title: The Erd\H{o}s-Ko-Rado property for some permutation groups

abstract:
  A subset in a group $G \leq Sym(n)$ is intersecting if for any pair of
permutations $\pi,\sigma$ in the subset there is an $i \in \{1,2,\dots,n\}$
such that $\pi(i) = \sigma(i)$. If the stabilizer of a point is the largest
intersecting set in a group, we say that the group has the Erd\H{o}s-Ko-Rado
(EKR) property. Moreover, the group has the strict EKR property if every
intersecting set of maximum size in the group is either the stabilizer of a
point or the coset of the stabilizer of a point. In this paper we look at
several families of permutation groups and determine if the groups have either
the EKR property or the strict EKR property. First, we prove that all cyclic
groups have the strict EKR property. Next we show that all dihedral and
Frobenius groups have the EKR property and we characterize which ones have the
strict EKR property. Further, we show that if all the groups in an external
direct sum or an internal direct sum have the EKR (or strict EKR) property,
then the product does as well. Finally, we show that the wreath product of two
groups with EKR property also has the EKR property.


title: Two-term tilting complexes over Brauer tree algebras

abstract:
  In this paper all two-term tilting complexes over a Brauer tree algebra with
multiplicity one are described using a classification of indecomposable
two-term partial tilting complexes obtained earlier in a joint paper with M.
Antipov. The endomorphism rings of such complexes are computed.


title: An Erd\H{o}s-Ko-Rado theorem for subset partitions

abstract:
  A $k\ell$-subset partition, or $(k,\ell)$-subpartition, is a $k\ell$-subset
of an $n$-set that is partitioned into $\ell$ distinct classes, each of size
$k$. Two $(k,\ell)$-subpartitions are said to $t$-intersect if they have at
least $t$ classes in common. In this paper, we prove an Erd\H{o}s-Ko-Rado
theorem for intersecting families of $(k,\ell)$-subpartitions. We show that for
$n \geq k\ell$, $\ell \geq 2$ and $k \geq 3$, the largest $1$-intersecting
family contains at most
$\frac{1}{(\ell-1)!}\binom{n-k}{k}\binom{n-2k}{k}\cdots\binom{n-(\ell-1)k}{k}$
$(k,\ell)$-subpartitions, and that this bound is only attained by the family of
$(k,\ell)$-subpartitions with a common fixed class, known as the
\emph{canonical intersecting family of $(k,\ell)$-subpartitions}. Further,
provided that $n$ is sufficiently large relative to $k,\ell$ and $t$, the
largest $t$-intersecting family is the family of $(k,\ell)$-subpartitions that
contain a common set of $t$ fixed classes.


title: Universality of random graphs and rainbow embedding

abstract:
  In this paper we show how to use simple partitioning lemmas in order to embed
spanning graphs in a typical member of $G(n,p)$. Let the \emph{maximum density}
of a graph $H$ be the maximum average degree of all the subgraphs of $H$.
First, we show that for $p=\omega(\Delta^{12} n^{-1/2d}\log^3n)$, a graph
$G\sim G(n,p)$ w.h.p.\ contains copies of all spanning graphs $H$ with maximum
degree at most $\Delta$ and maximum density at most $d$. For $d<\Delta/2$, this
improves a result of Dellamonica, Kohayakawa, R\"odl and Ruci\'ncki. Next, we
show that if we additionally restrict the spanning graphs to have girth at
least 7 then the random graph contains w.h.p.\ all such graphs for
$p=\omega(\Delta^{12} n^{-1/d}\log^3n)$. In particular, if
$p=\omega(\Delta^{12} n^{-1/2}\log^3 n)$, the random graph therefore contains
w.h.p.\ every spanning tree with maximum degree bounded by $\Delta$. This
improves a result of Johannsen, Krivelevich and Samotij.
  Finally, in the same spirit, we show that for any spanning graph $H$ with
constant maximum degree, and for suitable $p$, if we randomly color the edges
of a graph $G\sim G(n,p)$ with $(1 + o(1))|E(H)|$ colors, then w.h.p.\ there
exists a \emph{rainbow} copy of $H$ in $G$ (that is, a copy of $H$ with all
edges colored with distinct colors).


title:
On the Relationships between Zero Forcing Numbers and Certain Graph
  Coverings

abstract:
  The zero forcing number and the positive zero forcing number of a graph are
two graph parameters that arise from two types of graph colourings. The zero
forcing number is an upper bound on the minimum number of induced paths in the
graph, while the positive zero forcing number is an upper bound on the minimum
number of induced trees in the graph. We show that for a block-cycle graph the
zero forcing number equals the path cover number. We also give a purely graph
theoretical proof that the positive zero forcing number of any outerplanar
graphs equals the tree cover number of the graph. These ideas are then extended
to the setting of $k$-trees, where the relationship between the positive zero
forcing number and the tree cover number becomes more complex.


title: Individual and Time Effects in Nonlinear Panel Models with Large N, T

abstract:
  We derive fixed effects estimators of parameters and average partial effects
in (possibly dynamic) nonlinear panel data models with individual and time
effects. They cover logit, probit, ordered probit, Poisson and Tobit models
that are important for many empirical applications in micro and macroeconomics.
Our estimators use analytical and jackknife bias corrections to deal with the
incidental parameter problem, and are asymptotically unbiased under asymptotic
sequences where $N/T$ converges to a constant. We develop inference methods and
show that they perform well in numerical examples.


title: Initial Conditions for Idealised Clusters Mergers, simulating El Gordo

abstract:
  Simulations of isolated binary mergers of galaxy clusters are a useful tool
to study the evolution of these objects. For exceptionally massive systems they
even represent the only viable way of simulation, because these are rare in
typical cosmological simulations. We present a new practical model for these
simulations based on the Hernquist dark matter profile. The hydrostatic
equation is solved for a beta-model with $\beta$ = 2/3 in this potential and
approximate expressions for X-ray brightness and Compton-y parameter are
derived. We show in detail how to setup such a system using SPH. The
theoretical and several numerical models are compared to observed scaling
relations of galaxy clusters and satisfactory agreement with the self-similar
relations is found. The model is then applied to investigate the observed
cluster ACT-CT J0102-4915 (El Gordo), a particularly massive merging high
redshift cluster. We are able to reproduce the X-ray luminosity, SZ-effect and
dark matter core distance as well as the rough shape of the observed cluster
for reasonable model parameters. The lack of substruc- ture prevents us from
obtaining the fluctuations observed in the wake of the system and we argue that
the parent cluster of the system was highly disturbed even before the main
merger observed today.


title: Exchange Bias Effect in Au-Fe3O4 Nanocomposites

abstract:
  We report exchange bias (EB) effect in the Au-Fe3O4 composite nanoparticle
system, where one or more Fe3O4 nanoparticles are attached to an Au seed
particle forming dimer and cluster morphologies, with the clusters showing much
stronger EB in comparison with the dimers. The EB effect develops due to the
presence of stress in the Au-Fe3O4 interface which leads to the generation of
highly disordered, anisotropic surface spins in the Fe3O4 particle. The EB
effect is lost with the removal of the interfacial stress. Our atomistic
Monte-Carlo studies are in excellent agreement with the experimental results.
These results show a new path towards tuning EB in nanostructures, namely
controllably creating interfacial stress, and open up the possibility of tuning
the anisotropic properties of biocompatible nanoparticles via a controllable
exchange coupling mechanism.


title:
Ion Current as a Precise Measure of the Loading Rate of a
  Magneto-Optical Trap

abstract:
  We have demonstrated that the ion current resulting from collisions between
metastable krypton atoms in a magneto-optical trap can be used to precisely
measure the trap loading rate. We measured both the ion current of the abundant
isotope Kr-83 (isotopic abundance = 11%) and the single-atom counting rate of
the rare isotope Kr-85 (isotopic abundance ~ 1x10^-11), and found the two
quantities to be proportional at a precision level of 0.9%. This work results
in a significant improvement in using the magneto-optical trap as an analytical
tool for noble-gas isotope ratio measurements, and will benefit both atomic
physics studies and applications in the earth sciences.


title:
S-Duality and Modular Transformation as a non-perturbative deformation
  of the ordinary pq-duality

abstract:
  A recent claim that the S-duality between 4d SUSY gauge theories, which is
AGT related to the modular transformations of 2d conformal blocks, is no more
than an ordinary Fourier transform at the perturbative level, is further traced
down to the commutation relation [P,Q]=-i\hbar between the check-operator
monodromies of the exponential resolvent operator in the underlying
Dotsenko-Fateev matrix models and beta-ensembles. To this end, we treat the
conformal blocks as eigenfunctions of the monodromy check operators, what is
especially simple in the case of one-point toric block. The kernel of the
modular transformation is then defined as the intertwiner of the two
monodromies, and can be obtained straightforwardly, even when the eigenfunction
interpretation of the blocks themselves is technically tedious. In this way, we
provide an elementary derivation of the old expression for the modular kernel
for the one-point toric conformal block.


title: Standalone vertex finding in the ATLAS muon spectrometer

abstract:
  A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon
spectrometer is presented. The algorithm searches the region just upstream of
or inside the muon spectrometer volume for multi-particle vertices that
originate from the decay of particles with long decay paths. The performance of
the algorithm is evaluated using both a sample of simulated Higgs boson events,
in which the Higgs boson decays to long-lived neutral particles that in turn
decay to bb final states, and pp collision data at sqrt(s) = 7 TeV collected
with the ATLAS detector at the LHC during 2011.


title:
Sparse Linear Dynamical System with Its Application in Multivariate
  Clinical Time Series

abstract:
  Linear Dynamical System (LDS) is an elegant mathematical framework for
modeling and learning multivariate time series. However, in general, it is
difficult to set the dimension of its hidden state space. A small number of
hidden states may not be able to model the complexities of a time series, while
a large number of hidden states can lead to overfitting. In this paper, we
study methods that impose an $\ell_1$ regularization on the transition matrix
of an LDS model to alleviate the problem of choosing the optimal number of
hidden states. We incorporate a generalized gradient descent method into the
Maximum a Posteriori (MAP) framework and use Expectation Maximization (EM) to
iteratively achieve sparsity on the transition matrix of an LDS model. We show
that our Sparse Linear Dynamical System (SLDS) improves the predictive
performance when compared to ordinary LDS on a multivariate clinical time
series dataset.


title:
Dating a random walk: Statistics of the duration time of a random walk
  given its present position

abstract:
  We consider the distribution of the duration time, the time elapsed since it
began, of a diffusion process given its present position, under the assumption
that the process began at the origin. For unbiased diffusion, the distribution
does not exist (it is identically zero) for one and two dimensional systems. We
find the explicit expression for the distribution for three and higher
dimensions and discuss the behavior of the duration time statistics: we find
that the expected duration time exists only for dimensions five and higher,
whereas the variance becomes finite for seven dimensions and above. We then
turn to the case of biased diffusion. The drift velocity introduces a new time
scale and the resulting statistics arise from the interplay of the diffusive
time scale and the drift time scale. For these systems all the moments exist
and explicit expressions are presented and discussed for the expected duration
time and its variance for all dimensions.


title: Improved Bounds for Eigenpath Traversal

abstract:
  We present a bound on the length of the path defined by the ground states of
a continuous family of Hamiltonians in terms of the spectral gap G. We use this
bound to obtain a significant improvement over the cost of recently proposed
methods for quantum adiabatic state transformations and eigenpath traversal. In
particular, we prove that a method based on evolution randomization, which is a
simple extension of adiabatic quantum computation, has an average cost of order
1/G^2, and a method based on fixed-point search, has a maximum cost of order
1/G^(3/2). Additionally, if the Hamiltonians satisfy a frustration-free
property, such costs can be further improved to order 1/G^(3/2) and 1/G,
respectively. Our methods offer an important advantage over adiabatic quantum
computation when the gap is small, where the cost is of order 1/G^3.


abstract:
  In this paper the Gribov gap equation at finite temperature is analyzed. The
solutions of the gap equation (which depend explicitly on the temperature)
determine the structure of the gluon propagator within the semi-classical
Gribov approach. The present analysis is consistent with the standard
confinement scenario for low temperatures, while for high enough temperatures,
deconfinement takes place and a free gluon propagator is obtained. It also
suggests the presence of the so-called semi-quark-gluon-plasma phase in between
the confined and quark-gluon plasma phases.


title: A novel minimal in vitro system for analyzing HIV-1 Gag mediated budding

abstract:
  A biomimetic minimalist model membrane was used to study the mechanism and
kinetics of cell-free in vitro HIV-1 Gag budding from a giant unilamellar
vesicle (GUV). Real time interaction of Gag, RNA and lipid leading to the
formation of mini-vesicles was measured using confocal microscopy. Gag forms
resolution limited punctae on the GUV lipid membrane. Introduction of the Gag
and urea to a GUV solution containing RNA led to the budding of mini-vesicles
on the inside surface of the GUV. The GUV diameter showed a linear decrease in
time due to bud formation. Both bud formation and decrease in GUV size were
proportional to Gag concentration. In the absence of RNA, addition of urea to
GUVs incubated with Gag also resulted in subvesicle formation but exterior to
the surface. These observations suggest the possibility that clustering of GAG
proteins leads to membrane invagination even in the absence of host cell
proteins. The method presented here is promising, and allows for systematic
study of the dynamics of assembly of immature HIV and help classify the
hierarchy of factors that impact the Gag protein initiated assembly of
retroviruses such as HIV.


title: Reverse and dual Loomis-Whitney-type inequalities

abstract:
  Various results are proved giving lower bounds for the $m$th intrinsic volume
$V_m(K)$, $m=1,\dots,n-1$, of a compact convex set $K$ in ${\mathbb{R}}^n$, in
terms of the $m$th intrinsic volumes of its projections on the coordinate
hyperplanes (or its intersections with the coordinate hyperplanes). The bounds
are sharp when $m=1$ and $m=n-1$. These are reverse (or dual, respectively)
forms of the Loomis-Whitney inequality and versions of it that apply to
intrinsic volumes. For the intrinsic volume $V_1(K)$, which corresponds to mean
width, the inequality obtained confirms a conjecture of Betke and McMullen made
in 1983.


title: Mordell's equation : a classical approach

abstract:
  We solve the Diophantine equation $Y^2=X^3+k$ for all nonzero integers $k$
with $|k| \leq 10^7$. Our approach uses a classical connection between these
equations and cubic Thue equations. The latter can be treated algorithmically
via lower bounds for linear forms in logarithms in conjunction with
lattice-basis reduction.


title:
Heavy quarkonium fragmentation functions from a heavy quark pair. I. $S$
  wave

abstract:
  A QCD factorization formalism was recently proposed for evaluating heavy
quarkonium production at large $p_T$ at collider energies. With systematically
calculated short-distance partonic hard parts and evolution kernels of
fragmentation functions (FFs), the predictive power of this factorization
approach relies on our knowledge of a large number of universal FFs at an input
factorization scale $\mu_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$. With the
large heavy quark mass, the relative motion of the heavy quark pair inside a
heavy quarkonium is effectively non-relativistic. We evaluate these universal
input FFs using non-relativistic QCD (NRQCD) factorization, and express the
large number of FFs in terms of a few universal NRQCD long-distance matrix
elements (LDMEs) with perturbatively calculated coefficients. We derive
complete contributions to the single-parton FFs at both ${\cal O}(\alpha_s)$
and ${\cal O}(\alpha_s^2)$, and the heavy quark pair FFs at ${\cal
O}(\alpha_s)$. We present detailed derivation for all contributions involving
LDMEs of $S$-wave NRQCD $Q\bar{Q}$-states ($P$-wave contributions in a
companion paper). Our results bridge the gap between the QCD factorization
formalism and its phenomenological applications.


title: Universal central extensions of $sl_{m|n}$ over $Z/2Z$-graded algebras

abstract:
  We study central extensions of the Lie superalgebra $sl_{m|n}(A)$, where $A$
is a $Z/2Z$-graded superalgebra over a commutative ring $K$. The Steinberg Lie
superalgebra $st_{m|n}(A)$ plays a crucial role. We show that $st_{m|n}(A)$ is
a central extension of $sl_{m|n}(A)$ for $m+n\geq 3$. We use a $Z/2Z$-graded
version of cyclic homology to show that the center of the extension is
isomorphic to $HC_1(A)$ as $K$-modules. For $m+n\geq 5$, we prove that
$st_{m|n}(A)$ is the universal central extension of $sl_{m|n}(A)$. For
$m+n=3,4$, we prove that $st_{2|1}(A)$ and $st_{3|1}(A)$ are both centrally
closed. The universal central extension of $st_{2|2}(A)$ is constructed
explicitly.


title: Cross-Domain Sparse Coding

abstract:
  Sparse coding has shown its power as an effective data representation method.
However, up to now, all the sparse coding approaches are limited within the
single domain learning problem. In this paper, we extend the sparse coding to
cross domain learning problem, which tries to learn from a source domain to a
target domain with significant different distribution. We impose the Maximum
Mean Discrepancy (MMD) criterion to reduce the cross-domain distribution
difference of sparse codes, and also regularize the sparse codes by the class
labels of the samples from both domains to increase the discriminative ability.
The encouraging experiment results of the proposed cross-domain sparse coding
algorithm on two challenging tasks --- image classification of photograph and
oil painting domains, and multiple user spam detection --- show the advantage
of the proposed method over other cross-domain data representation methods.


title:
Ultracold hydrogen and deuterium production via Doppler-cooled Feshbach
  molecules

abstract:
  A counterintuitive scheme to produce ultracold hydrogen via fragmentation of
laser cooled diatomic hydrides is presented where the final atomic H
temperature is inversely proportional to the mass of the molecular parent. In
addition, the critical density for formation of a Bose-Einstein Condensate
(BEC) at a fixed temperature is reduced by a factor ratio hydrogen mass: parent
mass raised to power 3/2 over directly cooled hydrogen atoms. The narrow
Feshbach resonances between a singlet S atom and hydrogen are well suited to a
tiny center of mass energy release necessary during fragmentation. With the
support of ab initio quantum chemistry, it is demonstrated that BaH is an ideal
diatomic precursor that can be laser cooled to a Doppler temperature of ~37
microKelvin with just two rovibronic transitions, the simplest molecular
cooling scheme identified to date. Preparation of a hydrogen atom gas below the
critical BEC temperature Tc is feasible with present cooling technology, with
optical pulse control of the condensation process.


title: Degrees in oriented hypergraphs and sparse Ramsey theory

abstract:
  Let $G$ be an $r$-uniform hypergraph. When is it possible to orient the edges
of $G$ in such a way that every $p$-set of vertices has some $p$-degree equal
to $0$? (The $p$-degrees generalise for sets of vertices what in-degree and
out-degree are for single vertices in directed graphs.) Caro and Hansberg asked
if the obvious Hall-type necessary condition is also sufficient.
  Our main aim is to show that this is true for $r$ large (for given $p$), but
false in general. Our counterexample is based on a new technique in sparse
Ramsey theory that may be of independent interest.


title: Statistics of Spin Fluctuations in Quantum Dots with Ising Exchange

abstract:
  We explore the effect of single-particle level fluctuations on the Stoner
instability in a QD with a strong spin-orbit coupling in the framework of the
universal Hamiltonian with the Ising exchange interaction. We reduce the
problem to studying the statistics of extrema of a certain Gaussian process and
demonstrate that, in spite of the randomness of the single-particle levels, the
longitudinal spin susceptibility and all its moments diverge simultaneously at
the point of the Stoner instability which is determined by the standard
criterion involving the mean level spacing only.


title: Explicit rank-metric codes list-decodable with optimal redundancy

abstract:
  We construct an explicit family of linear rank-metric codes over any field
${\mathbb F}_h$ that enables efficient list decoding up to a fraction $\rho$ of
errors in the rank metric with a rate of $1-\rho-\epsilon$, for any desired
$\rho \in (0,1)$ and $\epsilon > 0$. Previously, a Monte Carlo construction of
such codes was known, but this is in fact the first explicit construction of
positive rate rank-metric codes for list decoding beyond the unique decoding
radius.
  Our codes are subcodes of the well-known Gabidulin codes, which encode
linearized polynomials of low degree via their values at a collection of
linearly independent points. The subcode is picked by restricting the message
polynomials to an ${\mathbb F}_h$-subspace that evades the structured subspaces
over an extension field ${\mathbb F}_{h^t}$ that arise in the linear-algebraic
list decoder for Gabidulin codes due to Guruswami and Xing (STOC'13). This
subspace is obtained by combining subspace designs contructed by Guruswami and
Kopparty (FOCS'13) with subspace evasive varieties due to Dvir and Lovett
(STOC'12).
  We establish a similar result for subspace codes, which are a collection of
subspaces, every pair of which have low-dimensional intersection, and which
have received much attention recently in the context of network coding. We also
give explicit subcodes of folded Reed-Solomon (RS) codes with small folding
order that are list-decodable (in the Hamming metric) with optimal redundancy,
motivated by the fact that list decoding RS codes reduces to list decoding such
folded RS codes. However, as we only list decode a subcode of these codes, the
Johnson radius continues to be the best known error fraction for list decoding
RS codes.


title:
On the characterization of infinitesimal symmetries of the relativistic
  phase space

abstract:
  The phase space of relativistic particle mechanics is defined as the 1st jet
space of motions regarded as timelike 1-dimensional submanifolds of spacetime.
A Lorentzian metric and an electromagnetic 2-form define naturally on the
odd-dimensional phase space a generalized contact structure. In the paper
infinitesimal symmetries of the phase structures are characterized. More
precisely, it is proved that all phase infinitesimal symmetries are special
Hamiltonian lifts of distinguished conserved quantities on the phase space. It
is proved that generators of infinitesimal symmetries constitute a Lie algebra
with respect to a special bracket. A momentum map for groups of symmetries of
the geometric structures is provided.


title: Robust Diffusive Proton Motions in Phase IV of Solid Hydrogen

abstract:
  Systematic first-principles molecular dynamics (MD) simulations with long
simulation times (7-13 ps) for phase IV of solid hydrogen using different
supercell sizes of 96, 288, 576, and 768 atoms established that the diffusive
proton motions process in the graphene-like layer is an intrinsic property and
independent of the simulation cell sizes. The present study highlights an often
overlook issue in first-principles calculations that long time MD is essential
to achieve ergodicity, which is mandatory for a proper description of dynamics
of a system. The present results contradict a recent work [Phys. Rev. B 87,
174110 (2013)] in which the analysis was relied on short time slices (1-3 ps).


title:
Spin-Layer Locking Effects in Optical Orientation of Exciton Spin in
  Bilayer WSe2

abstract:
  Coupling degrees of freedom of distinct nature plays a critical role in
numerous physical phenomena. The recent emergence of layered materials provides
a laboratory for studying the interplay between internal quantum degrees of
freedom of electrons. Here, we report experimental signatures of new coupling
phenomena connecting real spin with layer pseudospins in bilayer WSe2. In
polarization-resolved photoluminescence measurements, we observe large spin
orientation of neutral and charged excitons generated by both circularly and
linearly polarized light, with a splitting of the trion spectrum into a doublet
at large vertical electrical field. These observations can be explained by
locking of spin and layer pseudospin in a given valley. Because up and down
spin states are localized in opposite layers, spin relaxation is substantially
suppressed, while the doublet emerges as a manifestation of electrically
induced spin splitting resulting from the interlayer bias. The observed
distinctive behavior of the trion doublet under circularly and linearly
polarized light excitation further provides spectroscopic evidence of
interlayer and intralayer trion species, a promising step toward optical
manipulation in van der Waals heterostructures through the control of
interlayer excitons.


title:
Structures in the protoplanetary disk of HD142527 seen in polarized
  scattered light

abstract:
  We present H- and Ks-band polarized differential images (PDI) of the Herbig
Ae/Be star HD142527, revealing its optically thick outer disk and the nearly
empty gap. The very small inner working angle (~0.1") and high resolution
achievable with an 8m-class telescope, together with a careful polarimetric
calibration strategy, allow us to achieve images that surpass the quality of
previous scattered light images. Previously known substructures are resolved
more clearly and new structures are seen. Specifically, we are able to resolve
1) half a dozen spiral structures in the disk, including previously known
outer-disk spirals as well as new spiral arms and arcs close to the inner rim
of the disk; 2) peculiar holes in the polarized surface brightness at position
angles of ~0{\deg} and ~160{\deg}; 3) the inner rim on the eastern side of the
disk; 4) the gap between the outer and inner disk, ranging from the inner
working angle of 0.1" out to between 0.7 and 1.0", which is nearly devoid of
dust. We then use a Markov-chain Monte-Carlo algorithm to determine several
structural parameters of the disk, using very simple assumptions, including its
inclination, eccentricity, and the scale height of the inner rim. We compare
our results to previous work on this object, and try to produce a consistent
picture of the system and its transition disk.


title: A classification of affine fully commutative elements

abstract:
  We classify fully commutative elements in the affine Coxeter group of type
$\tilde{A_{n}}$. We give a normal form for such elements, then we propose an
application of this normal form: we lift these fully commutative elements to
the affine braid group of type $\tilde{A_{n}}$ and we get a form for "fully
commutative braids".


title: The role of logical interpretations in program development

abstract:
  Stepwise refinement of algebraic specifications is a well known formal
methodology for program development. However, traditional notions of refinement
based on signature morphisms are often too rigid to capture a number of
relevant transformations in the context of software design, reuse, and
adaptation. This paper proposes a new approach to refinement in which signature
morphisms are replaced by logical interpretations as a means to witness
refinements. The approach is first presented in the context of equational
logic, and later generalised to deductive systems of arbitrary dimension. This
allows, for example, refining sentential into equational specifications and the
latter into modal ones.


title:
Elucidating the event-by-event flow fluctuations in heavy-ion collisions
  via the event shape selection technique

abstract:
  The presence of large event-by-event flow fluctuations in heavy ion
collisions at RHIC and the LHC provides an opportunity to study a broad class
of flow observables. This paper explores the correlations among harmonic flow
coefficients $v_n$ and their phases $\Phi_n$, and the rapidity fluctuation of
$v_n$. The study is carried out usin Pb+Pb events generated by the AMPT model
with fixed impact parameter. The overall ellipticity/triangularity of events is
varied by selecting on the eccentricities $\epsilon_n$ or the magnitudes of the
flow vector $q_n$ for n=2 and 3, respectively. The responses of the $v_n$, the
event-plane correlations, and the rapidity fluctuations, to the change in
$\epsilon_n$ and $q_n$ are then systematized. Strong positive correlations are
observed among all even harmonics $v_2, v_4$, and $v_6$ (all increase with
$q_2$), between $v_2$ and $v_5$ (both increase with $q_2$) and between $v_3$
and $v_5$ (both increase with $q_3$), consistent with the effects of nonlinear
collective response. In contrast, an anti-correlation is observed between $v_2$
and $v_3$ similar to that seen between $\epsilon_2$ and $\epsilon_3$. These
correlation patterns are found to be independent of whether selecting on $q_n$
or $\epsilon_n$, validating the ability of $q_n$ in selecting the initial
geometry. A forward/backward asymmetry of $v_n(\eta)$ is observed for events
selected on $q_n$ but not on $\epsilon_n$, reflecting dynamical fluctuations
exposed by the $q_n$ selection. Many event-plane correlators show good
agreement between $q_n$ and $\epsilon_n$ selections, suggesting that their
variations with $q_n$ are controlled by the change of $\epsilon_n$ in the
initial geometry. Hence these correlators may serve as promising observables
for disentangling the fluctuations generated in various stages of the evolution
of the matter created in heavy ion collisions.


title:
Markov trace on a tower of affine Temperley-Lieb algebras of type
  $\tilde{A_{n}}$

abstract:
  We define a tower of affine Temperley-Lieb algebras of type $\tilde{A_{n}}$.
We prove that there exists a unique Markov trace on this tower, this trace
comes from the Markov-Ocneanu-Jones trace on the tower of Temperley-Lieb
algebras of type $A_{n}$.


title:
Infinite Horizon Optimal Impulsive Control Theory with Application to
  Internet Congestion Control

abstract:
  We develop Bellman equation based approach for infinite time horizon optimal
impulsive control problems. Both discounted and time average criteria are
considered. We establish very general and at the same time natural conditions
under which a canonical control triplet produces an optimal feedback policy.
Then, we apply our general results for Internet congestion control providing a
convenient setting for the design of active queue management algorithms. In
particular, our general theoretical results suggest a simple threshold-based
active queue management scheme which takes into account the main parameters of
the transmission control protocol.


title: On the Positive-Definiteness of an Anisotropic Operator

abstract:
  We study the positive-definiteness of a family of $L^2(\mathbf{R})$ integral
operators with kernel $K_{t, a}(x, y) = (1 + (x - y)^2 + a(x^2 + y^2)^t)^{-1}$,
with $t > 0$ and $a > 0$. When $0 < t \le 1$, the known theory of
positive-definite kernels ensures that the operator is positive-definite; when
$t > 1$, constructions disprove positive-definiteness for many $(t, a)$-pairs.


title:
Optomechanical Metamaterials: Dirac polaritons, Gauge fields, and
  Instabilities

abstract:
  Freestanding photonic crystals can be used to trap both light and mechanical
vibrations. These "optomechanical crystal" structures have already been
experimentally demonstrated to yield strong coupling between a photon mode and
a phonon mode, co-localized at a single defect site. Future devices may feature
a regular superlattice of such defects, turning them into "optomechanical
arrays". In this letter we predict that tailoring the optomechanical band
structure of such arrays can be used to implement Dirac physics of photons and
phonons, to create a photonic gauge field via mechanical vibrations, and to
observe a novel optomechanical instability.


title:
Perfect and robust phase-locking of a spin transfer vortex
  nano-oscillator to an external microwave source

abstract:
  We study the synchronization of the auto-oscillation signal generated by the
spin transfer driven dynamics of two coupled vortices in a spin-valve
nanopillar to an external source. Phase-locking to the microwave field hrf
occurs in a range larger than 10% of the oscillator frequency for drive
amplitudes of only a few Oersteds. Using synchronization at the double
frequency, the generation linewidth is found to decrease by more than five
orders of magnitude in the phase-locked regime (down to 1 Hz, limited by the
resolution bandwidth of the spectrum analyzer) in comparison to the free
running regime (140 kHz). This perfect phase-locking holds for frequency
detuning as large as 2 MHz, which proves its robustness. We also analyze how
the free running spectral linewidth impacts the main characteristics of the
synchronization regime.


title: Three-point Lie algebras and Grothendieck's dessins d'enfants

abstract:
  We define and classify the analogues of the affine Kac-Moody Lie algebras for
the ring corresponding to the complex projective line minus three points. The
classification is given in terms of Grothendieck's dessins d'enfants. We also
study the question of conjugacy of Cartan subalgebras for these algebras.


title:
Self-dual soliton solutions in a Chern-Simons-CP(1) model with a
  nonstandard kinetic term

abstract:
  A generalization of the Chern-Simons-CP(1) model is considered by introducing
a nonstandard kinetic term. For a particular case, of this nonstandard kinetic
term, we show that the model support self-dual Bogomolnyi equations. The BPS
energy has a bound proportional to the sum of the magnetic flux and the CP(1)
topological charge. The self-dual equations are solved analytically and
verified numerically.


title: Probabilistic and Set-based Model Invalidation and Estimation using LMIs

abstract:
  Probabilistic and set-based methods are two approaches for model
invalidation, parameter and state estimation. Both classes of methods use
different types of data, i.e. deterministic or probabilistic data, which allow
different statements and applications. Ideally, however, all available data
should be used in estimation and model invalidation methods. This paper
presents an estimation and model invalidation framework combining set-based and
probabilistically uncertain data for polynomial continuous-time systems. In
particular, uncertain data on the moments and the support is used without the
need to make explicit assumptions on the type of probability densities. The
paper derives pointwise-in-time outer approximations of the moments of the
probability densities associated with the states and parameters of the system.
These approximations can be interpreted as guaranteed confidence intervals for
the moment estimates. Furthermore, guaranteed bounds on the probability masses
on subsets are derived and allow an estimation of the unknown probability
densities. To calculate the estimates, the dynamics of the probability
densities of the state trajectories are found by occupation measures of the
nonlinear dynamics. This allows the construction of an infinite-dimensional
linear program which incorporates the set- and moment-based data. This linear
program is relaxed by a hierarchy of LMI problems providing, as shown
elsewhere, an almost uniformly convergent sequence of outer approximations of
the estimated sets. The approach is demonstrated with numerical examples.


title:
Galaxy formation on the largest scales: The impact of astrophysics on
  the BAO peak

abstract:
  We investigate the effects of galaxy formation on the baryonic acoustic
oscillations (BAO) peak by applying semi-analytic modelling techniques to the
Millennium-XXL, a $3 \times 10^{11}$ particle N-body simulation of similar
volume to the future EUCLID survey. Our approach explicitly incorporates the
effects of tidal fields and stochasticity on halo formation, as well as the
presence of velocity bias, spatially correlated merger histories, and the
connection of all these with the observable and physical properties of
galaxies. We measure significant deviations in the shape of the BAO peak from
the expectations of a linear bias model built on top of the nonlinear dark
matter distribution. We find that the galaxy correlation function shows an
excess close to the maximum of the BAO peak ($r\sim110 Mpc/h$) and a deficit at
$r\sim90 Mpc/h$. Depending on the redshift, selection criteria and number
density of the galaxy samples, these bias distortions can be up to 5% in
amplitude. They are, however, largely absorbed by marginalization over nuisance
parameters in current analytical modelling of the BAO peak in configuration
space, in particular into the parameter that controls the broadening due to
nonlinear evolution. As a result, the galaxy formation effects detected here
are unlikely to bias the high-precision measurements planned by the upcoming
generation of wide-field galaxy surveys.


title: Harmonic Maps to Buildings and Singular Perturbation Theory

abstract:
  The notion of a universal building associated with a point in the Hitchin
base is introduced. This is a building equipped with a harmonic map from a
Riemann surface that is initial among harmonic maps which induce the given
cameral cover of the Riemann surface. In the rank one case, the universal
building is the leaf space of the quadratic differential defining the point in
the Hitchin base.
  The main conjectures of this paper are: (1) the universal building always
exists; (2) the harmonic map to the universal building controls the asymptotics
of the Riemann-Hilbert correspondence and the non-abelian Hodge correspondence;
(3) the singularities of the universal building give rise to Spectral Networks;
and (4) the universal building encodes the data of a 3d Calabi-Yau category
whose space of stability conditions has a connected component that contains the
Hitchin base.
  The main theorem establishes the existence of the universal building,
conjecture (3), as well as the Riemann-Hilbert part of conjecture (2), in the
case of the rank two example introduced in the seminal work of
Berk-Nevins-Roberts on higher order Stokes phenomena. It is also shown that the
asymptotics of the Riemann-Hilbert correspondence is always controlled by a
harmonic map to a certain building, which is constructed as the asymptotic cone
of a symmetric space.


title:
A minimal lamination of the interior of a positive cone with quadratic
  curvature blowup

abstract:
  We use elementary methods to construct a minimal lamination of the interior
of a positive cone in R3.


title:
Shielded button electrodes for time-resolved measurements of electron
  cloud buildup

abstract:
  We report on the design, deployment and signal analysis for shielded button
electrodes sensitive to electron cloud buildup at the Cornell Electron Storage
Ring. These simple detectors, derived from a beam-position monitor electrode
design, have provided detailed information on the physical processes underlying
the local production and lifetime of electron densities in the storage ring.
Digitizing oscilloscopes are used to record electron fluxes incident on the
vacuum chamber wall in 1024 time steps of 100 ps or more. The fine time steps
provide a detailed characterization of the cloud, allowing the independent
estimation of processes contributing on differing time scales and providing
sensitivity to the characteristic kinetic energies of the electrons making up
the cloud. By varying the spacing and population of electron and positron beam
bunches, we map the time development of the various cloud production and
re-absorption processes. The excellent reproducibility of the measurements also
permits the measurement of long-term conditioning of vacuum chamber surfaces.


title:
Topological insulators and the QCD vacuum: the theta parameter as a
  Berry phase

abstract:
  There is considerable evidence, based on large $N_c$ chiral dynamics,
holographic QCD, and Monte Carlo studies, that the QCD vacuum is permeated by
discrete quasivacua separated by domain walls across which the local value of
the topological $\theta$ parameter jumps by $\pm2\pi$. In the 2-dimensional
$CP^{N-1}$ sigma model, a pointlike charge is a domain wall, and $\theta$
describes the background electric flux and the polarization of charged pairs in
the vacuum. We show that the screening process, and the role of $\theta$ as an
order parameter describing electric polarization, are naturally formulated in
terms of Bloch wave eigenstates of the Dirac Hamiltonian in the background
gauge field. This formulation is similar to the Berry phase description of
electric polarization and quantized charge transport in topological insulators.
The Bloch waves are quasiperiodic superpositions of localized Dirac zero modes.
They define a Berry connection around the Brillouin zone of the zero mode band
which describes the local polarization of vacuum pairs, analogous to its role
in topological insulator theory. In 4D Yang-Mills theory, the $\theta$ domain
walls are 2+1-dimensional Chern-Simons membranes. The interpretation of the
$\theta$ parameter as a Berry phase describing the local polarization of
brane-antibrane pairs follows from the descent equations of 4D Yang-Mills
theory.


title:
Deterministic Approximate Counting for Degree-$2$ Polynomial Threshold
  Functions

abstract:
  We give a {\em deterministic} algorithm for approximately computing the
fraction of Boolean assignments that satisfy a degree-$2$ polynomial threshold
function. Given a degree-2 input polynomial $p(x_1,\dots,x_n)$ and a parameter
$\eps > 0$, the algorithm approximates \[ \Pr_{x \sim \{-1,1\}^n}[p(x) \geq 0]
\] to within an additive $\pm \eps$ in time $\poly(n,2^{\poly(1/\eps)})$. Note
that it is NP-hard to determine whether the above probability is nonzero, so
any sort of multiplicative approximation is almost certainly impossible even
for efficient randomized algorithms. This is the first deterministic algorithm
for this counting problem in which the running time is polynomial in $n$ for
$\eps= o(1)$. For "regular" polynomials $p$ (those in which no individual
variable's influence is large compared to the sum of all $n$ variable
influences) our algorithm runs in $\poly(n,1/\eps)$ time. The algorithm also
runs in $\poly(n,1/\eps)$ time to approximate $\Pr_{x \sim N(0,1)^n}[p(x) \geq
0]$ to within an additive $\pm \eps$, for any degree-2 polynomial $p$.
  As an application of our counting result, we give a deterministic FPT
multiplicative $(1 \pm \eps)$-approximation algorithm to approximate the $k$-th
absolute moment $\E_{x \sim \{-1,1\}^n}[|p(x)^k|]$ of a degree-2 polynomial.
The algorithm's running time is of the form $\poly(n) \cdot f(k,1/\eps)$.


title:
Enhancement of electron spin lifetime in GaAs crystals: the benefits of
  dichotomous noise

abstract:
  The electron spin relaxation process in n-type GaAs crystals driven by a
fluctuating electric field is investigated. Two different sources of
fluctuations are considered: (i) a symmetric dichotomous noise and (ii) a
Gaussian correlated noise. Monte Carlo numerical simulations show, in both
cases, an enhancement of the spin relaxation time by increasing the amplitude
of the external noise. Moreover, we find that the electron spin lifetime versus
the noise correlation time: (i) increases up to a plateau in the case of
dichotomous random fluctuations, and (ii) shows a nonmonotonic behaviour with a
maximum in the case of bulks subjected to a Gaussian correlated noise.


title: Higgs Mediation with Strong Hidden Sector Dynamics

abstract:
  We present a simple model that achieves $m_h\approx 126$ GeV in the MSSM with
large $A$-terms and TeV-scale stops through a combination of gauge mediation
and Higgs-messenger interactions. The $\mu$/$B_\mu$ and $A$/$m_H^2$ problems
are both solved by a common mechanism -- partial sequestering from strong
hidden sector dynamics. Using the framework of General Messenger Higgs
Mediation, we explicitly calculate the soft masses in terms of the vacuum
expectation values, operator dimensions and OPE coefficients of the
strongly-coupled hidden sector. Along the way, we also present a general
analysis of the various constraints on sequestered Higgs mediation models. The
phenomenology of such models is similar to gaugino mediation, but with large
$A$-terms. The NLSP is always long-lived and is either the lightest stau or the
Higgsino. The colored states are typically out of reach of the 8 TeV LHC, but
may be accessible at 14 TeV, especially if the NLSP is the lightest stau.


title: Doping icosahedral Fe$_{13}$ with 3d transition elements

abstract:
  Our density functional theory calculations for Fe_{13-n}M_{n} for M = Sc, Ti,
V, Cr, Mn, Co, Ni, and Cu up to n = 4 show that the icosahedral symmetry of
Fe13, albeit minor changes in bond lengths, is robust despite doping and is
retained for all homotops of Mn, Co, Ni and Cu. Based on analysis of density of
states of the doped cluster, adsorption of carbon atom, and adhesion energies
for fragments of single walled carbon nanotubes, we propose a core-shell type
structure with a central Mn atom surrounded by Fe surface shell atoms as the
most favorable doped nanocatalyst for SWCNT nucleation and growth subject to
constraints of retention of icosahedral symmetry by the doped cluster. For
doping beyond the central atom involving the surface shell of the icosahedron,
Ni is the best candidate.


title: Bound State Effect on the Electron g-2

abstract:
  We evaluate a non-perturbative QED contribution to the electron g-2 which
comes from virtual positronium. We find it to be 9.0*10^{-14}. This value is
comparable to the five-loop contribution of usual perturbative calculation, and
several times larger than the electroweak correction.


title:
On the Pursuit of Generalizations for the Petrov Classification and the
  Goldberg-Sachs Theorem

abstract:
  The Petrov classification is an important algebraic classification for the
Weyl tensor valid in 4-dimensional space-times. In this thesis such
classification is generalized to manifolds of arbitrary dimension and
signature. This is accomplished by interpreting the Weyl tensor as a linear
operator on the bundle of p-forms, for any p, and computing the Jordan
canonical form of this operator. Throughout this work the spaces are assumed to
be complexified, so that different signatures correspond to different reality
conditions, providing a unified treatment. A higher-dimensional generalization
of the so-called self-dual manifolds is also investigated.
  The most important result related to the Petrov classification is the
Goldberg-Sachs theorem. Here are presented two partial generalizations of such
theorem valid in even-dimensional manifolds. One of these generalizations
states that certain algebraic constraints on the Weyl operator imply the
existence of an integrable maximally isotropic distribution. The other version
of the generalized Goldberg-Sachs theorem states that these algebraic
constraints imply the existence of a null congruence whose optical scalars obey
special restrictions.
  On the pursuit of these results the spinorial formalism in 6 dimensions was
developed from the very beginning, using group representation theory. Since the
spinors are full of geometric significance and are suitable tools to deal with
isotropic structures, it should not come as a surprise that they provide a
fruitful framework to investigate the issues treated on this thesis. In
particular, the generalizations of the Goldberg-Sachs theorem acquire an
elegant form in terms of the pure spinors.


title:
An experimental algorithm for identifying the topological nature of
  Kondo and mixed valence insulators

abstract:
  Possible topological nature of Kondo and mixed valence insulators has been a
recent topic of interest in condensed matter physics. Attention has focused on
SmB6, which has long been known to exhibit low temperature transport anomaly,
whose origin is of independent interest. We argue that it is possible to
resolve the topological nature of surface states by uniquely accessing the
surface electronic structure of the low temperature anomalous transport regime
through combining state-of-the-art laser- and synchrotron-based angle-resolved
photoemission spectroscopy (ARPES) with or without spin resolution. A
combination of low temperature and ultra-high resolution (laser) which is
lacking in previous ARPES studies of this compound is the key to resolve the
possible existence of topological surface state in SmB6. Here we outline an
experimental algorithm to systematically explore the topological versus trivial
or mixed (topological and trivial surface state admixture as in the first 3D TI
Bi$_{1-x}$Sb$_x$) nature of the surface states in Kondo and mixed valence
insulators. We conclude based on this methodology that the observed topology of
the surface Fermi surface in our low temperature data considered within the
level of current resolution is consistent with the theoretically predicted
topological picture, suggesting a topological origin of the dominant in-gap
ARPES signal in SmB6.}


title: N-body lensed CMB maps: lensing extraction and characterization

abstract:
  We reconstruct shear maps and angular power spectra from simulated weakly
lensed total intensity (TT) and polarised (EB) maps of the Cosmic Microwave
Background (CMB) anisotropies, obtained using Born approximated ray-tracing
through the N-body simulated Cold Dark Matter (CDM) structures in the
Millennium Simulations (MS). We compare the recovered signal with the
$\Lambda$CDM prediction, on the whole interval of angular scales which is
allowed by the finite box size, extending from the degree scale to the
arcminute, by applying a quadratic estimator in the flat sky limit; we consider
PRISM-like instrumental specification for future generation CMB satellites,
corresponding to arcminute angular resolution of 3.2' and sensitivity of 2.43
${\mu}$K-arcmin. -arcmin. The noise bias in the simulations closely follows the
estimator prediction, becoming dominated by limits in the angular resolution
for the EB signal, at l${\simeq}$1500. The de-biased signal shows no visible
departure from predictions of the weak lensing power within uncertainties, when
considering TT and EB data singularly. In particular, the reconstruction
precision reaches the level of a few percent in bins with $\Delta$l
${\simeq}$100 in the angular multiple interval 1000<l<2000 for TT, and about
10$%$ for EB. Within the adopted specifications, polarisation data do represent
a significant contribution to the lensing shear, which appear to faithfully
trace the underlying N-body structure down to the smallest angular scales
achievable with the present setup, validating at the same time the latter with
respect to semi-analytical predictions from ${\Lambda}$CDM cosmology at the
level of CMB lensing statistics. This work demonstrates the feasibility of CMB
lensing studies based on large scale simulations of cosmological structure
formation in the context of the current and future high resolution and
sensitivity CMB experiment.


title: Systematic Codes for Rank Modulation

abstract:
  The goal of this paper is to construct systematic error-correcting codes for
permutations and multi-permutations in the Kendall's $\tau$-metric. These codes
are important in new applications such as rank modulation for flash memories.
The construction is based on error-correcting codes for multi-permutations and
a partition of the set of permutations into error-correcting codes. For a given
large enough number of information symbols $k$, and for any integer $t$, we
present a construction for ${(k+r,k)}$ systematic $t$-error-correcting codes,
for permutations from $S_{k+r}$, with less redundancy symbols than the number
of redundancy symbols in the codes of the known constructions. In particular,
for a given $t$ and for sufficiently large $k$ we can obtain $r=t+1$. The same
construction is also applied to obtain related systematic error-correcting
codes for multi-permutations.


title:
Local operator partitioning of electronic energy for electronic energy
  transfer: An efficient algorithm

abstract:
  An efficient computational algorithm to implement a local operator approach
to partitioning electronic energy in general molecular systems is presented.
This approach, which rigorously defines the electronic energy on any subsystem
within a molecule, gives a precise meaning to the subsystem ground and excited
electronic energies, which is crucial for investigating electronic energy
transfer from first principles. We apply the technique to the
$9-$(($1-$naphthyl)$-$methyl)-anthracene (A1N) molecule by partitioning A1N
into anthracenyl and CH$_2-$naphthyl groups as subsystems, and examine their
electronic energies and populations for several excited states using
Configuration Interaction Singles method. The implemented approach shows a wide
variety of different behaviors amongst these excited electronic states.


title:
Deterministic Approximate Counting for Juntas of Degree-$2$ Polynomial
  Threshold Functions

abstract:
  Let $g: \{-1,1\}^k \to \{-1,1\}$ be any Boolean function and $q_1,\dots,q_k$
be any degree-2 polynomials over $\{-1,1\}^n.$ We give a \emph{deterministic}
algorithm which, given as input explicit descriptions of $g,q_1,\dots,q_k$ and
an accuracy parameter $\eps>0$, approximates \[\Pr_{x \sim
\{-1,1\}^n}[g(\sign(q_1(x)),\dots,\sign(q_k(x)))=1]\] to within an additive
$\pm \eps$. For any constant $\eps > 0$ and $k \geq 1$ the running time of our
algorithm is a fixed polynomial in $n$. This is the first fixed polynomial-time
algorithm that can deterministically approximately count satisfying assignments
of a natural class of depth-3 Boolean circuits.
  Our algorithm extends a recent result \cite{DDS13:deg2count} which gave a
deterministic approximate counting algorithm for a single degree-2 polynomial
threshold function $\sign(q(x)),$ corresponding to the $k=1$ case of our
result.
  Our algorithm and analysis requires several novel technical ingredients that
go significantly beyond the tools required to handle the $k=1$ case in
\cite{DDS13:deg2count}. One of these is a new multidimensional central limit
theorem for degree-2 polynomials in Gaussian random variables which builds on
recent Malliavin-calculus-based results from probability theory. We use this
CLT as the basis of a new decomposition technique for $k$-tuples of degree-2
Gaussian polynomials and thus obtain an efficient deterministic approximate
counting algorithm for the Gaussian distribution. Finally, a third new
ingredient is a "regularity lemma" for \emph{$k$-tuples} of degree-$d$
polynomial threshold functions. This generalizes both the regularity lemmas of
\cite{DSTW:10,HKM:09} and the regularity lemma of Gopalan et al \cite{GOWZ10}.
Our new regularity lemma lets us extend our deterministic approximate counting
results from the Gaussian to the Boolean domain.


title: Dirac Sigma Models from Gauging

abstract:
  The G/G WZW model results from the WZW-model by a standard procedure of
gauging. G/G WZW models are members of Dirac sigma models, which also contain
twisted Poisson sigma models as other examples. We show how the general class
of Dirac sigma models can be obtained from a gauging procedure adapted to Lie
algebroids in the form of an equivariantly closed extension. The rigid gauge
groups are generically infinite dimensional and a standard gauging procedure
would give a likewise infinite number of 1-form gauge fields; the proposed
construction yields the requested finite number of them.
  Although physics terminology is used, the presentation is kept accessible
also for a mathematical audience.


title: Secret Sharing using Non-Commutative Groups and the Shortlex Order

abstract:
  In this paper we review the Habeeb-Kahrobaei-Shpilrain secret sharing scheme
and introduce a variation based on the shortlex order on a free group. Drawing
inspiration from adjustments to classical schemes, we also present a method
that allows for the protocol to remain secure after multiple secrets are
shared.


title: Adaptive Sensing for Estimation of Structured Sparse Signals

abstract:
  In many practical settings one can sequentially and adaptively guide the
collection of future data, based on information extracted from data collected
previously. These sequential data collection procedures are known by different
names, such as sequential experimental design, active learning or adaptive
sensing/sampling. The intricate relation between data analysis and acquisition
in adaptive sensing paradigms can be extremely powerful, and often allows for
reliable signal estimation and detection in situations where non-adaptive
sensing would fail dramatically.
  In this work we investigate the problem of estimating the support of a
structured sparse signal from coordinate-wise observations under the adaptive
sensing paradigm. We present a general procedure for support set estimation
that is optimal in a variety of cases and shows that through the use of
adaptive sensing one can: (i) mitigate the effect of observation noise when
compared to non-adaptive sensing and, (ii) capitalize on structural information
to a much larger extent than possible with non-adaptive sensing. In addition to
a general procedure to perform adaptive sensing in structured settings we
present both performance upper bounds, and corresponding lower bounds for both
sensing paradigms.


title: Continuous Centrifuge Decelerator for Polar Molecules

abstract:
  Producing large samples of slow molecules from thermal-velocity ensembles is
a formidable challenge. Here we employ a centrifugal force to produce a
continuous molecular beam with a high flux at near-zero velocities. We
demonstrate deceleration of three electrically guided molecular species,
CH$_3$F, CF$_3$H, and CF$_3$CCH, with input velocities of up to
$200\,\rm{m\,s^{-1}}$ to obtain beams with velocities below
$15\,\rm{m\,s^{-1}}$ and intensities of several $10^9\,\rm{mm^{-2}\,s^{-1}}$.
The centrifuge decelerator is easy to operate and can, in principle, slow down
any guidable particle. It has the potential to become a standard technique for
continuous deceleration of molecules.


title:
On maximal inequalities for purely discontinuous $L_q$-valued
  martingales

abstract:
  We prove maximal inequalities for $L_q$-valued martingales obtained by
stochastic integration with respect to compensated random measures. A version
of these estimates for integrals with respect to compensated Poisson random
measures were first obtained by Dirksen (arXiv:1208:3885) using arguments based
on inequalities for sums of independent Banach-space-valued random variables,
geometric properties of Banach spaces, and decoupling inequalities. Our proofs
are completely different and rely almost exclusively on classical stochastic
analysis for real semimartingales.


title:
Gibbs u-states for the foliated geodesic flow and transverse invariant
  measures

abstract:
  This paper is devoted to the study of Gibbs u-states for the geodesic flow
tangent to a foliation with negatively curved leaves. On the one hand we give
sufficient conditions for the existence of transverse invariant measures. In
particular we prove that when this foliated geodesic flow preserves a Gibbs
su-state, i.e. a measure with Lebesgue disintegration both in the stable and
unstable horospheres, then it has to be obtained by combining a transverse
invariant measure and the Liouville measure on the leaves. On the other hand we
study in detail the projections of Gibbs u-states along the unit spheres
tangent to the foliation. We show that they have Lebesgue disintegration in the
leaves and that the local densities possess an integral representation analogue
to the Poisson representation of harmonic functions.


title: A Survival Copula Mixture Model for Comparing Two Genomic Rank Lists

abstract:
  Analyses of high-throughput genomic data often lead to ranked lists of
genomic loci. How to characterize concordant signals between two rank lists is
a common problem with many applications. One example is measuring the
reproducibility between two replicate experiments. Another is to characterize
the interaction and co-binding between two transcription factors (TF) based on
the overlap between their binding sites. As an exploratory tool, the simple
Venn diagram approach can be used to show the common loci between two lists.
However, this approach does not account for changes in overlap with decreasing
ranks, which may contain useful information for studying similarities or
dissimilarities of the two lists. The recently proposed irreproducible
discovery rate (IDR) approach compares two rank lists using a copula mixture
model. This model considers the rank correlation between two lists. However, it
only analyzes the genomic loci that appear in both lists, thereby only
measuring signal concordance in the overlapping set of the two lists. When two
lists have little overlap but loci in their overlapping set have high
concordance in terms of rank, the original IDR approach may misleadingly claim
that the two rank lists are highly reproducible when they are indeed not. In
this article, we propose to address the various issues above by translating the
problem into a bivariate survival problem. A survival copula mixture model is
developed to characterize concordant signals in two rank lists. The
effectiveness of this approach is demonstrated using both simulations and real
data.


title: Completed power operations for Morava E-theory

abstract:
  We construct and study an algebraic theory which closely approximates the
theory of power operations for Morava E-theory, extending previous work of
Charles Rezk in a way that takes completions into account. These algebraic
structures are made explicit in the case of K-theory. Methodologically, we
emphasize the utility of flat modules in this context, and prove a general
version of Lazard's flatness criterion for module spectra over associative ring
spectra.


title: Secondary Hochschild Cohomology

abstract:
  In this paper we define a new cohomology theory for a $B$-algebra $A$. We use
this cohomology to study deformations of algebras $A[[t]]$, that have a
$B$-algebra structure.


title: Non-semistable exceptional objects in hereditary categories

abstract:
  For a given stability condition $\sigma$ on a triangulated category we define
a $\sigma$-exceptional collection as an Ext-exceptional collection, whose
elements are $\sigma$-semistable with phases contained in an open interval of
length one. If there exists a full $\sigma$-exceptional collection, then
$\sigma$ is generated by this collection in a procedure described by E.
Macr\`i.
  Constructing $\sigma$-exceptional collections of length at least three in
$D^b(\mathcal A)$ from a non-semistable exceptional object, where $\mathcal A$
is a hereditary hom-finite abelian category, we introduce certain conditions on
the Ext-nontrivial couples (couples of exceptional objects $X,Y\in \mathcal A$
with ${\rm Ext}^1(X,Y)\neq 0$ and ${\rm Ext}^1(Y,X)\neq 0$).
  After a detailed study of the exceptional objects of two tame quivers $Q_1$
and $Q_2$ with three and four vertices, respectively, we observe that the
needed conditions do hold in $Rep_k(Q_1)$, $Rep_k(Q_2)$, where $k$ is an
algebraically closed field.
  Combining these findings, we prove that for each $\sigma\in {\rm
Stab}(D^b(Q_1))$ there exists a full $\sigma$-exceptional collection. It
follows that ${\rm Stab}(D^b(Q_1))$ is connected.


title: Local Central Limit Theorem for Determinantal Point Processes

abstract:
  We prove a local central limit theorem (LCLT) for the number of points $N(J)$
in a region $J$ in $\mathbb R^d$ specified by a determinantal point process
with an Hermitian kernel. The only assumption is that the variance of $N(J)$
tends to infinity as $|J| \to \infty$. This extends a previous result giving a
weaker central limit theorem (CLT) for these systems. Our result relies on the
fact that the Lee-Yang zeros of the generating function for $\{E(k;J)\}$ ---
the probabilities of there being exactly $k$ points in $J$ --- all lie on the
negative real $z$-axis. In particular, the result applies to the scaled bulk
eigenvalue distribution for the Gaussian Unitary Ensemble (GUE) and that of the
Ginibre ensemble. For the GUE we can also treat the properly scaled edge
eigenvalue distribution. Using identities between gap probabilities, the LCLT
can be extended to bulk eigenvalues of the Gaussian Symplectic Ensemble (GSE).
A LCLT is also established for the probability density function of the $k$-th
largest eigenvalue at the soft edge, and of the spacing between $k$-th neigbors
in the bulk.


title:
The wave-function is real but nonphysical: A view from counterfactual
  quantum cryptography

abstract:
  Counterfactual quantum cryptography (CQC) is used here as a tool to assess
the status of the quantum state: Is it real/ontic (an objective state of
Nature) or epistemic (a state of the observer's knowledge)? In contrast to
recent approaches to wave function ontology, that are based on realist models
of quantum theory, here we recast the question as a problem of communication
between a sender (Bob), who uses interaction-free measurements, and a receiver
(Alice), who observes an interference pattern in a Mach-Zehnder set-up. An
advantage of our approach is that it allows us to define the concept of
"physical", apart from "real". In instances of counterfactual quantum
communication, reality is ascribed to the interaction-freely measured wave
function ($\psi$) because Alice deterministically infers Bob's measurement. On
the other hand, $\psi$ does not correspond to the physical transmission of a
particle because it produced no detection on Bob's apparatus. We therefore
conclude that the wave function in this case (and by extension, generally) is
real, but not physical. Characteristically for classical phenomena, the reality
and physicality of objects are equivalent, whereas for quantum phenomena, the
former is strictly weaker. As a concrete application of this idea, the
nonphysical reality of the wavefunction is shown to be the basic nonclassical
phenomenon that underlies the security of CQC.


title:
Structured chaos shapes spike-response noise entropy in balanced neural
  networks

abstract:
  Large networks of sparsely coupled, excitatory and inhibitory cells occur
throughout the brain. A striking feature of these networks is that they are
chaotic. How does this chaos manifest in the neural code? Specifically, how
variable are the spike patterns that such a network produces in response to an
input signal? To answer this, we derive a bound for the entropy of multi-cell
spike pattern distributions in large recurrent networks of spiking neurons
responding to fluctuating inputs. The analysis is based on results from random
dynamical systems theory and is complimented by detailed numerical simulations.
We find that the spike pattern entropy is an order of magnitude lower than what
would be extrapolated from single cells. This holds despite the fact that
network coupling becomes vanishingly sparse as network size grows -- a
phenomenon that depends on ``extensive chaos," as previously discovered for
balanced networks without stimulus drive. Moreover, we show how spike pattern
entropy is controlled by temporal features of the inputs. Our findings provide
insight into how neural networks may encode stimuli in the presence of
inherently chaotic dynamics.


title:
Concise Security Bounds for Practical Decoy-State Quantum Key
  Distribution

abstract:
  Due to its ability to tolerate high channel loss, decoy-state quantum key
distribution (QKD) has been one of the main focuses within the QKD community.
Notably, several experimental groups have demonstrated that it is secure and
feasible under real-world conditions. Crucially, however, the security and
feasibility claims made by most of these experiments were obtained under the
assumption that the eavesdropper is restricted to particular types of attacks
or that the finite-key effects are neglected. Unfortunately, such assumptions
are not possible to guarantee in practice. In this work, we provide concise and
tight finite-key security bounds for practical decoy-state QKD that are valid
against general attacks.


title: Convex Optimal Uncertainty Quantification

abstract:
  Optimal uncertainty quantification (OUQ) is a framework for numerical
extreme-case analysis of stochastic systems with imperfect knowledge of the
underlying probability distribution. This paper presents sufficient conditions
under which an OUQ problem can be reformulated as a finite-dimensional convex
optimization problem, for which efficient numerical solutions can be obtained.
The sufficient conditions include that the objective function is piecewise
concave and the constraints are piecewise convex. In particular, we show that
piecewise concave objective functions may appear in applications where the
objective is defined by the optimal value of a parameterized linear program.


title: Determining the structure of dark-matter couplings at the LHC

abstract:
  The latest LHC mono-jet searches place stringent bounds on the pp -> chibar
chi cross section of dark matter. Further properties such as the dark matter
mass or the precise structure of the interactions between dark matter and the
standard model can however not be determined in this manner. We point out that
measurements of the azimuthal angle correlations between the two jets in 2 j +
chibar chi events may be used to disentangle whether dark matter pair
production proceeds dominantly through tree or loop diagrams. Our general
observation is illustrated by considering theories in which dark matter
interacts predominantly with the top quark. We show explicitly that in this
case the jet-jet azimuthal angle difference is a gold-plated observable to
probe the Lorentz structure of the couplings of dark matter to top quarks, thus
testing the CP nature of the particle mediating these interactions.


title: Cosmic String Loop Microlensing

abstract:
  Cosmic superstring loops within the galaxy microlens background point sources
lying close to the observer-string line of sight. For suitable alignments,
multiple paths coexist and the (achromatic) flux enhancement is a factor of
two. We explore this unique type of lensing by numerically solving for
geodesics that extend from source to observer as they pass near an oscillating
string. We characterize the duration of the flux doubling and the scale of the
image splitting. We probe and confirm the existence of a variety of fundamental
effects predicted from previous analyses of the static infinite straight
string: the deficit angle, the Kaiser-Stebbins effect, and the scale of the
impact parameter required to produce microlensing. Our quantitative results for
dynamical loops vary by O(1) factors with respect to estimates based on
infinite straight strings for a given impact parameter. A number of new
features are identified in the computed microlensing solutions. Our results
suggest that optical microlensing can offer a new and potentially powerful
methodology for searches for superstring loop relics of the inflationary era.


title: Weyl semimetals with short-range interactions

abstract:
  We construct a low-energy effective field theory of electrons interacting via
short-range interactions in a Weyl semimetal and investigate possible
broken-symmetry ground states through an unbiased one-loop renormalization
group (RG) analysis. Using the symmetries of the noninteracting Weyl semimetal
to constrain the form of the interaction term leads to four independent
coupling constants. We investigate the stability of RG flows towards strong
coupling and find a single stable trajectory. In order to determine the most
likely broken-symmetry ground state, we calculate susceptibilities in the
particle-hole and particle-particle channels along this trajectory and find
that the leading instability is towards a fully gapped spin-density wave (SDW)
ground state. The sliding mode of this SDW couples to the external
electromagnetic fields like the Peccei-Quinn axion field of particle physics.
We also study a maximally symmetric toy model of an interacting Weyl semimetal
with a single independent coupling constant. The most likely ground states in
this case are either gapless ferromagnetic states where the spin waves couple
to the Weyl fermions like the spatial components of a (possibly chiral) gauge
field, or a fully gapped spin-singlet Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
superconducting state.


title: The Zeldovich approximation: key to understanding Cosmic Web complexity

abstract:
  We describe how the dynamics of cosmic structure formation defines the
intricate geometric structure of the spine of the cosmic web. The Zeldovich
approximation is used to model the backbone of the cosmic web in terms of its
singularity structure. The description by Arnold et al. (1982) in terms of
catastrophe theory forms the basis of our analysis.
  This two-dimensional analysis involves a profound assessment of the
Lagrangian and Eulerian projections of the gravitationally evolving
four-dimensional phase-space manifold. It involves the identification of the
complete family of singularity classes, and the corresponding caustics that we
see emerging as structure in Eulerian space evolves. In particular, as it is
instrumental in outlining the spatial network of the cosmic web, we investigate
the nature of spatial connections between these singularities.
  The major finding of our study is that all singularities are located on a set
of lines in Lagrangian space. All dynamical processes related to the caustics
are concentrated near these lines. We demonstrate and discuss extensively how
all 2D singularities are to be found on these lines. When mapping this spatial
pattern of lines to Eulerian space, we find a growing connectedness between
initially disjoint lines, resulting in a percolating network. In other words,
the lines form the blueprint for the global geometric evolution of the cosmic
web.


title: The BATSE 5B Gamma-Ray Burst Spectral Catalog

abstract:
  We present systematic spectral analyses of GRBs detected with the Burst and
Transient Source Experiment (BATSE) onboard the Compton Gamma-Ray Observatory
(CGRO) during its entire nine years of operation. This catalog contains two
types of spectra extracted from 2145 GRBs and fitted with five different
spectral models resulting in a compendium of over 19000 spectra. The models
were selected based on their empirical importance to the spectral shape of many
GRBs, and the analysis performed was devised to be as thorough and objective as
possible. We describe in detail our procedures and criteria for the analyses,
and present the bulk results in the form of parameter distributions. This
catalog should be considered an official product from the BATSE Science Team,
and the data files containing the complete results are available from the
High-Energy Astrophysics Science Archive Research Center (HEASARC).


title: Dynamical signature of edge state in the 1D Aubry-Andr\'{e} model

abstract:
  Topological feature has become an intensively studied subject in many fields
of physics. As a witness of topological phase, the edge states are
topologically protected and may be helpful in quantum information processing.
In this paper, we define a measure to quantify the dynamical localization of
system and simulate the localization in the 1D Aubry-Andr\'{e} model. We find
an interesting connection between the edge states and the dynamical
localization of the system, this connection may be used as a signature of edge
state and topological phase.


title:
Deformations of the vacuum solutions of general relativity subjected to
  linear constraints

abstract:
  The problem of deforming geometries is particularly important in the context
of constructing new exact solutions of Einstein's equation. This issue often
appears when extensions of the general relativity are treated, for instance in
brane world scenarios. In this paper we investigate spacetimes in which the
energy-momentum tensor obeys a linear constraint. Extensions of the usual
vacuum and electrovacuum solutions of general relativity are derived and an
exact solution is presented. The classes of geometries obtained include a wide
variety of compact objects, among them black holes and wormholes. The general
metric derived in this work generalizes several solutions already published in
the literature. Perturbations around the exact solution are also considered.


title: On the ion-mediated interaction between protein and DNA

abstract:
  The mechanism allowing a protein to search of a target sequence on DNA is
currently described as an intermittent process composed of 3D diffusion in bulk
and 1D diffusion along the DNA molecule. Due to the relevant charge of protein
and DNA, electrostatic interaction should play a crucial role during this
search. In this paper, we explicitly derive the mean field theory allowing for
a description of the protein-DNA electrostatics in solution. This approach
leads to a unified model of the search process, where 1D and 3D diffusion
appear as a natural consequence of the diffusion on an extended interaction
energy profile.


title:
Introduction to Neutrosophic Measure, Neutrosophic Integral, and
  Neutrosophic Probability

abstract:
  In this paper, we introduce for the first time the notions of neutrosophic
measure and neutrosophic integral, and we develop the 1995 notion of
neutrosophic probability. We present many practical examples. It is possible to
define the neutrosophic measure and consequently the neutrosophic integral and
neutrosophic probability in many ways, because there are various types of
indeterminacies, depending on the problem we need to solve. Neutrosophics study
the indeterminacy. Indeterminacy is different from randomness. It can be caused
by physical space materials and type of construction, by items involved in the
space, etc.


title: Evolution at two levels of gene expression in yeast

abstract:
  Despite the greater functional importance of protein levels, our knowledge of
gene expression evolution is based almost entirely on studies of mRNA levels.
In contrast, our understanding of how translational regulation evolves has
lagged far behind. Here we have applied ribosome profiling - which measures
both global mRNA levels and their translation rates - to two species of
Saccharomyces yeast and their interspecific hybrid in order to assess the
relative contributions of changes in mRNA abundance and translation to
regulatory evolution. We report that both cis and trans-acting regulatory
divergence in translation are abundant, affecting at least 35% of genes. The
majority of translational divergence acts to buffer changes in mRNA abundance,
suggesting a widespread role for stabilizing selection acting across regulatory
levels. Nevertheless, we observe evidence of lineage-specific selection acting
on a number of yeast functional modules, including instances of reinforcing
selection acting at both levels of regulation. Finally, we also uncover
multiple instances of stop-codon readthrough that are conserved between
species. Our analysis reveals the under-appreciated complexity of
post-transcriptional regulatory divergence and indicates that partitioning the
search for the locus of selection into the binary categories of 'coding' vs.
'regulatory' may overlook a significant source of selection, acting at multiple
regulatory levels along the path from genotype to phenotype.


title: The VAST Survey - III. The multiplicity of A-type stars within 75 pc

abstract:
  With a combination of adaptive optics imaging and a multi-epoch common proper
motion search, we have conducted a large volume-limited (D $\le$ 75 pc)
multiplicity survey of A-type stars, sensitive to companions beyond 30 au. The
sample for the Volume-limited A-STar (VAST) survey consists of 435 A-type
stars: 363 stars were observed with adaptive optics, 228 stars were searched
for wide common proper motion companions and 156 stars were measured with both
techniques. The projected separation coverage of the VAST survey extends from
30 to 45,000 au. A total of 137 stellar companions were resolved, including 64
new detections from the VAST survey, and the companion star fraction, projected
separation distribution and mass ratio distribution were measured. The
separation distribution forms a log-normal distribution similar to the
solar-type binary distribution, but with a peak shifted to a significantly
wider value of 387 (+132,-98) au. Integrating the fit to the distribution over
the 30 to 10,000 au observed range, the companion star fraction for A-type
stars is estimated as 33.8%+-2.6%. The mass ratio distribution of closer (<125
au) binaries is distinct from that of wider systems, with a flat distribution
for close systems and a distribution that tends towards smaller mass ratios for
wider binaries. Combining this result with previous spectroscopic surveys of
A-type stars gives an estimate of the total companion star fraction of
68.9%+-7.0%. The most complete assessment of higher order multiples was
estimated from the 156-star subset of the VAST sample with both adaptive optics
and common proper motion measurements, combined with a literature search for
companions, yielding a lower limit on the frequency of single, binary, triple,
quadruple and quintuple A-type star systems of 56.4 (-4.0,+3.8), 32.1
(-3.5,+3.9), 9.0 (-1.8,+2.8), 1.9 (-0.6,+1.8) and 0.6 (-0.2,+1.4) per cent,
respectively.


title: Point-to-set correlations and instantons

abstract:
  For a generic many-body system, we define a soft point-to-set correlation
function. We then show that this function accepts a representation in terms of
an effective overlap field theory. In particular, instantons in this effective
field theory encode point-to-set correlations for supercooled liquids.


title: Hyperkahler Metrics from Monopole Walls

abstract:
  We present ALH hyperkahler metrics induced from well-separated SU(2) monopole
walls which are equivalent to monopoles on T^2 x R. The metrics are explicitly
obtained due to Manton's observation by using explicit monopole solutions.
These are doubly-periodic and have the modular invariance with respect to the
complex structure of the complex torus T^2. We also derive metrics from
monopole walls with Dirac-type singularities.


title:
Constraints on Einstein-\AE ther theory and Horava gravity from binary
  pulsar observations

abstract:
  Binary pulsars are ideal to test the foundations of General Relativity, such
as Lorentz symmetry, which requires that experiments produce the same results
in all free-falling (i.e.inertial) frames. We here break this symmetry in the
gravitational sector by specifying a preferred time direction, and thus a
preferred frame, at each spacetime point. We then examine the consequences of
this gravitational Lorentz symmetry breaking in the orbital evolution of binary
pulsars, focusing on the dissipative effects. We find that Lorentz symmetry
breaking modifies these effects, and thus the orbital dynamics, in two
different ways. First, it generically causes the emission of dipolar radiation,
which makes the orbital separation decrease faster than in General Relativity.
Second, the quadrupole component of the emission is also modified. The orbital
evolution depends critically on the sensitivities of the stars, which measure
how their binding energies depend on the motion relative to the preferred
frame. We calculate the sensitivities numerically and compute the predicted
orbital decay rate of binary pulsars in Lorentz-violating gravity. By testing
these predictions against observations, we place very stringent constraints on
gravitational Lorentz violation.


title: Gaugings and other aspects in supergravity

abstract:
  We discuss various topics in supergravity: gaugings, double field theory and
$N=2$ $D=4$ BPS multicenter black holes. We introduce the main features of
supergravity, focusing on the aspects of gauged supergravities. We study the
embedding-tensor formalism as a tool that facilitates the construction of
gauged supergravities due to its covariant formulation as well as its relevance
in the description of the magnetic higher-rank field potentials. In particular,
we present a full study of the general gaugings of maximal $d=9$ as an example
in which this formalism is applied. We obtain all the possible gaugings of the
theory and its extended field content. We also classify the orbits of gaugings
of maximal and half-maximal $d=9,8,7$ supergravity and study their
(non-)geometric origins by means of double field theory. By performing a
generalized Scherk-Schwarz dimensional reduction of this T-duality-invariant
formalism, we reproduce the orbits found by means of the embedding-tensor
formalism. Finally, we study a formalism to describe BPS multicenter solutions
for $N=2$, $D=4$ theories with quadratic prepotentials. Based on the charge
vector space, this approach allows for the treatment of these solutions in a
more general way.


title: Spacetime Entanglement Entropy in 1+1 Dimensions

abstract:
  arXiv:1205.2953 defines an entropy for a gaussian scalar field $\phi$ in an
arbitrary region of either a causal set or a continuous spacetime, given only
the correlator $\langle\phi(x)\phi(y)\rangle$ within the region. As a first
application, we compute numerically the entanglement entropy in two cases where
the asymptotic form is known or suspected from conformal field theory, finding
excellent agreement when the required ultraviolet cutoff is implemented as a
truncation on spacetime mode-sums. We also show how the symmetry of
entanglement entropy reflects the fact that $RS$ and $SR$ share the same
eigenvalues, $R$ and $S$ being arbitrary matrices.


title: Radio-loud AGNs at high redshifts and the cosmic microwave background

abstract:
  We discuss how the interaction between the electrons in a relativistic jet
and the Cosmic Microwave Background (CMB) affects the observable properties of
radio-loud AGN at early epochs. At high z the magnetic energy density in the
radio lobes of powerful radio-loud quasars can be exceeded by the energy
density of the CMB (because of its (1+z)^4 dependance). In this case,
relativistic electrons cool preferentially by scattering off CMB photons,
rather than by synchrotron. Thus, sources sharing the same intrinsic properties
have different extended radio and X-ray luminosities when located at different
z: more distant sources are less luminous in radio and more luminous in X-rays
than their closer counterparts. Instead, in compact regions where the local
magnetic field still exceeds the CMB in terms of energy density, synchrotron
radiation would be unaffected by the presence of the CMB. Such regions include
the compact inner jet and the so-called hot spots in the radio lobes. The
decrease in radio luminosity is larger in misaligned sources, whose radio flux
is dominated by the extended isotropic component. These sources can fail
detection in current flux limited radio surveys, and therefore they are
possibly under-represented in the associated samples. As the cooling time is
longer for lower energy electrons, the radio luminosity deficit due to the CMB
photons is less important at low radio frequencies. Therefore objects not
detected so far in current surveys at a few GHz could be picked up by low
frequency deep surveys, such as LOFAR and SKA. Until then, we can estimate the
number of high redshift radio-loud AGNs through the census of their aligned
proxies, i.e., blazars. Indeed, their observed radio emission arises in the
inner and strongly magnetized compact core of the relativistic jet, and not
affected by inverse Compton scattering off CMB photons.


title: Mean-field phase diagram of the Bose-Fermi Hubbard model

abstract:
  We analyze the ground state properties of Bose-Fermi mixtures using a
mean-field treatment of the boson-fermion interaction on a simple cubic
lattice. In the deep superfluid limit of the bosonic sector and the BCS regime
of the fermion sector, we derive BCS-type equations to determine the phase
diagram of the system. We find a competition between a charge density wave and
a superconducting phase. In the opposite limit, we study the Mott insulator to
superfluid transition of the bosonic sector in the presence of a staggered
density-induced alternating potential provided by the fermions, and determine
the mean-field transition line. In the two-superfluid phase of the mixture we
restrict to nearest-neighbor induced interactions between the fermions and
consider the extended Hubbard model. We perform a mean-field analysis of the
critical temperature for the formation of boson-assisted $s$-, extended $s^-$-,
$d$-, and $p$-wave pairs at fermionic half filling. We compare our results with
a recent dynamical mean-field study [Anders \emph{et al.} Phys. Rev. Lett. {\bf
109}, 206401].


title: Semiclassical theory of viscosity in quantum Hall states

abstract:
  Quantum Hall (QH) states are predicted to display an intriguing
non-dissipative stress response to a shear deformation rate, a phenomenon
variously known as asymmetric or Hall viscosity, or Lorentz shear response.
Just as the QH effect results from the coupling of Chern-Simons fields of the
effective theory to the electromagnetic field, so also Hall viscosity is found
to arise from coupling of these fields to the 'metric' of the quadratic kinetic
energy. In this paper I derive new physical insights for Hall viscosity by
using an extended semiclassical approach to compute the conductivity of a
single Landau level in a nonuniform electric field. I demonstrate that the
inhomogeneity of an applied electric field is a viable experimentally tunable
parameter for altering the metric, and hence creating strain in the QH state.
Using these results, I argue that Hall viscosity arises from the shearing of
local cyclotron orbits by the applied nonuniform electric fields.


title: Generating the Johnson filtration

abstract:
  For k >= 1, let Torelli_g^1(k) be the k-th term in the Johnson filtration of
the mapping class group of a genus g surface with one boundary component. We
prove that for all k, there exists some G_k >= 0 such that Torelli_g^1(k) is
generated by elements which are supported on subsurfaces whose genus is at most
G_k. We also prove similar theorems for the Johnson filtration of Aut(F_n) and
for certain mod-p analogues of the Johnson filtrations of both the mapping
class group and of Aut(F_n). The main tools used in the proofs are the related
theories of FI-modules (due to the first author together with Ellenberg and
Farb) and central stability (due to the second author), both of which concern
the representation theory of the symmetric groups over Z.


title: Many-body Localization with Dipoles

abstract:
  Systems of strongly interacting dipoles offer an attractive platform to study
many-body localized phases, owing to their long coherence times and strong
interactions. We explore conditions under which such localized phases persist
in the presence of power-law interactions and supplement our analytic treatment
with numerical evidence of localized states in one dimension. We propose and
analyze several experimental systems that can be used to observe and probe such
states, including ultracold polar molecules and solid-state magnetic spin
impurities.

categories: cond-mat.stat-mech cond-mat.dis-nn cond-mat.quant-gas cond-mat.str-el quant-ph


title: LHC and dark matter phenomenology of the NUGHM

abstract:
  We present a Bayesian analysis of the NUGHM, a supersymmetric scenario with
non-universal gaugino masses and Higgs masses, including all the relevant
experimental observables and dark matter constraints. The main merit of the
NUGHM is that it essentially includes all the possibilities for dark matter
(DM) candidates within the MSSM, since the neutralino and chargino spectrum
-and composition- are as free as they can be in the general MSSM. We identify
the most probable regions in the NUHGM parameter space, and study the
associated phenomenology at the LHC and the prospects for DM direct detection.
Requiring that the neutralino makes all of the DM in the Universe, we identify
two preferred regions around $m_{\chi_1^0}= 1\ {\rm TeV},\; 3\ {\rm TeV}$,
which correspond to the (almost) pure Higgsino and wino case. There exist other
marginal regions (e.g. Higgs-funnel), but with much less statistical weight.
The prospects for detection at the LHC in this case are quite pessimistic, but
future direct detection experiments like LUX and XENON1T, will be able to probe
this scenario. In contrast, when allowing other DM components, the prospects
for detection at the LHC become more encouraging -- the most promising signals
being, beside the production of gluinos and squarks, the production of the
heavier chargino and neutralino states, which lead to WZ and same-sign WW final
states -- and direct detection remains a complementary, and even more powerful,
way to probe the scenario.


title:
Strong Meissner screening change in superconducting radio frequency
  cavities due to mild baking

abstract:
  We investigate "hot" regions with anomalous high field dissipation in bulk
niobium superconducting radio frequency cavities for particle accelerators by
using low energy muon spin rotation (LE-$\mu$SR) on corresponding cavity
cutouts. We demonstrate that superconducting properties at the hot region are
well described by the non-local Pippard/BCS model for niobium in the clean
limit with a London penetration depth $\lambda_\mathrm{L} = 23 \pm 2$ nm. In
contrast, a cutout sample from the 120$^\circ$C baked cavity shows a much
larger $\lambda > 100$ nm and a depth dependent mean free path, likely due to
gradient in vacancy concentration. We suggest that these vacancies can
efficiently trap hydrogen and hence prevent the formation of hydrides
responsible for rf losses in hot regions.


title:
Interaction of Josephson junction and distant vortex in narrow thin-film
  superconducting strips

abstract:
  The phase difference between the banks of an edge-type planar Josephson
junction crossing the narrow thin-film strip depends on wether or not vortices
are present in the junction banks. For a vortex close to the junction this
effect has been seen by Golod, Rydh, and Krasnov, \prl {\bf 104}, 227003
(2010), who showed that the vortex may turn the junction into $\pi$-type. It is
shown here that even if the vortex is far away from the junction, it still
changes the 0-junction to $\pi$-junction when situated close to the strip
edges. Within the approximation used, the latter effect is independent of the
vortex-junction separation, a manifestation of topology of the vortex phase
which extends to macroscopic distances of superconducting coherence.


title: Potential Precision on Higgs Couplings and Total Width at the ILC

abstract:
  We outline a systematic approach to the determination of the Standard
Model-like Higgs boson total width and measurable coupling parameters in a
model-independent manner at the International Linear Collider (ILC) and
illustrate the complementarity for operating the ILC at $250$ GeV near the $Zh$
threshold and at $500$ GeV and $1$ TeV utilizing the $WW, ZZ$ fusion processes.
We perform detailed simulations for an important contributing channel to the
coupling determination and for invisible decays. Without model assumptions, and
combining the information for the coupling ratios from the LHC, the total width
can be determined to an accuracy of about $6%$, and the couplings for the
observable channels can be measured to the $(3-5)%$ level at 250 GeV, reaching
$(1-3)%$ level including the 500 GeV results, with further improvements
possible with a $1$ TeV run. The best precision for the branching fraction
measurement of the Higgs to invisible modes can be reached at $0.5-0.7%$ around
the $Zh$ threshold. Further studies from $ZZ$ fusion at higher energies may
provide significant improvement for the measurements. With modest theory
assumptions, the width and coupling determinations can be further improved to
the percent or sub-percent level.


title: Desingularization preserving stable simple normal crossings

abstract:
  The subject is partial resolution of singularities. Given an algebraic
variety X (not necessarily equidimensional) in characteristic zero (or, more
generally, a pair (X,D), where D is a divisor on X), we construct a functorial
desingularization of all but stable simple normal crossings (stable-snc)
singularities, by smooth blowings-up that preserve such singularities. A
variety has stable simple normal crossings at a point if, locally, its
irreducible components are smooth and tranverse in some smooth embedding
variety. We also show that our main assertion is false for more general simple
normal crossings singularities.