but gradually become inactive. Therefore the proposed method is
inclined to predict potential edges between active nodes, rather than edges
between inactive nodes. Experimental results on four real networks show that
the proposed method outperforms the state-of-the-art methods both in accuracy
and robustness in evolving networks.


title: Markov State Models of Gene Regulatory Networks

abstract:
  Gene regulatory networks with dynamics characterized by multiple stable
states underlie cell fate-decisions. Quantitative models that can link
molecular-level knowledge of gene regulation to a global understanding of
network dynamics have the potential to guide cell-reprogramming strategies.
Networks are often modeled by the stochastic Chemical Master Equation, but
methods for systematic identification of key properties of the global dynamics
are currently lacking. We present a method for analyzing global dynamics of
gene networks using the Markov State Model (MSM) framework, which utilizes a
separation-of-timescales based clustering method to obtain a coarse-grained
state transition graph that approximates global gene network dynamics. The
method identifies the number, phenotypes, and lifetimes of long-lived network
states. Application of transition path theory to the constructed MSM decomposes
global dynamics into a set of dominant transition paths and associated relative
probabilities for stochastic state-switching. In this proof-of-concept study,
we found that the MSM provides a general framework for analyzing and
visualizing stochastic multistability and state-transitions in gene networks.
Our results suggest that the MSM framework, adopted from the field of atomistic
Molecular Dynamics, can be a useful tool for quantitative Systems Biology at
the network scale.


title: Kazhdan-Lusztig polynomials of thagomizer matroids

abstract:
  We introduce thagomizer matroids and compute the Kazhdan-Lusztig polynomial
of a rank $n+1$ thagomizer matroid by showing that the coefficient of $t^k$ is
equal to the number of Dyck paths of semilength $n$ with $k$ long ascents. We
also give a conjecture for the $S_n$-equivariant Kazhdan-Lusztig polynomial of
a thagomizer matroid.


title: How Well Do Local Algorithms Solve Semidefinite Programs?

abstract:
  Several probabilistic models from high-dimensional statistics and machine
learning reveal an intriguing --and yet poorly understood-- dichotomy. Either
simple local algorithms succeed in estimating the object of interest, or even
sophisticated semi-definite programming (SDP) relaxations fail.
  In order to explore this phenomenon, we study a classical SDP relaxation of
the minimum graph bisection problem, when applied to Erd\H{o}s-Renyi random
graphs with bounded average degree $d>1$, and obtain several types of results.
First, we use a dual witness construction (using the so-called non-backtracking
matrix of the graph) to upper bound the SDP value. Second, we prove that a
simple local algorithm approximately solves the SDP to within a factor
$2d^2/(2d^2+d-1)$ of the upper bound. In particular, the local algorithm is at
most $8/9$ suboptimal, and $1+O(1/d)$ suboptimal for large degree.
  We then analyze a more sophisticated local algorithm, which aggregates
information according to the harmonic measure on the limiting Galton-Watson
(GW) tree. The resulting lower bound is expressed in terms of the conductance
of the GW tree and matches surprisingly well the empirically determined SDP
values on large-scale Erd\H{o}s-Renyi graphs.
  We finally consider the planted partition model. In this case, purely local
algorithms are known to fail, but they do succeed if a small amount of side
information is available. Our results imply quantitative bounds on the
threshold for partial recovery using SDP in this model.


title: Spline surfaces with T-junctions

abstract:
  This paper develops a new way to create smooth piecewise polynomial free-form
spline surfaces from quad- meshes that include T-junctions, where surface
strips start or terminate. All mesh nodes can be interpreted as control points
of geometrically-smooth, piecewise polynomials that we call GT-splines.
GT-splines are B-spline-like and cover T-junctions by two or four patches of
degree bi-4. They complement multi-sided surface constructions in generating
free-form surfaces with adaptive layout. Since GT-splines do not require a
global coordination of knot intervals, GT-constructions are easy to deploy and
can provide smooth surfaces with T-junctions where T-splines can not have a
smooth parameterization. GT-constructions display a uniform highlight line
distribution on input meshes where alternatives, such as Catmull-Clark
subdivision, exhibit oscillations.


title:
Effective electro-optic modulation in low-loss graphene-plasmonic slot
  waveguides

abstract:
  Surface plasmon polaritons enable light concentration within subwavelength
regions, opening thereby new avenues for miniaturizing the device and
strengthening light-matter interactions. Here we realize effective
electro-optic modulation in low-loss plasmonic waveguides with the aid of
graphene, and the devices are fully integrated in the silicon-on-insulator
platform. By advantageously exploiting low-loss plasmonic slot-waveguide modes,
which weakly leak into a substrate while feature strong fields within the
two-layer-graphene covered slots in metal, we successfully achieve a tunability
of 0.13 dB/um for our fabricated graphene-plasmonic waveguide devices with
extremely low insertion loss, which outperforms previously reported
graphene-plasmonic devices. Our results highlight the potential of graphene
plasmonic leaky-mode hybrid waveguides to realized active ultra-compact devices
for optoelectronic applications.


title: Classification of Homogeneous Fourier Matrices

abstract:
  Modular data are commonly studied in mathematics and physics. A modular datum
defines a finite-dimensional representation of the modular group
$SL_2(\mathbb{Z})$. In this paper, we show that there is a one-to-one
correspondence between Fourier matrices associated to modular data and
self-dual $C$-algebras that satisfy a certain condition. Also, we prove that a
homogenous $C$-algebra arising from a Fourier matrix has all the degrees equal
to $1$.


title: Reconstructing Partitions from their Multisets of $k$-Minors

abstract:
  For non-negative integers $n$ and $k$ with $n \ge k$, a {\em $k$-minor} of a
partition $\lambda = [\lambda_1, \lambda_2, \dots]$ of $n$ is a partition $\mu
= [\mu_1, \mu_2, \dots]$ of $n-k$ such that $\mu_i \le \lambda_i$ for all $i$.
The multiset $\widehat{M}_k(\lambda)$ of $k$-minors of $\lambda$ is defined as
the multiset of $k$-minors $\mu$ with multiplicity of $\mu$ equal to the number
of standard Young tableaux of skew shape $\lambda / \mu$. We show that there
exists a function $G(n)$ such that the partitions of $n$ can be reconstructed
from their multisets of $k$-minors if and only if $k \le G(n)$. Furthermore, we
prove that $\lim_{n \rightarrow \infty} G(n)/n = 1$ with $n-G(n) = O(n/\log
n)$. As a direct consequence of this result, the irreducible representations of
the symmetric group $S_n$ can be reconstructed from their restrictions to
$S_{n-k}$ if and only if $k \le G(n)$ for the same function $G(n)$. For a minor
$\mu$ of the partition $\lambda$, we study the excitation factor $E_\mu
(\lambda)$, which appears as a crucial part in Naruse's Skew-Shape Hook Length
Formula. We observe that certain excitation factors of $\lambda$ can be
expressed as a $\mathbb{Q}[k]$-linear combination of the elementary symmetric
polynomials of the hook lengths in the first row of $\lambda$ where $k =
\lambda_1$ is the number of cells in the first row of $\lambda$.


title: A simple finite element method for the Stokes equations

abstract:
  The goal of this paper is to introduce a simple finite element method to
solve the Stokes and the Navier-Stokes equations. This method is in primal
velocity-pressure formulation and is so simple such that both velocity and
pressure are approximated by piecewise constant functions. Implementation
issues as well as error analysis are investigated. A basis for a divergence
free subspace of the velocity field is constructed so that the original saddle
point problem can be reduced to a symmetric and positive definite system with
much fewer unknowns. The numerical experiments indicate that the method is
accurate and robust.


title: An alternative view on dissipation in turbulent flows

abstract:
  An original experimental setup has been elaborated in order to get a better
view of turbulent flows in a von Karman geometry. The availability of a very
fast camera allowed to follow in time the evolution of the flows. A surprising
finding is that the development of smaller whorls ceases earlier than expected
and the aspect of the flows remains the same above Reynolds number of a few
thousand. This fact provides an explanation of the constancy of the reduced
dissipation in the same range without the need of singularity. Its cause could
be in relation with the same type of behavior observed in a rotating frame.


title: The Standard-Model Extension and Gravitational Tests

abstract:
  The Standard-Model Extension (SME) provides a comprehensive effective
field-theory framework for the study of CPT and Lorentz symmetry. This work
reviews the structure and philosophy of the SME and provides some intuitive
examples of symmetry violation. The results of recent gravitational tests
performed within the SME are summarized including analysis of results from the
Laser Interferometer Gravitational-Wave Observatory (LIGO), sensitivities
achieved in short-range gravity experiments, constraints from cosmic-ray data,
and results achieved by studying planetary ephemerids. Some proposals and
ongoing efforts will also be considered including gravimeter tests, tests of
the Weak Equivalence Principle, and antimatter experiments. Our review of the
above topics is augmented by several original extensions of the relevant work.
We present new examples of symmetry violation in the SME and use the cosmic-ray
analysis to place first-ever constraints on 81 additional operators.


title: Psycho-Demographic Analysis of the Facebook Rainbow Campaign

abstract:
  Over the past decade, online social media has had a tremendous impact on the
way people engage in social activism. For instance, about 26M Facebook users
expressed their support in upholding the cause of marriage equality by
overlaying their profile pictures with rainbow-colored filters. Similarly,
hundreds of thousands of users changed their profile pictures to a black dot
condemning incidents of sexual violence in India. This act of demonstrating
support for social causes by changing online profile pictures is being referred
to as pictivism. In this paper, we analyze the psycho-demographic profiles,
social networking behavior, and personal interests of users who participated in
the Facebook Rainbow campaign. Our study is based on a sample of about 800K
detailed profiles of Facebook users combining questionnaire-based psychological
scores with Facebook profile data. Our analysis provides detailed insights into
psycho-demographic profiles of the campaign participants. We found that
personality traits such as openness and neuroticism are both positively
associated with the likelihood of supporting the campaign, while
conscientiousness exhibited a negative correlation. We also observed that
females, religious disbelievers, democrats and adults in the age group of 20 to
30 years are more likely to be a part of the campaign. Our research further
confirms the findings of several previous studies which suggest that a user is
more likely to participate in an online campaign if a large fraction of his/her
friends are already doing so. We also developed machine learning models for
predicting campaign participation. Users' personal interests, approximated by
Facebook user like activity, turned out to be the best indicator of campaign
participation. Our results demonstrated that a predictive model which leverages
the aforementioned features accurately identifies campaign participants
(AUC=0.76).


title:
A Machine Learns to Predict the Stability of Tightly Packed Planetary
  Systems

abstract:
  The requirement that planetary systems be dynamically stable is often used to
vet new discoveries or set limits on unconstrained masses or orbital elements.
This is typically carried out via computationally expensive N-body simulations.
We show that characterizing the complicated and multi-dimensional stability
boundary of tightly packed systems is amenable to machine learning methods. We
find that training an XGBoost machine learning algorithm on physically
motivated features yields an accurate classifier of stability in packed
systems. On the stability timescale investigated ($10^7$ orbits), it is 3
orders of magnitude faster than direct N-body simulations. Optimized machine
learning classifiers for dynamical stability may thus prove useful across the
discipline, e.g., to characterize the exoplanet sample discovered by the
upcoming Transiting Exoplanet Survey Satellite (TESS). This proof of concept
motivates investing computational resources to train algorithms capable of
predicting stability over longer timescales and over broader regions of phase
space.