title:
Sheldon Spectrum and the Plankton Paradox: Two Sides of the Same Coin. A
  trait-based plankton size-spectrum model

abstract:
  The Sheldon spectrum describes a remarkable regularity in aquatic ecosystems:
the biomass density as a function of logarithmic body mass is approximately
constant over many orders of magnitude. While size-spectrum models have
explained this phenomenon for assemblages of multicellular organisms, this
paper introduces a species-resolved size-spectrum model to explain the
phenomenon in unicellular plankton. A Sheldon spectrum spanning the cell-size
range of unicellular plankton necessarily consists of a large number of
coexisting species covering a wide range of characteristic sizes. The
coexistence of many phytoplankton species feeding on a small number of
resources is known as the Paradox of the Plankton. Our model resolves the
paradox by showing that coexistence is facilitated by the allometric scaling of
four physiological rates. Two of the allometries have empirical support, the
remaining two emerge from predator-prey interactions exactly when the
abundances follow a Sheldon spectrum. Our plankton model is a scale-invariant
trait-based size-spectrum model: it describes the abundance of phyto- and
zooplankton cells as a function of both size and species trait (the maximal
size before cell division). It incorporates growth due to resource consumption
and predation on smaller cells, death due to predation, and a flexible cell
division process. We give analytic solutions at steady state for both the
within-species size distributions and the relative abundances across species.


title:
Anderson Localization of Composite Excitations in Disordered
  Optomechanical Arrays

abstract:
  Optomechanical arrays are a promising future platform for studies of
transport, many-body dynamics, quantum control and topological effects in
systems of coupled photon and phonon modes. We introduce disordered
optomechanical arrays, focusing on features of Anderson localization of hybrid
photon-phonon excitations. It turns out that these represent a unique
disordered system, where basic parameters can be easily controlled by varying
the frequency and the amplitude of an external laser field. We show that the
two-species setting leads to a non-trivial frequency dependence of the
localization length for intermediate laser intensities. This could serve as a
convincing evidence of localization in a non-equilibrium dissipative situation.


title:
Control of the non-stationary spin-polarized tunneling currents by
  applied bias changing

abstract:
  We reveal that for the single Anderson impurity localized between
non-magnetic leads of the tunneling contact $"$magnetic$"$ state can be
distinguished from the $"$paramagnetic$"$ one only by the analysis of the
non-stationary system characteristics or the behavior of the second order
correlation functions for the localized electrons occupation numbers. We
investigate the response of the system to the sudden shift of the applied bias
and to the switching $"$on$"$ the coupling to the second lead of the tunneling
contact. We demonstrate that in addition to the changes of the relaxation
regimes and typical relaxation time scales, non-stationary spin-polarized
currents flowing in the both leads are present in the system. Spin polarization
and direction of the non-stationary currents in each lead can be simultaneously
inverted by the sudden changing of the applied bias voltage.


title: Light sterile neutrinos from a late phase transition

abstract:
  Light sterile neutrinos represent a well-motivated extension of the
3-neutrino paradigm. However, the impressive agreement between standard
cosmology and data casts doubts on their existence. Here we present a class of
scenarios that robustly avoids this tension. In these models the sterile
neutrinos are light, chiral states of a new sector interacting with the
Standard Model via the right-handed neutrino portal and, crucially,
active-sterile neutrino oscillations require a phase transition in the hidden
sector. We explore the hidden-couplings/critical-temperature plane and identify
regions where several sterile neutrinos can be accommodated. A late phase
transition is usually preferred and may also ward off a potential threat posed
by the formation of topologically stable defects.


title: Strong completions of spaces

abstract:
  A non-empty subset of a topological space is irreducible if whenever it is
covered by the union of two closed sets, then already it is covered by one of
them. Irreducible sets occur in proliferation: (1) every singleton set is
irreducible, (2) directed subsets (which of fundamental status in domain
theory) of a poset are exactly its Alexandroff irreducible sets, (3) directed
subsets (with respect to the specialization order) of a $T_0$ space are always
irreducible, and (4) the topological closure of every irreducible set is again
irreducible. In recent years, the usefulness of irreducible sets in domain
theory and non-Hausdorff topology has expanded. Notably, Zhao and Ho (2009)
developed the core of domain theory directly in the context of $T_0$ spaces by
choosing the irreducible sets as the topological substitute for directed sets.
Just as the existence of suprema of directed subsets is featured prominently in
domain theory (and hence the notion of a dcpo -- a poset in which all directed
suprema exist), so too is that of irreducible subsets in the topological domain
theory developed by Zhao and Ho (2009). The topological counterpart of a dcpo
is thus this: A $T_0$ space is said to be strongly complete if the suprema of
all irreducible subsets exist. In this paper, we show that the category,
$\mathbf{scTop^+}$, of strongly complete $T_0$ spaces forms are reflective
subcategory of a certain lluf subcategory, $\mathbf{Top^+}$, of $T_0$ spaces.


title:
On the stability of some isoperimetric inequalities for the fundamental
  tones of free plates

abstract:
  We provide a quantitative version of the isoperimetric inequality for the
fundamental tone of a biharmonic Neumann problem. Such an inequality has been
recently established by Chasman adapting Weinberger's argument for the
corresponding second order problem. Following a scheme introduced by Brasco and
Pratelli for the second order case, we prove that a similar quantitative
inequality holds also for the biharmonic operator. We also prove the sharpness
of both such an inequality and the corresponding one for the biharmonic Steklov
problem.


title:
Transparent Semiconductor-Superconductor Interface and Induced Gap in an
  Epitaxial Heterostructure Josephson Junction

abstract:
  Measurement of multiple Andreev reflection (MAR) in a Josephson junction made
from an InAs heterostructure with epitaxial aluminum is used to quantify the
highly transparent semiconductor-superconductor interface, indicating
near-unity transmission. The observed temperature dependence of MAR does not
follow a conventional BCS form, but instead agrees with a model in which the
density of states in the quantum well acquires an effective induced gap, in our
case 180 {\mu}eV, close to that of the epitaxial superconductor. Carrier
density dependence of MAR is investigated using a depletion gate, revealing the
subband structure of the semiconductor quantum well, consistent with
magnetotransport experiment of the bare InAs performed on the same wafer.


title:
The quasilinear theory in the approach of long-range systems to
  quasi-stationary states

abstract:
  We develop a quasilinear theory of the Vlasov equation in order to describe
the approach of systems with long-range interactions to quasi-stationary
states. We derive a diffusion equation governing the evolution of the velocity
distribution of the system towards a steady state. This steady state is
expected to correspond to the angle-averaged quasi-stationary distribution
function reached by the Vlasov equation as a result of a violent relaxation. We
compare the prediction of the quasilinear theory to direct numerical
simulations of the Hamiltonian Mean Field model, starting from an unstable
spatially homogeneous distribution, either Gaussian or semi-elliptical. We find
that the quasilinear theory works reasonably well for weakly unstable initial
conditions and that it is able to predict the energy marking the
out-of-equilibrium phase transition between unmagnetized and magnetized
quasi-stationary states. At energies lower than the out-of-equilibrium
transition the quasilinear theory works less well, the disagreement with the
numerical simulations increasing by decreasing the energy. In that case, we
observe, in agreement with our previous numerical study [A. Campa and P.-H.
Chavanis, Eur. Phys. J. B 86, 170 (2013)], that the quasi-stationary states are
remarkably well fitted by polytropic distributions (Tsallis distributions) with
index $n=2$ (Gaussian case) or $n=1$ (semi-elliptical case). In particular,
these polytropic distributions are able to account for the region of negative
specific heats in the out-of-equilibrium caloric curve, unlike the Boltzmann
and Lynden-Bell distributions.


title:
Rational approximation to the fractional Laplacian operator in
  reaction-diffusion problems

abstract:
  This paper provides a new numerical strategy to solve fractional in space
reaction-diffusion equations on bounded domains under homogeneous Dirichlet
boundary conditions. Using the matrix transform method the fractional Laplacian
operator is replaced by a matrix which, in general, is dense. The approach here
presented is based on the approximation of this matrix by the product of two
suitable banded matrices. This leads to a semi-linear initial value problem in
which the matrices involved are sparse. Numerical results are presented to
verify the effectiveness of the proposed solution strategy.


title: 21-year timing of the black-widow pulsar J2051-0827

abstract:
  Timing results for the black-widow pulsar J2051-0827 are presented, using a
21-year dataset from four European Pulsar Timing Array telescopes and the
Parkes radio telescope. This dataset, which is the longest published to date
for a black-widow system, allows for an improved analysis that addresses
previously unknown biases. While secular variations, as identified in previous
analyses, are recovered, short-term variations are detected for the first time.
Concurrently, a significant decrease of approx. 2.5x10-3 cm-3 pc in the
dispersion measure associated with PSR J2051-0827 is measured for the first
time and improvements are also made to estimates of the proper motion. Finally,
PSR J2051-0827 is shown to have entered a relatively stable state suggesting
the possibility of its eventual inclusion in pulsar timing arrays.


title:
Is the full susceptibility of the square-lattice Ising model a
  differentially algebraic function?

abstract:
  We study the class of non-holonomic power series with integer coefficients
that reduce, modulo primes, or powers of primes, to algebraic functions. In
particular we try to determine whether the susceptibility of the square-lattice
Ising model belongs to this class, and more broadly whether the susceptibility
is a solution of a differentially algebraic equation. Initial results on
Tutte's non-linear ordinary differential equation (ODE) and other simple
quadratic non-linear ODEs suggest that a large set of differentially algebraic
power series solutions with integer coefficients might reduce to algebraic
functions modulo primes, or powers of primes. Here we give several examples of
series with integer coefficients and non-zero radius of convergence that reduce
to algebraic functions modulo (almost) every prime (or power of a prime). These
examples satisfy differentially algebraic equations with the encoding
polynomial occasionally possessing quite high degree (and thus difficult to
identify even with long series). Additionally, we have extended both the high-
and low-temperature Ising square-lattice susceptibility series to 5043
coefficients. We find that even this long series is insufficient to determine
whether it reduces to algebraic functions modulo $3$, $5$, etc. This negative
result is in contrast to the comparatively easy confirmation that the
corresponding series reduce to algebraic functions modulo powers of $2$.

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


title: The network architecture of value learning

abstract:
  Value guides behavior. With knowledge of stimulus values and action
consequences, behaviors that maximize expected reward can be selected. Prior
work has identified several brain structures critical for representing both
stimuli and their values. Yet, it remains unclear how these structures interact
with one another and with other regions of the brain to support the dynamic
acquisition of value-related knowledge. Here, we use a network neuroscience
approach to examine how BOLD functional networks change as 20 healthy human
subjects learn the values of novel visual stimuli over the course of four
consecutive days. We show that connections between regions of the visual,
frontal, and cingulate cortices become increasingly stronger as learning
progresses, and that these changes are primarily confined to the temporal core
of the network. These results demonstrate that functional networks dynamically
track behavioral improvement in value judgments, and that interactions between
network communities form predictive biomarkers of learning.


title: Supersingular curves on Picard modular surfaces modulo an inert prime

abstract:
  We study the supersingular curves on Picard modular surfaces modulo a prime
$p$ which is inert in the underlying quadratic imaginary field. We analyze the
automorphic vector bundles in characteristic $p$, and as an application derive
a formula relating the number of irreducible components in the supersingular
locus to the second Chern class of the surface.


title: Scales, blow-up and quasimode constructions

abstract:
  In this expository article we show how the concepts of manifolds with
corners, blow-ups and resolutions can be used effectively for the construction
of quasimodes, i.e. approximate eigenfunctions of the Laplacian on certain
families of spaces, mostly exemplified by domains
$\Omega_h\subset\mathbb{R}^2$, that degenerate as $h\to0$. These include
standard adiabatic limit families and also families that exhibit several types
of scaling behavior. An introduction to manifolds with corners and resolutions,
and how they relate to the idea of (multiple) scales and matching, is included.


title:
Exact and approximate solutions of Schr\"odinger's equation with
  hyperbolic double-well potentials

abstract:
  Analytic and approximate solutions for the energy eigenvalues generated by
the hyperbolic potentials
$V_m(x)=-U_0\sinh^{2m}(x/d)/\cosh^{2m+2}(x/d),\,m=0,1,2,\dots$ are constructed.
A byproduct of this work is the construction of polynomial solutions for the
confluent Heun equation along with necessary and sufficient conditions for the
existence of such solutions based on the evaluation of a three-term recurrence
relation. Very accurate approximate solutions for the general problem with
arbitrary potential parameters are found by use of the {\it asymptotic
iteration method}.


title: Genuine localisation transition in a long-range hopping model

abstract:
  We introduce and study a new class of Banded Random Matrix model describing
sparse, long range quantum hopping in one dimension. Using a series of analytic
arguments, numerical simulations, and mappings to statistical physics models,
we establish the phase diagram of the model. A genuine localisation transition,
with well defined mobility edges, appears as the hopping rate decreases slower
than $\ell^{-2}$, where $\ell$ is the distance. Correspondingly, the decay of
the localised states evolves from a standard exponential shape to a stretched
exponential and finally to a novel $\exp(-C\ln^\kappa \ell)$ behaviour, with
$\kappa > 1$.


title:
Adaptable Precomputation for Random Walker Image Segmentation and
  Registration

abstract:
  The random walker (RW) algorithm is used for both image segmentation and
registration, and possesses several useful properties that make it popular in
medical imaging, such as being globally optimizable, allowing user interaction,
and providing uncertainty information. The RW algorithm defines a weighted
graph over an image and uses the graph's Laplacian matrix to regularize its
solutions. This regularization reduces to solving a large system of equations,
which may be excessively time consuming in some applications, such as when
interacting with a human user. Techniques have been developed that precompute
eigenvectors of a Laplacian offline, after image acquisition but before any
analysis, in order speed up the RW algorithm online, when segmentation or
registration is being performed. However, precomputation requires certain
algorithm parameters be fixed offline, limiting their flexibility. In this
paper, we develop techniques to update the precomputed data online when RW
parameters are altered. Specifically, we dynamically determine the number of
eigenvectors needed for a desired accuracy based on user input, and derive
update equations for the eigenvectors when the edge weights or topology of the
image graph are changed. We present results demonstrating that our techniques
make RW with precomputation much more robust to offline settings while only
sacrificing minimal accuracy.


title:
Steady solutions to viscous shallow water equations. The case of heavy
  water

abstract:
  In this note, we show the existence of regular solutions to the stationary
version of the Navier-Stokes system for compressible fluids with a density
dependent viscosity, known as the shallow water equations. For arbitrary large
forcing we are able to construct a solution, provided the total mass is
sufficiently large. The main mathematical part is located in the construction
of solutions. Uniqueness is impossible to obtain, since the gradient of the
velocity is of magnitude of the force. The investigation is connected to the
corresponding singular limit as Mach number goes to zero and methods for weak
solutions to the compressible Navier-Stokes system.


title:
Fast, deterministic computation of the Hermite normal form and
  determinant of a polynomial matrix

abstract:
  Given a nonsingular $n \times n$ matrix of univariate polynomials over a
field $\mathbb{K}$, we give fast and deterministic algorithms to compute its
determinant and its Hermite normal form. Our algorithms use
$\widetilde{\mathcal{O}}(n^\omega \lceil s \rceil)$ operations in $\mathbb{K}$,
where $s$ is bounded from above by both the average of the degrees of the rows
and that of the columns of the matrix and $\omega$ is the exponent of matrix
multiplication. The soft-$O$ notation indicates that logarithmic factors in the
big-$O$ are omitted while the ceiling function indicates that the cost is
$\widetilde{\mathcal{O}}(n^\omega)$ when $s = o(1)$. Our algorithms are based
on a fast and deterministic triangularization method for computing the diagonal
entries of the Hermite form of a nonsingular matrix.


title: Eberhardt's inequality and recent loophole-free experiments

abstract:
  Recent experiments using innovative optical detectors and techniques have
strongly increased the capacity of testing the violation of the Bell's
inequalities in the Nature. Most of them have used the Eberhardt's inequality
(EI) to close the "detection" loophole. Closing the "locality" loophole has
been attempted by space-like separated detections and fast and random changes
in the setting of the bases of observation. Also, pulsed pumping and time
stamped data to close the "time-coincidence" loophole, and sophisticated
statistical methods to close the "memory" loophole, have been used. In this
paper, the meaning of the EI is reviewed. A simple hidden-variables theory
based on a relaxation of the condition of "measurement independence", which was
devised long ago for the Clauser-Horne-Shimony and Holt inequality, is adapted
to the EI case. It is used here to evaluate the significance of the results of
the new experiments, which are briefly described. A Table summarizes the main
results.


title: Presence of Exotic Electronic Surface States in LaBi and LaSb

abstract:
  Extremely high magnetoresistance (XMR) in the lanthanum monopnictides La$X$
($X$ = Sb, Bi) has recently attracted interest in these compounds as candidate
topological materials. However, their perfect electron-hole compensation
provides an alternative explanation, so the possible role of topological
surface states requires verification through direct observation. Our
angle-resolved photoemission spectroscopy (ARPES) data reveal multiple
Dirac-like surface states near the Fermi level in both materials. Intriguingly,
we have observed circular dichroism in both surface and near-surface bulk
bands. Thus the spin-orbit coupling-induced orbital and spin angular momentum
textures may provide a mechanism to forbid backscattering in zero field,
suggesting that surface and near-surface bulk bands may contribute strongly to
XMR in La$X$. The extremely simple rock salt structure of these materials and
the ease with which high-quality crystals can be prepared suggests that they
may be an ideal platform for further investigation of topological matter.


title:
Quantitative shadowgraphy and proton radiography for large intensity
  modulations

abstract:
  Shadowgraphy is a technique widely used to diagnose objects or systems in
various fields in physics and engineering. In shadowgraphy, an optical beam is
deflected by the object and then the intensity modulation is captured on a
screen placed some distance away. However, retrieving quantitative information
from the shadowgrams themselves is a challenging task because of the non-linear
nature of the process. Here, a novel method to retrieve quantitative
information from shadowgrams, based on computational geometry, is presented for
the first time. This process can be applied to proton radiography for electric
and magnetic field diagnosis in high-energy-density plasmas and has been
benchmarked using a toroidal magnetic field as the object, among others. It is
shown that the method can accurately retrieve quantitative parameters with
error bars less than 10%, even when caustics are present. The method is also
shown to be robust enough to process real experimental results with simple pre-
and post-processing techniques. This adds a powerful new tool for research in
various fields in engineering and physics for both techniques.


title: Hazelnut: A Bidirectionally Typed Structure Editor Calculus

abstract:
  Structure editors allow programmers to edit the tree structure of a program
directly. This can have cognitive benefits, particularly for novice and
end-user programmers. It also simplifies matters for tool designers, because
they do not need to contend with malformed program text. This paper defines
Hazelnut, a structure editor based on a small bidirectionally typed lambda
calculus extended with holes and a cursor. Hazelnut goes one step beyond
syntactic well-formedness: its edit actions operate over statically meaningful
incomplete terms. Naively, this would force the programmer to construct terms
in a rigid "outside-in" manner. To avoid this problem, the action semantics
automatically places terms assigned a type that is inconsistent with the
expected type inside a hole. This safely defers the type consistency check
until the term inside the hole is finished. Hazelnut is a foundational
type-theoretic account of typed structure editing, rather than an end-user tool
itself. To that end, we describe how Hazelnut's rich metatheory, which we have
mechanized in Agda, guides the definition of an extension to the calculus. We
also discuss various plausible evaluation strategies for terms with holes, and
in so doing reveal connections with gradual typing and contextual modal type
theory, the Curry-Howard interpretation of contextual modal logic. Finally, we
discuss how Hazelnut's semantics lends itself to implementation as a functional
reactive program. Our reference implementation is written using js_of_ocaml.


title: Projective completions of graded unipotent quotients

abstract:
  The aim of this paper is to show that classical geometric invariant theory
(GIT) has an effective analogue for linear actions of a non-reductive algebraic
group $H$ with graded unipotent radical on a projective scheme $X$. Here the
linear action of $H$ is required to extend to a semi-direct product $\hat{H} =
H \rtimes \mathbb{G}_m$ with a multiplicative one-parameter group which acts on
the Lie algebra of the unipotent radical $U$ of $H$ with all weights strictly
positive, and which centralises a Levi subgroup $R \cong H/U$ of $H$.
  We show that $X$ has an $H$-invariant open subscheme (the 'hat-stable locus')
which has a geometric quotient by the $H$-action. This geometric quotient has a
projective completion which is a categorical quotient (indeed, a good quotient)
by $\hat{H}$ of an open subscheme of a blow-up of the product of $X$ with the
affine line; with additional blow-ups a projective completion which is itself a
geometric quotient can be obtained. Furthermore the hat-stable locus of $X$ and
the corresponding open subsets of the blow-ups of the product of $X$ with the
affine line can be described effectively using Hilbert-Mumford-like criteria
combined with the explicit blow-up constructions.
  Applications include the construction of moduli spaces of sheaves and Higgs
bundles of fixed Harder--Narasimhan type over a fixed nonsingular projective
scheme, and of moduli spaces of unstable projective curves of fixed
singularity. More recently, cohomology theory for reductive GIT quotients were
extended by the first and fourth author to the non-reductive situation studied
in this paper, and this was used to prove the Green--Griffiths--Lang and
Kobayashi hyperbolicity conjectures for generic projective hypersurfaces with
polynomial bounds on their degree.


title: On Social Optima of Non-Cooperative Mean Field Games

abstract:
  This paper studies the connections between mean-field games and the social
welfare optimization problems. We consider a mean field game in functional
spaces with a large population of agents, each of which seeks to minimize an
individual cost function. The cost functions of different agents are coupled
through a mean field term that depends on the mean of the population states. We
show that under some mild conditions any $\epsilon$-Nash equilibrium of the
mean field game coincides with the optimal solution to a convex social welfare
optimization problem. The results are proved based on a general formulation in
the functional spaces and can be applied to a variety of mean field games
studied in the literature. Our result also implies that the computation of the
mean field equilibrium can be cast as a convex optimization problem, which can
be efficiently solved by a decentralized primal dual algorithm. Numerical
simulations are presented to demonstrate the effectiveness of the proposed
approach.


title: On the continuous-time limit of the Barab\'asi-Albert random graph

abstract:
  We prove that the Barab\'asi-Albert model converges weakly to a set of
generalized Yule models via an appropriate scaling. To pursue this aim we
superimpose to its graph structure a suitable set of processes that we call the
planted model and we introduce an ad-hoc sampling procedure. The use of the
obtained limit process represents an alternative and advantageous way of
looking at some of the asymptotic properties of the Barab\'asi-Albert random
graph.


title: Strategic Bidding and Equilibria in Coupled Gas and Electricity Markets

abstract:
  The wide adoption of gas fired units and power-to-gas technology brings
remarkable interdependency between natural gas and electricity infrastructures.
This paper studies the equilibria of coupled gas and electricity energy markets
driven by the strategic bidding behavior: each producer endeavours to maximizes
its own profit subjecting to the market clearing outcome. The market equilibria
is formulated as an equilibrium problem with equilibrium constraints (EPEC). A
special diagonalization algorithm (DA) is devised, in which the unilateral
equilibria of the gas or electricity market is found in the inner loop given
the rival's strategy; the interaction of the two markets are tackled in the
outer loop. Case studies on two test systems validates the proposed
methodology.


title: X-ray Variability of SS 433: Evidence for Supercritical Accretion

abstract:
  We study the X-ray variability of SS433 based on data from the ASCA
observatory and the MAXI and RXTE/ASM monitoring missions. Based on the ASCA
data, we have constructed the power spectrum of SS433 in the frequency range
from $10^{-6}$ to 0.1 Hz, which confirms the presence of a flat portion
(flat-topped noise) in the spectrum at frequencies $3\times 10^{-5}$ -
$10^{-3}$ Hz. The periodic variability (precession, nutation, eclipses) begins
to dominate significantly over the stochastic variability at lower frequencies,
which does not allow the stochastic variability to be studied reliably. The
best agreement with the observations is reached by the model with the flat
portion extending to $9.5\times10^{-6}$ Hz and a power-law spectrum with index
of 2.6 below that frequency. The jet nutation with a period of about three days
suggests that the time for the passage of material through the disk is less
than this value. Therefore, at frequencies below $4\times10^{-6}$ Hz, the power
spectrum probably does not reflect the disk structure. It may depend on other
factors, for example, a variable mass accretion rate supplied by the donor. The
flat portion may arise from a rapid decrease in the viscous time in the
supercritical or radiative disk zones. It could be related to the variability
of the X-ray jets that are formed in the supercritical region.


title:
Large-scale Analysis of Chess Games with Chess Engines: A Preliminary
  Report

abstract:
  The strength of chess engines together with the availability of numerous
chess games have attracted the attention of chess players, data scientists, and
researchers during the last decades. State-of-the-art engines now provide an
authoritative judgement that can be used in many applications like cheating
detection, intrinsic ratings computation, skill assessment, or the study of
human decision-making. A key issue for the research community is to gather a
large dataset of chess games together with the judgement of chess engines.
Unfortunately the analysis of each move takes lots of times. In this paper, we
report our effort to analyse almost 5 millions chess games with a computing
grid. During summer 2015, we processed 270 millions unique played positions
using the Stockfish engine with a quite high depth (20). We populated a
database of 1+ tera-octets of chess evaluations, representing an estimated time
of 50 years of computation on a single machine. Our effort is a first step
towards the replication of research results, the supply of open data and
procedures for exploring new directions, and the investigation of software
engineering/scalability issues when computing billions of moves.


title: Diphoton resonance at the ILC

abstract:
  In this paper we study the direct production of the diphoton resonance $X$
which has been suggested by 2015 data at the LHC, in $e^+e^-\to X\gamma/XZ$
processes at the ILC. We derive an analytic expression for the scattering
amplitudes of these processes, and present a comprehensive analysis for
determining the properties of $X$ at the ILC. A realistic simulation study for
$e^+e^-\to X\gamma$ is performed based on the full detector simulation to
demonstrate the capabilities of the ILC experiment. Complementary to the
searches at the LHC, prospects of the measurement of the absolute values of
production cross-section are obtained for the ILC using recoil technique
without assuming decay modes of $X$. In addition, we have studied the searches
for $X\to\rm{invisible}$ and $X\to b\bar{b}$ modes, which are challenging at
the LHC, and found that these decay modes can be discovered with high
significance if their branching ratios are large enough.


title:
Methodology of Parameterization of Molecular Mechanics Force Field From
  Quantum Chemistry Calculations using Genetic Algorithm: A case study of
  methanol

abstract:
  In molecular dynamics (MD) simulation, force field determines the capability
of an individual model in capturing physical and chemistry properties. The
method for generating proper parameters of the force field form is the key
component for computational research in chemistry, biochemistry, and
condensed-phase physics. Our study showed that the feasibility to predict
experimental condensed phase properties (i.e., density and heat of
vaporization) of methanol through problem specific force field from only
quantum chemistry information. To acquire the satisfying parameter sets of the
force field, the genetic algorithm (GA) is the main optimization method. For
electrostatic potential energy, we optimized both the electrostatic parameters
of methanol using the GA method, which leads to low deviations of between the
quantum mechanics (QM) calculations and the GA optimized parameters. We
optimized the van der Waals (vdW) parameters both using GA and guided GA
methods by calibrating interaction energy of various methanol homo-clusters,
such as nonamers, undecamers, or tridecamers. Excellent agreement between the
training dataset from QM calculations (i.e., MP2) and GA optimized parameters
can be achieved. However, only the guided GA method, which eliminates the
overestimation of interaction energy from MP2 calculations in the optimization
process, provides proper vdW parameters for MD simulation to get the condensed
phase properties (i.e., density and heat of vaporization) of methanol.
Throughout the whole optimization process, the experimental value were not
involved in the objective functions, but were only used for the purpose of
justifying models (i.e., nonamers, undecamers, or tridecamers) and validating
methods (i.e., GA or guided GA). Our method shows the possibility of developing
descriptive polarizable force field using only QM calculations.


title:
The Bose-Hubbard model on a triangular lattice with diamond
  ring-exchange

abstract:
  Ring-exchange interactions have been proposed as a possible mechanism for a
Bose-liquid phase at zero temperature, a phase that is compressible with no
superfluidity. Using the Stochastic Green Function algorithm (SGF), we study
the effect of these interactions for bosons on a two-dimensional triangular
lattice. We show that the supersolid phase, that is known to exist in the
ground state for a wide range of densities, is rapidly destroyed as the
ring-exchange interactions are turned on. We establish the ground-state phase
diagram of the system, which is characterized by the absence of the expected
Bose-liquid phase.


title:
Trade-offs between spatial and temporal resolutions in stochastic
  super-resolution microscopy techniques

abstract:
  Widefield stochastic microscopy techniques such as PALM or STORM rely on the
progressive accumulation of a large number of frames, each containing a scarce
number of super-resolved point images. We justify that the redundancy in the
localization of detected events imposes a specific limit on the temporal
resolution. Based on a theoretical model, we derive analytical predictions for
the minimal time required to obtain a reliable image at a given spatial
resolution, called image completion time. In contrast to standard assumptions,
we find that the image completion time scales logarithmically with the ratio of
the image size by the spatial resolution volume. We justify that this
non-linear relation is the hallmark of a random coverage problem. We propose a
method to estimate the risk that the image reconstruction is not complete,
which we apply to an experimental data set. Our results provide a theoretical
framework to quantify the pattern detection efficiency and to optimize the
trade-off between image coverage and acquisition time, with applications to
$1$, $2$ or $3$ dimension structural imaging.

categories: physics.bio-ph cond-mat.soft physics.data-an physics.optics


title:
The self-consistent analysis for sub-barrier fusion enhancement effect
  in Ca + Ca and Ni + Ni

abstract:
  The fusion dynamic mechanism of heavy-ions at energies near the Coulomb
barrier is complicated and still not very clear up to now. Accordingly, a
self-consistent method based on the CCFULL calculations has been developed and
applied for an ingoing study of the effect of the positive Q-value neutron
transfer (PQNT) channels in this work. The typical experimental fusion data of
Ca + Ca and Ni + Ni is analyzed within the unified calculation scheme. The PQNT
effect in near-barrier fusion is further confirmed based on the self-consistent
analysis and extracted quantitatively.


title:
Crossing the phantom divide with dissipative normal matter in the
  Israel-Stewart-Hiscock formalism

abstract:
  A phantom solution in the framework of the causal Israel-Stewart (IS)
formalism is discussed. We assume a late time behavior of the cosmic evolution
by considering only one dominant matter fluid with viscosity. In the model it
is assumed a bulk viscosity of the form $\xi= \xi_{0}\rho^{1/2}$, where $\rho$
is the energy density of the fluid. We evaluate and discuss the behavior of the
thermodynamical parameters associated to this solution, like the temperature,
rate of entropy, entropy, relaxation time, effective pressure and effective
EoS. A discussion about the assumption of near equilibrium of the formalism and
the accelerated expansion of the solution is presented. The solution allows to
cross the phantom divide without evoking an exotic matter fluid and the
effective EoS parameter is always lesser than $-1$ and time independent. A
future singularity (big rip) occurs, but different from the Type I (big rip)
solution classified in S. Nojiri, S. D. Odintsov and S. Tsujikawa, Phys. Rev. D
71, 063004 (2005), if we consider others thermodynamics parameters like, for
example, the effective pressure in the presence of viscosity or the relaxation
time.


title:
Spectral Clustering for Optical Confirmation and Redshift Estimation of
  X-ray Selected Galaxy Cluster Candidates in the SDSS Stripe 82

abstract:
  We develop a galaxy cluster finding algorithm based on spectral clustering
technique to identify optical counterparts and estimate optical redshifts for
X-ray selected cluster candidates. As an application, we run our algorithm on a
sample of X-ray cluster candidates selected from the third XMM-Newton
serendipitous source catalog (3XMM-DR5) that are located in the Stripe 82 of
the Sloan Digital Sky Survey (SDSS). Our method works on galaxies described in
the color-magnitude feature space. We begin by examining 45 galaxy clusters
with published spectroscopic redshifts in the range of 0.1 to 0.8 with a median
of 0.36. As a result, we are able to identify their optical counterparts and
estimate their photometric redshifts, which have a typical accuracy of 0.025
and agree with the published ones. Then, we investigate another 40 X-ray
cluster candidates (from the same cluster survey) with no redshift information
in the literature and found that 12 candidates are considered as galaxy
clusters in the redshift range from 0.29 to 0.76 with a median of 0.57. These
systems are newly discovered clusters in X-rays and optical data. Among them 7
clusters have spectroscopic redshifts for at least one member galaxy.


title:
The $L^{2}$ weak sequential convergence of radial mass critical NLS
  solutions with mass above the ground state

abstract:
  We study the non-scattering $L^{2}$ solution $u$ to the radial mass critical
nonlinear Schr\"odinger equation with mass just above the ground state, and
show that there exists a time sequence $\{t_{n}\}_{n}$, such that $u(t_{n})$
weakly converges to the ground state $Q$ up to scaling and phase
transformation. We also give some partial results on the mass concentration of
the minimal mass blow up solution.


title:
The cosmological constant problem in heterotic-M-theory and the orbifold
  of time

abstract:
  Chameleon fields are quantum fields with an increasing mass as a function of
the matter density of the environment. Recently chameleon fields have been
exploited to solve the cosmological constant problem in the Modified Fujii's
Model - MFM [Phys Rev D82 (2010) 044006]. However, gravity has been treated
basically at a semiclassical level in that paper. In this article the stringy
origin of the MFM is further discussed: as we will see, the MFM can be obtained
from heterotic-M-theory. Consequently, a quantum description of gravity is
obtained and the theory is finite because we choose the string mass as our UV
cut-off. This stringy origin of the MFM creates stronger theoretical grounds
for our solution to the cosmological constant problem. In our analysis, time
will be compactified on a $S^1/Z_2$ orbifold and this peculiar compactification
of time has a number of consequences. For example, as we will see, quantum
gravity and a quantum gauge theory are actually the same theory in the sense
that gravity is the time-evolution of a gauge theory. This might be the key to
obtain a non-approximated stabilizing potential for the dilaton in the string
frame. In this paper we will further discuss the non-equivalence of different
conformal frames at the quantum level. As we will see, in our approach we use
basically a unique conformal frame: the frame where the masses of particles are
field dependent. A word of caution is necessary: we do not take into account
massive string states and IR divergences.


title:
Is There Really "Retrocausation" in Time-Symmetric Approaches to Quantum
  Mechanics?

abstract:
  Time-symmetric interpretations of quantum theory are often presented as
featuring "retrocausal" effects in addition to the usual forward notion of
causation. This paper examines the ontological implications of certain
timesymmetric theories, and finds that no dynamical notion of causation applies
to them, either forward or backward. It is concluded that such theories
actually describe a static picture, in which the notion of causation is
relegated to a descriptor of static relationships among events. In addition,
these theories lead to an epistemic rather than ontologically referring,
realist view of quantum states.


title: Design of an intermediate representation for query languages

abstract:
  Data oriented applications, usually written in a high-level, general-purpose
programming language (such as Java) interact with database through a coarse
interface. Informally, the text of a query is built on the application side
(either via plain string concatenation or through an abstract notion of
statement) and shipped to the database over the wire where it is executed. The
results are then serialized and sent back to the "client-code" where they are
translated in the language's native datatypes. This round trip is detrimental
to performances but, worse, such a programming model prevents one from having
richer queries, namely queries containing user-defined functions (that is
functions defined by the programmer and used e.g. in the filter condition of a
SQL query). While some databases also possess a "server-side" language (e.g.
PL/SQL in Oracle database), its integration with the very-optimized query
execution engine is still minimal and queries containing (PL/SQL) user-defined
functions remain notoriously inefficient. In this setting, we reviewed existing
language-integrated query frameworks, highlighting that existing database query
languages (including SQL) share high-level querying primitives (e.g.,
filtering, joins, aggregation) that can be represented by operators, but differ
widely regarding the semantics of their expression language. In order to
represent queries in an application language- and database-agnostic manner, we
designed a small calculus, dubbed "QIR" for Query Intermediate Representation.
QIR contains expressions, corresponding to a small extension of the pure
lambda-calculus, and operators to represent usual querying primitives. In the
effort to send efficient queries to the database, we abstracted the idea of
"good" query representations in a measure on QIR terms. Then, we designed an
evaluation strategy rewriting QIR query representations into "better" ones.


title: Light-field driven currents in graphene

abstract:
  Ultrafast electron dynamics in solids under strong optical fields has
recently found particular attention. In dielectrics and semiconductors, various
light-field-driven effects have been explored, such as high-harmonic
generation, sub-optical-cycle interband population transfer and nonperturbative
increase of transient polarizability. In contrast, much less is known about
field-driven electron dynamics in metals because charge carriers screen an
external electric field in ordinary metals. Here we show that atomically thin
monolayer Graphene offers unique opportunities to study light-field-driven
processes in a metal. With a comparably modest field strength of up to 0.3
V/{\AA}, we drive combined interband and intraband electron dynamics, leading
to a light-field-waveform controlled residual conduction current after the
laser pulse is gone. We identify the underlying pivotal physical mechanism as
electron quantum-path interference taking place on the 1-femtosecond
($10^{-15}$ second) timescale. The process can be categorized as
Landau-Zener-St\"uckelberg interferometry. These fully coherent electron
dynamics in graphene take place on a hitherto unexplored timescale faster than
electron-electron scattering (tens of femtoseconds) and electron-phonon
scattering (hundreds of femtoseconds). These results broaden the scope of
light-field control of electrons in solids to an entirely new and eminently
important material class -- metals -- promising wide ramifications for band
structure tomography and light-field-driven electronics.


title:
Very low-energy nucleon + 16O coupled-channel scattering: results with a
  phenomenological vibrational model

abstract:
  We employ a collective vibration coupled-channel model to describe the
nucleon-16O cluster systems, obtaining low-excitation spectra for 17O and 17F.
Bound and resonance states of the compound systems have been deduced, showing
good agreement with experimental spectra. Low energy scattering cross sections
of neutrons and protons from 16O also have been calculated and the results
compare well with available experimental data.


title: Edit Distance: Sketching, Streaming and Document Exchange

abstract:
  We show that in the document exchange problem, where Alice holds $x \in
\{0,1\}^n$ and Bob holds $y \in \{0,1\}^n$, Alice can send Bob a message of
size $O(K(\log^2 K+\log n))$ bits such that Bob can recover $x$ using the
message and his input $y$ if the edit distance between $x$ and $y$ is no more
than $K$, and output "error" otherwise. Both the encoding and decoding can be
done in time $\tilde{O}(n+\mathsf{poly}(K))$. This result significantly
improves the previous communication bounds under polynomial encoding/decoding
time. We also show that in the referee model, where Alice and Bob hold $x$ and
$y$ respectively, they can compute sketches of $x$ and $y$ of sizes
$\mathsf{poly}(K \log n)$ bits (the encoding), and send to the referee, who can
then compute the edit distance between $x$ and $y$ together with all the edit
operations if the edit distance is no more than $K$, and output "error"
otherwise (the decoding). To the best of our knowledge, this is the first
result for sketching edit distance using $\mathsf{poly}(K \log n)$ bits.
Moreover, the encoding phase of our sketching algorithm can be performed by
scanning the input string in one pass. Thus our sketching algorithm also
implies the first streaming algorithm for computing edit distance and all the
edits exactly using $\mathsf{poly}(K \log n)$ bits of space.


title: Extended Gelfand-Tsetlin graph, its q-boundary, and q-B-splines

abstract:
  A continuation of the joint work by Vadim Gorin and the author, J. Funct.
Anal. 270 (2016), 375-418; arXiv:1504.06832.
  The extended Gelfand-Tsetlin graph, introduced in that paper, is a novel
combinatorial object. Its q-boundary is formed by infinite point configurations
on a two-sided q-lattice. The q-boundary carries a continuous family of
probability measures that are a q-analogue of the so-called zw-measures, which
originated in the problem of harmonic analysis on the infinite-dimensional
unitary group.
  In the present paper, it is proved that certain transition Markov kernels,
linked to the extended Gelfand-Tsetlin graph and its q-boundary, possess the
Feller property. This property is needed for constructing a model of Markov
dynamics on the q-boundary. A connection with the classical B-splines and their
q-analogues is discussed. Some results of the paper arXiv:1504.06832 are
rederived in another way.


title: Theory of Gravitational Waves

abstract:
  The existence of gravitational radiation is a natural prediction of any
relativistic description of the gravitational interaction. In this chapter, we
focus on gravitational waves, as predicted by Einstein's general theory of
relativity. First, we introduce those mathematical concepts that are necessary
to properly formulate the physical theory, such as the notions of manifold,
vector, tensor, metric, connection and curvature. Second, we motivate,
formulate and then discuss Einstein's equation, which relates the geometry of
spacetime to its matter content. Gravitational waves are later introduced as
solutions of the linearized Einstein equation around flat spacetime. These
waves are shown to propagate at the speed of light and to possess two
polarization states. Gravitational waves can interact with matter, allowing for
their direct detection by means of laser interferometers. Finally, Einstein's
quadrupole formulas are derived and used to show that nonspherical compact
objects moving at relativistic speeds are powerful gravitational wave sources.


title: Random quantum correlations are generically non-classical

abstract:
  It is now a well-known fact that the correlations arising from local
dichotomic measurements on an entangled quantum state may exhibit intrinsically
non-classical features. In this paper we delve into a comprehensive study of
random instances of such bipartite correlations. The main question we are
interested in is: given a quantum correlation, taken at random, how likely is
it that it is truly non-explainable by a classical model? We show that, under
very general assumptions on the considered distribution, a random correlation
which lies on the border of the quantum set is with high probability outside
the classical set. What is more, we are able to provide the Bell inequality
certifying this fact. On the technical side, our results follow from (i)
estimating precisely the "quantum norm" of a random matrix, and (ii) lower
bounding sharply enough its "classical norm", hence proving a gap between the
two. Along the way, we need a non-trivial upper bound on the
$\infty{\rightarrow}1$ norm of a random orthogonal matrix, which might be of
independent interest.


title:
Differentially Private Model Selection with Penalized and Constrained
  Likelihood

abstract:
  In statistical disclosure control, the goal of data analysis is twofold: The
released information must provide accurate and useful statistics about the
underlying population of interest, while minimizing the potential for an
individual record to be identified. In recent years, the notion of differential
privacy has received much attention in theoretical computer science, machine
learning, and statistics. It provides a rigorous and strong notion of
protection for individuals' sensitive information. A fundamental question is
how to incorporate differential privacy into traditional statistical inference
procedures. In this paper we study model selection in multivariate linear
regression under the constraint of differential privacy. We show that model
selection procedures based on penalized least squares or likelihood can be made
differentially private by a combination of regularization and randomization,
and propose two algorithms to do so. We show that our private procedures are
consistent under essentially the same conditions as the corresponding
non-private procedures. We also find that under differential privacy, the
procedure becomes more sensitive to the tuning parameters. We illustrate and
evaluate our method using simulation studies and two real data examples.


title:
Non-perturbative Contributions from Complexified Solutions in
  $\mathbb{C}P^{N-1}$ Models

abstract:
  We discuss the non-perturbative contributions from real and complex saddle
point solutions in the $\mathbb{C}P^1$ quantum mechanics with fermionic degrees
of freedom, using the Lefschetz thimble formalism beyond the gaussian
approximation. We find bion solutions, which correspond to (complexified)
instanton-antiinstanton configurations stabilized in the presence of the
fermionic degrees of freedom. By computing the one-loop determinants in the
bion backgrounds, we obtain the leading order contributions from both the real
and complex bion solutions. To incorporate quasi zero modes which become nearly
massless in a weak coupling limit, we regard the bion solutions as
well-separated instanton-antiinstanton configurations and calculate a
complexified quasi moduli integral based on the Lefschetz thimble formalism.
The non-perturbative contributions from the real and complex bions are shown to
cancel out in the supersymmetric case and give an (expected) ambiguity in the
non-supersymmetric case, which plays a vital role in the resurgent
trans-series. For nearly supersymmetric situation, evaluation of the Lefschetz
thimble gives results in precise agreement with those of the direct evaluation
of the Schr\"odinger equation. We also perform the same analysis for the
sine-Gordon quantum mechanics and point out some important differences showing
that the sine-Gordon quantum mechanics does not correctly describe the 1d limit
of the $\mathbb{C}P^{N-1}$ field theory of $\mathbb{R} \times S^1$.


title:
Reliable MIMO Optical Wireless Communications Through Super-Rectangular
  Cover

abstract:
  In this paper, we consider an intensity modulated direct detection MIMO
optical wireless communication (OWC) system. For such a system, a novel
super-rectangular cover theory is developed to characterize both the unique
identifiability and full reliability. This theory states that a transmitted
matrix signal can be uniquely identified if and only if the cover order is
equal to the transmitter aperture number, i.e., full cover. In addition, we
prove that full reliability is guaranteed for space-time block coded MIMO-OWC
over commonly used log-normal fading channels with an ML detector if and only
if the STBC enables full cover. In addition, the diversity gain can be
geometrically interpreted as the cover order of the super-rectangle, which
should be maximized, and the volume of this super-rectangle, as the diversity
loss, should be minimized. Using this established error performance criterion,
the optimal linear STBC for block fading channels is proved to be spatial
repetition code with an optimal power allocation. The design of the optimal
non-linear STBC is shown to be equivalent to constructing the optimal
multi-dimensional constellation. Specifically, a multi-dimensional
constellation from Diophantine equations is proposed and then, shown to be more
energy-efficient than the commonly used nonnegative pulse amplitude modulation
constellation.


title: SETI Observations of Exoplanets with the Allen Telescope Array

abstract:
  We report radio SETI observations on a large number of known exoplanets and
other nearby star systems using the Allen Telescope Array (ATA). Observations
were made over about 19000 hours from May 2009 to Dec 2015. This search focused
on narrow-band radio signals from a set totaling 9293 stars, including 2015
exoplanet stars and Kepler objects of interest and an additional 65 whose
planets may be close to their Habitable Zone. The ATA observations were made
using multiple synthesized beams and an anticoincidence filter to help identify
terrestrial radio interference. Stars were observed over frequencies from 1- 9
GHz in multiple bands that avoid strong terrestrial communication frequencies.
Data were processed in near-real time for narrow-band (0.7- 100 Hz) continuous
and pulsed signals, with transmitter/receiver relative accelerations from -0.3
to 0.3 m/s^2. A total of 1.9 x 10^8 unique signals requiring immediate
follow-up were detected in observations covering more than 8 x 10^6 star-MHz.
We detected no persistent signals from extraterrestrial technology exceeding
our frequency-dependent sensitivity threshold of 180 - 310 x 10^-26 W / m^2.


title: On circular strings in $(AdS_3 \times S^3)_{\varkappa}$

abstract:
  The so called one-parameter (often called $\varkappa$) deformed $AdS$ string
sigma models have attracted a lot of attention lately in the study of
integrability in string theory. We construct various circular string solutions
in the $(AdS_3 \times S^3)_{\varkappa}$ background and describe the
characteristics of such solutions qualitatively. We study the Bohr-Sommerfeld
like quantization for these string states to characterise the motion. Further
we find a `long' string limit of such circular strings in the
$\varkappa$-deformed $AdS_3$ and find a novel dependence of the oscillation
number on the energy in the next to leading order expansion.


title: Dynamic Question Ordering in Online Surveys

abstract:
  Online surveys have the potential to support adaptive questions, where later
questions depend on earlier responses. Past work has taken a rule-based
approach, uniformly across all respondents. We envision a richer interpretation
of adaptive questions, which we call dynamic question ordering (DQO), where
question order is personalized. Such an approach could increase engagement, and
therefore response rate, as well as imputation quality. We present a DQO
framework to improve survey completion and imputation. In the general
survey-taking setting, we want to maximize survey completion, and so we focus
on ordering questions to engage the respondent and collect hopefully all
information, or at least the information that most characterizes the
respondent, for accurate imputations. In another scenario, our goal is to
provide a personalized prediction. Since it is possible to give reasonable
predictions with only a subset of questions, we are not concerned with
motivating users to answer all questions. Instead, we want to order questions
to get information that reduces prediction uncertainty, while not being too
burdensome. We illustrate this framework with an example of providing energy
estimates to prospective tenants. We also discuss DQO for national surveys and
consider connections between our statistics-based question-ordering approach
and cognitive survey methodology.


title:
Optimization with affine homogeneous quadratic integral inequality
  constraints

abstract:
  We introduce a new technique to optimize a linear cost function subject to a
one-dimensional affine homogeneous quadratic integral inequality, i.e., the
requirement that a homogeneous quadratic integral functional, affine in the
optimization variables, is non-negative over a space of functions defined by
homogeneous boundary conditions. Such problems arise in stability analysis,
input-to-state/output analysis, and control of many systems governed by partial
differential equations (PDEs), in particular fluid dynamical systems. First, we
derive outer approximations for the feasible set of a homogeneous quadratic
integral inequality in terms of linear matrix inequalities (LMIs), and show
that under mild assumptions a convergent, non-decreasing sequence of lower
bounds for the optimal cost can be computed with a sequence of semidefinite
programs (SDPs). Second, we obtain inner approximations in terms of LMIs and
sum-of-squares constraints, so upper bounds for the optimal cost and strictly
feasible points for the integral inequality can also be computed with SDPs. To
aid the formulation and solution of our SDP relaxations, we implement our
techniques in QUINOPT, an open-source add-on to YALMIP. We demonstrate our
techniques by solving problems arising from the stability analysis of PDEs.


title:
Special L-values and shtuka functions for Drinfeld modules on elliptic
  curves

abstract:
  We make a detailed account of sign-normalized rank 1 Drinfeld A-modules, for
A the coordinate ring of an elliptic curve over a finite field, in order to
provide a parallel theory to the Carlitz module for F_q[t]. Using precise
formulas for the shtuka function for A, we obtain a product formula for the
fundamental period of the Drinfeld module. Using the shtuka function we find
identities for deformations of reciprocal sums and as a result prove special
value formulas for Pellarin L-series in terms of an Anderson-Thakur function.
We also give a new proof of a log-algebraicity theorem of Anderson.


title:
A comparison between methods of analytical continuation for bosonic
  functions

abstract:
  In this article we perform a critical assessment of different known methods
for the analytical continuation of bosonic functions, namely the maximum
entropy method, the non-negative least-square method, the non-negative Tikhonov
method, the Pad\'e approximant method, and a stochastic sampling method. Three
functions of different shape are investigated, corresponding to three
physically relevant scenarios. They include a simple two-pole model function
and two flavours of the non-interacting Hubbard model on a square lattice, i.e.
a single-orbital metallic system and a two-orbitals insulating system. The
effect of numerical noise in the input data on the analytical continuation is
discussed in detail. Overall, the stochastic method by Mishchenko et al. [Phys.
Rev. B \textbf{62}, 6317 (2000)] is shown to be the most reliable tool for
input data whose numerical precision is not known. For high precision input
data, this approach is slightly outperformed by the Pad\'e approximant method,
which combines a good resolution power with a good numerical stability.
Although none of the methods retrieves all features in the spectra in the
presence of noise, our analysis provides a useful guideline for obtaining
reliable information of the spectral function in cases of practical interest.


title:
Thermoelectricity in a junction between interacting cold atomic Fermi
  gases

abstract:
  A gas of interacting ultracold fermions can be tuned into a strongly
interacting regime using a Feshbach resonance. Here we theoretically study
quasiparticle transport in a system of two reservoirs of interacting ultracold
fermions on the BCS side of the BCS-BEC crossover coupled weakly via a tunnel
junction. Using the generalized BCS theory we calculate the time evolution of
the system that is assumed to be initially prepared in a non-equilibrium state
characterized by a particle number imbalance or a temperature imbalance. A
number of characteristic features like sharp peaks in quasiparticle currents,
or transitions between the normal and superconducting states are found. We
discuss signatures of the Seebeck and the Peltier effect and the resulting
temperature difference of the two reservoirs as a function of the interaction
parameter $(k_Fa)^{-1}$. The Peltier effect may lead to an additional cooling
mechanism for ultracold fermionic atoms.


title:
Existence and uniqueness results for BSDEs with jumps: the whole nine
  yards

abstract:
  This paper is devoted to obtaining a wellposedness result for
multidimensional BSDEs with possibly unbounded random time horizon and driven
by a general martingale in a filtration only assumed to satisfy the usual
hypotheses, i.e. the filtration may be stochastically discontinuous. We show
that for stochastic Lipschitz generators and unbounded, possibly infinite, time
horizon, these equations admit a unique solution in appropriately weighted
spaces. Our result allows in particular to obtain a wellposedness result for
BSDEs driven by discrete--time approximations of general martingales.


title: Semi-Parametric Survival Estimation for pedigrees

abstract:
  Mendelian diseases are determined by a single mutation in a given gene.
However, in the case of diseases with late onset, the age at onset is variable;
it can even be the case that the onset is not observed in a lifetime.
Estimating the survival function of the mutation carriers and the effect of
modifying factors such as the sex, mutation, origin, etc, is a task of
importance, both for management of mutation carriers and for prevention. In
this work, we present a semi-parametric method based on a proportional to
estimate the survival function using pedigrees ascertained through affected
individuals (probands). Not all members of the pedigree need to be genotyped.
The ascertainment bias is corrected by using only the phenotypic information
from the relatives of the proband, and not of the proband himself. The method
manage ungenotyped individuals through belief propagation in Bayesian networks
and uses an EM algorithm to compute a Kaplan-Meier estimator of the survival
function. The method is illustrated on simulated data and on a samples of
families with transthyretin-related hereditary amyloidosis, a rare autosomal
dominant disease with highly variable age of onset.


title:
Searches for Lepton Number Violation and resonances in the $K^{\pm} \to
  \pi\mu\mu$ decays at the NA48/2 experiment

abstract:
  The NA48/2 experiment at CERN collected a large sample of charged kaon decays
into final states with multiple charged particles in 2003--2004. A new upper
limit on the rate of the lepton number violating decay $K^{\pm} \to \pi^{\mp}
\mu^{\pm} \mu^{\pm}$ obtained from this sample is reported:
$\mathcal{B}(K^{\pm} \to \pi^{\mp} \mu^{\pm} \mu^{\pm})<8.6 \times 10^{-11}$ at
90\% CL. Searches for two-body resonances in the $K^{\pm} \to \pi\mu\mu$ decays
(including heavy neutral leptons~$N_4$ and inflatons~$\chi$) in the accessible
range of masses and lifetimes are also presented. In the absence of a signal,
upper limits are set on the products of branching ratios~$\mathcal{B}(K^{\pm}
\to \mu^{\pm} N_{4})\mathcal{B}(N_{4} \to \pi^{\mp}\mu^{\pm})$ and
$\mathcal{B}(K^{\pm} \to \pi^{\pm} \chi)\mathcal{B}(\chi \to \mu^{+}\mu^{-})$
as functions of the resonance mass and lifetime. These limits are in the
$10^{-10}-10^{-9}$ range for resonance lifetimes below 100~ps.


title:
Nontrivial critical fixed point for replica-symmetry-breaking
  transitions

abstract:
  The transformation of the free-energy landscape from smooth to hierarchical
is one of the richest features of mean-field disordered systems. A well-studied
example is the de Almeida-Thouless transition for spin glasses in a magnetic
field, and a similar phenomenon--the Gardner transition--has recently been
predicted for structural glasses. The existence of these
replica-symmetry-breaking phase transitions has, however, long been questioned
below their upper critical dimension, d_u=6. Here, we obtain evidence for the
existence of these transitions in d<d_u using a two-loop calculation. Because
the critical fixed point is found in the strong-coupling regime, we corroborate
the result by resumming the perturbative series with inputs from a three-loop
calculation and an analysis of its large-order behavior. Our study offers a
resolution of the long-lasting controversy surrounding phase transitions in
finite-dimensional disordered systems.


title:
Self-Consistent Modeling of Reionization in Cosmological Hydrodynamical
  Simulations

abstract:
  The ultraviolet background (UVB) emitted by quasars and galaxies governs the
ionization and thermal state of the intergalactic medium (IGM), regulates the
formation of high-redshift galaxies, and is thus a key quantity for modeling
cosmic reionization. The vast majority of cosmological hydrodynamical
simulations implement the UVB via a set of spatially uniform photoionization
and photoheating rates derived from UVB synthesis models. We show that
simulations using canonical UVB rates reionize and, perhaps more importantly,
spuriously heat the IGM, much earlier z ~ 15 than they should. This problem
arises because at z > 6, where observational constraints are nonexistent, the
UVB amplitude is far too high. We introduce a new methodology to remedy this
issue, and we generate self-consistent photoionization and photoheating rates
to model any chosen reionization history. Following this approach, we run a
suite of hydrodynamical simulations of different reionization scenarios and
explore the impact of the timing of reionization and its concomitant heat
injection on the the thermal state of the IGM. We present a comprehensive study
of the pressure smoothing scale of IGM gas, illustrating its dependence on the
details of both hydrogen and helium reionization, and argue that it plays a
fundamental role in interpreting Lyman-alpha forest statistics and the thermal
evolution of the IGM. The premature IGM heating we have uncovered implies that
previous work has likely dramatically overestimated the impact of
photoionization feedback on galaxy formation, which sets the minimum halo mass
able to form stars at high redshifts. We make our new UVB photoionization and
photoheating rates publicly available for use in future simulations.


title: Superconvergence of Kernel-Based Interpolation

abstract:
  It is well-known that univariate cubic spline interpolation, if carried out
on point sets with fill distance $h$, converges only like ${\cal O}(h^2)$ in
$L_2[a,b]$ for functions in $W_2^2[a,b]$ if no additional assumptions are made.
But superconvergence up to order $h^4$ occurs if more smoothness is assumed and
if certain additional boundary conditions are satisfied. This phenomenon was
generalized in 1999 to multivariate interpolation in Reproducing Kernel Hilbert
Spaces on domains $\Omega\subset R^d$ for continuous positive definite
Fourier-transformable shift-invariant kernels on $R^d$. But the sufficient
condition for superconvergence given in 1999 still needs further analysis,
because the interplay between smoothness and boundary conditions is not clear
at all. Furthermore, if only additional smoothness is assumed, superconvergence
is numerically observed in the interior of the domain, but without explanation,
so far. This paper first generalizes the "improved error bounds" of 1999 by an
abstract theory that includes the Aubin-Nitsche trick and the known
superconvergence results for univariate polynomial splines. Then the paper
analyzes what is behind the sufficient conditions for superconvergence. They
split into conditions on smoothness and localization, and these are
investigated independently. If sufficient smoothness is present, but no
additional localization conditions are assumed, it is proven that
superconvergence always occurs in the interior of the domain. If smoothness and
localization interact in the kernel-based case on $R^d$, weak and strong
boundary conditions in terms of pseudodifferential operators occur. A special
section on Mercer expansions is added, because Mercer eigenfunctions always
satisfy the sufficient conditions for superconvergence. Numerical examples
illustrate the theoretical findings.


title: Computational Complexity of Arranging Music

abstract:
  This paper proves that arrangement of music is NP-hard when subject to
various constraints: avoiding musical dissonance, limiting how many notes can
be played simultaneously, and limiting transition speed between chords. These
results imply the computational complexity of related musical problems,
including musical choreography and rhythm games.


title:
The effects of cooling rate on particle rearrangement statistics:
  Rapidly cooled glasses are more ductile and less reversible

abstract:
  Amorphous solids, such as metallic, polymeric, and colloidal glasses, display
complex spatiotemporal response to applied deformations. In contrast to
crystalline solids, during loading, amorphous solids exhibit a smooth crossover
from elastic response to plastic flow. In this study, we investigate the
mechanical response of binary Lennard-Jones glasses to athermal, quasistatic
pure shear as a function of the cooling rate used to prepare them. We find
several key results concerning the connection between strain-induced particle
rearrangements and mechanical response. We show that more rapidly cooled
glasses undergo more frequent and larger particle rearrangements than slowly
cooled glasses. We find that the ratio of the shear to bulk moduli decreases
with increasing cooling rate, which suggests that more rapidly cooled glasses
are more ductile than slowly cooled samples. In addition, we characterized the
degree of reversibility of particle motion during cyclic shear. We find that
irreversible particle motion occurs even in the putative linear regime of
stress versus strain. However, slowly cooled glasses, which undergo smaller
rearrangements, are more reversible under cyclic shear than rapidly cooled
glasses. Thus, we show that more ductile glasses are also less reversible.


title:
Comments On The Two-Dimensional Landau-Ginzburg Approach To Link
  Homology

abstract:
  We describe rules for computing a homology theory of knots and links in
$\mathbb{R}^3$. It is derived from the theory of framed BPS states bound to
domain walls separating two-dimensional Landau-Ginzburg models with (2,2)
supersymmetry. We illustrate the rules with some sample computations, obtaining
results consistent with Khovanov homology. We show that of the two
Landau-Ginzburg models discussed in this context by Gaiotto and Witten one,
(the so-called Yang-Yang-Landau-Ginzburg model) does not lead to topological
invariants of links while the other, based on a model with target space equal
to the universal cover of the moduli space of $SU(2)$ magnetic monopoles, will
indeed produce a topologically invariant theory of knots and links.


title:
On the approximate periodicity of sequences attached to
  noncrystallographic root systems

abstract:
  We study Fomin-Zelevinsky's mutation rule in the context of
noncrystallographic root systems. In particular, we construct approximately
periodic sequences of real numbers for the noncrystallographic root systems of
rank 2 by adjusting the exchange relation for cluster algebras. Moreover, we
describe matrix mutation classes for type H3 and H4.


title: Quantum Electrodynamics vacuum polarization solver

abstract:
  The self-consistent modeling of vacuum polarization due to virtual
electron-positron fluctuations is of relevance for many near term experiments
associated with high intensity radiation sources and represents a milestone in
describing scenarios of extreme energy density. We present a generalized
finite-difference time-domain solver that can incorporate the modifications to
Maxwell's equations due to vacuum polarization. Our multidimensional solver
reproduced in one-dimensional configurations the results for which an analytic
treatment is possible, yielding vacuum harmonic generation and birefringence.
The solver has also been tested for two-dimensional scenarios where finite
laser beam spot sizes must be taken into account. We employ this solver to
explore different types of laser configurations that can be relevant for future
planned experiments aiming to detect quantum vacuum dynamics at ultra-high
electromagnetic field intensities.


title: Imaging the photoevaporating disk and radio jet of GM Aur

abstract:
  Photoevaporation is probably the main agent for gas dispersal during the last
stages of protoplanetary disk evolution. However, the overall mass loss rate in
the photoevaporative wind and its driving mechanism are still not well
understood. Here we report multi-configuration Very Large Array observations at
0.7, 3, and 5 cm towards the transitional disk of GM Aur. Our radio continuum
observations allow us to image and spatially resolve, for the first time, the
three main components at work in this stage of the disk evolution: the disk of
dust, the ionized radio jet perpendicular to it, and the photoevaporative wind
arising from the disk. The mass loss rate inferred from the flux density of the
radio jet is consistent with the ratio between ejection and accretion rates
found in younger objects, suggesting that transitional disks can power
collimated ejections of material apparently following the same physical
mechanisms as much younger protostars. Our results indicate that extreme-UV
(EUV) radiation is the main ionizing mechanism of the photoevaporative wind
traced by the free-free emission. The required low EUV photon luminosity of
$\sim6\times10^{40}$ s$^{-1}$ would produce a photoevaporation rate of only
$\dot{M}_{\rm w,EUV}\simeq1.3\times10^{-10}~M_{\odot}$ yr$^{-1}$. Therefore,
other mechanisms are required to disperse the disk in the timescale imposed by
observations.


title: Arrival Times of Gravitational Radiation Peaks for Binary Inspiral

abstract:
  Modeling of gravitational waves (GWs) from binary black hole inspiral brings
together early post-Newtonian waveforms and late quasinormal ringing waveforms.
Attempts to bridge the two limits without recourse to numerical relativity
involve predicting the time of the peak GW amplitude. This prediction will
require solving the question of why the peak of the "source," i.e., the peak of
the binary angular velocity, does not correspond to the peak of the GW
amplitude. We show here that this offset can be understood as due to the
existence two distinct components of the radiation: the "direct" radiation
analogous to that in flat spacetime, and "scattered" radiation associated with
curved spacetime. The time dependence of these two components, and of their
relative phases determines the location of the peak amplitude. We use a highly
simplified model to clarify the twocomponent nature of the source, then
demonstrate that the explanation is valid also for an extreme mass ratio binary
inspiral.


title: Probing the nodal structure of Landau level wave functions in real space

abstract:
  The inversion layer of p-InSb(110) obtained by Cs adsorption of 1.8 % of a
monolayer is used to probe the Landau level wave functions within smooth
potential valleys by scanning tunnelling spectroscopy at 14 T. The nodal
structure becomes apparent as a double peak structure of each spin polarized
first Landau level, while the zeroth Landau level exhibits a single peak per
spin level only. The real space data show single rings of the valley-confined
drift states for the zeroth Landau level and double rings for the first Landau
level. The result is reproduced by a recursive Green's function algorithm using
the potential landscape obtained experimentally. We show that the result is
generic by comparing the local density of states from the Green's function
algorithm with results from a well controlled analytic model based on the
guiding center approach.


title:
Fifty Shades of Ratings: How to Benefit from a Negative Feedback in
  Top-N Recommendations Tasks

abstract:
  Conventional collaborative filtering techniques treat a top-n recommendations
problem as a task of generating a list of the most relevant items. This
formulation, however, disregards an opposite - avoiding recommendations with
completely irrelevant items. Due to that bias, standard algorithms, as well as
commonly used evaluation metrics, become insensitive to negative feedback. In
order to resolve this problem we propose to treat user feedback as a
categorical variable and model it with users and items in a ternary way. We
employ a third-order tensor factorization technique and implement a higher
order folding-in method to support online recommendations. The method is
equally sensitive to entire spectrum of user ratings and is able to accurately
predict relevant items even from a negative only feedback. Our method may
partially eliminate the need for complicated rating elicitation process as it
provides means for personalized recommendations from the very beginning of an
interaction with a recommender system. We also propose a modification of
standard metrics which helps to reveal unwanted biases and account for
sensitivity to a negative feedback. Our model achieves state-of-the-art quality
in standard recommendation tasks while significantly outperforming other
methods in the cold-start "no-positive-feedback" scenarios.


title:
Improving Viterbi is Hard: Better Runtimes Imply Faster Clique
  Algorithms

abstract:
  The classic algorithm of Viterbi computes the most likely path in a Hidden
Markov Model (HMM) that results in a given sequence of observations. It runs in
time $O(Tn^2)$ given a sequence of $T$ observations from a HMM with $n$ states.
Despite significant interest in the problem and prolonged effort by different
communities, no known algorithm achieves more than a polylogarithmic speedup.
  In this paper, we explain this difficulty by providing matching conditional
lower bounds. We show that the Viterbi algorithm runtime is optimal up to
subpolynomial factors even when the number of distinct observations is small.
Our lower bounds are based on assumptions that the best known algorithms for
the All-Pairs Shortest Paths problem (APSP) and for the Max-Weight $k$-Clique
problem in edge-weighted graphs are essentially tight.
  Finally, using a recent algorithm by Green Larsen and Williams for online
Boolean matrix-vector multiplication, we get a $2^{\Omega(\sqrt {\log n})}$
speedup for the Viterbi algorithm when there are few distinct transition
probabilities in the HMM.


title: Mixed symmetry Wilson-loop interactions in the worldline formalism

abstract:
  Using the worldline formalism of the Dirac field with a non-Abelian gauge
symmetry we show how to describe the matter field transforming in an arbitrary
representation of the gauge group. Colour degrees of freedom are carried on the
worldline by auxiliary fields, responsible for providing path ordering and the
Wilson-loop coupling. The Hilbert space of these fields is reducible but we
make use of recent work in order to project onto a single, arbitrary,
irreducible representation. By functionally quantising the resulting theory we
show that this procedure correctly generates the Wilson-loop interaction
between the gauge field and the matter field taken to transform in a chosen
representation. This work has direct application to physical observables such
as scattering amplitudes in the presence of such a matter multiplet and lifts
the restriction on the type of matter that has previously featured in worldline
calculations.


title: Unstable loci in flag varieties and variation of quotients

abstract:
  We consider the action of a semisimple subgroup $\hat G$ of a semisimple
complex group $G$ on the flag variety $X=G/B$, and the linearizations of this
action by line bundles $\mathcal L$ on $X$. The main result is an explicit
description of the associated unstable locus in dependence of $\mathcal L$, as
well as a combinatorial formula for its (co)dimension. We observe that the
codimension is equal to 1 on the regular boundary of the $\hat G$-ample cone,
and grows towards the interior in steps by 1, in a way that the line bundles
with unstable locus of codimension $q$ form a convex polyhedral cone. We also
give a recursive algorithm for determining all GIT-classes in the $\hat
G$-ample cone of $X$.
  As an application, we give conditions ensuring the existence of GIT-classes
$C$ with an unstable locus of codimension at least two and which moreover yield
geometric GIT quotients. Such quotients $Y_C$ reflect global information on
$\hat G$-invariants. They are always Mori dream spaces, and the Mori chambers
of the pseudoeffective cone $\overline{{\rm Eff}}(Y_C)$ correspond to the
GIT-chambers of the $\hat G$-ample cone of $X$. Moreover, all rational
contractions $f: Y_{C} --\to Y'$ to normal projective varieties $Y'$ are
induced by GIT from linearizations of the action of $\hat G$ on $X$. In
particular, this is shown to hold for a diagonal embedding $\hat G
\hookrightarrow (\hat G)^k$, with sufficiently large $k$.


title: Layerwise computability and image randomness

abstract:
  Algorithmic randomness theory starts with a notion of an individual random
object. To be reasonable, this notion should have some natural properties; in
particular, an object should be random with respect to image distribution if
and only if it has a random preimage. This result (for computable distributions
and mappings, and Martin-L\"of randomness) was known for a long time
(folklore); in this paper we prove its natural generalization for layerwise
computable mappings, and discuss the related quantitative results.


title: Circuit partitions and signed interlacement in 4-regular graphs

abstract:
  Let $F$ be a 4-regular graph. Each circuit partition $P$ of $F$ has a
corresponding touch-graph $Tch(P)$; the circuits in $P$ correspond to vertices
of $Tch(P)$, and the vertices of $F$ correspond to edges of $Tch(P)$. We
discuss the connection between modified versions of the interlacement matrix of
an Euler system of $F$ and the cycle space of $Tch(P)$, over $GF(2)$ and
$\mathbb{R}$.


title: Fundamental limits for cooling of linear quantum refrigerators

abstract:
  We study the asymptotic dynamics of arbitrary linear quantum open systems
which are periodically driven while coupled with generic bosonic reservoirs. We
obtain exact results for the heat flowing into the network, which are valid
beyond the usual weak coupling or Markovian approximations. We prove the
validity of the dynamical third law of thermodynamics (Nernst unattainability
principle), showing that the ultimate limit for cooling is imposed by a
fundamental heating mechanism which becomes dominant at low temperatures: the
non resonant creation of pairs of excitations in the reservoirs induced by the
driving field. This quantum effect, which is missed in the weak coupling
approximation, restores the unattainability principle whose validity was
recently challenged.


title: Saturation and geometrical scaling in small systems

abstract:
  Saturation and geometrical scaling (GS) of gluon distributions are a
consequence of the non-linear evolution equations of QCD. We argue that in pp
GS holds for the inelastic cross-section rather than for the multiplicity
distributions. We also discuss possible fluctuations of the proton saturation
scale in pA collisions at the LHC.


title: Eternal Picaria

abstract:
  Picaria is a traditional board game, played by the Zuni tribe of the American
Southwest and other parts of the world, such as a rural Southwest region in
Sweden. It is related to the popular children's game of Tic-tac-toe, but the 2
players have only 3 stones each, and in the second phase of the game, pieces
are slided, along specified move edges, in attempts to create the
three-in-a-row. We provide a rigorous solution, and prove that the game is a
draw; moreover our solution gives insights to strategies that players can use.


title: Protostring Scattering Amplitudes

abstract:
  We calculate some tree level scattering amplitudes for a generalization of
the protostring, which is a novel string model implied by the simplest string
bit models. These bit models produce a lightcone worldsheet which supports $s$
integer moded Grassmann fields. In the generalization we supplement this
Grassmann worldsheet system with $d=24-s$ transverse coordinate worldsheet
fields. The protostring corresponds to $s=24$ and the bosonic string to $s=0$.
The interaction vertex is a simple overlap with no operator insertions at the
break/join point. Assuming that $s$ is even we calculate the multi-string
scattering amplitudes by bosonizing the Grassmann fields, each pair equivalent
to one compactified bosonic field, and applying Mandelstam's interacting string
formalism to a system of $s/2$ compactified and $d$ uncompactified bosonic
worldsheet fields. We obtain all amplitudes for open strings with no oscillator
excitations and for closed strings with no oscillator excitations and zero
winding number. We then study in detail some simple special cases. Multi-string
processes with maximal helicity violation have much simplified amplitudes. We
also specialize to general four string amplitudes and discuss their high energy
behavior. Most of these models are not covariant under the full Lorentz group
$O(d+1,1)$. The exceptions are the bosonic string whose Lorentz group is
$O(25,1)$ and the protostring whose Lorentz group is $O(1,1)$. The models in
between only enjoy an $O(1,1)\times O(d)$ spacetime symmetry.


title:
Criticality-Enhanced Magnetocaloric Effect in Quantum Spin Chain
  Material Copper Nitrate

abstract:
  Low-dimensional quantum magnets, due to the existence of abundant exotic
quantum phases therein and experimental feasibilities in laboratories,
continues intriguing people in condensed matter physics. In this work, a
comprehensive study of Cu(NO$_3$)$_2$ $\cdot$ 2.5H$_2$O (copper nitrate
hemipentahydrate, CN), a spin chain material, is performed with multi-technique
approach including thermal tensor network (TTN) simulations, first-principles
calculations, as well as magnetization measurements in experiments. Employing a
cutting-edge TTN method developed in the present work, we determine the
couplings $J=5.13$ K, $\alpha=0.23(1)$ and Land\'e factors
$g_{\parallel}=2.31$, $g_{\perp}=2.14$ in an alternating Heisenberg
antiferromagnetic chain model, with which one can fit strikingly well the
magnetothermodynamic properties. Part of the fitted experimental data are
measured on the single-crystal CN specimens synthesized by us. Based on
first-principles calculations, we reveal explicitly the spin chain scenario in
CN by displaying the calculated electron density distributions, from which the
distinct superexchange paths are visualized. On top of that, we investigated
the magnetocaloric effect (MCE) in CN by calculating its isentropes and
magnetic Gr\"ueisen parameter (GP). Prominent quantum-criticality-enhanced MCE
was uncovered, the TTN simulations are in good agreements with measured
isentropic lines in the sub-Kelvin region. We propose that CN is potentially a
very promising quantum critical coolant, due to the remarkably enhanced MCE
near both critical fields of moderate strengths as 2.87 and 4.08 T,
respectively.


title:
The upGREAT 1.9 THz multi-pixel high resolution spectrometer for the
  SOFIA Observatory

abstract:
  We present a new multi-pixel high resolution (R >10^7) spectrometer for the
Stratospheric Observatory for Far-Infrared Astronomy (SOFIA). The receiver uses
2 x 7-pixel subarrays in orthogonal polarization, each in an hexagonal array
around a central pixel. We present the first results for this new instrument
after commissioning campaigns in May and December 2015 and after science
observations performed in May 2016 . The receiver is designed to ultimately
cover the full 1.8-2.5 THz frequency range but in its first implementation, the
observing range was limited to observations of the [CII] line at 1.9 THz in
2015 and extended to 1.83-2.07 THz in 2016. The instrument sensitivities are
state-of-the-art and the first scientific observations performed shortly after
the commissioning confirm that the time efficiency for large scale imaging is
improved by more than an order of magnitude as compared to single pixel
receivers. An example of large scale mapping around the Horsehead Nebula is
presented here illustrating this improvement. The array has been added to
SOFIA's instrument suite already for ongoing observing cycle 4.


title: Conditional probabilities and van Lambalgen theorem revisited

abstract:
  The definition of conditional probability in case of continuous distributions
was an important step in the development of mathematical theory of
probabilities. How can we define this notion in algorithmic probability theory?
In this survey we discuss the developments in this direction trying to explain
what are the difficulties and what can be done to avoid them. Almost all the
results discussed in this paper have been published (and we provide the
references), but we tried to put them into perspective and to explain the
proofs in a more intuitive way. We assume that the reader is familiar with
basic notions of measure theory and algorithmic randomness.


title:
Configuration interaction in symmetry-conserving covariant density
  functional theory

abstract:
  A new method to calculate spectroscopic properties of deformed nuclei is
proposed: configuration interaction on top of projected density functional
theory (CI-PDFT). The general concept of this approach is discussed in the
framework of covariant density functional theory and its validity is
illustrated in an application to the yrast band of the nucleus Cr-54. It is
found that the experimentally observed excitation energies for the yrast band
in Cr-54 can be well reproduced. In contrast to conventional shell-model
calculations, there is no core and only a relatively small number of
configurations is sufficient for a satisfying description. No new parameters
are necessary, because the effective interaction is derived from an universal
density functional given in the literature.


title: Contractivity properties of a quantum diffusion semigroup

abstract:
  We consider a quantum generalization of the classical heat equation, and
study contractivity properties of its associated semigroup. We prove a Nash
inequality and a logarithmic Sobolev inequality. The former leads to an
ultracontractivity result. This in turn implies that the largest eigenvalue and
the purity of a state with positive Wigner function, evolving under the action
of the semigroup, decrease at least inverse polynomially in time, while its
entropy increases at least logarithmically in time.


title: A real-time analysis of rock fragmentation using UAV technology

abstract:
  Accurate measurement of blast-induced rock fragmentation is of great
importance for many mining operations. The post-blast rock size distribution
can significantly influence the efficiency of all the downstream mining and
comminution processes. Image analysis methods are one of the most common
methods used to measure rock fragment size distribution in mines regardless of
criticism for lack of accuracy to measure fine particles and other perceived
deficiencies. The current practice of collecting rock fragmentation data for
image analysis is highly manual and provides data with low temporal and spatial
resolution. Using UAVs for collecting images of rock fragments can not only
improve the quality of the image data but also automate the data collection
process. Ultimately, real-time acquisition of high temporal- and
spatial-resolution data based on UAV technology will provide a broad range of
opportunities for both improving blast design without interrupting the
production process and reducing the cost of the human operator. This paper
presents the results of a series of laboratory-scale rock fragment measurements
using a quadrotor UAV equipped with a camera. The goal of this work is to
highlight the benefits of aerial fragmentation analysis in terms of both
prediction accuracy and time effort. A pile of rock fragments with different
fragment sizes was placed in a lab that is equipped with a motion capture
camera system for precise UAV localization and control. Such an environment
presents optimal conditions for UAV flight and thus, is well-suited for
conducting proof-of-concept experiments before testing them in large-scale
field experiments. The pile was photographed by a camera attached to the UAV,
and the particle size distribution curves were generated in almost real-time.
The pile was also manually photographed and the results of the manual method
were compared to the UAV method.


title: Sigma-Adequate Link Diagrams and the Tutte Polynomial

abstract:
  In this paper, we characterize the sigma-adequacy of a link diagram in two
ways: in terms of a certain edge subset of its Tait graph and in terms of a
certain product of Tutte polynomials. Furthermore, we show that the symmetrized
Tutte polynomial of the Tait graph of a link diagram can be written as a sum of
these products of Tutte polynomials, where the sum is over the sigma-adequate
states of the given link diagram. Using this state sum, we show that the number
of sigma-adequate states of a link diagram is bounded above by the number of
spanning trees in its associated Tait graph. By combining results, we give a
method to find all of the sigma-adequate states of a link diagram. Finally, we
give necessary and sufficient conditions for a link diagram to be
sigma-adequate and sigma-homogeneous (also called homogeneously adequate) with
respect to a given state.


title: Finite Element Integration with Quadrature on the GPU

abstract:
  We present a novel, quadrature-based finite element integration method for
low-order elements on GPUs, using a pattern we call \textit{thread
transposition} to avoid reductions while vectorizing aggressively. On the
NVIDIA GTX580, which has a nominal single precision peak flop rate of 1.5 TF/s
and a memory bandwidth of 192 GB/s, we achieve close to 300 GF/s for element
integration on first-order discretization of the Laplacian operator with
variable coefficients in two dimensions, and over 400 GF/s in three dimensions.
From our performance model we find that this corresponds to 90\% of our
measured achievable bandwidth peak of 310 GF/s. Further experimental results
also match the predicted performance when used with double precision (120 GF/s
in two dimensions, 150 GF/s in three dimensions). Results obtained for the
linear elasticity equations (220 GF/s and 70 GF/s in two dimensions, 180 GF/s
and 60 GF/s in three dimensions) also demonstrate the applicability of our
method to vector-valued partial differential equations.


title:
On an analogue of the Markov equation for exceptional collections of
  length 4

abstract:
  We classify the solutions to a system of equations, introduced by Bondal,
which encode numerical constraints on full exceptional collections of length 4
on surfaces. The corresponding result for length 3 is well-known and states
that there is essentially one solution, namely the one corresponding to the
standard exceptional collection on the surface $\mathbb{P}^2$. This was
essentially proven by Markov in 1879. It turns out that in the length 4 case,
there is one special solution which corresponds to
$\mathbb{P}^1\times\mathbb{P}^1$ whereas the other solutions are obtained from
$\mathbb{P}^2$ by a procedure we call numerical blowup. Among these solutions,
three are of geometric origin ($\mathbb{P}^2\cup \{\bullet\}$,
$\mathbb{P}^1\times\mathbb{P}^1$ and the ordinary blowup of $\mathbb{P}^2$ at a
point). The other solutions are parametrized by $\mathbb{N}$ and very likely do
not correspond to commutative surfaces. However they can be realized as
noncommutative surfaces, as was recently shown by Dennis Presotto and the first
author.