title:
Scale invariance and scaling law of Thomson backscatter spectra by
  electron moving in laser-magnetic resonance regime

abstract:
  The Thomson scattering spectra by an electron moving in the laser-magnetic
resonance acceleration regime are computed numerically and analytically. The
dependence of fundamental frequency on the laser intensity and magnetic
resonance parameter is examined carefully. By calculating the emission of a
single electron in a circularly polarized plane-wave laser field and constant
external magnetic field, the scale invariance of the radiation spectra is
evident in terms of harmonic orders. The scaling law of backscattered spectra
are exhibited remarkably for the laser intensity as well for the initial axial
momentum of the electron when the cyclotron frequency of the electron
approaches the laser frequency. The results indicate that the magnetic
resonance parameter plays an important role on the strength of emission. And
the rich features of scattering spectra found may be applicable to the
radiation source tunability.


title:
Addendum to `Algebraic equations for the exceptional eigenspectrum of
  the generalized Rabi model'

abstract:
  In our recent paper (Li and Batchelor J. Phys. A: Math. Theor. 48, 454005
(2015)) we obtained exceptional points in the eigenspectrum of the generalized
Rabi model in terms of a set of algebraic equations. We also gave a proof for
the number of roots of the constraint polynomials defining these exceptional
solutions as a function of the system parameters and discussed the number of
crossing points in the eigenspectrum. This approach however, only covered a
subset of all exceptional points in the eigenspectrum. In this addendum, we
clarify the distinction between the exceptional parts of the eigenspectrum for
this model and discuss the subset of exceptional points not determined in our
paper.


title:
A scheme for quantum teleportation between discrete and continuous
  encodings of an optical qubit

abstract:
  Transfer of quantum information between physical systems of a different
nature is a central matter in quantum technologies. Particularly challenging is
the transfer between discrete- and continuous degrees of freedom of various
harmonic oscillator systems. Here we implement a protocol for teleporting a
continuous-variable optical qubit, encoded by means of coherent states, onto a
discrete-variable, single-rail qubit - a superposition of the vacuum- and
single-photon optical states - via a hybrid entangled resource. We test our
protocol on coherent states of different phases and obtain the teleported qubit
with a fidelity of $0.83\pm0.04$. We also find that the phase of the resulting
qubit varies consistently with that of the input, having a standard deviation
of $3.8^\circ$ from the target value. Our work opens up the way to wide
application of quantum information processing techniques where discrete- and
continuous-variable encodings are combined within the same optical circuit.


title: Spherical Isentropic Protostars in General Relativity

abstract:
  In the process of protostar formation, astrophysical gas clouds undergo
thermodynamically irreversible processes and emit heat and radiation to their
surroundings. Due the emission of this energy one can envision an idealized
situation in which the gas entropy remains nearly constant. In this setting, we
derive in this paper interior solutions to the Einstein equations of General
Relativity for spheres which consist of isentropic gas. To accomplish this
objective we derive a single equation for the cumulative mass distribution in
the protostar. From a solution of this equation one can infer readily the
coefficients of the metric tensor. In this paper we present analytic and
numerical solutions for the structure of the isentropic self-gravitating gas.
In particular we look for solutions in which the mass distribution indicates
the presence of shells, a possible precursor to solar system formation. Another
possible physical motivation for this research comes from the observation that
gamma ray bursts are accompanied by the ejection of large amounts of
thermodynamically active gas at relativistic velocities. Under these conditions
it is natural to use the equations of general relativity to inquire about the
structure of the ejected mass.


title: Slope meets Lasso: improved oracle bounds and optimality

abstract:
  We show that two polynomial time methods, a Lasso estimator with adaptively
chosen tuning parameter and a Slope estimator, adaptively achieve the exact
minimax prediction and $\ell_2$ estimation rate $(s/n)\log (p/s)$ in
high-dimensional linear regression on the class of $s$-sparse target vectors in
$\mathbb R^p$. This is done under the Restricted Eigenvalue (RE) condition for
the Lasso and under a slightly more constraining assumption on the design for
the Slope. The main results have the form of sharp oracle inequalities
accounting for the model misspecification error. The minimax optimal bounds are
also obtained for the $\ell_q$ estimation errors with $1\le q\le 2$ when the
model is well-specified. The results are non-asymptotic, and hold both in
probability and in expectation. The assumptions that we impose on the design
are satisfied with high probability for a large class of random matrices with
independent and possibly anisotropically distributed rows. We give a
comparative analysis of conditions, under which oracle bounds for the Lasso and
Slope estimators can be obtained. In particular, we show that several known
conditions, such as the RE condition and the sparse eigenvalue condition are
equivalent if the $\ell_2$-norms of regressors are uniformly bounded.


title: On the nature of the Mott transition in multiorbital systems

abstract:
  We analyze the nature of Mott metal-insulator transition in multiorbital
systems using dynamical mean-field theory (DMFT). The auxiliary multiorbital
quantum impurity problem is solved using continuous time quantum Monte Carlo
(CTQMC) and the rotationally invariant slave-boson (RISB) mean field
approximation. We focus our analysis on the Kanamori Hamiltonian and find that
there are two markedly different regimes determined by the nature of the lowest
energy excitations of the atomic Hamiltonian. The RISB results at $T\to0$
suggest the following rule of thumb for the order of the transition at zero
temperature: a second order transition is to be expected if the lowest lying
excitations of the atomic Hamiltonian are charge excitations, while the
transition tends to be first order if the lowest lying excitations are in the
same charge sector as the atomic ground state. At finite temperatures the
transition is first order and its strength, as measured e.g. by the jump in the
quasiparticle weight at the transition, is stronger in the parameter regime
where the RISB method predicts a first order transition at zero temperature.
Interestingly, these results seem to apply to a wide variety of models and
parameter regimes.


title: Quantum metrology beyond the Quantum Cram\'er-Rao theorem

abstract:
  A usual assumption in quantum estimation is that the unknown parameter labels
the possible states of the system, while it influences neither the sample space
of outcomes nor the measurement aimed at extracting information on the
parameter itself. This assumption is crucial to prove the quantum Cram\'er-Rao
theorem and to introduce the quantum Fisher information as an upper bound to
the Fisher information of any possible measurement. However, there are relevant
estimation problems where this assumption does not hold and an alternative
approach should be developed to find the genuine ultimate bound to precision of
quantum measurements. We investigate physical situations where there is an
intrinsic dependence of the measurement strategy on the parameter and find that
quantum-enhanced measurements may be more precise than previously thought.


title: Asymptotic Limit of Continuous Dual Hahn Polynomial

abstract:
  Using Darboux method, we obtain an asymptotic limit for Continuous Dual Hahn
Polynomial.The basic concept is to construct a comparison function which is the
singular part of the generating function; then expand the comparison function.
With little simplification and modification,the asymptotic limit is achieved.


title:
Truncated Wigner function theory of coherent Ising machines based on
  degenerate optical parametric oscillator network

abstract:
  We present the quantum theory of coherent Ising machines based on networks of
degenerate optical parametric oscillators (DOPOs).
  In a simple model consisting of two coupled DOPOs, both positive-$P$
representation and truncated Wigner representation predict quantum correlation
and inseparability between the two DOPOs in spite of the open-dissipative
nature of the system.
  Here, we apply the truncated Wigner representation method to coherent Ising
machines with thermal, vacuum, and squeezed reservoir fields. We find that the
probability of finding the ground state of a one-dimensional Ising model
increases substantially as a result of reducing excess thermal noise and
squeezing the incident vacuum fluctuation on the out-coupling port.


title: Twistor interpretation of slice regular functions

abstract:
  Given a slice regular function $f:\Omega\subset\mathbb{H}\to \mathbb{H}$,
with $\Omega\cap\mathbb{R}\neq \emptyset$, it is possible to lift it to a
surface in the twistor space $\mathbb{CP}^{3}$ of $\mathbb{S}^4\simeq
\mathbb{H}\cup \{\infty\}$ (see~\cite{gensalsto}). In this paper we show that
the same result is true if one removes the hypothesis $\Omega\cap\mathbb{R}\neq
\emptyset$ on the domain of the function $f$. Moreover we find that if a
surface $\mathcal{S}\subset\mathbb{CP}^{3}$ contains the image of the twistor
lift of a slice regular function, then $\mathcal{S}$ has to be ruled by lines.
Starting from these results we find all the projective classes of algebraic
surfaces up to degree 3 in $\mathbb{CP}^{3}$ that contain the lift of a slice
regular function. In addition we extend and further explore the so-called
twistor transform, that is a curve in $\mathbb{G}r_2(\mathbb{C}^4)$ which,
given a slice regular function, returns the arrangement of lines whose lift
carries on. With the explicit expression of the twistor lift and of the twistor
transform of a slice regular function we exhibit the set of slice regular
functions whose twistor transform describes a rational line inside
$\mathbb{G}r_2(\mathbb{C}^4)$, showing the role of slice regular functions not
defined on $\mathbb{R}$. At the end we study the twistor lift of a particular
slice regular function not defined over the reals. This example shows the
effectiveness of our approach and opens some questions.


title:
Generalized Finite Element Systems for smooth differential forms and
  Stokes problem

abstract:
  We provide both a general framework for discretizing de Rham sequences of
differential forms of high regularity, and some examples of finite element
spaces that fit in the framework. The general framework is an extension of the
previously introduced notion of Finite Element Systems, and the examples
include conforming mixed finite elements for Stokes' equation. In dimension 2
we detail four low order finite element complexes and one infinite family of
highorder finite element complexes. In dimension 3 we define one low order
complex, which may be branched into Whitney forms at a chosen index. Stokes
pairs with continuous or discontinuous pressure are provided in arbitrary
dimension. The finite element spaces all consist of composite polynomials. The
framework guarantees some nice properties of the spaces, in particular the
existence of commuting interpolators. It also shows that some of the examples
are minimal spaces.


title:
Howe-Moore type theorems for quantum groups and rigid C*-tensor
  categories

abstract:
  We formulate and study Howe-Moore type properties in the setting of quantum
groups and in the setting of rigid $C^{\ast}$-tensor categories. We say that a
rigid $C^{\ast}$-tensor category $\mathcal{C}$ has the Howe-Moore property if
every completely positive multiplier on $\mathcal{C}$ has a limit at infinity.
We prove that the representation categories of $q$-deformations of connected
compact simple Lie groups with trivial center satisfy the Howe-Moore property.
As an immediate consequence, we deduce the Howe-Moore property for
Temperley-Lieb-Jones standard invariants with principal graph $A_{\infty}$.
These results form a special case of a more general result on the convergence
of completely bounded multipliers on the aforementioned categories. This more
general result also holds for the representation categories of the free
orthogonal quantum groups and for the Kazhdan-Wenzl categories. Additionally,
in the specific case of the quantum groups $\mathrm{SU}_q(N)$, we are able,
using a result of the first-named author, to give an explicit characterization
of the central states on the quantum coordinate algebra of $\mathrm{SU}_q(N)$,
which coincide with the completely positive multipliers on the representation
category of $\mathrm{SU}_q(N)$.


title:
Statistical properties of the one-dimensional Burridge-Knopoff model of
  earthquakes obeying the rate and state dependent friction law

abstract:
  Statistical properties of the one-dimensional spring-block (Burridge-Knopoff)
model of earthquakes obeying the rate and state dependent friction law are
studied by extensive computer simulations. The quantities computed include the
magnitude distribution, the rupture-length distribution, the mainshock
recurrence-time distribution, the seismic time correlations before and after
the mainshock, the mean slip amount, and the mean stress drop at the mainshock,
etc. Events of the model can be classified into two distinct categories. One
tends to be unilateral with its epicenter located at the rim of the rupture
zone of the preceding event, while the other tends to be bilateral with
enhanced "characteristic" features resembling the so-called "asperity". For
both types events, the distribution of the rupture length $L_r$ exhibits an
exponential behavior at larger sizes, $\approx \exp[-L_r/L_0]$ with a
characteristic "seismic correlation length" $L_0$. The mean slip as well as the
mean stress drop tends to be rupture-length independent for larger events. The
continuum limit of the model is examined, where the model is found to exhibit
pronounced characteristic features. In the continuum limit, the characteristic
rupture length $L_0$ is estimated to be $\sim $100 [km]. This means that, even
in a hypothetical homogenous infinite fault, events cannot be indefinitely
large in the exponential sense, the upper limit being of order $\sim 10^3$
kilometers. Implications to real seismicity are discussed.


title: Symmetric function kernels and sweeping of measures

abstract:
  This is a potential theoretic study of balayage (sweeping) of a positive
Radon measure on a locally compact (Hausdorff) space onto a closed, or more
generally a quasiclosed set (that is, a set which can be approximated in outer
capacity by closed sets). The setting is that of potentials with respect to a
suitable positive symmetric function kernel. Following Choquet (1959) we
consider energy capacity, not as a set function, but as a functional, acting on
positive numerical functions. The finiteness of the upper capacity of the
potential restricted to the set in question is sufficient for the possibility
of the sweeping.


title: Three-lane and multi-lane signatures of planets in planetesimal disks

abstract:
  In massive numerical experiments we show that a planet embedded in a
planetesimal disk induces a characteristic multi-lane "planetosignature"
representing a pattern of several stellar-centric rings. If the planet's mass
is large enough, the multi-lane signature degenerates to a three-lane one: then
it consists of three rings, one bright coorbital with the planet, and two dark
gaps in the radial distribution of the particles. The gaps correspond to
orbital resonances 2:1 and 1:2 with the planet. This theoretical prediction may
explain recent ALMA observations of the disk of HL Tau.


title:
A comparison between grid and particle methods on the small-scale dynamo
  in magnetised supersonic turbulence

abstract:
  We perform a comparison between the smoothed particle magnetohydrodynamics
(SPMHD) code, Phantom, and the Eulerian grid-based code, Flash, on the
small-scale turbulent dynamo in driven, Mach 10 turbulence. We show, for the
first time, that the exponential growth and saturation of an initially weak
magnetic field via the small-scale dynamo can be successfully reproduced with
SPMHD. The two codes agree on the behaviour of the magnetic energy spectra, the
saturation level of magnetic energy, and the distribution of magnetic field
strengths during the growth and saturation phases. The main difference is that
the dynamo growth rate, and its dependence on resolution, differs between the
codes, caused by differences in the numerical dissipation and shock capturing
schemes leading to differences in the effective Prandtl number in Phantom and
Flash.


title:
A unified explanation for dark matter and electroweak baryogenesis with
  direct detection and gravitational wave signatures

abstract:
  A minimal extension of the Standard Model that provides both a dark matter
candidate and a strong first-order electroweak phase transition (EWPT) consists
of two additional Lorentz and gauge singlets. In this paper we work out a
composite Higgs version of this scenario, based on the coset $SO(7)/SO(6)$. We
show that by embedding the elementary fermions in appropriate representations
of $SO(7)$, all dominant interactions are described by only three free
effective parameters. Within the model dependencies of the embedding, the
theory predicts one of the singlets to be stable and responsible for the
observed dark matter abundance. At the same time, the second singlet introduces
new $CP$-violation phases and triggers a strong first-order EWPT, making
electroweak baryogenesis feasible. It turns out that this scenario does not
conflict with current observations and it is promising for solving the dark
matter and baryon asymmetry puzzles. The tight predictions of the model will be
accessible at the forthcoming dark matter direct detection and gravitational
wave experiments.


title: Near-Optimal Fingerprinting with Constraints

abstract:
  Several recent studies have demonstrated that people show large behavioural
uniqueness. This has serious privacy implications as most individuals become
increasingly re-identifiable in large datasets or can be tracked while they are
browsing the web using only a couple of their attributes, called as their
fingerprints. Often, the success of these attacks depend on explicit
constraints on the number of attributes learnable about individuals, i.e., the
size of their fingerprints. These constraints can be budget as well as
technical constraints imposed by the data holder. For instance, Apple restricts
the number of applications that can be called by another application on iOS in
order to mitigate the potential privacy threats of leaking the list of
installed applications on a device. In this work, we address the problem of
identifying the attributes (e.g., smartphone applications) that can serve as a
fingerprint of users given constraints on the size of the fingerprint. We give
the best fingerprinting algorithms in general, and evaluate their effectiveness
on several real-world datasets. Our results show that current privacy guards
limiting the number of attributes that can be queried about individuals is
insufficient to mitigate their potential privacy risks in many practical cases.


title: Combinatorial methods for the spectral p-norm of hypermatrices

abstract:
  The spectral $p$-norm of $r$-matrices generalizes the spectral $2$-norm of
$2$-matrices. In 1911 Schur gave an upper bound on the spectral $2$-norm of
$2$-matrices, which was extended in 1934 by Hardy, Littlewood, and Polya to
$r$-matrices. Recently, Kolotilina, and independently the author, strengthened
Schur's bound for $2$-matrices. The main result of this paper extends the
latter result to $r$-matrices, thereby improving the result of Hardy,
Littlewood, and Polya.
  The proof is based on combinatorial concepts like $r$-partite $r$-matrix and
symmetrant of a matrix, which appear to be instrumental in the study of the
spectral $p$-norm in general. Thus, another application shows that the spectral
$p$-norm and the $p$-spectral radius of a symmetric nonnegative $r$-matrix are
equal whenever $p\geq r$. This result contributes to a classical area of
analysis, initiated by Mazur and Orlicz around 1930.
  Additionally, a number of bounds are given on the $p$-spectral radius and the
spectral $p$-norm of $r$-matrices and $r$-graphs.


title: Left-Right Entanglement Entropy of Dp-branes

abstract:
  We compute the left-right entanglement entropy for Dp-branes in string
theory. We employ the CFT approach to string theory Dp-branes, in particular,
its presentation as coherent states of the closed string sector. The
entanglement entropy is computed as the von Neumann entropy for a density
matrix resulting from integration over the left-moving degrees of freedom. We
discuss various crucial ambiguities related to sums over spin structures and
argue that different choices capture different physics; however, we advance a
themodynamic argument that seems to favor a particular choice of replica. We
also consider Dp branes on compact dimensions and verify that the effects of
T-duality act covariantly on the Dp brane entanglement entropy. We find that
generically the left-right entanglement entropy provides a suitable
generalization of boundary entropy and of the D-brane tension.


title:
Structural break detection method based on the Adaptive Regression
  Splines technique

abstract:
  For many real data, long term observation consists of different processes
that coexist or occur one after the other. Those processes very often exhibit
different statistical properties and thus before the further analysis the
observed data should be segmented. This problem one can find in different
applications and therefore new segmentation techniques have been appeared in
the literature during last years. In this paper we propose a new method of time
series segmentation, i.e. extraction from the analysed vector of observations
homogeneous parts with similar behaviour. This method is based on the absolute
deviation about the median of the signal and is an extension of the previously
proposed techniques also based on the simple statistics. In this paper we
introduce the method of structural break point detection which is based on the
Adaptive Regression Splines technique, one of the form of regression analysis.
Moreover we propose also the statistical test which allows testing hypothesis
of behaviour related to different regimes. First, the methodology we apply to
the simulated signals with different distributions in order to show the
effectiveness of the new technique. Next, in the application part we analyse
the real data set that represents the vibration signal from a heavy duty
crusher used in a mineral processing plant.


title:
Silicon Photonics WDM Transceiver with SOA and Semiconductor Mode-Locked
  Laser

abstract:
  We demonstrate a complete Silicon Photonics WDM link relying on a single
section semiconductor mode-locked laser and a single SOA to support up to 12
multiplexed channels with a bit error rate of 1e-12 at serial data rates of 14
Gbps without channel pre-emphasis, equalization or forward error correction.
Individual channels reach error free operation at 25 Gbps and multi-channel
operation at 25 Gbps is shown to be compatible with standard 7% overhead hard
decision forward error correction. Silicon Photonics transmitter and receiver
chips are hybridly integrated with driver and receiver electronics. A detailed
link model is derived and verified. Particular emphasis is placed on accurate
system level modeling of laser RIN, SOA amplified spontaneous emission noise
and receiver noise. The impact of the electrical receiver bandwidth and
non-Gaussian statistics on level dependent amplified spontaneous emission noise
are investigated in detail. The channel count scalability as limited by SOA
saturation is further analyzed taking cross gain modulation and four wave
mixing into account. While semiconductor mode-locked lasers have been
identified as a potential light source for low cost Datacom WDM transceivers
for some time, this is, to the best of our knowledge, the first comprehensive
investigation of the overall link budget in a Silicon Photonics implementation
showing this technology to be a credible contender for low latency datacenter
interconnects.


title:
A basis for the implicit representation of planar rational cubic
  B\'ezier curves

abstract:
  We present an approach to finding the implicit equation of a planar rational
parametric cubic curve, by defining a new basis for the representation. The
basis, which contains only four cubic bivariate polynomials, is defined in
terms of the B\'ezier control points of the curve. An explicit formula for the
coefficients of the implicit curve is given. Moreover, these coefficients lead
to simple expressions which describe aspects of the geometric behaviour of the
curve. In particular, we present an explicit barycentric formula for the
position of the double point, in terms of the B\'ezier control points of the
curve. We also give conditions for when an unwanted singularity occurs in the
region of interest. Special cases in which the method fails, such as when three
of the control points are collinear, or when two points coincide, will be
discussed separately.


title: Angle measures, general rotations, and roulettes in normed planes

abstract:
  In this paper a special group of bijective maps of a normed plane, called the
group of general rotations, is introduced; it contains the isometry group as a
subgroup. The concept of general rotations leads to the notion of flexible
motions of the plane, and to the concept of Minkowskian roulettes. As a nice
consequence of this new approach to motions the validity of a strong analogue
to the Euler-Savary equations for Minkowskian roulettes is proved.


title: An optimal algorithm for the Thresholding Bandit Problem

abstract:
  We study a specific \textit{combinatorial pure exploration stochastic bandit
problem} where the learner aims at finding the set of arms whose means are
above a given threshold, up to a given precision, and \textit{for a fixed time
horizon}. We propose a parameter-free algorithm based on an original heuristic,
and prove that it is optimal for this problem by deriving matching upper and
lower bounds. To the best of our knowledge, this is the first non-trivial pure
exploration setting with \textit{fixed budget} for which optimal strategies are
constructed.


title:
Logarithmic stability in determining the time-dependent zero order
  coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map.
  Application to the determination of a nonlinear term

abstract:
  We give a new stability estimate for the problem of determining the
time-dependent zero order coefficient in a parabolic equation from a partial
parabolic Dirichlet-to-Neumann map. The novelty of our result is that, contrary
to the previous works, we do not need any measurement on the final time. We
also show how this result can be used to establish a stability estimate for the
problem of determining the nonlinear term in a semilinear parabolic equation
from the corresponding "linearized" Dirichlet-to-Neumann map. The key
ingredient in our analysis is a parabolic version of an elliptic Carleman
inequality due to Bukhgeim and Uhlmann. This parabolic Carleman inequality
enters in an essential way in the construction of complex geometric optics
solutions that vanish at a part of the lateral boundary.


title:
Tunable transmission of quantum Hall edge channels with full degeneracy
  lifting in split-gated graphene devices

abstract:
  Charge carriers in the quantum Hall regime propagate via one-dimensional
conducting channels that form along the edges of a two-dimensional electron
gas. Controlling their transmission through a gate-tunable constriction, also
called quantum point contact (QPC), is fundamental for many coherent transport
experiments. However, in graphene, tailoring a QPC with electrostatic gates
remains challenging due to the formation of p-n junctions below gate electrodes
along which electron and hole edge channels co-propagate and mix,
short-circuiting the constriction. Here we show that this electron-hole mixing
is drastically reduced in high mobility boron-nitride/graphene/boron-nitride
van-der-Waals heterostructures thanks to the full degeneracy lifting of the
Landau levels, enabling QPC operation with full channel pinch-off. We
demonstrate gate-tunable selective transmission of quantum Hall edge channels
through the QPC, both in the integer and the fractional quantum Hall regimes.
This gate-control of edge channel propagation in graphene van-der-Waals
heterostructures opens the door to quantum Hall interferometry and electron
quantum optics experiments in the integer and fractional quantum Hall regimes
of graphene.


title: Discrepancy densities for planar and hyperbolic Zero Packing

abstract:
  We study the problem of geometric zero packing, recently introduced by
Hedenmalm. There are two natural densities associated to this problem: the
discrepancy density $\rho_{\mathbb{H}}$, given by $$ \rho_{\mathbb{H}} =
\liminf_{r\to 1^-} \inf_{f} \frac{\int_{\mathbb{D}(0,r)} \left((1-\lvert
z\rvert^2) \lvert f(z)\rvert-1\right)^2 \frac{dA(z)}{1-\lvert z\rvert^2}}
{\int_{\mathbb{D}(0,r)} \frac{dA(z)}{1-\lvert z\rvert^2}} $$ which measures the
discrepancy in optimal approximation of $(1-\lvert z\rvert^2)^{-1}$ with the
modulus of polynomials $f$, and it's relative, the tight discrepancy density
$\rho_{\mathbb{H}}^*$, which will trivially satisfy
$\rho_{\mathbb{H}}\leq\rho_{\mathbb{H}}^*$. These densities have deep
connections to the boundary behaviour of conformal mappings with
$k$-quasiconformal extensions, which can be seen from the Hedenmalm's result
that the universal asymptotic variance $\Sigma^2$ is related to
$\rho_{\mathbb{H}}^*$ by $\Sigma^2=1-\rho_{\mathbb{H}}^*$. Here we prove that
in fact $\rho_{\mathbb{H}}=\rho_{\mathbb{H}}^*$, resolving a conjecture by
Hedenmalm in the positive. The natural planar analogues $\rho_{\mathbb{C}}$ and
$\rho_{\mathbb{C}}^*$ to these densities make contact with work of Abrikosov on
Bose-Einstein condensates. As a second result we prove that also
$\rho_{\mathbb{C}}=\rho_{\mathbb{C}}^*$. The methods are based on Ameur,
Hedenmalm and Makarov's H\"ormander-type $\bar\partial$-estimates with
polynomial growth control. As a consequence we obtain sufficiency results on
the degrees of approximately optimal polynomials.


title: Boosting Question Answering by Deep Entity Recognition

abstract:
  In this paper an open-domain factoid question answering system for Polish,
RAFAEL, is presented. The system goes beyond finding an answering sentence; it
also extracts a single string, corresponding to the required entity. Herein the
focus is placed on different approaches to entity recognition, essential for
retrieving information matching question constraints. Apart from traditional
approach, including named entity recognition (NER) solutions, a novel
technique, called Deep Entity Recognition (DeepER), is introduced and
implemented. It allows a comprehensive search of all forms of entity references
matching a given WordNet synset (e.g. an impressionist), based on a previously
assembled entity library. It has been created by analysing the first sentences
of encyclopaedia entries and disambiguation and redirect pages. DeepER also
provides automatic evaluation, which makes possible numerous experiments,
including over a thousand questions from a quiz TV show answered on the grounds
of Polish Wikipedia. The final results of a manual evaluation on a separate
question set show that the strength of DeepER approach lies in its ability to
answer questions that demand answers beyond the traditional categories of named
entities.


title:
Ground-state properties and elementary excitations of quantum droplets
  in dipolar Bose-Einstein condensates

abstract:
  Recent experiments have revealed the formation of stable droplets in dipolar
Bose-Einstein condensates. This surprising result has been explained by the
stabilization given by quantum fluctuations. We study in detail the properties
of a BEC in the presence of quantum stabilization. The ground-state phase
diagram presents three main regimes: mean-field regime, in which the quantum
correction is perturbative, droplet regime, in which quantum stabilization is
crucial, and a multi-stable regime. In the absence of a multi-stable region,
the condensate undergoes a crossover from the mean-field to the droplet
solution marked by a characteristic growth of the peak density that may be
employed to clearly distinguish quantum stabilization from other stabilization
mechanisms. Interestingly quantum stabilization allows for three-dimensionally
self-bound condensates. We characterized these self-bound solutions, and
discuss their realization in experiments. We conclude with a discussion of the
lowest-lying excitations both for trapped condensates, and for self-bound
solutions.


title: Induced Hyperon-Nucleon-Nucleon Interactions and the Hyperon Puzzle

abstract:
  We present the first ab initio calculations for $p$-shell hypernuclei
including hyperon-nucleon-nucleon (YNN) contributions induced by a Similarity
Renormalization Group transformation of the initial hyperon-nucleon
interaction. The transformation including the YNN terms conserves the spectrum
of the Hamiltonian while drastically improving model-space convergence of the
Importance-Truncated No-Core Shell Model, allowing a precise extraction of
binding and excitation energies. Results using a hyperon-nucleon interaction at
leading order in chiral effective field theory for lower- to mid-$p$-shell
hypernuclei show a good reproduction of experimental excitation energies while
hyperon binding energies are typically overestimated. The induced YNN
contributions are strongly repulsive and we show that they are related to a
decoupling of the $\Sigma$ hyperons from the hypernuclear system, i.e., a
suppression of the $\Lambda$-$\Sigma$ conversion terms in the Hamiltonian. This
is linked to the so-called hyperon puzzle in neutron-star physics and provides
a basic mechanism for the explanation of strong $\Lambda$NN three-baryon
forces.


title: Free energy of singular sticky-sphere clusters

abstract:
  Networks of particles connected by springs model many condensed-matter
systems, from colloids interacting with a short-range potential, to complex
fluids near jamming, to self-assembled lattices, to origami-inspired materials.
Under small thermal fluctuations the vibrational entropy of a ground state is
given by the harmonic approximation if it has no zero-frequency vibrational
modes, yet such singular modes are at the epicenter of many interesting
behaviors in the systems above. We consider a system of $N$ spherical
particles, and directly account for the singularities that arise in the sticky
limit where the pairwise interaction is strong and short ranged. Although the
contribution to the partition function from singular clusters diverges in the
limit, its asymptotic value can be calculated and depends on only two
parameters, characterizing the depth and range of the potential. The result
holds for systems that are second-order rigid, a geometric characterization
that describes all known ground-state (rigid) sticky clusters.
  To illustrate our theory we address the question of emergence: how does
crystalline order arise in large systems when it is strongly disfavored in
small ones? We calculate the partition functions of all known rigid clusters up
to $N\leq 19$, and show the cluster landscape is dominated by hyperstatic
clusters (those with more than $3N-6$ contacts) -- singular and isostatic
clusters are far less frequent, despite their extra vibrational and
configurational entropies. Since the most hyperstatic clusters are close to
fragments of a close-packed lattice, this underlies the emergence of order in
sticky-sphere systems, even those as small as $N=10$.


title: One Dimensional 1H, 2H and 3H

abstract:
  The ground-state properties of one-dimensional electron-spin-polarized
hydrogen $^1$H, deuterium $^2$H, and tritium $^3$H are obtained by means of
quantum Monte Carlo methods. The equations of state of the three isotopes are
calculated for a wide range of linear densities. The pair correlation function
and the static structure factor are obtained and interpreted within the
framework of the Luttinger liquid theory. We report the density dependence of
the Luttinger parameter and use it to identify different physical regimes:
Bogoliubov Bose gas, super-Tonks-Girardeau gas, and quasi-crystal regimes for
bosons; repulsive, attractive Fermi gas, and quasi-crystal regimes for
fermions. We find that the tritium isotope is the one with the richest
behaviour. Our results show unambiguously the relevant role of the isotope mass
in the properties of this quantum system.


title:
Achieving stable subspace clustering by post-processing generic
  clustering results

abstract:
  We propose an effective subspace selection scheme as a post-processing step
to improve results obtained by sparse subspace clustering (SSC). Our method
starts by the computation of stable subspaces using a novel random sampling
scheme. Thus constructed preliminary subspaces are used to identify the
initially incorrectly clustered data points and then to reassign them to more
suitable clusters based on their goodness-of-fit to the preliminary model. To
improve the robustness of the algorithm, we use a dominant nearest subspace
classification scheme that controls the level of sensitivity against
reassignment. We demonstrate that our algorithm is convergent and superior to
the direct application of a generic alternative such as principal component
analysis. On several popular datasets for motion segmentation and face
clustering pervasively used in the sparse subspace clustering literature the
proposed method is shown to reduce greatly the incidence of clustering errors
while introducing negligible disturbance to the data points already correctly
clustered.


title: The Higgs of the Higgs and the diphoton channel

abstract:
  LHC results do not confirm conventional natural solutions to the Higgs mass
hierarchy problem, motivating alternative interpretations where a
hierarchically small weak scale is generated from a dimension-less quantum
dynamics. We propose weakly and strongly-coupled models where the field that
breaks classical scale invariance giving mass to itself and to the Higgs is
identified with a possible new resonance within the LHC reach. As an example,
we identify such resonance with the 750 GeV diphoton excess recently reported
by ATLAS and CMS. Such models can be extrapolated up to the Planck scale,
provide Dark Matter candidates and eliminate the SM vacuum instability.


title: The Dose of the Threat Makes the Resistance for Cooperation

abstract:
  We propose to reformulate the payoff matrix structure of Prisoner's Dilemma
Game, by introducing threat and greed factors, and show their effect on the
co-evolution of memory and cooperation. Our findings are as follows. (i) Memory
protects cooperation. (ii) To our surprise, greater memory size is unfavorable
to evolutionary success when there is no threat. In the absence of threat,
subsequent generations lose their memory and are consequently invaded by
defectors. (iii) In contrast, the presence of an appropriate level of threat
triggers the emergence of a self-protection mechanism for cooperation, which
manifests itself as an increase in memory size within subsequent generations.
On the evolutionary level, memory size acts like an immune response of the
generations against aggressive defection. (iv) Even more extreme threat results
again in defection. Our findings boil down to the following: The dose of the
threat makes the resistance for cooperation.


title: The Fourier and Hilbert transforms under the Bargmann transform

abstract:
  There is a canonical unitary transformation from $L^2(\R)$ onto the Fock
space $F^2$, called the Bargmann transform. We study the action of the Bargmann
transform on several classical integral operators on $L^2(\R)$, including the
fractional Fourier transform, the fractional Hilbert transform, and the wavelet
transform.


title: Heat kernel for Newton-Cartan trace anomalies

abstract:
  We compute the leading part of the trace anomaly for a free non-relativistic
scalar in 2+1 dimensions coupled to a background Newton-Cartan metric. The
anomaly is proportional to 1/m, where m is the mass of the scalar. We comment
on the implications of a conjectured a-theorem for non-relativistic theories
with boost invariance.


title: Modelling turbulent stellar convection zones: sub-grid scales effects

abstract:
  The impressive development of global numerical simulations of turbulent
stellar interiors unveiled a variety of possible differential rotation (solar
or anti-solar), meridional circulation (single or multi-cellular), and dynamo
states (stable large scale toroidal field or periodically reversing magnetic
fields). Various numerical schemes, based on the so-called anelastic set of
equations, were used to obtain these results. It appears today mandatory to
assess their robustness with respect to the details of the numerics, and in
particular to the treatment of turbulent sub-grid scales. We report on an
ongoing comparison between two global models, the ASH and EULAG codes. In EULAG
the sub-grid scales are treated implicitly by the numerical scheme, while in
ASH their effect is generally modelled by using enhanced dissipation
coefficients. We characterize the sub-grid scales effect in a turbulent
convection simulation with EULAG. We assess their effect at each resolved scale
with a detailed energy budget. We derive equivalent eddy-diffusion coefficients
and use the derived diffusivities in twin ASH numerical simulations. We find a
good agreement between the large-scale flows developing in the two codes in the
hydrodynamic regime, which encourages further investigation in the
magnetohydrodynamic regime for various dynamo solutions.


title:
High accuracy position response calibration method for a micro-channel
  plate ion detector

abstract:
  We have developed a position response calibration method for a micro-channel
plate (MCP) detector with a delay-line anode position readout scheme. Using an
{\em in situ} calibration mask, an accuracy of 8~$\mu$m and a resolution of
85~$\mu$m (FWHM) have been achieved for MeV-scale $\alpha$ particles and ions
with energies of $\sim$10~keV. At this level of accuracy, the difference
between the MCP position responses to high-energy $\alpha$ particles and
low-energy ions is significant. The improved performance of the MCP detector
can find applications in many fields of AMO and nuclear physics. In our case,
it helps reducing systematic uncertainties in a high-precision nuclear
$\beta$-decay experiment.


title:
The Minc-type bound and the eigenvalue inclusion sets of the general
  product of tensors

abstract:
  In this paper, we give the Minc-type bound for spectral radius of nonnegative
tensors. We also present the bounds for the spectral radius and the eigenvalue
inclusion sets of the general product of tensors.


title: Principal eigenvector and spectral radius of uniform hypergraphs

abstract:
  In this paper, we give some bounds for principal eigenvector and spectral
radius of connected uniform hypergraphs in terms of vertex degrees, the
diameter, and the number of vertices and edges.


title:
Schottky barrier and contact resistance of InSb nanowire field effect
  transistors

abstract:
  Understanding of the electrical contact properties of semiconductor nanowire
(NW) field effect transistors (FETs) plays a crucial role in employing
semiconducting NWs as building blocks for future nanoelectronic devices and in
the study of fundamental physics problems. Here, we report on a study of the
contact properties of Ti/Au, a widely used contact metal combination, to
individual InSb NWs via both two-probe and four-probe transport measurements.
We show that a Schottky barrier of height $\Phi_{\rm{SB}}\sim20\ \rm{meV}$ is
present at the metal-InSb NW interfaces and its effective height is gate
tunable. The contact resistance ($R_{\rm{c}}$) in the InSb NWFETs is also
analyzed by magnetotransport measurements at low temperatures. It is found that
$R_{\rm{c}}$ at on-state exhibits a pronounced magnetic field dependent
feature, namely it is increased strongly with increasing magnetic field after
an onset field $B_{\rm{c}}$. A qualitative picture that takes into account
magnetic depopulation of subbands in the NWs is provided to explain the
observation. Our results provide a solid experimental evidence for the presence
of a Schottky barrier at Ti/Au-InSb NW interfaces and can be used as a basis
for design and fabrication of novel InSb NW based nanoelectronic devices and
quantum devices.


title: The Role of Noise in the Spatial Public Goods Game

abstract:
  In this work we aim to analyze the role of noise in the spatial Public Goods
Game, one of the most famous games in Evolutionary Game Theory. The dynamics of
this game is affected by a number of parameters and processes, namely the
topology of interactions among the agents, the synergy factor, and the strategy
revision phase. The latter is a process that allows agents to change their
strategy. Notably, rational agents tend to imitate richer neighbors, in order
to increase the probability to maximize their payoff. By implementing a
stochastic revision process, it is possible to control the level of noise in
the system, so that even irrational updates may occur. In particular, in this
work we study the effect of noise on the macroscopic behavior of a finite
structured population playing the Public Goods Game. We consider both the case
of a homogeneous population, where the noise in the system is controlled by
tuning a parameter representing the level of stochasticity in the strategy
revision phase, and a heterogeneous population composed of a variable
proportion of rational and irrational agents. In both cases numerical
investigations show that the Public Goods Game has a very rich behavior which
strongly depends on the amount of noise in the system and on the value of the
synergy factor. To conclude, our study sheds a new light on the relations
between the microscopic dynamics of the Public Goods Game and its macroscopic
behavior, strengthening the link between the field of Evolutionary Game Theory
and statistical physics.


title: Stockwell-Like Frames for Sobolev Spaces

abstract:
  We construct a family of frames describing Sobolev norm and Sobolev seminorm
of the space $H^s(\mathbb{R}^d)$. Our work is inspired by the Discrete
Orthonormal Stockwell Transform introduced by R.G. Stockwell, which provides a
time-frequency localized version of Fourier basis of $L^2([0,1])$. This
approach is a hybrid between Gabor and Wavelet frames. We construct explicit
and computable examples of these frames, discussing their properties.


title:
Computerized Processing and Analysis of CT Images for Developing a New
  Criterion in COPD Diagnosis

abstract:
  Background: Chronic obstructive pulmonary disease (COPD) is one of the most
prevalent and dangerous pulmonary diseases in the world. It is forecasted that
COPD will be the third deadly disease in the future. Therefore, developing
non-invasive methods for diagnosis of the disease would be helpful for
physicians and patients.
  Methods: Based on clinical investigations and spirometry tests, ten adult
patients with COPD (6 male and 4 female) with mean age of 49.8 years were
enrolled as the case group. In addition, ten age and sex-matched healthy,
non-COPD individuals (6 male and 4 female) with mean age of 45.4 years were
recruited as the controls. Lung CT-scan images of the subjects were processed
and analyzed by a computer to find a relationship.
  Findings: The elasticity of lung parenchyma variation was obtained with
digital image processing. The normalized average of this pattern was found to
be 21.6% in patients and 40.7% in controls. In addition, normalized mean value
of Hounsfield unit variations in square 10 pixel * 10 pixel windows in the
expiratory images were calculated as a parameter of air-trapping in COPD.
Differences between the groups were shown by student t-test (P < 0.05).
  Conclusion: This study showed that the variation of lung parenchyma
elasticity and Hounsfield units are found by processing and analysis of the
full inspiration and expiration images. These factors can be used as criteria
in diagnosis of COPD. Moreover, the severity of the disease can be presented by
the proposed method.
  Keywords: Air-trapping, Chronic obstructive pulmonary disease, Image
processing and analysis, CT-scan lung images


title:
A Single-Photon Imager Based on Microwave Plasmonic Superconducting
  Nanowire

abstract:
  Detecting spatial and temporal information of individual photons by using
single-photon-detector (SPD) arrays is critical to applications in
spectroscopy, communication, biological imaging, astronomical observation, and
quantum-information processing. Among the current SPDs1,detectors based on
superconducting nanowires have outstanding performance2, but are limited in
their ability to be integrated into large scale arrays due to the engineering
difficulty of high-bandwidth cryogenic electronic readout3-8. Here, we address
this problem by demonstrating a scalable single-photon imager using a single
continuous photon-sensitive superconducting nanowire microwave-plasmon
transmission line. By appropriately designing the nanowire's local
electromagnetic environment so that the nanowire guides microwave plasmons, the
propagating voltages signals generated by a photon-detection event were slowed
down to ~ 2% of the speed of light. As a result, the time difference between
arrivals of the signals at the two ends of the nanowire naturally encoded the
position and time of absorption of the photon. Thus, with only two readout
lines, we demonstrated that a 19.7-mm-long nanowire meandered across an area of
286 {\mu}m * 193 {\mu}m was capable of resolving ~590 effective pixels while
simultaneously recording the arrival times of photons with a temporal
resolution of 50 ps. The nanowire imager presents a scalable approach to
realizing high-resolution photon imaging in time and space.


title:
Relativistic hydrodynamics in heavy-ion collisions: general aspects and
  recent developments

abstract:
  Relativistic hydrodynamics has been quite successful in explaining the
collective behaviour of the QCD matter produced in high energy heavy-ion
collisions at RHIC and LHC. We briefly review the latest developments in the
hydrodynamical modeling of relativistic heavy-ion collisions. Essential
ingredients of the model such as the hydrodynamic evolution equations,
dissipation, initial conditions, equation of state, and freeze-out process are
reviewed. We discuss observable quantities such as particle spectra and
anisotropic flow and effect of viscosity on these observables. Recent
developments such as event-by-event fluctuations, flow in small systems
(proton-proton and proton-nucleus collisions), flow in ultra central
collisions, longitudinal fluctuations and correlations and flow in intense
magnetic field are also discussed.


title: TensorFlow: A system for large-scale machine learning

abstract:
  TensorFlow is a machine learning system that operates at large scale and in
heterogeneous environments. TensorFlow uses dataflow graphs to represent
computation, shared state, and the operations that mutate that state. It maps
the nodes of a dataflow graph across many machines in a cluster, and within a
machine across multiple computational devices, including multicore CPUs,
general-purpose GPUs, and custom designed ASICs known as Tensor Processing
Units (TPUs). This architecture gives flexibility to the application developer:
whereas in previous "parameter server" designs the management of shared state
is built into the system, TensorFlow enables developers to experiment with
novel optimizations and training algorithms. TensorFlow supports a variety of
applications, with particularly strong support for training and inference on
deep neural networks. Several Google services use TensorFlow in production, we
have released it as an open-source project, and it has become widely used for
machine learning research. In this paper, we describe the TensorFlow dataflow
model in contrast to existing systems, and demonstrate the compelling
performance that TensorFlow achieves for several real-world applications.


title: Reactive strip method for mixing and reaction in two dimensions

abstract:
  A numerical method to efficiently solve for mixing and reaction of scalars in
a two-dimensional flow field at large P\'eclet numbers but otherwise arbitrary
Damk\"ohler numbers is reported. We consider a strip of one reactant in a pool
of another reactant, both of which are advected with the known velocity field.
We first establish that the system evolution for such a system under certain
conditions is described by a locally one-dimensional reaction-diffusion
problem. The approximation of a locally one-dimensional dynamics is true for
cases where the strip thickness is smaller than the local radius of curvature
and also when the strip thickness is smaller than the distance between adjacent
strips. We first demonstrate the method for the transport of a conservative
scalar under a linear shear flow, point vortex and a chaotic sine flow. We then
proceed to consider the situation with a simple bimolecular reaction between
two reactants to yield a single product. The methodology presented herewith
essentially generalizes nontrivially the Diffusive Strip Method developed by
Meunier and Villermaux (J. Fluid Mech. 662, 134-172 (2010)) to address passive
scalar transport, to the generalized situation with multiple reacting species.
In essence, the reduction of dimensionality of the problem, which renders the
2D problem 1D, allows one to efficiently model reactive transport under high
P\'eclet numbers which are otherwise prohibitively difficult to resolve from
classical finite difference or finite element based methods.


title: Exploring soft constraints on effective actions

abstract:
  We study effective actions for simultaneous breaking of space-time and
internal symmetries. Novel features arise due to the mixing of Goldstone modes
under the broken symmetries which, in contrast to the usual Adler's zero, leads
to non-vanishing soft limits. Such scenarios are common for spontaneously
broken SCFT's. We explicitly test these soft theorems for $\mathcal{N}=4$ sYM
in the Coulomb branch both perturbatively and non-perturbatively. We explore
the soft constraints systematically utilizing recursion relations. In the pure
dilaton sector of a general CFT, we show that all amplitudes up to order $s^{n}
\sim \partial^{2n}$ are completely determined in terms of the $k$-point
amplitudes at order $s^k$ with $k \leq n$. Terms with at most one derivative
acting on each dilaton insertion are completely fixed and coincide with those
appearing in the conformal DBI, i.e. DBI in AdS. With maximal supersymmetry,
the effective actions are further constrained, leading to new
non-renormalization theorems. In particular, the effective action is fixed up
to eight derivatives in terms of just one unknown four-point coefficient and
one more coefficient for ten-derivative terms. Finally, we also study the
interplay between scale and conformal invariance in this context.


title:
A reduced model for precessional switching of thin-film nanomagnets
  under the influence of spin-torque

abstract:
  We study the magnetization dynamics of thin-film magnetic elements with
in-plane magnetization subject to a spin-current flowing perpendicular to the
film plane. We derive a reduced partial differential equation for the in-plane
magnetization angle in a weakly damped regime. We then apply this model to
study the experimentally relevant problem of switching of an elliptical element
when the spin-polarization has a component perpendicular to the film plane,
restricting the reduced model to a macrospin approximation. The macrospin
ordinary differential equation is treated analytically as a weakly damped
Hamiltonian system, and an orbit-averaging method is used to understand
transitions in solution behaviors in terms of a discrete dynamical system. The
predictions of our reduced model are compared to those of the full
Landau--Lifshitz--Gilbert--Slonczewski equation for a macrospin.


title:
Validity of the linear viscoelastic model for a polymer cylinder with
  ultrasonic hysteresis-type absorption in a nonviscous fluid

abstract:
  A necessary condition for the validity of the linear viscoelastic model for a
(passive) polymeric cylinder with an ultrasonic hysteresis-type absorption
submerged in a non-viscous fluid requires that the absorption efficiency is
positive (Qabs > 0) satisfying the law of the conservation of energy. This
condition imposes restrictions on the values attributed to the normalized
absorption coefficients for the compressional and shear-wave wavenumbers for
each partial-wave mode n. The forbidden values produce negative axial radiation
force, absorption and extinction efficiencies, as well as an enhancement of the
scattering efficiency, not in agreement with the conservation of energy law.
Numerical results for the radiation force, extinction, absorption and
scattering efficiencies are performed for three viscoelastic (VE) polymer
cylinders immersed in a non-viscous host liquid (i.e. water) with particular
emphasis on the shear-wave absorption coefficient of the cylinder, the
dimensionless size parameter and the partial-wave mode number n. Mathematical
constraints are established for the non-dimensional absorption coefficients of
the longitudinal and shear waves for a cylinder (i.e. 2D case) and a sphere
(i.e. 3D case) in terms of the sound velocities in the VE material. The
analysis suggests that the domain of validity for any viscoelastic model
describing acoustic attenuation inside a lossy cylinder (or sphere) in a
non-viscous fluid must be verified based upon the optical theorem.


title:
Observations of metals in the $z\approx3.5$ intergalactic medium and
  comparison to the EAGLE simulations

abstract:
  We study the $z\approx3.5$ intergalactic medium (IGM) by comparing new,
high-quality absorption spectra of eight QSOs with $\langle z_{\rm QSO}
\rangle=3.75$, to virtual observations of the EAGLE cosmological hydrodynamical
simulations. We employ the pixel optical depth method and uncover strong
correlations between various combinations of HI, CIII, CIV, SiIII, SiIV, and
OVI. We find good agreement between many of the simulated and observed
correlations, including OVI(HI). However, the observed median optical depths
for the CIV(HI) and SiIV(HI) relations are higher than those measured from the
mock spectra. The discrepancy increases from up to $\approx0.1$ dex at
$\tau_{\rm HI}=1$ to $\approx1$ dex at $\tau_{\rm HI}=10^2$, where we are
likely probing dense regions at small galactocentric distances. As possible
solutions, we invoke (a) models of ionizing radiation softened above 4 Ryd to
account for delayed completion of HeII reionization; (b) simulations run at a
higher resolution; (c) the inclusion of additional line broadening due to
unresolved turbulence; and (d) increased elemental abundancess; however, none
of these factors can fully explain the observed differences. Enhanced
photoionization of HI by local sources, which was not modelled, could offer a
solution. However, the much better agreement with the observed OVI(HI)
relation, which we find probes a hot and likely collisionally-ionized gas
phase, indicates that the simulations are not in tension with the hot phase of
the IGM, and suggests that the simulated outflows may entrain insufficient cool
gas.


title: On the Calibration of Multilevel Monte Carlo Ensemble Forecasts

abstract:
  Multilevel Monte Carlo can efficiently compute statistical estimates of
discretized random variables, for a given error tolerance. Traditionally, only
a certain statistic is computed from a particular implementation of multilevel
Monte Carlo. This paper considers the multilevel case when one wants to verify
and evaluate a single ensemble that forms an empirical approximation to many
different statistics, namely an ensemble forecast. We propose a simple
algorithm that, in the univariate case, allows one to derive a statistically
consistent single ensemble forecast from the hierarchy of ensembles that are
formed during an implementation of multilevel Monte Carlo. This ensemble
forecast then allows the entire multilevel hierarchy of ensembles to be
evaluated using standard ensemble forecast verification techniques. We
demonstrate the case of evaluating the calibration of the forecast in this
paper.


title:
Reply to "Comment on "Normalization of quasinormal modes in leaky
  optical cavities and plasmonic resonators" " by E. A. Muljarov and W.
  Langbein

abstract:
  We refute all claims of the "Comment on "Normalization of quasinormal modes
in leaky optical cavities and plasmonic resonators" " by E. A. Muljarov and W.
Langbein (arXiv:1602.07278v1). Based entirely on information already contained
in our original article (P. T. Kristensen, R.-C. Ge and S. Hughes, Physical
Review A 92, 053810 (2015)), we dismiss every point of criticism as being
completely unjustified and point out how important parts of our argumentation
appear to have been overlooked by the Comment Authors. In addition, we provide
additional calculations showing directly the link between the normalizations by
Sauvan et al. and Muljarov et al., which were not included in our original
article.


title:
Maximum information entropy principle and the interpretation of
  probabilities in statistical mechanics - a short review

abstract:
  In this paper an alternative approach to statistical mechanics based on the
maximum information entropy principle (MaxEnt) is examined, specifically its
close relation with the Gibbs method of ensembles. It is shown that the MaxEnt
formalism is the logical extension of the Gibbs formalism of equilibrium
statistical mechanics that is entirely independent of the frequentist
interpretation of probabilities only as factual (i.e. experimentally
verifiable) properties of the real world. Furthermore, we show that,
consistently with the law of large numbers, the relative frequencies of the
ensemble of systems prepared under identical conditions (i.e. identical
constraints) actually correspond to the MaxEnt probabilites in the limit of a
large number of systems in the ensemble. This result implies that the
probabilities in statistical mechanics can be interpreted, independently of the
frequency interpretation, on the basis of the maximum information entropy
principle.


title:
Existence of long time solutions and validity of the Nonlinear
  Schr\"odinger approximation for a quasilinear dispersive equation

abstract:
  We consider a nonlinear dispersive equation with a quasilinear quadratic
term. We establish two results. First, we show that solutions to this equation
with initial data of order $\mathcal{O}(\varepsilon)$ in Sobolev norms exist
for a time span of order $\mathcal{O}(\varepsilon^{-2})$ for sufficiently small
$\varepsilon$. Secondly, we derive the Nonlinear Schr\"odinger (NLS) equation
as a formal approximation equation describing slow spatial and temporal
modulations of the envelope of an underlying carrier wave, and justify this
approximation with the help of error estimates in Sobolev norms between exact
solutions of the quasilinear equation and the formal approximation obtained via
the NLS equation. The proofs of both results rely on estimates of appropriate
energies whose constructions are inspired by the method of normal-form
transforms. To justify the NLS approximation, we have to overcome additional
difficulties caused by the occurrence of resonances. We expect that the method
developed in the present paper will also allow to prove the validity of the NLS
approximation for a larger class of quasilinear dispersive systems with
resonances.


title: Manifold boundaries give "gray-box" approximations of complex models

abstract:
  We discuss a method of parameter reduction in complex models known as the
Manifold Boundary Approximation Method (MBAM). This approach, based on a
geometric interpretation of statistics, maps the model reduction problem to a
geometric approximation problem. It operates iteratively, removing one
parameter at a time, by approximating a high-dimension, but thin manifold by
its boundary. Although the method makes no explicit assumption about the
functional form of the model, it does require that the model manifold exhibit a
hierarchy of boundaries, i.e., faces, edges, corners, hyper-corners, etc. We
empirically show that a variety of model classes have this curious feature,
making them amenable to MBAM. These model classes include models composed of
elementary functions (e.g., rational functions, exponentials, and partition
functions), a variety of dynamical system (e.g., chemical and biochemical
kinetics, Linear Time Invariant (LTI) systems, and compartment models), network
models (e.g., Bayesian networks, Markov chains, artificial neural networks, and
Markov random fields), log-linear probability distributions, and models with
symmetries. We discuss how MBAM recovers many common approximation methods for
each model class and discuss potential pitfalls and limitations.


title:
Boosting the accuracy and speed of quantum Monte Carlo: size-consistency
  and time-step

abstract:
  Diffusion Monte Carlo (DMC) simulations for fermions are becoming the
standard to provide high quality reference data in systems that are too large
to be investigated via quantum chemical approaches. DMC with the fixed-node
approximation relies on modifications of the Green function to avoid
singularities near the nodal surface of the trial wavefunction. We show that
these modifications affect the DMC energies in a way that is not
size-consistent, resulting in large time-step errors. Building on the
modifications of Umrigar {\em et al.} and of DePasquale {\em et al.} we propose
a simple Green function modification that restores size-consistency to large
values of time-step; substantially reducing the time-step errors. The new
algorithm also yields remarkable speedups of up to two orders of magnitude in
the calculation of molecule-molecule binding energies and crystal cohesive
energies, thus extending the horizons of what is possible with DMC.

categories: physics.chem-ph cond-mat.mtrl-sci cond-mat.str-el physics.comp-ph quant-ph


title:
An inductive Julia-Caratheodory theorem for Pick functions in two
  variables

abstract:
  We study the asymptotic behavior of Pick functions, analytic functions which
take the upper half plane to itself. We show that if a two variable Pick
function $f$ has real residues to order $2N-1$ at infinity and the imaginary
part of the remainder between $f$ and this expansion is of order $2N+1,$ then
$f$ has real residues to order $2N$ and directional residues to order $2N+1.$
Furthermore, $f$ has real residues to order $2N+1$ if and only if the $2N+1$-th
derivative is given by a polynomial, thus obtaining a two variable analogue of
a higher order Julia-Carath\'eodory type theorem.


title: Binary Operations for Homotopy Groups with Coefficients

abstract:
  We define and study binary operations for homotopy groups with coefficients.
We give conditions to prove that certain binary operations are the homomorphic
image of the generalized Whitehead product. This allows carrying over
properties of the generalized Whitehead product to these operations. We discuss
two classes of binary operations, the Whitehead products and the Torsion
products. We introduce a new class of operations called Ext operations and
determine some of its properties. We compare the Torsion product to the
Whitehead product in a special case. We prove that the smash product of two
Moore spaces has the homotopy type of a wedge of two Moore spaces.


title:
Invariants and Umbilical Points on Three Dimensional CR Manifolds
  embedded in $\mathbb C^2$

abstract:
  We introduce a new sequence of CR invariant determinants on a three
dimensional CR manifold $M$ embedded in $\mathbb C^2$. The lowest order
invariant $\det A_3$ represents E. Cartan's 6th order invariant (the umbilical
"tensor"), whose zero locus yields the set of umbilical points on $M$. As an
application of this new presentation of the umbilical invariant, we show that
generic, almost circular perturbations of the unit sphere always contain curves
or surfaces of umbilical points.


title: Inverse scattering for a random potential

abstract:
  In this paper we consider an inverse problem for the $n$-dimensional random
Schr\"{o}dinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of
plane waves in the presence of a potential $q$ which is assumed to be a
Gaussian random function such that its covariance is described by a
pseudodifferential operator. Our main result is as follows: given the
backscattered far field, obtained from a single realization of the random
potential $q$, we uniquely determine the principal symbol of the covariance
operator of $q$. Especially, for $n=3$ this result is obtained for the full
non-linear inverse backscattering problem. Finally, we present a physical
scaling regime where the method is of practical importance.


title:
The isomorphism problem for quantum affine spaces, homogenized quantized
  Weyl algebras, and quantum matrix algebras

abstract:
  Bell and Zhang have shown that if $A$ and $B$ are two connected graded
algebras finitely generated in degree one that are isomorphic as ungraded
algebras, then they are isomorphic as graded algebras. We exploit this result
to solve the isomorphism problem in the cases of quantum affine spaces, quantum
matrix algebras, and homogenized multiparameter quantized Weyl algebras. Our
result involves determining the degree one normal elements, factoring out, and
then repeating. This creates an iterative process that allows one to determine
relationships between relative parameters.


title: "Efficient" Subgradient Methods for General Convex Optimization

abstract:
  A subgradient method is presented for solving general convex optimization
problems, the main requirement being that a strictly-feasible point is known. A
feasible sequence of iterates is generated, which converges to within
user-specified error of optimality. Feasibility is maintained with a
line-search at each iteration, avoiding the need for orthogonal projections
onto the feasible region (the operation that limits practicality of traditional
subgradient methods). Lipschitz continuity is not required, yet the algorithm
is shown to possess a convergence rate analogous to rates for traditional
methods, albeit with error measured relatively, whereas traditionally error has
been absolute. The algorithm is derived using an elementary framework that can
be utilized to design other such algorithms.


title:
Helical turbulent Prandtl number in the $A$ model of passive advection:
  Two loop approximation

abstract:
  Using the field theoretic renormalization group technique in the two-loop
approximation, turbulent Prandtl numbers are obtained in the general $A$ model
of passive vector advected by fully developed turbulent velocity field with
violation of spatial parity introduced via continuous parameter $\rho$ ranging
from $\rho=0$ (no violation of spatial parity) to $|\rho|=1$ (maximum violation
of spatial parity). In non-helical environments, we demonstrate that $A$ is
restricted to $-1.723 \leq A \leq 2.800$ (rounded on the last presented digit)
due to the constraints of two-loop calculations. When $\rho >0.749$
restrictions may be removed. Furthermore, three physically important cases $A
\in \{-1, 0, 1\}$ are shown to lie deep within the allowed interval of $A$ for
all values of $\rho$. For the model of linearized Navier-Stokes equations ($A =
-1$) up to date unknown helical values of turbulent Prandtl number have been
shown to equal $1$ regardless of parity violation. Furthermore, we have shown
that interaction parameter $A$ exerts strong influence on advection diffusion
processes in turbulent environments with broken spatial parity. In explicit,
depending on actual value of $A$ turbulent Prandtl number may increase or
decrease with $\rho$. By varying $A$ continuously we explain high stability of
kinematic MHD model ($A=1$) against helical effects as a result of its
closeness to $A = 0.912$ (rounded on the last presented digit) case where
helical effects are completely suppressed. Contrary, for the physically
important $A=0$ model we show that it lies deep within the interval of models
where helical effects cause the turbulent Prandtl number to decrease with
$|\rho|$. We thus identify internal structure of interactions given by
parameter $A$, and not the vector character of the admixture itself to be the
dominant factor influencing diffusion advection processes in the helical $A$
model.

categories: cond-mat.stat-mech hep-th math-ph math.MP


title: I Accidentally the Whole Internet

abstract:
  Whether as telecommunications or power systems, networks are very important
in everyday life. Maintaining these networks properly functional and connected,
even under attacks or failures, is of special concern. This topic has been
previously studied with a whole network robustness perspective,modeling
networks as undirected graphs (such as roads or simply cables). This
perspective measures the average behavior of the network after its last node
has failed. In this article we propose two alternatives to well-known studies
about the robustness of the backbone Internet: to use a supply network model
and metrics for its representation (we called it the Go-Index), and to use
robustness metrics that can be calculated while disconnections appear. Our
research question is: if a smart adversary has a limited number of strikes to
attack the Internet, how much will the damage be after each one in terms of
network disconnection? Our findings suggest that in order to design robust
networks it might be better to have a complete view of the robustness evolution
of the network, from both the infrastructure and the users perspective.


title: A Landauer formulation of photon transport in driven systems

abstract:
  Understanding the behavior of light in non-equilibrium scenarios underpins
much of quantum optics and optical physics. While lasers provide a severe
example of a non-equilibrium problem, recent interests in the near-equilibrium
physics of so-called photon `gases', such as in Bose condensation of light or
in attempts to make photonic quantum simulators, suggest one re-examine some
near-equilibrium cases. Here we consider how a sinusoidal parametric coupling
between two semi-infinite photonic transmission lines leads to the creation and
flow of photons between the two lines. Our approach provides a photonic analog
to the Landauer transport formula, and using non-equilbrium Green's functions,
we can extend it to the case of an interacting region between two photonic
`leads' where the sinusoid frequency plays the role of a voltage bias.
Crucially, we identify both the mathematical framework and the physical regime
in which photonic transport is directly analogous to electronic transport and
regimes in which other behavior such as two-mode squeezing can emerge.


title: Fixed point indices of planar continuous maps

abstract:
  We characterize the sequences of fixed point indices $\{i(f^n, p)\}_{n\ge 1}$
of fixed points that are isolated as an invariant set and continuous maps in
the plane. In particular, we prove that the sequence is periodic and $i(f^n, p)
\le 1$ for every $n \ge 1$. This characterization allows us to compute
effectively the Lefschetz zeta functions for a wide class of continuous maps in
the 2-sphere, to obtain new results of existence of infinite periodic orbits
inspired on previous articles of J. Franks and to give a partial answer to a
problem of Shub about the growth of the number of periodic orbits of
degree--$d$ maps in the 2-sphere.


title:
Predicting patterns of long-term adaptation and extinction with
  population genetics

abstract:
  Population genetics struggles to model extinction; standard models track the
relative rather than absolute fitness of genotypes, while the exceptions
describe only the short-term transition from imminent doom to evolutionary
rescue. But extinction can result from failure to adapt not only to
catastrophes, but also to a backlog of environmental challenges. We model
long-term evolution to long series of small challenges, where fitter
populations reach higher population sizes. The population's long-term fitness
dynamic is well approximated by a simple stochastic Markov chain model.
Long-term persistence occurs when the rate of adaptation exceeds the rate of
environmental deterioration for some genotypes. Long-term persistence times are
consistent with typical fossil species persistence times of several million
years. Immediately preceding extinction, fitness declines rapidly, appearing as
though a catastrophe disrupted a stably established population, even though
gradual evolutionary processes are responsible. New populations go through an
establishment phase where, despite being demographically viable, their
extinction risk is elevated. Should the population survive long enough,
extinction risk later becomes constant over time.


title: Indices of fixed points not accumulated by periodic points

abstract:
  We prove that for every integer sequence $I$ satisfying Dold relations there
exists a map $f : \mathbb{R}^d \to \mathbb{R}^d$, $d \ge 2$, such that
$\mathrm{Per(f)} = \mathrm{Fix(f)} = \{o\}$, where $o$ denotes the origin, and
$(i(f^n, o))_n = I$.


title:
Stabilising Model Predictive Control for Discrete-time Fractional-order
  Systems

abstract:
  In this paper we propose a model predictive control scheme for constrained
fractional-order discrete-time systems. We prove that all constraints are
satisfied at all time instants and we prescribe conditions for the origin to be
an asymptotically stable equilibrium point of the controlled system. We employ
a finite-dimensional approximation of the original infinite-dimensional
dynamics for which the approximation error can become arbitrarily small. We use
the approximate dynamics to design a tube-based model predictive controller
which steers the system state to a neighbourhood of the origin of controlled
size. We finally derive stability conditions for the MPC-controlled system
which are computationally tractable and account for the infinite dimensional
nature of the fractional-order system and the state and input constraints. The
proposed control methodology guarantees asymptotic stability of the
discrete-time fractional order system, satisfaction of the prescribed
constraints and recursive feasibility.


title: S5-invariant Nonsingular Quartic Surfaces

abstract:
  All S5-invariant nonsingular quartic surfaces are obtained. There exist no
A6- invariant nonsingular quartic surfaces.


title:
Probability, Minimax Approximation and Nash-Equilibrium. Estimating the
  Parameter of a Biased Coin

abstract:
  This paper deals with the application of Approximation Theory type techniques
to study a classical problem in Probability: estimating the parameter of a
biased coin. For this purpose, a Minimax Estimation problem is considered and
the characterization of the optimal estimator is shown, together with the weak
asymptotics of such optimal choices as the number of coin tosses approaches
infinity; in addition, a number of numerical examples and graphs are displayed.
At the same time, the problem is also discussed from the Game Theory viewpoint,
as a non-cooperative, two-player game, and a Nash-equilibrium is established.
The particular case of n=2 tosses is completely solved.


title:
An algorithm with nearly optimal pseudo-regret for both stochastic and
  adversarial bandits

abstract:
  We present an algorithm that achieves almost optimal pseudo-regret bounds
against adversarial and stochastic bandits. Against adversarial bandits the
pseudo-regret is $O(K\sqrt{n \log n})$ and against stochastic bandits the
pseudo-regret is $O(\sum_i (\log n)/\Delta_i)$. We also show that no algorithm
with $O(\log n)$ pseudo-regret against stochastic bandits can achieve
$\tilde{O}(\sqrt{n})$ expected regret against adaptive adversarial bandits.
This complements previous results of Bubeck and Slivkins (2012) that show
$\tilde{O}(\sqrt{n})$ expected adversarial regret with $O((\log n)^2)$
stochastic pseudo-regret.


title: Thermometry of Guided Molecular Beams from a Cryogenic Buffer-Gas Cell

abstract:
  We present a comprehensive characterization of cold molecular beams from a
cryogenic buffer-gas cell, providing an insight into the physics of buffer-gas
cooling. Cold molecular beams are extracted from a cryogenic cell by
electrostatic guiding, which is also used to measure their velocity
distribution. Molecules' rotational-state distribution is probed via
radio-frequency resonant depletion spectroscopy. With the help of complete
trajectory simulations, yielding the guiding efficiency for all of the
thermally populated states, we are able to determine both the rotational and
the translational temperature of the molecules at the output of the buffer-gas
cell. This thermometry method is demonstrated for various regimes of buffer-gas
cooling and beam formation as well as for molecular species of different sizes,
$\rm{CH_3F}$ and $\rm{CF_3CCH}$. Comparison between the rotational and
translational temperatures provides evidence of faster rotational
thermalization for the $\rm{CH_3F-He}$ system in the limit of low He density.
In addition, the relaxation rates for different rotational states appear to be
different.


title: Absence of equilibrium chiral magnetic effect

abstract:
  We analyse the $3+1$ D equilibrium chiral magnetic effect (CME). We apply
derivative expansion to the Wigner transform of the two - point Green function.
This technique allows us to express the response of electric current to
external electromagnetic field strength through the momentum space topological
invariant. We consider the wide class of the lattice regularizations of quantum
field theory (that includes, in particular, the regularization with Wilson
fermions) and also certain lattice models of solid state physics (including
those of Dirac semimetals). It appears, that in these models the mentioned
topological invariant vanishes identically at nonzero chiral chemical
potential. That means, that the bulk equilibrium CME is absent in those
systems.


title: Uniqueness of dynamical zeta functions and symmetric products

abstract:
  A characterization of dynamically defined zeta functions is presented. It
comprises a list of axioms, natural extension of the one which characterizes
topological degree, and a uniqueness theorem. Lefschetz zeta function is the
main (and proved unique) example of such zeta functions. Another interpretation
of this function arises from the notion of symmetric product from which some
corollaries and applications are obtained.


title:
An Outbreak Vector-host Epidemic Model with Spatial Structure: The 2015
  Zika Outbreak in Rio de Janeiro

abstract:
  Background: A deterministic model is developed for the spatial spread of an
epidemic disease in a geographical setting. The disease is borne by vectors to
susceptible hosts through criss-cross dynamics. The model is focused on an
epidemic outbreak that initiates from a small number of cases in a small
sub-region of the geographical setting. Methods: Partial differential equations
are formulated to describe the interaction of the model compartments. Results:
The partial differential equations of the model are analyzed and proven to be
well-posed. The epidemic outcomes of the model are correlated to the spatially
dependent parameters and initial conditions of the model. Conclusions: A
version of the model is applied to the 2015-2016 Zika outbreak in the Rio de
Janeiro Municipality in Brazil.


title: Reducing the Solar Neutrino Background Using Polarised Helium-3

abstract:
  Future dark matter detectors plan to have sensitivities such that solar
neutrinos will start to become a problematic background. In this work we show
that a polarised helium-3 detector would in principle be able to eliminate 98%
of these events when the orientation of the polarisation axis is antiparallel
to the direction of the Sun. We comment on the possible improvement in
sensitivity of dark matter direct detection experiments due to this effect and
the feasibility of building such a detector.


title:
Functional renormalization group study of orbital fluctuation mediated
  superconductivity: Impact of the electron-boson coupling vertex corrections

abstract:
  In various multiorbital systems, the emergence of the orbital fluctuations
and its role on the pairing mechanism attract increasing attention. To archive
deep understanding on these issues, we perform the
functional-renormalization-group (fRG) study for the two-orbital Hubbard model.
The vertex corrections for the electron-boson coupling ($U$-VC), which are
dropped in the Migdal-Eliashberg gap equation, are obtained by solving the RG
equation. We reveal that the dressed electron-boson coupling for the
charge-channel, $U_{eff}^c$, becomes much larger than the bare Coulomb
interaction, $U^0$, due to the $U$-VC in the presence of moderate spin
fluctuations. For this reason, the attractive pairing interaction due to the
charge or orbital fluctuations is enlarged by the factor $(U_{eff}^c/U^0)^2 >>
1$. In contrast, the spin fluctuation pairing interaction is suppressed by the
spin-channel $U$-VC, because of the relation $U_{eff}^s << U^0$. The present
study demonstrates that the orbital or charge fluctuation pairing mechanism can
be realized in various multiorbital systems thanks to the $U$-VC, such as in
Fe-based superconductors.


title:
Two-phase Cryogenic Avalanche Detector with electroluminescence gap
  operated in argon doped with nitrogen

abstract:
  A two-phase Cryogenic Avalanche Detector (CRAD) with electroluminescence (EL)
gap, operated in argon doped with a minor (49$\pm$7 ppm) admixture of nitrogen,
has been studied. The EL gap was optically read out using cryogenic PMTs
located on the perimeter of the gap. We present the results of the measurements
of the N$_2$ content, detector sensitivity to X-ray-induced signals, EL gap
yield and electron lifetime in the liquid. The detector sensitivity, at a drift
field in liquid Ar of 0.6 kV/cm, was measured to be 9 and 16 photoelectrons
recorded at the PMTs per keV of deposited energy at 23 and 88 keV respectively.
Such two-phase detectors, with enhanced sensitivity to the S2
(ionization-induced) signal, are relevant in the field of argon detectors for
dark matter search and low energy neutrino detection.


title: Three dimensional central configurations in H3 and S3

abstract:
  We show that each central configuration in the three-dimensional hyperbolic
sphere is equivalent to one central configuration on a particular two-
dimensional hyperbolic sphere. However, there exist both special and ordinary
central configurations in the three-dimensional sphere that are not confined to
any two-dimensional sphere.


title: An elementary proof of a Theorem by Matsumoto

abstract:
  Matsumoto proved in arXiv:1012.0981 that the prime end rotation numbers
associated to an invariant annular continuum are contained in its rotation set.
An alternative proof of this fact using only simple planar topology is
presented.


title: Computing the Bergsma Dassios sign-covariance

abstract:
  Bergsma and Dassios (2014) introduced an independence measure which is zero
if and only if two random variables are independent. This measure can be
naively calculated in $O(n^4)$. Weihs et al. (2015) showed that it can be
calculated in $O(n^2 \log n)$. In this note we will show that using the methods
described in Heller et al. (2016), the measure can easily be calculated in only
$O(n^2)$.


title:
Screening and Many-Body Effects in Two-Dimensional Crystals: Monolayer
  MoS$_{2}$

abstract:
  We present a systematic study of the variables affecting the electronic and
optical properties of two-dimensional(2D) crystals within \textit{ab initio} GW
and GW plus Bethe Salpeter Equation (GW-BSE) calculations. As a prototypical 2D
transition metal dichalcogenide material, we focus our study on monolayer
MoS${}_2$. We find that the reported variations in GW-BSE results in the
literature for monolayer MoS${}_2$ and related systems arise from different
treatments of the long-range Coulomb interaction in supercell calculations and
convergence of k-grid sampling and cutoffs for various quantities such as the
dielectric screening. In particular, the quasi-2D nature of the system gives
rise to fast spatial variations in the screening environment, which are
computationally challenging to resolve. We also show that common numerical
treatments to remove the divergence in the Coulomb interaction can shift the
exciton continuum leading to false convergence with respect to k-point
sampling. Our findings apply to GW-BSE calculations on any low-dimensional
semiconductors.


title:
Generalization of Noether's theorem in modern form to non-variational
  partial differential equations

abstract:
  A general method using multipliers for finding the conserved integrals for
any system of partial differential equations (PDEs) is reviewed and further
developed in several ways. Multipliers are expressions whose (summed) product
with a PDE (system) yields a local divergence identity which has the physical
meaning of a continuity equation involving a conserved density and a spatial
flux for solutions of the PDE (system). On spatial domains, the integral form
of a continuity equation yields a conserved integral. When a PDE (system) is
variational, multipliers correspond to symmetries of the variational principle,
and the local divergence identity relating a multiplier to a conserved integral
is the same as the variational identity used in Noether's theorem for
connecting conserved integrals to invariance of a variational principle. From
this viewpoint, the multiplier method is shown to constitute a modern form of
Noether's theorem in which the variational principle is not used. When a PDE
(system) is non-variational, multipliers are shown to be an adjoint counterpart
to symmetries, and the local divergence identity relating a multiplier to a
conserved integral is shown to be an adjoint generalization of the variational
identity underling Noether's theorem. Two main results are established for PDE
systems having a solved-form for leading derivatives, which encompasses all
typical PDEs of physical interest. First, all non-trivial conserved integrals
are shown to arise from non-trivial multipliers in a one-to-one manner, taking
into account certain equivalence freedoms. Second, a scaling formula based on
dimensional analysis is derived to obtain the conserved density and spatial
flux in any conserved integral, just using the corresponding multiplier and the
given PDE system. The derivations use a few basic tools from variational
calculus, for which a self-contained formulation is provided.


title: Students' epistemological framing in quantum mechanics problem solving

abstract:
  Students' difficulties in quantum mechanics may be the result of unproductive
framing and not a fundamental inability to solve the problems or misconceptions
about physics content. We observed groups of students solving quantum mechanics
problems in an upper-division physics course. Using the lens of epistemological
framing, we investigated four frames in our observational data: algorithmic
math, conceptual math, algorithmic physics, and conceptual physics. We discuss
the characteristics of each frame as well as causes for transitions between
different frames, arguing that productive problem solving may occur in any
frame as long as students' transition appropriately between frames. Our work
extends epistemological framing theory on how students frame discussions in
upper-division physics courses.


title: LHC Signatures of WIMP-triggered Baryogenesis

abstract:
  A robust mechanism was recently proposed in which thermal freeze-out of WIMPs
can provide a unified origin of dark matter and baryon abundances in our
universe. We point out that this WIMP-triggered baryogenesis mechanism can
exhibit a rich collider phenomenology and be tested at the current and
near-future experiments at LHC, even in the case where the WIMPs are completely
devoid of SM gauge and higgs portal interactions, as may be motivated by the
persistent null results of WIMP dark matter searches. We catalogue a rich array
of LHC signatures robustly present in such a scenario. In particular, the
simplest such implementation can already offer a very clean signal of a
TeV-scale resonance that decays to diphotons with a cross section that can
easily be within the reach of the current and near-future LHC runs in the
region of parameter space that leads to a successful baryogenesis. Other
characteristic signatures include the production of multi-bottom and/or
multi-top quarks, promptly or displaced. An even more exotic possibility is the
production of two separate sets of isolated emerging jets connected by a
charged track, which may require new dedicated studies. Finally, di-nucleon
decay can also provide a powerful probe of the mechanism.


title:
Efficient Estimation of Partially Linear Models for Spatial Data over
  Complex Domain

abstract:
  In this paper, we study the estimation of partially linear models for spatial
data distributed over complex domains. We use bivariate splines over
triangulations to represent the nonparametric component on an irregular
two-dimensional domain. The proposed method is formulated as a constrained
minimization problem which does not require constructing finite elements or
locally supported basis functions. Thus, it allows an easier implementation of
piecewise polynomial representations of various degrees and various smoothness
over an arbitrary triangulation. Moreover, the constrained minimization problem
is converted into an unconstrained minimization via a QR decomposition of the
smoothness constraints, which allows for the development of a fast and
efficient penalized least squares algorithm to fit the model. The estimators of
the parameters are proved to be asymptotically normal under some regularity
conditions. The estimator of the bivariate function is consistent, and its rate
of convergence is also established. The proposed method enables us to construct
confidence intervals and permits inference for the parameters. The performance
of the estimators is evaluated by two simulation examples and by a real data
analysis.


title: Parameterized Resiliency Problems via Integer Linear Programming

abstract:
  We introduce an extension of decision problems called resiliency problems. In
resiliency problems, the goal is to decide whether an instance remains positive
after any (appropriately defined) perturbation has been applied to it. To
tackle these kinds of problems, some of which might be of practical interest,
we introduce a notion of resiliency for Integer Linear Programs (ILP) and show
how to use a result of Eisenbrand and Shmonin (Math. Oper. Res., 2008) on
Parametric Linear Programming to prove that ILP Resiliency is fixed-parameter
tractable (FPT) under a certain parameterization. To demonstrate the utility of
our result, we consider natural resiliency versions of several concrete
problems, and prove that they are FPT under natural parameterizations. Our
first results concern a four-variate problem which generalizes the Disjoint Set
Cover problem and which is of interest in access control. We obtain a complete
parameterized complexity classification for every possible combination of the
parameters. Then, we introduce and study a resiliency version of the Closest
String problem, for which we extend an FPT result of Gramm et al.
(Algorithmica, 2003). We also consider problems in the fields of scheduling and
social choice. We believe that many other problems can be tackled by our
framework.


title: Random Toric Surfaces and a Threshold for Smoothness

abstract:
  We present a notion of a random toric surface modeled on a notion of a random
graph. We then study some threshold phenomena related to the smoothness of the
resulting surfaces.


title:
Mind the scales: Harnessing spatial big data for infectious disease
  surveillance and inference

abstract:
  Spatial big data have the "velocity," "volume," and "variety" of big data
sources and additional geographic information about the record. Digital data
sources, such as medical claims, mobile phone call data records, and geo-tagged
tweets, have entered infectious disease epidemiology as novel sources of data
to complement traditional infectious disease surveillance. In this work, we
provide examples of how spatial big data have been used thus far in
epidemiological analyses and describe opportunities for these sources to
improve public health coordination and disease mitigation strategies. In
addition, we consider the technical, practical, and ethical challenges with the
use of spatial big data in infectious disease surveillance and inference.
Finally, we discuss the implications of the rising use of spatial big data in
epidemiology to health risk communications, across-scale public health
coordination, and public health policy recommendation.


title: The 750 GeV threshold to a new particle world

abstract:
  We show how an excess in the diphoton channel can be the effect of neither a
resonance nor an end-point in a cascade decay, but rather of a threshold for
virtual production of a pair of extra quarks, each with half of peak invariant
mass, onsetting in both the $gg$-initiated production and the
$\gamma\gamma$-induced decay of an off-shell $Z$ boson. For our analysis we
consider as paradigmatic example the 750 GeV excess previously seen at the end
of 2015 with the Run 2 data of the LHC but not confirmed with 2016 data.


title:
On an optimal constraint aggregation method for integer programming and
  on an analytic expression of the number of integer points in a polytope

abstract:
  In this paper we give a new aggregation framework for linear Diophantine
equations. In particular, we prove that an aggregated system of minimum size
can be built in polynomial time. We also derive an analytic formula that gives
the number of solutions of the system when it is possible to aggregate the
system into one equation.