title: A Deep Hierarchical Approach to Lifelong Learning in Minecraft

abstract:
  We propose a lifelong learning system that has the ability to reuse and
transfer knowledge from one task to another while efficiently retaining the
previously learned knowledge-base. Knowledge is transferred by learning
reusable skills to solve tasks in Minecraft, a popular video game which is an
unsolved and high-dimensional lifelong learning problem. These reusable skills,
which we refer to as Deep Skill Networks, are then incorporated into our novel
Hierarchical Deep Reinforcement Learning Network (H-DRLN) architecture using
two techniques: (1) a deep skill array and (2) skill distillation, our novel
variation of policy distillation (Rusu et. al. 2015) for learning skills. Skill
distillation enables the HDRLN to efficiently retain knowledge and therefore
scale in lifelong learning, by accumulating knowledge and encapsulating
multiple reusable skills into a single distilled network. The H-DRLN exhibits
superior performance and lower learning sample complexity compared to the
regular Deep Q Network (Mnih et. al. 2015) in sub-domains of Minecraft.


title: Wavelet Algorithm for Circuit Simulation

abstract:
  We present a new adaptive circuit simulation algorithm based on spline
wavelets. The unknown voltages and currents are expanded into a wavelet
representation, which is determined as solution of nonlinear equations derived
from the circuit equations by a Galerkin discretization. The spline wavelet
representation is adaptively refined during the Newton iteration. The resulting
approximation requires an almost minimal number of degrees of freedom, and in
addition the grid refinement approach enables very efficient numerical
computations. Initial numerical tests on various types of electronic circuits
show promising results when compared to the standard transient analysis.


title: Isomorphic copies of $l^\infty$ in Ces\`aro-Orlicz function spaces

abstract:
  We characterize Ces\`aro-Orlicz function spaces $Ces_\varphi$ containing
isomorphic copy of $l^\infty$. We also describe the subspaces $(Ces_\varphi)_a$
of all order continuous elements of $Ces_\varphi$. Finally, we study the
monotonicity structure of the spaces $Ces_\varphi$ and $(Ces_\varphi)_a$.


title:
Control of valley dynamics in silicon quantum dots in the presence of an
  interface step

abstract:
  Recent experiments on silicon nanostructures have seen breakthroughs toward
scalable, long-lived quantum information processing. The valley degree of
freedom plays a fundamental role in these devices, and the two lowest-energy
electronic states of a silicon quantum dot can form a valley qubit. In this
work, we show that a single-atom high step at the silicon/barrier interface
induces a strong interaction of the qubit and in-plane electric fields, and
analyze the consequences of this enhanced interaction on the dynamics of the
qubit. The charge densities of the qubit states are deformed differently by the
interface step, allowing non-demolition qubit readout via valley-to-charge
conversion. A gate-induced in-plane electric field together with the interface
step enables fast control of the valley qubit via electrically driven valley
resonance. We calculate single- and two-qubit gate times, as well as relaxation
and dephasing times, and present predictions for the parameter range where the
gate times can be much shorter than the relaxation time and dephasing is
reduced.


title:
A Distributed Auctioneer for Resource Allocation in Decentralized
  Systems

abstract:
  In decentralized systems, nodes often need to coordinate to access shared
resources in a fair manner. One approach to perform such arbitration is to rely
on auction mechanisms. Although there is an extensive literature that studies
auctions, most of these works assume the existence of a central, trusted
auctioneer. Unfortunately, in fully decentralized systems, where the nodes that
need to cooperate operate under separate spheres of control, such central
trusted entity may not exist. Notable examples of such decentralized systems
include community networks, clouds of clouds, cooperative nano data centres,
among others. In this paper, we make theoretical and practical contributions to
distribute the role of the auctioneer. From the theoretical perspective, we
propose a framework of distributed simulations of the auctioneer that are Nash
equilibria resilient to coalitions and asynchrony. From the practical
perspective, our protocols leverage the distributed nature of the simulations
to parallelise the execution. We have implemented a prototype that instantiates
the framework for bandwidth allocation in community networks, and evaluated it
in a real distributed setting.


title: Characterization of greedy bases in Banach spaces

abstract:
  We shall present a new characterization of greedy bases and 1-greedy bases in
terms of certain functionals defined using distances to one dimensional
subspaces generated by the basis. We also introduce a new property that unifies
the notions of unconditionality and democracy and allows us to recover a better
dependence on the constants.


title:
Adaptive Leader-Following Consensus for Uncertain Euler-Lagrange Systems
  under Directed Switching Networks

abstract:
  The leader-following consensus problem for multiple Euler-Lagrange systems
was studied recently by the adaptive distributed observer approach under the
assumptions that the leader system is neurally stable and the communication
network is jointly connected and undirected. In this paper, we will study the
same problem without assuming that the leader system is neutrally stable, and
the communication network is undirected. The effectiveness of this new result
will be illustrated by an example.


title: Magnon based logic in a multi-terminal YIG/Pt nanostructure

abstract:
  Boolean logic is the foundation of modern digital information processing.
Recently, there has been a growing interest in phenomena based on pure spin
currents, which allow to move from charge to spin based logic gates. We study a
proof-of-principle logic device based on the ferrimagnetic insulator Yttrium
Iron Garnet (YIG), with Pt strips acting as injectors and detectors for
nonequilibrium magnons. We experimentally observe incoherent superposition of
magnons generated by different injectors. This allows to implement a fully
functional majority gate, enabling multiple logic operations (AND and OR) in
one and the same device. Clocking frequencies of the order of several GHz and
straightforward down-scaling make our device promising for applications.


title: A note on the Gauge Symmetries of Unimodular Gravity

abstract: The symmetries of Unimodular Gravity are clarified somewhat.


title:
Scalable Bayesian Variable Selection for Structured High-dimensional
  Data

abstract:
  Variable selection for structured covariates lying on an underlying known
graph is a problem motivated by practical applications, and has been a topic of
increasing interest. However, most of the existing methods may not be scalable
to high dimensional settings involving tens of thousands of variables lying on
known pathways such as the case in genomics studies. We propose an adaptive
Bayesian shrinkage approach which incorporates prior network information by
smoothing the shrinkage parameters for connected variables in the graph, so
that the corresponding coefficients have a similar degree of shrinkage. We fit
our model via a computationally efficient expectation maximization algorithm
which scalable to high dimensional settings (p~100,000). Theoretical properties
for fixed as well as increasing dimensions are established, even when the
number of variables increases faster than the sample size. We demonstrate the
advantages of our approach in terms of variable selection, prediction, and
computational scalability via a simulation study, and apply the method to a
cancer genomics study.


title:
Logical inference approach to relativistic quantum mechanics: derivation
  of the Klein-Gordon equation

abstract:
  The logical inference approach to quantum theory, proposed earlier [Ann.
Phys. 347 (2014) 45-73], is considered in a relativistic setting. It is shown
that the Klein-Gordon equation for a massive, charged, and spinless particle
derives from the combination of the requirements that the space-time data
collected by probing the particle is obtained from the most robust experiment
and that on average, the classical relativistic equation of motion of a
particle holds.


title:
Theoretical assessment of the disparity in the electrostatic forces
  between two point charges and two conductive spheres of equal radii

abstract:
  The Coulomb's formula for the force FC of electrostatic interaction between
two point charges is well known. In reality, however, interactions occur not
between point charges, but between charged bodies of certain geometric form,
size and physical structure. This leads to deviation of the estimated force FC
from the real force F of electrostatic interaction, thus imposing the task to
evaluate the disparity. In the present paper the problem is being solved
theoretically for two charged conductive spheres of equal radii and arbitrary
electric charges. Assessment of the deviation is given as a function of the
ratio of the distance R between the spheres centers to the sum of their radii.
For the purpose, relations between FC and F derived in a preceding work of
ours, are employed to generalize the Coulomb's interactions. At relatively
short distances between the spheres, the Coulomb force FC, as estimated to be
induced by charges situated at the centers of the spheres, differ significantly
from the real force F of interaction between the spheres. In the case of zero
and non-zero charge we prove that with increasing the distance between the two
spheres, the force F decrease rapidly, virtually to zero values, i.e. it
appears to be short-acting force.


title:
The existence of non-inner automorphisms of order p in finite thin
  p-groups

abstract:
  In this paper we study the existence of at least one non-inner automorphism
of order p of a finite thin p-group, for any prime p.


title: On the zone complexity of a vertex

abstract:
  Let $L$ be a set of $n$ lines in the real projective plane in general
position. We show that there exists a vertex $v\in \A(L)$ such that $v$ is
positioned in a face of size at most 5 in the arrangement obtained by removing
the two lines passing through $v$.


title: CMA-ES for Hyperparameter Optimization of Deep Neural Networks

abstract:
  Hyperparameters of deep neural networks are often optimized by grid search,
random search or Bayesian optimization. As an alternative, we propose to use
the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which is known
for its state-of-the-art performance in derivative-free optimization. CMA-ES
has some useful invariance properties and is friendly to parallel evaluations
of solutions. We provide a toy example comparing CMA-ES and state-of-the-art
Bayesian optimization algorithms for tuning the hyperparameters of a
convolutional neural network for the MNIST dataset on 30 GPUs in parallel.


title: Equivariant Gromov-Witten Theory of GKM Orbifolds

abstract:
  In this paper, we study the all genus Gromov-Witten theory for any GKM
orbifold $X$. We generalize the Givental formula which is studied in the smooth
case in \cite{Giv2} \cite{Giv3} \cite{Giv4} to the orbifold case. Specifically,
we recover the higher genus Gromov-Witten invariants of a GKM orbifold $X$ by
its genus zero data. When $X$ is toric, the genus zero Gromov-Witten invariants
of $X$ can be explicitly computed by the mirror theorem studied in \cite{CCIT}
and our main theorem gives a closed formula for the all genus Gromov-Witten
invariants of $X$. When $X$ is a toric Calabi-Yau 3-orbifold, our formula leads
to a proof of the Remodeling Conjecture in \cite{Fang-Liu-Zong3}.


title: A metric interpretation of reflexivity for Banach spaces

abstract:
  We define two metrics $d_{1,\alpha}$ and $d_{\infty,\alpha}$ on each Schreier
family $\mathcal{S}_\alpha$, $\alpha<\omega_1$, with which we prove the
following metric characterization of reflexivity of a Banach space $X$: $X$ is
reflexive if and only if there is an $\alpha<\omega_1$, so that there is no
mapping $\Phi:\mathcal{S}_\alpha\to X$ for which $$ cd_{\infty,\alpha}(A,B)\le
\|\Phi(A)-\Phi(B)\|\le C d_{1,\alpha}(A,B) \text{ for all
$A,B\in\mathcal{S}_\alpha$.}$$ Secondly, we prove for separable and reflexive
Banach spaces $X$, and certain countable ordinals $\alpha$ that $\max(\text{
Sz}(X),\text{ Sz}(X^*))\le \alpha$ if and only if $({\mathcal S}_\alpha,
d_{1,\alpha})$ does not bi-Lipschitzly embed into $X$. Here $\text{Sz}(Y)$
denotes the Szlenk index of a Banach space $Y$.


title:
Loss-induced enhanced transmission in anisotropic density-near-zero
  acoustic metamaterials

abstract:
  Anisotropic density-near-zero (ADNZ) acoustic metamaterials are investigated
theoretically and numerically in this letter and are shown to exhibit
extraordinary transmission enhancement when material loss is induced. The
enhanced transmission is due to the enhanced propagating and evanescent wave
modes inside the ADNZ medium thanks to the interplay of near-zero density,
material loss, and high wave impedance matching in the propagation direction.
The equi-frequency contour (EFC) is used to reveal whether the propagating wave
mode is allowed in ADNZ metamaterials. Numerical simulations based on
plate-type acoustic metamaterials with different material losses were performed
to demonstrate collimation enabled by the induced loss in ADNZ media. This work
provides a different way for manipulating acoustic waves.


title: The number of labeled graphs of bounded treewidth

abstract:
  We focus on counting the number of labeled graphs on $n$ vertices and
treewidth at most $k$ (or equivalently, the number of labeled partial
$k$-trees), which we denote by $T_{n,k}$. So far, only the particular cases
$T_{n,1}$ and $T_{n,2}$ had been studied. We show that $$ \left(c \cdot
\frac{k\cdot 2^k \cdot n}{\log k} \right)^n \cdot 2^{-\frac{k(k+3)}{2}} \cdot
k^{-2k-2}\ \leq\ T_{n,k}\ \leq\ \left(k \cdot 2^k \cdot n\right)^n \cdot
2^{-\frac{k(k+1)}{2}} \cdot k^{-k}, $$ for $k > 1$ and some explicit absolute
constant $c > 0$. The upper bound is an immediate consequence of the well-known
number of labeled $k$-trees, while the lower bound is obtained from an explicit
algorithmic construction. It follows from this construction that both bounds
also apply to graphs of pathwidth and proper-pathwidth at most $k$.


title:
Spacetime characterizations of $\Lambda$-vacuum metrics with a null
  Killing 2-form

abstract:
  An exhaustive list of four-dimensional $\Lambda$-vacuum spacetimes admitting
a Killing vector whose self-dual Killing two-form ${\cal F}$ is null is
obtained assuming that the self-dual Weyl tensor is proportional to the tensor
product of ${\cal F}$ by itself. Our analysis complements previous results
concerning the case with non-null ${\cal F}$. We analyze both cases with
$\Lambda$ vanishing or not. In the latter case we prove that $\Lambda< 0$ must
hold necessarily, and we find a characterization of the Einstein spacetimes
conformal to pp-waves. In the former case we obtain spacetime characterizations
of vacuum plane waves and of the stationary vacuum Brinkmann spacetimes. At the
light of the full set of results, old and new, we reformulate the case with
non-null ${\cal F}$ and $\Lambda= 0$. We finally present a table collecting the
results for both null, and non-null, ${\cal F}$.


title: Coulomb excitations of monolayer germanene

abstract:
  The feature-rich electronic excitations of monolayer germanene lie in the
significant spin-orbital coupling and the buckled structure. The collective and
single- particle excitations are diversified by the magnitude and direction of
transferred momentum, the Fermi energy and the gate voltage. There are four
kinds of plasmon modes, according to the unique frequency- and
momentum-dependent phase diagrams. They behave as two-dimensional acoustic
modes at long wavelength. However, for the larger momenta, they might change
into another kind of undamped plasmons, become the seriously suppressed modes
in the heavy intraband e-h excitations, keep the same undamped plasmons, or
decline and then vanish in the strong interband e-h excitations. Germanene,
silicene and graphene are quite different from one another in the main features
of the diverse plasmon modes.


title: A graphical calculus for semi-groupal categories

abstract:
  Around the year 1988, Joyal and Street established a graphical calculus for
monoidal categories, which provides a firm foundation for many explorations of
graphical notations in mathematics and physics. For a deeper understanding of
their work, we consider a similar graphical calculus for semi-groupal
categories. We introduce two frameworks to formalize this graphical calculus, a
topological one based on the notion of a processive plane graph and a
combinatorial one based on the notion of a planarly ordered processive graph,
which serves as a combinatorial counterpart of a deformation class of
processive plane graphs. We demonstrate the equivalence of Joyal and Street's
graphical calculus and the theory of upward planar drawings. We introduce the
category of semi-tensor schemes, and give a construction of a free monoidal
category on a semi-tensor scheme. We deduce the unit convention as a kind of
quotient construction, and show an idea to generalize the unit convention.
Finally, we clarify the relation of the unit convention and Joyal and Street's
construction of a free monoidal category on a tensor scheme.


title:
Frequency-based nanoparticle sensing over large field ranges using the
  ferromagnetic resonances of a magnetic nanodisc

abstract:
  Using finite element micromagnetic simulations, we study how resonant
magnetisation dynamics in thin magnetic discs with perpendicular anisotropy are
influenced by magnetostatic coupling to a magnetic nanoparticle. We identify
resonant modes within the disc using direct magnetic eigenmode calculations and
study how their frequencies and profiles are changed by the nanoparticle's
stray magnetic field. We demonstrate that particles can generate shifts in the
resonant frequency of the disc's fundamental mode which exceed resonance
linewidths in recently studied spin torque oscillator devices. Importantly, it
is shown that the simulated shifts can be maintained over large field ranges
(here up to 1T). This is because the resonant dynamics (the basis of
nanoparticle detection here) respond directly to the nanoparticle stray field,
i.e. detection does not rely on nanoparticle-induced changes to the magnetic
ground state of the disk. A consequence of this is that in the case of small
disc-particle separations, sensitivities to the particle are highly mode- and
particle-position-dependent, with frequency shifts being maximised when the
intense stray field localised directly beneath the particle can act on a large
proportion of the disc's spins that are undergoing high amplitude precession.


title:
Geometric entanglement and quantum phase transitions in two-dimensional
  quantum lattice models

abstract:
  Geometric entanglement(GE), as a measure of multipartite entanglement, has
been investigated as a universal tool to detect phase transitions in quantum
many-body lattice models. We outline a systematic method to compute GE for
two-dimensional (2D) quantum many-body lattice models based on the
translational invariant structure of infinite projected entangled pair state
(iPEPS) representations. By employing this method, the $q$-state quantum Potts
model on the square lattice with $q \in \{2, 3 ,4, 5\}$ is investigated as a
prototypical example. Further, we have explored three 2D Heisenberg models,
such as the spin-$\frac{1}{2}$ XXX and antiferromagnetic anisotropic XYX models
in an external magnetic field, and the spin-1 antiferromagnetic XXZ model. We
find that continuous GE does not guarantee a continuous phase transition across
a phase transition point. We observe and thus classify three different types of
continuous GE across a phase transition point: (i) GE is continuous with
maximum value at the transition point and the phase transition is continuous,
(ii) GE is continuous with maximum value at the transition point but the phase
transition is discontinuous, and (iii) GE is continuous with non-maximum value
at the transition point and the phase transition is continuous. For the models
under consideration we find that the second and the third types are related to
a point of dual symmetry and a fully polarized phase, respectively.


title: Actionness Estimation Using Hybrid Fully Convolutional Networks

abstract:
  Actionness was introduced to quantify the likelihood of containing a generic
action instance at a specific location. Accurate and efficient estimation of
actionness is important in video analysis and may benefit other relevant tasks
such as action recognition and action detection. This paper presents a new deep
architecture for actionness estimation, called hybrid fully convolutional
network (H-FCN), which is composed of appearance FCN (A-FCN) and motion FCN
(M-FCN). These two FCNs leverage the strong capacity of deep models to estimate
actionness maps from the perspectives of static appearance and dynamic motion,
respectively. In addition, the fully convolutional nature of H-FCN allows it to
efficiently process videos with arbitrary sizes. Experiments are conducted on
the challenging datasets of Stanford40, UCF Sports, and JHMDB to verify the
effectiveness of H-FCN on actionness estimation, which demonstrate that our
method achieves superior performance to previous ones. Moreover, we apply the
estimated actionness maps on action proposal generation and action detection.
Our actionness maps advance the current state-of-the-art performance of these
tasks substantially.


title:
Fast stochastic variability study of two SU UMa systems V1504 Cyg and
  V344 Lyr observed by Kepler satellite

abstract:
  We analysed Kepler data of two similar dwarf novae V344 Lyr and V1504 Cyg in
order to study optical fast stochastic variability (flickering) by searching
for characteristic break frequencies in their power density spectra. Two
different stages of activity were analysed separately, i.e. regular outbursts
and quiescence. Both systems show similar behaviour during both activity
stages. The quiescent power density spectra show a dominant low break frequency
which is also present during outburst with a more or less stable value in V344
Lyr while it is slightly higher in V1504 Cyg. The origin of this variability is
probably the whole accretion disc. Both outburst power density spectra show
additional high frequency components which we interpret as generated by the
rebuilt inner disc that was truncated during quiescence. Moreover, V344 Lyr
shows the typical linear rms-flux relation which is strongly deformed by a
possible negative superhump variability.


title: Phase Retrieval Without Small-Ball Probability Assumptions

abstract:
  In the context of the phase retrieval problem, it is known that certain
natural classes of measurements, such as Fourier measurements and random
Bernoulli measurements, do not lead to the unique reconstruction of all
possible signals, even in combination with certain practically feasible random
masks. To avoid this difficulty, the analysis is often restricted to
measurement ensembles (or masks) that satisfy a small-ball probability
condition, in order to ensure that the reconstruction is unique.
  This paper shows a complementary result: for random Bernoulli measurements,
there is still a large class of signals that can be reconstructed uniquely,
namely those signals that are "non-peaky." In fact, this result is much more
general: it holds for random measurements sampled from any subgaussian
distribution D, without any small-ball conditions. This is demonstrated in two
ways: first, a proof of stability and uniqueness, and second, a uniform
recovery guarantee for the PhaseLift algorithm. In all of these cases, the
number of measurements m approaches the information-theoretic lower bound.
  Finally, for random Bernoulli measurements with erasures, it is shown that
PhaseLift achieves uniform recovery of all signals (including peaky ones).


title: A blow-up lemma for approximate decompositions

abstract:
  We develop a new method for constructing approximate decompositions of dense
graphs into sparse graphs and apply it to longstanding decomposition problems.
For instance, our results imply the following. Let $G$ be a quasi-random
$n$-vertex graph and suppose $H_1,\dots,H_s$ are bounded degree $n$-vertex
graphs with $\sum_{i=1}^{s} e(H_i) \leq (1-o(1)) e(G)$. Then $H_1,\dots,H_s$
can be packed edge-disjointly into $G$. The case when $G$ is the complete graph
$K_n$ implies an approximate version of the tree packing conjecture of
Gy\'arf\'as and Lehel for bounded degree trees, and of the Oberwolfach problem.
  We provide a more general version of the above approximate decomposition
result which can be applied to super-regular graphs and thus can be combined
with Szemer\'edi's regularity lemma. In particular our result can be viewed as
an extension of the classical blow-up lemma of Koml\'os, S\'ark\H{o}zy and
Szemer\'edi to the setting of approximate decompositions.


title: Two-regular subgraphs of odd-uniform hypergraphs

abstract:
  Let $k\ge 3$ be an odd integer and let $n$ be a sufficiently large integer.
We prove that the maximum number of edges in an $n$-vertex $k$-uniform
hypergraph containing no $2$-regular subgraphs is $\binom{n-1}{k-1} +
\lfloor\frac{n-1}{k} \rfloor$, and the equality holds if and only if $H$ is a
full $k$-star with center $v$ together with a maximal matching omitting $v$.
This verifies a conjecture of Mubayi and Verstra\"{e}te.


title:
Commensurate lattice distortion in the layered titanium oxypnictides
  Na$_{2}$Ti$_{2}Pn_{2}$O ($Pn =$ As, Sb) determined by X-ray diffraction

abstract:
  We report single crystal X-ray diffraction measurements on
Na$_2$Ti$_{2}Pn_{2}$O ($Pn$ = As, Sb) which reveal a charge superstructure that
appears below the density wave transitions previously observed in bulk data.
From symmetry-constrained structure refinements we establish that the
associated distortion mode can be described by two propagation vectors, ${\bf
q}_{1} = (1/2, 0, l)$ and ${\bf q}_{2} = (0, 1/2, l)$, with $l=0$ (Sb) or $l =
1/2$ (As), and primarily involves in-plane displacements of the Ti atoms
perpendicular to the Ti--O bonds. The results provide direct evidence for
phonon-assisted charge density wave order in Na$_2$Ti$_{2}Pn_{2}$O and identify
a proximate ordered phase that could compete with superconductivity in doped
BaTi$_{2}$Sb$_{2}$O.


title: The Winds from HL Tau

abstract:
  Outflowing motions, whether a wind launched from the disk, a jet launched
from the protostar, or the entrained molecular outflow, appear to be an
ubiquitous feature of star formation. These outwards motions have a number of
root causes, and how they manifest is intricately linked to their environment
as well as the process of star formation itself.
  Using the ALMA Science Verification data of HL Tau, we investigate the high
velocity molecular gas being removed from the system as a result of the star
formation process. We aim to place these motions in context with the optically
detected jet, and the disk. With these high resolution ($\sim 1"$) ALMA
observations of CO (J=1-0), we quantify the outwards motions of the molecular
gas. We find evidence for a bipolar outwards flow, with an opening angle, as
measured in the red-shifted lobe, starting off at 90$^\circ$, and narrowing to
60$^\circ$ further from the disk, likely because of magnetic collimation. Its
outwards velocity, corrected for inclination angle is of order 2.4 km s$^{-1}$.


title:
About the Structure of the Integer Cone and its Application to Bin
  Packing

abstract:
  We consider the bin packing problem with $d$ different item sizes and revisit
the structure theorem given by Goemans and Rothvo\ss [6] about solutions of the
integer cone. We present new techniques on how solutions can be modified and
give a new structure theorem that relies on the set of vertices of the
underlying integer polytope. As a result of our new structure theorem, we
obtain an algorithm for the bin packing problem with running time
$|V|^{2^{O(d)}} \cdot enc(I)^{O(1)}$, where $V$ is the set of vertices of the
integer knapsack polytope and $enc(I)$ is the encoding length of the bin
packing instance. The algorithm is fixed parameter tractable, parameterized by
the number of vertices of the integer knapsack polytope $|V|$. This shows that
the bin packing problem can be solved efficiently when the underlying integer
knapsack polytope has an easy structure, i.e. has a small number of vertices.
  Furthermore, we show that the presented bounds of the structure theorem are
asymptotically tight. We give a construction of bin packing instances using new
structural insights and classical number theoretical theorems which yield the
desired lower bound.


title:
Diffusion MRI microstructure models with in vivo human brain Connectom
  data: results from a multi-group comparison

abstract:
  A large number of mathematical models have been proposed to describe the
measured signal in diffusion-weighted (DW) magnetic resonance imaging (MRI) and
infer properties about the white matter microstructure. However, a head-to-head
comparison of DW-MRI models is critically missing in the field. To address this
deficiency, we organized the "White Matter Modeling Challenge" during the
International Symposium on Biomedical Imaging (ISBI) 2015 conference. This
competition aimed at identifying the DW-MRI models that best predict unseen DW
data. in vivo DW-MRI data was acquired on the Connectom scanner at the
A.A.Martinos Center (Massachusetts General Hospital) using gradients strength
of up to 300 mT/m and a broad set of diffusion times. We focused on assessing
the DW signal prediction in two regions: the genu in the corpus callosum, where
the fibres are relatively straight and parallel, and the fornix, where the
configuration of fibres is more complex. The challenge participants had access
to three-quarters of the whole dataset, and their models were ranked on their
ability to predict the remaining unseen quarter of data. In this paper we
provide both an overview and a more in-depth description of each evaluated
model, report the challenge results, and infer trends about the model
characteristics that were associated with high model ranking. This work
provides a much needed benchmark for DW-MRI models. The acquired data and model
details for signal prediction evaluation are provided online to encourage a
larger scale assessment of diffusion models in the future.


title: Instanton solutions on the polymer harmonic oscillator

abstract:
  It is computed, using instanton methods, the first allowed energy band for
the polymer harmonic oscillator. The result is consistent with the band
structure of the standard quantum pendulum but with pure point spectrum. An
effective infinite degeneracy emerges in the formal limit $\mu/l_0 \to 0$ where
$l_0$ is the characteristic length of the vacuum eigenfunction of a quantum
harmonic oscillator. As an additional result, it is shown along the article the
role played by the lattice reference point $\lambda$ in the full quantization
of the polymer harmonic oscillator.


title:
Some Identities involving Two Sets of Basis Vectors and the Metric and
  Mixed Matrices

abstract:
  Given two sets of basis vectors in n-dimensional space, there exists a
relation between their lengths and mutual angles, expressed as relations
between the two metric matrices and the mixed matrix. In this paper these
relations are given, and their consequences for 2-dimensional and 3-dimensional
space are investigated, using a computer algebra program for simplifying
expressions.


title:
The VMC Survey - XXI. New star cluster candidates discovered from
  infrared photometry in the Small Magellanic Cloud

abstract:
  We report the first search for new star clusters performed using the VISTA
near-infrared YJKs Magellanic Clouds survey (VMC) data sets. We chose a pilot
field of ~ 0.4 deg^2 located in the South-West of the Small Magelllanic Cloud
(SMC) bar, where the star field is among the densest and highest reddened
region in the galaxy. In order to devise an appropriate automatic procedure we
made use of dimensions and stellar densities observed in the VMC data sets of
the known clusters in this area. We executed different kernel density
estimations over a sample of more than 358000 stars with magnitudes measured in
the three YJKs filters. We analysed the new cluster candidates whose
colour-magnitude diagrams (CMDs), cleaned from field star contamination, were
used to assess the clusters' reality and estimate reddenings and ages of the
genuine systems. As a result 38 objects (~ a 55% increase in the known star
clusters located in the surveyed field) of 0.15 - 0.40 arcmin (2.6 - 7.0 pc) in
radius resulted to have near-infrared CMD features which resemble those of star
clusters of young to moderate intermediate age (log(t /yr ) ~ 7.5-9.0). Most of
the new star cluster candidates are hardly recognizable in optical images
without the help of a sound star field decontaminated CMD analysis. For highly
reddened star cluster candidates (E(B - V ) >= 0.6 mag) the VMC data sets were
necessary in order to recognize them.


title: Cosmic Infrared Background Fluctuations and Zodiacal Light

abstract:
  We have performed a specific observational test to measure the effect that
the zodiacal light can have on measurements of the spatial fluctuations of the
near-IR background. Previous estimates of possible fluctuations caused by
zodiacal light have often been extrapolated from observations of the thermal
emission at longer wavelengths and low angular resolution, or from IRAC
observations of high latitude fields where zodiacal light is faint and not
strongly varying with time. The new observations analyzed here target the
COSMOS field, at low ecliptic latitude where the zodiacal light intensity
varies by factors of $\sim2$ over the range of solar elongations at which the
field can be observed. We find that the white noise component of the spatial
power spectrum of the background is correlated with the modeled zodiacal light
intensity. Roughly half of the measured white noise is correlated with the
zodiacal light, but a more detailed interpretation of the white noise is
hampered by systematic uncertainties that are evident in the zodiacal light
model. At large angular scales ($\gtrsim100"$) where excess power above the
white noise is observed, we find no correlation of the power with the modeled
intensity of the zodiacal light. This test clearly indicates that the large
scale power in the infrared background is not being caused by the zodiacal
light.


title:
Quasi-idempotent Rota-Baxter operators arising from quasi-idempotent
  elements

abstract:
  In this short note, we construct quasi-idempotent Rota-Baxter operators by
quasi-idempotent elements and show that every finite dimensional Hopf algebra
admits nontrivial Rota-Baxter algebra structures and tridendriform algebra
structures. Several concrete examples are provided, including finite quantum
groups and Iwahori-Hecke algebras.


title: Mean Topological Dimension for random bundle transformations

abstract:
  We introduce the mean topological dimension for random bundle
transformations, and show that continuous bundle random dynamical systems with
finite topological entropy, or the small boundary property have zero mean
topological dimensions.


title:
A model for the non-thermal emission of the very massive colliding-wind
  binary HD 93129A

abstract:
  The binary stellar system HD 93129A is one of the most massive known binaries
in our Galaxy. This system presents non-thermal emission in the radio band,
which can be used to infer its physical conditions and predict its emission in
the high-energy band. We intend to constrain some of the unknown parameters of
HD 93129A through modelling the non-thermal emitter, and also to analyse the
detectability of this source in hard X-rays and $\gamma$-rays. We develop a
broadband radiative model for the wind-collision region taking into account the
evolution of the accelerated particles streaming along the shocked region, the
emission by different radiative processes, and the attenuation of the emission
propagating through the local matter and radiation fields. From the analysis of
the radio emission, we find that the binary HD~93129A is more likely to have a
low inclination and a high eccentricity. The minimum energy of the non-thermal
electrons seems to be between $\sim 20 - 100$MeV, depending on the intensity of
the magnetic field in the wind-collision region. The latter can be in the range
$\sim 20 - 1500$ mG. Our model is able to reproduce the observed radio
emission, and predicts that the non-thermal radiation from HD~93129A will
increase in the near future. With instruments such as \textit{NuSTAR},
\textit{Fermi}, and CTA, it will be possible to constrain the relativistic
particle content of the source, and other parameters such as the magnetic field
strength in the wind collision zone, which in turn can be used to obtain
upper-limits of the magnetic field on the surface of the very massive stars,
thereby inferring whether magnetic field amplification is taking place in the
particle acceleration region.


title:
Optimal linear drift for the speed of convergence of an hypoelliptic
  diffusion

abstract:
  Among all generalized Ornstein-Uhlenbeck processes which sample the same
invariant measure and for which the same amount of randomness (a
$N$-dimensional Brownian motion) is injected in the system, we prove that the
asymptotic rate of convergence is maximized by a non-reversible hypoelliptic
one.


title:
Covariant energy density functionals: nuclear matter constraints and
  global ground state properties

abstract:
  The correlations between global description of the ground state properties
(binding energies, charge radii) and nuclear matter properties of the
state-of-the-art covariant energy density functionals have been studied. It was
concluded that the strict enforcement of the constraints on the nuclear matter
properties (NMP) defined in Ref.\ \cite{RMF-nm} will not necessary lead to the
functionals with good description of the binding energies and other ground and
excited state properties. In addition, it will not substantially reduce the
uncertainties in the predictions of the binding energies in neutron-rich
systems. It turns out that the functionals, which come close to satisfying
these NMP constraints, have some problems in the description of existing data.
On the other hand, these problems are either absent or much smaller in the
functionals which are carefully fitted to finite nuclei but which violate some
NMP constraints. This is a consequence of the fact that the properties of
finite nuclei are defined not only by nuclear matter properties but also by
underlying shell effects. The mismatch of phenomenological content, existing in
all modern functionals, related to nuclear matter physics and the physics of
finite nuclei could also be responsible.


title:
Structural characterization of APPJ treated Bismaleimide coatings and
  heat treated Titania-BMI

abstract:
  Bismaleimide (BMI) are thermosetting polymers mainly used in aerospace
applications having properties of dimensional stability, low shrinkage,
chemical resistance, fire resistance, good mechanical properties and high
resistance against various solvents, acids, and water. BMI is commercially
available as Homide 250. BMI coating has also been used for the corrosion
protection. Metallization (AL) of BMI using vacuum evaporation was done which
serves the purpose of prevention of space charge accumulation in aircraft
bodies. Addition of inorganic materials like metal oxides can influence the
properties of the polymer as an inorganic-organic composite. The
organic-ionorganic composites have wide applications in electronics, optics,
chemistry and medicine. Titanium dioxide (TiO2, Titania) has a wide range of
applications starting from photocatalysis, dye-sensitized solar cells to
optical coatings and electronics. A BMI-TiO2 composite was prepared by chemical
route. Atmospheric Plasma Jet (APPJ) using Helium gas was also treated on BMI.
XRD and FTIR studies of the composite system prepared at different temperatures
showed its crystalline and structural configuration.


title:
Stationary states of an aggregation equation with degenerate diffusion
  and bounded attractive potential

abstract:
  We investigate stationary solutions of a non-local aggregation equation with
degenerate power-law diffusion and bounded attractive potential in arbitrary
dimensions. Compact stationary solutions are characterized and compactness
considerations are used to derive the existence of global minimizers of the
corresponding energy depending on the prefactor of the degenerate diffusion for
all exponents of the degenerate diffusion greater than one. We show that a
global minimizer is compactly supported and, in case of quadratic diffusion, we
prove that it is the unique stationary solution up to a translation. The
existence of stationary solutions being only local minimizers is discussed.


title: Bayesian modelling and quantification of Raman spectroscopy

abstract:
  Raman spectroscopy can be used to identify molecules such as DNA by the
characteristic scattering of light from a laser. It is sensitive at very low
concentrations and can accurately quantify the amount of a given molecule in a
sample. The presence of a large, nonuniform background presents a major
challenge to analysis of these spectra. To overcome this challenge, we
introduce a sequential Monte Carlo (SMC) algorithm to separate each observed
spectrum into a series of peaks plus a smoothly-varying baseline, corrupted by
additive white noise. The peaks are modelled as Lorentzian, Gaussian, or
pseudo-Voigt functions, while the baseline is estimated using a penalised cubic
spline. This latent continuous representation accounts for differences in
resolution between measurements. The posterior distribution can be
incrementally updated as more data becomes available, resulting in a scalable
algorithm that is robust to local maxima. By incorporating this representation
in a Bayesian hierarchical regression model, we can quantify the relationship
between molecular concentration and peak intensity, thereby providing an
improved estimate of the limit of detection, which is of major importance to
analytical chemistry.


title:
Non-parametric estimation of the spiking rate in systems of interacting
  neurons

abstract:
  We consider a model of interacting neurons where the membrane potentials of
the neurons are described by a multidimensional piecewise deterministic Markov
process (PDMP) with values in ${\mathbb R}^N, $ where $ N$ is the number of
neurons in the network. A deterministic drift attracts each neuron's membrane
potential to an equilibrium potential $m.$ When a neuron jumps, its membrane
potential is reset to $0,$ while the other neurons receive an additional amount
of potential $\frac{1}{N}.$ We are interested in the estimation of the jump (or
spiking) rate of a single neuron based on an observation of the membrane
potentials of the $N$ neurons up to time $t.$ We study a Nadaraya-Watson type
kernel estimator for the jump rate and establish its rate of convergence in
$L^2 .$ This rate of convergence is shown to be optimal for a given H\"older
class of jump rate functions. We also obtain a central limit theorem for the
error of estimation. The main probabilistic tools are the uniform ergodicity of
the process and a fine study of the invariant measure of a single neuron.


title: Spherical analysis on homogeneous vector bundles

abstract:
  Given a Lie group $G$, a compact subgroup $K$ and a representation
$\tau\in\hat K$, we assume that the algebra of $\text{End}(V_\tau)$-valued,
bi-$\tau$-equivariant, integrable functions on $G$ is commutative. We present
the basic facts of the related spherical analysis, putting particular emphasis
on the r\^ole of the algebra of $G$-invariant differential operators on the
homogeneous bundle $E_\tau$ over $G/K$. In particular, we observe that, under
the above assumptions, $(G,K)$ is a Gelfand pair and show that the Gelfand
spectrum for the triple $(G,K,\tau)$ admits homeomorphic embeddings in $\mathbb
C^n$.
  In the second part, we develop in greater detail the spherical analysis for
$G=K\ltimes H$ with $H$ nilpotent. In particular, for $H=\mathbb R^n$ and
$K\subset SO(n)$ and for the Heisenberg group $H_n$ and $K\subset U(n)$, we
characterize the representations $\tau \in \hat K$ giving a commutative
algebra. \end{abstract}


title:
A Set-Oriented Numerical Approach for Dynamical Systems with Parameter
  Uncertainty

abstract:
  In this article, we develop a set-oriented numerical methodology which allows
to perform uncertainty quantification (UQ) for dynamical systems from a global
point of view. That is, for systems with uncertain parameters we approximate
the corresponding global attractors and invariant measures in the related
stochastic setting. Our methods do not rely on generalized polynomial chaos
techniques. Rather, we extend classical set-oriented methods designed for
deterministic dynamical systems to the UQ-context, and this allows us to
analyze the long-term uncertainty propagation. The algorithms have been
integrated into the software package GAIO, and we illustrate the use and
efficiency of these techniques by a couple of numerical examples.


title:
On approximation of planar curves by circular arcs with length
  preservation

abstract:
  The method for approximation of planar curve by circular arcs with length
preservation, proposed by I.Kh. Sabitov and A.V. Slovesnov, is analyzed. We
extend the applicability of the method, and consider some corollaries, not
related to the approximation problem. Inequalities for the length of a convex
spiral arc with prescribed two-point $G^1$ or $G^2$ Hermite data are derived.
We propose a scheme of computer modelling to explore properties of planar
curves. As an example, closeness of ovals is tested, leading to some
conjectures about closeness conditions.


title: A Note on the Posterior Inference for the Yule-Simon Distribution

abstract:
  The Yule--Simon distribution has been out of the radar of the Bayesian
community, so far. In this note, we propose an explicit Gibbs sampling scheme
when a Gamma prior is chosen for the shape parameter. The performance of the
algorithm is illustrated with simulation studies, including count data
regression, and a real data application to text analysis. We compare our
proposal to the frequentist counterparts showing better performance of our
algorithm when a small sample size is considered.


title:
A global approximation result by Al Taylor and the strong openness
  conjecture in C^n

abstract:
  We improve a global approximation result by Al Taylor in C^n for holomorphic
functions in weighted Hilbert spaces. The main tools are a variation of the
theorem of Hormander on weighted L^2-estimates for the dbar-equation together
with the solution of the strong openness conjecture. A counterexample to a
global strong openness conjecture in Cn is also given here.


title: Cosmology in massive gravity with effective composite metric

abstract:
  This paper is dedicated to scrutinizing the cosmology in massive gravity. A
matter field of the dark sector is coupled to an effective composite metric
while a standard matter field couples to the dynamical metric in the usual way.
For this purpose, we study the dynamical system of cosmological solutions by
using phase analysis, which provides an overview of the class of cosmological
solutions in this setup. This also permits us to study the critical points of
the cosmological equations together with their stability. We show the presence
of stable attractor de Sitter critical points relevant to the late-time cosmic
acceleration. Furthermore, we study the tensor, vector and scalar perturbations
in the presence of standard matter fields and obtain the conditions for the
absence of ghost and gradient instabilities. Hence, massive gravity in the
presence of the effective composite metric can accommodate interesting dark
energy phenomenology, that can be observationally distinguished from the
standard model according to the expansion history and cosmic growth.


title: Counting connected graphs with large excess

abstract:
  We enumerate the connected graphs that contain a linear number of edges with
respect to the number of vertices. So far, only the first term of the
asymptotics was known. Using analytic combinatorics, i.e. generating function
manipulations, we derive the complete asymptotic expansion.


title: Oblique internal-wave chain resonance over seabed corrugations

abstract:
  We show that monochromatic long-crested corrugations on an otherwise flat
seafloor can coherently scatter the energy of an oblique incident internal wave
to multiple multi-directional higher-mode waves via a series of resonant
interactions. We demonstrate that a resonance between seabed corrugations and a
normally or slightly oblique incident internal wave results in a series of
follow-up resonant interactions, which take place between the same corrugations
and successively resonated shorter waves. A chain resonance of internal waves
that carries energy to small scales is thus obtained, and we find that the
Richardson number decreases by several orders of magnitude over the corrugated
patch. If the incidence angle is large, and the incident wave perfectly
satisfies a resonance condition with the topography, it turns out that not many
higher-mode resonance or near-resonance conditions can be satisfied, such that
energy stays confined within the first few modes. Nevertheless, if the incident
waves are sufficiently detuned from satisfying a perfect resonance condition
with the seabed corrugations, then we show that this frequency detuning may
balance off the large detuning due to oblique incidence, leading to a chain
resonance that again carries energy to small scales. The evolution of the
incident and resonated wave amplitudes is predicted from the envelope equation
for internal waves over resonant seabed topography in a three-dimensional
rotating fluid, which we derive considering the Boussinesq and $f$-plane
approximations with $f$ the Coriolis frequency, linear density stratification
and small-amplitude corrugations. Our results suggest that topographic features
on the ocean floor with a dominant wavenumber vector, through the chain
resonance mechanism elucidated here, may play a more important role than
previously thought in the enhancement of diapycnal mixing and energy
dissipation.


title: Division by zero

abstract:
  For any sufficiently strong theory of arithmetic, the set of Diophantine
equations provably unsolvable in the theory is algorithmically undecidable, as
a consequence of the MRDP theorem. In contrast, we show decidability of
Diophantine equations provably unsolvable in Robinson's arithmetic Q. The
argument hinges on an analysis of a particular class of equations, hitherto
unexplored in Diophantine literature. We also axiomatize the universal fragment
of Q in the process.


title: The free $\sigma$CFTs

abstract:
  We introduce the conformal field theories that describe the shadows of the
lowest dimension composites made out of massless free scalars and fermions in
$d$ dimensions. We argue that these theories can be consistently defined as
free CFTs for even $d\geq 4$. We use OPE techniques to study their spectrum and
show that for $d\rightarrow\infty$ it matches that of free bosonic CFTs in
$d=6$ and $d=4$ dimensions. For these $\sigma$CFTs we calculate $c_T$ in
$d=6,8,10$ and $12$ dimensions using the OPE and also a direct construction of
their higher-derivative energy momentum tensors. Our results agree with the
general proposal of arXiv:1601.07198.


title:
Stability Selection for Lasso, Ridge and Elastic Net Implemented with
  AFT Models

abstract:
  The instability in the selection of models is a major concern with data sets
containing a large number of covariates. We focus on stability selection which
is used as a technique to improve variable selection performance for a range of
selection methods, based on aggregating the results of applying a selection
procedure to sub-samples of the data where the observations are subject to
right censoring. The accelerated failure time (AFT) models have proved useful
in many contexts including the heavy censoring (as for example in cancer
survival) and the high dimensionality (as for example in micro-array data). We
implement the stability selection approach using three variable selection
techniques--Lasso, ridge regression, and elastic net applied to censored data
using AFT models. We compare the performances of these regularized techniques
with and without stability selection approaches with simulation studies and a
breast cancer data analysis. The results suggest that stability selection gives
always stable scenario about the selection of variables and that as the
dimension of data increases the performance of methods with stability selection
also improves compared to methods without stability selection irrespective of
the collinearity between the covariates.


title: Endgame Analysis of Dou Shou Qi

abstract:
  Dou Shou Qi is a game in which two players control a number of pieces, each
of them aiming to move one of their pieces onto a given square. We implemented
an engine for analyzing the game. Moreover, we created a series of endgame
tablebases containing all configurations with up to four pieces. These
tablebases are the first steps towards theoretically solving the game. Finally,
we constructed decision trees based on the endgame tablebases. In this note we
report on some interesting patterns.


title:
An extensive numerical survey of the correlation between outflow
  dynamics and accretion disk magnetization

abstract:
  We investigate the accretion-ejection process of jets from magnetized
accretion disks. We apply a novel approach to the jet-launching problem in
order to obtain correlations between the physical properties of the jet and the
underlying disk. We extend and confirm the previous works of
\citet{2009MNRAS.400..820T} and \citet{2010A&A...512A..82M} by scanning a large
parameter range for the disk magnetization, $\mu_{\rm D} = 10^{-3.5} ...
10^{-0.7}$. We disentangle the disk magnetization at the foot point of the
outflow as the main parameter that governs the properties of the outflow. We
show how the four jet integrals known from steady-state MHD are correlated to
the disk magnetization at the jet foot point. This agrees with the usual
findings of the steady-state theory, however, here we obtain these correlations
from time-dependent simulations that include the dynamical evolution of the
disk in the treatment. In particular, we obtain robust correlations between the
local disk magnetization and (i)the outflow velocity, (ii) the jet mass
loading, (iii) jet angular momentum, and (iv) the local mass accretion rate.
Essentially we find that strongly magnetized disks launch more energetic and
faster jets, and, due to a larger Alfv\'en lever arm, these jets extract more
angular momentum from the underlying disk. These kind of disk-jet systems have,
however, a smaller mass loading parameter and a lower mass
ejection-to-accretion ratio. The jets are launched at the disk surface where
the magnetization is $\mu(r,z) \simeq 0.1$. The magnetization rapidly increases
vertically providing the energy reservoir for subsequent jet acceleration. We
find indication for a critical disk magnetization $\mu_{\rm D} \simeq 0.01$
that separates the regimes of magnetocentrifugally-driven and magnetic
pressure-driven jets.


title: Feynman Rules of Higher-order Poles in CHY Construction

abstract:
  In this paper, we generalize the integration rules for scattering equations
to situations where higher-order poles are present. We describe the strategy to
deduce the Feynman rules of higher-order poles from known analytic results of
simple CHY-integrands, and propose the Feynman rules for single double pole and
triple pole as well as duplex-double pole and triplex-double pole structures.
We demonstrate the validation and strength of these rules by ample non-trivial
examples.


title: Spatially Coupled Turbo-Like Codes

abstract:
  In this paper, we introduce the concept of spatially coupled turbo-like codes
(SC-TCs) as the spatial coupling of a number of turbo-like code ensembles. In
particular, we consider the spatial coupling of Berrou et al. parallel
concatenated codes (PCCs) and Benedetto et al. serially concatenated codes
(SCCs). Furthermore, we propose two extensions of braided convolutional codes
(BCCs), a class of turbo-like codes which have an inherent spatially coupled
structure, to higher coupling memories, and show that these yield improved
belief propagation (BP) thresholds as compared to the original BCC ensemble. We
derive the exact density evolution (DE) equations for SC-TCs and analyze their
asymptotic behavior on the binary erasure channel. We also consider the
construction of families of rate-compatible SC-TC ensembles. Our numerical
results show that threshold saturation of the belief propagation (BP) decoding
threshold to the maximum a-posteriori threshold of the underlying uncoupled
ensembles occurs for large enough coupling memory. The improvement of the BP
threshold is especially significant for SCCs and BCCs, whose uncoupled
ensembles suffer from a poor BP threshold. For a wide range of code rates,
SC-TCs show close-to-capacity performance as the coupling memory increases. We
further give a proof of threshold saturation for SC-TC ensembles with identical
component encoders. In particular, we show that the DE of SC-TC ensembles with
identical component encoders can be properly rewritten as a scalar recursion.
This allows us to define potential functions and prove threshold saturation
using the proof technique recently introduced by Yedla et al..


title: End to End Learning for Self-Driving Cars

abstract:
  We trained a convolutional neural network (CNN) to map raw pixels from a
single front-facing camera directly to steering commands. This end-to-end
approach proved surprisingly powerful. With minimum training data from humans
the system learns to drive in traffic on local roads with or without lane
markings and on highways. It also operates in areas with unclear visual
guidance such as in parking lots and on unpaved roads.
  The system automatically learns internal representations of the necessary
processing steps such as detecting useful road features with only the human
steering angle as the training signal. We never explicitly trained it to
detect, for example, the outline of roads.
  Compared to explicit decomposition of the problem, such as lane marking
detection, path planning, and control, our end-to-end system optimizes all
processing steps simultaneously. We argue that this will eventually lead to
better performance and smaller systems. Better performance will result because
the internal components self-optimize to maximize overall system performance,
instead of optimizing human-selected intermediate criteria, e.g., lane
detection. Such criteria understandably are selected for ease of human
interpretation which doesn't automatically guarantee maximum system
performance. Smaller networks are possible because the system learns to solve
the problem with the minimal number of processing steps.
  We used an NVIDIA DevBox and Torch 7 for training and an NVIDIA DRIVE(TM) PX
self-driving car computer also running Torch 7 for determining where to drive.
The system operates at 30 frames per second (FPS).


title:
Quantitative determination of bond order and lattice distortions in
  nickel oxide heterostructures by resonant x-ray scattering

abstract:
  We present a combined study of Ni $K$-edge resonant x-ray scattering and
density functional calculations to probe and distinguish electronically driven
ordering and lattice distortions in nickelate heterostructures. We demonstrate
that due to the low crystal symmetry, contributions from structural distortions
can contribute significantly to the energy-dependent Bragg peak intensities of
a bond-ordered NdNiO$_3$ reference film. For a LaNiO$_3$-LaAlO$_3$ superlattice
that exhibits magnetic order, we establish a rigorous upper bound on the
bond-order parameter. We thus conclusively confirm predictions of a dominant
spin density wave order parameter in metallic nickelates with a
quasi-two-dimensional electronic structure.


title: Impact of Mobility on the Sum Rate of NB-OFDMA Based Mobile IoT Networks

abstract:
  In future Internet of Things (IoT) networks, the explosive growth of mobile
devices compel us to reconsider the effectiveness of the current
frequency-division multiple access (FDMA) schemes. Devices' differentiated
mobility features and diversified scattering environments make it more
complicated to characterize the multi-user interference. In this paper, we
thoroughly analyze the impacts of devices' mobility on the inter-sub-carrier
interference (ICI) in an IoT system based on the 3GPP narrow-band orthogonal
frequency-division multiple access (NB-OFDMA) protocol, and obtain the
relationship between the system sum-rate and devices' mobility. Our results may
shed some lights on the system design under the mobile scenarios.


title:
Semi-supervised Dictionary Learning Based on Hilbert-Schmidt
  Independence Criterion

abstract:
  In this paper, a novel semi-supervised dictionary learning and sparse
representation (SS-DLSR) is proposed. The proposed method benefits from the
supervisory information by learning the dictionary in a space where the
dependency between the data and class labels is maximized. This maximization is
performed using Hilbert-Schmidt independence criterion (HSIC). On the other
hand, the global distribution of the underlying manifolds were learned from the
unlabeled data by minimizing the distances between the unlabeled data and the
corresponding nearest labeled data in the space of the dictionary learned. The
proposed SS-DLSR algorithm has closed-form solutions for both the dictionary
and sparse coefficients, and therefore does not have to learn the two
iteratively and alternately as is common in the literature of the DLSR. This
makes the solution for the proposed algorithm very fast. The experiments
confirm the improvement in classification performance on benchmark datasets by
including the information from both labeled and unlabeled data, particularly
when there are many unlabeled data.


title: Ballistic graphene Josephson junctions from the short to the long regime

abstract:
  We investigate the critical current, $I_C$, of ballistic Josephson junctions
made of encapsulated graphene/boron-nitride heterostructures. We observe a
crossover from the short to the long junction regimes as the length of the
device increases. In long ballistic junctions, $I_S$ is found to scale as
$\propto \exp(-k_bT/\delta E)$. The extracted energies $\delta E$ are
independent of the carrier density and proportional to the level spacing of the
ballistic cavity, as determined from Fabry-Perot oscillations of the junction
normal resistance. As $T\rightarrow 0$ the critical current of a long (or
short) junction saturates at a level determined by the product of $\delta E$
(or $\Delta$) and the number of the junction's transversal modes.


title:
Tuning High-Harmonic Generation by Controlled Deposition of Ultrathin
  Ionic Layers on Metal Surfaces

abstract:
  High harmonic generation (HHG) from semiconductors and insulators has become
a very active area of research due to its great potential for developing
compact HHG devices. Here we show that by growing monolayers (ML) of insulators
on single-crystal metal surfaces, one can tune the harmonic spectrum by just
varying the thickness of the ultrathin layer, not the laser properties. This is
shown from numerical solutions of the time-dependent Schr\"odinger equation for
$n$ML NaCl/Cu(111) systems ($n=1-50$) based on realistic potentials available
in the literature. Remarkably, the harmonic cutoff increases linearly with $n$
and as much as an order of magnitude when going from $n$ $=$ 1 to 30, while
keeping the laser intensity low and the wavelength in the near-infrared range.
Furthermore, the degree of control that can be achieved in this way is much
higher than by varying the laser intensity. The origin of this behavior is the
reduction of electronic "friction" when moving from the essentially discrete
energy spectrum associated with a few-ML system to the continuous energy
spectrum (bands) inherent to an extended periodic system.


title: Predictive No-Reference Assessment of Video Quality

abstract:
  Among the various means to evaluate the quality of video streams,
No-Reference (NR) methods have low computation and may be executed on thin
clients. Thus, NR algorithms would be perfect candidates in cases of real-time
quality assessment, automated quality control and, particularly, in adaptive
mobile streaming. Yet, existing NR approaches are often inaccurate, in
comparison to Full-Reference (FR) algorithms, especially under lossy network
conditions. In this work, we present an NR method that combines machine
learning with simple NR metrics to achieve a quality index comparably as
accurate as the Video Quality Metric (VQM) Full-Reference algorithm. Our method
is tested in an extensive dataset (960 videos), under lossy network conditions
and considering nine different machine learning algorithms. Overall, we achieve
an over 97% correlation with VQM, while allowing real-time assessment of video
quality of experience in realistic streaming scenarios.


title: The rings of Chariklo under close encounters with the giant planets

abstract:
  The Centaur population is composed by minor bodies wandering between the
giant planets and that frequently perform close gravitational encounters with
these planets, which leads to a chaotic orbital evolution. Recently, the
discovery of two well-defined narrow rings was announced around the Centaur
10199 Chariklo. The rings are assumed to be in the equatorial plane of Chariklo
and to have circular orbits. The existence a well-defined system of rings
around a body in such perturbed orbital region poses an interesting new
problem. Are the rings of Chariklo stable when perturbed by close gravitational
encounters with the giant planets? Our approach to address this question
consisted of forward and backward numerical simulations of 729 clones of
Chariklo, with similar initial orbits, for a period of 100 Myrs. We found, on
average, that each clone suffers along its lifetime more than 150 close
encounters with the giant planets within one Hill radius of the planet in
question. We identified some extreme close encounters able to significantly
disrupt or to disturb the rings of Chariklo. About 3% of the clones lose the
rings and about 4% of the clones have the ring significantly disturbed.
Therefore, our results show that in most of the cases (more than 90%) the close
encounters with the giant planets do not affect the stability of the rings in
Chariklo-like systems. Thus, if there is an efficient mechanism that creates
the rings, then these structures may be common among these kinds of Centaurs.


title:
Updated $1/N_c$ expansion analysis of $[{\bf 56, 2^+}]$ and $[{\bf 70,
  \ell^+}]$ baryon multiplets

abstract:
  The mass spectra of the $[{\bf 56, 2^+}]$ and $[{\bf 70, \ell+}]$ multiplets,
both belonging to the $N$ = 2 band, is reviewed in the $1/N_c$ expansion
method. Previous studies, separately made for each multiplet, are presently
updated to the 2014 Particle Data Group. The mass formula including corrections
up to $\mathcal{O}(1/N_c)$ and first order in SU(3) flavor symmetry breaking,
has the same independent operator basis in both cases. A special emphasis is
made on the role of the SU(3) symmetry breaking operators $B_i$ $(i = 1,2,3)$.
This can allow for multiplet assignment of $\Lambda$ and $\Sigma$ hyperons,
which generally is quite difficult to make. Tentative assignments of hyperons
with two- and one-star resonances are made to the $[{\bf 70, \ell+}]$
multiplet. Another important aim is to find out whether or not a common value
of the coefficient $c_1$ of the dominant operator in the mass formula, can well
fit the present data in both multiplets. A negative answer, which is here the
case, implies distinct Regge trajectories for symmetric and mixed symmetric
states.


title: Plasma compression in magnetic reconnection regions in the solar corona

abstract:
  It has been proposed that particles bouncing between magnetized flows
converging in a reconnection region can be accelerated by the first order Fermi
mechanism. Analytical considerations of this mechanism have shown that the
spectral index of accelerated particles is related to the total plasma
compression within the reconnection region similarly to the case of diffusive
shock acceleration mechanism. As a first step to investigate the efficiency of
Fermi acceleration in reconnection regions in producing hard energy spectra of
particles in the solar corona, we explore the degree of plasma compression that
can be achieved at reconnection sites. In particular, we aim to determine the
conditions for the strong compressions to form. Using a two-dimensional
resistive MHD numerical model we consider a set of magnetic field
configurations where magnetic reconnection can occur including a Harris current
sheet, a force-free current sheet, and two merging flux ropes. Plasma
parameters are taken to be characteristic of the solar corona. Numerical
simulations show that strong plasma compressions ($\geq 4$) in the reconnection
regions can form when the plasma heating due to reconnection is efficiently
removed by fast thermal conduction or radiative cooling process. The radiative
cooling process which is negligible in the typical 1 MK corona can play an
important role in the low corona/transition region. It is found that plasma
compression is expected to be strongest in low-beta plasma $\beta \sim
0.01-0.07$ at reconnection magnetic nulls.


title:
Probing variations of the Rashba spin-orbit coupling at the nanometer
  scale

abstract:
  The Rashba effect as an electrically tunable spin-orbit interaction is the
base for a multitude of possible applications such as spin filters, spin
transistors, and quantum computing using Majorana states in nanowires.
Moreover, this interaction can determine the spin dephasing and
antilocalization phenomena in two dimensions. However, the real space pattern
of the Rashba parameter has never been probed, albeit it critically influences,
e.g., the more robust spin transistors using the spin helix state and the
otherwise forbidden electron backscattering in topologically protected
channels. Here, we map this pattern down to nanometer length scales by
measuring the spin splitting of the lowest Landau level using scanning
tunnelling spectroscopy. We reveal strong fluctuations correlated with the
local electrostatic potential for an InSb inversion layer with a large Rashba
coefficient (~1 eV{\AA}). The novel type of Rashba field mapping enables a more
comprehensive understanding of the critical fluctuations, which might be
decisive towards robust semiconductor-based spintronic devices.


title: The Practical Pomeron for High Energy Proton Collimation

abstract:
  We present a model which describes proton scattering data from ISR to
Tevatron energies, and which can be applied to collimation n high energy
accelerators, such as the LHC and FCC. Collimators remove beam halo particles,
so that they do not impinge on vulnerable regions of the machine, such as the
superconducting magnets and the experimental areas. In simulating the effect of
the collimator jaws it is crucial to model the scattering of protons at small
momentum transfer~$t$,as these protons can subsequently survive several turns
of the ring before being lost. At high energies these soft processes are well
described by Pomeron exchange models. We study the behaviour of elastic and
single-diffractive dissociation cross sections over a wide range of energy, and
show that the model can be used as a global description of the wide variety of
high energy elastic and diffractive data presently available. In particular it
models low mass diffraction dissociation, where a rich resonance structure is
present, and thus predicts the differential and integrated cross sections in
the kinematical range appropriate to the LHC.We incorporate the physics of this
model into the beam tracking code MERLIN and use it to simulate the resulting
loss maps of the beam halo lost in the collimators in the LHC.


title: Paquets d'Arthur des groupes classiques complexes

abstract:
  Nous d\'ecrivons explicitement les paquets d'Arthur des groupes classiques
complexes, ainsi que leur param\'etrisation interne par les caract\`eres du
groupe des composantes connexes du centralisateur de leur param\`etre. Nous
montrons d'abord qu'ils sont obtenus par induction parabolique pr\'eservant
l'irr\'eductibilit\'e \`a partir des paquets unipotents de "bonne parit\'e".
Pour ceux-ci, nous montrons qu'ils co\"incident avec les paquets d\'efinis par
Barbasch-Vogan. Nous utilisons des r\'esultats profonds de Barbasch entrant
dans sa classification du dual unitaire de ces groupes.
  We describe explicitly Arthur packets for complex classical groups, as well
as their internal parametrization by the group of characters of the component
group of the stabilizer of their parameter. We first show that they are
obtained by parabolic induction preserving irreducibility from unipotent
packets of "good parity". For these, we show that they coincide with the
packets defined by Barbasch and Vogan. We use deep results of Barbasch entering
his classification of the unitary dual of these groups.


title: Semi-linear stars are contractible

abstract:
  Let $\cal R$ be an ordered vector space over an ordered division ring. We
prove that every definable set $X$ is a finite union of relatively open
definable subsets which are definably simply-connected, settling a conjecture
from [5]. The proof goes through the stronger statement that the star of a cell
in a special linear decomposition of $X$ is definably simply-connected. In
fact, if the star is bounded, then it is definably contractible.


title: Marginalized Fisher Forecast for Horndeski Dark Energy Models

abstract:
  We use effective field theory (EFT) formalism to forecast the constraint on
Horndeski class of dark energy models with future supernova and galaxy surveys.
Previously (Gleyzes {\it et al.}) computed unmarginalized constraints (68\% CL
error $\sim 10^{-3}$--$10^{-2}$) on EFT dark energy parameters by fixing all
other parameters. We extend the previous work by allowing all cosmological
parameters and nuisance parameters to vary and marginalizing over them. We find
that (i) the constraints on EFT dark energy parameters are typically worsen by
a factor of few after marginalization, and (ii) the constraint on the dark
energy equation of state $w$ is not significantly affected by the inclusion of
EFT dark energy parameters.


title:
Electron wave packet evolution under the influence of random electric
  field

abstract:
  We consider an electron wave packet evolution in the external deterministic
electric field with Gaussian white noise addition. An explicit expression was
given for the averaged probability flux with Gaussian initial wave function. We
show that the noise addition increases wave packet spreading rate, which has a
significant influence on flux amplitude and may play both destructive and
constructive role. This depends on the form and amplitude of external
deterministic field.


title: Supernova Neutrinos: Theory

abstract:
  Neutrinos play a key role in core-collapse supernova explosions. Carrying
information from deep inside the stellar core, neutrinos are direct probes of
the supernova mechanism. Intriguing recent developments on the role of
neutrinos in supernovae are reviewed, as well as our current understanding of
the flavor conversions in the stellar envelope, and the detection perspectives
of the next burst.


title: A filtration on rings of representations of non-Archimedean $GL_n$

abstract:
  Let $F$ be a $p$-adic field. Let $\mathcal{R}$ be the Grothendieck ring of
complex smooth finite-length representations of the groups
$\{GL_n(F)\}_{n=0}^\infty$ taken together, with multiplication defined in the
sense of parabolic induction. We introduce a width invariant for elements of
$\mathcal{R}$ and show that it gives an increasing filtration on the ring.
Irreducible representations of width $1$ are precisely those known as ladder
representations. We thus obtain a necessary condition on irreducible factors of
a product of two ladder representations. For such a product we further
establish a multiplicity-one phenomenon, which was previously observed in
special cases.


title: Quasiparticle interference on cubic perovskite oxide surfaces

abstract:
  We report the first observation of coherent surface states on cubic
perovskite oxide SrVO3(001) thin films through spectroscopic imaging scanning
tunneling microscopy. A direct link between the observed atomic-scale
interference patterns and the formation of a dxy-derived surface state is
supported by first-principles calculations. Furthermore, we show that the
apical oxygens on the topmost VO2 plane play a critical role in controlling the
spectral weight of the observed coherent surface state.


title: Scalable Gaussian Processes for Supervised Hashing

abstract:
  We propose a flexible procedure for large-scale image search by hash
functions with kernels. Our method treats binary codes and pairwise semantic
similarity as latent and observed variables, respectively, in a probabilistic
model based on Gaussian processes for binary classification. We present an
efficient inference algorithm with the sparse pseudo-input Gaussian process
(SPGP) model and parallelization. Experiments on three large-scale image
dataset demonstrate the effectiveness of the proposed hashing method, Gaussian
Process Hashing (GPH), for short binary codes and the datasets without
predefined classes in comparison to the state-of-the-art supervised hashing
methods.


title: Supersymmetric Dark Matter or Not

abstract:
  The lack of evidence for low energy supersymmetry at the LHC implies a
supersymmetry scale in excess a TeV. While this is consistent (and even
helpful) with a Higgs boson mass at $\approx$ 125 GeV, simple supersymmetric
models with scalar and gaugino mass universality are being pushed into strips
of parameter space. These often require coannihilations to obtain an acceptable
relic density and the extent of these coannihilation strips will be discussed.
In contrast, non-supersymmetric grand unified theories such as SO(10) may also
provide a dark matter candidate. Because of the presence of an intermediate
scale, these theories may unify gauge couplings, provide for neutrino masses
and a suitably long lived proton.


title: Bias-free spin-wave phase shifter for magnonic logic

abstract:
  A design of a magnonic phase shifter operating without an external bias
magnetic field is proposed. The phase shifter uses a localized collective spin
wave mode propagating along a domain wall "waveguide" in a dipolarly-coupled
magnetic dot array existing in a chessboard antiferromagnetic (CAFM) ground
state. It is demonstrated numerically that remagnetization of a single magnetic
dot adjacent to the domain wall waveguide introduces a controllable phase shift
in the propagating spin wave mode without significant change of the mode
amplitude. It is also demonstrated that a logic XOR gate can be realized in the
same system.


title: Long Wavelength Fluctuations and the Glass Transition in 2D and 3D

abstract:
  Phase transitions significantly differ between two-dimensional and
three-dimensional systems, but the influence of dimensionality on the glass
transition is unresolved. We use microscopy to study colloidal systems as they
approach their glass transitions at high concentrations, and find differences
between 2D and 3D. We find that in 2D particles can undergo large displacements
without changing their position relative to their neighbors, in contrast with
3D. This is related to Mermin-Wagner long-wavelength fluctuations that
influence phase transitions in 2D. However, when measuring particle motion only
relative to their neighbors, 2D and 3D have similar behavior as the glass
transition is approached, showing that the long wavelength fluctuations do not
cause a fundamental distinction between 2D and 3D glass transitions.


title: Compressed-domain visual saliency models: A comparative study

abstract:
  Computational modeling of visual saliency has become an important research
problem in recent years, with applications in video quality estimation, video
compression, object tracking, retargeting, summarization, and so on. While most
visual saliency models for dynamic scenes operate on raw video, several models
have been developed for use with compressed-domain information such as motion
vectors and transform coefficients. This paper presents a comparative study of
eleven such models as well as two high-performing pixel-domain saliency models
on two eye-tracking datasets using several comparison metrics. The results
indicate that highly accurate saliency estimation is possible based only on a
partially decoded video bitstream. The strategies that have shown success in
compressed-domain saliency modeling are highlighted, and certain challenges are
identified as potential avenues for further improvement.


title:
The turbulent diffusion of toroidal magnetic flux as inferred from
  properties of the sunspot butterfly diagram

abstract:
  In order to match observed properties of the solar cycle, flux-transport
dynamo models require the toroidal magnetic flux to be stored in a region of
low magnetic diffusivity, typically located at or below the bottom of the
convection zone.
  We infer the turbulent magnetic diffusivity affecting the toroidal field on
the basis of empirical data.
  We consider the time evolution of mean latitude and width of the activity
belts of solar cycles 12--23 and their dependence on cycle strength. We
interpret the decline phase of the cycles as a diffusion process.
  The activity level of a given cycle begins to decline when the centers of its
equatorward propagating activity belts come within their width (at half
maximum) from the equator. This happens earlier for stronger cycles because
their activity belts are wider. From that moment on, the activity and the belt
width decrease in the same manner for all cycles, independent of their maximum
activity level. In terms of diffusive cancellation of opposite-polarity
toroidal flux across the equator, we infer the turbulent diffusivity
experienced by the toroidal field, wherever it is located, to be in the range
150--450~km$^2$s$^{-1}$. Strong diffusive latitudinal spreading of the toroidal
flux underneath the activity belts can be inhibited by an inflow towards the
toroidal field bands in the convection zone with a magnitude of several meters
per second.
  The inferred value of the turbulent magnetic diffusivity affecting the
toroidal field agrees, to order of magnitude, with estimates based on
mixing-length models for the solar convection zone. This is at variance with
the requirement of flux-transport dynamo models. The inflows required to keep
the toroidal field bands together before they approach the equator are similar
to the inflows towards the activity belts observed with local helioseismology.


title:
Shape selection of surface-bound helical filaments: biopolymers on
  curved membranes

abstract:
  Motivated to understand the behavior of biological filaments interacting with
membranes of various types, we study a theoretical model for the shape and
thermodynamics of intrinsically-helical filaments bound to curved membranes. We
show filament-surface interactions lead to a host of non-uniform shape
equilibria, in which filaments progressively unwind from their native twist
with increasing surface interaction and surface curvature, ultimately adopting
uniform-contact curved shapes. The latter effect is due to non-linear coupling
between elastic twist and bending of filaments on anisotropically-curved
surfaces, such as the cylindrical surfaces considered here. Via a combination
of numerical solutions and asymptotic analysis of shape equilibria we show that
filament conformations are critically sensitive to the surface curvature in
both the strong- and weak-binding limits. These results suggest that local
structure of membrane-bound chiral filaments is generically sensitive to the
curvature-radius of the surface to which it is bound, even when that radius is
much larger than the filament intrinsic pitch. Typical values of elastic
parameters and interaction energies for several prokaryotic and eukaryotic
filaments indicate that biopolymers are inherently very sensitive to the
coupling between twist, interactions and geometry and that this could be
exploited for regulation of a variety of processes such as the targeted
exertion of forces, signaling and self-assembly in response to geometric cues
including the local mean and Gaussian curvatures.


title: Supervised Incremental Hashing

abstract:
  We propose an incremental strategy for learning hash functions with kernels
for large-scale image search. Our method is based on a two-stage classification
framework that treats binary codes as intermediate variables between the
feature space and the semantic space. In the first stage of classification,
binary codes are considered as class labels by a set of binary SVMs; each
corresponds to one bit. In the second stage, binary codes become the input
space of a multi-class SVM. Hash functions are learned by an efficient
algorithm where the NP-hard problem of finding optimal binary codes is solved
via cyclic coordinate descent and SVMs are trained in a parallelized
incremental manner. For modifications like adding images from a previously
unseen class, we describe an incremental procedure for effective and efficient
updates to the previous hash functions. Experiments on three large-scale image
datasets demonstrate the effectiveness of the proposed hashing method,
Supervised Incremental Hashing (SIH), over the state-of-the-art supervised
hashing methods.


title: Hybrid Monte Carlo with Chaotic Mixing

abstract:
  We propose a hybrid Monte Carlo (HMC) technique applicable to
high-dimensional multivariate normal distributions that effectively samples
along chaotic trajectories. The method is predicated on the freedom of choice
of the HMC momentum distribution, and due to its mixing properties, exhibits
sample-to-sample autocorrelations that decay far faster than those in the
traditional hybrid Monte Carlo algorithm. We test the methods on distributions
of varying correlation structure, finding that the proposed technique produces
superior covariance estimates, is less reliant on step-size tuning, and can
even function with sparse or no momentum re-sampling. The method presented here
is promising for more general distributions, such as those that arise in
Bayesian learning of artificial neural networks and in the state and parameter
estimation of dynamical systems.


title: The $q$-deformed Bogoliubov transformations

abstract:
  An approach for $q$-deformed Bogoliubov transformations is presented.
Assuming a left-right module action together with an *-operation and deformed
commutation relations, we construct a q-deformation of the nonlinear Bogoliubov
transformation. Moreover we give a general result which can be applied in
Quantum Field Theory. Finally, we introduce a Hopf structure when q is a root
of unity.


title:
Slowdown of microparticles by an electromagnetic potential well
  deepening over time

abstract:
  We analyze possible motion control of microparticles by means of external
electromagnetic fields which induce potential wells having fixed spatial
distribution but deepening over time up to some limit. It is assumed that given
particles are under conditions of the high vacuum and forces acting on these
particles are not dissipative. We have established slowdown of comparatively
fast particles as a result of their transit through considered potential wells.
This process is demonstrated on example of the nonresonance laser beam with the
intensity amplifying over time. More detailed research of particle slowdown in
such electromagnetic fields is carried out on the basis of simple analytical
relationships obtained from basic equations of classical mechanics for the
model of the one-dimensional rectangular potential well deepening over time.
Method for cooling of particles, demonstrated in the present work, may be
applied for essential increase of spectroscopy resolution of various
microparticles, including in definite cases also atoms and molecules in the
ground quantum state.


title:
A characterization of involutes and evolutes of a given curve in
  $\mathbb{E}^{n}$

abstract:
  The orthogonal trajectories of the first tangents of the curve are called the
involutes of $x$. The hyperspheres which have higher order contact with a curve
$x$ are known osculating hyperspheres of $x$. The centers of osculating
hyperspheres form a curve which is called generalized evolute of the given
curve $x$ in $n$-dimensional Euclidean space $\mathbb{E}^{n}$. In the present
study, we give a characterization of involute curves of order $k$ (resp.
evolute curves) of the given curve $x$ in $n$-dimensional Euclidean space
$\mathbb{E}^{n}$. Further, we obtain some results on these type of curves in
$\mathbb{E}^{3}$ and $\mathbb{E}^{4}$, respectively.


title:
Detecting entanglement of continuous variables with three mutually
  unbiased bases

abstract:
  An uncertainty relation is introduced for a symmetric arrangement of three
mutually unbiased bases in continuous variable phase space, and then used to
derive a bipartite entanglement criterion based on the variance of global
operators composed of these three phase space variables. We test this criterion
using spatial variables of photon pairs, and show that the entangled photons
are correlated in three pairs of bases.


title: On the gravitational seesaw in higher-derivative gravity

abstract:
  Local gravitational theories with more than four derivatives are
superrenormalizable, and also may be unitary in the Lee-Wick sense. Thus, it is
relevant to study the low-energy properties of these theories, especially to
identify observables which might be useful for experimental detection of higher
derivatives. Using an analogy with the neutrino Physics, we explore the
possibility of a gravitational seesaw mechanism, in which several dimensional
parameters of the same order of magnitude produce a hierarchy in the masses of
propagating particles. Such a mechanism could make a relatively light degree of
freedom detectable in low-energy laboratory and astrophysical observations,
such as torsion balance experiments and the bending of light. We demonstrate
that such a seesaw mechanism in the six- and more-derivative theories is unable
to reduce the lightest mass more than in the simplest four-derivative model.
Adding more derivatives to the four-derivative action of gravity makes heavier
masses even greater, while the lightest massive ghost is not strongly affected.
This fact is favorable for protecting the theory from instabilities, but makes
the experimental detection of higher derivatives more difficult.


title:
Measurable versions of the Lov\'{a}sz Local Lemma and measurable graph
  colorings

abstract:
  In this paper we investigate the extent to which the Lov\'asz Local Lemma (an
important tool in probabilistic combinatorics) can be adapted for the
measurable setting. In most applications, the Lov\'asz Local Lemma is used to
produce a function $f \colon X \to Y$ with certain properties, where $X$ is
some underlying combinatorial structure and $Y$ is a (typically finite) set.
Can this function $f$ be chosen to be Borel or $\mu$-measurable for some
probability Borel measure $\mu$ on $X$ (assuming that $X$ is a standard Borel
space)? In the positive direction, we prove that if the set of constraints put
on $f$ is, in a certain sense, "locally finite," then there is always a Borel
choice for $f$ that is "$\varepsilon$-close" to satisfying these constraints,
for any $\varepsilon > 0$. Moreover, if the combinatorial structure on $X$ is
"induced" by the $[0;1]$-shift action of a countable group $\Gamma$, then, even
without any local finiteness assumptions, there is a Borel choice for $f$ which
satisfies the constraints on an invariant conull set (i.e., with $\varepsilon =
0$). A direct corollary of our results is an upper bound on the measurable
chromatic number of the graph $G_n$ generated by the shift action of the free
group $\mathbb{F}_n$ that is asymptotically tight up to a factor of at most $2$
(which answers a question of Lyons and Nazarov). On the other hand, our result
for structures induced by measure-preserving group actions is, at least for
amenable groups, sharp in the following sense: a probability measure-preserving
action of a countably infinite amenable group satisfies the measurable version
of the Lov\'asz Local Lemma if and only if it admits a factor map to the
$[0;1]$-shift action. To prove this, we combine the tools of the
Ornstein--Weiss theory of entropy for actions of amenable groups with concepts
from computability theory, specifically, Kolmogorov complexity.


title: A direct approach to the stable distributions

abstract:
  The explicit form for the characteristic function of a stable distribution on
the line is derived analytically by solving the associated functional equation
and applying theory of regular variation, without appeal to the general
L\'evy-Khintchine integral representation of infinitely divisible
distributions.


title: Realizing quantum advantage without entanglement in single-photon states

abstract:
  We discuss the realization of quantum advantage in a system without quantum
entanglement but with non-zero quantum discord. We propose an optical
realization of symmetric two-qubit $X$-states with controllable anti-diagonal
elements. This approach does not requires initially entangled states, and it
can generate states that have quantum discord, with or without entanglement. We
discuss how quantum advantage can be attained in the context of a two-qubit
game. We show that when entanglement is not present, the maximum quantum
advantage is 1/3 bit. A comparable quantum advantage, 0.311 bit, can be
realized with a simplified transaction protocol involving one vs. the three
unitary operations needed for the maximum advantage.


title: Tree algebras over topological vector spaces in rough path theory

abstract:
  We work with non-planar rooted trees which have a label set given by an
arbitrary vector space $V$. By equipping $V$ with a complete locally convex
topology, we show how a natural topology is induced on the tree algebra over
$V$. In this context, we introduce the Grossman-Larson and Connes-Kreimer
topological Hopf algebras over $V$, and prove that they form a dual pair in a
certain sense. As an application we define the class of branched rough paths
over a general Banach space, and propose a new definition of a solution to a
rough differential equation (RDE) driven by one of these branched rough paths.
We show equivalence of our definition with a Davie-Friz-Victoir-type
definition, a version of which is widely used for RDEs with geometric drivers,
and we comment on applications to RDEs with manifold-valued solutions.


title: A heuristic model for MRI turbulent stresses in Hall MHD

abstract:
  Although the Shakura-Sunyaev $\alpha$ viscosity prescription has been highly
successful in characterizing myriad astrophysical environments, it has proven
to be partly inadequate in modelling turbulent stresses driven by the MRI.
Hence, we adopt the approach employed by \citet{GIO03}, but in the context of
Hall magnetohydrodynamics (MHD), to study MRI turbulence. We utilize the exact
evolution equations for the stresses, and the non-linear terms are closed
through the invocation of dimensional analysis and physical considerations. We
demonstrate that the inclusion of the Hall term leads to non-trivial results,
including the modification of the Reynolds and Maxwell stresses, as well as the
(asymptotic) non-equipartition between the kinetic and magnetic energies; the
latter issue is also addressed via the analysis of non-linear waves. The
asymptotic ratio of the kinetic and magnetic energies is shown to be
\emph{independent} of the choice of initial conditions, but it is governed by
the \emph{Hall parameter}. We contrast our model with the Kazantsev
prescription from small-scale dynamo theory, and the Hall term does not
contribute in the latter approach, illustrating the limitations of the
Kazantsev formalism. We indicate potential astrophysical applications of our
model, including the solar wind where a lack of equipartition has been
observed.

categories: astro-ph.SR astro-ph.HE physics.plasm-ph physics.space-ph