title:
Antisymmetric tensor Z_p gauge symmetries in field theory and string
  theory

abstract:
  We consider discrete gauge symmetries in D dimensions arising as remnants of
broken continuous gauge symmetries carried by general antisymmetric tensor
fields, rather than by standard 1-forms. The lagrangian for such a general
${\bf Z}_p$ gauge theory can be described in terms of a $r$-form gauge field
made massive by a $(r-1)$-form, or other dual realizations, that we also
discuss. The theory contains charged topological defects of different
dimensionalities, generalizing the familiar charged particles and strings in
D=4. We describe realizations in string theory compactifications with torsion
cycles, or with background field strength fluxes. We also provide examples of
non-abelian discrete groups, for which the group elements are associated with
charged objects of different dimensionality.


title: Bridge connection of quantum Hall elementary devices

abstract:
  Multiple-series and multiple-parallel connections of quantum Hall elementary
devices allow the realization of multiple or fractional values of the quantized
Hall resistance, rejecting the effect of contact and wiring resistances. We
introduce here the multiple-bridge connection, which maintains the properties
of multiple-series and parallel connections and allows more freedom in the
choice of the topology of networks composed of quantum Hall elements, and the
design of more efficient quantum Hall array resistance standards (and other
devices). As an example, a 5-element network is analyzed in detail.


title:
Cosmic dichotomy in the hosts of rapidly star-forming systems at low and
  high redshifts

abstract:
  This paper presents a compilation of clustering results taken from the
literature for galaxies with highly enhanced (SFR [30-10^3] Msun/yr) star
formation activity observed in the redshift range z=[0-3]. We show that,
irrespective of the selection technique and only very mildly depending on the
star forming rate, the clustering lengths of these objects present a sharp
increase of about a factor 3 between z~1 and z~2, going from values of ~5 Mpc
to about 15 Mpc and higher. This behaviour is reflected in the trend of the
masses of the dark matter hosts of star-forming galaxies which increase from
~10^11.5 Msun to ~10^13.5 Msun between z~1 and z~2. Our analysis shows that
galaxies which actively form stars at high redshifts are not the same
population of sources we observe in the more local universe. In fact, vigorous
star formation in the early universe is hosted by very massive structures,
while for z~1 a comparable activity is encountered in much smaller systems,
consistent with the down-sizing scenario. The available clustering data can
hardly be reconciled with merging as the main trigger for intense star
formation activity at high redshifts.
  We further argue that, after a characteristic time-scale of ~1 Gyr, massive
star-forming galaxies at z>~2 evolve into z<~1.5 passive galaxies with large
(Mstellar=[10^11 - 10^12] Msun) stellar masses.


title:
A framework towards understanding mesoscopic phenomena: Emergent
  unpredictability, symmetry breaking and dynamics across scales

abstract:
  By integrating 4 lines of thoughts: symmetry breaking originally advanced by
Anderson, bifurcation from nonlinear dynamics, Landau's theory of phase
transition, and the mechanism of emergent rare events studied by Kramers, we
introduce a possible framework for understanding mesoscopic dynamics that links
(i) fast lower level microscopic motions, (ii) movements within each basin at
the mid-level, and (iii) higher-level rare transitions between neighboring
basins, which have rates that decrease exponentially with the size of the
system. In this mesoscopic framework, multiple attractors arise as emergent
properties of the nonlinear systems. The interplay between the stochasticity
and nonlinearity leads to successive jump-like transitions among different
basins. We argue each transition is a dynamic symmetry breaking, with the
potential of exhibiting Thom-Zeeman catastrophe as well as phase transition
with the breakdown of ergodicity (e.g., cell differentiation). The slow-time
dynamics of the nonlinear mesoscopic system is not deterministic, rather it is
a discrete stochastic jump process. The existence of these discrete states and
the Markov transitions among them are both emergent phenomena. This emergent
stochastic jump dynamics then serves as the stochastic element for the
nonlinear dynamics of a higher level aggregates on an even larger spatial and
slower time scales (e.g., evolution). This description captures the
hierarchical structure outlined by Anderson and illustrates two distinct types
of limit of a mesoscopic dynamics: A long-time ensemble thermodynamics in terms
of time $t$ tending infinity followed by the size of the system $N$ tending
infinity, and a short-time trajectory steady state with $N$ tending infinity
followed by $t$ tending infinity. With these limits, symmetry breaking and cusp
catastrophe are two perspectives of the same mesoscopic system on different
time scales.


title: Ultrafast magnetization switching by spin-orbit torques

abstract:
  Spin-orbit torques induced by spin Hall and interfacial effects in heavy
metal/ferromagnetic bilayers allow for a switching geometry based on in-plane
current injection. Using this geometry, we demonstrate deterministic
magnetization reversal by current pulses ranging from 180~ps to ms in
Pt/Co/AlOx dots with lateral dimensions of 90~nm. We characterize the switching
probability and critical current $I_c$ as function of pulse length, amplitude,
and external field. Our data evidence two distinct regimes: a short-time
intrinsic regime, where $I_c$ scales linearly with the inverse of the pulse
length, and a long-time thermally assisted regime where $I_c$ varies weakly.
Both regimes are consistent with magnetization reversal proceeding by
nucleation and fast propagation of domains. We find that $I_c$ is a factor 3-4
smaller compared to a single domain model and that the incubation time is
negligibly small, which is a hallmark feature of spin-orbit torques.


title:
Flat parameter-space metric for all-sky searches for gravitational-wave
  pulsars

abstract:
  All-sky, broadband, coherent searches for gravitational-wave pulsars are
computationally limited. It is therefore important to make efficient use of
available computational resources, notably by minimizing the number of
templates used to cover the signal parameter space of sky position and
frequency evolution. For searches over the sky, however, the required template
density (determined by the parameter-space metric) is different at each sky
position, which makes it difficult in practice to achieve an efficient
covering. Previous work on this problem has found various choices of sky and
frequency coordinates that render the parameter-space metric approximately
constant, but which are limited to coherent integration times of either less
than a few days, or greater than several months. These limitations restrict the
sensitivity achievable by hierarchical all-sky searches, and hinder the
development of follow-up pipelines for interesting gravitational-wave pulsar
candidates. We present a new flat parameter-space metric approximation, and
associated sky and frequency coordinates, that do not suffer from these
limitations. Furthermore, the new metric is numerically well-conditioned, which
facilitates its practical use.


title: New measurements of neutron electric dipole moment

abstract:
  We report a new measurement of the neutron electric dipole moment with the
PNPI EDM spectrometer using the ultracold neutron source PF2 at the research
reactor of the ILL. Its first results can be interpreted as a limit on the
neutron EDM of $|d_{\rm n}| < 5.5 \times 10^{-26} \rm{e} \cdot \rm{cm}$ (90%
confidence level).


title: Fair amenability for semigroups

abstract:
  A new flavour of amenability for discrete semigroups is proposed that
generalises group amenability and follows from a \Folner-type condition. Some
examples are explored, to argue that this new notion better captures some
essential ideas of amenability. A semigroup $S$ is left fairly amenable if, and
only if, it supports a mean $m\in\ell^\infty(S)^*$ satisfying $m(f) = m(s\ast
f)$ whenever $s\ast f\in\ell^\infty(S)$, thus justifying the nomenclature
"fairly amenable''.


title: Cardinal-Recognizing Infinite Time Turing Machines

abstract:
  We introduce a model of infinitary computation which enhances the infinite
time Turing machine model slightly but in a natural way by giving the machines
the capability of detecting cardinal stages of computation. The computational
strength with respect to ITTMs is determined to be precisely that of the strong
halting problem and the nature of the new characteristic ordinals (clockable,
writable, etc.) is explored.


title: Integral of Map into Abelian $\Omega$-group

abstract:
  The common in ring, module and algebra is that they are Abelian group with
respect to addition. This property is enough to study integration. I treat
integral of measurable map into normed Abelian $\Omega$-group. Theory of
integration of maps into $\Omega$-group has a lot of common with theory of
integration of functions of real variable. However I had to change some
statements, since they implicitly assume either compactness of range or total
order in $\Omega$-group.


title:
Global Pad\'e approximations of the generalized Mittag-Leffler function
  and its inverse

abstract:
  This paper proposes a global Pad\'{e} approximation of the generalized
Mittag-Leffler function $E_{\alpha,\beta}(-x)$ with $x\in[0,+\infty)$. This
uniform approximation can account for both the Taylor series for small
arguments and asymptotic series for large arguments. Based on the complete
monotonicity of the function $E_{\alpha,\beta}(-x)$, we work out the global
Pad\'{e} approximation [1/2] for the particular cases $\{0<\alpha<1,
\beta>\alpha\}$, $\{0<\alpha=\beta<1\}$, and $\{\alpha=1, \beta>1\}$,
respectively. Moreover, these approximations are inverted to yield a global
Pad\'{e} approximation of the inverse generalized Mittag-Leffler function
$-L_{\alpha,\beta}(x)$ with $x\in(0,1/\Gamma(\beta)]$. We also provide several
examples with selected values $\alpha$ and $\beta$ to compute the relative
error from the approximations. Finally, we point out the possible applications
using our established approximations in the ordinary and partial
time-fractional differential equations in the sense of Riemann-Liouville.


title:
$GHZ$ state generation of three Josephson qubits in presence of bosonic
  baths

abstract:
  We analyze an entangling protocol to generate tripartite
Greenberger-Horne-Zeilinger states in a system consisting of three
superconducting qubits with pairwise coupling. The dynamics of the open quantum
system is investigated by taking into account the interaction of each qubit
with an independent bosonic bath with an ohmic spectral structure. To this end
a microscopic master equation is constructed and exactly solved. We find that
the protocol here discussed is stable against decoherence and dissipation due
to the presence of the external baths.


title:
Generating squeezed vacuum field with non-zero orbital angular momentum
  with atomic ensembles

abstract:
  We demonstrated that by using a pump field with non-zero orbital angular
momentum (OAM) in the polarization self-rotation squeezing process it is
possible to generate a squeezed vacuum optical field with the matching OAM. We
found a similar level of maximum quantum noise reduction for a first-order
Laguerre-Gaussian pump beam and a regular Gaussian pump beam, even though the
optimal operational conditions differed in these two cases. Also, we
investigated the effect of self-defocusing on the level of the vacuum squeezing
by simultaneously monitoring the minimum quantum noise level and the output
beam transverse profile at various pump laser powers and atomic densities, and
found no direct correlations between the increased beam size and the degree of
measured squeezing.


title: Models for subhomogeneous C*-algebras

abstract:
  A new category of topological spaces with additional structures, called
m-towers, is introduced. It is shown that there is a covariant functor which
establishes a one-to-one correspondences between unital (resp. arbitrary)
subhomogeneous C*-algebras and proper (resp. proper pointed) m-towers of finite
height, and between all *-homomorphisms between two such algebras and morphisms
between m-towers corresponding to these algebras.


title: Al-Jabar: A Mathematical Game of Strategy

abstract:
  We detail the rules and mathematical structure of Al-Jabar, a game invented
by the authors based on intuitive concepts of color-mixing and ideas from
abstract algebra. Game-play consists of manipulating colored game pieces; we
discuss how these colored pieces form a group structure and how this structure,
along with an operation used to combine the pieces, is used to create a game of
strategy. We also consider extensions of the game rules to other group
structures.
  Note: While this is an article for general readership originally published
online by Gathering for Gardner in honor of Martin Gardner's birthday (Oct.
2011), Al-Jabar has been played in university abstract algebra courses as a
teaching tool, as well as by game enthusiasts, since its release. Moreover, the
algebraic game structure described has sparked further work by other
mathematicians and game designers. Thus, we submit this article to the ArXiV as
a resource for educators as well as those interested in mathematical games.


title:
CIDS country rankings: comparing documents and citations of USA, UK and
  China top researchers

abstract:
  This technical report presents a bibliometric analysis of the top 30 cited
researchers from USA, UK and China. The analysis is based on Google Scholar
data using CIDS. The researchers were identified using their email suffix: edu,
uk and cn. This na\"{i}ve approach was able to produce rankings consistent with
the SCImago country rankings using mininal resources in a fully automated way.


title: The projective dimension of sequentially Cohen-Macaulay monomial ideals

abstract:
  In this short note we prove that the projective dimension of a sequentially
Cohen-Macaulay square-free monomial ideal is equal to the maximal height of its
minimal primes (also known as the big height), or equivalently, the maximal
cardinality of a minimal vertex cover of its facet complex. This in particular
gives a formula for the projective dimension of facet ideals of these classes
of ideals, which are known to be sequentially Cohen-Macaulay: graph trees and
simplicial trees, chordal graphs and some cycles, chordal clutters and graphs,
and some path ideals to mention a few. Since polarization preserves projective
dimension, our result also gives the projective dimension of any sequentially
Cohen-Macaulay monomial ideal.


title:
At the origins and in the vanguard of peri-dynamics, non-local and
  higher gradient continuum mechanics. An underestimated and still topical
  contribution of Gabrio Piola

abstract:
  Gabrio Piola's scientific papers have been underestimated in the
mathematical-physics literature. Indeed a careful reading of them proves that
they are original, deep and far reaching. Actually -even if his contribution to
mechanical sciences is not completely ignored- one can undoubtedly say that the
greatest part of his novel contributions to mechanics, although having provided
a great impetus and substantial influence on the work of many preminent
mechanicians, is in fact generally ignored. It has to be remarked that authors
[10] dedicated many efforts to the aim of unveiling the true value of Gabrio
Piola as a scientist; however, some deep parts of his scientific results remain
not yet sufficiently illustrated. Our aim is to prove that non-local and higher
gradient continuum mechanics was conceived already in Piola's works and to try
to explain the reasons of the unfortunate circumstance which caused the erasure
of the memory of this aspect of Piola's contribution. Some relevant
differential relationships obtained in Piola [Piola, 1845-6] are carefully
discussed, as they are still nowadays too often ignored in the continuum
mechanics literature and can be considered the starting point of Levi-Civita's
theory of Connection for Riemannian manifolds.


title: Resonant state expansion applied to planar waveguides

abstract:
  The resonant state expansion, a recently developed method in electrodynamics,
is generalized here to planar open optical systems with non-normal incidence of
light. The method is illustrated and verified on exactly solvable examples,
such as a dielectric slab and a Bragg reflector microcavity, for which explicit
analytic formulas are developed. This comparison demonstrates the accuracy and
convergence of the method. Interestingly, the spectral analysis of a dielectric
slab in terms of resonant states reveals an influence of waveguide modes in the
transmission. These modes, which on resonance do not couple to external light,
surprisingly do couple to external light for off-resonant excitation.


title: Neuronal Growth as Diffusion in an Effective Potential

abstract:
  Current understanding of neuronal growth is mostly qualitative, as the
staggering number of physical and chemical guidance cues involved prohibit a
fully quantitative description of axonal dynamics. We report on a general
approach that describes axonal growth in vitro, on poly-D-lysine coated glass
substrates, as diffusion in an effective external potential, representing the
collective contribution of all causal influences on the growth cone. We use
this approach to obtain effective growth rules that reveal an emergent
regulatory mechanism for axonal pathfinding on these substrates.


title:
High Energy pp Elastic Scattering in Condensate Enclosed Chiral Bag
  Model and TOTEM Elastic Measurements at LHC at 7 TeV

abstract:
  We study high energy $\small{\rm{pp}}$ and $\small{\rm{\bar {p}p}}$ elastic
scattering in the TeV region based on an effective field theory model of the
proton. We phenomenologically investigate the main processes underlying elastic
scattering and quantitatively describe the measured elastic
d$\small{\sigma}$/dt at energies 7.0 TeV (LHC $\small{\rm{pp}}$), 1.96 TeV
(Tevatron $\small{\rm{\bar {p}p}}$), and 0.630 TeV (SPS $\small{\rm{\bar
{p}p}}$). Finally, we give our prediction for $\small{\rm{pp}}$ elastic
d$\small{\sigma}$/dt at 14 TeV that will be measured by the TOTEM
Collaboration.


title:
GRE: A Graph Runtime Engine for Large-Scale Distributed Graph-Parallel
  Applications

abstract:
  Large-scale distributed graph-parallel computing is challenging. On one hand,
due to the irregular computation pattern and lack of locality, it is hard to
express parallelism efficiently. On the other hand, due to the scale-free
nature, real-world graphs are hard to partition in balance with low cut. To
address these challenges, several graph-parallel frameworks including Pregel
and GraphLab (PowerGraph) have been developed recently. In this paper, we
present an alternative framework, Graph Runtime Engine (GRE). While retaining
the vertex-centric programming model, GRE proposes two new abstractions: 1) a
Scatter-Combine computation model based on active message to exploit massive
fined-grained edge-level parallelism, and 2) a Agent-Graph data model based on
vertex factorization to partition and represent directed graphs. GRE is
implemented on commercial off-the-shelf multi-core cluster. We experimentally
evaluate GRE with three benchmark programs (PageRank, Single Source Shortest
Path and Connected Components) on real-world and synthetic graphs of millions
billion of vertices. Compared to PowerGraph, GRE shows 2.5~17 times better
performance on 8~16 machines (192 cores). Specifically, the PageRank in GRE is
the fastest when comparing to counterparts of other frameworks (PowerGraph,
Spark,Twister) reported in public literatures. Besides, GRE significantly
optimizes memory usage so that it can process a large graph of 1 billion
vertices and 17 billion edges on our cluster with totally 768GB memory, while
PowerGraph can only process less than half of this graph scale.


title:
Arithmetic of fuzzy numbers and intervals -- a new perspective with
  examples

abstract:
  This article is meant to give a lucid and widely accessible, self-contained
account of a novel way of performing arithmetic operations on fuzzy intervals.
Based on two formulae of generalized inversion (the first in close analogy to
the inversion of cumulative distribution functions in probability and
statistics, and subsequent re-inversion which in this form seems to be new in
the literature) the technique could prove to be of some importance for the
practical handling of fuzzy intervals whose characterizing functions are
discontinuous and/or not strictly monotonic, e.g. piecewise constant.
Notwithstanding its innovative nature, the article is written in the style of
an introductory textbook featuring a multitude of illustrated examples.


title:
A Recursive Sparse Grid Collocation Method for Differential Equations
  with White Noise

abstract:
  We consider a sparse grid collocation method in conjunction with a time
discretization of the differential equations for computing expectations of
functionals of solutions to differential equations perturbed by time-dependent
white noise. We first analyze the error of Smolyak's sparse grid collocation
used to evaluate expectations of functionals of solutions to stochastic
differential equations discretized by the Euler scheme. We show theoretically
and numerically that this algorithm can have satisfactory accuracy for small
magnitude of noise or small integration time, however it does not converge
neither with decrease of the Euler scheme's time step size nor with increase of
Smolyak's sparse grid level. Subsequently, we use this method as a building
block for proposing a new algorithm by combining sparse grid collocation with a
recursive procedure. This approach allows us to numerically integrate linear
stochastic partial differential equations over longer times, which is
illustrated in numerical tests on a stochastic advection-diffusion equation.


title:
Codimension one stability of the catenoid under the vanishing mean
  curvature flow in Minkowski space

abstract:
  We study time-like hypersurfaces with vanishing mean curvature in the (3+1)
dimensional Minkowski space, which are the hyperbolic counterparts to minimal
embeddings of Riemannian manifolds. The catenoid is a stationary solution of
the associated Cauchy problem. This solution is linearly unstable, and we show
that this instability is the only obstruction to the global nonlinear stability
of the catenoid. More precisely, we prove in a certain symmetry class the
existence, in the neighborhood of the catenoid initial data, of a co-dimension
1 Lipschitz manifold transverse to the unstable mode consisting of initial data
whose solutions exist globally in time and converge asymptotically to the
catenoid.


title: Three irradiated and bloated hot Jupiters: WASP-76b, WASP-82b & WASP-90b

abstract:
  We report three new transiting hot-Jupiter planets discovered from the WASP
surveys combined with radial velocities from OHP/SOPHIE and Euler/CORALIE and
photometry from Euler and TRAPPIST. All three planets are inflated, with radii
1.7-1.8 Rjup. All orbit hot stars, F5-F7, and all three stars have evolved,
post-MS radii (1.7-2.2 Rsun). Thus the three planets, with orbits of 1.8-3.9 d,
are among the most irradiated planets known. This reinforces the correlation
between inflated planets and stellar irradiation.


title:
On the determination of the quasiparticle scattering rate in
  unconventional superconductors by microwave surface impedance

abstract:
  In the approximation of validity of the Drude expression for quasiparticle
conductivity and the assumption that all electrons at T = 0 transform into a
superfluide condensate, the expression for the quasiparticle scattering rate
tau -1 in terms of the real and imaginary parts of the microwave surface
impedance has been obtained. The resulting expression is a generalization of
the well-known expression for tau^-1, valid for omega x tau is much less 1, to
an arbitrary value of omega x tau, where omega is the frequency of the
microwave field. From experimental Ka-band impedance measurements, temperature
dependence of tau^-1 in superconducting single crystal pnictides
Ba(Fe1-xCox)2As2 is obtained using the generalized expression. It is shown that
under condition of the given work, the approximation omega x tau is much less 1
gives the considerable error in determination of tau^-1.


title: Functional calculus in finite type I von Neumann algebras

abstract:
  A certain class of matrix-valued Borel matrix functions is introduced and it
is shown that all functions of that class naturally operate on any operator T
in a finite type I von Neumann algebra M in a way such that uniformly bounded
sequences f_1,f_2,... of functions that converge pointwise to 0 transform into
sequences f_1[T],f_2[T],... of operators in M that converge to 0 in the
*-strong operator topology. It is also demonstrated that the double *-commutant
of any such operator T which acts on a separable Hilbert space coincides with
the set of all operators of the form f[T] where f runs over all function from
the aforementioned class. Some conclusions concerning so-called
operator-spectra of such operators are drawn and a new variation of the
spectral theorem for them is formulated.


title:
The comparative efficiency of the different methods in which Pi is
  calculated

abstract:
  An investigation of the comparative efficiency of the different methods in
which {\pi} is cal- culated. This thesis will compare and contrast five
different methods in calculating {\pi} by first deriving the various proofs to
each method and then creating graphical displays and tables with percentage
errors on each to allow a thorough comparison between each method. It is
important to realize that usually people refer to {\pi} as 3.142 and use this
shortened value in everyday calculations. However, most people in society do
not know that in some of NASAs calculations, must be calculated to 15 decimal
places (3.141592653589793) for calculations involving the Space Station
Guidance Navigation and Control (GNC) code [9]. Furthermore, some people use
the world renown constant everyday yet have no idea where it comes from.
  This thesis allows a thorough exploration of the different methods of
calculating pi by us- ing Mathematica to provide the necessary iterations
needed and Microsoft excel to plot the various graphs for convergence
comparisons. Finally, the conclusions that have come from this thesis
demonstrate that methods in which oscillations between the positive and
negative region of the line y = {\pi} slow down the rate of convergence and out
of the five methods investigated, The infinite series formulated from
{\zeta}(8) proves to be one of the fastest infinite series today to converge
towards {\pi}.


title: Some mathematical properties of the Bartlett chi ratio

abstract:
  Based on artistic interpretations, art professor Christopher Bartlett (Towson
University, USA) suggested introducing a new mathematical constant related to
the golden ratio. He called it the chi ratio, as chi follows phi in the Greek
alphabet. Without going too much into the artistic considerations, which may be
subject to criticism similar to the golden ratio debunking, we focus on showing
that the chi ratio is interesting as a number as such, with remarkable
geometric properties, just as the golden ratio is.


title:
A Unifying Approach to Quaternion Adaptive Filtering: Addressing the
  Gradient and Convergence

abstract:
  A novel framework for a unifying treatment of quaternion valued adaptive
filtering algorithms is introduced. This is achieved based on a rigorous
account of quaternion differentiability, the proposed I-gradient, and the use
of augmented quaternion statistics to account for real world data with
noncircular probability distributions. We first provide an elegant solution for
the calculation of the gradient of real functions of quaternion variables
(typical cost function), an issue that has so far prevented systematic
development of quaternion adaptive filters. This makes it possible to unify the
class of existing and proposed quaternion least mean square (QLMS) algorithms,
and to illuminate their structural similarity. Next, in order to cater for both
circular and noncircular data, the class of widely linear QLMS (WL-QLMS)
algorithms is introduced and the subsequent convergence analysis unifies the
treatment of strictly linear and widely linear filters, for both proper and
improper sources. It is also shown that the proposed class of HR gradients
allows us to resolve the uncertainty owing to the noncommutativity of
quaternion products, while the involution gradient (I-gradient) provides
generic extensions of the corresponding real- and complex-valued adaptive
algorithms, at a reduced computational cost. Simulations in both the strictly
linear and widely linear setting support the approach.


title: Abelian-by-Central Galois groups of fields I: a formal description

abstract:
  Let $K$ be a field whose characteristic is prime to a fixed integer $n$ with
$\mu_n \subset K$, and choose $\omega \in \mu_n$ a primitive $n$th root of
unity. Denote the absolute Galois group of $K$ by $\operatorname{Gal}(K)$, and
the mod-$n$ central-descending series of $\operatorname{Gal}(K)$ by
$\operatorname{Gal}(K)^{(i)}$. Recall that Kummer theory, together with our
choice of $\omega$, provides a functorial isomorphism between
$\operatorname{Gal}(K)/\operatorname{Gal}(K)^{(2)}$ and
$\operatorname{Hom}(K^\times,\mathbb{Z}/n)$. Analogously to Kummer theory, in
this note we use the Merkurjev-Suslin theorem to construct a continuous,
functorial and explicit embedding
$\operatorname{Gal}(K)^{(2)}/\operatorname{Gal}(K)^{(3)} \hookrightarrow
\operatorname{Fun}(K\smallsetminus\{0,1\},(\mathbb Z/n)^2)$, where
$\operatorname{Fun}(K\smallsetminus\{0,1\},(\mathbb Z/n)^2)$ denotes the group
of $(\mathbb Z/n)^2$-valued functions on $K\smallsetminus\{0,1\}$. We
explicitly determine the functions associated to the image of commutators and
$n$th powers of elements of $\operatorname{Gal}(K)$ under this embedding. We
then apply this theory to prove some new results concerning relations between
elements in abelian-by-central Galois groups.


title: Three-dimensional Quantum Slit Diffraction and Diffraction in Time

abstract:
  We study the quantum slit diffraction problem in three dimensions. In the
treatment of diffraction of particles by a slit, it is usually assumed that the
motion perpendicular to the slit is classical. Here we take into account the
effect of the quantum nature of the motion perpendicular to the slit using the
Green function approach [18]. We treat the diffraction of a Gaussian wave
packet for general boundary conditions on the shutter. The difference between
the standard and our three-dimensional slit diffraction models is analogous to
the diffraction in time phenomenon introduced in [16]. We derive corrections to
the standard formula for the diffraction pattern, and we point out situations
in which this might be observable. In particular, we discuss the diffraction in
space and time in the presence of gravity.


title: Broad Leaves in Strong Flow

abstract:
  Flexible broad leaves are thought to reconfigure in the wind and water to
reduce the drag forces that act upon them. Simple mathematical models of a
flexible beam immersed in a two-dimensional flow will also exhibit this
behavior. What is less understood is how the mechanical properties of a leaf in
a three-dimensional flow will passively allow roll up into a cone shape and
reduce both drag and vortex induced oscillations. In this fluid dynamics video,
the flows around the leaves are compared with those of simplified sheets using
3D numerical simulations and physical models. For some reconfiguration shapes,
large forces and oscillations due to strong vortex shedding are produced. In
the actual leaf, a stable recirculation zone is formed within the wake of the
reconfigured cone. In physical and numerical models that reconfigure into
cones, a similar recirculation zone is observed with both rigid and flexible
tethers. These results suggest that the three-dimensional cone structure in
addition to flexibility is significant to both the reduction of vortex-induced
vibrations and the forces experienced by the leaf.


title: Euclid-Euler Heuristics for Perfect Numbers

abstract:
  An odd perfect number $N$ is said to be given in Eulerian form if $N =
{q^k}{n^2}$ where $q$ is prime with $q \equiv k \equiv 1 \pmod 4$ and
$\gcd(q,n) = 1$. Similarly, an even perfect number $M$ is said to be given in
Euclidean form if $M = (2^p - 1)\cdot{2^{p - 1}}$ where $p$ and $2^p - 1$ are
primes. In this article, we show how simple considerations surrounding the
differences between the underlying properties of the Eulerian and Euclidean
forms of perfect numbers give rise to what we will call the Euclid-Euler
heuristics for perfect numbers.


title: Properties of the Ornstein-Uhlenbeck bridge

abstract:
  This paper presents a study of the properties of the Ornstein-Uhlenbeck
bridge, specifically, we derive its Karhunen-Lo\`eve expansion for any value of
the initial variance and mean-reversion parameter (or mean-repulsion if
negative). We also show that its canonical decomposition can be obtained using
some techniques related to generalized bridges. Finally, we present an
application to the optimal functional quantization of the Ornstein-Uhlenbeck
bridge.


title: On The Generalized Riemann Hypothesis

abstract:
  The study of the global mapping properties of arbitrary Dirichlet L-functions
is undertaken. The results are applied to the proof of the Generalized Riemann
Hypothesis.


title:
Devnagari Handwritten Numeral Recognition using Geometric Features and
  Statistical Combination Classifier

abstract:
  This paper presents a Devnagari Numerical recognition method based on
statistical discriminant functions. 17 geometric features based on pixel
connectivity, lines, line directions, holes, image area, perimeter,
eccentricity, solidity, orientation etc. are used for representing the
numerals. Five discriminant functions viz. Linear, Quadratic, Diaglinear,
Diagquadratic and Mahalanobis distance are used for classification. 1500
handwritten numerals are used for training. Another 1500 handwritten numerals
are used for testing. Experimental results show that Linear, Quadratic and
Mahalanobis discriminant functions provide better results. Results of these
three Discriminants are fed to a majority voting type Combination classifier.
It is found that Combination classifier offers better results over individual
classifiers.


title:
Towards Energy Efficiency: Forecasting Indoor Temperature via
  Multivariate Analysis

abstract:
  The small medium large system (SMLSystem) is a house built at the Universidad
CEU Cardenal Herrera (CEU-UCH) for participation in the Solar Decathlon 2013
competition. Several technologies have been integrated to reduce power
consumption. One of these is a forecasting system based on artificial neural
networks (ANNs), which is able to predict indoor temperature in the near future
using captured data by a complex monitoring system as the input. A study of the
impact on forecasting performance of different covariate combinations is
presented in this paper. Additionally, a comparison of ANNs with the standard
statistical forecasting methods is shown. The research in this paper has been
focused on forecasting the indoor temperature of a house, as it is directly
related to HVAC---heating, ventilation and air conditioning---system
consumption. HVAC systems at the SMLSystem house represent 53.9% of the overall
power consumption. The energy used to maintain temperature was measured to be
30--38.9% of the energy needed to lower it. Hence, these forecasting measures
allow the house to adapt itself to future temperature conditions by using home
automation in an energy-efficient manner. Experimental results show a high
forecasting accuracy and therefore, they might be used to efficiently control
an HVAC system.


title:
Resolved photometry of Young Massive Clusters in the starburst galaxy
  NGC 4214

abstract:
  We present the results of deep high resolution imaging performed with
ACS/HRC@HST in the most active region of the nearby starburst galaxy NGC 4214.
We resolved the stellar populations of five Young Massive Clusters and their
surrounding galactic field. The star formation history of this region is
characterized by two main bursts occurred within the last 500 Myr, with the
oldest episode spread out across an area larger than that covered by the most
recent one. The ages derived for the analysed clusters cover a wide range
between 6.4<log(t/yr)<8.1 in agreement with those predicted by recent analyses
based on integrated photometry. The comparison between the mass of the young
associations and that of the surrounding field population with similar ages
indicates a high cluster formation efficiency (Gamma~33%) which decreases when
old populations are considered. The mass function of the major assembly has
been found to be slightly flatter than the Salpeter (1955) law with a hint of
mass segregation. We found no clear signatures of multiple stellar populations
in the two young (log(t/yr)<6.8) associations where we were able to resolve
their innermost region. The masses and sizes of three clusters indicate that at
least one of them could evolve toward a globular cluster-like structure.


title:
X-ray and UV correlation in the quiescent emission of Cen X-4, evidence
  of accretion and reprocessing

abstract:
  We conducted the first long-term (60 days), multiwavelength (optical,
ultraviolet, and X-ray) simultaneous monitoring of Cen X-4 with daily Swift
observations, with the goal of understanding variability in the low mass X-ray
binary Cen X-4 during quiescence. We found Cen X-4 to be highly variable in all
energy bands on timescales from days to months, with the strongest quiescent
variability a factor of 22 drop in the X-ray count rate in only 4 days. The
X-ray, UV and optical (V band) emission are correlated on timescales down to
less than 110 s. The shape of the correlation is a power law with index gamma
about 0.2-0.6. The X-ray spectrum is well fitted by a hydrogen NS atmosphere
(kT=59-80 eV) and a power law (with spectral index Gamma=1.4-2.0), with the
spectral shape remaining constant as the flux varies. Both components vary in
tandem, with each responsible for about 50% of the total X-ray flux, implying
that they are physically linked. We conclude that the X-rays are likely
generated by matter accreting down to the NS surface. Moreover, based on the
short timescale of the correlation, we also unambiguously demonstrate that the
UV emission can not be due to either thermal emission from the stream impact
point, or a standard optically thick, geometrically thin disc. The spectral
energy distribution shows a small UV emitting region, too hot to arise from the
accretion disk, that we identified as a hot spot on the companion star.
Therefore, the UV emission is most likely produced by reprocessing from the
companion star, indeed the vertical size of the disc is small and can only
reprocess a marginal fraction of the X-ray emission. We also found the
accretion disc in quiescence to likely be UV faint, with a minimal contribution
to the whole UV flux.


title: Time Evolution Altitude of an Observed Coronal Wave

abstract:
  The nature of coronal wave fronts is deeply debated. They are observed in
several wavelength bandpasses in spectra, and are frequently interpreted as
magnetosonic waves propagating in the lower solar atmosphere. However, they can
be attributed to the line of sight projection of the edges of coronal mass
ejections. Therefore, the altitude estimation of these features is crucial to
discriminate in favor of one of these two interpretations. We take advantage of
a set of observations obtained from two different points of view by
EUVI/SECCHI/STEREO on December, 7th 2007 to derive the time evolution of the
altitude of a coronal wave front. We develop a new technique to compute the
altitude.
  We find that the observed brightness has an increasing altitude during 5
minutes, then the altitude decreases slightly back to the low corona. We
interpret the evolution of the altitude as following: the increase of altitude
of the wave front is linked to the rise of a bubble like structure whether it
is a magnetosonic wave front or a CME in the first phase. During the second
phase, the observed brightness is mixed with the brightening of the underlying
magnetic structures as the emission of the plasma of the wave front fades due
to the plasma dilution with the altitude.


abstract:
  We study the statistical properties of spectrum and eigenstates of the Google
matrix of the citation network of Physical Review for the period 1893 - 2009.
The main fraction of complex eigenvalues with largest modulus is determined
numerically by different methods based on high precision computations with up
to $p=16384$ binary digits that allows to resolve hard numerical problems for
small eigenvalues. The nearly nilpotent matrix structure allows to obtain a
semi-analytical computation of eigenvalues. We find that the spectrum is
characterized by the fractal Weyl law with a fractal dimension $d_f \approx 1$.
It is found that the majority of eigenvectors are located in a localized phase.
The statistical distribution of articles in the PageRank-CheiRank plane is
established providing a better understanding of information flows on the
network. The concept of ImpactRank is proposed to determine an influence domain
of a given article. We also discuss the properties of random matrix models of
Perron-Frobenius operators.


title:
Final comment to the results of Bustamante et al. on discrete
  Rossby/drift wave resonant and quasi-resonant triads

abstract:
  In this final note we demonstrate that the authors of manuscripts
arXiv:1210.2036, arXiv:1309.0405 and arXiv:1309.5513 use mathematical notations
and notions sometimes in the standard meaning and sometimes in a sense which
differs from the standard. As this specific use is not defined beforehand, the
authors' statements are self-contradictory which makes any further scientific
discussion meaningless.


title:
On the sizes of burnt and fireproof components for fires on a large
  Cayley tree

abstract:
  We continue the study initiated by Jean Bertoin in 2012 of a random dynamics
on the edges of a uniform Cayley tree with $n$ vertices in which, successively,
each edge is either set on fire with some fixed probability $p_n$ or fireproof
with probability $1-p_n$. An edge which is set on fire burns and sets on fire
its flammable neighbors, the fire then propagates in the tree, only stopped by
fireproof edges. We study the distribution of the proportion of burnt and
fireproof vertices and the sizes of the burnt or fireproof connected components
as $n \to \infty$ regarding the asymptotic behavior of $p_n$.


title: Microscopic calculations and energy expansions for neutron-rich matter

abstract:
  We investigate asymmetric nuclear matter with two- and three-nucleon
interactions based on chiral effective field theory, where three-body forces
are fit only to light nuclei. Focusing on neutron-rich matter, we calculate the
energy for different proton fractions and include estimates of the theoretical
uncertainty. We use our ab-initio results to test the quadratic expansion
around symmetric matter with the symmetry energy term, and confirm its validity
for highly asymmetric systems. Our calculations are in remarkable agreement
with an empirical parametrization for the energy density. These findings are
very useful for astrophysical applications and for developing new equations of
state.


title:
Supersymmetric partners of the harmonic oscillator with an infinite
  potential barrier

abstract:
  Supersymmetry transformations of first and second order are used to generate
Hamiltonians with known spectra departing from the harmonic oscillator with an
infinite potential barrier. It is studied also the way in which the
eigenfunctions of the initial Hamiltonian are transformed. The first and
certain second order supersymmetric partners of the initial Hamiltonian possess
third-order differential ladder operators. Since systems with this kind of
operators are linked with the Painlev\'e IV equation, several solutions of this
non-linear second-order differential equation will be simply found.


title:
Gluon screening mass at finite temperature from Landau gauge gluon
  propagator in lattice QCD

abstract:
  We address the interpretation of the Landau gauge gluon propagator at finite
temperature as a massive type bosonic propagator. Using pure gauge SU(3)
lattice simulations at a fixed lattice volume $\sim(6.5fm)^3$, we compute the
electric and magnetic form factors, extract a gluon mass from Yukawa-like fits,
and study its temperature dependence. This is relevant both for the Debye
screening at high temperature $T$ and for confinement at low $T$.


title:
Transiting hot Jupiters from WASP-South, Euler and TRAPPIST: WASP-95b to
  WASP-101b

abstract:
  We report the discovery of the transiting exoplanets WASP-95b, WASP-96b,
WASP-97b, WASP-98b, WASP-99b, WASP-100b and WASP-101b. All are hot Jupiters
with orbital periods in the range 2.1 to 5.7 d, masses of 0.5 to 2.8 Mjup, and
radii of 1.1 to 1.4 Rjup. The orbits of all the planets are compatible with
zero eccentricity. WASP-99b shows the shallowest transit yet found by
WASP-South, at 0.4%. The host stars are of spectral type F2 to G8. Five have
metallicities of [Fe/H] from -0.03 to +0.23, while WASP-98 has a metallicity of
-0.60, exceptionally low for a star with a transiting exoplanet. Five of the
host stars are brighter than V = 10.8, which significantly extends the number
of bright transiting systems available for follow-up studies. WASP-95 shows a
possible rotational modulation at a period of 20.7 d. We discuss the
completeness of WASP survey techniques by comparing to the HAT project.


title: The Integral Field View of the Orion Nebula

abstract:
  This paper reviews the major advances achieved in the Orion Nebula through
the use of integral field spectroscopy (IFS). Since the early work of
Vasconcelos and collaborators in 2005, this technique has facilitated the
investigation of global properties of the nebula and its morphology, providing
new clues to better constrain its 3D structure. IFS has led to the discovery of
shock-heated zones at the leading working surfaces of prominent Herbig-Haro
objects as well as the first attempt to determine the chemical composition of
Orion protoplanetary disks, also known as proplyds. The analysis of these
morphologies using IFS has given us new insights into the abundance discrepancy
problem, a long-standing and unresolved issue that casts doubt on the
reliability of current methods used for the determination of metallicities in
the universe from the analysis of H II regions. Results imply that high-density
clumps and high-velocity flows may play an active role in the production of
such discrepancies. Future investigations based on the large-scale IFS mosaic
of Orion will be very valuable for exploring how the integrated effect of
small-scale structures may have impact at larger scales in the framework of
star-forming regions.


title:
An algorithmic proof of Bachet's conjecture and the Lagrange-Euler
  method

abstract:
  The goal of this notice is to present a proof of Bachet's conjecture based
exclusively on the fundamental theorem of arithmetic. The novelty of this proof
consists in its introduction of a partial order on rational integers through
the unique factorization property. In general, the proofs of Bachet's
conjecture by Lagrange - Euler's method assume necessary the use of infinite
descent. In the proposed proof we do not assume the existence of a "minimal
solution", but rather we show the existence of the desired solution through an
algorithmic method.


title:
Improving the sensitivity of a search for coalescing binary black holes
  with non-precessing spins in gravitational wave data

abstract:
  We demonstrate the implementation of a sensitive search pipeline for
gravitational waves from coalescing binary black holes whose components have
spins aligned with the orbital angular momentum. We study the pipeline recovery
of simulated gravitational wave signals from aligned-spin binary black holes
added to real detector noise, comparing the pipeline performance with
aligned-spin filter templates to the same pipeline with non-spinning filter
templates. Our results exploit a three-parameter phenomenological waveform
family that models the full inspiral-merger-ringdown coalescence and treats the
effect of aligned spins with a single effective spin parameter \chi. We
construct template banks from these waveforms by a stochastic placement method
and use these banks as filters in the recently-developed gstlal search
pipeline. We measure the observable volume of the analysis pipeline for binary
black hole signals with total mass in [15,25] solar masses and \chi in [0,
0.85]. We find an increase in observable volume of up to 45% for systems with
0.2 <= \chi <= 0.85 with almost no loss of sensitivity to signals with 0 <=
\chi <= 0.2. We demonstrate this analysis on 25.9 days of data obtained from
the Hanford and Livingston detectors in LIGO's fifth observation run.


title:
Upper bounds on the number of perfect matchings and directed 2-factors
  in graphs with given number of vertices and edges

abstract:
  We give an upper bound on the number of perfect matchings in simple graphs
with a given number of vertices and edges. We apply this result to give an
upper bound on the number of 2-factors in a directed complete bipartite
balanced graph on 2n vertices. The upper bound is sharp for n even. For n odd
we state a conjecture on a sharp upper bound.


title:
Modifications in the frustrated magnetism, oxidation state of Co and
  magnetoelectric coupling effects induced by a partial replacement of Ca by Gd
  in the spin chain compound Ca3Co2O6

abstract:
  We have systematically investigated the influence of gradual replacement of
Ca by Gd on the magnetic and complex dielectric properties of the well-known
geometrically frustrated spin-chain system, Ca3Co2O6 (T_N= 24 K with additional
magnetic transitions below 12K), by studying the series, Ca3-xGdxCo2O6 (x less
than 0.7), down to 1.8K. Heat capacity measurements establish that the
reduction of T_N with Gd substitution is much less as compared to that by Y
substitution. The magnetic moment data reveal that there are changes in the
oxidation state of Co as well, unlike for Y-substitution, beyond x= 0.2. Thus,
despite being isovalent, both these substitutions interestingly differ in
changing these magnetic properties in these oxides. We propose that the valence
electrons of Y and those of R ions play different roles on deciding these
magnetic characteristics of these mixed oxides. It is observed that a small
amount (x= 0.3) of Gd substitution for Ca is enough to suppress glassy ac
magnetic susceptibility behavior for the peak around 12 K. An additional
low-temperature magnetic anomaly close to 5 K gets more prominent with
increasing Gd concentration as revealed by heat-capacity data. Trends in
temperature dependence of complex dielectric behavior were also tracked with
varying composition and a frequency dependence is observed, not only for the
transition in the region around 10 K (for some compositions), but also for the
5 K transition which is well-resolved for a higher concentration of Gd. Thus,
Gd-substituted Ca3Co2O6 series is shown to reveal interesting magnetic and
dielectric behavior of this family of oxides.


title:
On the Structure of the Solution Set of a Sign Changing Perturbation of
  the p-Laplacian under Dirichlet Boundary Condition

abstract:
  In a recent paper D. D. Hai showed that the equation $ -\Delta_{p} u =
\lambda f(u) \mbox{in} \Omega$, under Dirichlet boundary condition, where
$\Omega \subset {\bf R^N}$ is a bounded domain with smooth boundary
$\partial\Omega$, $\Delta_{p}$ is the p-Laplacian, $f : (0,\infty) \rightarrow
{\bf R} $ is a continuous function which may blow up to $\pm \infty$ at the
origin, admits a solution if $\lambda > \lambda_0$ and has no solution if $0 <
\lambda < \lambda_0$. In this paper we show that the solution set $\mathcal{S}$
of the equation above, which is not empty by Hai's results, actually admits a
continuum of positive solutions.


title:
Searching for feasible stationary states in reaction networks by solving
  a Boolean constraint satisfaction problem

abstract:
  We analyze the solutions, on single network instances, of a recently
introduced class of constraint-satisfaction problems (CSPs), describing
feasible steady states of chemical reaction networks. First, we show that the
CSPs generalize the scheme known as Network Expansion, which is recovered in a
specific limit. Next, a full statistical mechanics characterization (including
the phase diagram and a discussion of physical origin of the phase transitions)
for Network Expansion is obtained. Finally, we provide a message-passing
algorithm to solve the original CSPs in the most general form.


title: Interacting Weyl semimetals on a lattice

abstract:
  Electron-electron interactions in a Weyl semimetal are rigorously
investigated in a lattice model by non perturbative methods. The absence of
quantum phase transitions is proved for interactions not too large and short
ranged. The anisotropic Dirac cones persist with angles (Fermi velocities)
renormalized by the interaction, and with generically shifted Fermi points. As
in graphene, the optical conductivity shows universality properties: it is
equal to the massless Dirac fermions one with renormalized velocities, up to
corrections which are subdominant in modulus.


title: Relativistic Non-Thermal Bremsstrahlung Radiation

abstract:
  By applying a method of virtual quanta we derive formulae for relativistic
non-thermal bremsstrahlung radiation from relativistic electrons as well as
from protons and heavier particles with power-law momentum distribution $N(p)dp
= k p^{-q} dp.$ We show that emission which originates from an electron
scattering on an ion, represents the most significant component of relativistic
non-thermal bremsstrahlung. Radiation from an ion scattering on electron, known
as inverse bremsstrahlung, is shown to be negligible in overall non-thermal
bremsstrahlung emission. These results arise from theory refinement, where we
introduce the dependence of relativistic kinetic energy of an incident
particle, upon the energy of scattered photon. In part, it is also a
consequence of a different mass of particles and relativistic effects.


title:
Entanglement witnessing and quantum cryptography with non-ideal
  ferromagnetic detectors

abstract:
  We investigate theoretically the use of non-ideal ferromagnetic contacts as a
mean to detect quantum entanglement of electron spins in transport experiments.
We use a designated entanglement witness and find a minimal spin polarization
of $\eta > 1/\sqrt{3} \approx 58 %$ required to demonstrate spin entanglement.
This is significantly less stringent than the ubiquitous tests of Bell's
inequality with $\eta > 1/\sqrt[4]{2}\approx 84%$. In addition, we discuss the
impact of decoherence and noise on entanglement detection and apply the
presented framework to a simple quantum cryptography protocol. Our results are
directly applicable to a large variety of experiments.


title:
Clumpy stellar winds and high-energy emission in high-mass binaries
  hosting a young pulsar

abstract:
  High-mass binaries hosting young pulsars can be powerful gamma-ray emitters.
The stellar wind of the massive star in the system is expected to be clumpy.
Since the high-energy emission comes from the pulsar-star wind interaction, the
presence of clumps can affect the spectrum and variability of this radiation.
We look for the main effects of the clumps on the two-wind interaction region
and on the non-thermal radiation. A simple analytical model for the two-wind
interaction dynamics was developed accounting for the lifetime of clumps under
the pulsar-wind impact. This time plays a very important role with regard to
the evolution of the clump, the magnetic field in the clump-pulsar wind
interaction region, and the non-radiative and radiative cooling of the
non-thermal particles. We also computed the high-energy emission produced at
the interaction of long-living clumps with the pulsar wind. For reasonable
parameters, the clumps will induce small variability on the X-ray and gamma-ray
radiation. Sporadically, large clumps can reach closer to the pulsar increasing
the magnetic field, triggering synchrotron X-ray flares and weakening other
emission components like inverse Compton. The reduction of the emitter size
induced by clumps also makes non-radiative losses faster. Stellar wind clumps
can also enhance instability development and matter entrainment in the shocked
pulsar wind when it leaves the binary. Growth limitations of the clumps from
the wind acceleration region may imply that a different origin for the largest
clumps is required. The large-scale wind structures behind the observed
discrete absorption components in the UV may be the source of these large
clumps. The presence of structure in the stellar wind can produce substantial
energy-dependent variability and should not be neglected when studying the
broadband emission from high-mass binaries hosting young pulsars.


title: A posteriori estimates for Euler and Navier-Stokes equations

abstract:
  The first two sections of this work review the framework of [6] for
approximate solutions of the incompressible Euler or Navier-Stokes (NS)
equations on a torus T^d, in a Sobolev setting. This approach starts from an
approximate solution u_a of the Euler/NS Cauchy problem and, analyzing it a
posteriori, produces estimates on the interval of existence of the exact
solution u and on the distance between u and u_a. The next two sections present
an application to the Euler Cauchy problem, where u_a is a Taylor polynomial in
the time variable t; a special attention is devoted to the case d=3, with an
initial datum for which Behr, Necas and Wu have conjectured a finite time
blowup [1]. These sections combine the general approach of [6] with the
computer algebra methods developed in [9]; choosing the Behr-Necas-Wu datum,
and using for u_a a Taylor polynomial of order 52, a rigorous lower bound is
derived on the interval of existence of the exact solution u, and an estimate
is obtained for the H^3 Sobolev distance between u(t) and u_a(t).


title: Stimulated Neutrino Transformation Through Turbulence

abstract:
  We derive an analytical solution for the flavor evolution of a neutrino
through a turbulent density profile which is found to accurately predict the
amplitude and transition wavelength of numerical solutions on a case-by-case
basis. The evolution is seen to strongly depend upon those Fourier modes in the
turbulence which are approximately the same as the splitting between neutrino
eigenvalues. Transitions are strongly enhanced by those Fourier modes in the
turbulence which are approximately the same as the splitting between neutrino
eigenvalues. We also find a suppression of transitions due to the long
wavelength modes when the ratio of their amplitude and the wavenumber is of
order, or greater than, the first root of the Bessel function $J_0$.


title: On compression of non-classically correlated bit strings

abstract:
  In this short note we present a new approach to non-classical correlations
that is based on the compression rates for bit strings generated by Alice and
Bob. We use normalised compression distance introduced by Cilibrasi and Vitanyi
to derive information-theoretic inequalities that must be obeyed by classically
correlated bit strings and that are violated by PR-boxes. We speculate about a
violation of our inequalities by quantum mechanical correlations.


title:
Generalized Harmonic, Cyclotomic, and Binomial Sums, their
  Polylogarithms and Special Numbers

abstract:
  A survey is given on mathematical structures which emerge in multi-loop
Feynman diagrams. These are multiply nested sums, and, associated to them by an
inverse Mellin transform, specific iterated integrals. Both classes lead to
sets of special numbers. Starting with harmonic sums and polylogarithms we
discuss recent extensions of these quantities as cyclotomic, generalized
(cyclotomic), and binomially weighted sums, associated iterated integrals and
special constants and their relations.


title:
Branching Laws of Generalized Verma Modules for Non-symmetric Polar
  Pairs

abstract:
  We give branching formulas from $so(7,\mathbb{C})$ to $\mathfrak{g}_2$ for
generalized Verma modules attached to $\mathfrak{g}_2$-compatible parabolic
subalgebras of $so(7,\mathbb{C})$, and branching formulas from $\mathfrak{g}_2$
to $sl(3,\mathbb{C})$ for generalized Verma modules attached to
$sl(3,\mathbb{C})$-compatible parabolic subalgebras of $\mathfrak{g}_2$
respectively, under some assumptions on the parameters of generalized Verma
modules.


title: Union of Random Minkowski Sums and Network Vulnerability Analysis

abstract:
  Let $\mathcal{C}=\{C_1,\ldots,C_n\}$ be a set of $n$ pairwise-disjoint convex
sets of constant description complexity, and let $\pi$ be a probability density
function (pdf for short) over the non-negative reals. For each $i$, let $K_i$
be the Minkowski sum of $C_i$ with a disk of radius $r_i$, where each $r_i$ is
a random non-negative number drawn independently from the distribution
determined by $\pi$. We show that the expected complexity of the union of $K_1,
\ldots, K_n$ is $O(n^{1+\varepsilon})$ for any $\varepsilon > 0$; here the
constant of proportionality depends on $\varepsilon$ and on the description
complexity of the sets in $\mathcal{C}$, but not on $\pi$. If each $C_i$ is a
convex polygon with at most $s$ vertices, then we show that the expected
complexity of the union is $O(s^2n\log n)$.
  Our bounds hold in the stronger model in which we are given an arbitrary
multi-set $R=\{r_1,\ldots,r_n\}$ of expansion radii, each a non-negative real
number. We assign them to the members of $\mathcal{C}$ by a random permutation,
where all permutations are equally likely to be chosen; the expectations are
now with respect to these permutations.
  We also present an application of our results to a problem that arises in
analyzing the vulnerability of a network to a physical attack. %


title: Local Mixed Hodge Structure on Brill-Noether Stacks

abstract:
  On a smooth algebraic curve X with genus greater than 1 we consider a flat
principal bundle with a reductive structure group S and a vector bundle
associated with it. To this set of information we put in correspondence a
pro-algebraic group on whose functional algebra we introduce a mixed Hodge
structure. This construction, in fact, works for any smooth algebraic variety X
which, considered as an analytic space, has a nonabelian first homotopy group,
and the rest are trivial. The Hodge structure defined in this way can be
expressed in terms of iterated integrals.
  Furthermore, considered in the context of previous work by C. Simpson, this
MHS is the local mixed Hodge structure on a nonabelian cohomological space on X
with coefficients into a Brill-Noether stack, i.e., a stack with two
non-trivial homotopy groups: a fundamental group isomorphic to the group S and
an n-th homotopy group represented by a vector space, the fiber of the vector
bundle discussed above above.
  My construction is compatible and generalizes the work of R. Hain on Hodge
structure on relative Malcev completion of the fundamental group of X.


title: Nonabelian Mixed Hodge Structure on Brill-Noether Stacks

abstract:
  A Brill-Noether stack is an algebraic very presentable stack whose homotopy
type has two nontrivial homotopy groups. We consider one with a fundamental
group --- a reductive algebraic group-scheme S and one higher homotopy group,
represented by a vector space V. The homotopy type also defines an action of S
on V. This stack is used as coefficient space for nonabelian cohomological
space on a smooth algebraic variety X.
  We define nonabelian MHS on cohomological spaces of this type in the context
of the work of C. Simpson related to MHS on the space of local systems. It is
defined via an action of the multiplicative complex group on a appropriately
chosen category. The exhibited structure in fact generalizes Simpson's work.
Allowing a more general type of coefficient stack.
  Furthermore, the so-defined MHS, when considered at a vicinity of an object,
which remains fixed under the structural action of C*, produces the local MHS
on Brill-Noether Stacks as defined in our earlier work.
  The nonabelian mixed Hodge structure on a Brill-Noether stack is a example of
the mixed Hodge structure on a schematic homotopy type, studied by Katzarkov,
Pantev and Toen. It has the advantage, due to the relative simplicity of the
coefficient stack, that it could be locally written out in terms of iterated
integrals.


title:
Expansion in generalized eigenfunctions for Laplacians on graphs and
  metric measure spaces

abstract:
  We consider an arbitrary selfadjoint operator on a separable Hilbert space.
To this operator we construct an expansion in generalized eigenfunctions in
which the original Hilbert space is decomposed as a direct integral of Hilbert
spaces consisting of general eigenfunctions. This automatically gives a
Plancherel type formula. For suitable operators on metric measure spaces we
discuss some growth restrictions on the generalized eigenfunctions. For
Laplacians on locally finite graphs the generalized eigenfunctions are exactly
the solutions of the corresponding difference equation.


title:
Nonlinear modes in a generalized ${\cal PT}$-symmetric discrete
  nonlinear Schr\"odinger equation

abstract:
  We generalize a finite parity-time (${\cal PT}$-) symmetric network of the
discrete nonlinear Schr\"odinger type and obtain general results on linear
stability of the zero equilibrium, on the nonlinear dynamics of the dimer
model, as well as on the existence and stability of large-amplitude stationary
nonlinear modes. A result of particular importance and novelty is the
classification of all possible stationary modes in the limit of large
amplitudes. We also discover a new integrable configuration of a ${\cal
PT}$-symmetric dimer.


title:
Ab initio calculations of indium arsenide in the wurtzite phase:
  structural, electronic and optical properties

abstract:
  Most III-V semiconductors, which acquire the zinc-blende phase as bulk
materials, adopt the metastable wurtzite phase when grown in the form of
nanowires. These are new semiconductors with new optical properties, in
particular, a different electronic band gap when compared with that grown in
the zinc-blende phase. The electronic gap of wurtzite InAs at the Gamma-point
of the Brillouin zone (E0 gap) has been recently measured, E0 = 0.46 eV at low
temperature. The electronic gap at the A point of the Brillouin zone
(equivalent to the L point in the zinc-blende structure, E1) has also been
obtained recently based on a resonant Raman scattering experiment. In this
work, we calculate the band structure of InAs in the zinc-blende and wurtzite
phases, using the full potential linearized augmented plane wave method,
including spin-orbit interaction. The electronic band gap has been improved
through the modified Becke-Johnson exchange-correlation potential. Both the E0
and E1 gaps agree very well with the experiment. From the calculations, a
crystal field splitting of 0.122 eV and a spin-orbit splitting of 0.312 eV (the
experimental value in zinc-blende InAs is 0.4 eV) has been obtained. Finally,
we calculate the dielectric function of InAs in both the zinc-blende and
wurtzite phases and a comparative discussion is given.


title: Blind and robust images watermarking based on wavelet and edge insertion

abstract:
  This paper gives a new scheme of watermarking technique related to insert the
mark by adding edge in HH sub-band of the host image after wavelet
decomposition. Contrary to most of the watermarking algorithms in wavelet
domain, our method is blind and results show that it is robust against the JPEG
and GIF compression, histogram and spectrum spreading, noise adding and small
rotation. Its robustness against compression is better than others watermarking
algorithms reported in the literature. The algorithm is flexible because its
capacity or robustness can be improved by modifying some parameters.


title:
Three sub-Jupiter-mass planets: WASP-69b & WASP-84b transit active K
  dwarfs and WASP-70Ab transits the evolved primary of a G4+K3 binary

abstract:
  We report the discovery of the transiting exoplanets WASP-69b, WASP-70Ab and
WASP-84b, each of which orbits a bright star ($V\sim10)$. WASP-69b is a bloated
Saturn-mass planet (0.26 $M_{\rm Jup}$, 1.06 $R_{\rm Jup}$) in a 3.868-d period
around an active, $\sim$1-Gyr, mid-K dwarf. ROSAT detected X-rays $60 \pm 27"$
from WASP-69. If the star is the source then the planet could be undergoing
mass-loss at a rate of $\sim$10$^{12}$ g s$^{-1}$. This is 1 to 2 orders of
magnitude higher than the evaporation rate estimated for HD 209458b and HD
189733b, both of which have exhibited anomalously-large Lyman-$\alpha$
absorption during transit. WASP-70Ab is a sub-Jupiter-mass planet (0.59 $M_{\rm
Jup}$, 1.16 $R_{\rm Jup}$) in a 3.713-d orbit around the primary of a
spatially-resolved, 9-to-10-Gyr, G4+K3 binary, with a separation of 3.3$'$
($\geq$800 AU). WASP-84b is a sub-Jupiter-mass planet (0.69 $M_{\rm Jup}$, 0.94
$R_{\rm Jup)}$ in an 8.523-d orbit around an active, $\sim$1-Gyr, early-K
dwarf. Of the transiting planets discovered from the ground to date, WASP-84b
has the third-longest period. For the active stars WASP-69 and WASP-84, we
pre-whitened the radial velocities using a low-order harmonic series. We found
this reduced the residual scatter more than did the oft-used method of
pre-whitening with a fit between residual radial velocity and bisector span.
The system parameters were essentially unaffected by pre-whitening.


title: Lagrangian flows driven by $BV$ fields in Wiener spaces

abstract:
  We establish the renormalization property for essentially bounded solutions
of the continuity equation associated to $BV$ fields in Wiener spaces, with
values in the associated Cameron-Martin space; thus obtaining, by standard
arguments, new uniqueness and stability results for correspondent Lagrangian
$L^\infty$-flows. An example related to Neumann elliptic problems is also
discussed.


title: Approximation systems for functions in topological and in metric spaces

abstract:
  A notable feature of the TTE approach to computability is the representation
of the argument values and the corresponding function values by means of
infinitistic names. Two ways to eliminate the using of such names in certain
cases are indicated in the paper. The first one is intended for the case of
topological spaces with selected indexed denumerable bases. Suppose a partial
function is given from one such space into another one whose selected base has
a recursively enumerable index set, and suppose that the intersection of base
open sets in the first space is computable in the sense of Weihrauch-Grubba.
Then the ordinary TTE computability of the function is characterized by the
existence of an appropriate recursively enumerable relation between indices of
base sets containing the argument value and indices of base sets containing the
corresponding function value.This result can be regarded as an improvement of a
result of Korovina and Kudinov. The second way is applicable to metric spaces
with selected indexed denumerable dense subsets. If a partial function is given
from one such space into another one, then, under a semi-computability
assumption concerning these spaces, the ordinary TTE computability of the
function is characterized by the existence of an appropriate recursively
enumerable set of quadruples. Any of them consists of an index of element from
the selected dense subset in the first space, a natural number encoding a
rational bound for the distance between this element and the argument value, an
index of element from the selected dense subset in the second space and a
natural number encoding a rational bound for the distance between this element
and the function value. One of the examples in the paper indicates that the
computability of real functions can be characterized in a simple way by using
the first way of elimination of the infinitistic names.


title: Higher ramification loci over homogeneous spaces

abstract:
  We generalize the Gaffney-Lazarsfeld theorem on higher ramification loci of
branched coverings of $\mathbb{P}^n$ to homogeneous spaces with Picard number
one.


title:
Relaxation of surface tension in the liquid-solid interfaces of
  Lennard-Jones liquids

abstract:
  We have established the surface tension relaxation time in the liquid-solid
interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in
molecular dynamics (MD) simulations. The main result is that the relaxation
time is found to be weakly dependent on the molecular structures used in our
study and lies in such a range that in slow hydrodynamic motion the interfaces
are expected to be at equilibrium. The implications of our results for the
modelling of dynamic wetting processes and interpretation of dynamic contact
angle data are discussed.


title:
Minimal Liouville Gravity correlation numbers from Douglas string
  equation

abstract:
  We continue the study of $(q,p)$ Minimal Liouville Gravity with the help of
Douglas string equation. We generalize the results of \cite{Moore:1991ir},
\cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to
$(3,3s+p_0)$ Minimal Liouville Gravity, where $p_0=1,2$. We demonstrate that
there exist such coordinates $\tau_{m,n}$ on the space of the perturbed Minimal
Liouville Gravity theories, in which the partition function of the theory is
determined by the Douglas string equation. The coordinates $\tau_{m,n}$ are
related in a non-linear fashion to the natural coupling constants
$\lambda_{m,n}$ of the perturbations of Minimal Lioville Gravity by the
physical operators $O_{m,n}$. We find this relation from the requirement that
the correlation numbers in Minimal Liouville Gravity must satisfy the conformal
and fusion selection rules. After fixing this relation we compute three- and
four-point correlation numbers when they are not zero. The results are in
agreement with the direct calculations in Minimal Liouville Gravity available
in the literature \cite{Goulian:1990qr}, \cite{Zamolodchikov:2005sj},
\cite{Belavin:2006ex}.


title:
Uncoupled Learning Rules for Seeking Equilibria in Repeated Plays: An
  Overview

abstract:
  In this note, we consider repeated play of a finite game using learning rules
whose period-by-period behavior probabilities or empirical distributions
converge to some notion of equilibria of the stage game. Our primary focus is
on uncoupled and completely uncoupled learning rules. While the former relies
on players being aware of only their own payoff functions and able to monitor
the action taken by the others, the latter assumes that players only know their
own past realized payoffs. We highlight the border between possible and
impossible results using these rules. We also overview several uncoupled and
completely uncoupled learning rules, most of which leverage notions of regret
as the solution concept to seek payoff-improving action profiles.


title:
Relaxation of surface tension in the free-surface boundary layer of
  simple Lennard-Jones liquids

abstract:
  In this paper we use molecular dynamics (MD) to answer a classical question:
how does the surface tension on a liquid/gas interface appear? After defining
surface tension from the first principles and performing several consistency
checks, we perform a dynamic experiment with a single simple liquid
nanodroplet. At time zero, we remove all molecules of the interfacial layer,
creating a fresh bare interface with the bulk arrangement of molecules. After
that the system evolves towards equilibrium, and the expected surface tension
is re-established. We found that the system relaxation consists of three
distinct stages. First, the mechanical balance is quickly re-established.
During this process the notion of surface tension is meaningless. In the second
stage, the surface tension equilibrates, and the density profile broadens to a
value which we call "intrinsic" interfacial width. During the third stage, the
density profile continues to broaden due to capillary wave excitations, which
does not however affect the surface tension. We have observed this scenario for
monatomic Lennard-Jones (LJ) liquid as well as for binary LJ mixtures at
different temperatures, monitoring a wide range of physical observables.


title:
Snowmass Cosmic Frontiers 6 (CF6) Working Group Summary --The Bright
  Side of the Cosmic Frontier: Cosmic Probes of Fundamental Physics

abstract:
  Report of the CF6 Working Group at Snowmass 2013. Topics addressed include
ultra-high energy cosmic rays, neutrinos, gamma rays, baryogenesis, and
experiments probing the fundamental nature of spacetime.

categories: hep-ph astro-ph.CO astro-ph.HE astro-ph.IM hep-ex


title: Mean-Based Error Measures for Intermittent Demand Forecasting

abstract:
  To compare different forecasting methods on demand series we require an error
measure. Many error measures have been proposed, but when demand is
intermittent some become inapplicable, some give counter-intuitive results, and
there is no agreement on which is best. We argue that almost all known measures
rank forecasters incorrectly on intermittent demand series. We propose several
new error measures with wider applicability, and correct forecaster ranking on
several intermittent demand patterns. We call these "mean-based" error measures
because they evaluate forecasts against the (possibly time-dependent) mean of
the underlying stochastic process instead of point demands.


title: Quantum Locally Testable Codes

abstract:
  We initiate the study of quantum Locally Testable Codes (qLTCs). We provide a
definition together with a simplification, denoted sLTCs, for the special case
of stabilizer codes, together with some basic results using those definitions.
The most crucial parameter of such codes is their soundness, $R(\delta)$,
namely, the probability that a randomly chosen constraint is violated as a
function of the distance of a word from the code ($\delta$, the relative
distance from the code, is called the proximity). We then proceed to study
limitations on qLTCs. In our first main result we prove a surprising,
inherently quantum, property of sLTCs: for small values of proximity, the
better the small-set expansion of the interaction graph of the constraints, the
less sound the qLTC becomes. This phenomenon, which can be attributed to
monogamy of entanglement, stands in sharp contrast to the classical setting.
The complementary, more intuitive, result also holds: an upper bound on the
soundness when the code is defined on poor small-set expanders (a bound which
turns out to be far more difficult to show in the quantum case). Together we
arrive at a quantum upper-bound on the soundness of stabilizer qLTCs set on any
graph, which does not hold in the classical case. Many open questions are
raised regarding what possible parameters are achievable for qLTCs. In the
appendix we also define a quantum analogue of PCPs of proximity (PCPPs) and
point out that the result of Ben-Sasson et. al. by which PCPPs imply LTCs with
related parameters, carries over to the sLTCs. This creates a first link
between qLTCs and quantum PCPs.


title:
Learning Theory and Algorithms for Revenue Optimization in Second-Price
  Auctions with Reserve

abstract:
  Second-price auctions with reserve play a critical role for modern search
engine and popular online sites since the revenue of these companies often
directly de- pends on the outcome of such auctions. The choice of the reserve
price is the main mechanism through which the auction revenue can be influenced
in these electronic markets. We cast the problem of selecting the reserve price
to optimize revenue as a learning problem and present a full theoretical
analysis dealing with the complex properties of the corresponding loss
function. We further give novel algorithms for solving this problem and report
the results of several experiments in both synthetic and real data
demonstrating their effectiveness.


title:
Distributed parameter estimation of discrete hierarchical models via
  marginal likelihoods

abstract:
  We consider discrete graphical models Markov with respect to a graph $G$ and
propose two distributed marginal methods to estimate the maximum likelihood
estimate of the canonical parameter of the model. Both methods are based on a
relaxation of the marginal likelihood obtained by considering the density of
the variables represented by a vertex $v$ of $G$ and a neighborhood. The two
methods differ by the size of the neighborhood of $v$. We show that the
estimates are consistent and that those obtained with the larger neighborhood
have smaller asymptotic variance than the ones obtained through the smaller
neighborhood.


title:
Measurement of the $^{90, 92}$Zr(p,$\gamma$)$^{91,93}$Nb reactions for
  the nucleosynthesis of elements around A=90

abstract:
  Cross section measurements of the reactions $^{90,
92}$Zr(p,$\gamma$)$^{91,93}$Nb were performed using the NSCL SuN detector at
the University of Notre Dame. These reactions are part of the nuclear reaction
flow for the synthesis of the light p nuclei. For the
$^{90}$Zr(p,$\gamma$)$^{91}$Nb reaction the new measurement resolves the
disagreement between previous results. For the $^{92}$Zr(p,$\gamma$)$^{93}$Nb
reaction the present work reports the first measurement of this reaction cross
section. Both reaction cross sections are compared to theoretical calculations
and a very good agreement with the standard NON-SMOKER model is observed.


title: Optimizing snake locomotion on an inclined plane

abstract:
  We develop a model to study the locomotion of snakes on an inclined plane. We
determine numerically which snake motions are optimal for two retrograde
traveling-wave body shapes---triangular and sinusoidal waves---across a wide
range of frictional parameters and incline angles. In the regime of large
transverse friction coefficient, we find power-law scalings for the optimal
wave amplitudes and corresponding costs of locomotion. We give an asymptotic
analysis to show that the optimal snake motions are traveling-wave motions with
amplitudes given by the same scaling laws found in the numerics.


title: On Gauss sums and the evaluation of Stechkin's constant

abstract:
  For the Gauss sums which are defined by S_n(a,q) := \sum_{x (mod q)}
e(ax^n/q), Stechkin (1975) conjectured that the quantity A := \sup_{n,q\ge 2}
\max_{\gcd(a,q)=1} |S_n(a,q)|/q^(1-1/n) is finite. Shparlinski (1991) proved
that A is finite, but in the absence of effective bounds on the sums S_n(a,q)
the precise determination of A has remained intractable for many years. Using
recent work of Cochrane and Pinner (2011) on Gauss sums with prime moduli, in
this paper we show that with the constant given by A =
|S_6(4787,4606056)|/4606056^(5/6) = 4.709236... one has the sharp inequality
|S_n(a,q)| \le Aq^(1-1/n) for all n,q \ge 2 and all integers a with gcd(a,q)=1.
One interesting aspect of our method is that we apply effective lower bounds
for the center density in the sphere packing problem due to Cohn and Elkies
(2003) to optimize the running time of our primary computational algorithm.


title: A simple authentication by common strings

abstract:
  It was the problem of finding the minimum value of the sum of the distances
of the path through all cities Overview TSP. We propose an authentication with
the problem that the deformation sum of the distances of the path to be a
constant value. In this document, it is intended to construct an authentication
function robust implementation is easy and the Blog. After it was shown that
the first, to determine the replacement group and path are the same, we propose
the authentication method to consider the deformation of the traveling salesman
problem in the directed graph, using a sequence of bytes. Instead of providing
illumination mathematically rigorous, describes a verifiable algorithm.


title:
A Characterization of totally real Carleman continua and an application
  to products of stratified totally real sets

abstract:
  We give a characterization of stratified totally real sets that admit
Carleman approximation by entire functions. As an application we show that the
product of two stratified totally real Carleman continua is a Carleman
continuum.


title:
Degree distribution of shortest path trees and bias of network sampling
  algorithms

abstract:
  In this article, we explicitly derive the limiting degree distribution of the
shortest path tree from a single source on various random network models with
edge weights. We determine the asymptotics of the degree distribution for large
degrees of this tree and compare it to the degree distribution of the original
graph. We perform this analysis for the complete graph with edge weights that
are powers of exponential random variables (weak disorder in the stochastic
mean-field model of distance), as well as on the configuration model with
edge-weights drawn according to any continuous distribution. In the latter, the
focus is on settings where the degrees obey a power law, and we show that the
shortest path tree again obeys a power law with the same degree power-law
exponent. We also consider random $r$-regular graphs for large $r$, and show
that the degree distribution of the shortest path tree is closely related to
the shortest path tree for the stochastic mean-field model of distance. We use
our results to shed light on an empirically observed bias in network sampling
methods. This is part of a general program initiated in previous works by
Bhamidi, van der Hofstad and Hooghiemstra [Ann. Appl. Probab. 20 (2010)
1907-1965], [Combin. Probab. Comput. 20 (2011) 683-707], [Adv. in Appl. Probab.
42 (2010) 706-738] of analyzing the effect of attaching random edge lengths on
the geometry of random network models.


title: The Bell states in noncommutative algebraic geometry

abstract:
  We introduce new mathematical aspects of the Bell states using matrix
factorizations, nonnoetherian singularities, and noncommutative blowups. A
matrix factorization of a polynomial $p$ consists of two matrices
$\phi_1,\phi_2$ such that $\phi_1\phi_2 = \phi_2\phi_1 = p \operatorname{id}$.
Using this notion, we show how the Bell states emerge from the separable
product of two mixtures, by defining pure states over complex matrices rather
than just the complex numbers.
  We then show in an idealized algebraic setting that pure states are supported
on nonnoetherian singularities. Moreover, we find that the collapse of a Bell
state is intimately related to the representation theory of the noncommutative
blowup along its singular support. This presents an exchange in geometry: the
nonlocal commutative spacetime of the entangled state emerges from an
underlying local noncommutative spacetime.


title:
Quasar broad absorption line variability measurements using
  reconstructions of un-absorbed spectra

abstract:
  We present a two-epoch Sloan Digital Sky Survey and Gemini/GMOS+William
Herschel Telescope/ISIS variability study of 50 broad absorption line quasars
of redshift range 1.9 < z < 4.2, containing 38 Si IV and 59 C IV BALs and
spanning rest-frame time intervals of approximately 10 months to 3.7 years. We
find that 35/50 quasars exhibit one or more variable BALs, with 58% of Si IV
and 46% of C IV BALs showing variability across the entire sample. On average,
Si IV BALs show larger fractional change in BAL pseudo equivalent width than C
IV BALs, as referenced to an unabsorbed continuum+emission-line spectrum
constructed using non-negative matrix factorisation. No correlation is found
between BAL variability and quasar luminosity, suggesting that ionizing
continuum changes do not play a significant role in BAL variability (assuming
the gas is in photoionization equilibrium with the ionizing continuum). A
subset of 14 quasars have one variable BAL from each of Si IV and C IV with
significant overlap in velocity space and for which variations are in the same
sense (strengthening or weakening) and which appear to be correlated (98%
confidence). We find examples of both appearing and disappearing BALs in
weaker/shallower lines with disappearance rates of 2.3% for C IV and 5.3% for
Si IV, suggesting average lifetimes of 142 and 43 years respectively. We
identify 5 objects in which the BAL is coincident with the broad emission-line,
but appears to cover only the continuum source. Assuming a clumpy inhomogeneous
absorber model and a typical size for the continuum source, we infer a maximum
cloud radius of 10^13 to 10^14 cm, assuming Eddington limited accretion.


title:
A general study of extremes of stationary tessellations with
  applications

abstract:
  Let $\mathfrak{m}$ be a random tessellation in $\mathbf{R}^d$ observed in a
bounded Borel subset $W$ and $f(\cdot)$ be a measurable function defined on the
set of convex bodies. To each cell $C$ of $\mathfrak{m}$ we associate a point
$z(C)$ which is the nucleus of $C$. Applying $f(\cdot)$ to all the cells of
$\mathfrak{m}$, we investigate the order statistics of $f(C)$ over all cells
$C\in\mathfrak{m}$ with nucleus in $\mathbf{W}_{\rho}=\rho^{1/d}W$ when $\rho$
goes to infinity. Under a strong mixing property and a local condition on
$\mathfrak{m}$ and $f(\cdot)$, we show a general theorem which reduces the
study of the order statistics to the random variable $f(\mathscr{C})$ where
$\mathscr{C}$ is the typical cell of $\mathfrak{m}$. The proof is deduced from
a Poisson approximation on a dependency graph via the Chen-Stein method. We
obtain that the point process $\left\{(\rho^{-1/d}z(C),
a_{\rho}^{-1}(f(C)-b_{\rho})), C\in\mathfrak{m}, z(C)\in
\mathbf{W}_{\rho}\right\}$, where $a_{\rho}>0$ and $b_{\rho}$ are two suitable
functions depending on $\rho$, converges to a non-homogeneous Poisson point
process. Several applications of the general theorem are derived in the
particular setting of Poisson-Voronoi and Poisson-Delaunay tessellations and
for different functions $f(\cdot)$ such as the inradius, the circumradius, the
area, the volume of the Voronoi flower and the distance to the farthest
neighbor. When the local condition does not hold and the normalized maximum
converges, the asymptotic behaviour depends on two quantities that are the
distribution function of $f(\mathscr{C})$ and a constant $\theta\in [0,1]$
which is the so-called extremal index.


title: Reaching Fermi degeneracy via universal dipolar scattering

abstract:
  We report on the creation of a degenerate dipolar Fermi gas of erbium atoms.
We force evaporative cooling in a fully spin-polarized sample down to
temperatures as low as 0.2 times the Fermi temperature. The strong magnetic
dipole-dipole interaction enables elastic collisions between identical fermions
even in the zero-energy limit. The measured elastic scattering cross section
agrees well with the predictions from dipolar scattering theory, which follow a
universal scaling law depending only on the dipole moment and on the atomic
mass. Our approach to quantum degeneracy proceeds with very high cooling
efficiency and provides large atomic densities, and it may be extended to
various dipolar systems.


title: Penalized Split Criteria for Interpretable Trees

abstract:
  This paper describes techniques for growing classification and regression
trees designed to induce visually interpretable trees. This is achieved by
penalizing splits that extend the subset of features used in a particular
branch of the tree. After a brief motivation, we summarize existing methods and
introduce new ones, providing illustrative examples throughout. Using a number
of real classification and regression datasets, we find that these procedures
can offer more interpretable fits than the CART methodology with very modest
increases in out-of-sample loss.


title:
Numerical calculations of radiative and non-radiative relaxation of
  molecules near metal particles

abstract:
  The dependence of the radiative emission and the non-radiative (energy
transfer to the metal) relaxation rates of a molecule near a small metal
particle on the molecule-to-particle distance and on the molecular orientation
is calculated using a numerical solution of the Maxwell equations for a model
that described the metal as a dispersive dielectric particle and the molecule
as an oscillating point dipole. The emission rate is obtained by evaluating the
total oscillating dipole in the system, while the non-radiative rate is
inferred from the rate of heat production on the particle. For the distance
dependence of the non-radiative rate we find, in agreement with experimental
observations, marked deviation from the prediction of the standard theory of
fluorescence resonance energy transfer (FRET). In departure from previous
interpretations, we find that electromagnetic retardation is the main source of
this deviation at large molecule-particle separations. The radiative emission
rate reflects the total dipole induced in the molecule- particle system, and
its behavior as function of distance and orientation stems mostly from the
magnitude of the oscillating polarization on the metal particle (which, at
resonance, is strongly affected by plasmon excitation), and from the way this
polarization combines with the molecular dipole to form the total system
dipole.


title:
A minimal stable vertical planar end in H^2 x R has finite total
  curvature

abstract:
  We prove that a minimal oriented stable annular end in H^2 x R whose
asymptotic boundary is contained in two vertical lines has finite total
curvature and converges to a vertical plane. Furthermore, if the end is
embedded then it is a horizontal graph.


title: Nonadiabatic quantum state engineering driven by fast quench dynamics

abstract:
  There are a number of tasks in quantum information science that exploit
non-transitional adiabatic dynamics. Such a dynamics is bounded by the
adiabatic theorem, which naturally imposes a speed limit in the evolution of
quantum systems. Here, we investigate an approach for quantum state engineering
exploiting a shortcut to the adiabatic evolution, which is based on rapid
quenches in a continuous-time Hamiltonian evolution. In particular, this
procedure is able to provide state preparation faster than the adiabatic
brachistochrone. Remarkably, the evolution time in this approach is shown to be
ultimately limited by its "thermodynamical cost,"provided in terms of the
average work rate (average power) of the quench process. We illustrate this
result in a scenario that can be experimentally implemented in a nuclear
magnetic resonance setup.


title:
Skyrmion magnetic structure of an ordered FePt monolayer deposited on
  Pt(111)

abstract:
  The effect of the Dzyaloshinsky-Moriya interaction on the magnetic structure
of an ordered FePt monolayer deposited on Pt (111) surface has been
investigated. In the ground state, the pronounced anisotropic geometry of the
FePt layer with alternating Fe and Pt chains gives rise to a helimagnetic
structure with a strong difference in the helicity period along the chains and
perpendicular to them. In the presence of an external magnetic field, the
region of stable Skyrmion magnetic structures in the $B-T$ phase diagram has
been demonstrated via Monte Carlo simulations using the parameters obtained
within first-principles electronic structure calculations. The present study
demonstrates clearly that the ratio of the exchange coupling parameters J/D for
a deposited magnetic film - being of central importance for the formation of
Skyrmions - can be manipulated by growing an overlayer of 2-dimensional (2D)
compounds with the atoms carrying spontaneous magnetic moments separated by the
atoms of non-magnetic elements.


title: Ghost numbers of group algebras II

abstract:
  We study several closely related invariants of the group algebra $kG$ of a
finite group. The basic invariant is the ghost number, which measures the
failure of the generating hypothesis and involves finding non-trivial
composites of maps each of which induces the zero map in Tate cohomology
("ghosts"). The related invariants are the simple ghost number, which considers
maps which are stably trivial when composed with any map from a suspension of a
simple module, and the strong ghost number, which considers maps which are
ghosts after restriction to every subgroup of $G$. We produce the first
computations of the ghost number for non-$p$-groups, e.g., for the dihedral
groups at all primes, as well as many new bounds. We prove that there are close
relationships between the three invariants, and make computations of the new
invariants for many families of groups.


title: Ac Josephson Effect in Topological Josephson Junctions

abstract:
  Topological superconductors admit zero-energy Majorana bound states at their
boundaries. In this review article, we discuss how to probe these Majorana
bound states in Josephson junctions between two topological superconductors. In
the absence of an applied bias, the presence of these states gives rise to an
Andreev bound state whose energy varies $4\pi$-periodically in the
superconducting phase difference. An applied voltage bias leads to a
dynamically varying phase according to the Josephson relation. Furthermore, it
leads to dynamics of the occupation of the bound state via its non-adiabatic
coupling to the continuum. While the Josephson relation suggests a fractional
Josephson effect due to the $4\pi$-periodicity of the bound state, its
observability relies on the conservation of the occupation of the bound state
on the experimentally probed time scale. We study the lifetime of the bound
state and identify the time scales it has to be compared to. In particular, we
are interested in signatures of the fractional Josephson effect in the Shapiro
steps and in current noise measurements. We also discuss manifestations of the
zero-energy Majorana states on the dissipative subgap current.


title: Linear tree codes and the problem of explicit constructions

abstract:
  We reduce the problem of constructing asymptotically good tree codes to the
construction of triangular totally nonsingular matrices over fields with
polynomially many elements. We show a connection of this problem to Birkhoff
interpolation in finite fields.