title: Combinatorics of the Lipschitz polytope

abstract:
  Let $\rho$ be a metric on the set $X=\{1,2,\dots,n+1\}$. Consider the
$n$-dimensional polytope of functions $f:X\rightarrow \mathbb{R}$, which
satisfy the conditions $f(n+1)=0$, $|f(x)-f(y)|\leq \rho(x,y)$. The question on
classifying metrics depending on the combinatorics of this polytope have been
recently posed by A. M. Vershik \cite{V}. We prove that for any "generic"
metric the number of $(n-m)$-dimensional faces, $0\leq m\leq n$, equals
$\binom{n+m}{m,m,n-m}=(n+m)!/m!m!(n-m)!$. This fact is intimately related to
regular triangulations of the root polytope (the convex hull of the roots of
$A_n$ root system). Also we get two-sided estimates for the logarithm of the
number of Vershik classes of metrics: $n^3\log n$ from above and $n^2$ from
below.


title: Chemodynamic evolution of dwarf galaxies in tidal fields

abstract:
  The mass-metallicity relation shows that the galaxies with the lowest mass
have the lowest metallicities. As most dwarf galaxies are in group
environments, interaction effects such as tides could contribute to this trend.
We perform a series of smoothed particle hydrodynamics (SPH) simulations of
dwarf galaxies in external tidal fields to examine the effects of tides on
their metallicities and metallicity gradients. In our simulated galaxies,
gravitational instabilities drive gas inwards and produce centralized star
formation and a significant metallicity gradient. Strong tides can contribute
to these instabilities, but their primary effect is to strip the outer
low-metallicity gas, producing a truncated gas disk with a large metallicity.
This suggests that the role of tides on the mass-metallicity relation is to
move dwarf galaxies to higher metallicities.


title: Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution

abstract:
  Influence maximization in social networks has typically been studied in the
context of contagion models and irreversible processes. In this paper, we
consider an alternate model that treats individual opinions as spins in an
Ising system at dynamic equilibrium. We formalize the \textit{Ising influence
maximization} problem, which has a natural physical interpretation as
maximizing the magnetization given a budget of external magnetic field. Under
the mean-field (MF) approximation, we present a gradient ascent algorithm that
uses the susceptibility to efficiently calculate local maxima of the
magnetization, and we develop a number of sufficient conditions for when the MF
magnetization is concave and our algorithm converges to a global optimum. We
apply our algorithm on random and real-world networks, demonstrating,
remarkably, that the MF optimal external fields (i.e., the external fields
which maximize the MF magnetization) shift from focusing on high-degree
individuals at high temperatures to focusing on low-degree individuals at low
temperatures. We also establish a number of novel results about the structure
of steady-states in the ferromagnetic MF Ising model on general graph
topologies, which are of independent interest.


title: Posterior consistency for partially observed Markov models

abstract:
  In this work we establish the posterior consistency for a parametrized family
of partially observed, fully dominated Markov models. As a main assumption, we
suppose that the prior distribution assigns positive probability to all
neighborhoods of the true parameter, for a distance induced by the expected
Kullback-Leibler divergence between the family members' Markov transition
densities. This assumption is easily checked in general. In addition, under
some additional, mild assumptions we show that the posterior consistency is
implied by the consistency of the maximum likelihood estimator. The latter has
recently been established also for models with non-compact state space. The
result is then extended to possibly non-compact parameter spaces and
non-stationary observations. Finally, we check our assumptions on examples
including the partially observed Gaussian linear model with correlated noise
and a widely used stochastic volatility model.


title:
Solutions of the main boundary value problems for the time-fractional
  telegraph equation by the Green function method

abstract:
  The inhomogenous time-fractional telegraph equation with Caputo derevatives
with constant coefficients is considered. For considered equation the general
representation of regular solution in rectangular domain is obtained, and the
fundamental solution is presented. Using this representation and the properties
of fundamental solution, the Cauchy problem and the basic problems in
half-strip and rectangular domains are studied. For Cauchy problem the theorems
of existence and uniqueness of solution are proved, and the explicit form of
solution is constructed. The solutions of the investigated problems are
constructed in terms of the appropriate Green functions, which are also
constructed an explicit form.


title:
Inverse design of high-Q wave filters in two-dimensional phononic
  crystals by topology optimization

abstract:
  Topology optimization of a waveguide-cavity structure in phononic crystals
for designing narrow band filters under the given operating frequencies is
presented in this paper. We show that it is possible to obtain an ultra-high-Q
filter by only optimizing the cavity topology without introducing any other
coupling medium. The optimized cavity with highly symmetric resonance can be
utilized as the multi-channel filter, raising filter and T-splitter. In
addition, most optimized high-Q filters have the Fano resonances near the
resonant frequencies. Furthermore, our filter optimization based on the
waveguide and cavity, and our simple illustration of a computational approach
to wave control in phononic crystals can be extended and applied to design
other acoustic devices or even opto-mechanical devices.


title: A generalized cubic moment and the Petersson formula for newforms

abstract:
  Using a cubic moment, we prove a Weyl-type subconvexity bound for the
quadratic twists of a holomorphic newform of square-free level, trivial
nebentypus, and arbitrary even weight. This generalizes work of Conrey and
Iwaniec in that the newform that is being twisted may have arbitrary
square-free level, and also that the quadratic character may have even
conductor. One of the new tools developed in this paper is a more general
Petersson formula for newforms of square-free level.


title:
Environmental Effects in Mechanical Properties of Few-layer Black
  Phosphorus

abstract:
  We report on the mechanical properties of few-layer black phosphorus (BP)
nanosheets, in high vacuum and as a function of time of exposure to atmospheric
conditions [1]. BP flakes with thicknesses ranging from 4 to 30 nm suspended
over circular holes are characterized by nanoindentations using an atomic force
microscope tip. From measurements in high vacuum an elastic modulus of 46+/-10
GPa and breaking strength of 2.4+/-1 GPa are estimated. Both magnitudes are
independent of the thickness of the flakes. Our results show that the exposure
to air has substantial influence in the mechanical response of flakes thinner
than 6 nm but small effects on thicker flakes.


title: Full counting statistics in the Haldane-Shastry chain

abstract:
  We present analytical and numerical results regarding the magnetization full
counting statistics (FCS) of a subsystem in the ground-state of the
Haldane-Shastry chain. Exact Pfaffian expressions are derived for the cumulant
generating function, as well as any observable diagonal in the spin basis. In
the limit of large systems, the scaling of the FCS is found to be in agreement
with the Luttinger liquid theory. The same techniques are also applied to
inhomogeneous deformations of the chain. This introduces a certain amount of
disorder in the system; however we show numerically that this is not sufficient
to flow to the random singlet phase, that corresponds to $XXZ$ chains with
uncorrelated bond disorder.


title:
ATCA observations of the MACS-Planck Radio Halo Cluster Project - I. New
  detection of a radio halo in PLCK G285.0-23.7

abstract:
  We investigate the possible presence of diffuse radio emission in the
intermediate redshift, massive cluster PLCK G285.0-23.7 (z=0.39, M_500 = 8.39 x
10^(14) M_Sun). Our 16cm-band ATCA observations of PLCK G285.0-23.7 allow us to
reach a rms noise level of ~11 microJy/beam on the wide-band (1.1-3.1 GHz),
full-resolution (~5 arcsec) image of the cluster, making it one of the deepest
ATCA images yet published. We also re-image visibilities at lower resolution in
order to achieve a better sensitivity to low-surface-brightness extended radio
sources. We detect one of the lowest luminosity radio halos known at z>0.35,
characterised by a slight offset from the well-studied 1.4 GHz radio power vs.
cluster mass correlation. Similarly to most known radio-loud clusters (i.e.
those hosting diffuse non-thermal sources), PLCK G285.0-23.7 has a disturbed
dynamical state. Our analysis reveals a similarly elongated X-ray and radio
morphology. While the size of the radio halo in PLCK G285.0-23.7 is smaller
than lower redshift radio-loud clusters in the same mass range, it shows a
similar correlation with the cluster virial radius, as expected in the
framework of hierarchical structure formation.


title:
Probability distributions of continuous measurement results for
  conditioned quantum evolution

abstract:
  We address the statistics of continuous weak linear measurement on a
few-state quantum system that is subject to a conditioned quantum evolution.
For a conditioned evolution, both the initial and final states of the system
are fixed: the latter is achieved by the post-selection in the end of the
evolution. The statistics may drastically differ from the non-conditioned case,
and the interference between initial and final states can be observed in the
probability distributions of measurement outcomes as well as in the average
values exceeding the conventional range of non-conditioned averages. We develop
a proper formalism to compute the distributions of measurement outcomes,
evaluate and discuss the distributions in experimentally relevant setups. We
demonstrate the manifestations of the interference between initial and final
states in various regimes. We consider analytically simple examples of
non-trivial probability distributions. We reveal peaks (or dips) at
half-quantized values of the measurement outputs. We discuss in detail the case
of zero overlap between initial and final states demonstrating anomalously big
average outputs and sudden jump in time-integrated output. We present and
discuss the numerical evaluation of the probability distribution aiming at
extend- ing the analytic results and describing a realistic experimental
situation of a qubit in the regime of resonant fluorescence.


title:
Mechanical Isolation of Highly Stable Antimonene under Ambient
  Conditions

abstract:
  Using mechanical exfoliation combined with a controlled double step transfer
procedure we demonstrate that single layers of antimony can be readily
produced. These flakes are not significantly contaminated upon exposure to
ambient conditions and they do not react with water. DFT calculations confirm
our experimental observations and predict a band gap of 1.2-1.3 eV (ambient
conditions) for single layer antimonene, which is smaller than that calculated
under vacuum conditions at 0 K. Our work confirms antimonene as a highly stable
2D material with promising relevant applications in optoelectronics.


title:
Some implications of the Hartree product treatment of the quantum nuclei
  in the ab initio Nuclear-electronic orbital methodology

abstract:
  In this letter the conceptual and computational implications of the Hartree
product type nuclear wavefunction introduced recently within the context of the
ab initio non-Born-Oppenheimer Nuclear-electronic orbital (NEO) methodology are
considered. It is demonstrated that this wavefunction may imply a
pseudo-adiabatic separation of the nuclei and electrons and each nucleus is
conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian
is deduced for electrons. Using the variational principle this Hamiltonian is
employed to derive a modified set of single-component Hartree-Fock equations
which are equivalent to the multi-component version derived previously within
the context of the NEO and, easy to be implemented computationally.


title: Parallel K-Medoids++ Spatial Clustering Algorithm Based on MapReduce

abstract:
  Clustering analysis has received considerable attention in spatial data
mining for several years. With the rapid development of the geospatial
information technologies, the size of spatial information data is growing
exponentially which makes clustering massive spatial data a challenging task.
In order to improve the efficiency of spatial clustering for large scale data,
many researchers proposed several efficient clustering algorithms in parallel.
In this paper, a new K-Medoids++ spatial clustering algorithm based on
MapReduce for clustering massive spatial data is proposed. The initialization
algorithm to decrease the number of iterations is combined with the MapReduce
framework. Comparative Experiments conducted over different dataset and
different number of nodes indicate that the proposed K-Medoids spatial
clustering algorithm provides better efficiency than traditional K-Medoids and
scales well while processing massive spatial data on commodity hardware.


title:
Superfluid-Mott glass quantum multicritical point on a percolating
  lattice

abstract:
  We employ large-scale Monte Carlo simulations to study a particle-hole
symmetric site-diluted quantum rotor model in two dimensions. The ground state
phase diagram of this system features two distinct quantum phase transitions
between the superfluid and the insulating (Mott glass) phases. They are
separated by a multicritical point. The generic transition for dilutions below
the lattice percolation threshold is driven by quantum fluctuations while the
transition across the percolation threshold is due to the geometric
fluctuations of the lattice. We determine the location of the multicritical
point between these two transitions and find its critical behavior. The
multicritical exponents read $z=1.72(2)$, $\beta/\nu=0.41(2)$, and
$\gamma/\nu=2.90(5)$ . We compare our results to other quantum phase
transitions in disordered systems, and we discuss experiments.


title:
Kullback-Leibler Penalized Sparse Discriminant Analysis for
  Event-Related Potential Classification

abstract:
  A brain computer interface (BCI) is a system which provides direct
communication between the mind of a person and the outside world by using only
brain activity (EEG). The event-related potential (ERP)-based BCI problem
consists of a binary pattern recognition. Linear discriminant analysis (LDA) is
widely used to solve this type of classification problems, but it fails when
the number of features is large relative to the number of observations. In this
work we propose a penalized version of the sparse discriminant analysis (SDA),
called Kullback-Leibler penalized sparse discriminant analysis (KLSDA). This
method inherits both the discriminative feature selection and classification
properties of SDA and it also improves SDA performance through the addition of
Kullback-Leibler class discrepancy information. The KLSDA method is design to
automatically select the optimal regularization parameters. Numerical
experiments with two real ERP-EEG datasets show that this new method
outperforms standard SDA.


title: The MHS algebra and supercongruences

abstract:
  A supercongruence is a congruence between rational numbers modulo a power of
a prime. In this paper, we give a technique for finding and algorithmically
proving supercongruences by expressing terms as infinite series involving
certain generalizations of the harmonic numbers. We apply the technique to
derive many new supercongruences. We also provide software for finding and
proving supercongruences using our technique.


title:
Bayesian Statistics in Software Engineering: Practical Guide and Case
  Studies

abstract:
  Statistics comes in two main flavors: frequentist and Bayesian. For
historical and technical reasons, frequentist statistics has dominated data
analysis in the past; but Bayesian statistics is making a comeback at the
forefront of science. In this paper, we give a practical overview of Bayesian
statistics and illustrate its main advantages over frequentist statistics for
the kinds of analyses that are common in empirical software engineering, where
frequentist statistics still is standard. We also apply Bayesian statistics to
empirical data from previous research investigating agile vs. structured
development processes, the performance of programming languages, and random
testing of object-oriented programs. In addition to being case studies
demonstrating how Bayesian analysis can be applied in practice, they provide
insights beyond the results in the original publications (which used
frequentist statistics), thus showing the practical value brought by Bayesian
statistics.


title:
Anderson-Mott transition in a disordered Hubbard model with correlated
  hopping

abstract:
  We study the ground state phase diagram of the Anderson-Hubbard model with
correlated hopping at half filling in one-dimension. The Hamiltonian has a
local Coulomb repulsion $U$ and a disorder potential with local energies
randomly distributed in the interval $(-W,+W)$ with equal probability, acting
on the singly occupied sites. The hopping process which modifies the number of
doubly occupied sites is forbidden. The hopping between nearest-neighbor singly
occupied and empty sites or between singly occupied and doubly occupied sites
have the same amplitude $t$. We identify three different phases as functions of
the disorder amplitude $W$ and Coulomb interaction strength $U>0$. When $U<4t$
the system shows a metallic phase (i) only when no disorder is present $W=0$ or
an Anderson-localized phase (ii) when disorder is introduced $W\neq 0$. When
$U>4t$ the Anderson-localized phase survives as long as disorder effects
dominates on the interaction effects, otherwise a Mott insulator phase (iii)
arises. The phases (i) and (ii) are characterized by a finite density of
doublons and a vanishing charge gap between the ground state and the excited
states. The phase (iii) is characterized by vanishing density of doublons and a
finite gap for the charge excitations.


title: Velocity Gradients as a Tracer for Magnetic Fields

abstract:
  Strong Alfv\'enic turbulence develops eddy-like motions perpendicular to the
local direction of magnetic fields. This local alignment induces velocity
gradients perpendicular to the local direction of the magnetic field. We use
this fact to propose a new technique of studying the direction of magnetic
fields from observations, the Velocity Gradient Technique. We test our idea by
employing the synthetic observations obtained via 3D MHD numerical simulations
for different sonic and Alfv\'en Mach numbers. We calculate the velocity
gradient, $\mathbf{\Omega}$, using the velocity centroids. We find that
$\mathbf{\Omega}$ traces the projected magnetic field best for the synthetic
maps obtained with sub-Alfv\'enic simulations providing good point-wise
correspondence between the magnetic field direction and that of
$\mathbf{\Omega}$. The reported alignment is much better than the alignment
between the density gradients and the magnetic field and we demonstrated that
it can be used to find the magnetic field strength using the
Chandrasekhar-Fermi method. Our study opens a new way of studying magnetic
fields using spectroscopic data.


title:
Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the
  Distribution of Prime Numbers

abstract:
  The occurrence and frequency of a phenomenon of resonance (namely the
coalescence of some Dubrovin canonical coordinates) in the locus of Small
Quantum Cohomology of complex Grassmannians is studied. It is shown that
surprisingly this frequency is strictly subordinate and highly influenced by
the distribution of prime numbers. Two equivalent formulations of the Riemann
Hypothesis are given in terms of numbers of complex Grassmannians without
coalescence: the former as a constraint on the disposition of singularities of
the analytic continuation of the Dirichlet series associated to the sequence
counting non-coalescing Grassmannians, the latter as asymptotic estimate (whose
error term cannot be improved) for their distribution function.


title:
Improving the Flux Calibration in Reverberation Mapping by Spectral
  Fitting: Application to the Seyfert Galaxy MCG--6-30-15

abstract:
  We propose a method for the flux calibration of reverberation mapping spectra
based on accurate measurement of [O III] $\lambda 5007$ emission by spectral
fitting. The method can achieve better accuracy than the traditional method of
van Groningen & Wanders (1992), allowing reverberation mapping measurements for
object with variability amplitudes as low as $\sim$ 5%. As a demonstration, we
reanalyze the data of the Seyfert 1 galaxy MCG--6-30-15 taken from the 2008
campaign of the Lick AGN Monitoring Project, which previously failed to obtain
a time lag for this weakly variable object owing to a relatively large flux
calibration uncertainty. We detect a statistically significant rest-frame time
lag of $6.38_{-2.69}^{+3.07}$ days between the H$\beta$ and $V$-band light
curves. Combining this lag with FWHM(H$\beta$) = $1933\pm81$ $\rm km~s^{-1}$
and a virial coefficient of $f$ = 0.7, we derive a virial black hole mass of
$3.26_{-1.40}^{+1.59}\times10^6$ $M_{\odot}$, which agrees well with previous
estimates by other methods.


title:
Chemical ordering beyond the superstructure in long-range ordered
  systems

abstract:
  To describe chemical ordering in solid solutions systems Warren-Cowley
short-range parameters are ordinarily used. However, they are not directly
suited for application to long-range ordered systems, as they do not converge
to zero for large separations. It is the aim of this paper to generalize the
theory to long-range ordered systems and quantitatively discuss chemical
short-range order beyond the superstructure arrangements. This is demonstrated
on the example of a non-stoichiometric B2-ordered intermetallic alloy.
Parameters of interatomic potentials are taken from an embedded atom method
(EAM) calculations and the degree of order is simulated by the Monte Carlo
method. Both on-lattice and off-lattice methods, where the latter allows
individual atoms to deviate from their regular lattice sites, were used, and
the resulting effects are discussed.


title:
High resolution inverse scattering in two dimensions using recursive
  linearization

abstract:
  We describe a fast, stable algorithm for the solution of the inverse acoustic
scattering problem in two dimensions. Given full aperture far field
measurements of the scattered field for multiple angles of incidence, we use
Chen's method of recursive linearization to reconstruct an unknown sound speed
at resolutions of thousands of square wavelengths in a fully nonlinear regime.
Despite the fact that the underlying optimization problem is formally ill-posed
and non-convex, recursive linearization requires only the solution of a
sequence of linear least squares problems at successively higher frequencies.
By seeking a suitably band-limited approximation of the sound speed profile,
each least squares calculation is well-conditioned and involves the solution of
a large number of forward scattering problems, for which we employ a recently
developed, spectrally accurate, fast direct solver. For the largest problems
considered, involving 19,600 unknowns, approximately one million partial
differential equations were solved, requiring approximately two days to compute
using a parallel MATLAB implementation on a multi-core workstation.


title:
The genus one Complex Quantum Chern-Simons representation of the Mapping
  Class Group

abstract:
  In this paper we compute explicitly, following Witten's prescription, the
quantum representation of the mapping class group in genus one for complex
quantum Chern-Simons theory associated to any simple and simply connected
complex gauge group $G_{\mathbb C}$. We use a generalization of the
Weil-Gel'fand-Zak transform to exhibit an explicit expression for the
representation.


title: On properties of the exotic hadrons from QCD sum rules

abstract:
  We discuss the specific features of extracting properties of the exotic
polyquark hadrons (tetraquarks, pentaquarks) compared to the usual hadrons by
the QCD sum-rule approach. In the case of the ordinary hadrons, already the
one-loop leading-order correlation functions provide the bulk of the hadron
observables, e.g., of the form factor; inclusion of radiative corrections
modifies already nonzero one-loop contributions. In the case of an exotic
hadron, the situation is qualitatively different: discussing strong decays of
an exotic tetraquark meson, which provide the main contribution to its width,
we show that the disconnected leading-order diagrams are not related to the
tetraquark properties. For a proper description of the tetraquark decay width,
it is mandatory to calculate specific radiative corrections which generate the
connected diagrams.


title:
Perfect vector sets, properly overlapping partitions, and largest empty
  box

abstract:
  We revisit the following problem (along with its higher dimensional variant):
Given a set $S$ of $n$ points inside an axis-parallel rectangle $U$ in the
plane, find a maximum-area axis-parallel sub-rectangle that is contained in $U$
but contains no points of $S$. (I) We present an algorithm that finds a large
empty box amidst $n$ points in $[0,1]^d$: a box whose volume is at least
$\frac{\log{d}}{4(n + \log{d})}$ can be computed in $O(n+d \log{d})$ time. (II)
To better analyze the above approach, we introduce the concepts of perfect
vector sets and properly overlapping partitions, in connection to the minimum
volume of a maximum empty box amidst $n$ points in the unit hypercube
$[0,1]^d$, and derive bounds on their sizes.


title: Fefferman-Graham ambient metrics of Patterson-Walker metrics

abstract:
  Given an $n$-dimensional manifold $N$ with an affine connection $D$, we show
that the associated Patterson-Walker metric $g$ on $T^*N$ admits a global and
explicit Fefferman-Graham ambient metric. This provides a new and large class
of conformal structures which are generically not conformally Einstein but for
which the ambient metric exists to all orders and can be realized in a natural
and explicit way. In particular, it follows that Patterson-Walker metrics have
vanishing Fefferman-Graham obstruction tensors. As an application of the
concrete ambient metric realization we show in addition that Patterson-Walker
metrics have vanishing Q-curvature.


title: Sedano: A News Stream Processor for Business

abstract:
  We present Sedano, a system for processing and indexing a continuous stream
of business-related news. Sedano defines pipelines whose stages analyze and
enrich news items (e.g., newspaper articles and press releases). News data
coming from several content sources are stored, processed and then indexed in
order to be consumed by Atoka, our business intelligence product. Atoka users
can retrieve news about specific companies, filtering according to various
facets. Sedano features both an entity-linking phase, which finds mentions of
companies in news, and a classification phase, which classifies news according
to a set of business events. Its flexible architecture allows Sedano to be
deployed on commodity machines while being scalable and fault-tolerant.


title: On Primes, Graphs and Cohomology

abstract:
  The counting function on the natural numbers defines a discrete Morse-Smale
complex with a cohomology for which topological quantities like Morse indices,
Betti numbers or counting functions for critical points of Morse index are
explicitly given in number theoretical terms. The Euler characteristic of the
Morse filtration is related to the Mertens function, the Poincar\'e-Hopf
indices at critical points correspond to the values of the Moebius function.
The Morse inequalities link number theoretical quantities like the prime
counting functions relevant for the distribution of primes with cohomological
properties of the graphs. The just given picture is a special case of a
discrete Morse cohomology equivalent to simplicial cohomology. The special
example considered here is a case where the graph is the Barycentric refinement
of a finite simple graph.


title: Taking physical infinity seriously

abstract:
  The concept of infinity took centuries to achieve recognized status in the
field of mathematics, despite the fact that it was implicitly present in nearly
all mathematical endeavors. Here I explore the idea that a similar development
might be warranted in physics. Several threads will be speculatively examined,
including some involving nonstandard analysis. While there are intriguing
possibilities, there also are noteworthy difficulties.


title: AIDE: Fast and Communication Efficient Distributed Optimization

abstract:
  In this paper, we present two new communication-efficient methods for
distributed minimization of an average of functions. The first algorithm is an
inexact variant of the DANE algorithm that allows any local algorithm to return
an approximate solution to a local subproblem. We show that such a strategy
does not affect the theoretical guarantees of DANE significantly. In fact, our
approach can be viewed as a robustification strategy since the method is
substantially better behaved than DANE on data partition arising in practice.
It is well known that DANE algorithm does not match the communication
complexity lower bounds. To bridge this gap, we propose an accelerated variant
of the first method, called AIDE, that not only matches the communication lower
bounds but can also be implemented using a purely first-order oracle. Our
empirical results show that AIDE is superior to other communication efficient
algorithms in settings that naturally arise in machine learning applications.


title: Correlation between Adomian and Partial Exponential Bell Polynomials

abstract:
  We obtain some recurrence relationships among the partition vectors of the
partial exponential Bell polynomials. On using such results, the $n$-th Adomian
polynomial for any nonlinear operator can be expressed explicitly in terms of
the partial exponential Bell polynomials. Some new identities for the partial
exponential Bell polynomials are obtained by solving certain ordinary
differential equations using Adomian decomposition method.


title:
Valley Phase and Voltage Control of Coherent Manipulation in Si Quantum
  Dots

abstract:
  With any roughness at the interface of an indirect-bandgap semiconducting
dot, the phase of the valley-orbit coupling can take on a random value. This
random value, in double quantum dots, causes a large change in the exchange
splitting. We demonstrate a simple analytical method to calculate the phase,
and thus the exchange splitting and singlet-triplet qubit frequency, for an
arbitrary interface. We then show that, with lateral control of the position of
a quantum dot using a gate voltage, the valley-orbit phase can be controlled
over a wide range, so that variations in the exchange splitting can be
controlled for individual devices. Finally, we suggest experiments to measure
the valley phase and the concomitant gate voltage control.


title:
On the strength of the $U_A(1)$ anomaly at the chiral phase transition
  in $N_f=2$ QCD

abstract:
  We study the thermal transition of QCD with two degenerate light flavours by
lattice simulations using $O(a)$-improved Wilson quarks. Temperature scans are
performed at a fixed value of $N_t = (aT)^{-1}=16$, where $a$ is the lattice
spacing and $T$ the temperature, at three fixed zero-temperature pion masses
between 200 MeV and 540 MeV. In this range we find that the transition is
consistent with a broad crossover. As a probe of the restoration of chiral
symmetry, we study the static screening spectrum. We observe a degeneracy
between the transverse isovector vector and axial-vector channels starting from
the transition temperature. Particularly striking is the strong reduction of
the splitting between isovector scalar and pseudoscalar screening masses around
the chiral phase transition by at least a factor of three compared to its value
at zero temperature. In fact, the splitting is consistent with zero within our
uncertainties. This disfavours a chiral phase transition in the $O(4)$
universality class.


title:
Comment on: "The Frenkel Line: a direct experimental evidence for the
  new thermodynamic boundary"

abstract:
  In a recent publication (D. Bolmatov et al. Sci.Rep. 5, 15850 (2015)) the
experimental observation of structural transformations on crossing the Frenkel
line in supercritical argon is claimed. Here we show that no experimental
evidence of the structural transformation was presented. The reported
experimental observations which Bolmatov et al. claim as evidence of a
transition across the Frenkel line are instead due to the irregularity of the
experimental (P,T) path in their work.


title: Towards Bayesian Deep Learning: A Framework and Some Existing Methods

abstract:
  While perception tasks such as visual object recognition and text
understanding play an important role in human intelligence, the subsequent
tasks that involve inference, reasoning and planning require an even higher
level of intelligence. The past few years have seen major advances in many
perception tasks using deep learning models. For higher-level inference,
however, probabilistic graphical models with their Bayesian nature are still
more powerful and flexible. To achieve integrated intelligence that involves
both perception and inference, it is naturally desirable to tightly integrate
deep learning and Bayesian models within a principled probabilistic framework,
which we call Bayesian deep learning. In this unified framework, the perception
of text or images using deep learning can boost the performance of higher-level
inference and in return, the feedback from the inference process is able to
enhance the perception of text or images. This paper proposes a general
framework for Bayesian deep learning and reviews its recent applications on
recommender systems, topic models, and control. In this paper, we also discuss
the relationship and differences between Bayesian deep learning and other
related topics like Bayesian treatment of neural networks.


title:
Quantum dimensions and fusion products for irreducible V_Q^s-modules,
  where s is an isometry of Q with s^2=1

abstract:
  Every isometry s of a positive-definite even lattice Q can be lifted to an
automorphism of the lattice vertex algebra V_Q. An important problem in vertex
algebra theory and conformal field theory is to classify the representations of
the s-invariant subalgebra V_Q^s of V_Q, known as an orbifold. In the case when
s is an isometry of Q of order two, we have classified the irreducible modules
of the orbifold vertex algebra V_Q^s and identified them as submodules of
twisted or untwisted V_Q-modules in [Bavalov-Elsinger]. Here we calculate their
quantum dimensions and fusion products. The examples where Q is the orthogonal
direct sum of two copies of the A_2 root lattice and s is the 2-cycle
permutation as well as where Q is the A_n root latice and s is a Dynkin diagram
automorphism are presented in detail.


title: Behaviour of asymptotically electro-$\Lambda$ spacetimes

abstract:
  We present the asymptotic solutions for spacetimes with non-zero cosmological
constant $\Lambda$ coupled to Maxwell fields, using the Newman-Penrose
formalism. This extends a recent work that dealt with the vacuum Einstein
(Newman-Penrose) equations with $\Lambda\neq0$. The results are given in two
different null tetrads: the Newman-Unti and Szabados-Tod null tetrads, where
the peeling property is exhibited in the former but not the latter. Using these
asymptotic solutions, we discuss the mass-loss of an isolated
electro-gravitating system with cosmological constant. In a universe with
$\Lambda>0$, the physics of electromagnetic (EM) radiation is relatively
straightforward compared to those of gravitational radiation: 1) It is clear
that outgoing EM radiation results in a decrease to the Bondi mass of the
isolated system. 2) It is also perspicuous that if any incoming EM radiation
from elsewhere is present, those beyond the isolated system's cosmological
horizon would eventually arrive at the spacelike $\mathcal{I}$ and increase the
Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM
radiation fields do not couple with $\Lambda$ in the Bondi mass-loss formula in
an unusual manner, unlike the gravitational counterpart where outgoing
gravitational radiation induces non-conformal flatness of $\mathcal{I}$. These
asymptotic solutions to the Einstein-Maxwell-de Sitter equations presented here
may be used to extend a raft of existing results based on Newman-Unti's
asymptotic solutions to the Einstein-Maxwell equations where $\Lambda=0$, to
now incorporate the cosmological constant $\Lambda$.


title:
Multi-objective Compositions for Collision-Free Connectivity Maintenance
  in Teams of Mobile Robots

abstract:
  Compositional barrier functions are proposed in this paper to systematically
compose multiple objectives for teams of mobile robots. The objectives are
first encoded as barrier functions, and then composed using AND and OR logical
operators. The advantage of this approach is that compositional barrier
functions can provably guarantee the simultaneous satisfaction of all composed
objectives. The compositional barrier functions are applied to the example of
ensuring collision avoidance and static/dynamical graph connectivity of teams
of mobile robots. The resulting composite safety and connectivity barrier
certificates are verified experimentally on a team of four mobile robots.


title:
Extended Poisson-Tweedie: properties and regression models for count
  data

abstract:
  We propose a new class of discrete generalized linear models based on the
class of Poisson-Tweedie factorial dispersion models with variance of the form
$\mu + \phi\mu^p$, where $\mu$ is the mean, $\phi$ and $p$ are the dispersion
and Tweedie power parameters, respectively. The models are fitted by using an
estimating function approach obtained by combining the quasi-score and Pearson
estimating functions for estimation of the regression and dispersion
parameters, respectively. This provides a flexible and efficient regression
methodology for a comprehensive family of count models including Hermite,
Neyman Type A, P\'olya-Aeppli, negative binomial and Poisson-inverse Gaussian.
The estimating function approach allows us to extend the Poisson-Tweedie
distributions to deal with underdispersed count data by allowing negative
values for the dispersion parameter $\phi$. Furthermore, the Poisson-Tweedie
family can automatically adapt to highly skewed count data with excessive
zeros, without the need to introduce zero-inflated or hurdle components, by the
simple estimation of the power parameter. Thus, the proposed models offer a
unified framework to deal with under, equi, overdispersed, zero-inflated and
heavy-tailed count data. The computational implementation of the proposed
models is fast, relying only on a simple Newton scoring algorithm. Simulation
studies showed that the estimating function approach provides unbiased and
consistent estimators for both regression and dispersion parameters. We
highlight the ability of the Poisson-Tweedie distributions to deal with count
data through a consideration of dispersion, zero-inflated and heavy tail
indices, and illustrate its application with four data analyses. We provide an
\texttt{R} implementation and the data sets as supplementary materials.


title:
Detection methods for stochastic gravitational-wave backgrounds: a
  unified treatment

abstract:
  We review detection methods that are currently in use or have been proposed
to search for a stochastic background of gravitational radiation. We consider
both Bayesian and frequentist searches using ground-based and space-based laser
interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we
allow for anisotropy, non-Gaussianity, and non-standard polarization states.
Our focus is on relevant data analysis issues, and not on the particular
astrophysical or early Universe sources that might give rise to such
backgrounds. We provide a unified treatment of these searches at the level of
detector response functions, detection sensitivity curves, and, more generally,
at the level of the likelihood function, since the choice of signal and noise
models and prior probability distributions are actually what define the search.
Pedagogical examples are given whenever possible to compare and contrast
different approaches. We have tried to make the article as self-contained and
comprehensive as possible, targeting graduate students and new researchers
looking to enter this field.


title: On the curvature of conic Kaehler-Einstein metrics

abstract:
  We prove a regularity result for Monge-Amp\`ere equations degenerate along
smooth divisor on Kaehler manifolds in Donaldson's spaces of $\beta$-weighted
functions. We apply this result to study the curvature of Kaehler metrics with
conical singularities along divisors and give a geometric sufficient condition
on the divisor for its boundedness.


title:
Absolute Pose Estimation from Line Correspondences using Direct Linear
  Transformation

abstract:
  This work is concerned with camera pose estimation from correspondences of
3D/2D lines, i. e. with the Perspective-n-Line (PnL) problem. We focus on large
line sets, which can be efficiently solved by methods using linear formulation
of PnL. We propose a novel method "DLT-Combined-Lines" based on the Direct
Linear Transformation (DLT) algorithm, which benefits from a new combination of
two existing DLT methods for pose estimation. The method represents 2D
structure by lines, and 3D structure by both points and lines. The redundant 3D
information reduces the minimum required line correspondences to 5. A
cornerstone of the method is a combined projection matri xestimated by the DLT
algorithm. It contains multiple estimates of camera rotation and translation,
which can be recovered after enforcing constraints of the matrix. Multiplicity
of the estimates is exploited to improve the accuracy of the proposed method.
For large line sets (10 and more), the method is comparable to the
state-of-theart in accuracy of orientation estimation. It achieves
state-of-the-art accuracy in estimation of camera position and it yields the
smallest reprojection error under strong image noise. The method achieves top-3
results on real world data. The proposed method is also highly computationally
effective, estimating the pose of 1000 lines in 12 ms on a desktop computer.


title:
Neutron-rich rare isotope production from projectile fission of heavy
  beams in the energy range of 20 MeV/nucleon

abstract:
  We investigate the possibilities of producing neutron-rich nuclides in
projectile fission of heavy beams in the energy range of 20 MeV/nucleon
expected from low-energy facilities. We report our efforts to theoretically
describe the reaction mechanism of projectile fission following a multinucleon
transfer collision at this energy range. Our calculations are mainly based on a
two-step approach: the dynamical stage of the collision is described with
either the phenomenological Deep-Inelastic Transfer model (DIT), or with the
microscopic Constrained Molecular Dynamics model (CoMD). The
deexcitation/fission of the hot heavy projectile fragments is performed with
the Statistical Mul- tifragmentation Model (SMM). We compared our model
calculations with our previous experimental projectile-fission data of 238U (20
MeV/nucleon)+208Pb and 197Au (20 MeV/nucleon)+197Au and found an overall
reasonable agreement. Our study suggests that projectile fission following
periph- eral heavy-ion collisions at this energy range offers an effective
route to access very neutron-rich rare isotopes toward and beyond the
astrophysical r-process path.


title:
Discontinuous Cell Method (DCM) for the Simulation of Cohesive Fracture
  and Fragmentation of Continuous Media

abstract:
  In this paper, the Discontinuous Cell Method (DCM) is formulated with the
objective of simulating cohesive fracture propagation and fragmentation in
homogeneous solids without issues relevant to excessive mesh deformation
typical of available Finite Element formulations. DCM discretizes solids by
using the Delaunay triangulation and its associated Voronoi tessellation giving
rise to a system of discrete cells interacting through shared facets. For each
Voronoi cell, the displacement field is approximated on the basis of rigid body
kinematics, which is used to compute a strain vector at the centroid of the
Voronoi facets. Such strain vector is demonstrated to be the projection of the
strain tensor at that location. At the same point stress tractions are computed
through vectorial constitutive equations derived on the basis of classical
continuum tensorial theories. Results of analysis of a cantilever beam are used
to perform convergence studies and comparison with classical finite element
formulations in the elastic regime. Furthermore, cohesive fracture and
fragmentation of homogeneous solids are studied under quasi-static and dynamic
loading conditions. The mesh dependency problem, typically encountered upon
adopting softening constitutive equations, is tackled through the crack band
approach. This study demonstrates the capabilities of DCM by solving multiple
benchmark problems relevant to cohesive crack propagation. The simulations show
that DCM can handle effectively a wide range of problems from the simulation of
a single propagating fracture to crack branching and fragmentation.


title:
Implicit Finite Volume and Discontinuous Galerkin Methods for
  Multicomponent Flow in Unstructured 3D Fractured Porous Media

abstract:
  We present a new implicit higher-order finite element (FE) approach to
efficiently model compressible multicomponent fluid flow on unstructured grids
and in fractured porous subsurface formations. The scheme is sequential
implicit: pressures and fluxes are updated with an implicit Mixed Hybrid Finite
Element (MHFE) method, and the transport of each species is approximated with
an implicit second-order Discontinuous Galerkin (DG) FE method. Discrete
fractures are incorporated with a cross-flow equilibrium approach. This is the
first investigation of all-implicit higher-order MHFE-DG for unstructured
triangular, quadrilateral (2D), and hexahedral (3D) grids and discrete
fractures. A lowest-order implicit finite volume (FV) transport update is also
developed for the same grid types. The implicit methods are compared to an
Implicit-Pressure-Explicit-Composition (IMPEC) scheme. For fractured domains,
the unconditionally stable implicit transport update is shown to increase
computational efficiency by orders of magnitude as compared to IMPEC, which has
a time-step constraint proportional to the pore volume of discrete fracture
grid cells. However, when lowest-order Euler time-discretizations are used,
numerical errors increase linearly with the larger implicit time-steps,
resulting in high numerical dispersion. Second-order Crank-Nicolson implicit
MHFE-DG and MHFE-FV are therefore presented as well. Convergence analyses show
twice the convergence rate for the DG methods as compared to FV, resulting in
two to three orders of magnitude higher computational efficiency. Numerical
experiments demonstrate the efficiency and robustness in modeling compressible
multicomponent flow on irregular and fractured 2D and 3D grids, even in the
presence of fingering instabilities.


title:
Superconducting gap structure of the skutterudite LaPt4Ge12 probed by
  specific heat and thermal transport

abstract:
  We investigated the superconducting order parameter of the filled
skutterudite LaPt4Ge12, with a transition temperature of Tc = 8.3 K. To this
end, we performed temperature and magnetic-field dependent specific-heat and
thermal-conductivity measurements. All data are compatible with a single
superconducting s-wave gap. However, a multiband scenario cannot be ruled out.
The results are discussed in the context of previous studies on the
substitution series Pr1-xLaxPt4Ge12. They suggest compatible order parameters
for the two end compounds LaPt4Ge12 and PrPt4Ge12. This is not consistent with
a single s-wave gap in LaPt4Ge12 considering previous reports of unconventional
and/or multiband superconductivity in PrPt4Ge12.


title: Charge radii of heavy flavored mesons in a potential model

abstract:
  We report the results for charge radii of heavy flavored mesons ($D^+, D^0,
D^+_s, B^+, B^0, B^0_s$) in an improved QCD potential model. To enhance the
effectiveness of short range and long range effect of the potential
$V(r)=-4\frac{\alpha_s}{3r}+br+c$ in the perturbative procedure a cut-off
parameter $r^P$ is introduced as an integration limit. The obtained results are
found to be comparable with other available data. The limitation of the
approach is discussed in the manuscript.


title:
Full Computational Reproducibility in Biological Science: Methods,
  Software and a Case Study in Protein Biology

abstract:
  Independent computational reproducibility of scientific results is rapidly
becoming of pivotal importance in scientific progress as computation itself
plays a more and more central role in so many branches of science.
Historically, reproducibility has followed the familiar Popperian [38] model
whereby theory cannot be verified by scientific testing, it can only be
falsified. Ultimately, this implies that if an experiment cannot be reproduced
independently to some satisfactory level of precision, its value is essentially
unquantifiable; put brutally, it is impossible to determine its scientific
value. The burgeoning presence of software in most scientific work adds a new
and particularly opaque layer of complexity [29]. In spite of much recent
interest in many scientific areas, emphasis remains more on procedures,
strictures and discussion [12, 14, 16, 29, 30, 37, 41], reflecting the
inexperience of most scientific journals when it comes to software, rather than
the details of how computational reproducibility is actually achieved, for
which there appear to be relatively few guiding examples [6, 10, 17]. After
considering basic principles, here we show how full computational
reproducibility can be achieved in practice at every stage using a case study
of a multi-gigabyte protein study on the open SwissProt protein database, from
data download all the way to individual figure by figure reproduction as an
exemplar for general scientific computation.


title: Geometric control of active collective motion

abstract:
  Recent experimental studies have shown that confinement can profoundly affect
self-organization in semi-dilute active suspensions, leading to striking
features such as the formation of steady and spontaneous vortices in circular
domains and the emergence of unidirectional pumping motions in periodic
racetrack geometries. Motivated by these findings, we analyze the
two-dimensional dynamics in confined suspensions of active self-propelled
swimmers using a mean-field kinetic theory where conservation equations for the
particle configurations are coupled to the forced Navier-Stokes equations for
the self-generated fluid flow. In circular domains, a systematic exploration of
the parameter space casts light on three distinct states: equilibrium with no
flow, stable vortex, and chaotic motion, and the transitions between these are
explained and predicted quantitatively using a linearized theory. In periodic
racetracks, similar transitions from equilibrium to net pumping to traveling
waves to chaos are observed in agreement with experimental observations and are
also explained theoretically. Our results underscore the subtle effects of
geometry on the morphology and dynamics of emerging patterns in active
suspensions and pave the way for the control of active collective motion in
microfluidic devices.


title: Chiral fermions on 2D curved spacetimes

abstract:
  The theory of free Majorana-Weyl spinors is the prototype of conformal field
theory in two dimensions in which the gravitational anomaly and the Weyl
anomaly obstruct extending the flat spacetime results to curved backgrounds. In
this paper, we investigate a quantization scheme in which the short distance
singularity in the two-point function of chiral fermions on a two dimensional
curved spacetime is given by the Green's function corresponding to the
classical field equation. We compute the singular term in the Green's function
explicitly and observe that the short distance limit is not well-defined in
general. We identify constraints on the geometry which are necessary to resolve
this problem. On such special backgrounds the theory has locally
$c=\frac{1}{2}$ conformal symmetry.


title:
Characterization of the Quasi-Stationary State of an Impurity Driven by
  Monochromatic Light II - Microscopic Foundations

abstract:
  From quantum mechanical first principles only, we rigorously study the
time-evolution of a $N$-level atom (impurity) interacting with an external
monochromatic light source within an infinite system of free electrons at
thermal equilibrium (reservoir). In particular, we establish the relation
between the full dynamics of the compound system and the effective dynamics for
the $N$-level atom, which is studied in detail in [Bru-de Siqueira
Pedra-Westrich, Annales Henri Poincar\'e, 13(6):1305-1370, 2012]. Together with
[Bru-de Siqueira Pedra-Westrich, Annales Henri Poincar\'e, 13(6):1305-1370,
2012] the present paper yields a purely microscopic theory of optical pumping
in laser physics. The model we consider is general enough to describe gauge
invariant atom-reservoir interactions.


title:
Electrical tuning of exciton-plasmon polariton coupling in monolayer
  MoS2 integrated with plasmonic nanoantenna lattice

abstract:
  Active control of light-matter interactions in semiconductors is critical for
realizing next generation optoelectronic devices, with tunable control of the
systems optical properties via external fields. The ability to manipulate
optical interactions in active materials coupled to cavities via geometrical
parameters, which are fixed along with dynamic control with applied fields
opens up possibilities of controlling exciton lifetimes, oscillator strengths
and their relaxation properties. Here, we demonstrate electrical control of
exciton-plasmon polariton coupling strength of a two-dimensional semiconductor
integrated with plasmonic nanoresonators assembled in a field-effect transistor
device between strong and weak coupling limits by electrostatic doping. As a
result, the exciton-plasmon polarion dispersion can be altered dynamically with
applied electric field by modulating the excitonic properties of monolayer MoS2
arising from many-body effects with carrier concentration. In addition, strong
coupling between charged excitons plasmons was also observed upon increased
carrier injection. The ability to dynamically control the optical properties of
an ultra-thin semiconductor with plasmonic nanoresonators and electric fields
demonstrates the versatility of the coupled system and offers a new platform
for the design of optoelectronic devices with precisely tailored responses.


title: Recurrent Neural Networks With Limited Numerical Precision

abstract:
  Recurrent Neural Networks (RNNs) produce state-of-art performance on many
machine learning tasks but their demand on resources in terms of memory and
computational power are often high. Therefore, there is a great interest in
optimizing the computations performed with these models especially when
considering development of specialized low-power hardware for deep networks.
One way of reducing the computational needs is to limit the numerical precision
of the network weights and biases. This has led to different proposed rounding
methods which have been applied so far to only Convolutional Neural Networks
and Fully-Connected Networks. This paper addresses the question of how to best
reduce weight precision during training in the case of RNNs. We present results
from the use of different stochastic and deterministic reduced precision
training methods applied to three major RNN types which are then tested on
several datasets. The results show that the weight binarization methods do not
work with the RNNs. However, the stochastic and deterministic ternarization,
and pow2-ternarization methods gave rise to low-precision RNNs that produce
similar and even higher accuracy on certain datasets therefore providing a path
towards training more efficient implementations of RNNs in specialized
hardware.


title:
Stochastic Comparison of Parallel Systems with Log-Lindley Distributed
  Components

abstract:
  In this paper, we study stochastic comparisons of parallel systems having
log-Lindley distributed components. These comparisons are carried out with
respect to reversed hazard rate and likelihood ratio ordering.


title: Thick Subcategories of Discrete Derived Categories

abstract:
  We classify the thick subcategories of discrete derived categories. To do
this we introduce certain generating sets called arc-collections which
correspond to configurations of non-crossing arcs on a geometric model. We show
that every thick subcategory is generated by an arc-collection, each thick
subcategory is determined by the topology of the corresponding configuration,
and we describe a version of mutation which acts transitively on the set of
arc-collections generating a given thick subcategory.


title: P\'olya's conjecture fails for the fractional Laplacian

abstract:
  The analogue of P\'olya's conjecture is shown to fail for the fractional
Laplacian (-Delta)^{alpha/2} on an interval in 1-dimension, whenever 0 < alpha
< 2. The failure is total: every eigenvalue lies below the corresponding term
of the Weyl asymptotic.
  In 2-dimensions, the fractional P\'olya conjecture fails already for the
first eigenvalue, when 0 < alpha < 0.984.


title: Modelling electroweak physics for the forward region

abstract:
  This note presents a study of matching and merging schemes and weak showering
at the LHC as applied to the production of electroweak bosons in association
with jets. These advanced theoretical tools are seen to provide a good
description of event shapes in the central region when compared to measurements
performed by the ATLAS and CMS collaborations at a centre-of-mass energy of 7
TeV. Matching and merging schemes also provide a superior description of
forward $Z+$jets production. The study constitutes a test of matching and
merging schemes in a novel region of phase space and can be considered as a
validation of the universality of these techniques. Finally, it was determined
that current measurements of electroweak physics at LHCb do not yet fully probe
the effect of weak showers.


title: Tunable orbital angular momentum in high-harmonic generation

abstract:
  Optical vortices are currently one of the most intensively studied topics in
optics. These light beams, which carry orbital angular momentum (OAM), have
been successfully utilized in the visible and infrared in a wide variety of
applications. Moving to shorter wavelengths may open up completely new research
directions in the areas of optical physics and material characterization. Here,
we report on the generation of extreme-ultraviolet optical vortices with
femtosecond duration carrying a controllable amount of OAM. From a basic
physics viewpoint, our results help to resolve key questions such as the
conservation of angular momentum in highly-nonlinear light-matter interactions,
and the disentanglement and independent control of the intrinsic and extrinsic
components of the photon's angular momentum at short-wavelengths. The methods
developed here will allow testing some of the recently proposed concepts such
as OAM-induced dichroism, magnetic switching in organic molecules, and
violation of dipolar selection rules in atoms.


title:
Exploring plausible formation scenarios for the planet candidate
  orbiting Proxima Centauri

abstract:
  We present a study of four different formation scenarios that may be able to
explain the origin of the recently announced planet (`Proxima b') orbiting
Proxima Centauri. The aim is to examine how the formation scenarios differ in
their predictions for the multiplicity of the Proxima system, the
water/volatile content of Proxima b and its orbital eccentricity, so that these
can be tested by future observations. A scenario of in situ formation via giant
impacts from a locally enhanced disc of planetary embryos/planetesimals
predicts that Proxima b will be in a multiplanet system with a measurably
finite eccentricity. Assuming that the local solid enhancement needed to form a
Proxima b analogue arises because of the inwards drift of solids in the form of
small planetesimals/boulders, this scenario also results in Proxima b analogues
being only moderately endowed with water/volatiles. A scenario in which
multiple embryos form, migrate and mutually collide within a gas disc results
in Proxima b being a member of a multiple system, possibly displaying mean
motion resonances, but where the constituent members are Ocean planets due to
accretion occurring mainly outside of the snowline. A scenario in which a
single accreting embryo forms outside the snowline, and migrates inwards while
accreting planetesimals/pebbles results in Proxima b being an isolated Ocean
planet on a circular orbit. A scenario in which Proxima b formed via pebble
accretion interior to the snowline produces a dry planet on a circular orbit.
Future observations that characterise the physical and orbital properties of
Proxima b, and any additional planets in the system, will provide valuable
insights into the formation history of this neighbouring planetary system.


title:
Apparent rippling with honeycomb symmetry and tunable periodicity
  observed by scanning tunneling microscopy on suspended graphene

abstract:
  Suspended graphene is difficult to image by scanning probe microscopy due to
the inherent van-der-Waals and dielectric forces exerted by the tip which are
not counteracted by a substrate. Here, we report scanning tunneling microscopy
data of suspended monolayer graphene in constant-current mode revealing a
surprising honeycomb structure with amplitude of 50$-$200 pm and lattice
constant of 10-40 nm. The apparent lattice constant is reduced by increasing
the tunneling current $I$, but does not depend systematically on tunneling
voltage $V$ or scan speed $v_{\rm scan}$. The honeycomb lattice of the rippling
is aligned with the atomic structure observed on supported areas, while no
atomic corrugation is found on suspended areas down to the resolution of about
$3-4$ pm. We rule out that the honeycomb structure is induced by the feedback
loop using a changing $v_{\rm scan}$, that it is a simple enlargement effect of
the atomic resolution as well as models predicting frozen phonons or standing
phonon waves induced by the tunneling current. Albeit we currently do not have
a convincing explanation for the observed effect, we expect that our intriguing
results will inspire further research related to suspended graphene.


title:
A Parallel Memory-efficient Epistemic Logic Program Solver: Harder,
  Better, Faster

abstract:
  As the practical use of answer set programming (ASP) has grown with the
development of efficient solvers, we expect a growing interest in extensions of
ASP as their semantics stabilize and solvers supporting them mature. Epistemic
Specifications, which adds modal operators K and M to the language of ASP, is
one such extension. We call a program in this language an epistemic logic
program (ELP). Solvers have thus far been practical for only the simplest ELPs
due to exponential growth of the search space. We describe a solver that is
able to solve harder problems better (e.g., without exponentially-growing
memory needs w.r.t. K and M occurrences) and faster than any other known ELP
solver.


title: Collapse of Axion Stars

abstract:
  Axion stars, gravitationally bound states of low-energy axion particles, have
a maximum mass allowed by gravitational stability. Weakly bound states
obtaining this maximum mass have sufficiently large radii such that they are
dilute, and as a result, they are well described by a leading-order expansion
of the axion potential. Heavier states are susceptible to gravitational
collapse. Inclusion of higher-order interactions, present in the full
potential, can give qualitatively different results in the analysis of
collapsing heavy states, as compared to the leading-order expansion. In this
work, we find that collapsing axion stars are stabilized by repulsive
interactions present in the full potential, providing evidence that such
objects do not form black holes. In the last moments of collapse, the binding
energy of the axion star grows rapidly, and we provide evidence that a large
amount of its energy is lost through rapid emission of relativistic axions.


title: Majority choosability of digraphs

abstract:
  A \emph{majority coloring} of a digraph is a coloring of its vertices such
that for each vertex $v$, at most half of the out-neighbors of $v$ has the same
color as $v$. A digraph $D$ is \emph{majority $k$-choosable} if for any
assignment of lists of colors of size $k$ to the vertices there is a majority
coloring of $D$ from these lists. We prove that every digraph is majority
$4$-choosable. This gives a positive answer to a question posed recently by
Kreutzer, Oum, Seymour, van der Zypen, and Wood in \cite{Kreutzer}. We obtain
this result as a consequence of a more general theorem, in which majority
condition is profitably extended. For instance, the theorem implies also that
every digraph has a coloring from arbitrary lists of size three, in which at
most $2/3$ of the out-neighbors of any vertex share its color. This solves
another problem posed in \cite{Kreutzer}, and supports an intriguing conjecture
stating that every digraph is majority $3$-colorable.


title:
The B850/B875 Photosynthetic Complex Ground and Excited State are Both
  Coherent

abstract:
  A bacterial photosynthetic light harvesting complex PLHC absorbs a photon and
transfers this energy almost perfectly at room temperature RT to a Reaction
Center RC, where charge separation occurs. While there are a number of possible
light absorbers involved in this process, our focus is the B850 and B875
complexes. We propose that the dominant feature of the ground states in the
B850 ring and the B875 open chain are pseudo one dimensional metals due to each
bacteriochlorophyll a BChl containing a coordinated magnesium ion Mg2+. The Mg
ion structure undergoes a static Peierls distortion that results in symmetry
breaking that changes the even spacing of the Mg/BChl molecules comprising the
chains to the experimentally observed Mg/BChl dimers. The results are charge
density waves CDW, one for each type of the two complexes that result in an
energy gap in the single particle electronic spectrum and coherent phonon s
spanning the entire rings. The ground state CDWs seem to have two functions the
first is to form a stable optical platform and the second is to suppress
radical formation and energy dissipation of the coherent excited state by
creating single particle energy gaps. After excitation by a photon, the B850
exciton delocalizes on the ring a second photon can form a two-level exciton
polariton that could be an alternative explanation for the splitting of the
B850 exciton band. The coherent polariton formed could actively participate in
uphill electronic energy transfer EET. Additionally we suggest other possible
energy storage mechanisms and entanglement possibilities. We suggest
experimental studies to clarify these proposals.


title: Activation of Nonmonogamous Multipartite Quantum States

abstract:
  The monogamy relation for quantum correlations is not satisfied by all
measures for all multiparty quantum states. We prove that an arbitrary quantum
state which is nonmonogamous for negativity will become monogamous if a finite
number of copies of the same state is provided. We refer this as activation of
nonmonogamous states. We also show that multiple copies of a state satisfy
monogamy for negativity if it does so for a single copy. The results are true
for all quantum states of an arbitrary number of parties. Moreover, we find
that two different three-qubit pure states which individually violate monogamy
relation for negativity, taken together can satisfy the three-party monogamy
relation. This holds for almost all three-qubit pure states while it is true
for all three-qubit pure states when a four-party monogamy relation is used to
check for their activation. We finally connect monogamy of negativity with
genuine multipartite entanglement.


title: Grid refinement for entropic lattice Boltzmann models

abstract:
  We propose a novel multi-domain grid refinement technique with extensions to
entropic incompressible, thermal and compressible lattice Boltzmann models. Its
validity and accuracy are accessed by comparison to available direct numerical
simulation and experiment for the simulation of isothermal, thermal and viscous
supersonic flow. In particular, we investigate the advantages of grid
refinement for the set-ups of turbulent channel flow, flow past a sphere,
Rayleigh-Benard convection as well as the supersonic flow around an airfoil.
Special attention is payed to analyzing the adaptive features of entropic
lattice Boltzmann models for multi-grid simulations.


title: Microscopic Theory of Equilibrium Polariton Condensates

abstract:
  We present a microscopic theory of the equilibrium polariton condensate state
of a semiconductor quantum well in a planar optical cavity. The theory accounts
for the adjustment of matter excitations to the presence of a coherent photon
field, predicts effective polariton-polariton interaction strengths that are
weaker and condensate exciton fractions that are smaller than in the commonly
employed exciton-photon model, and yields effective Rabi coupling strengths
that depend on the detuning of the cavity photon energy relative to the bare
exciton energy. The dressed quasiparticle bands that appear naturally in the
theory provide a mechanism for electrical manipulation of polariton
condensates.


title: Ab initio Green-Kubo Approach for the Thermal Conductivity of Solids

abstract:
  We herein present a first-principles formulation of the Green-Kubo method
that allows the accurate assessment of the non-radiative thermal conductivity
of solid semiconductors and insulators in equilibrium ab initio molecular
dynamics calculations. Using the virial for the nuclei, we propose a unique ab
initio definition of the heat flux. Accurate size- and time convergence are
achieved within moderate computational effort by a robust, asymptotically exact
extrapolation scheme. We demonstrate the capabilities of the technique by
investigating the thermal conductivity of extreme high and low heat conducting
materials, namely diamond Si and tetragonal ZrO$_2$.


title: Growth and Scaling during Development and Regeneration

abstract:
  Life presents fascinating examples of self-organization and emergent
phenomena. In multi-cellular organisms, a multitude of cells interact to form
and maintain highly complex body plans of well-defined size. In this thesis, we
investigate theoretical feedback mechanisms for both self-organized body plan
patterning and size control.
  The thesis is inspired by the astonishing scaling and regeneration abilities
of flatworms. These worms can perfectly regrow their entire body plan even from
tiny amputation fragments like the tip of the tail. Moreover, they can grow and
actively de-grow by more than a factor of 40 in length depending on feeding
conditions. These capabilities prompt for remarkable physical mechanisms of
self-organized pattern formation and scaling.
  First, we explore the basic principles and challenges of pattern scaling in
mechanisms previously proposed to describe biological pattern formation. Next,
we present a novel class of patterning mechanisms yielding entirely
self-organized and self-scaling patterns. This framework captures essential
features of body plan regeneration and scaling in flatworms. Further, we
analyze shape and motility of flatworms. By applying principal component
analysis, we characterize shape dynamics during different motility modes and
also identify shape variations between different flatworm species. Finally, we
investigate the metabolic control of cell turnover and growth. We identify
three mechanisms of metabolic energy storage; theoretical descriptions thereof
can explain the measured organism growth by rules on the cellular scale.
  In a close collaboration with experimental biologists, we combine minimal
theoretical descriptions with state-of-the-art experiments and data analysis.
This allows us to identify generic principles of scalable body plan patterning
and growth control in flatworms.


title: The Habitability of Proxima Centauri b I: Evolutionary Scenarios

abstract:
  We analyze the evolution of the potentially habitable planet Proxima Centauri
b to identify environmental factors that affect its long-term habitability. We
consider physical processes acting on size scales ranging from the galactic to
the stellar system to the planet's core. We find that there is a significant
probability that Proxima Centauri has had encounters with its companion stars,
Alpha Centauri A and B, that are close enough to destabilize an extended
planetary system. If the system has an additional planet, as suggested by the
discovery data, then it may perturb planet b's eccentricity and inclination,
possibly driving those parameters to non-zero values, even in the presence of
strong tidal damping. We also model the internal evolution of the planet,
evaluating the roles of different radiogenic abundances and tidal heating and
find that magnetic field generation is likely for billions of years. We find
that if planet b formed in situ, then it experienced 169 +/- 13 million years
in a runaway greenhouse as the star contracted during its formation. This early
phase could remove up to 5 times as much water as in the modern Earth's oceans,
possibly producing a large abiotic oxygen atmosphere. On the other hand, if
Proxima Centauri b formed with a substantial hydrogen atmosphere (0.01 - 1% of
the planet's mass), then this envelope could have shielded the water long
enough for it to be retained before being blown off itself. After modeling this
wide range of processes we conclude that water retention during the host star's
pre-main sequence phase is the biggest obstacle for Proxima b's habitability.
These results are all obtained with a new software package called VPLANET.


title:
On the integrability conditions for a family of the Li\'enard-type
  equations

abstract:
  We study a family of Li\'enard--type equations. Such equations are used for
the description of various processes in physics, mechanics and biology and also
appear as traveling--wave reductions of some nonlinear partial differential
equations. In this work we find new conditions for the integrability of this
equations family. To this end we use an approach, which is bases on application
of nonlocal transformations. By studying connections between this family of
Li\'enard--type equations and type III Painlev\'e--Gambier equations, we obtain
four new integrability criteria. We illustrate our results by providing
examples of some integrable Li\'enard--type equations. We also discuss
relationships between linearizability via nonlocal transformations of this
family of Li\'enard--type equations and other integrability conditions for this
family of equations.


title: Transitive endomorphisms with critical points

abstract:
  We show that a non-wandering endomorphism of the torus with invertible linear
part without invariant directions and for which the critical points are in some
sense generic is transitive. This improves a result of Andersson by allowing
critical points and improving the volume preserving assumption.


abstract:
  Microscopic imaging of local magnetic fields provides a window into the
organizing principles of complex and technologically relevant condensed matter
materials. However, a wide variety of intriguing strongly correlated and
topologically nontrivial materials exhibit poorly understood phenomena outside
the detection capability of state-of-the-art high-sensitivity, high-resolution
scanning probe magnetometers. We introduce a quantum-noise-limited scanning
probe magnetometer that can operate from room to cryogenic temperatures with
unprecedented DC-field sensitivity and micron-scale resolution. The Scanning
Quantum Cryogenic Atom Microscope (SQCRAMscope) employs a magnetically
levitated atomic Bose-Einstein condensate (BEC), thereby providing immunity to
conductive and blackbody radiative heating. It has a field sensitivity of 1.4
nT per resolution-limited point ($\sim$2 $\mu$m), or 6 nT/$\sqrt{\text{Hz}}$
per point at its duty cycle. Compared to point-by-point sensors, the long
length of the BEC provides a naturally parallel measurement, allowing one to
measure nearly one-hundred points with an effective field sensitivity of 600
pT$/\sqrt{\text{Hz}}$ for each point during the same time as a point-by-point
scanner would measure these points sequentially. Moreover, it has a noise floor
of 300 pT and provides nearly two orders of magnitude improvement in magnetic
flux sensitivity (down to $10^{-6}$ $\Phi_0/\sqrt{\text{Hz}}$) over previous
atomic probe magnetometers capable of scanning near samples. These capabilities
are, for the first time, carefully benchmarked by imaging magnetic fields
arising from microfabricated wire patterns, in a system where samples may be
scanned, cryogenically cooled, and easily exchanged. The SQCRAMscope will
provide charge transport images at temperatures from room to 4 K in
unconventional superconductors and topologically nontrivial materials.

categories: cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.quant-gas physics.atom-ph quant-ph


title: An Integrated Mirror and Surface Ion Trap with a Tunable Trap Location

abstract:
  We report a demonstration of a surface ion trap fabricated directly on a
highly reflective mirror surface, which includes a secondary set of radio
frequency (RF) electrodes allowing for translation of the quadrupole RF null
location. We introduce a position-dependent photon scattering rate for a
$^{174}$Yb$^+$ ion in the direction perpendicular to the trap surface using a
standing wave of retroreflected light off the mirror surface directly below the
trap. Using this setup, we demonstrate the capability of fine-tuning the RF
trap location with nanometer scale precision and characterize the charging
effects of the dielectric mirror surface upon exposure to ultra-violet light.


title: Hypothesis: Homologous recombination depends on parallel search

abstract:
  It is not known how a cell manages to find a specific DNA sequence
sufficiently fast to repair a broken chromosome through homologous
recombination. I propose that the solution is based on a parallelized search
implemented by freely diffusing molecules programmed with sequences
corresponding to those flanking the break site.


title:
Retrieving the saddle-splay elastic constant $K_{24}$ of nematic liquid
  crystals from an algebraic approach

abstract:
  The physics of light interference experiments is well established for nematic
liquid crystals. Using well-known techniques, it is possible to obtain
important quantities, such as the differential scattering cross section and the
saddl-splay elastic constant $K_{24}$. However, the usual methods to retrieve
the latter involves an adjusting of computational parameters through the visual
comparisons between the experimental light interference pattern or a
$^{2}H-NMR$ spectral pattern produced by an escaped-radial disclination, and
their computational simulation counterparts. To avoid such comparisons, we
develop an algebraic method for obtaining of saddle-splay elastic constant
$K_{24}$. Considering an escaped-radial disclination inside a capillary tube
with radius $R_{0}$ of tens of micrometers, we use a metric approach to study
the propagation of the light (in the scalar wave approximation), near to the
surface of the tube and to determine the light interference pattern due to the
defect. The latter is responsible for the existence of a well-defined
interference peak associated to a unique angle $\phi_{0}$. Since this angle
depends on factors such as refractive indexes, curvature elastic constants,
anchoring regime, surface anchoring strength and radius $R_{0}$, the
measurement of $\phi_{0}$ from the interference experiments involving two
different radii allows us to algebraically retrieve $K_{24}$. Our method
allowed us to give the first reported estimation of $K_{24}$ for the lyotropic
chromonic liquid crystal Sunset Yellow FCF: $K_{24}=2.1\ pN$.


title:
Spaces of $\sigma(p)$-nuclear linear and multilinear operators and their
  duals

abstract:
  The theory of $\tau$-summing and $\sigma$-nuclear linear operators on Banach
spaces was developed by Pietsch [12, Chapter 23]. Extending the linear case to
the range p > 1 and generalizing all cases to the multilinear setting, in this
paper we introduce the concept of $\sigma(p)$-nuclear linear and multilinear
operators. In order to develop the duality theory for the spaces of such
operators, we introduce the concept of quasi-tau(p)-summing linear/multilinear
operators and prove Pietsch-type domination theorems for such operators. The
main result of the paper shows that, under usual conditions, linear functionals
on the space of $\sigma(p)$-nuclear $n$-linear operators are represented, via
the Borel transform, by quasi-$\tau(p)$-summing $n$-linear operators. As far as
we know, this result is new even in the linear case $n = 1$.


title:
Exact critical exponents for the antiferromagnetic quantum critical
  metal in two dimensions

abstract:
  Unconventional metallic states which do not support well defined
single-particle excitations can arise near quantum phase transitions as strong
quantum fluctuations of incipient order parameters prevent electrons from
forming coherent quasiparticles. Although antiferromagnetic phase transitions
occur commonly in correlated metals, understanding the nature of the strange
metal realized at the critical point in layered systems has been hampered by a
lack of reliable theoretical methods that take into account strong quantum
fluctuations. We present a non-perturbative solution to the low-energy theory
for the antiferromagnetic quantum critical metal in two spatial dimensions.
Being a strongly coupled theory, it can still be solved reliably in the
low-energy limit as quantum fluctuations are organized by a new control
parameter that emerges dynamically. We predict the exact critical exponents
that govern the universal scaling of physical observables at low temperatures.


title:
The Formulas for the Distribution of the 3-Smooth, 5-Smooth, 7-Smooth
  and all other Smooth Numbers

abstract:
  In this paper we present and prove rapidly convergent formulas for the
distribution of the $3$-smooth, $5$-smooth, $7$-smooth and all other smooth
numbers. One of these formulas is another version of a formula due to Hardy and
Littlewood for the arithmetic function $N_{a,b}(x)$, which counts the number of
positive integers of the form $a^{p}b^{q}$ less than or equal to $x$.


title:
Stability of ground states for logarithmic Schr\"{o}dinger equation with
  a $\delta^{\prime}$-interaction

abstract:
  In this paper we study the one-dimensional logarithmic Schr\"odinger equation
perturbed by an attractive $\delta^{\prime}$-interaction \[
i\partial_{t}u+\partial^{2}_{x}u+ \gamma\delta^{\prime}(x)u+u\,
\mbox{Log}\left|u\right|^{2}=0, \quad (x,t)\in\mathbb{R}\times\mathbb{R}, \]
where $\gamma>0$. We establish the existence and uniqueness of the solutions of
the associated Cauchy problem in a suitable functional framework. In the
attractive $\delta^{\prime}$-interaction case, the set of the ground state is
completely determined. More precisely: if $0<\gamma\leq 2$, then there is a
single ground state and it is an odd function; if $\gamma>2$, then there exist
two non-symmetric ground states. Finally, we show that the ground states are
orbitally stable via a variational approach.


title:
Biofluorescent Worlds II. Biological fluorescence induced by stellar UV
  flares, a new temporal biosignature

abstract:
  Our first targets in the search for signs of life are orbiting nearby M
stars, such as the planets in the Proxima Centauri, Ross-128, LHS-1140, and
TRAPPIST-1 systems. Future ground-based discoveries, and those from the TESS
mission, will provide additional close-by targets. However, young M stars tend
to be very active, flaring frequently and causing UV fluxes on the surfaces of
HZ planets to become biologically harmful. Common UV-protection methods used by
life (e.g. living underground, or underwater) would make a biosphere harder to
detect. However, photoprotective biofluorescence, 'up-shifting' UV to longer,
safer wavelengths, could increase a biosphere's detectability. Here we model
intermittent emission at specific wavelengths in the visible spectrum caused by
biofluorescence as a new temporal biosignature for planets around active M
stars. We use the absorption and emission characteristics of common coral
fluorescent pigments and proteins to create model spectra and colours for an
Earth-like planet in such a system, accounting for different surface features,
atmospheric absorption, and cloud cover. We find that for a cloud-free planet
biofluorescence could induce a temporary change in brightness that is
significantly higher than the reflected flux alone, causing up to two
orders-of-magnitude change in planet-star contrast, compared to a
non-fluorescent state, if the surface is fully covered by a highly efficient
fluorescent biosphere. Hence, UV-flare induced biofluorescence presents
previously unexplored possibilities for a new temporal biosignature that could
be detectable by instruments like those planned for the extremely large
telescope and could reveal hidden biospheres.


title:
Prolific permutations and permuted packings: downsets containing many
  large patterns

abstract:
  A permutation of n letters is k-prolific if each (n-k)-subset of the letters
in its one-line notation forms a unique pattern. We present a complete
characterization of k-prolific permutations for each k, proving that k-prolific
permutations of m letters exist for every m \ge k^2/2+2k+1, and that none exist
of smaller size. Key to these results is a natural bijection between k-prolific
permutations and certain "permuted" packings of diamonds.


title:
Experimental Identification of Non-Abelian Topological Orders on a
  Quantum Simulator

abstract:
  Topological orders can be used as media for topological quantum computing ---
a promising quantum computation model due to its invulnerability against local
errors. Conversely, a quantum simulator, often regarded as a quantum computing
device for special purposes, also offers a way of characterizing topological
orders. Here, we show how to identify distinct topological orders via measuring
their modular $S$ and $T$ matrices. In particular, we employ a nuclear magnetic
resonance quantum simulator to study the properties of three topologically
ordered matter phases described by the string-net model with two string types,
including the $\Z_2$ toric code, doubled semion, and doubled Fibonacci. The
third one, non-Abelian Fibonacci order is notably expected to be the simplest
candidate for universal topological quantum computing. Our experiment serves as
the basic module, built on which one can simulate braiding of non-Abelian
anyons and ultimately topological quantum computation via the braiding, and
thus provides a new approach of investigating topological orders using quantum
computers.


title: Yang-Mills Replacement

abstract:
  We develop an analog of harmonic replacement in the gauge theory context. The
idea behind harmonic replacement dates back to Schwarz and Perron. The
technique, as introduced by Jost and further developed by Colding and
Minicozzi, involves taking a map $v\colon\Sigma\to M$ defined on a surface
$\Sigma$ and replacing its values on a small ball $B^2\subset\Sigma$ with a
harmonic map $u$ that has the same values as $v$ on the boundary $\partial
B^2$. The resulting map on $\Sigma$ has lower energy, and repeating this
process on balls covering $\Sigma$, one can obtain a global harmonic map in the
limit. We develop the analogous procedure in the gauge theory context. We take
a connection $B$ on a bundle over a four-manifold $X$, and replace it on a
small ball $B^4\subset X$ with a Yang--Mills connection $A$ that has the same
restriction to the boundary $\partial B^4$ as $B$. As in the harmonic
replacement results of Colding and Minicozzi, we have bounds on the difference
$\lVert B-A\rVert_{L^2_1(X)}^2$ in terms of the drop in energy, and we only
require that the connection $B$ have small energy on the ball, rather than
small $C^0$ oscillation. Throughout, we work with connections of the lowest
possible regularity $L^2_1(X)$, the natural choice for this context, and so our
gauge transformations are in $L^2_2(X)$ and therefore almost but not quite
continuous, leading to more delicate arguments than in higher regularity.


title: Waiting for the W and the Higgs

abstract:
  The search for the left-handed $W^{\pm}$ bosons, the proposed quanta of the
weak interaction, and the Higgs boson, which spontaneously breaks the symmetry
of unification of electromagnetic and weak interactions, has driven
elementary-particle physics research from the time that I entered college to
the present and has led to many unexpected and exciting discoveries which
revolutionized our view of subnuclear physics over that period. In this article
I describe how these searches and discoveries have intertwined with my own
career.


title:
Search for Violation of CPT and Lorentz Invariance in $B^0_s$ Meson
  Oscillations using the D0 Detector

abstract:
  A search is presented for CPT-violating effects in the mixing of $B^0_s$
mesons using the D0 detector at the Fermilab Tevatron Collider. The
CPT-violating asymmetry in the decay $B^0_s \rightarrow \mu^{\pm} D_s^{\mp} X$
as a function of sidereal phase is measured. No evidence for CPT-violating
effects is observed and limits are placed on CPT- and Lorentz-invariance
violating coupling coefficients.


title:
A simple setup to measure muon lifetime and electron energy spectrum of
  muon decay and its Monte Carlo simulation

abstract:
  We designed a simple setup to measure the muon lifetime and the electron
energy spectra of muon decay. A low cost coincidental circuit was designed to
select the signals of muon decay events detected by a plastic scintillator
detector. It triggered a digital oscilloscope to record the signals of muon
decay events for measuring the muon lifetime and electron energy spectrum. A
Landau-distribution energy loss method was introduced to conduct the energy
calibration of the system. The experimental results were well reproduced by the
Monte Carlo simulation. The software and hardware of the system are completely
open to students, thus more helpful for instruction and motivation.


title: Nonrelativistic Short-Distance Completions of a Naturally Light Higgs

abstract:
  Nonrelativistic scalar field theories can exhibit a natural cascading
hierarchy of scales, protected by a hierarchy of polynomial shift symmetries.
Using a simple model, we argue that a high-energy cross-over to such
nonrelativistic behavior naturally leads to light scalars, and thus represents
a useful ingredient for technically natural resolutions of scalar mass
hierarchies, perhaps even the Higgs mass hierarchy puzzle.


title:
The impact of baryonic physics on the subhalo mass function and
  implications for gravitational lensing

abstract:
  We investigate the impact of baryonic physics on the subhalo population by
analyzing the results of two recent hydrodynamical simulations (EAGLE and
Illustris), which have very similar configuration, but a different model of
baryonic physics. We concentrate on haloes with a mass between $10^{12.5}$ and
$10^{14}M_{\odot}h^{-1}$ and redshift between 0.2 and 0.5, comparing with
observational results and subhalo detections in early-type galaxy lenses. We
compare the number and the spatial distribution of subhaloes in the fully hydro
runs and in their dark matter only counterparts, focusing on the differences
between the two simulations. We find that the presence of baryons reduces the
number of subhaloes, especially at the low mass end ($\leq
10^{10}M_{\odot}h^{-1}$), by different amounts depending on the model. The
variations in the subhalo mass function are strongly dependent on those in the
halo mass function, which is shifted by the effect of stellar and AGN feedback.
Finally, we search for analogues of the observed lenses (SLACS) in the
simulations, selecting them in velocity dispersion and dynamical properties. We
use the selected galaxies to quantify detection expectations based on the
subhalo populations in the different simulations, calculating the detection
probability and the predicted values for the projected dark matter fraction in
subhaloes $f_{DM}$ and the slope of the mass function $\alpha$. We compare
these values with those derived from subhalo detections in observations and
conclude that the dark-matter-only and hydro EAGLE runs are both compatible
with observational results, while results from the hydro Illustris run do not
lie within the errors.


title: Spin mixing in Cs ultralong-range Rydberg molecules: a case study

abstract:
  We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules
which form in an ultracold gas of Cs atoms. We account for the partial-wave
scattering of the Rydberg electrons from the ground Cs perturber atoms by
including the full set of spin-resolved ${}^{1,3}S_J$ and ${}^{1,3}P_J$
scattering phase shifts, and allow for the mixing of singlet (S=0) and triplet
(S=1) spin states through Rydberg electron spin-orbit and ground electron
hyperfine interactions. Excellent agreement with observed data in
Sa{\ss}mannshausen et al. [Phys. Rev. Lett. 113, 133201(2015)] in line
positions and profiles is obtained. We also determine the spin-dependent
permanent electric dipole moments for these molecules. This is the first such
calculation of ultralong-range Rydberg molecules in which all of the
relativistic contributions are accounted for.


title:
Operational General Relativity: Possibilistic, Probabilistic, and
  Quantum

abstract:
  In this paper we develop an operational formulation of General Relativity
similar in spirit to existing operational formulations of Quantum Theory. To do
this we introduce an operational space (or op-space) built out of scalar
fields. A point in op-space corresponds to some nominated set of scalar fields
taking some given values in coincidence. We assert that op-space is the space
in which we observe the world. We introduce also a notion of agency (this
corresponds to the ability to set knob settings just like in Operational
Quantum Theory). The effects of agents' actions should only be felt to the
future so we introduce also a time direction field. Agency and time direction
can be understood as effective notions. We show how to formulate General
Relativity as a possibilistic theory and as a probabilistic theory. In the
possibilistic case we provide a compositional framework for calculating whether
some operationally described situation is possible or not. In the probabilistic
version we introduce probabilities and provide a compositional framework for
calculating the probability of some operationally described situation. Finally
we look at the quantum case. We review the operator tensor formulation of
Quantum Theory and use it to set up an approach to Quantum Field Theory that is
both operational and compositional. Then we consider strategies for solving the
problem of Quantum Gravity. By referring only to operational quantities we are
able to provide formulations for the possibilistic, probabilistic, and (the
nascent) quantum cases that are manifestly invariant under diffeomorphisms.


title:
Kerr effect from diffractive skew scattering in chiral $p_x \pm i p_y$
  superconductors

abstract:
  We calculate the temperature dependent anomalous ac Hall conductance
$\sigma_H(\Omega, T)$ for a two-dimensional chiral p-wave superconductor. This
quantity determines the polar Kerr effect, as it was observed in Sr$_2$RuO$_4$
[J. Xia $et$ $al.$, Phys. Rev. Lett. 97, 167002 (2006)]. We concentrate on a
single band model with arbitrary isotropic dispersion relation subjected to
rare, weak impurities treated in the Born approximation. As we explicitly show
by detailed computation, previously omitted contributions to extrinsic part of
an anomalous Hall response, physically originating from diffractive skew
scattering on quantum impurity complexes, appear to the leading order in
impurity concentration. By direct comparison with published results from the
literature we demonstrate the relevance of our findings for the interpretation
of the Kerr effect measurements in superconductors.