title:
Abelian Hopf Galois structures from almost trivial commutative nilpotent
  algebras

abstract:
  Let $L/K$ be a Galois extension of fields with Galois group $G$, an
elementary abelian $p$-group of rank $n$ for $p$ an odd prime. It is known that
nilpotent $\mathbb{F}_p$-algebra structures $A$ on $G$ yield regular subgroups
of the holomorph of $G$, hence Hopf Galois structures on $L/K$. In this paper
we illustrate the richness of Hopf Galois structures on $L/K$ by examining the
case where $A$ is abelian of dimension $n$ where the dimension of $A^2 = 1$. We
determine the number of Hopf Galois structures that arise in these cases,
describe those structures explicitly, and estimate the extent of failure of
surjectivity of the Galois correspondence for those structures.


title:
A Theoretical Investigation of Orientation Relationships and
  Transformation Strains in Steels

abstract:
  The identification of orientation relationships (ORs) plays a crucial r\^ole
in the understanding of solid phase transformations. In steels, the most common
models of ORs are the ones by Nishiyama-Wassermann (NW) and Kurdjumov-Sachs
(KS). The defining feature of these and other OR models is the matching of
directions and planes in the parent face-centred cubic $\gamma$-phase to ones
in the product body-centred cubic/tetragonal $\alpha/\alpha'$-phase.
  In this paper a novel method that identifies transformation strains with ORs
is introduced and used to develop a new strain-based approach to phase
transformation models in steels. Using this approach, it is shown that the
transformation strains that leave a close packed plane in the $\gamma$-phase
and a close packed direction within that plane unrotated are precisely those
giving rise to the NW and KS ORs when a cubic product phase is considered.
Further, it is outlined how, by choosing different pairs of unrotated planes
and directions, other common ORs such as the ones by Pitsch (PT) and
Greninger-Troiano (GT) can be derived.
  One of the advantages of our approach is that it leads to a natural
generalisation of the NW, KS and other ORs for different ratios of
tetragonality $r$ of the product bct $\alpha'$-phase. These generalised ORs
predict a sharpening of the transformation textures with increasing
tetragonality and are thus in qualitative agreement with experiments on steels
with varying alloy concentration.


title:
Translational and rotational Brownian displacements of colloidal
  particles of complex shapes

abstract:
  The exact analytical expressions for the time-dependent cross-correlations of
the translational and rotational Brownian displacements of a particle with
arbitrary shape were derived by us in [J. Chem. Phys. 142, 214902 (2015) and
144, 076101 (2016)]. They are in this work applied to construct a method to
analyze Brownian motion of a particle of an arbitrary shape, and to extract
accurately the self-diffusion matrix from the measurements of the
cross-correlations, which in turn allows to gain some information on the
particle structure. As an example, we apply our new method to analyze the
experimental results of D. J. Kraft et al. for the micrometer-sized aggregates
of the beads [Phys. Rev. E 88, 050301 (R) (2013)]. We explicitly demonstrate
that our procedure, based on the measurements of the time-dependent
cross-correlations in the whole range of times, allows to determine the self
diffusion (or alternatively the friction matrix) with a much higher precision
than the method based only on their initial slopes. Therefore, the analytical
time-dependence of the cross-correlations serves as a useful tool to extract
information about particle structure from trajectory measurements.


title:
A Novel Approach for Mining Similarity Profiled Temporal Association
  Patterns

abstract:
  The problem of frequent pattern mining from non-temporal databases is studied
extensively by various researchers working in areas of data mining, temporal
databases and information retrieval. However, Conventional frequent pattern
algorithms are not suitable to find similar temporal association patterns from
temporal databases. A Temporal database is a database which can store past,
present and future information. The objective of this research is to come up
with a novel approach so as to find similar temporal association patterns w.r.t
user specified threshold and a given reference support time sequence using
concept of Venn diagrams. For this, we maintain two types of supports called
positive support and negative support values to find similar temporal
association patterns of user interest. The main advantage of our method is
that, it performs only a single scan of temporal database to find temporal
association patterns similar to specified reference support sequence. This
single database scan approach hence eliminates the huge overhead incurred when
the database is scanned multiple times. The present approach also eliminates
the need to compute and maintain true support values of all the subsets of
temporal patterns of previous stages when computing temporal patterns of next
stage.


title: Learning Possibilistic Logic Theories from Default Rules

abstract:
  We introduce a setting for learning possibilistic logic theories from
defaults of the form "if alpha then typically beta". We first analyse this
problem from the point of view of machine learning theory, determining the VC
dimension of possibilistic stratifications as well as the complexity of the
associated learning problems, after which we present a heuristic learning
algorithm that can easily scale to thousands of defaults. An important property
of our approach is that it is inherently able to handle noisy and conflicting
sets of defaults. Among others, this allows us to learn possibilistic logic
theories from crowdsourced data and to approximate propositional Markov logic
networks using heuristic MAP solvers. We present experimental results that
demonstrate the effectiveness of this approach.


title:
A Novel Gaussian Based Similarity Measure for Clustering Customer
  Transactions Using Transaction Sequence Vector

abstract:
  Clustering Transactions in sequence, temporal and time series databases is
achieving an important attention from the database researchers and software
industry. Significant research is carried out towards defining and validating
the suitability of new similarity measures for sequence, temporal, time series
databases which can accurately and efficiently find the similarity between user
transactions in the given database to predict the user behavior. The
distribution of items present in the transactions contributes to a great extent
in finding the degree of similarity between them. This forms the key idea of
the proposed similarity measure. The main objective of the research is to first
design the efficient similarity measure which essentially considers the
distribution of the items in the item set over the entire transaction data set
and also considers the commonality of items present in the transactions, which
is the major drawback in the Jaccard, Cosine, Euclidean similarity measures. We
then carry out the analysis for worst case, the average case and best case
situations. The Similarity measure designed is Gaussian based and preserves the
properties of Gaussian function. The proposed similarity measure may be used to
both cluster and classify the user transactions and predict the user behaviors.


title:
Universal fast gradient method for stochastic composit optimization
  problems

abstract:
  We propose a new simple variant of Fast Gradient Method that requires only
one projection per iteration. We called this method Triangle Method (TM)
because it has a corresponding geometric description. We generalize TM for
convex and strictly convex composite optimization problems. Then we propose
Universal Triangle Method (UTM) for convex and strictly convex composite
optimization problems (see Yu. Nesterov, Math. Program. 2015. for more details
about what is Universal Fast Gradient Method). Finally, based on mini-batch
technique we propose Stochastic Universal Triangle Method (SUTM). SUTM can be
applied to stochastic convex and strictly convex composite optimization
problems. Denote, that all the methods TM, UTM, SUTM are continuous on strictly
convexity parameter and all of them reach known lower bounds. With additional
assumption about the structure of the problems these methods work better than
the lower bounds.


title: Toward Effective Liouvillian Integration

abstract:
  We prove that foliations on the projective plane admitting a Liouvillian
first integral but not admitting a rational first integral always have
invariant algebraic curves of degree bounded by a function of the degree of the
foliation. We establish, for the same class of foliations, the existence of a
bound for the degree of the simplest integrating factor depending only on the
degree of the foliation and on the nature of its singularities. We also prove
the existence of invariant algebraic curves of small degree for foliations with
rational first integral and intermediate Kodaira dimension.


title:
Spin-transfer torques in antiferromagnets: efficiency and quantification
  method

abstract:
  We formulate a theory of spin-transfer torques in antiferromagnets, which
covers the small to large limits of the exchange coupling energy relative to
the kinetic energy of the inter-sublattice electron dynamics. Our theory
suggests a natural definition of the efficiency of spin-transfer torques in
antiferromagnets in terms of well-defined material parameters, revealing that
the charge current couples predominantly to the antiferromagnetic order
parameter and the sublattice-canting moment in, respectively, the limits of
large and small exchange coupling. The effects can be quantified by analyzing
the antiferromagnetic spin-wave dispersions in the presence of charge current:
in the limit of large exchange coupling the spin-wave Doppler shift always
occurs, whereas, in the opposite limit, the only spin-wave modes to react to
the charge current are ones that carry a pronounced sublattice-canting moment.
The findings offer a framework for understanding and designing spin-transfer
torques in antiferromagnets belonging to different classes of sublattice
structures such as, e.g., bipartite and layered antiferromagnets.


title:
The Nu Class of Low-Degree-Truncated, Rational, Generalized Functions.
  I. IMSPE in Design of Computer Experiments: Integrals and Very-Low-N,
  Single-Factor, Free-Ranging Designs

abstract:
  We provide detailed algebra for determining the integrated mean-squared
prediction error (IMSPE) of designs of computer experiments, with one factor
and one or two points, under the exponential, Gaussian, or either of two Matern
correlation functions. This algebra shall provide the basis for the
identification of the IMSPE as a member of a special class of
low-degree-truncated rational functions, which we name, here, the Nu class. We
shall detail this function class in a series of papers, of which this is the
first.


title: Dynamics of a network fluid within the liquid-gas coexistence region

abstract:
  Low-density networks of molecules or colloids are formed at low temperatures
when the interparticle interactions are valence limited. Prototypical examples
are networks of patchy particles, where the limited valence results from highly
directional pairwise interactions. We combine extensive Langevin simulations
and Wertheim's theory of association to study these networks. We find a
scale-free (relaxation) dynamics within the liquid-gas coexistence region,
which differs from that usually observed for isotropic particles. While for
isotropic particles the relaxation dynamics is driven by surface tension
(coarsening), when the valence is limited, the slow relaxation proceeds through
the formation of an intermediate non-equilibrium gel via a geometrical
percolation transition in the Random Percolation universality class.


title: Asymptotic Convergence in Online Learning with Unbounded Delays

abstract:
  We study the problem of predicting the results of computations that are too
expensive to run, via the observation of the results of smaller computations.
We model this as an online learning problem with delayed feedback, where the
length of the delay is unbounded, which we study mainly in a stochastic
setting. We show that in this setting, consistency is not possible in general,
and that optimal forecasters might not have average regret going to zero.
However, it is still possible to give algorithms that converge asymptotically
to Bayes-optimal predictions, by evaluating forecasters on specific sparse
independent subsequences of their predictions. We give an algorithm that does
this, which converges asymptotically on good behavior, and give very weak
bounds on how long it takes to converge. We then relate our results back to the
problem of predicting large computations in a deterministic setting.


title: Higher Jacobi identities

abstract:
  By definition the identities $[x_1,x_2]+[x_2,x_1]=0$ and
$[x_1,x_2,x_3]+[x_2,x_3,x_1]+[x_3,x_1,x_2]=0$ hold in any Lie algebra. It is
easy to check that the identity
$[x_1,x_2,x_3,x_4]+[x_2,x_1,x_4,x_3]+[x_3,x_4,x_1,x_2]+[x_4,x_3,x_2,x_1] = 0$
holds in any Lie algebra as well. We investigate sets of permutations that give
identities of this kind. In particular, we construct a family of such subsets
$T_{k,l,n}$ of the symmetric group $S_n,$ and hence, a family of identities
that hold in any Lie algebra.


title: Capacity of Cellular Networks with Femtocache

abstract:
  The capacity of next generation of cellular networks using femtocaches is
studied when multihop communications and decentralized cache placement are
considered. We show that the storage capability of future network User
Terminals (UT) can be effectively used to increase the capacity in random
decentralized uncoded caching. We further propose a random decentralized coded
caching scheme which achieves higher capacity results than the random
decentralized uncoded caching. The result shows that coded caching which is
suitable for systems with limited storage capabilities can improve the capacity
of cellular networks by a factor of log(n) where n is the number of nodes
served by the femtocache.


title: Non-additivity of van der Waals forces on liquid surfaces

abstract:
  We present an approach for modeling nanoscale wetting and dewetting of liquid
surfaces that exploits recently developed, sophisticated techniques for
computing van der Waals (vdW) or (more generally) Casimir forces in arbitrary
geometries. We solve the variational formulation of the Young--Laplace equation
to predict the equilibrium shapes of fluid--vacuum interfaces near solid
gratings and show that the non-additivity of vdW interactions can have a
significant impact on the shape and wetting properties of the liquid surface,
leading to very different surface profiles and wetting transitions compared to
predictions based on commonly employed additive approximations, such as Hamaker
or Derjaguin approximations.


title:
Tails of Polynomials of Random Variables and Stable Limits for
  Nonconventional Sums

abstract:
  We obtain decay rates of probabilities of tails of polynomials in several
independent random variables with heavy tails and derive stable limit theorems
for nonconventional sums of such polynomials


title:
Bound states of the $\phi^4$ model via the nonperturbative
  renormalization group

abstract:
  Using the nonperturbative renormalization group, we study the existence of
bound states in the symmetry-broken phase of the scalar $\phi^4$ theory in all
dimensions between two and four and as a function of the temperature. The
accurate description of the momentum dependence of the two-point function,
required to get the spectrum of the theory, is provided by means of the
Blaizot--M\'endez-Galain--Wschebor approximation scheme. We confirm the
existence of a bound state in dimension three, with a mass within 1% of
previous Monte-Carlo and numerical diagonalization values.


title:
The MV Model of the Color Glass Condensate for a Finite Number of
  Sources Including Coulomb Interactions

abstract:
  We modify the McLerran-Venugopalan model to include only a finite number of
sources of color charge. We argue that Coulombic interactions between these
color charges generates a source-source correlation function that properly
includes the effects of color charge screening, a generalization of Debye
screening for the Color Glass Condensate. Such a model may be useful for
computing angular harmonics of flow measured in high energy hadron collisions
for small systems. In this paper we provide a basic formulation of the problem
on a lattice.


title:
Pairs of subsets of spheres and Cartesian products thereof with the same
  distribution of distance

abstract:
  We prove the following three statements: 1) Let $(A, \bar A)$ be a partition
of the spherical surface $S^n$ into two measurable sets. Let $st_A$ and
$st_{\bar A}$ be their measure density functions of distance. Then $|st_A -
st_{\bar A}|$ depends only on the difference of their $n$-areas. 2) If the
spherical surface $S^n$ is divided in two measurable subsets $A$ and $\bar A$
of equal $n$-surface, then these two subsets have the same distribution of
distance. 3) Let there be a pair $(S, S')$ of subsets of a sphere $S^{n}$ such
that $st_S = st_{S'}$. Then their complementary subsets satisfy $st_{\bar S} =
st_{\bar S'}$ and $st_{S, \bar S} = st_{S', \bar S'}$, where $st_{A, B}$ is the
measure density function of distance between a point in $A$ and a point in $B$.
Furthermore, it is shown that the statements remain true when $S^n$ is
substituted by the Cartesian product $S^{n_1} \times ... \times S^{n_r}$
endowed with the metric which is naturally inherited from its factors.


title: Inductive Coherence

abstract:
  While probability theory is normally applied to external environments, there
has been some recent interest in probabilistic modeling of the outputs of
computations that are too expensive to run. Since mathematical logic is a
powerful tool for reasoning about computer programs, we consider this problem
from the perspective of integrating probability and logic. Recent work on
assigning probabilities to mathematical statements has used the concept of
coherent distributions, which satisfy logical constraints such as the
probability of a sentence and its negation summing to one. Although there are
algorithms which converge to a coherent probability distribution in the limit,
this yields only weak guarantees about finite approximations of these
distributions. In our setting, this is a significant limitation: Coherent
distributions assign probability one to all statements provable in a specific
logical theory, such as Peano Arithmetic, which can prove what the output of
any terminating computation is; thus, a coherent distribution must assign
probability one to the output of any terminating computation. To model
uncertainty about computations, we propose to work with approximations to
coherent distributions. We introduce inductive coherence, a strengthening of
coherence that provides appropriate constraints on finite approximations, and
propose an algorithm which satisfies this criterion.


title:
Robust Likelihoods for Inflationary Gravitational Waves from Maps of
  Cosmic Microwave Background Polarization

abstract:
  The B-mode polarization of the cosmic microwave background (CMB) provides a
unique window into tensor perturbations from inflationary gravitational waves.
Survey effects complicate the estimation and description of the power spectrum
on the largest angular scales. The pixel-space likelihood yields parameter
distributions without the power spectrum as an intermediate step, but it does
not have the large suite of tests available to power spectral methods. Searches
for primordial B-modes must rigorously reject and rule out contamination. Many
forms of contamination vary or are uncorrelated across epochs, frequencies,
surveys, or other data treatment subsets. The cross power and the power
spectrum of the difference of subset maps provide approaches to reject and
isolate excess variance. We develop an analogous joint pixel-space likelihood.
Contamination not modeled in the likelihood produces parameter-dependent bias
and complicates the interpretation of the difference map. We describe a null
test that consistently weights the difference map. Excess variance should
either be explicitly modeled in the covariance or be removed through
reprocessing the data.


title: Milnor fibrations and regularity conditions for real analytic mappings

abstract:
  When f : R power n to R power p, is a surjective real analytic map with
isolated critical value, we prove that the (m)-regularity condition (in a sense
we define) ensures that f ||f|| is a fibration on small spheres, f induces a
fibration on the tubes and both fibrations are equivalent. In particular, we
make the statement of [12] more precise in the case of isolated critical point
and we extend it to the case of an isolated critical value.


title: A Lagrangian formulation of relativistic Israel-Stewart hydrodynamics

abstract:
  We rederive relativistic hydrodynamics as a Lagrangian effective theory using
the doubled coordinates technique, allowing us to include dissipative terms. We
include Navier-Stokes shear and bulk terms, as well as Israel-Stewart
relaxation time terms, within this formalism. We show how the inclusion of
shear viscosity, and the requirement of a bounded energy-momentum "vacuum",
forces the inclusion of the Israel-Stewart term into the theory, thereby
providing a justification for the origin and uniqueness of these terms.


title: Magnon Hall effect in AB-stacked bilayer honeycomb quantum magnets

abstract:
  Motivated by the fact that many bilayer quantum magnets occur in nature, we
generalize the study of thermal Hall transports of spin excitations to bilayer
magnetic systems. It is shown that bilayer magnetic systems can be coupled
either ferromagnetically or antiferromagnetically. We study both scenarios on
the honeycomb lattice and show that the system realizes topologically
nontrivial magnon bands induced by alternating next-nearest-neighbour
Dzyaloshinsky-Moriya interaction (DMI). As a result, the bilayer system
realizes both magnon Hall effect and magnon spin Nernst effect. We show that
antiferromagnetically coupled layers differ from ferromagnetically coupled
layers by a sign change in the conductivities as the magnetic field is
reversed. Furthermore, Chern number protected magnon edge states are observed
and propagate in the same direction on the top and bottom layers in
ferromagnetically coupled layers, whereas the magnon edge states propagate in
opposite directions for antiferromagnetically coupled layers.


title: Multiple surface plasmons on an unbounded quantum plasma half-space

abstract:
  The propagation of surface plasmons on a quantum plasma half-space in the
absence of any external confinement is investigated. By means of Quantum
Hydrodynamic Model in the electrostatic limit it is found that the equilibrium
density profile is a smooth continuous function which, in the linear regime,
supports multiple non-normal surface modes. Defining a spectrum function and
using a cutting condition, the dispersion relations of these modes and their
relevance for realistic dynamics are computed. It is found that the multiple
surface plasmons present a significant red-shift with respect to the case of
fully bounded quantum plasmas.


title: Vector-valued modular forms and the Mock Theta Conjectures

abstract:
  The mock theta conjectures are ten identities involving Ramanujan's
fifth-order mock theta functions. The conjectures were proven by Hickerson in
1988 using q-series methods. Using methods from the theory of harmonic Maass
forms, specifically work of Zwegers and Bringmann-Ono, Folsom reduced the proof
of the mock theta conjectures to a finite computation. Both of these approaches
involve proving the identities individually, relying on work of Andrews-Garvan.
Here we give a unified proof of the mock theta conjectures by realizing them as
an equality between two nonholomorphic vector-valued modular forms which
transform according to the Weil representation. We then show that the
difference of these vectors lies in a zero-dimensional vector space.


title: Generalised partition functions: Inferences on phase space distributions

abstract:
  The statistical mechanical partition function can be used to construct
different forms of phase space distributions not restricted to the
Gibbs-Boltzmann factor. With a generalised Lorentzian both the Kappa-Bose and
Kappa-Fermi partition functions are obtained in straightforward way, from which
the conventional Bose and Fermi distributions follow for $\kappa\to\infty$. For
$\kappa\neq\infty$ these are subject to the restrictions that they can be used
only at temperatures far from zero. They thus, as shown earlier, have little
value for quantum physics. This is reasonable, because physical
$\kappa$-systems imply strong correlations which are absent at zero temperature
where appart from stochastics all dynamical interactions are frozen. In the
classical large temperature limit one obtains physically reasonable
$\kappa$-distributions which depend on energy respectively momentum as well as
on chemical potential. Looking for other functional dependencies, we examine
Bessel functions whether they can be used for obtaining valid distributions.
Again and for the same reason, no Fermi and Bose distributions exist in the low
temperature limit. However, a classical Bessel-Boltzmann distribution can be
constructed which is a Bessel-modified Lorentzian distribution. Whether it
makes any physical sense remains an open question. This is not investigated
here. The choice of Bessel functions is motivated solely by their convergence
properties and not by reference to any physical demands. This result suggests
that the Gibbs-Boltzmann partition function is fundamental not only to
Gibbs-Boltzmann but also to a large class of generalised Lorentzian
distributions as well as to the corresponding nonextensive statistical
mechanics.


title: Large thermopower in the antiferromagnetic semiconductor BaMn$_2$Bi$_2$

abstract:
  We report electrical and thermal transport properties of Mn-based material
BaMn$_2$Bi$_2$ with ThCr$_2$Si$_2$ structure. The resistivity of the
antiferromagnetic BaMn$_2$Bi$_2$ shows a metal-semiconductor transition at
$\sim 80$ K with decreasing temperature. Correspondingly, the thermopower $S$
shows a peak at the same temperature, approaching ~150 $\mu$V/K. With
increasing temperature $S$ decreases to about 125 $\mu$V/K at the room
temperature. The magnetic field enhances the peak value to 210 $\mu$V/K. The
Hall resistivity reveals an abrupt change of the carrier density close to the
metal-semiconductor transition temperature.


title:
Israel-Stewart approach to viscous dissipative extended holographic
  Ricci dark energy dominated universe

abstract:
  This paper reports a study on the truncated Israel-Stewart formalism for bulk
viscosity using the extended holographic Ricci dark energy (EHRDE), where the
density of dark energy is given as a combination of the Hubble parameter and
its derivative. The equations of motion are integrated and the resulting model
is analysed under many aspects, including the state finder parameters and the
generalised thermodynamics second law. Under the consideration that the
universe is dominated by EHRDE the evolution equation for the bulk viscous
pressure $\Pi$ in the framework of the truncated Israel-Stewart theory has been
taken as $\tau \dot{\Pi}+\Pi=-3\xi H$, where $\tau$ is the relaxation time and
$\xi$ is the bulk viscosity coefficient. Considering effective pressure as a
sum of thermodynamic pressure of EHRDE and bulk viscous pressure it has been
observed that under the influence of bulk viscosity the EoS parameter $w_{DE}$
is behaving like phantom i.e. $w_{DE}\leq -1$. It has been observed that the
magnitude of the effective pressure $p_{eff}=p+\Pi$ is decaying with time. We
also investigated the case for a specific choice of scale factor namely
$a(t)=(t-t_0)^{\frac{\beta}{1-\alpha}}$. For this choice we have observed that
a transition from quintessence to phantom is possible for the equation of state
parameter. However, the $\Lambda$CDM phase is not attainable by the statefinder
trajectories for this choice. Finally it has been observed that in both of the
cases the generalized second law of thermodynamics is valid for the viscous
EHRDE dominated universe enveloped by the apparent horizon.


title: Remarks on bounded operators in $\ell$-K\"othe spaces

abstract:
  For locally convex spaces $X$ and $Y$, the continuous linear map $T:X \to Y$
is said to be bounded if it maps zero neighborhoods of $X$ into bounded sets of
$Y$. We denote $(X,Y) \in \mathcal{B}$ when every operator between $X$ and $Y$
is bounded. For a Banach space $\ell$ with a monotone norm $\|\cdot\|$ in which
the canonical system $(e_n)$ forms an unconditional basis, we consider
$\ell$-K\"othe spaces as a generalization of usual K\"othe spaces. In this
note, we characterize $\ell$-K\"othe spaces $\ell(a_{pn})$ and $\ell(b_{sm})$
such that $(\ell(a_{pn}), \ell(b_{sm})) \in \mathcal{B}$. A pair $(X,Y)$ is
said to have the bounded factorization property, and denoted $(X,Y) \in
\mathcal{BF}$, if each linear continuous operator $T : X \to X$ that factors
over $Y$ is bounded. We also prove that injective tensor products of some
classical K\"othe spaces have bounded factorization property.


title:
An inertial primal-dual fixed point algorithm for composite optimization
  problems

abstract:
  We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute
the minimizations of the following Problem (1.1). This is a full splitting
approach, in the sense that the nonsmooth functions are processed individually
via their proximity operators. The convergence of the IPDFP is obtained by
reformulating the Problem (1.1) to the sum of three convex functions. This work
brings together and notably extends several classical splitting schemes, like
the primaldual method proposed by Chambolle and Pock, and the recent proximity
algorithms of Charles A. et al designed for the L1/TV image denoising model.
The iterative algorithm is used for solving nondifferentiable convex
optimization problems arising in image processing. The experimental results
indicate that the proposed IPDFP iterative algorithm performs well with respect
to state-of-the-art methods.


title:
Thermodynamics of charged rotating dilaton black branes coupled to
  logarithmic nonlinear electrodynamics

abstract:
  We construct a new class of charged rotating black brane solutions in the
presence of logarithmic nonlinear electrodynamics with complete set of the
rotation parameters in arbitrary dimensions. The topology of the horizon of
these rotating black branes are flat, while, due to the presence of the dilaton
field the asymptotic behaviour of them are neither flat nor (anti)-de Sitter
[(A)dS]. We investigate the physical properties of the solutions. The mass and
angular momentum of the spacetime are obtained by using the counterterm method
inspired by AdS/CFT correspondence. We derive temperature, electric potential
and entropy associated with the horizon and check the validity of the first law
of thermodynamics on the black brane horizon. We study thermal stability of the
solutions in both canonical and grand canonical ensemble and disclose the
effects of the rotation parameter, nonlinearity of electrodynamics and dilaton
field on the thermal stability conditions. We find the solutions are thermally
stable for $\alpha<1$, while for $\alpha>1$ the solutions may encounter an
unstable phase where $\alpha$ is dilaton-electromagnetic coupling constant.


title: Solving higher curvature gravity theories

abstract:
  Solving field equations in the context of higher curvature gravity theories
is a formidable task. However in many situations, e.g., in the context of
$f(R)$ theories the higher curvature gravity action can be written as
Einstein-Hilbert action plus a scalar field action. We show that not only the
action but the field equations derived from the action are also equivalent
provided the spacetime is regular. We also demonstrate that such equivalence
continues to hold even when gravitational field equations are projected on a
lower dimensional hypersurface. We have further depicted explicit examples in
which the solutions for Einstein-Hilbert and a scalar field system lead to
solutions of the equivalent higher curvature theory. The same, but on the lower
dimensional hypersurface, has been illustrated in the reverse order as well. We
conclude with a brief discussion on this technique of solving higher curvature
field equations.


title: Chen-Nester-Tung quasi-local energy and Wang-Yau quasi-local mass

abstract:
  In this paper, we show that the Chen-Nester-Tung (CNT) quasi-local energy is
closely related to the Wang-Yau (WY) quasi-local mass. As a particular example,
we compute the second variation of the CNT quasi-local energy for axially
symmetric Kerr-like spacetimes with axially symmetric embeddings at the obvious
critical point (0,0) and find that it is a saddle critical point in most of the
cases. Also, as a byproduct, we generalize a previous result about the
coincidence of CNT quasi-local energy and Brown-York mass for Kerr-like
spacetimes by Tam and the first author to general spacetimes.


title:
Large solar energetic particle event that occurred on 2012 March 7 and
  its VDA analysis

abstract:
  On 2012 March 7, the STEREO Ahead and Behind spacecraft, along with the
near-earth spacecraft (e.g. SOHO, Wind) situated between the two STEREO
spacecraft, observed an extremely large global solar energetic particle (SEP)
event in Solar Cycle 24. Two successive coronal mass ejections (CMEs) have been
detected close in time. From the multi-point in-situ observations, it can be
found that this SEP event was caused by the first CME, and the second one was
not involved. Using the velocity dispersion analysis (VDA), we find that for
well magnetically connected point, the energetic protons and electrons are
released nearly at the same time. The path lengths to STEREO-B(STB) of protons
and electrons have distinct difference and deviate remarkably from the nominal
Parker spiral path length, which is likely due to the presence of
interplanetary magnetic structures situated between the source and the STB.
Also the VDA method seems only to obtain reasonable results at well-connected
locations and the inferred energetic particles release times in different
energy channels are similar. We suggest that good-connection is crucial for
obtaining both accurate release time and path length simultaneously, agreeing
with the modeling result of Wang & Qin (2015).


title:
Plasmonic Effect on the Population Dynamics and the Optical Response in
  a Hybrid V-Type Three-Level Quantum Dot-Metallic Nanoparticle Nanosystem

abstract:
  We investigated theoretically the exciton-plasmon coupling effects on the
population dynamics and the absorption properties of a hybrid nanosystem
composed of a metal nanoparticle (MNP) and a V-type three level semiconductor
quantum dot (SQD), which are created by the interaction with the induced dipole
moments in the SQD and the MNP, respectively. Excitons of the SQD and the
plasmons of the MNP in such a hybrid nanosystem could be coupled strongly or
weakly to demonstrate novel properties of the hybrid system. Our results show
that the nonlinear optical response of the hybrid nanosystem can be greatly
enhanced or depressed due to the exciton-plasmon couplings.


title:
Radiative transfer with POLARIS: I. Analysis of magnetic fields through
  synthetic dust continuum polarization measurements

abstract:
  Aims: We present POLARIS (POLArized RadIation Simulator), a newly developed
three-dimensional Monte-Carlo radiative transfer code. POLARIS was designed to
calculate dust temperature, polarization maps, and spectral energy
distributions. It is optimized to handle data that results from sophisticated
magneto-hydrodynamic simulations. The main purpose of the code is to prepare
and analyze multi-wavelength continuum polarization measurements in the context
of magnetic field studies in the interstellar medium. An exemplary application
is the investigation of the role of magnetic fields in star formation
processes.
  Methods: We combine currently discussed state-of-the-art grain alignment
theories with existing dust heating and polarization algorithms. We test the
POLARIS code on multiple scales in complex astrophysical systems that are
associated with different stages of star formation. POLARIS uses the full
spectrum of dust polarization mechanisms to trace the underlying magnetic field
morphology.
  Results: Resulting temperature distributions are consistent with the density
and position of radiation sources resulting from magneto-hydrodynamic (MHD) -
collapse simulations. The calculated layers of aligned dust grains in the
considered cirumstellar disk models are in excellent agreement with theoretical
predictions. Finally, we compute unique patterns in synthetic multi-wavelength
polarization maps that are dependent on applied dust-model and grain-alignment
theory in analytical cloud models.


title:
Cosmological reconstruction and energy bounds in $f(R,R_{\alpha
  \beta}R^{\alpha\beta},\phi)$ gravity

abstract:
  We discuss the cosmological reconstruction of
$f(R,R_{\alpha\beta}R^{\alpha\beta},\phi)$ (where $R$,
$R_{\alpha\beta}R^{\alpha\beta}$ and $\phi$ represents the Ricci scalar, Ricci
invariant and scalar field) corresponding to power law and de Sitter evolution
in the framework of FRW universe model. We derive the energy conditions for
this modified theory which seem to be more general and can be reduced to some
known forms of these conditions in general relativity, $f(R)$ and $f(R,\phi)$
theories. We have presented the general constraints in terms of recent values
of snap, jerk, deceleration and Hubble parameters. The energy bounds are
analyzed for reconstructed as well as known models in this theory. Finally, the
free parameters are analyzed comprehensively.


title: Learning Sparse Additive Models with Interactions in High Dimensions

abstract:
  A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is referred to as a
Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in
\mathcal{S}}\phi_{l}(x_l)$, where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll
d$. Assuming $\phi_l$'s and $\mathcal{S}$ to be unknown, the problem of
estimating $f$ from its samples has been studied extensively. In this work, we
consider a generalized SPAM, allowing for second order interaction terms. For
some $\mathcal{S}_1 \subset [d], \mathcal{S}_2 \subset {[d] \choose 2}$, the
function $f$ is assumed to be of the form: $$f(\mathbf{x}) = \sum_{p \in
\mathcal{S}_1}\phi_{p} (x_p) + \sum_{(l,l^{\prime}) \in
\mathcal{S}_2}\phi_{(l,l^{\prime})} (x_{l},x_{l^{\prime}}).$$ Assuming
$\phi_{p},\phi_{(l,l^{\prime})}$, $\mathcal{S}_1$ and, $\mathcal{S}_2$ to be
unknown, we provide a randomized algorithm that queries $f$ and exactly
recovers $\mathcal{S}_1,\mathcal{S}_2$. Consequently, this also enables us to
estimate the underlying $\phi_p, \phi_{(l,l^{\prime})}$. We derive sample
complexity bounds for our scheme and also extend our analysis to include the
situation where the queries are corrupted with noise -- either stochastic, or
arbitrary but bounded. Lastly, we provide simulation results on synthetic data,
that validate our theoretical findings.


title: Entanglement entropy from one-point functions in holographic states

abstract:
  For holographic CFT states near the vacuum, entanglement entropies for
spatial subsystems can be expressed perturbatively as an expansion in the
one-point functions of local operators dual to light bulk fields. Using the
connection between quantum Fisher information for CFT states and canonical
energy for the dual spacetimes, we describe a general formula for this
expansion up to second-order in the one-point functions, for an arbitrary
ball-shaped region, extending the first-order result given by the entanglement
first law. For two-dimensional CFTs, we use this to derive a completely
explicit formula for the second-order contribution to the entanglement entropy
from the stress tensor. We show that this stress tensor formula can be
reproduced by a direct CFT calculation for states related to the vacuum by a
local conformal transformation. This result can also be reproduced via the
perturbative solution to a non-linear scalar wave equation on an auxiliary de
Sitter spacetime, extending the first-order result in arXiv/1509.00113.


title:
Star-disc interaction in galactic nuclei: orbits and rates of accreted
  stars

abstract:
  We examine the effect of an accretion disc on the orbits of stars in the
central star cluster surrounding a central massive black hole by performing a
suite of 39 high-accuracy direct N-body simulations using state-of-the art
software and accelerator hardware, with particle numbers up to 128k. The
primary focus is on the accretion rate of stars by the black hole (equivalent
to their tidal disruption rate for black holes in the small to medium mass
range) and the eccentricity distribution of these stars. Our simulations vary
not only the particle number, but disc model (two models examined), spatial
resolution at the centre (characterised by the numerical accretion radius) and
softening length. The large parameter range and physically realistic modelling
allow us for the first time to confidently extrapolate these results to real
galactic centres. While in a real galactic centre both particle number and
accretion radius differ by a few orders of magnitude from our models, which are
constrained by numerical capability, we find that the stellar accretion rate
converges for models with N > 32k. The eccentricity distribution of accreted
stars, however, does not converge. We find that there are two competing effects
at work when improving the resolution: larger particle number leads to a
smaller fraction of stars accreted on nearly-circular orbits, while higher
spatial resolution increases this fraction. We scale our simulations to some
nearby galaxies and find that the expected boost in stellar accretion (or tidal
disruption, which could be observed as X-ray flares) in the presence of a gas
disc is about a factor of 10. Even with this boost, the accretion of mass from
stars is still a factor of ~ 100 slower than the accretion of gas from the
disc. Thus, it seems accretion of stars is not a major contributor to black
hole mass growth.


title:
Active galactic nuclei at z ~ 1.5: III. Accretion discs and black hole
  spin

abstract:
  This is the third paper in a series describing the spectroscopic properties
of a sample of 39 AGN at $z \sim 1.5$, selected to cover a large range in black
hole mass ($M_{BH}$) and Eddington ratio ($L/L_{Edd}$). In this paper, we
continue the analysis of the VLT/X-shooter observations of our sample with the
addition of 9 new sources. We use an improved Bayesian procedure, which takes
into account intrinsic reddening, and improved $M_{BH}$ estimates, to fit thin
accretion disc (AD) models to the observed spectra and constrain the spin
parameter ($a_*$) of the central black holes. We can fit 37 out of 39 AGN with
the thin AD model, and for those with satisfactory fits, we obtain constraints
on the spin parameter of the BHs, with the constraints becoming generally less
well defined with decreasing BH mass. Our spin parameter estimates range from
$\sim$$-$0.6 to maximum spin for our sample, and our results are consistent
with the "spin-up" scenario of BH spin evolution. We also discuss how the
results of our analysis vary with the inclusion of non-simultaneous GALEX
photometry in our thin AD fitting. Simultaneous spectra covering the rest-frame
optical through far-UV are necessary to definitively test the thin AD theory
and obtain the best constraints on the spin parameter.


title: Topological density-wave states in a particle-hole symmetric Weyl metal

abstract:
  We study the instabilities of a particle-hole symmetric Weyl metal with both
electron and hole Fermi surfaces (FS) around the Weyl points. For a repulsive
interaction, we find that the leading instability is towards a longitudinal
spin-density-wave order (SDW$_z$). Besides, there exist three degenerate
subleading instabilities: a charge-density-wave (CDW) instability and two
transverse spin-density-wave (SDW$_{x,y}$) instabilities. For an attractive
interaction the leading instabilities are towards two pair-density-wave orders
(PDW) which pair the two FS's separately. Both the PDW and SDW$_z$ order
parameters fully gap out FS's, while the CDW and SDW$_{x,y}$ ones leave line
nodes on both FS's. For the SDW$_z$ and the PDW states, the surface Fermi arc
in the metallic state evolves to a chiral Fermi line which passes the
projection of the Weyl points and traverses the full momentum space. For the
CDW state, the line node projects to a "drumhead" band localized on the
surface, which can lead to a topological charge polarization. We verify the
surface states by numerically simulating the angular-resolved photoemission
spectroscopy data.


title:
High-cadence spectroscopy of M-dwarfs. I. Analysis of systematic effects
  in HARPS-N line profile measurements on the bright binary GJ 725A+B

abstract:
  Understanding the sources of instrumental systematic noise is a must to
improve the design of future spectrographs. In this study, we alternated
observations of the well-suited pair of M-stars GJ 725A+B to delve into the
sub-night HARPS-N response. Besides the possible presence of a low-mass planet
orbiting GJ 725B, our observations reveal changes in the spectral energy
distribution (SED) correlated with measurements of the width of the
instrumental line profile and, to a lower degree, with the Doppler
measurements. To study the origin of these effects, we searched for
correlations among several quantities defined and measured on the spectra and
on the acquisition images.
  We find that the changes in apparent SED are very likely related to flux
losses at the fibre input. Further tests indicate that such flux losses do not
seriously affect the shape of the instrumental point spread function of
HARPS-N, but identify an inefficient fitting of the continuum as the most
likely source of the systematic variability observed in the FWHM. This index,
accounting for the HARPS-N cross-correlation profiles width, is often used to
decorrelate Doppler time-series. We show that the Doppler measurement obtained
by a parametric least-squares fitting of the spectrum accounting for continuum
variability is insensitive to changes in the slope of the SED, suggesting that
forward modeling techniques to measure moments of the line profile are the
optimal way to achieve higher accuracy. Remaining residual variability at ~1
m/s suggests that for M-stars Doppler surveys the current noise floor still has
an instrumental origin.


title: Convergent series for lattice models with polynomial interactions

abstract:
  The standard perturbative weak-coupling expansions in lattice models are
asymptotic. The reason for this is hidden in the incorrect interchange of the
summation and integration. However, substituting the Gaussian initial
approximation of the perturbative expansions by a certain interacting model or
regularizing original lattice integrals, one can construct desired convergent
series. In this paper we develop methods, which are based on the joint and
separate utilization of the regularization and new initial approximation. We
prove, that the convergent series exist and can be expressed as the re-summed
standard perturbation theory for any model on the finite lattice with the
polynomial interaction of even degree. We discuss properties of such series and
make them applicable to practical computations. The workability of the methods
is demonstrated on the example of the lattice $\phi^4$-model. We calculate the
operator $\langle\phi_n^2\rangle$ using the convergent series, the comparison
of the results with the Borel re-summation and Monte Carlo simulations shows a
good agreement between all these methods.


title:
The Bursty Star Formation Histories of Low-mass Galaxies at $0.4<z<1$
  Revealed by Star Formation Rates Measured from H$\beta$ and FUV

abstract:
  We investigate the burstiness of star formation histories (SFHs) of galaxies
at $0.4<z<1$ by using the ratio of star formation rates (SFRs) measured from
H$\beta$ and FUV (1500 \AA) (H$\beta$--to--FUV ratio). Our sample contains 164
galaxies down to stellar mass (M*) of $10^{8.5} M_\odot$ in the CANDELS GOODS-N
region, where Team Keck Redshift Survey DEIMOS spectroscopy and HST/WFC3 F275W
images from CANDELS and Hubble Deep UV Legacy Survey are available. When the
{\it ratio} of H$\beta$- and FUV-derived SFRs is measured, dust extinction
correction is negligible (except for very dusty galaxies) with the Calzetti
attenuation curve. The H$\beta$--to--FUV ratio of our sample increases with M*
and SFR. The median ratio is $\sim$0.7 at M*$\sim10^{8.5} M_\odot$ (or SFR$\sim
0.5 M_\odot/yr$) and increases to $\sim$1 at M*$\sim10^{10} M_\odot$ (or SFR
$\sim 10 M_\odot/yr$). At M*$<10^{9.5} M_\odot$, our median H$\beta$--to--FUV
ratio is lower than that of local galaxies at the same M*, implying a redshift
evolution. Bursty SFH on a timescale of a few tens of megayears on galactic
scales provides a plausible explanation of our results, and the importance of
the burstiness increases as M* decreases. Due to sample selection effects, our
H$\beta$--to--FUV ratio may be an upper limit of the true value of a complete
sample, which strengthens our conclusions. Other models, e.g., non-universal
initial mass function or stochastic star formation on star cluster scales, are
unable to plausibly explain our results.


title: Evolution of galaxy groups in the Illustris simulation

abstract:
  We present the first study of evolution of galaxy groups in the Illustris
simulation. We focus on dynamically relaxed and unrelaxed galaxy groups
representing dynamically evolved and evolving galaxy systems, respectively. The
evolutionary state of a group is probed from its luminosity gap and separation
between the brightest group galaxy and the center of mass of the group members.
We find that the Illustris simulation, over-produces large luminosity gap
galaxy systems, known as fossil systems, in comparison to observations and the
probed semi-analytical predictions. However, this simulation is equally
successful in recovering the correlation between luminosity gap and luminosity
centroid offset, in comparison to the probed semi-analytic model. We find
evolutionary tracks based on luminosity gap which indicate that a large
luminosity gap group is rooted in a small luminosity gap group, regardless of
the position of the brightest group galaxy within the halo. This simulation
helps, for the first time, to explore the black hole mass and its accretion
rate in galaxy groups. For a given stellar mass of the brightest group
galaxies, the black hole mass is larger in dynamically relaxed groups with a
lower rate of mass accretion. We find this consistent with the latest
observational studies of the radio activities in the brightest group galaxies
in fossil groups. We also find that the IGM in dynamically evolved groups is
hotter for a given halo mass than that in evolving groups, again consistent
with earlier observational studies.


title:
The EMPIRE Survey: Systematic Variations in the Dense Gas Fraction and
  Star Formation Efficiency from Full-Disk Mapping of M51

abstract:
  We present the first results from the EMPIRE survey, an IRAM large program
that is mapping tracers of high density molecular gas across the disks of nine
nearby star-forming galaxies. Here, we present new maps of the 3-mm transitions
of HCN, HCO+, and HNC across the whole disk of our pilot target, M51. As
expected, dense gas correlates with tracers of recent star formation, filling
the "luminosity gap" between Galactic cores and whole galaxies. In detail, we
show that both the fraction of gas that is dense, f_dense traced by HCN/CO, and
the rate at which dense gas forms stars, SFE_dense traced by IR/HCN, depend on
environment in the galaxy. The sense of the dependence is that high surface
density, high molecular gas fraction regions of the galaxy show high dense gas
fractions and low dense gas star formation efficiencies. This agrees with
recent results for individual pointings by Usero et al. 2015 but using unbiased
whole-galaxy maps. It also agrees qualitatively with the behavior observed
contrasting our own Solar Neighborhood with the central regions of the Milky
Way. The sense of the trends can be explained if the dense gas fraction tracks
interstellar pressure but star formation occurs only in regions of high density
contrast.


title:
Theoretical reevaluations of the black hole mass - bulge mass relation -
  I. Effect of the seed black hole mass

abstract:
  We explore the effect of varying the mass of the seed black hole on the
resulting black hole mass - bulge mass relation at z ~ 0, using a semi-analytic
model of galaxy formation combined with large cosmological N-body simulations.
We constrain our model by requiring the observed properties of galaxies at z ~
0 are reproduced. In keeping with previous semi-analytic models, we place a
seed black hole immediately after a galaxy forms. When the mass of the seed is
set at 10^5 M_sun, we find that the model results become inconsistent with
recent observational results of the black hole mass - bulge mass relation for
dwarf galaxies. In particular, the model predicts that bulges with ~ 10^9 M_sun
harbour larger black holes than observed. On the other hand, when we employ
seed black holes with 10^3 M_sun, or randomly select their mass within a
10^(3-5) M_sun range, the resulting relation is consistent with observation
estimates, including the observed dispersion. We find that to obtain stronger
constraints on the mass of seed black holes, observations of less massive
bulges at z ~ 0 are a more powerful comparison than the relations at higher
redshifts.


title: Implications of solar wind measurements for solar models and composition

abstract:
  We critically examine recent claims of a high solar metallicity by von
Steiger \& Zurbuchen (2016) based on \textit{in situ} measurements of the solar
wind, rather than the standard spectroscopically-inferred abundances (Asplund
et al. 2009). We test the claim by Vagnozzi et al. (2016) that a composition
based on the solar wind enables one to construct a standard solar model in
agreement with helioseismological observations and thus solve the decades-old
solar modelling problem. We show that, although some helioseismological
observables are improved compared to models computed with spectroscopic
abundances, most are in fact worse. The high abundance of refractory elements
leads to an overproduction of neutrinos, with a predicted $^8$B flux that is
nearly twice its observed value, and $^7$Be and CNO fluxes that are
experimentally ruled out at high confidence. A combined likelihood analysis
shows that models using the vSZ16 abundances fare worse than AGSS09 despite a
higher metallicity. We also present astrophysical and spectroscopic arguments
showing the vSZ16 composition to be an implausible representation of the solar
interior, identifying the first ionisation potential effect in the outer solar
atmosphere and wind as the likely culprit.


title: New Forces and the 750 GeV Resonance

abstract:
  Recently, the ATLAS and CMS collaborations have pointed out the possible
existence of a new resonance with a mass around 750 GeV. We investigate the
possibility to identify this new resonance with a spin zero field responsible
for the breaking of a new gauge symmetry. We focus on a simple theory where the
baryon number is a local symmetry spontaneously broken at the low scale. In
this context new vector-like quarks are needed to cancel all baryonic anomalies
and define the production mechanism and decays of the new Higgs at the LHC.
Assuming the existence of the new Higgs with a mass of 750 GeV at the LHC we
find an upper bound on the symmetry breaking scale. Therefore, one expects that
a new force associated with baryon number could be discovered at the LHC.


title:
The lightest visible-sector supersymmetric particle is likely to be
  unstable

abstract:
  We argue, based on typical properties of known solutions of
string/$M$-theory, that the lightest supersymmetric particle of the visible
sector will not be stable. In other words, dark matter is {\em not} a particle
with Standard Model quantum numbers, such as a WIMP. The argument is simple and
based on the typical occurrence of a) hidden sectors, b) interactions between
the Standard Model (visible) sector and these hidden sectors, and c) the lack
of an argument against massive neutral hidden sector particles being lighter
than the lightest visible supersymmetric particle. These conclusions do not
rely on arguments such as R-parity violation.


title: Effect of observational holes in fractal analysis of galaxy survey masks

abstract:
  Observations reveal that the Universe has a hierarchy of galaxy clustering
with transition to homogeneity on large scales according to the $\Lambda$CDM
model. On the other hand some observational estimates suggest a multifractal
behavior where galactic clustering is based on generalization of the
correlation dimension. We study the influence of veto areas on fractal
measurements in masks of galaxy surveys. We investigate if these holes can
produce fractal behaviors or modify the scale of cosmic homogeneity. From the
footprint of BOSS-DR12, we build a homogeneous sample following the radial
selection function for 73,412 points limited to the redshift range
$0.002<z<0.2$. Different percentages of observational holes were created
cumulatively in RA and dec on the sample. For the synthetic sample and for a
real sample of galaxies we determined the fractal dimension $D_q(r)$ in the
range $2\leq q\leq6$ using the sliding window technique to characterize the
spatial point distribution. Our results show that generalized dimension varies
with the scale, for low scales there are a fractal behavior with fluctuations
for all hole percentages studied and for larger scales than 113 Mpc/h the
statistical homogeneity is achieved in concordance with other analysis. We find
that observational holes cause a shift in the homogeneity scale $r_H$, in
particular for synthetic samples with percentages of holes between 0-10% the
homogeneity scale is reached at $(83\pm1)$Mpc/h while the fractal dimension
changes as $2.83^{\pm0.09}\leq D_q\leq2.855^{\pm0.09}$. For synthetic samples
with percentages of holes greater than 10%, we find that the value of $r_H$
increases proportionally. Consequently future results about homogeneity scale
based in fractal analyses must be corrected by observational holes and regions
of incompleteness in the geometry of the galaxy catalogue if the size of the
veto mask is significant.


title: Radio polarimetry of Galactic centre pulsars

abstract:
  To study the strength and structure of the magnetic field in the Galactic
centre (GC) we measured Faraday rotation of the radio emission of pulsars which
are seen towards the GC. Three of these pulsars have the largest rotation
measures (RMs) observed in any Galactic object with the exception of Sgr A*.
Their large dispersion measures, RMs and the large RM variation between these
pulsars and other known objects in the GC implies that the pulsars lie in the
GC and are not merely seen in projection towards the GC. The large RMs of these
pulsars indicate large line-of-sight magnetic field components between ~ 16-33
microgauss; combined with recent model predictions for the strength of the
magnetic field in the GC this implies that the large-scale magnetic field has a
very small inclination angle with respect to the plane of the sky (~ 12
degrees). Foreground objects like the Radio Arc or possibly an ablated, ionized
halo around the molecular cloud G0.11-0.11 could contribute to the large RMs of
two of the pulsars. If these pulsars lie behind the Radio Arc or G0.11-0.11
then this proves that low-scattering corridors with lengths >~ 100 pc must
exist in the GC. This also suggests that future, sensitive observations will be
able to detect additional pulsars in the GC. Finally, we show that the GC
component in our most accurate electron density model oversimplifies structure
in the GC.


title:
Measuring galaxy environment with the synergy of future photometric and
  spectroscopic surveys

abstract:
  We exploit the synergy between low-resolution spectroscopy and photometric
redshifts to study environmental effects on galaxy evolution in slitless
spectroscopic surveys from space. As a test case, we consider the future Euclid
Deep survey (~40deg$^2$), which combines a slitless spectroscopic survey
limited at H$\alpha$ flux $\geq5\times 10^{-17}$ erg cm$^{-2}$ s$^{-1}$ and a
photometric survey limited in H-band ($H\leq26$). We use Euclid-like galaxy
mock catalogues, in which we anchor the photometric redshifts to the 3D galaxy
distribution of the available spectroscopic redshifts. We then estimate the
local density contrast by counting objects in cylindrical cells with radius
from 1 to 10 h$^{-1}$Mpc over the redshift range 0.9<z<1.8. We compare this
density field with the one computed in a mock catalogue with the same depth as
the Euclid Deep survey (H=26) but without redshift measurement errors. We find
that our method successfully separates high from low density environments (the
last from the first quintile of the density distribution), with higher
efficiency at low redshift and large cell: the fraction of low density regions
mistaken by high density peaks is <1% for all scales and redshifts explored,
but for scales of 1 h$^{-1}$Mpc for which is a few percent. These results show
that we can efficiently study environment in photometric samples if
spectroscopic information is available for a smaller sample of objects that
sparsely samples the same volume. We demonstrate that these studies are
possible in the Euclid Deep survey, i.e. in a redshift range in which
environmental effects are different from those observed in the local universe,
hence providing new constraints for galaxy evolution models.


title: The Higgs Portal and Cosmology

abstract:
  Higgs portal interactions provide a simple mechanism for addressing two open
problems in cosmology: dark matter and the baryon asymmetry. In the latter
instance, Higgs portal interactions may contain the ingredients for a strong
first order electroweak phase transition as well as new CP-violating
interactions as needed for electroweak baryogenesis. These interactions may
also allow for a viable dark matter candidate. We survey the opportunities for
probing the Higgs portal as it relates to these questions in cosmology at the
LHC and possible future colliders.


title: Quantum periods of Calabi-Yau fourfolds

abstract:
  In this work we study the quantum periods together with their Picard-Fuchs
differential equations of Calabi-Yau fourfolds. In contrast to Calabi-Yau
threefolds, we argue that the large volume points of Calabi-Yau fourfolds
generically are regular singular points of the Picard-Fuchs operators of
non-maximally unipotent monodromy. We demonstrate this property in explicit
examples of Calabi-Yau fourfolds with a single Kahler modulus. For these
examples we construct integral quantum periods and study their global
properties in the quantum Kahler moduli space with the help of numerical
analytic continuation techniques. Furthermore, we determine their genus zero
Gromov-Witten invariants, their Klemm-Pandharipande meeting invariants, and
their genus one BPS invariants. In our computations we emphasize the features
attributed to the non-maximally unipotent monodromy property. For instance, it
implies the existence of integral quantum periods that at large volume are
purely worldsheet instanton generated. To verify our results, we also present
intersection theory techniques to enumerate lines with a marked point on
complete intersection Calabi-Yau fourfolds in Grassmannian varieties.


title: Plateau Inflation from Random Non-Minimal Coupling

abstract:
  A generic non-minimal coupling can push any higher-order terms of the scalar
potential sufficiently far out in field space to yield observationally viable
plateau inflation. We provide analytic and numerical evidence that this
generically happens for a non-minimal coupling strength $\xi$ of the order
$N_e^2$. In this regime, the non-minimally coupled field is sub-Planckian
during inflation and is thus protected from most higher-order terms. For larger
values of $\xi$, the inflationary predictions converge towards the sweet spot
of PLANCK. The latter includes $\xi\simeq 10^4$ obtained from CMB normalization
arguments, thus providing a natural explanation for the inflationary
observables measured.


title: Comments on Thermalization in 2D CFT

abstract:
  We revisit certain aspects of thermalization in 2D CFT. In particular, we
consider similarities and differences between the time dependence of
correlation functions in various states in rational and non-rational CFTs. We
also consider the distinction between global and local thermalization and
explain how states obtained by acting with a diffeomorphism on the ground state
can appear locally thermal, and we review why the time-dependent expectation
value of the energy-momentum tensor is generally a poor diagnostic of global
thermalization. Since all 2D CFTs have an infinite set of commuting conserved
charges, generic initial states might be expected to give rise to a generalized
Gibbs ensemble rather than a pure thermal ensemble at late times. We construct
the holographic dual of the generalized Gibbs ensemble and show that, to
leading order, it is still described by a BTZ black hole. The extra conserved
charges, while rendering $c < 1$ theories essentially integrable, therefore
seem to have little effect on large-$c$ conformal field theories.


title: Minimal Dilaton Model and the Diphoton Excess

abstract:
  In light of the recent 750 GeV diphoton excesses reported by the ATLAS and
CMS collaborations, we investigate the possibility of explaining this excess
using the Minimal Dilaton Model. We find that this model is able to explain the
observed excess with the presence of additional top partner(s), with same
charge as the top quark, but with mass in the TeV region. First, we constrain
model parameters using in addition to the 750 GeV diphoton signal strength,
precision electroweak tests, single top production measurements, as well as
Higgs signal strength data collected in the earlier runs of the LHC. In
addition we discuss interesting phenomenolgy that could arise in this model,
relevant for future runs of the LHC.


title: Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids

abstract:
  Spin liquids are conventionally described by gauge theories with a vector
gauge field. However, there exists a wider class of spin liquids with higher
rank tensors as the gauge variable. In this work, we focus on (3+1)-dimensional
spin liquids described by U(1) symmetric tensor gauge theories, which have
recently been shown to be stable gapless spin liquids. We investigate the
particle structure of these tensor gauge theories and find that they have deep
connections with the "fracton" models recently discovered by Vijay, Haah, and
Fu. Tensor gauge theories have more conservation laws than the simple charge
conservation law of rank 1 theories. These conservation laws place severe
restrictions on the motion of particles. Particles in some models are fully
immobile (fractons), while other models have particles restricted to motion
along lower-dimensional subspaces.


title:
Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization
  Around (A)dS Space

abstract:
  We investigate the four-derivative free Weyl action for two-column
mixed-symmetry field that makes use of maximal gauge symmetries. In flat space,
the action can be uniquely determined from gauge and Weyl (trace shift)
symmetry requirements. We show that there is a smooth and unique deformation of
the flat action to (A)dS which keeps the same amount of gauge symmetries. This
action admits a factorization into two distinct two-derivative actions having
gauge parameters of different Young diagrams. Hence, this factorization pattern
naturally extends that of the Weyl actions of symmetric higher spin fields to
mixed-symmetry cases. The mass-deformation for these actions can be realized
preserving one of the gauge symmetries. Although generically non-unitary, in
special dimensions, unitarity is achieved selecting different mass deformations
for dS and AdS. We consider particular examples of our construction such as New
Massive Gravity in three dimensions, linearized bigravity in four dimensions
and their arbitrary dimensional generalizations.


title: Giga-Year Evolution of Jupiter Trojans and the Asymmetry Problem

abstract:
  We present a series of numerical integrations of observed and fictitious
Jupiter Trojan asteroids, under the gravitational effects of the four outer
planets, for time-spans comparable with the age of the Solar System. From these
results we calculate the escape rate from each Lagrange point, and construct
dynamical maps of "permanence" time in different regions of the phase space.
Fictitious asteroids in L4 and L5 show no significant difference, showing
almost identical dynamical maps and escape rates. For real Trojans, however, we
found that approximately 23% o f the members of the leading swarm escaped after
4.5 Gyrs, while this number increased to 28.3% for L5. This implies that the
asymmetry between the two populations increases with time, indicating that it
may have been smaller at the time of formation/capture of these asteroids.
Nevertheless, the difference in chaotic diffusion cannot, in itself, account
for the current observed asymmetry (~40%), and must be primarily primordial and
characteristic of the capture mechanism of the Trojans. Finally, we calculate
new proper elements for all the numbered Trojans using the semi-analytical
approach of Beaug\'e and Roig (2001), and compare the results with the
numerical estimations by Bro\v{z} and Rosehnal (2011). For asteroids that were
already numbered in 2011, both methods yield very similar results, while
significant differences were found for those bodies that became numbered after
2011.


title:
Correction methods for finite-acceptance effects in two-particle
  correlation analyses

abstract:
  Two-particle angular correlations have been widely used as a tool to explore
particle production mechanisms in heavy-ion collisions. The mixed-event
technique is generally used as a standard method to correct for
finite-acceptance effects. We demonstrate that event mixing only provides an
approximate acceptance correction, and propose new methods for
finite-acceptance corrections. Starting from discussions about 2-dimensional
correction procedures, new methods are derived for specific assumptions on the
properties of the signal, such as uniform signal distribution or
$\delta$-function-like trigger particle distribution, and suitable for
two-particle correlation analyses from particles at mid-rapidity and jet-hadron
or high $p_{\text{T}}$-triggered hadron-hadron correlations. Per-trigger
associated particle yields from the mixed-event method and the new methods are
compared through Monte Carlo simulations containing well-defined correlation
signals. Significant differences are observed at large pseudorapidity
differences in general and especially for asymmetric particle distribution like
that produced in proton--nucleus collisions. The applicability and validity of
the new methods are discussed in detail.


title:
Stellar and Black Hole Mass Densities as Empirical Tracers of
  Co-evolution Show Lock-step Growth since $z{\sim}3$

abstract:
  At redshifts beyond $z{\sim}1$ measuring the black hole galaxy relations
proves to be a difficult task. The bright light of the AGN aggravates
deconvolution of black hole and galaxy properties. On the other hand high
redshift data on these relations is vital to understand in what ways galaxies
and black holes co-evolve and in what ways they don't. In this work we use
black hole (BHMDs) and stellar mass densities (SMDs) to constrain the possible
co-evolution of black holes with their host galaxies since $z{\sim}5$. The
BHMDs are calculated from quasar luminosity functions (QLF) using the Soltan
argument, while we use integrals over stellar mass functions (SMFs) or the star
formation rate density to obtain values for the stellar mass density. We find
that both quantities grow in lock-step below redshifts of $z{\sim}3$ with a
non-evolving BHMD to SMD ratio. A fit to the data assuming a power law relation
between the BHMD and the SMD yields exponents around unity ($1.0{-}1.5$). Up to
$z{\sim}5$ the BHMD to SMD ratio doesn't show a strong evolution given the
larger uncertainty in the completeness of high-redshift datasets. Our results,
always applying the same analysis technique, seem to be consistent across all
adopted data sets.


title: Difference of powers of consecutive primes which are perfect squares

abstract:
  We investigate the consecutive primes $p$ and $q$ ($p > q$) for which there
exists a pair of natural numbers $(x,y)$ such that $p^x-q^y$ is a perfect
square and make some conjectures.


title: The Higgs mass in the CP violating MSSM, NMSSM, and beyond

abstract:
  We discuss the automatised calculation of the Higgs mass in renormalisable
supersymmetric models with complex parameters at the two-loop level. Our setup
is based on the public codes SARAH and SPheno, which can now compute the
two-loop corrections to masses of all neutral scalars in such theories. The
generic ansatz for these calculations and the handling of the `Goldstone Boson
catastrophe' is described. It is shown that we find perfect agreement with
other existing two-loop calculations performed in the DR-bar scheme. We also
use the functionality to derive results for the MSSM and NMSSM not available
before: the Higgs mass in the constrained version of the complex MSSM, and the
impact of CP phases in the two-loop corrections beyond order alpha-strong
alpha-top for the scale invariant NMSSM are briefly analysed.


title:
A Neutron Star-White Dwarf Binary Model for Repeating Fast Radio Burst
  121102

abstract:
  We propose a compact binary model for the fast radio burst (FRB) repeaters,
where the system consists of a magnetic white dwarf (WD) and a neutron star
(NS) with strong bipolar magnetic fields. When the WD fills its Roche lobe,
mass transfer will occur from the WD to the NS through the inner Lagrange
point. The accreted magnetized materials may trigger magnetic reconnection when
they approach the NS surface, and therefore the electrons can be accelerated to
an ultra-relativistic speed. In this scenario, the curvature radiation of the
electrons moving along the NS magnetic field lines can account for the
characteristic frequency and the timescale of an FRB. Owing to the conservation
of angular momentum, the WD may be kicked away after a burst, and the next
burst may appear when the system becomes semi-detached again through the
gravitational radiation. By comparing our analyses with the observations, we
show that such an intermittent Roche lobe overflow mechanism can be responsible
for the observed repeating behavior of FRB 121102.


title: Design of Dynamic Algorithms via Primal-Dual Method

abstract:
  We develop a dynamic version of the primal-dual method for optimization
problems, and apply it to obtain the following results. (1) For the dynamic
set-cover problem, we maintain an $O(f^2)$-approximately optimal solution in
$O(f \cdot \log (m+n))$ amortized update time, where $f$ is the maximum
"frequency" of an element, $n$ is the number of sets, and $m$ is the maximum
number of elements in the universe at any point in time. (2) For the dynamic
$b$-matching problem, we maintain an $O(1)$-approximately optimal solution in
$O(\log^3 n)$ amortized update time, where $n$ is the number of nodes in the
graph.


title: Ces\`aro summability of integrals of fuzzy-number-valued functions

abstract:
  In the present study, we have introduced Ces\`{a}ro summability of integrals
of fuzzy-number-valued functions and given one-sided Tauberian conditions under
which convergence of improper fuzzy Riemann integrals follows from Ces\`{a}ro
summability. Also, fuzzy analogues of Schmidt type slow decrease and Landau
type one-sided Tauberian conditions have been obtained.


title:
Statistical approximation by $(p,q)$-analogue of Bernstein-Stancu
  Operators

abstract:
  In this paper, some approximation properties of $(p,q)$-analogue of
Bernstein-Stancu Operators has been studied. Rate of statistical convergence by
means of modulus of continuity and Lipschitz type maximal functions has been
investigated. Monotonicity of $(p,q)$-Bernstein-Stancu Operators and a global
approximation theorem by means of Ditzian-Totik modulus of smoothness is
established. A quantitative Voronovskaja type theorem is developed for these
operators.
  Furthermore, we show comparisons and some illustrative graphics for the
convergence of operators to a function


title:
Chromatic effects in beam wander correction for free-space quantum
  communications

abstract:
  Beam wander caused by atmospheric turbulence can significantly degrade the
performance of horizontal free-space quantum communication links. Classical
beam wander correction techniques cannot be applied due to the stronger
requirements of transmitting single photons. One strategy to overcome this
limitation consists in using a separate wavelength from that of the quantum
signal to analyze the beam wander and use this information for its correction.
For this strategy to work adequately, both wavelengths should be affected
equally by atmospheric turbulence, i.e. no chromatic effects should be
originated from beam wander. In this letter, a series of experiments are
performed to prove that this is the case for {\lambda} ~ 850 nm as the quantum
signal and {\lambda} ~ 1550 nm as the tracking signal of a quantum
communication system.


title: Metcalfe's Law Revisited

abstract:
  Rudimentary mathematical analysis of simple network models suggests
bandwidth-independent saturation of network growth dynamics and hints at linear
decrease in information density of the data. However it strongly confirms
Metcalfe's law as a measure of network utility and suggests it can play an
important role in network calculations. This paper establishes mathematical
notion of network value and analyses two conflicting models of network. One,
traditional model, fails to manifest Metcalfe's law. Another model, one that
observes network in a wider context, both confirms Metcalfe's law and reveals
its upper boundary.


title: Long Duration Flare Emission: Impulsive or Gradual Heating?

abstract:
  Flare emissions in X-ray and EUV wavelengths have previously been modeled as
the plasma response to impulsive heating from magnetic reconnection. Some
flares exhibit gradually evolving X-ray and EUV light curves, which are
believed to result from superposition of an extended sequence of impulsive
heating events occurring in different adjacent loops or even unresolved threads
within each loop. In this paper, we apply this approach to a long duration
two-ribbon flare SOL2011-09-13T22 observed by the Atmosphere Imaging Assembly
(AIA). We find that to reconcile with observed signatures of flare emission in
multiple EUV wavelengths, each thread should be heated in two phases, an
intense impulsive heating followed by a gradual, low-rate heating tail that is
attenuated over 20-30 minutes. Each AIA resolved single loop may be composed of
several such threads. The two-phase heating scenario is supported by modeling
with both a zero-dimensional and a 1D hydrodynamic code. We discuss viable
physical mechanisms for the two-phase heating in a post-reconnection thread.


title: Multiple commutation relations in the models with gl(2|1) symmetry

abstract:
  We consider quantum integrable models with $\mathfrak{gl}(2|1)$ symmetry. We
derive a set of multiple commutation relations between the monodromy matrix
entries. These multiple commutation relations allow us to obtain different
representations for Bethe vectors.


title: A new technique for solving singular IVPs of Emden-Fowler type

abstract:
  A new analytic approximate technique for addressing nonlinear problems,
namely the optimal perturbation iteration method, is introduced and implemented
to singular initial value Lane-Emden type problems to test the effectiveness
and performance of the method. This technique provides us to adjust the
convergence regions when necessary.Comparing different methods reveals that the
proposed method is highly accurate and has great potential to be a new kind of
powerful analytical tool for nonlinear differential equations.


title:
Congruences modulo powers of $2$ for the number of unique path
  partitions

abstract:
  We compute the congruence class modulo 16 of the number of unique path
partitions of $n$ (as defined by Olsson), thus generalising previous results by
Bessenrodt, Olsson and Sellers [Ann. Combin. 13 (2013), 591-602].


title:
Relationship between chromospheric evaporation and magnetic field
  topology in M-class solar flare

abstract:
  Chromospheric evaporation is observed as Doppler blueshift during solar
flares. It plays one of key roles in dynamics and energetics of solar flares,
however, its mechanism is still unknown. In this paper we present a detailed
analysis of spatially-resolved multi-wavelength observations of chromospheric
evaporation during an M 1.0 class solar flare (SOL2014-06-12T21:12) using data
from the NASA's IRIS (Interface Region Imaging Spectrograph) and HMI/SDO
(Helioseismic and Magnetic Imager onboard Solar Dynamics Observatory)
telescopes, and VIS/NST (Visible Imaging Spectrometer at New Solar Telescope)
high-resolution observations, covering the temperature range from 10^4 K to
10^7 K. The results show that the averaged over the region Fe XXI blueshift of
the hot evaporating plasma is delayed relative to the C II redshift of the
relatively cold chromospheric plasma by about 1 min. The spatial distribution
of the delays is not uniform across the region and can be as long as 2 min in
several zones. Using vector magnetograms from HMI we reconstruct the magnetic
field topology and the quasi-separatrix layer (QSL) and find that the blueshift
delay regions as well as the H-alpha flare ribbons are connected to the region
of magnetic polarity inversion line (PIL) and an expanding flux rope via a
system of low-lying loop arcades with height < ~4.5 Mm. This allows us to
propose an interpretation of the chromospheric evaporation based on the
geometry of local magnetic fields, and the primary energy source associated
with the PIL.


title:
Pseudorapidity dependence of long-range two-particle correlations in pPb
  collisions at sqrt(s[NN]) = 5.02 TeV

abstract:
  Two-particle correlations in pPb collisions at a nucleon-nucleon
center-of-mass energy of 5.02 TeV are studied as a function of the
pseudorapidity separation (Delta eta) of the particle pair at small relative
azimuthal angle (abs(Delta phi) < pi/3). The correlations are decomposed into a
jet component that dominates the short-range correlations (abs(Delta eta) < 1),
and a component that persists at large Delta eta and may originate from
collective behavior of the produced system. The events are classified in terms
of the multiplicity of the produced particles. Finite azimuthal anisotropies
are observed in high-multiplicity events. The second and third Fourier
components of the particle-pair azimuthal correlations, V[2] and V[3], are
extracted after subtraction of the jet component. The single-particle
anisotropy parameters v[2] and v[3] are normalized by their lab frame
mid-rapidity value and are studied as a function of eta[cm]. The normalized
v[2] distribution is found to be asymmetric about eta[cm] = 0, with smaller
values observed at forward pseudorapidity, corresponding to the direction of
the proton beam, while no significant pseudorapidity dependence is observed for
the normalized v[3] distribution within the statistical uncertainties.


title: MCD-finite Domains and Ascent of IDF Property in Polynomial Extensions

abstract:
  An integral domain is said to have the IDF property when every non-zero
element of it has only a finite number of non-associate irreducible divisors. A
counterexample has already been found showing that IDF property does not
necessarily ascend in polynomial extensions.
  In this paper, we introduce a new class of integral domains, called
MCD-finite domains, and show that for any domain $D$, $D[X]$ is an IDF domain
if and only if $D$ is both IDF and MCD-finite. This result entails all the
previously known sufficient conditions for the ascent of the IDF property.
  Our new characterization of polynomial domains with the IDF property enables
us to use a different construction and build another counterexample which
strengthen the previously known result on this matter.


title: Constraints on primordial black holes from Galactic gamma-ray background

abstract:
  The fraction of the Universe going into primordial black holes (PBHs) with
initial mass M_* \approx 5 \times 10^{14} g, such that they are evaporating at
the present epoch, is strongly constrained by observations of both the
extragalactic and Galactic gamma-ray backgrounds. However, while the dominant
contribution to the extragalactic background comes from the time-integrated
emission of PBHs with initial mass M_*, the Galactic background is dominated by
the instantaneous emission of those with initial mass slightly larger than M_*
and current mass below M_*. Also, the instantaneous emission of PBHs smaller
than 0.4 M_* mostly comprises secondary particles produced by the decay of
directly emitted quark and gluon jets. These points were missed in the earlier
analysis by Lehoucq et al. using EGRET data. For a monochromatic PBH mass
function, with initial mass (1+\mu) M_* and \mu << 1, the current mass is
(3\mu)^{1/3} M_* and the Galactic background constrains the fraction of the
Universe going into PBHs as a function of \mu. However, the initial mass
function cannot be precisely monochromatic and even a tiny spread of mass
around M_* would generate a current low-mass tail of PBHs below M_*. This tail
would be the main contributor to the Galactic background, so we consider its
form and the associated constraints for a variety of scenarios with both
extended and nearly-monochromatic initial mass functions. In particular, we
consider a scenario in which the PBHs form from critical collapse and have a
mass function which peaks well above M_*. In this case, the largest PBHs could
provide the dark matter without the M_* ones exceeding the gamma-ray background
limits.


title: Counting and Enumerating Crossing-free Geometric Graphs

abstract:
  We describe a framework for counting and enumerating various types of
crossing-free geometric graphs on a planar point set. The framework generalizes
ideas of Alvarez and Seidel, who used them to count triangulations in time
$O(2^nn^2)$ where $n$ is the number of points. The main idea is to reduce the
problem of counting geometric graphs to counting source-sink paths in a
directed acyclic graph.
  The following new results will emerge. The number of all crossing-free
geometric graphs can be computed in time $O(c^nn^4)$ for some $c < 2.83929$.
The number of crossing-free convex partitions can be computed in time
$O(2^nn^4)$. The number of crossing-free perfect matchings can be computed in
time $O(2^nn^4)$. The number of convex subdivisions can be computed in time
$O(2^nn^4)$. The number of crossing-free spanning trees can be computed in time
$O(c^nn^4)$ for some $c < 7.04313$. The number of crossing-free spanning cycles
can be computed in time $O(c^nn^4)$ for some $c < 5.61804$.
  With the same bounds on the running time we can construct data structures
which allow fast enumeration of the respective classes. For example, after
$O(2^nn^4)$ time of preprocessing we can enumerate the set of all crossing-free
perfect matchings using polynomial time per enumerated object. For
crossing-free perfect matchings and convex partitions we further obtain
enumeration algorithms where the time delay for each (in particular, the first)
output is bounded by a polynomial in $n$.
  All described algorithms are comparatively simple, both in terms of their
analysis and implementation.


title: On the volume of sections of a convex body by cones

abstract:
  Let $K$ be a convex body in $\mathbb R^n$. We prove that in small
codimensions, the sections of a convex body through the centroid are quite
symmetric with respect to volume. As a consequence of our estimates we give a
positive answer to a problem posed by M. Meyer and S. Reisner regarding convex
intersection bodies.


title: Two dimensional quantum repeaters

abstract:
  The endeavour to develop quantum networks gave rise to a rapidly developing
field with far reaching applications such as secure communication and the
realisation of distributed computing tasks. This ultimately calls for the
creation of flexible multi-user structures that allow for quantum communication
between arbitrary pairs of parties in the network and facilitate also
multi-user applications. To address this challenge, we propose a 2D quantum
repeater architecture to establish long-distance entanglement shared between
multiple communication partners in the presence of channel noise and imperfect
local control operations. The scheme is based on the creation of self-similar
multi-qubit entanglement structures at growing scale, where variants of
entanglement swapping and multi-party entanglement purification are combined to
create high fidelity entangled states. We show how such networks can be
implemented using trapped ions in cavities.


title: Anderson localization on random regular graphs

abstract:
  A numerical study of Anderson transition on random regular graphs (RRG) with
diagonal disorder is performed. The problem can be described as a tight-binding
model on a lattice with N sites that is locally a tree with constant
connectivity. In certain sense, the RRG ensemble can be seen as
infinite-dimensional ($d\to\infty$) cousin of Anderson model in d dimensions.
We focus on the delocalized side of the transition and stress the importance of
finite-size effects. We show that the data can be interpreted in terms of the
finite-size crossover from small ($N\ll N_c$) to large ($N\gg N_c$) system,
where $N_c$ is the correlation volume diverging exponentially at the
transition. A distinct feature of this crossover is a nonmonotonicity of the
spectral and wavefunction statistics, which is related to properties of the
critical phase in the studied model and renders the finite-size analysis highly
non-trivial. Our results support an analytical prediction that states in the
delocalized phase (and at $N\gg N_c$) are ergodic in the sense that their
inverse participation ratio scales as $1/N$.


title: Quantum Vertex Model for Reversible Classical Computing

abstract:
  Mappings of classical computation onto statistical mechanics models have led
to remarkable successes in addressing some complex computational problems.
However, such mappings display thermodynamic phase transitions that may prevent
reaching solution even for easy problems known to be solvable in polynomial
time. Here we map universal reversible classical computations onto a planar
vertex model that exhibits no bulk classical thermodynamic phase transition,
independent of the computational circuit. Within our approach the solution of
the computation is encoded in the ground state of the vertex model and its
complexity is reflected in the dynamics of the relaxation of the system to its
ground state. We use thermal annealing with and without 'learning' to explore
typical computational problems. We also construct a mapping of the vertex model
into the Chimera architecture of the D-Wave machine, initiating an approach to
reversible classical computation based on state-of-the-art implementations of
quantum annealing.

categories: cond-mat.stat-mech cond-mat.dis-nn cs.CC quant-ph


title:
Technical Report: Design, Implementation and Deployment of
  Intermittency-aware Cellular Edge Services for Rural areas

abstract:
  Rural areas continue to be plagued by limited data connectivity due to poor
and unreliable power infrastructure, poor backhaul connectivity and lack of
economic incentives for telecom providers. These factors continue to be an
impediment to providing reliable, highly available and bandwidth intensive
mobile services and applications to function well in such contexts. This paper
presents the design, implementation and deployment of GreenLinks, a new
ground-up platform that enables intermittency-aware, reliable and available
cellular services and application support in rural contexts under extreme
operational environments with limited power and no existing cellular coverage.
Unlike the conventional monolithic cellular network architecture, GreenLinks
enables a distributed (and potentially disjoint) collection of open,
programmable cellular base stations to offer a gamut of both conventional
cellular services and new forms of distributed edge services. GreenLinks offers
new application primitives to support different types of intermittency-aware
distributed mobile edge services including P2P transactions, voice-based social
media applications, and distributed mobile sensing applications. Using a
participatory sensing white spaces approach, a GreenLinks base stati


title: The Atmosphere of Pluto as Observed by New Horizons

abstract:
  Observations made during the New Horizons flyby provide a detailed snapshot
of the current state of Pluto's atmosphere. While the lower atmosphere (at
altitudes <200 km) is consistent with ground-based stellar occultations, the
upper atmosphere is much colder and more compact than indicated by
pre-encounter models. Molecular nitrogen (N$_2$) dominates the atmosphere (at
altitudes <1800 km or so), while methane (CH$_4$), acetylene (C$_2$H$_2$),
ethylene (C$_2$H$_4$), and ethane (C$_2$H$_6$) are abundant minor species, and
likely feed the production of an extensive haze which encompasses Pluto. The
cold upper atmosphere shuts off the anticipated enhanced-Jeans,
hydrodynamic-like escape of Pluto's atmosphere to space. It is unclear whether
the current state of Pluto's atmosphere is representative of its average
state--over seasonal or geologic time scales.


title:
Solution of the nonlinear equation of a divergent type in the corner
  point domain

abstract:
  The algorithm for generation of exact solutions of the nonlinear equation in
partial derivatives of a divergent type which is included in the formulation of
magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary
Schr\"odinger equation) has been suggested. The properties of smoothness of
solutions in domains with corner points (piecewise smooth boundary) have been
considered. The solutions with unlimited derivatives in the corner point domain
have been presented on the basis of a new class of special functions.


title: Text-based LSTM networks for Automatic Music Composition

abstract:
  In this paper, we introduce new methods and discuss results of text-based
LSTM (Long Short-Term Memory) networks for automatic music composition. The
proposed network is designed to learn relationships within text documents that
represent chord progressions and drum tracks in two case studies. In the
experiments, word-RNNs (Recurrent Neural Networks) show good results for both
cases, while character-based RNNs (char-RNNs) only succeed to learn chord
progressions. The proposed system can be used for fully automatic composition
or as semi-automatic systems that help humans to compose music by controlling a
diversity parameter of the model.


title: Polynomial splitting measures and cohomology of the pure braid group

abstract:
  We study for each $n$ a one-parameter family of complex-valued measures on
the symmetric group $S_n$, which interpolate the probability of a monic, degree
$n$, square-free polynomial in $\mathbb{F}_q[x]$ having a given factorization
type. For a fixed factorization type, indexed by a partition $\lambda$ of $n$,
the measure is known to be a Laurent polynomial. We express the coefficients of
this polynomial in terms of characters associated to $S_n$-subrepresentations
of the cohomology of the pure braid group $H^{\bullet}(P_n, \mathbb{Q})$. We
deduce that the splitting measures for all parameter values $z= -\frac{1}{m}$
(resp. $z= \frac{1}{m}$), after rescaling, are characters of
$S_n$-representations (resp. virtual $S_n$-representations.)


title:
Casimir effect between pinned particles in two-dimensional jammed
  systems

abstract:
  The Casimir effect arises when long-ranged fluctuations are geometrically
confined between two surfaces, leading to a macroscopic force. Traditionally,
these forces have been observed in quantum systems and near critical points in
classical systems. Here we show the existence of Casimir-like forces between
two pinned particles immersed in two-dimensional systems near the jamming
transition. We observe two components to the total force: a short-ranged,
depletion force and a long-ranged, repulsive Casimir-like force. The
Casimir-like force dominates as the jamming transition is approached, and when
the pinned particles are much larger than the ambient jammed particles. We show
that this repulsive force arises due to a clustering of particles with strong
contact forces around the perimeter of the pinned particles. As the separation
between the pinned particles decreases, a region of high-pressure develops
between them, leading to a net repulsive force.


title: When do links admit homeomorphic C-complexes?

abstract:
  Any two knots admit orientation preserving homeomorphic Seifert surfaces, as
can be seen by stabilizing. There is a generalization of a Seifert surface to
the setting of links called a C-complex. In this paper, we ask when two links
will admit orientation preserving homeomorphic C-complexes. In the case of
2-component links, we find that the pairwise linking number provides a complete
obstruction. In the case of links with 3 or more components and zero pairwise
linking number, Milnor's triple linking number provides a complete obstruction.