title: Nonnilpotent subsets in the susuki groups

abstract:
  Let G be a group and N be the class of nilpotent groups. A subset A of G is
said to be nonnilpotent if for any two distinct elements a and b in A, ha, bi
62 N. If, for any other nonnilpotent subset B in G, |A| ? |B|, then A is said
to be a maximal nonnilpotent subset and the cardinality of this subset (if it
exists) is denoted by !(NG). In this paper, among other results, we obtain
!(NSuz(q)) and !(NPGL(2,q)), where Suz(q) is the Suzuki simple group over the
field with q elements and PGL(2, q) is the projective general linear group of
degree 2 over the finite field of size q, respectively.


title: Pairwise non-coprimality of triples

abstract:
  We say that $(a_1,...,a_k)$ is pairwise non-coprime if $\gcd(a_i,a_j) \ne 1$
for all $1 \le i <j \le k$. Let $a_1,a_2,a_3$ be positive integers less than
$H$. We obtain an asymptotic formula for the number of $(a_1,a_2,a_3)$ that are
pairwise non-coprime. The probability that a randomly chosen unbounded positive
integer triple is pairwise non-coprime is approximately 17.4%. Let $\varphi(n)$
be the Euler totient function. We also give an upper bound on the error term in
an asymptotic formula for $\sum_{n=1}^H (\varphi(n)/n)^m$ for $m \ge 2$ and as
$H \rightarrow \infty$.


title:
Asymmetric-detection time-stretch optical microscopy (ATOM) for
  ultrafast high-contrast cellular imaging in flow

abstract:
  Accelerating imaging speed in optical microscopy is often realized at the
expense of image contrast, image resolution, and detection sensitivity- a
common predicament for advancing high-speed and high-throughput cellular
imaging. We here demonstrate a new imaging approach, called
asymmetric-detection time-stretch optical microscopy (ATOM), which can deliver
ultrafast label-free high-contrast flow imaging with well delineated cellular
morphological resolution and in-line optical image amplification to overcome
the compromised imaging sensitivity at high speed. We show that ATOM can
separately reveal the enhanced phase-gradient and absorption contrast in
microfluidic live-cell imaging at a flow speed as high as ~10 m/s,
corresponding to an imaging throughput of ~100,000 cells/sec. ATOM could thus
be the enabling platform to meet the pressing need for intercalating optical
microscopy in cellular assay, e.g. imaging flow cytometry- permitting
high-throughput access to the morphological information of the individual cells
simultaneously with a multitude of parameters obtained in the standard assay.


title:
The interface heterogeneous nucleation and dynamic dispersion of nuclei
  in solidification process

abstract:
  By comparing the grain sizes under different nucleation conditions, the
different nucleation mechanisms were investigated. The primitive nuclei origin
at some specific interface, and subsequently disperse into the bulk melt with
melt flow. The survival probability of nuclei decides the nuclei density in
bulk melt, and the growth of survived nuclei finally constitutes the solidified
grains. The nucleation process is highly dynamic, evolving and variable with
actual experimental condition and production condition.


title: Unconventional thermal cloak hiding an object outside the cloak

abstract:
  All the thermal cloaks reported in the literature can be used to thermally
hide an object inside the cloak. However, a common limitation of this kind of
thermal cloaks is that the cloaked object cannot feel the external heat flow
since it is located inside the cloak; thus we call these cloaks ``conventional
thermal cloaks''. Here we manage to overcome this limitation by exploiting a
class of unconventional thermal cloaks that enable the cloaked object to feel
the external heat flow. Our finite element simulations in two dimensions show
the desired cloaking effect. The underlying mechanism originates from the
complementary effect of thermal metamaterials with negative thermal
conductivities. This work suggests a different method to design thermal devices
where heat conduction can be controlled at will.


title: The sum-capture problem for abelian groups

abstract:
  Let $G$ be a finite abelian group, let $0 < \alpha < 1$, and let $A \subseteq
G$ be a random set of size $|G|^\alpha$. We let $$ \mu(A) =
\max_{B,C:|B|=|C|=|A|}|\{(a,b,c) \in A \times B \times C : a = b + c \}|. $$
The issue is to determine upper bounds on $\mu(A)$ that hold with high
probability over the random choice of $A$. Mennink and Preneel \cite{BM}
conjecture that $\mu(A)$ should be close to $|A|$ (up to possible logarithmic
factors in $|G|$) for $\alpha \leq 1/2$ and that $\mu(A)$ should not much
exceed $|A|^{3/2}$ for $\alpha \leq 2/3$. We prove the second half of this
conjecture by showing that $$ \mu(A) \leq |A|^3/|G| + 4|A|^{3/2}\ln(|G|)^{1/2}
$$ with high probability, for all $0 < \alpha < 1$. We note that $3\alpha - 1
\leq (3/2)\alpha$ for $\alpha \leq 2/3$.
  In previous work, Alon et al$.$ have shown that $\mu(A) \leq O(1)|A|^3/|G|$
with high probability for $\alpha \geq 2/3$ while Kiltz, Pietrzak and Szegedy
show that $\mu(A) \leq |A|^{1 + 2\alpha}$ with high probability for $\alpha
\leq 1/4$. Current bounds on $\mu(A)$ are essentially sharp for the range $2/3
\leq \alpha \leq 1$. Finding better bounds remains an open problem for the
range $0 < \alpha < 2/3$ and especially for the range $1/4 < \alpha < 2/3$ in
which the bound of Kiltz et al$.$ doesn't improve on the bound given in this
paper (even if that bound applied). Moreover the conjecture of Mennink and
Preneel for $\alpha \leq 1/2$ remains open.


title:
Creating a tunable spin squeezing via a time-dependent collective
  atom-photon coupling

abstract:
  We present an experimentally feasible method to produce a large and tunable
spin squeezing when an ensemble of many four-level atoms interacts
simultaneously with a single-mode photon and classical driving lasers. Our
approach is to simply introduce a time-dependent collective atom-photon
coupling. We show that the maximal squeezing factor measured experimentally can
be well controlled by both its driving magnitude and driving frequency. In
particular, when increasing the driving magnitude, the maximal squeezing factor
increases and thus can be rapidly enhanced. We also demonstrate explicitly in
the high-frequency approximation that this spin squeezing arises from a strong
repulsive spin-spin interaction induced by the time-dependent collective
atom-photon coupling. Finally, we evaluate analytically, by using current
experimental parameters, the maximal squeezing factor, which can reach 40 dB.
This squeezing factor is far larger than previous ones.


title: On Pyber's base size conjecture

abstract:
  Let $G$ be a permutation group on a finite set $\Omega$. A subset $B
\subseteq \Omega$ is a base for $G$ if the pointwise stabilizer of $B$ in $G$
is trivial. The base size of $G$, denoted $b(G)$, is the smallest size of a
base. A well known conjecture of Pyber from the early 1990s asserts that there
exists an absolute constant $c$ such that $b(G) \le c\log |G| / \log n$ for any
primitive permutation group $G$ of degree $n$. Some special cases have been
verified in recent years, including the almost simple and diagonal cases. In
this paper, we prove Pyber's conjecture for all non-affine primitive groups.


title: Irreducible almost simple subgroups of classical algebraic groups

abstract:
  Let G be a simple classical algebraic group over an algebraically closed
field K of characteristic $p \ge 0$ with natural module W. Let H be a closed
subgroup of G and let V be a nontrivial p-restricted irreducible tensor
indecomposable rational KG-module such that the restriction of V to H is
irreducible. In this paper we classify the triples (G,H,V) of this form, where
$V \ne W, W^{*}$ and H is a disconnected almost simple positive-dimensional
closed subgroup of G acting irreducibly on W. Moreover, by combining this
result with earlier work, we complete the classification of the irreducible
triples (G,H,V) where G is a simple algebraic group over K, and H is a maximal
closed subgroup of positive dimension.


title:
Statistically preferred basis of an open quantum system: Its relation to
  the eigenbasis of a renormalized self-Hamiltonian

abstract:
  We study the problem of the basis of an open quantum system, under a quantum
chaotic environment, which is preferred in view of its stationary reduced
density matrix (RDM), that is, the basis in which the stationary RDM is
diagonal. It is shown that, under an initial condition composed of sufficiently
many energy eigenstates of the total system, such a basis is given by the
eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of
large Hilbert space of the environment. Here, the renormalized self-Hamiltonian
is given by the unperturbed self-Hamiltonian plus a certain average of the
interaction Hamiltonian over the environmental degrees of freedom. Numerical
simulations, performed in two models, both with the kicked rotor as the
environment, give results consistent with the above analytical predictions for
the limit of large environment.


title:
High-rate quantum low-density parity-check codes assisted by reliable
  qubits

abstract:
  Quantum error correction is an important building block for reliable quantum
information processing. A challenging hurdle in the theory of quantum error
correction is that it is significantly more difficult to design
error-correcting codes with desirable properties for quantum information
processing than for traditional digital communications and computation. A
typical obstacle to constructing a variety of strong quantum error-correcting
codes is the complicated restrictions imposed on the structure of a code.
Recently, promising solutions to this problem have been proposed in quantum
information science, where in principle any binary linear code can be turned
into a quantum error-correcting code by assuming a small number of reliable
quantum bits. This paper studies how best to take advantage of these latest
ideas to construct desirable quantum error-correcting codes of very high
information rate. Our methods exploit structured high-rate low-density
parity-check codes available in the classical domain and provide quantum
analogues that inherit their characteristic low decoding complexity and high
error correction performance even at moderate code lengths. Our approach to
designing high-rate quantum error-correcting codes also allows for making
direct use of other major syndrome decoding methods for linear codes, making it
possible to deal with a situation where promising quantum analogues of
low-density parity-check codes are difficult to find.


title: Erd\H{o}s-Ginzburg-Ziv theorem for finite commutative semigroups

abstract:
  Let $\mathcal{S}$ be a finite commutative semigroup written additively, and
let $\exp(\mathcal{S})$ be its exponent which is defined as the least common
multiple of all periods of the elements in $\mathcal{S}$. For every sequence
$T$ of elements in $\mathcal{S}$ (repetition allowed), let $\sigma(T) \in
\mathcal{S}$ denote the sum of all terms of $T$. Define the Davenport constant
$D(\mathcal{S})$ of $\mathcal{S}$ to be the least positive integer $d$ such
that every sequence $T$ over $\mathcal{S}$ of length at least $d$ contains a
proper subsequence $T'$ with $\sigma(T')=\sigma(T)$, and define the
Erd\H{o}s-Ginzburg-Ziv Theorem constant $E(\mathcal{S})$ to be the least
positive integer $\ell$ such that every sequence $T$ over $\mathcal{S}$ of
length at least $\ell$ contains a subsequence $T'$ with
$|T|-|T'|=\left\lceil\frac{|\mathcal{S}|}{\exp(\mathcal{S})}\right\rceil\exp(\mathcal{S})$
and $\sigma(T')=\sigma(T)$. When $\mathcal{S}$ is a finite abelian group, it is
well known that
$\left\lceil\frac{|\mathcal{S}|}{\exp(\mathcal{S})}\right\rceil\exp(\mathcal{S})=|\mathcal{S}|$
and $E(\mathcal{S})=D(\mathcal{S})+|\mathcal{S}|-1$. In this paper we
investigate whether $E(\mathcal{S})\leq
D(\mathcal{S})+\left\lceil\frac{|\mathcal{S}|}{\exp(\mathcal{S})}\right\rceil
\exp(\mathcal{S})-1$ holds true for all finite commutative semigroups
$\mathcal{S}$. We provide a positive answer to the question above for some
classes of finite commutative semigroups, including group-free semigroups,
elementary semigroups, and archimedean semigroups with certain constraints.


title: A generalization of \'Ciri\'c fixed point theorem

abstract:
  In this paper, we state and prove a generalization of \'Ciri\'c fixed point
theorems in metric space by using a new generalized quasi-contractive map.
These theorems extend other well known fundamental metrical fixed point
theorems in the literature. Moreover, a multi-valued version for generalized
quasi-contraction is also established.


title:
Controlling electron propagation on a topological insulator surface via
  proximity interactions

abstract:
  The possibility of electron beam guiding is theoretically explored on the
surface of a topological insulator through the proximity interaction with a
magnetic material. The electronic band modification induced by the exchange
coupling at the interface defines the path of electron propagation in analogy
to the optical fiber for photons. Numerical simulations indicate the guiding
efficiency much higher than that in the "waveguide" formed by an electrostatic
potential barrier such as p-n junctions. Further, the results illustrate
effective flux control and beam steering that can be realized by altering the
magnetization/spin texture of the adjacent magnetic materials. Specifically,
the feasibility to switch on/off and make a large-angle turn is demonstrated
under realistic conditions. Potential implementation to logic and interconnect
applications is also examined in connection with electrically controlled
magnetization switching.


title: Low temperature MQ NMR dynamics in dipolar ordered state

abstract:
  We investigate analytically and numerically the Multiple Quantum (MQ) NMR
dynamics in dipolar ordered spin systems of nuclear spins 1/2 at a low
temperatures. We suggest two different methods of MQ NMR. One of them is based
on the measurement of the dipolar energy. The other method uses an additional
resonance ({\pi}/4)_{y}-pulse after the preparation period of the standard MQ
NMR experiment in solids and allows one to measure the Zeeman energy. The both
considered methods are sensitive to the contribution of remote spins in the
interaction and to the spin system structure. The QS method is sensitive to the
spin number in the molecule while the PS method gives very similar time
dependencies of the intensities of MQ coherences for different spin numbers. It
is shown that the use of the dipolar ordered initial state has the advantage of
exciting the highest order MQ coherences in clusters of 4m identical spins,
where m=1,2,3..., that is impossible to do with the standard MQ method. MQ NMR
methods based on the dipolar ordered initial states at low temperatures
complement the standard NMR spectroscopy for better studying structures and
dynamic processes in solids.


title: A nice lima\c{c}on-like spiral

abstract:
  A lima\c{c}on-like curve, allowing 2{\pi}-transition with monotone curvature
between concentric curvature elements, is presented. The curve is 4th degree
algebraic, 4th degree rational, and shares other common features with Pascal's
lima\c{c}on.


title:
Effect of growth oxygen pressure on anisotropic-strain-induced phase
  separation in epitaxial La$_{0.67}$Ca$_{0.33}$MnO$_{3}$/NdGaO$_{3}$(001)
  films

abstract:
  The effect of deposition oxygen pressure (P$_{O}$) on phase separation (PS)
induced in epitaxial La$_{0.67}$Ca$_{0.33}$MnO$_{3}$/NdGaO$_{3}$(001) films was
investigated. Fully oxygenated films grown at high P$_{O}$ are anisotropically
strained. They exhibit PS over a wide temperature range, because of the large
orthorhombicity of NdGaO$_{3}$ substrates. The paramagnetic
insulator-to-ferromagnetic metal (FM) and FM-to-antiferromagnetic insulator
(AFI) transitions gradually shift to lower temperatures with decreasing PO. The
AFI state is initially weakened (P$_{O}$ >= 30 Pa), but then becomes more
robust against the magnetic field (P$_{O}$ < 30 Pa). The out-of-plane film
lattice parameter increases with decreasing P$_{O}$. For films grown at
P$_{O}$>= 30 Pa, the slight oxygen deficiency may enlarge the lattice unit
cell, reduce the anisotropic strain and suppress the AFI state. Films deposited
at P$_{O}$ < 30 Pa instead experience an average compressive strain. The
enhanced compressive strain and structural defects in the films may lead to the
robust AFI state. These results aid our understanding of PS in manganite films.


title: Generic Image Classification Approaches Excel on Face Recognition

abstract:
  The main finding of this work is that the standard image classification
pipeline, which consists of dictionary learning, feature encoding, spatial
pyramid pooling and linear classification, outperforms all state-of-the-art
face recognition methods on the tested benchmark datasets (we have tested on
AR, Extended Yale B, the challenging FERET, and LFW-a datasets). This
surprising and prominent result suggests that those advances in generic image
classification can be directly applied to improve face recognition systems. In
other words, face recognition may not need to be viewed as a separate object
classification problem.
  While recently a large body of residual based face recognition methods focus
on developing complex dictionary learning algorithms, in this work we show that
a dictionary of randomly extracted patches (even from non-face images) can
achieve very promising results using the image classification pipeline. That
means, the choice of dictionary learning methods may not be important. Instead,
we find that learning multiple dictionaries using different low-level image
features often improve the final classification accuracy. Our proposed face
recognition approach offers the best reported results on the widely-used face
recognition benchmark datasets. In particular, on the challenging FERET and
LFW-a datasets, we improve the best reported accuracies in the literature by
about 20% and 30% respectively.


title:
Local Lipschitz continuity in the initial value and strong completeness
  for nonlinear stochastic differential equations

abstract:
  Recently, Hairer et. al (2012) showed that there exist SDEs with infinitely
often differentiable and globally bounded coefficient functions whose solutions
fail to be locally Lipschitz continuous in the strong L^p-sense with respect to
the initial value for every p \in [1,\infty). In this article we provide
sufficient conditions on the coefficient functions of the SDE and on p \in
(0,\infty] which ensure local Lipschitz continuity in the strong L^p-sense with
respect to the initial value and we establish explicit estimates for the local
Lipschitz continuity constants. In particular, we prove local Lipschitz
continuity in the initial value for several nonlinear SDEs from the literature
such as the stochastic van der Pol oscillator, Brownian dynamics, the
Cox-Ingersoll-Ross processes and the Cahn-Hilliard-Cook equation. As an
application of our estimates, we obtain strong completeness for several
nonlinear SDEs.


title:
Homotopy Perturbation Method for Solving a Spatially Flat FRW
  Cosmological Model

abstract:
  In the present paper, we study a homogeneous cosmological model in
Friedmann-Robertson-Walker (FRW) space-time by means of the so-called Homotopy
Perturbation Method (HPM). First, we briefly recall the main equations of the
cosmological model and the basic idea of HPM. Next we consider the test example
when the exact solution of the model is known, in order to approbate the HPM in
cosmology and present the main steps in solving by this method. Finally, we
obtain a solution for the spatially flat FRW model of the universe filled with
the dust and quintessence when the exact solution cannot be found. A comparison
of our solution with the corresponding numerical solution shows that it is of a
high degree of accuracy.


title: Special Sets of Primes in Function Fields

abstract:
  When investigating the distribution of the Euler totient function, one
encounters sets of primes P where if p is in P then r is in P for all r|(p-1).
While it is easy to construct finite sets of such primes, the only infinite set
known is the set of all primes. We translate this problem into the function
field setting and construct an infinite such set in F_p[x] whenever p is
equivalent to 2 or 5 modulo 9.


title: Stabilizer formalism for generalized concatenated quantum codes

abstract:
  The concept of generalized concatenated quantum codes (GCQC) provides a
systematic way for constructing good quantum codes from short component codes.
We introduce a stabilizer formalism for GCQCs, which is achieved by defining
quantum coset codes. This formalism offers a new perspective for GCQCs and
enables us to derive a lower bound on the code distance of stabilizer GCQCs
from component codes parameters,for both non-degenerate and degenerate
component codes. Our formalism also shows how to exploit the error-correcting
capacity of component codes to design good GCQCs efficiently.


title: Generalizing Zeckendorf's Theorem to f-decompositions

abstract:
  A beautiful theorem of Zeckendorf states that every positive integer can be
uniquely decomposed as a sum of non-consecutive Fibonacci numbers $\{F_n\}$,
where $F_1 = 1$, $F_2 = 2$ and $F_{n+1} = F_n + F_{n-1}$. For general
recurrences $\{G_n\}$ with non-negative coefficients, there is a notion of a
legal decomposition which again leads to a unique representation, and the
number of summands in the representations of uniformly randomly chosen $m \in
[G_n, G_{n+1})$ converges to a normal distribution as $n \to \infty$.
  We consider the converse question: given a notion of legal decomposition, is
it possible to construct a sequence $\{a_n\}$ such that every positive integer
can be decomposed as a sum of terms from the sequence? We encode a notion of
legal decomposition as a function $f:\N_0\to\N_0$ and say that if $a_n$ is in
an "$f$-decomposition", then the decomposition cannot contain the $f(n)$ terms
immediately before $a_n$ in the sequence; special choices of $f$ yield many
well known decompositions (including base-$b$, Zeckendorf and factorial). We
prove that for any $f:\N_0\to\N_0$, there exists a sequence
$\{a_n\}_{n=0}^\infty$ such that every positive integer has a unique
$f$-decomposition using $\{a_n\}$. Further, if $f$ is periodic, then the unique
increasing sequence $\{a_n\}$ that corresponds to $f$ satisfies a linear
recurrence relation. Previous research only handled recurrence relations with
no negative coefficients. We find a function $f$ that yields a sequence that
cannot be described by such a recurrence relation. Finally, for a class of
functions $f$, we prove that the number of summands in the $f$-decomposition of
integers between two consecutive terms of the sequence converges to a normal
distribution.


title:
A Generalization of Fibonacci Far-Difference Representations and
  Gaussian Behavior

abstract:
  A natural generalization of base B expansions is Zeckendorf's Theorem: every
integer can be uniquely written as a sum of non-consecutive Fibonacci numbers
$\{F_n\}$, with $F_{n+1} = F_n + F_{n-1}$ and $F_1=1, F_2=2$. If instead we
allow the coefficients of the Fibonacci numbers in the decomposition to be zero
or $\pm 1$, the resulting expression is known as the far-difference
representation. Alpert proved that a far-difference representation exists and
is unique under certain restraints that generalize non-consecutiveness,
specifically that two adjacent summands of the same sign must be at least 4
indices apart and those of opposite signs must be at least 3 indices apart. We
prove that a far-difference representation can be created using sets of
Skipponacci numbers, which are generated by recurrence relations of the form
$S^{(k)}_{n+1} = S^{(k)}_{n} + S^{(k)}_{n-k}$ for $k \ge 0$. Every integer can
be written uniquely as a sum of the $\pm S^{(k)}_n $'s such that every two
terms of the same sign differ in index by at least 2k+2, and every two terms of
opposite signs differ in index by at least k+2. Additionally, we prove that the
number of positive and negative terms in given Skipponacci decompositions
converges to a Gaussian, with a computable correlation coefficient that is a
rational function of the smallest root of the characteristic polynomial of the
recurrence. The proof uses recursion to obtain the generating function for
having a fixed number of summands, which we prove converges to the generating
function of a Gaussian. We next explore the distribution of gaps between
summands, and show that for any k the probability of finding a gap of length $j
\ge 2k+2$ decays geometrically, with decay ratio equal to the largest root of
the given k-Skipponacci recurrence. We conclude by finding sequences that have
an (s,d) far-difference representation for any positive integers s,d.


title: Multiple Domain Secure Routing for Wireless Sensor Networks

abstract:
  Secure Transmission of data packets in Wireless Sensor Networks is an
important area of Research. There is a possibility of an attacker creating
security holes in the network. Hence, network security and reliability can be
achieved by discovering random multiple paths using multiple domains, and
forwarding data packets from the source node to the destination node. We have
designed, Multiple Domain Routing with Overlap of Nodes (MDRON) and Multiple
Domain Routing Without Overlap of Nodes (MDRWON) algorithms, in which packets
follow multiple optimized paths simultaneously. The Special node algorithm
searches the node which has maximum power and these nodes are used for
transferring the packet from one domain to another domain. Simulation results
using MATLAB shows that performance is better than Purely Random Propagation
(PRP) and Non Repetitive Random Propagation(NRRP) Algorithms.


title:
Thermodynamic perturbation theory for self assembling mixtures of multi
  - patch colloids and colloids with spherically symmetric attractions

abstract:
  In this paper we extend our previous theory [B. D. Marshall and W.G. Chapman,
J. Chem. Phys. 139, 104904 (2013)] for mixtures of single patch colloids (p
colloids) and colloids with spherically symmetric attractions (s colloids) to
the case that the p colloids can have multiple patches. The theory is then
applied to the case of a binary mixture of bi-functional p colloids which have
an A and B type patch and s colloids which are not attracted to other s
colloids and are attracted to only patch A on the p colloids. This mixture
reversibly self assembles into both colloidal star molecules, where the s
colloid is the articulation segment and the p colloids form the arms, and free
chains composed of only p colloids. It is shown that temperature, density,
composition and relative attractive strengths can all be varied to manipulate
the number of arms per colloidal star molecule, average arm length and the
fraction of chains (free chains + arms) which are star arms.


title: Benford's Law and Continuous Dependent Random Variables

abstract:
  Many mathematical, man-made and natural systems exhibit a leading-digit bias,
where a first digit (base 10) of 1 occurs not 11\% of the time, as one would
expect if all digits were equally likely, but rather 30\%. This phenomenon is
known as Benford's Law. Analyzing which datasets adhere to Benford's Law and
how quickly Benford behavior sets in are the two most important problems in the
field. Most previous work studied systems of independent random variables, and
relied on the independence in their analyses.
  Inspired by natural processes such as particle decay, we study the dependent
random variables that emerge from models of decomposition of conserved
quantities. We prove that in many instances the distribution of lengths of the
resulting pieces converges to Benford behavior as the number of divisions grow,
and give several conjectures for other fragmentation processes. The main
difficulty is that the resulting random variables are dependent. We handle this
by using tools from Fourier analysis and irrationality exponents to obtain
quantified convergence rates as well as introducing and developing techniques
to measure and control the dependencies. The construction of these tools is one
of the major motivations of this work, as our approach can be applied to many
other dependent systems. As an example, we show that the $n!$ entries in the
determinant expansions of $n\times n$ matrices with entries independently drawn
from nice random variables converges to Benford's Law.


title: Bounds for the spectral radius of nonnegative matrices

abstract:
  We give upper and lower bounds for the spectral radius of a nonnegative
matrix by using its average 2-row sums, and characterize the equality cases if
the matrix is irreducible. We also apply these bounds to various nonnegative
matrices associated with a graph, including the adjacency matrix, the signless
Laplacian matrix, the distance matrix, the distance signless Laplacian matrix,
and the reciprocal distance matrix.


title: Stochastic Bound Majorization

abstract:
  Recently a majorization method for optimizing partition functions of
log-linear models was proposed alongside a novel quadratic variational
upper-bound. In the batch setting, it outperformed state-of-the-art first- and
second-order optimization methods on various learning tasks. We propose a
stochastic version of this bound majorization method as well as a low-rank
modification for high-dimensional data-sets. The resulting stochastic
second-order method outperforms stochastic gradient descent (across variations
and various tunings) both in terms of the number of iterations and computation
time till convergence while finding a better quality parameter setting. The
proposed method bridges first- and second-order stochastic optimization methods
by maintaining a computational complexity that is linear in the data dimension
and while exploiting second order information about the pseudo-global curvature
of the objective function (as opposed to the local curvature in the Hessian).


title: Coherence Factors Beyond the BCS Expressions -- A Derivation

abstract:
  We present a derivation of a previously announced result for matrix elements
between exact eigenstates of the pairing Hamiltnonian. Our results, which
generalize the well known BCS (Bardeen-Cooper-Schrieffer) expressions for what
is known as 'coherence factors', are derived based on the Slavnov formula for
overlaps between Bethe-ansatz states, thus making use of the known connection
between the exact diagonalization of the BCS Hamiltonian, due to Richardson,
and the algebraic Bethe ansatz. The resulting formula has a compact form after
a suitable parameterization of the Energy plane. Although we apply our method
here to the pairing Hamiltonian, it may be adjusted to study what is termed the
'Sutherland limit' for exactly solvable models, namely where a macroscopic
number of rapidities form a large string.


title: Unveiling the Influence of Dark Matter in Axially Symmetric Galaxies

abstract:
  We investigate the regular or chaotic nature of orbits of stars moving in the
meridional plane (R,z) of an axially symmetric galactic model with a dense,
massive spherical nucleus and a dark matter halo component. In particular, we
study the influence of the fractional portion of the dark matter, by computing
in each case the percentage of chaotic orbits, as well as the percentages of
orbits of the main regular resonant families. In an attempt to distinguish
between regular and chaotic motion, we use the Fast Lyapunov Indicator (FLI)
method to extensive samples of orbits obtained by integrating numerically the
equations of motion as well as the variational equations. Furthermore, a
technique which is based mainly on the field of spectral dynamics that utilizes
the Fourier transform of the time series of each coordinate is used for
identifying the various families of regular orbits and also to recognize the
secondary resonances that bifurcate from them. Two cases are studied in our
work: (i) the case where we have a disk galaxy model (ii) the case where our
model represents an elliptical galaxy. Comparison with early related work is
also made.


title: Optimal Switching at Poisson Random Intervention Times

abstract:
  This paper introduces a new class of optimal switching problems, where the
player is allowed to switch at a sequence of exogenous Poisson arrival times,
and the underlying switching system is governed by an infinite horizon backward
stochastic differential equation system. The value function and the optimal
switching strategy are characterized by the solution of the underlying
switching system. In a Markovian setting, the paper gives a complete
description of the structure of switching regions by means of the comparison
principle.


title: Destriping Cosmic Microwave Background Polarimeter data

abstract:
  Destriping is a well-established technique for removing low-frequency
correlated noise from Cosmic Microwave Background (CMB) survey data. In this
paper we present a destriping algorithm tailored to data from a polarimeter,
i.e. an instrument where each channel independently measures the polarization
of the input signal.
  We also describe a fully parallel implementation in Python released as Free
Software and analyze its results and performance on simulated datasets, both
the design case of signal and correlated noise, and with additional systematic
effects.
  Finally we apply the algorithm to 30 days of 37.5 GHz polarized microwave
data gathered from the B-Machine experiment, developed at UCSB. The B-Machine
data and destriped maps are made publicly available.
  The purpose is the development of a scalable software tool to be applied to
the upcoming 12 months of temperature and polarization data from LATTE (Low
frequency All sky TemperaTure Experiment) at 8 GHz and to even larger datasets.


title:
Separation of neutral and charge modes in one dimensional chiral edge
  channels

abstract:
  Coulomb interactions have a major role in one-dimensional electronic
transport. They modify the nature of the elementary excitations from Landau
quasiparticles in higher dimensions to collective excitations in one dimension.
Here we report the direct observation of the collective neutral and charge
modes of the two chiral co-propagating edge channels of opposite spins of the
quantum Hall effect at filling factor 2. Generating a charge density wave at
frequency f in the outer channel, we measure the current induced by
inter-channel Coulomb interaction in the inner channel after a 3-mm propagation
length. Varying the driving frequency from 0.7 to 11 GHz, we observe damped
oscillations in the induced current that result from the phase shift between
the fast charge and slow neutral eigenmodes. We measure the dispersion relation
and dissipation of the neutral mode from which we deduce quantitative
information on the interaction range and parameters.


title: Mass of the $b$ Quark from QCD Sum Rules for $f_{B_{(s)}}$

abstract:
  We demonstrate that Borel QCD sum rules for heavy-light currents entail a
very strong correlation between the $b$-quark mass $m_b$ and the $B$-meson
decay constant $f_B,$ that is, $\delta f_B/f_B\approx-8\delta m_b/m_b.$ By
starting from $f_B$ as input, this observation allows for an accurate sum-rule
determination of $m_b.$ Employing precise lattice QCD results for $f_B$ in our
sum-rule study based on the three-loop $O(\alpha_s^2)$ heavy-light correlation
function implies $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)$ GeV for the $b$-quark
$\bar{\rm MS}$ mass.


title: Cosmological Time Dilation in Durations of Swift Long Gamma-Ray Bursts

abstract:
  Cosmological time dilation is a fundamental phenomenon in an expanding
universe, which stresses that both the duration and wavelength of the emitted
light from a distant object at the redshift $z$ will be dilated by a factor of
$1+z$ at the observer. By using a sample of 139 \emph{Swift} long GRBs with
known redshift ($z\leq8.2$), we measure the observed duration ($T_{90}$) in the
observed energy range between $140/(1+z)$ keV and $350/(1+z)$ keV,
corresponding to a fixed energy range of 140-350 keV in the rest frame. We
obtain a significant correlation between the duration and the factor $1+z$,
i.e., $T_{\rm{90}}=10.5(1+z)^{0.94\pm0.26}$, which is well consistent with that
expected from cosmological time dilation effect.


title:
Data Assimilation for hyperbolic conservation laws. A Luenberger
  observer approach based on a kinetic description

abstract:
  Developing robust data assimilation methods for hyperbolic conservation laws
is a challenging subject. Those PDEs indeed show no dissipation effects and the
input of additional information in the model equations may introduce errors
that propagate and create shocks. We propose a new approach based on the
kinetic description of the conservation law. A kinetic equation is a first
order partial differential equation in which the advection velocity is a free
variable. In certain cases, it is possible to prove that the nonlinear
conservation law is equivalent to a linear kinetic equation. Hence, data
assimilation is carried out at the kinetic level, using a Luenberger observer
also known as the nudging strategy in data assimilation. Assimilation then
resumes to the handling of a BGK type equation. The advantage of this framework
is that we deal with a single "linear" equation instead of a nonlinear system
and it is easy to recover the macroscopic variables. The study is divided into
several steps and essentially based on functional analysis techniques. First we
prove the convergence of the model towards the data in case of complete
observations in space and time. Second, we analyze the case of partial and
noisy observations. To conclude, we validate our method with numerical results
on Burgers equation and emphasize the advantages of this method with the more
complex Saint-Venant system.


title: Has our brain grown too big to think effectively?

abstract:
  A variant of microcephalin, MCPH1 gene, was introgressed about 37,000 years
ago into Homo sapiens genetic pool from an archaic (Homo erectus) lineage and
rose to exceptionally high frequency of around 70 percent worldwide today. It
is involved in regulating neuroblast proliferation and its changes alter the
rate of division and/or differentiation of neuroblasts during the neurogenic
phase of embriogenesis, which could alter the size and structure of the
resulting brain.
  At the time of introgression, images had already been painted on the walls of
caves and speech has been in use for over 100,000 years, as had been abstract
thinking. Like today, reasoning and thinking were the primary faculties of
individuals. Homo erectus either did not possess those faculties or was
markedly inferior to Homo sapiens in them. Its brain was smaller and the cortex
was apparently less convoluted. Thus, introgressed microcephalin allele
directed neurogenesis evolutionary back to less complicated brain structure
typical for our evolutionary forefathers, slightly decreasing the level of
complexity already achieved by Homo sapiens 37,000 years ago. Despite that, it
proliferated at a rapid pace.
  It yields a supposition: 37,000 years ago the brains of Homo sapiens were too
big and too complicated for the kind of thinking needed for the highest fitness
of individuals. Since adaptation cannot by definition surpass selection
requirements, the volume and complication of the human brain did not originate
under selective pressure to improve effective thinking and they cannot be
explained in terms of such selection.
  A proposal to solve this quandary is presented, claiming that Homo sapiens
originated just by chance. Endurance running led to the emergence of Homo
sapiens. The human mind and larynx used for speech are side-effects of more
than a million years of endurance running by pre-human hunters.


title: Higgs Phenomenology in the Two-Singlet Model

abstract:
  We study the phenomenology of the Standard Model (SM) Higgs sector extended
by two singlet scalars. The model predicts two CP-even scalars $h_{1,2}$ which
are a mixture of doublet and singlet components as well as a pure singlet
scalar $S_{0}$ which is a dark matter candidate. We show that the model can
satisfy the relic density and direct detection constraints as well as all the
recent ATLAS and CMS measurements. We also discuss the effect of the extra
Higgs bosons on the different Higgs triple couplings $h_{i}h_{j}h_{k}$,
$i,j,k=1,2$. A particular attention is given to the triple self-coupling of the
SM-like Higgs where we found that the one loop corrections can reach $150\%$ is
some cases. We also discuss some production mechanisms for $h_{1}$ and $h_{2}$
at the LHC as well as at the future International Linear Collider. It is found
that the production cross section of a pair of SM-like Higgs bosons could be
much larger than the corresponding one in the SM and would reveal physics
beyond the SM if observable. We also show that in this model the branching
ratio of the SM-like Higgs decaying to two singlet scalars could be of the
order of $20\%$, therefore the production of the SM Higgs followed by its decay
to a pair of singlets would be an important source of production of singlet
scalars.


title:
Scan statistic tail probability assessment based on process covariance
  and window size

abstract:
  A scan statistic is examined for the purpose of testing the existence of a
global peak in a random process with dependent variables of any distribution.
The scan statistic tail probability is obtained based on the covariance of the
moving sums process, thereby accounting for the spatial nature of the data as
well as the size of the searching window. Exact formulas linking this
covariance to the window size and the correlation coefficient are developed
under general, common and auto covariance structures of the variables in the
original process. The implementation and applicability of the formulas are
demonstrated on families of multiple processes of t-statistics. A sensitivity
analysis provides further insight into the variant interaction of the tail
probability with the influence parameters. An R code for the tail probability
computation is offered within the supplementary material.


title: A Novel Type of Very Long Baseline Astronomical Intensity Interferometer

abstract:
  This article presents a novel type of very long baseline astronomical
interferometer that uses the fluctuations, as a function of time, of the
intensity measured by a quadratic detector, which is a common type of
astronomical detector. The theory on which the technique is based is validated
by laboratory experiments. Its outstanding principal advantages comes from the
fact that the angular structure of an astronomical object is simply determined
from the visibility of the minima of the spectrum of the intensity fluctuations
measured by the detector, as a function of the frequency of the fluctuations,
while keeping the spacing between mirrors constant. This would allow a simple
setup capable of high angular resolutions because it could use an extremely
large baseline. Another major interest is that it allows for a more efficient
use of telescope time because observations at a single baseline are sufficient,
while amplitude and intensity interferometers need several observations at
different baselines. The fact that one does not have to move the telescopes
would also allow detecting faster time variations because having to move the
telescopes sets a lower limit to the time variations that can be detected. The
technique uses wave interaction effects and thus has some characteristics in
common with intensity interferometry. A disadvantage of the technique, like in
intensity interferometry, is that it needs strong sources if observing at high
frequencies (e.g. the visible). This is a minor disadvantage in the radio
region. At high frequencies, this disadvantage is mitigated by the fact that,
like in intensity interferometry, the requirements of the optical quality of
the mirrors used are far less severe than in amplitude interferometry so that
poor quality large reflectors (e.g. Cherenkov telescopes) can be used in the
optical region.


title: Substring Suffix Selection

abstract:
  We study the following substring suffix selection problem: given a substring
of a string T of length n, compute its k-th lexicographically smallest suffix.
This a natural generalization of the well-known question of computing the
maximal suffix of a string, which is a basic ingredient in many other problems.
We first revisit two special cases of the problem, introduced by Babenko,
Kolesnichenko and Starikovskaya [CPM'13], in which we are asked to compute the
minimal non-empty and the maximal suffixes of a substring. For the maximal
suffixes problem, we give a linear-space structure with O(1) query time and
linear preprocessing time, i.e., we manage to achieve optimal construction and
optimal query time simultaneously. For the minimal suffix problem, we give a
linear-space data structure with O(\tau) query time and O(n log n / \tau)
preprocessing time, where 1 <= \tau <= log n is a parameter of the data
structure. As a sample application, we show that this data structure can be
used to compute the Lyndon decomposition of any substring of T in O(k \tau)
time, where k is the number of distinct factors in the decomposition.
  Finally, we move to the general case of the substring suffix selection
problem, where using any combinatorial properties seems more difficult.
Nevertheless, we develop a linear-space data structure with O(log^{2+\epsilon}
n) query time.


title:
Efficiency and dissipation in a two-terminal thermoelectric junction,
  emphasizing small dissipation

abstract:
  The efficiency and cooling power of a two-terminal thermoelectric
refrigerator are analyzed near the limit of vanishing dissipation (ideal
system), where the optimal efficiency is the Carnot one, but the cooling power
then unfortunately vanishes. This limit, where transport occurs only via a
single sharp electronic energy, has been referred to as "strong coupling" or
"the best thermoelectric". It follows however, that "parasitic" effects that
make the system deviate from the ideal limit, and reduce the efficiency from
the Carnot limit, are crucial for the usefulness of the device. Among these
parasitics, there are: parallel phonon conduction, finite width of the
electrons' transport band and more than a single energy transport channel. In
terms of a small parameter characterizing the deviation from the ideal limit,
the efficiency and power grow linearly, and the dissipation {\em
quadratically}. The results are generalized to the case of broken time-reversal
symmetry, and the major nontrivial changes are discussed. Finally, the recent
universal relation between the thermopower and the asymmetry of the dissipation
between the two terminals is briefly discussed, including the small dissipation
limit.


title:
Covariant Differential Identities and Conservation Laws in
  Metric-Torsion Theories of Gravitation. II. Manifestly Generally Covariant
  Theories

abstract:
  The present paper continues the work of the authors [arXiv:1306.6887
[gr-qc]]. Here, we study generally covariant metric-torsion theories of gravity
presented more concretely, setting that their Lagrangians are \emph{manifestly}
generally covariant scalars. It is assumed that Lagrangians depend on metric
tensor, curvature tensor, torsion tensor and its first and second covariant
derivatives, besides, on an arbitrary set of other tensor (matter) fields and
their first and second covariant derivatives. Thus, both the standard minimal
coupling with the Riemann-Cartan geometry and non-minimal coupling with the
curvature and torsion tensors are considered.
  The studies and results are as follow. (a) A physical interpretation of the
Noether and Klein identities is examined. It was found that they are the basis
for constructing equations of balance of energy-momentum tensors of various
types (canonical, metrical and Belinfante symmetrized). The equations of
balance are presented. (b) Using the generalized equations of balance, new
(generalized) manifestly generally covariant expressions for canonical
energy-momentum and spin tensors of the matter fields are constructed. In the
cases, when the matter Lagrangian contains both the higher derivatives and
non-minimal coupling with curvature and torsion, such generalizations are
non-trivial. (c) The Belinfante procedure is generalized for an arbitrary
Riemann-Cartan space. (d) A more convenient in applications generalized
expression for the canonical superpotential is obtained. (e) A total system of
equations for the gravitational fields and matter sources are presented in the
form more naturally generalizing the Einstein-Cartan equations with matter.
This result, being a one of more important results itself, is to be also a
basis for constructing physically sensible conservation laws and their
applications.


title:
Five-loop numerical evaluation of critical exponents of the $\varphi^4$
  theory

abstract:
  We present a new approach to calculation of anomalous dimensions in the
framework of $\epsilon$-expansion and renormalization group method. This
approach allows one to skip the calculation of renormalization constants and
express anomalous dimensions in terms of renormalized diagrams, which are
presented in a form suitable for numerical calculations. This approach can be
easily automated and extended to a wide range of models. The power of this
approach is illustrated on 5 loop calculations of beta-function and anomalous
dimensions in $\phi^4$ model.


title:
Excitation properties and effects of mass imbalance in the BCS-BEC
  crossover regime of an ultracold Fermi gas

abstract:
  We investigate single-particle properties of a mass-imbalanced Fermi gas in
the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover
region. In the presence of mass imbalance, we point out that the ordinary
$T$-matrix approximation, which has been extensively used to clarify various
BCS-BEC crossover physics in the mass-balanced case, unphysically gives a
double-valued solution in terms of the superfluid phase transition temperature
$T_{\rm c}$ in the crossover region. To overcome this serious problem, we
include higher order strong-coupling corrections beyond the $T$-matrix level.
Using this extended $T$-matrix theory, we calculate single-particle excitations
in the normal state above $T_{\rm c}$. The so-called pseudogap phenomena
originating from pairing fluctuations are shown to be different between the
light mass component and heavy mass component, which becomes more remarkable at
higher temperatures. Since Fermi condensates with hetero-Cooper pairs have
recently been discussed in various fields, such as exciton (polariton)
condensates, as well as color superconductivity, our results would be useful
for the further development of Fermi superfluid physics, beyond the
conventional superfluid state with homo-Cooper pairs.


title:
A Pohozaev identity and critical exponents of some complex Hessian
  equations

abstract:
  In this note, we prove some non-existence results for Dirichlet problems of
complex Hessian equations. The non-existence results are proved using the
Pohozaev method. We also prove existence results for radially symmetric
solutions. The main difference of the complex case with the real case is that
we don't know if a priori radially symmetric property holds in the complex
case.


title: Toeplitz Operators on Poly-analytic Spaces via Time-Scale Analysis

abstract:
  This is a review paper based on the series of our papers devoted to a
structure of true-poly-analytic Bergman function spaces over the upper
half-plane in the complex plane and to a detailed study of properties of
Toeplitz operators with separate symbols acting on them via methods of
time-scale analysis.


title: Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps

abstract:
  In this paper, we propose a stochastic process, which is a Cox-Ingersoll-Ross
process with Hawkes jumps. It can be seen as a generalization of the classical
Cox-Ingersoll-Ross process and the classical Hawkes process with exponential
exciting function. Our model is a special case of the affine point processes.
Laplace transforms and limit theorems have been obtained, including law of
large numbers, central limit theorems and large deviations.


title:
On the theoretical RF field limits of multilayer coating structures of
  superconducting resonator cavities

abstract:
  This Comment addresses theoretical field limits for
superconducting-insulating (S-I) thin films multilayers discussed by S. Posen,
G. Catelani, M. Liepe, J. Sethna, and M. Transtrum [1]. It is shown that their
criticism of the SIS multilayer approach [2] to reduce vortex dissipation in
superconducting RF resonator cavities is unsubstantiated


title: Twisted rods, helices and buckling solutions in three dimensions

abstract:
  The study of slender elastic structures is an archetypical problem in
continuum mechanics, dynamical systems and bifurcation theory, with a rich
history dating back to Euler's seminal work in the 18th century. These
filamentary elastic structures have widespread applications in engineering and
biology, examples of which include cables, textile industry, DNA experiments,
collagen modelling etc. One is typically interested in the equilibrium
configurations of these rod-like structures, their stability and dynamic
evolution and all three questions have been extensively addressed in the
literature. However, it is generally recognized that there are still several
open non-trivial questions related to three-dimensional analysis of rod
equilibria, inclusion of topological and positional constraints and different
kinds of boundary conditions.


title:
Probabilistic-valued decomposable set functions with respect to triangle
  functions

abstract:
  In the framework of the generalized measure theory the decomposable
probabilistic-valued set functions are introduced with triangle functions
$\tau$ in an appropriate probabilistic metric space as natural candidates for
the "addition", leading to the concept of $\tau$-decomposable measures. Several
set functions, among them the classical (sub)measures, previously defined
$\tau_T$-submeasures, $\tau_{L,A}$-submeasures as well as recently introduced
Shen's (sub)measures are described and investigated in a unified way. Basic
properties and characterizations of $\tau$-decomposable (sub)measures are also
studied and numerous extensions of results from the above mentioned papers are
provided.


title:
Groups having complete bipartite divisor graphs for their conjugacy
  class sizes

abstract:
  Given a finite group G, the bipartite divisor graph for its conjugacy class
sizes is the bipartite graph with bipartition consisting of the set of
conjugacy class sizes of G-Z (where Z denotes the centre of G) and the set of
prime numbers that divide these conjugacy class sizes, and with {p,n} being an
edge if gcd(p,n)\neq 1.
  In this paper we construct infinitely many groups whose bipartite divisor
graph for their conjugacy class sizes is the complete bipartite graph K_{2,5},
giving a solution to a question of Taeri.


title:
Probing weak force induced parity violation by high resolution
  mid-infrared molecular spectroscopy

abstract:
  To date no experiment has reached the level of sensitivity required to
observe weak nuclear force induced parity violation (PV) energy differences in
chiral molecules. In this paper, we present the approach, adopted at
Laboratoire de Physique des Lasers (LPL), to measure frequency differences in
the vibrational spectrum of enantiomers. We review different spectroscopic
methods developed at LPL leading to the highest resolutions, as well as 20
years of CO2 laser stabilization work enabling such precise measurements. After
a first attempt to observe PV vibrational frequency shifts using sub-Doppler
saturated absorption spectroscopy in a cell, we are currently aiming at an
experiment based on Doppler-free two-photon Ramsey interferometry on a
supersonic beam. We report on our latest progress towards observing PV with
chiral organo-metallic complexes containing a heavy rhenium atom.


title: Evolution of Random Wave Fields in the Water of Finite Depth

abstract:
  The evolution of random wave fields on the free surface is a complex process
which is not completely understood nowadays. For the sake of simplicity in this
study we will restrict our attention to the 2D physical problems only (i.e. 1D
wave propagation). However, the full Euler equations are solved numerically in
order to predict the wave field dynamics. We will consider the most studied
deep water case along with several finite depths (from deep to shallow waters)
to make a comparison. For each depth we will perform a series of Monte--Carlo
runs of random initial conditions in order to deduce some statistical
properties of an average sea state.


title: Orthogonal polynomials and diffusion operators

abstract:
  We want to describe the triplets (\Omega, (g), \mu) where (g) is the
(co)metric associated to some symmetric second order differential operator L
defined on the domain \Omega of R^d and such that L is expandable on a basis of
orthogonal polynomials of L_2(\mu), and \mu is some admissible measure. Up to
affine transformation, we find 11 compact domains in dimension 2, and also give
some non--compact cases in this dimension.


title: Splitting up method for the 2D stochastic Navier-Stokes equations

abstract:
  In this paper, we deal with the convergence of an iterative scheme for the
2-D stochastic Navier-Stokes Equations on the torus suggested by the
Lie-Trotter product formulas for stochastic differential equations of parabolic
type. The stochastic system is split into two problems which are simpler for
numerical computations. An estimate of the approximation error is given either
with periodic boundary conditions. In particular, we prove that the strong
speed of the convergence in probability is almost $1/2$. This is shown by means
of an $L^2(\Omega,P)$ convergence localized on a set of arbitrary large
probability. The assumptions on the diffusion coefficient depend on the fact
that some multiple of the Laplace operator is present or not with the
multiplicative stochastic term. Note that if one of the splitting steps only
contains the stochastic integral, then the diffusion coefficient may not
contain any gradient of the solution.


title: Fast transport of two ions in an anharmonic trap

abstract:
  We design fast trajectories of a trap to transport two ions using a
shortcut-to-adiabaticity technique based on invariants. The effects of
anharmonicity are analyzed first perturbatively, with an approximate, single
relative-motion mode, description. Then we use classical calculations and full
quantum calculations. This allows to identify discrete transport times that
minimize excitation in the presence of anharmonicity. An even better strategy
to suppress the effects of anharmonicity in a continuous range of transport
times is to modify the trajectory using an effective trap frequency shifted
with respect to the actual frequency by the coupling between relative and
center of mass motions.


title:
Universal Conductivity in a Two-Dimensional Superfluid-to-Insulator
  Quantum Critical System

abstract:
  We compute the universal conductivity of the (2+1)-dimensional XY
universality class, which is realized for a superfluid-to-Mott insulator
quantum phase transition at constant density. Based on large-scale Monte Carlo
simulations of the classical (2+1)-dimensional $J$-current model and the
two-dimensional Bose-Hubbard model, we can precisely determine the conductivity
on the quantum critical plateau, $\sigma(\infty)=0.359(4)\sigma_Q$ with
$\sigma_Q$ the conductivity quantum. The universal conductivity curve is the
standard example with the lowest number of components where the bottoms-up
AdS/CFT correspondence from string theory can be tested and made to use [R. C.
Myers, S. Sachdev, and A. Singh, Phys. Rev. D83, 066017 (2011)]. For the first
time, the shape of the $\sigma(i\omega_n)- \sigma(\infty)$ function in the
Matsubara representation is accurate enough for a conclusive comparison and
establishes the particle-like nature of charge transport. We find that the
holographic gauge/gravity duality theory for transport properties can be made
compatible with the data if temperature of the horizon of the black brane is
different from the temperature of the conformal field theory. The requirements
for measuring the universal conductivity in a cold gas experiment are also
determined by our calculation.

categories: cond-mat.str-el cond-mat.quant-gas gr-qc hep-th


title:
On weighted strong type inequalities for the generalized weighted mean
  operator

abstract:
  The generalized weighted mean operator $\mathbf{M}^{g}_{w}$ is given by
$$[\mathbf{M}^{g}_{w}f](x)=
g^{-1}\left(\frac{1}{W(x)}\int_{0}^{x}w(t)g(f(t))\,\mathrm{d}t\right),$$ with
$$W(x)=\int_{0}^{x} w(s)\,\mathrm{d}s, \quad \textrm{for} x \in (0, +\infty),$$
where $w$ is a positive measurable function on $(0,+\infty)$ and $g$ is a real
continuous strictly monotone function with its inverse $g^{-1}$. We give some
sufficient conditions on weights $u,v$ on $(0,+\infty)$ for which there exists
a positive constant $C$ such that the weighted strong type $(p,q)$ inequality
$$\left(\int_{0}^{\infty}
u(x)\Bigl([\mathbf{M}^{g}_{w}f](x)\Bigr)^{q}\,\mathrm{d}x \right)^{1 \over q}
\leq C \left(\int_{0}^{\infty}v(x)f(x)^{p}\,\mathrm{d}x \right)^{1 \over p} $$
holds for every measurable non-negative function $f$, where the positive reals
$p,q$ satisfy certain restrictions.


title:
Accessing interior magnetic field vector components in neutron electric
  dipole moment experiments via exterior measurements, I. Boundary-value
  techniques

abstract:
  We propose a new concept for determining the interior magnetic field vector
components in neutron electric dipole moment experiments. If a closed
three-dimensional boundary surface surrounding the fiducial volume of an
experiment can be defined such that its interior encloses no currents or
sources of magnetization, each of the interior vector field components and the
magnetic scalar potential will satisfy a Laplace equation. Therefore, if either
the vector field components or the normal derivative of the scalar potential
can be measured on the surface of this boundary, thus defining a Dirichlet or
Neumann boundary-value problem, respectively, the interior vector field
components or the scalar potential (and, thus, the field components via the
gradient of the potential) can be uniquely determined via solution of the
Laplace equation. We discuss the applicability of this technique to the
determination of the interior magnetic field components during the operating
phase of neutron electric dipole moment experiments when it is not, in general,
feasible to perform direct in situ measurements of the interior field
components. We also study the specifications that a vector field probe must
satisfy in order to determine the interior vector field components to a certain
precision. The technique we propose here may also be applicable to experiments
requiring monitoring of the vector magnetic field components within some closed
boundary surface, such as searches for neutron-antineutron oscillations along a
flight path or measurements in storage rings of the muon anomalous magnetic
moment $g-2$ and the proton electric dipole moment.


title: Abelian groups yield many large families for the diamond problem

abstract:
  There is much recent interest in excluded subposets. Given a fixed poset $P$,
how many subsets of $[n]$ can found without a copy of $P$ realized by the
subset relation? The hardest and most intensely investigated problem of this
kind is when $P$ is a diamond, i.e. the power set of a 2 element set. In this
paper, we show infinitely many asymptotically tight constructions using random
set families defined from posets based on Abelian groups. They are provided by
the convergence of Markov chains on groups. Such constructions suggest that the
diamond problem is hard.


title: Independence Conditions for Nets of Local Algebras as Sheaf Conditions

abstract:
  We apply constructions from topos-theoretic approaches to quantum theory to
algebraic quantum field theory. Thus a net of operator algebras is reformulated
as a functor that maps regions of spacetime into a category of ringed topoi. We
ask whether this functor is a sheaf, a question which is related to the net
satisfying certain kinematical independence conditions. In addition, we
consider a C*-algebraic version of Nuiten's recent sheaf condition, and
demonstrate how it relates to C*-independence of the underlying net of operator
algebras.


title: Topos Models for Physics and Topos Theory

abstract:
  What is the role of topos theory in the topos models for quantum theory as
used by Isham, Butterfield, Doring, Heunen, Landsman, Spitters and others? In
other words, what is the interplay between physical motivation for the models
and the mathematical framework used in these models? Concretely, we show that
the presheaf topos model of Butterfield, Isham and Doring resembles classical
physics when viewed from the internal language of the presheaf topos, similar
to the copresheaf topos model of Heunen, Landsman and Spitters. Both the
presheaf and copresheaf models provide a `quantum logic' in the form of a
complete Heyting algebra. Although these algebras are natural from a topos
theoretic stance, we seek a physical interpretation for the logical operations.
Finally, we investigate dynamics. In particular we describe how an automorphism
on the operator algebra induces a homeomorphism (or isomorphism of locales) on
the associated state spaces of the topos models, and how elementary
propositions and truth values transform under the action of this homeomorphism.
Also with dynamics the focus is on the internal perspective of the topos.


title: Holographic Superconducting Quantum Interference Device

abstract:
  We present a holographic model of the SQUID (Superconducting QUantum
Interference Device) in the external magnetic field. The model of the
gravitational theory considered in this paper is the Einstein-Maxwell-complex
scalar model on the four-dimensional Anti-de Sitter Schwarzschild black brane
geometry, where one space direction is compacted into a circle and we arrange
the coefficient of the time components profile so that we can model the SQUID,
where the profile plays the role of the chemical potential for the cooper pair.


abstract:
  In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for
Baumslag-Solitar groups with coefficients in an additive category.


title: Multiple Instance Learning with Bag Dissimilarities

abstract:
  Multiple instance learning (MIL) is concerned with learning from sets (bags)
of objects (instances), where the individual instance labels are ambiguous. In
this setting, supervised learning cannot be applied directly. Often,
specialized MIL methods learn by making additional assumptions about the
relationship of the bag labels and instance labels. Such assumptions may fit a
particular dataset, but do not generalize to the whole range of MIL problems.
Other MIL methods shift the focus of assumptions from the labels to the overall
(dis)similarity of bags, and therefore learn from bags directly. We propose to
represent each bag by a vector of its dissimilarities to other bags in the
training set, and treat these dissimilarities as a feature representation. We
show several alternatives to define a dissimilarity between bags and discuss
which definitions are more suitable for particular MIL problems. The
experimental results show that the proposed approach is computationally
inexpensive, yet very competitive with state-of-the-art algorithms on a wide
range of MIL datasets.


title:
Symmetric operations for all primes and Steenrod operations in Algebraic
  Cobordism

abstract:
  In this article we construct Symmetric operations for all primes (previously
known only for p=2). These unstable operations are more subtle than the
Landweber-Novikov operations, and encode all p-primary divisibilities of
characteristic numbers. Thus, taken together (for all primes) they plug the gap
left by the Hurewitz map L ---> Z[b_1,b_2,...], providing an important
structure on Algebraic Cobordism. Applications include: questions of
rationality of Chow group elements - see [11], and the structure of the Graded
Algebraic Cobordism. We also construct Steenrod operations of T.tom Dieck-style
in Algebraic Cobordism. These unstable multiplicative operations are more
canonical and subtle than Quillen-style operations, and complement the latter.


title: Possible Divergences in Tsallis' Thermostatistics

abstract:
  Trying to compute the nonextensive q-partition function for the Harmonic
Oscillator in more than two dimensions, one encounters that it diverges, which
poses a serious threat to the whole of Tsallis' thermostatistics. Appeal to the
so called q-Laplace Transform, where the q-exponential function plays the role
of the ordinary exponential, is seen to save the day.


title: On the Thermal Stability of Radiation Dominated Accretion Disks

abstract:
  We study the long-term thermal stability of radiation dominated disks in
which the vertical structure is determined self-consistently by the balance of
heating due to dissipation of MHD turbulence driven by the magneto-rotational
instability (MRI), and cooling due to radiation emitted at the photosphere. The
calculations adopt the local shearing box approximation, and utilize the
recently developed radiation transfer module in the Athena MHD code based on a
variable Eddington tensor rather than an assumed local closure. After
saturation of the MRI, in many cases the disk maintains a steady vertical
structure for many thermal times. However, in every case in which the box size
in the horizontal directions is at least one pressure scale height,
fluctuations associated with MRI turbulence and dynamo action in the disk
eventually trigger a thermal runaway which causes the disk to either expand or
contract until the calculation must be terminated. During runaway, the
dependence of the heating and cooling rates on total pressure satisfy the
simplest criterion for classical thermal instability. We identify several
physical reasons why the thermal runaway observed in our simulations differ
from the standard alpha disk model, for example the advection of radiation
contributes a non-negligible fraction to the vertical energy flux at the
largest radiation pressure, most of the dissipation does not happen in the disk
mid-plane, and the change of dissipation scale height with mid-plane pressure
is slower than the change of density scale height. We discuss how and why our
results differ from those published previously. Such thermal runaway behavior
might have important implications for interpreting temporal variability in
observed systems, but fully global simulations are required to study the
saturated state before detailed predictions can be made.


title:
A Cache-Coloring Based Technique for Saving Leakage Energy In
  Multitasking Systems

abstract:
  There has been a significant increase in leakage energy dissipation of CMOS
circuits with each technology generation. Further, due to their large size,
last level caches (LLCs) spend a large fraction of their energy in the form of
leakage energy and hence, addressing this has become extremely important to
meet the challenges of chip power budget. For addressing this, several
techniques have been proposed. However, most of these techniques require
offline profiling and hence cannot be used for real-life systems which usually
run multitasking programs, with possible pre-emptions. In this paper, we
propose a dynamic profiling based technique for saving cache leakage energy in
multitasking systems. Our technique uses a small coloring-based profiling
cache, to estimate performance and energy consumption of multiple cache
configurations and then selects the best (least-energy) configuration among
them. Our technique uses non-intrusive profiling and saves energy despite
intra-task and inter-task variations; thus, it is suitable for multitasking
systems. Simulations performed using workloads from SPEC2006 suite show the
superiority of our technique over an existing cache energy saving technique.
With a 2MB baseline cache, the average saving in memory sub-system energy is
22.8%.


title:
A new determination of the eta transition form factor in the Dalitz
  decay eta -> e^+ e^- gamma with the Crystal Ball/TAPS detectors at the Mainz
  Microtron

abstract:
  The Dalitz decay eta -> e^+ e^- gamma has been measured in the gamma p -> eta
p reaction with the Crystal Ball and TAPS multiphoton spectrometers, together
with the photon tagging facility at the Mainz Microtron MAMI. The experimental
statistic used in this work is one order of magnitude greater than in any
previous measurement of eta -> e^+ e^- gamma. The value obtained for the slope
parameter 1/Lambda^2 of the eta transition form factor, 1/Lambda^2 = (1.95 +/-
0.15_stat +/- 0.10_syst) [1/GeV^2], is in good agreement with recent
measurements conducted in eta -> e^+ e^- gamma and eta -> mu^+ mu^- gamma
decays, as well as with recent form-factor calculations. The uncertainty
obtained in the value of 1/Lambda^2 is lower compared to results from previous
measurements of the eta -> e^+ e^- gamma decay.


title:
A geometric reformulation of the representational assembly conjecture
  for the K-theory of fields with pro-l absolute Galois group

abstract:
  In this paper we prove a result which establishes an equivalence between the
representational assembly conjecture proposed by the author and a rigidity
question, in the case of Galois groups which are pro-l groups. In additional
work with R. Joshua, we will confirm the validity of this rigidity conjecture,
thereby proving the conjecture in the case of a pro-l absolute Galois group.


title: Alexander Duality and Rational Associahedra

abstract:
  A recent pair of papers of Armstrong, Loehr, and Warrington and Armstrong,
Williams, and the author initiated the systematic study of {\em rational
Catalan combinatorics} which is a generalization of Fuss-Catalan combinatorics
(which is in turn a generalization of classical Catalan combinatorics). The
latter paper gave two possible models for a rational analog of the
associahedron which attach simplicial complexes to any pair of coprime positive
integers a < b. These complexes coincide up to the Fuss-Catalan level of
generality, but in general one may be a strict subcomplex of the other.
Verifying a conjecture of Armstrong, Williams, and the author, we prove that
these complexes agree up to homotopy and, in fact, that one complex collapses
onto the other. This reconciles the two competing models for rational
associahedra. As a corollary, we get that the involution (a < b)
\longleftrightarrow (b-a < b) on pairs of coprime positive integers manifests
itself topologically as Alexander duality of rational associahedra. This
collapsing and Alexander duality are new features of rational Catalan
combinatorics which are invisible at the Fuss-Catalan level of generality.


title: The Brownian Net with Killing

abstract:
  Motivated by its relevance for the study of perturbations of one-dimensional
voter models, including stochastic Potts models at low temperature, we consider
diffusively rescaled coalescing random walks with branching and killing. Our
main result is convergence to a new continuum process, in which the random
space-time paths of the Sun-Swart Brownian net are terminated at a Poisson
cloud of killing points. We also prove existence of a percolation transition as
the killing rate varies. Key issues for convergence are the relations of the
discrete model killing points and their Poisson intensity measure to the
continuum counterparts.


title: LDC Arabic Treebanks and Associated Corpora: Data Divisions Manual

abstract:
  The Linguistic Data Consortium (LDC) has developed hundreds of data corpora
for natural language processing (NLP) research. Among these are a number of
annotated treebank corpora for Arabic. Typically, these corpora consist of a
single collection of annotated documents. NLP research, however, usually
requires multiple data sets for the purposes of training models, developing
techniques, and final evaluation. Therefore it becomes necessary to divide the
corpora used into the required data sets (divisions). This document details a
set of rules that have been defined to enable consistent divisions for old and
new Arabic treebanks (ATB) and related corpora.


title: Lie-Poisson theory for direct limit Lie algebras

abstract:
  In this paper, we develop the fundamentals of Lie-Poisson theory for direct
limits $G=\dirlim G_{n}$ of complex algebraic groups $G_{n}$ and their Lie
algebras $\fg=\dirlim \fg_{n}$. We show that $\fg^{*}=\invlim\fg_{n}^{*}$ has
the structure of a Poisson provariety and that each coadjoint orbit of $G$ on
$\fg^{*}$ has the structure of an ind-variety. We construct a weak symplectic
form on every coadjoint orbit and prove that the coadjoint orbits form a weak
symplectic foliation of the Poisson provariety $\fg^{*}$. We apply our results
to the specific setting of $G=GL(\infty)=\dirlim GL(n,\C)$ and $\fg^{*}=
M(\infty)=\invlim \fgl(n,\C)$, the space of infinite complex matrices with
arbitrary entries. We construct a Gelfand-Zeitlin integrable system on
$M(\infty)$, which generalizes the one constructed by Kostant and Wallach on
$\fgl(n,\C)$. The system integrates to an action of a direct limit group
$A(\infty)$ on $M(\infty)$, whose generic orbits are Lagrangian
ind-subvarieties of the corresponding coadjoint orbit of $GL(\infty)$ on
$M(\infty)$.


title:
Multiband Superconductivity in KFe2As2: Evidence for one Isotropic and
  several Liliputian Energy Gaps

abstract:
  We report a detailed low-temperature thermodynamic investigation (heat
capacity and magnetization) of the superconducting state of KFe2As2 for H || c
axis. Our measurements reveal that the properties of KFe2As2 are dominated by a
relatively large nodeless energy gap (Delta?0 = 1.9 kBTc) which excludes dx2-y2
symmetry. We prove the existence of several additional extremely small gaps
(?Delta0 < 1.0 kBTc) that have a profound impact on the low-temperature and
low-field behavior, similar to MgB2, CeCoIn5 and PrOs4Sb12. The zero-field heat
capacity is analyzed in a realistic self-consistent 4-band BCS model which
qualitatively reproduces the recent laser ARPES results of Okazaki et al.
(Science 337 (2012) 1314). Our results show that extremely low-temperature
measurements, i.e. T < 0.1 K, will be required in order to resolve the question
of the existence of line nodes in this compound.


title: A new look at reweighted message passing

abstract:
  We propose a new family of message passing techniques for MAP estimation in
graphical models which we call {\em Sequential Reweighted Message Passing}
(SRMP). Special cases include well-known techniques such as {\em Min-Sum
Diffusion} (MSD) and a faster {\em Sequential Tree-Reweighted Message Passing}
(TRW-S). Importantly, our derivation is simpler than the original derivation of
TRW-S, and does not involve a decomposition into trees. This allows easy
generalizations. We present such a generalization for the case of higher-order
graphical models, and test it on several real-world problems with promising
results.


title:
Some fourth order nonlinear elliptic problems related to epitaxial
  growth

abstract:
  This paper deals with some mathematical models arising in the theory of
epitaxial growth of crystal. We focalize the study on a stationary problem
which presents some analytical difficulties. We study the existence of
solutions. The central model in this work is given by the following fourth
order elliptic equation, $$\begin{array}{rclll} \Delta^2 u=\text{det} \left(D^2
u \right) &+&\lambda f, \quad & x\in \Omega\subset\mathbb{R}^2\\
\hbox{conditions on} &\quad& & \partial \Omega. \end{array} $$ The framework to
study the problem deeply depends on the boundary conditions.


title: A Hybrid Algorithm for Matching Arabic Names

abstract:
  In this paper, a new hybrid algorithm which combines both of token-based and
character-based approaches is presented. The basic Levenshtein approach has
been extended to token-based distance metric. The distance metric is enhanced
to set the proper granularity level behavior of the algorithm. It smoothly maps
a threshold of misspellings differences at the character level, and the
importance of token level errors in terms of token's position and frequency.
Using a large Arabic dataset, the experimental results show that the proposed
algorithm overcomes successfully many types of errors such as: typographical
errors, omission or insertion of middle name components, omission of
non-significant popular name components, and different writing styles character
variations. When compared the results with other classical algorithms, using
the same dataset, the proposed algorithm was found to increase the minimum
success level of best tested algorithms, while achieving higher upper limits .


title: On radial stationary solutions to a model of nonequilibrium growth

abstract:
  We present the formal geometric derivation of a nonequilibrium growth model
that takes the form of a parabolic partial differential equation. Subsequently,
we study its stationary radial solutions by means of variational techniques.
Our results depend on the size of a parameter that plays the role of the
strength of forcing. For small forcing we prove the existence and multiplicity
of solutions to the elliptic problem. We discuss our results in the context of
nonequilibrium statistical mechanics.


title:
Existence and nonexistence results for a singular boundary value problem
  arising in the theory of epitaxial growth

abstract:
  The existence of stationary radial solutions to a partial differential
equation arising in the theory of epitaxial growth is studied. Our results
depend on the size of a parameter that plays the role of the velocity at which
mass is introduced into the system. For small values of this parameter we prove
existence of solutions to this boundary value problem. For large values of the
same parameter we prove nonexistence of solutions. We also provide rigorous
bounds for the values of this parameter which separate existence from
nonexistence. The proofs come as a combination of several differential
inequalities and the method of upper and lower functions.


title: Spike Synchronization Dynamics of Small-World Networks

abstract:
  In this research report, we examine the effects of small-world network
organization on spike synchronization dynamics in networks of Izhikevich
spiking units. We interpolate network organizations from regular ring lattices,
through the small-world region, to random networks, and measure global spike
synchronization dynamics. We examine how average path length and clustering
effect the dynamics of global and neighborhood clique spike organization and
propagation. We show that the emergence of global synchronization undergoes a
phase transition in the small-world region, between the clustering and path
length phase transitions that are known to exist. We add additional realistic
constraints on the dynamics by introducing propagation delays of spiking
signals proportional to wiring length. The addition of delays interferes with
the ability of random networks to sustain global synchronization, in relation
to the breakdown of clustering in the networks. The addition of delays further
enhances the finding that small-world organization is beneficial for balancing
neighborhood synchronized waves of organization with global synchronization
dynamics.


title: Gap probabilities and applications to geometry and random topology

abstract:
  We give an exact formula for the value of the derivative at zero of the gap
probability in finite n x n Gaussian ensembles. As n goes to infinity our
computation provides an asymptotic (with an explicit constant) of the order
n^(1/2).
  As a first application, we consider the set of n x n (Real, Complex or
Quaternionic) Hermitian matrices with Frobenius norm one and determinant zero.
We give an exact formula for the intrinsic volume of this set and as n goes to
infinity its asymptotic (with an explicit constant) is of the order n^(1/2).
  As a second application we consider the problem of computing Betti numbers of
an intersection of k random Kostlan quadrics in RP^n. We show that the i-th
Betti number is asymptotically expected to be one (for i sufficiently away from
n/2).
  In the case k=2 the the sum of all Betti numbers was recently shown by the
first author to equal n+o(n). Here we sharpen this asymptotic proving an
asymptotic with two orders of precision and explicit constants.


title: Hydrodynamic capture of microswimmers into sphere-bound orbits

abstract:
  Self-propelled particles can exhibit surprising non-equilibrium behaviors,
and how they interact with obstacles or boundaries remains an important open
problem. Here we show that chemically propelled micro-rods can be captured,
with little change in their speed, into close orbits around solid spheres
resting on or near a horizontal plane. We show that this interaction between
sphere and particle is short-range, occurring even for spheres smaller than the
particle length, and for a variety of sphere materials. We consider a simple
model, based on lubrication theory, of a force- and torque-free swimmer driven
by a surface slip (the phoretic propulsion mechanism) and moving near a solid
surface. The model demonstrates capture, or movement towards the surface, and
yields speeds independent of distance. This study reveals the crucial aspects
of activity-driven interactions of self-propelled particles with passive
objects, and brings into question the use of colloidal tracers as probes of
active matter.


title: Link-based formalism for time evolution of adaptive networks

abstract:
  Network topology and nodal dynamics are two fundamental stones of adaptive
networks. Detailed and accurate knowledge of these two ingredients is crucial
for understanding the evolution and mechanism of adaptive networks. In this
paper, by adopting the framework of the adaptive SIS model proposed by Gross et
al. [Phys. Rev. Lett. 96, 208701 (2006)] and carefully utilizing the
information of degree correlation of the network, we propose a link-based
formalism for describing the system dynamics with high accuracy and subtle
details. Several specific degree correlation measures are introduced to reveal
the coevolution of network topology and system dynamics.


title:
A 7-core erbium doped double-clad fiber amplifier with side-coupled
  pumping

abstract:
  We demonstrate a 7-core erbium doped fiber amplifier employing side pumping
using tapered multimode fiber. The amplifier has multicore inputs and outputs
which can be readily spliced to multicore transmission fiber for amplifying
space division multiplexed signals. Gain over 25dB was obtained in each of the
cores over a 40-nm bandwidth covering C-band.


title: The Two-Loop Ladder Diagram and Representations of U(2,2)

abstract:
  Feynman diagrams are a pictorial way of describing integrals predicting
possible outcomes of interactions of subatomic particles in the context of
quantum field physics. It is highly desirable to have an intrinsic mathematical
interpretation of Feynman diagrams, and in this article we find the
representation-theoretic meaning of a particular kind of Feynman diagrams
called the two-loop ladder diagram. This is done in the context of
representations of a Lie group U(2,2), its Lie algebra u(2,2) and quaternionic
analysis. The results and techniques developed in this article are used in [L]
to provide a mathematical interpretation of all conformal four-point integrals
- including those described by the n-loop ladder diagrams - in the context of
representations U(2,2) and quaternionic analysis. Moreover, this
representation-quaternionic model produces a proof of "magic identities" in the
Minkowski metric space.
  No prior knowledge of physics or Feynman diagrams is assumed from the reader.
We provide a summary of all relevant results from quaternionic analysis to make
the article self-contained.


title:
Cox rings of moduli of quasi parabolic principal bundles and the K-Pieri
  rule

abstract:
  We study a toric degeneration of the Cox ring of the moduli of principal
$SL_m(\mathbb{C})$ bundles on the projective line, with quasi parabolic data
given by the the stabilizer of the highest weight vector in $\mathbb{C}^m$ and
its dual $\bigwedge^{m-1}(\mathbb{C}^m)$. The affine semigroup algebra
resulting from this degeneration is described using the $K-$Pieri rule from
Kac-Moody representation theory. Along the way we give a proof of the $K-$Pieri
rule which utilizes the classical Pieri rule and elements of commutative
algebra, and we describe a relationship between the Cox ring and a classical
invariant ring studied by Weyl.


title: The Fate of Evolutionary Archaeology: Survival or Extinction?

abstract:
  It is important to be clear as to whether a theory such as evolutionary
archaeology pertains to biological evolution, in which acquired change is
obliterated at the end of each generation, or cultural change, in which
acquired change is retained. In evolutionary archaeology, (1) the population is
said to consist of artifacts, yet (2) artifacts are said to be phenotypic.
Neither (1) nor (2) is necessarily problematic in and of itself, but the two
are inconsistent, as the first pertains to cultural change whereas the second
to the biological evolution of humans. A first step to avoiding this problem is
to recognize that there is a need for a theory of change specific to human
culture. Referring to ongoing work using a related approach to cultural change,
it is suggested that the inconsistencies in evolutionary archaeology, though
problematic, are not insurmountable.


title:
Pseudorandomness for Multilinear Read-Once Algebraic Branching Programs,
  in any Order

abstract:
  We give deterministic black-box polynomial identity testing algorithms for
multilinear read-once oblivious algebraic branching programs (ROABPs), in
n^(lg^2 n) time. Further, our algorithm is oblivious to the order of the
variables. This is the first sub-exponential time algorithm for this model.
Furthermore, our result has no known analogue in the model of read-once
oblivious boolean branching programs with unknown order, as despite recent work
there is no known pseudorandom generator for this model with sub-polynomial
seed-length (for unbounded-width branching programs).
  This result extends and generalizes the result of Forbes and Shpilka that
obtained a n^(lg n)-time algorithm when given the order. We also extend and
strengthen the work of Agrawal, Saha and Saxena that gave a black-box algorithm
running in time exp((lg n)^d) for set-multilinear formulas of depth d. We note
that the model of multilinear ROABPs contains the model of set-multilinear
algebraic branching programs, which itself contains the model of
set-multilinear formulas of arbitrary depth. We obtain our results by
recasting, and improving upon, the ideas of Agrawal, Saha and Saxena. We phrase
the ideas in terms of rank condensers and Wronskians, and show that our results
improve upon the classical multivariate Wronskian, which may be of independent
interest.
  In addition, we give the first n^(lglg n) black-box polynomial identity
testing algorithm for the so called model of diagonal circuits. This model,
introduced by Saxena has recently found applications in the work of Mulmuley,
as well as in the work of Gupta, Kamath, Kayal, Saptharishi. Previously work
had given n^(lg n)-time algorithms for this class. More generally, our result
holds for any model computing polynomials whose partial derivatives (of all
orders) span a low dimensional linear space.


title:
Obtaining topological degenerate ground states by the density matrix
  renormalization group

abstract:
  We develop the density matrix renormalization group approach to
systematically identify the topological order of the quantum spin liquid (QSL)
through adiabatically obtaining different topological sectors of the QSL on an
infinite cylinder. As an application, we study the anisotropic kagome
Heisenberg model known for hosting a Z$_2$ QSL, however no numerical
simulations have been able to access all four sectors before. We obtain the
complete set of four topological degenerate ground states distinguished by the
presence or absence of the spinon and vison quasiparticle line, which fully
characterizes the topological nature of the quantum phase. We have also studied
the kagome Heisenberg model, which has attracted a lot of recent attention. We
find two topological sectors accurately and also estimate various properties of
the other topological sectors, where the larger correlation length is found
indicating the possible proximity to another phase.


title:
Applying Complexity Theory to a Dynamical Process Model of the
  Development of Pathological Belief Systems

abstract:
  A general dynamical process model of psychiatric disorders is proposed that
specifies the basic cognitive processes involved in the transition from beliefs
about self, others and world that are normal and adaptive, to beliefs that are
rigid, extreme, and maladaptive. The relevant thought trajectories are
self-confirming, and are considered to underlie the corresponding trajectories
in symptoms. In contrast with previous work, the model focuses on underlying
mechanisms, and it provides an evolutionary basis for the widespread
susceptibility to psychiatric symptoms and disorders without the problematic
claim that such disorders were selected by evolutionary forces. The model
thereby incorporates both normality and abnormality in the same framework.


title: Vive la Diff\'erence: Paxos vs. Viewstamped Replication vs. Zab

abstract:
  Paxos, Viewstamped Replication, and Zab are replication protocols that ensure
high-availability in asynchronous environments with crash failures. Various
claims have been made about similarities and differences between these
protocols. But how does one determine whether two protocols are the same, and
if not, how significant the differences are?
  We propose to address these questions using refinement mappings, where
protocols are expressed as succinct specifications that are progressively
refined to executable implementations. Doing so enables a principled
understanding of the correctness of the different design decisions that went
into implementing the various protocols. Additionally, it allowed us to
identify key differences that have a significant impact on performance.


title: Completeness for sparse potential scattering

abstract:
  The current paper is devoted to the scattering theory of a class of continuum
Schr\"{o}dinger operators with deterministic sparse potentials. We first
establish the limiting absorption principle for both modified free resolvents
and modified perturbed resolvents. This actually is a weak form of the
classical limiting absorption principle. We then prove the existence and
completeness of local wave operators, which, in particular, imply the existence
of wave operators. Under additional assumptions on the sparse potential, we
prove the completeness of wave operators. In the context of continuum
Schr\"{o}dinger operators with sparse potentials, this paper gives the first
proof of the completeness of wave operators.


title: Introduction to the Special Issue on Quantum Cognition

abstract:
  The subject of this special issue is quantum models of cognition. At first
sight it may seem bizarre, even ridiculous, to draw a connection between
quantum mechanics, a highly successful theory usually understood as modeling
sub-atomic phenomena, and cognitive science. However, a growing number of
researchers are looking to quantum theory to circumvent stubborn problems
within their own fields. This is also true within cognitive science and related
areas, hence this special issue.


title:
A note on the five valued conjectures of Johansen and Helleseth and zeta
  functions

abstract:
  For the complete five-valued cross-correlation distribution between two
$m$-sequences ${s_t}$ and ${s_{dt}}$ of period $2^m-1$ that differ by the
decimation $d={{2^{2k}+1}\over {2^k+1}}$ where $m$ is odd and
$\mbox{gcd}(k,m)=1$, Johansen and Hellseth expressed it in terms of some
exponential sums. And two conjectures are presented that are of interest in
their own right. In this correspondence we study these conjectures for the
particular case where $k=3$, and the cases $k=1,2$ can also be analyzed in a
similar process. When $k>3$, the degrees of the relevant polynomials will
become higher.
  Here the multiplicity of the biggest absolute value of the cross-correlation
is no more than one-sixth of the multiplicity corresponding the smallest
absolute value.


title: Interactive proofs for BQP via self-tested graph states

abstract:
  Using the measurement-based quantum computation model, we construct
interactive proofs with non-communicating quantum provers and a classical
verifier. Our construction gives interactive proofs for all languages in BQP
with a polynomial number of quantum provers, each of which, in the honest case,
performs only a single measurement.
  Our techniques use self-tested graph states. In this regard we introduce two
important improvements over previous work. Specifically, we derive new error
bounds which scale polynomially with the size of the graph compared with
exponential dependence on the size of the graph in previous work. We also
extend the self-testing error bounds on measurements to a very general set
which includes the adaptive measurements used for measurement-based quantum
computation as a special case.