title:
Spin-down in a rapidly rotating cylinder container with mixed rigid and
  stress-free boundary conditions

abstract:
  A comprehensive study of the classical linear spin-down of a constant density
viscous fluid (kinematic viscosity \nu) rotating rapidly (angular velocity
\Omega) inside an axisymmetric cylindrical container (radius L, height H) with
rigid boundaries, that follows the instantaneous small change in the boundary
angular velocity at small Ekman number $E=\nu/H^2\Omega \ll 1$, was provided by
Greenspan & Howard (1963). $E^{1/2}$-Ekman layers form quickly triggering
inertial waves together with the dominant spin-down of the quasi-geostrophic
(QG) interior flow on the $O(E^{-1/2}\Omega^{-1})$ time-scale. On the longer
lateral viscous diffusion time-scale $O(L^2/\nu)$, the QG-flow responds to the
$E^{1/3}$-side-wall shear-layers. In our variant the side-wall and top
boundaries are stress-free; a setup motivated by the study of isolated
atmospheric structures, such as tropical cyclones, or tornadoes. Relative to
the unbounded plane layer case, spin-down is reduced (enhanced) by the presence
of a slippery (rigid) side-wall. This is evinced by the QG-angular velocity,
\omega*, evolution on the O(L^2/\nu) time-scale: Spatially, \omega* increases
(decreases) outwards from the axis for a slippery (rigid) side-wall;
temporally, the long-time ($\gg L^2/\nu)$ behaviour is dominated by an
eigensolution with a decay rate slightly slower (faster) than that for an
unbounded layer. In our slippery side-wall case, the $E^{1/2} \times E^{1/2}$
corner region that forms at the side-wall intersection with the rigid base is
responsible for a $\ln E$ singularity within the $E^{1/3}$-layer causing our
asymptotics to apply only at values of E far smaller than can be reached by our
Direct Numerical Simulation (DNS) of the entire spin-down process. Instead, we
solve the $E^{1/3}$-boundary-layer equations for given E numerically. Our
hybrid asymptotic-numerical approach yields results in excellent agreement with
our DNS.


title: Sodium catalytic effect in the NaxLi6-xC60 hydrogen storage process

abstract:
  We report on the hydrogen sorption investigation of the mixed alkali cluster
intercalated fulleride series NaxLi6-xC60. These compounds are isostructural to
Na6C60 and Li6C60 while the cubic lattice parameter is linearly dependent on x.
The H2 absorption/desorption was studied by means of charge/discharge kinetic
and coupled calorimetric - manometric measurements. By varying the
stoichiometry, we found the best compromise between absorption rate,
temperature and amount of hydrogen in Na1Li5C60. This system is able to
reversibly absorb up to 4.3 wt% H2 at 280 {\deg}C, which is 70 {\deg}C lower in
temperature than its parent compound Li6C60. Furthermore, the kinetics is
improved of 67% with respect Li6C60 and the dehydrogenation enthalpy is 13
kJ/mol H2 lower.


title: On the role of thermal boundary conditions in dynamo scaling laws

abstract:
  In dynamo power-based scaling laws, the power $P$ injected by buoyancy forces
is measured by a so-called flux-based Rayleigh number, denoted as ${\rm
Ra}_Q^*$ (see Christensen and Aubert, 2006). Whereas it is widely accepted that
this parameter is measured (as opposite to controlled) in dynamos driven by
differential heating, the literature is much less clear concerning its nature
in the case of imposed heat flux. We clarify this issue by highlighting that in
that case, the ${\rm Ra}_{Q}^*$ parameter becomes controlled only in the limit
of large Nusselt numbers (${\rm Nu} \gg 1$).
  We then address the issue of the robustness of the original relation between
$P$ and ${\rm Ra}_Q^*$ with the geometry and the thermal boundary conditions.
We show that in the cartesian geometry, as in the spherical geometry with a
central mass distribution, this relation is purely linear, in both differential
and fixed-flux heating. However, we show that in the geometry commonly studied
by geophysicists (spherical with uniform mass distribution), its validity
places an upper-bound on the strength of the driving which can be envisaged in
a fixed Ekman number simulation. An increase of the Rayleigh number indeed
yields deviations (in terms of absolute correction) from the linear relation
between $P$ and ${\rm Ra}_Q^*$. We conclude that in such configurations, the
parameter range for which $P$ is controlled is limited.


title:
A scenario-based framework for supply planning under uncertainty:
  stochastic programming versus robust optimization approaches

abstract:
  In this paper we analyze the effect of two modelling approaches for supply
planning problems under uncertainty: two-stage stochastic programming (SP) and
robust optimization (RO). The comparison between the two approaches is
performed through a scenario-based framework methodology, which can be applied
to any optimization problem affected by uncertainty. For SP we compute the
minimum expected cost based on the specific probability distribution of the
uncertain parameters related to a set of scenarios. For RO we consider static
approaches where random parameters belong to box or ellipsoidal uncertainty
sets in compliance with the data used to generate SP scenarios. Dynamic
approaches for RO, via the concept of adjustable robust counterpart, are also
considered. The efficiency of the methodology has been illustrated for a supply
planning problem to optimize vehicle-renting and procurement transportation
activities involving uncertainty on demands and on buying costs for
extra-vehicles. Numerical experiments through the scenario-based framework
allow a fair comparison in real case instances. Advantages and disadvantages of
RO and SP are discussed.


title:
How Magnetic Field Inhomogeneity of Plane Wiggler Affects Spontaneous
  Radiation of Electrons

abstract:
  The spectral distribution of spontaneous emission of electrons moving in a
plane wiggler with inhomogeneous magnetic field is calculated. We show that
electrons do complicated motion consisting of slow(strophotron) and
fast(undulator) parts. The equations of motion are averaged over fast undulator
part and we obtain equations for connected motion. It is shown, that the
account of inhomogenity of the magnetic field leads to appearance of additional
peaks in the spectral distribution of spontaneous radiation.


title: A gauge invariant Debye mass for the complex heavy-quark potential

abstract:
  The concept of a screening mass is a powerful tool to simplify the intricate
physics of in-medium test charges surrounded by light charge carriers. While it
has been successfully used to describe electromagnetic properties, its
definition and computation in QCD is plagued by questions of gauge invariance
and the presence of non-perturbative contributions from the magnetic sector.
Here we present a recent alternative definition of a gauge invariant Debye mass
parameter following closely the original idea of Debye and Hueckel. Our test
charges are a static heavy quark-antiquark pair whose complex potential and its
in-medium modification can be extracted using lattice QCD. By combining in a
generalized Gauss-Law the non-perturbative aspects of quark binding with a
perturbative ansatz for the medium effects, we succeed to describe the lattice
values of the potential with a single temperature dependent parameter, in turn
identified with a Debye mass. We find that its behavior, as evaluated in a
recent quenched lattice QCD study, deviates from that in other approaches, such
as hard-thermal-loop perturbation theory or from electric field correlators on
the lattice. In particular around the phase transition its values tend to zero
significantly faster than at weak-coupling.


title:
What lattice QCD spectral functions can tell us about heavy quarkonium
  in the QGP

abstract:
  The bound states of a heavy quark and antiquark ($c\bar{c}, b\bar{b}$) are
ideal probes to explore the quark-gluon plasma created in relativistic
heavy-ion collisions at the RHIC and LHC. Not only have they become
experimentally accessible with high precision but also efficient tools, so
called effective field theories (EFT) have been developed to treat them
theoretically. Here we present recent progress in understanding the in-medium
behavior of heavy-quarkonium with the help of EFT's combined with
non-perturbative and first principles simulations in lattice QCD. In particular
we discuss computations of heavy quarkonium spectral functions with the help of
Bayesian unfolding methods and the physics we can extract from them.
Limitations and the underlying assumptions of the used approaches are pointed
out.


title: Quarkonia at $T>0$ and lattice QCD

abstract:
  We report here on recent progress in the determination of S-wave and P-wave
heavy-quarkonium states at finite temperature. Our results are based on the
combination of effective field theories with numerical lattice QCD simulations.
These non-perturbative tools allow us to compute the heavy-quarkonium in-medium
spectral functions, from which we in turn determine the melting temperatures of
individual states and estimate phenomenologically relevant observables, such as
the $\psi^\prime$ to J/$\psi$ ratio in heavy-ion collisions.


title: A Dual Field-of-View Zoom Metalens

abstract:
  Conventional optical zoom system is bulky, expensive and complicated for real
time adjustment. Recent progress in the metasurface research has provided a new
solution to achieve innovative compact optical systems. In this paper, we
propose a highly integrated zoom lens with dual field-of-view (FOV) based on
double sided metasurfaces. With silicon nanobrick arrays of spatially varying
orientations sitting on both side of a transparent substrate, this ultrathin
zoom metalens can be designed to focus an incident circular polarized beam with
spin-dependent FOVs without varying the focal plane, which is important for
practical applications. The proposed dual FOV zoom metalens, with the
advantages such as ultracompactness, flexibility and replicability, can find
applications in fields which require ultracompact zoom imaging and beam
focusing.


title: Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma

abstract:
  We verify new cases of the Arithmetic Fundamental Lemma (AFL) of Wei Zhang.
This relies on a recursive algorithm which allows, under certain conditions, to
reduce the AFL identity in question to an AFL identity in lower dimension. The
main ingredient for this reduction is a comparison isomorphism between
different moduli problems of PEL-type for p-divisible groups. The construction
of this comparison isomorphism is based on the theory of relative displays and
frames, as developed by Tobias Ahsendorf, Eike Lau and Thomas Zink.


title:
Cohomogeneity one Kahler and Kahler-Einstein manifolds with one
  singular orbit, I

abstract:
  Let $M$ be a cohomogeneity one manifold of a compact semisimple Lie group $G$
with one singular orbit $S_0 = G/H$. Then $M$ is $G$- diffeomorphic to the
total space $G \times_H V$ of the homogeneous vector bundle over $S_0$ defined
by a sphere transitive representation of $G$ in a vector space $V$. We describe
all such manifolds $M$ which admit an invariant Kahler structure of standard
type. This means that the restriction $\mu: S = Gx = G/L \rightarrow F = G/K$
of the moment map of $M$ to a regular orbit $S = G/L$ is a holomorphic map of
$S$ with the induced CR structure onto a flag manifold $F = G/K$, where $K =
N_G(L)$, endowed with an invariant complex structure $J^F$ . We describe all
such standard Kahler cohomogeneity one manifolds in terms of the painted
Dynkin diagram associated with $(F=G/K; J^F)$ and a parametrized interval in
some T-Weyl chamber. We determine which of these manifolds admit invariant
Kahler-Einstein metrics.


title: Composite Operators in Asymptotic Safety

abstract:
  We study the role of composite operators in the Asymptotic Safety program for
quantum gravity. By including in the effective average action an explicit
dependence on new sources we are able to keep track of operators which do not
belong to the exact theory space and/or are normally discarded in a truncation.
Typical examples are geometric operators such as volumes, lengths, or geodesic
distances. We show that this set-up allows to investigate the scaling
properties of various interesting operators via a suitable exact
renormalization group equation. We test our framework in several settings,
including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert
truncation, and two dimensional quantum gravity. Finally, we briefly argue that
our construction paves the way to approach observables in the Asymptotic Safety
program.


title:
Analytic results for planar three-loop integrals for massive form
  factors

abstract:
  We use the method of differential equations to analytically evaluate all
planar three-loop Feynman integrals relevant for form factor calculations
involving massive particles. Our results for ninety master integrals at general
$q^2$ are expressed in terms of multiple polylogarithms, and results for
fiftyone master integrals at the threshold $q^2=4m^2$ are expressed in terms of
multiple polylogarithms of argument one, with indices equal to zero or to a
sixth root of unity.


title: ${\rm t\bar{t}}$ cross section measurements in CMS

abstract:
  An overview of the most recent measurements of inclusive top quark pair
production cross section is presented. The results are obtained using data
collected with the CMS experiment in proton-proton collisions at centre-of-mass
energies of 5.02, 7, 8 and 13 TeV. The data are compared with the predictions
from perturbative QCD calculations at full NNLO+NNLL accuracy.


title:
Mixed quantum-classical dynamics using collective electronic variables:
  A better alternative to electronic friction theories

abstract:
  An accurate description of nonadiabatic dynamics of molecular species on
metallic surfaces poses a serious computational challenge associated with a
multitude of closely-spaced electronic states. We propose a mixed
quantum-classical scheme that addresses this challenge by introducing
collective electronic variables. These variables are defined through analytic
block-diagonalization applied to the time-dependent Hamiltonian matrix
governing the electronic dynamics. We compare our scheme with the Ehrenfest
approach and with a full-memory electronic friction model on a one-dimensional
"adatom + atomic chain" model. Our simulations demonstrate that collective-mode
dynamics with only few (2-3) electronic variables is robust and can describe a
variety of situations: from a chemisorbed atom on an insulator to an atom on a
metallic surface. Our molecular model also reveals that the friction approach
is prone to unpredictable and catastrophic failures.


title:
Elliptic complexes of first-order cone operators: ideal boundary
  conditions

abstract:
  The purpose of this paper is to provide a detailed description of the spaces
that can be specified as $L^2$ domains for the operators of a first order
elliptic complex on a compact manifold with conical singularities. This entails
an analysis of the nature of the minimal domain and of a complementary space in
the maximal domain of each of the operators. The key technical result is the
nondegeneracy of a certain pairing of cohomology classes associated with the
indicial complex. It is further proved that the set of choices of domains
leading to Hilbert complexes in the sense of Br\"uning and Lesch form a
variety, as well as a theorem establishing a necessary and sufficient condition
for the operator in a given degree to map its maximal domain into the minimal
domain of the next operator.


title:
Robust Regularized Least-Squares Beamforming Approach to Signal
  Estimation

abstract:
  In this paper, we address the problem of robust adaptive beamforming of
signals received by a linear array. The challenge associated with the
beamforming problem is twofold. Firstly, the process requires the inversion of
the usually ill-conditioned covariance matrix of the received signals.
Secondly, the steering vector pertaining to the direction of arrival of the
signal of interest is not known precisely. To tackle these two challenges, the
standard capon beamformer is manipulated to a form where the beamformer output
is obtained as a scaled version of the inner product of two vectors. The two
vectors are linearly related to the steering vector and the received signal
snapshot, respectively. The linear operator, in both cases, is the square root
of the covariance matrix. A regularized least-squares (RLS) approach is
proposed to estimate these two vectors and to provide robustness without
exploiting prior information. Simulation results show that the RLS beamformer
using the proposed regularization algorithm outperforms state-of-the-art
beamforming algorithms, as well as another RLS beamformers using a standard
regularization approaches.


title: On the rigidity of symbolic powers

abstract:
  We deal with the rigidity conjecture of symbolic powers over regular rings.
This was asked by Huneke. Along with our investigation, we confirm a conjecture
[7, Conjecture 3.8].


title: A note on distance labeling in planar graphs

abstract:
  A distance labeling scheme is an assignments of labels, that is binary
strings, to all nodes of a graph, so that the distance between any two nodes
can be computed from their labels and the labels are as short as possible. A
major open problem is to determine the complexity of distance labeling in
unweighted and undirected planar graphs. It is known that, in such a graph on
$n$ nodes, some labels must consist of $\Omega(n^{1/3})$ bits, but the best
known labeling scheme uses labels of length $O(\sqrt{n}\log n)$ [Gavoille,
Peleg, P\'erennes, and Raz, J. Algorithms, 2004]. We show that, in fact, labels
of length $O(\sqrt{n})$ are enough.


title: Prototypical Recurrent Unit

abstract:
  Despite the great successes of deep learning, the effectiveness of deep
neural networks has not been understood at any theoretical depth. This work is
motivated by the thrust of developing a deeper understanding of recurrent
neural networks, particularly LSTM/GRU-like networks. As the highly complex
structure of the recurrent unit in LSTM and GRU networks makes them difficult
to analyze, our methodology in this research theme is to construct an
alternative recurrent unit that is as simple as possible and yet also captures
the key components of LSTM/GRU recurrent units. Such a unit can then be used
for the study of recurrent networks and its structural simplicity may allow
easier analysis. Towards that goal, we take a system-theoretic perspective to
design a new recurrent unit, which we call the prototypical recurrent unit
(PRU). Not only having minimal complexity, PRU is demonstrated experimentally
to have comparable performance to GRU and LSTM unit. This establishes PRU
networks as a prototype for future study of LSTM/GRU-like recurrent networks.
This paper also studies the memorization abilities of LSTM, GRU and PRU
networks, motivated by the folk belief that such networks possess long-term
memory. For this purpose, we design a simple and controllable task, called
``memorization problem'', where the networks are trained to memorize certain
targeted information. We show that the memorization performance of all three
networks depends on the amount of targeted information, the amount of
``interfering" information, and the state space dimension of the recurrent
unit. Experiments are also performed for another controllable task, the adding
problem, and similar conclusions are obtained.


title:
Latest results on $\Upsilon$ production in heavy-ion collisions from the
  STAR experiment

abstract:
  We report on the latest measurements of the production of $\Upsilon$ mesons
in heavy-ion collisions from the STAR experiment at RHIC. New measurements of
the nuclear modification factors of the $\Upsilon$(1S+2S+3S) and $\Upsilon$(1S)
states in U+U collisions at $\sqrt{s_{NN}}$ = 193 GeV are presented as a
function of the number of participants ($N_{part}$) in the collisions. In
addition, the suppression of $\Upsilon$(1S) and $\Upsilon$(2S+2S) is presented
versus the quark-antiquark binding energy. Preliminary results on Upsilon
suppression in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, reconstructed via
the dimuon channel, are also reported.


title: $3$-webs generated by confocal conics and circles

abstract:
  We consider families of confocal conics and two pencils of Apollonian circles
having the same foci. We will show that these families of curves generate
trivial 3-webs and find the exact formulas describing them.


title:
Point-contact measurements of the energy gap of lead-chalcogenide-based
  superconducting superlattices

abstract:
  The energy gap of superconducting $PbTe-PbS$ semiconductor superlattices has
been analyzed with the help of point contacts for the first time below the
critical temperature, $T_{c}=3.9~K$, and in the fluctuation region $T>T_{c}$.
The size of the gap and its dependence on the temperature and field are
determined by the position of the point contact inside the superlattice.
\pacs{73.40.Jn, 74.25.Kc, 74.45.+c, 74.50.+r., 73.40.-c, 74.78.-w, 74.78.Fk,
74.20.Mn, 74.40.+k.-n, 74.45.+c, 74.62.Dn, 74.70.Ad


title: Linear Thompson Sampling Revisited

abstract:
  We derive an alternative proof for the regret of Thompson sampling (\ts) in
the stochastic linear bandit setting. While we obtain a regret bound of order
$\widetilde{O}(d^{3/2}\sqrt{T})$ as in previous results, the proof sheds new
light on the functioning of the \ts. We leverage on the structure of the
problem to show how the regret is related to the sensitivity (i.e., the
gradient) of the objective function and how selecting optimal arms associated
to \textit{optimistic} parameters does control it. Thus we show that \ts can be
seen as a generic randomized algorithm where the sampling distribution is
designed to have a fixed probability of being optimistic, at the cost of an
additional $\sqrt{d}$ regret factor compared to a UCB-like approach.
Furthermore, we show that our proof can be readily applied to regularized
linear optimization and generalized linear model problems.


title: Inverses of Bipartite Graphs

abstract:
  Let $G$ be a bipartite graph and its adjacency matrix $\mathbb A$. If $G$ has
a unique perfect matching, then $\mathbb A$ has an inverse $\mathbb A^{-1}$
which is a symmetric integral matrix, and hence the adjacency matrix of a
multigraph. The inverses of bipartite graphs with unique perfect matchings have
a strong connection to M\"obius functions of posets. In this note, we
characterize all bipartite graphs with a unique perfect matching whose
adjacency matrices have inverses diagonally similar to non-negative matrices,
which settles an open problem of Godsil on inverses of bipartite graphs in
[Godsil, Inverses of Trees, Combinatorica 5 (1985) 33-39].


title: T-Duality from super Lie n-algebra cocycles for super p-branes

abstract:
  We compute the $L_\infty$-theoretic dimensional reduction of the
F1/D$p$-brane super $L_\infty$-cocycles with coefficients in rationalized
twisted K-theory from the 10d type IIA and type IIB super Lie algebras down to
9d. We show that the two resulting coefficient $L_\infty$-algebras are
naturally related by an $L_\infty$-isomorphism which we find to act on the
super $p$-brane cocycles by the infinitesimal version of the rules of
topological T-duality and inducing an isomorphism between $K^0$ and $K^1$,
rationally. In particular this is a derivation of the Buscher rules for
RR-fields (Hori's formula) from first principles. Moreover, we show that these
$L_\infty$-algebras are the homotopy quotients of the RR-charge coefficients by
the "T-duality Lie 2-algebra". We find that the induced $L_\infty$-extension is
a gerby extension of a 9+(1+1) dimensional (i.e. "doubled") T-duality
correspondence super-spacetime, which serves as a local model for T-folds. We
observe that this still extends, via the D0-brane cocycle of its type IIA
factor, to a 10+(1+1)-dimensional super Lie algebra. Finally we observe that
this satisfies expected properties of a local model space for F-theory elliptic
fibrations.


title:
Point-contact studies of semiconductor $PbTe-PbS$ superconducting
  superlattice as a model of HTS

abstract:
  Superconducting (SC) superlattices (SL) of the epitaxial semiconductor
$PbTe-PbS$/(001) $KCl$ with two-dimensional ordered misfit dislocation (MD)
networks across heteroboundaries (HB) are studied, and the obtained results are
compared with the corresponding data for $YBaCuO$. An analysis of the
fluctuational region showed that the pairing of electrons in SL takes place at
the sites of dislocation networks. In the region of SC fluctuations, the IVC
derivatives of point-contacts (PC) based on SL and HTS display a
metal-insulator transition associated with delocalization of carriers from the
vicinity of the structural elements responsible for the emergence of SC. The
critical current density in a superlattice is determined, and a mechanism is
proposed for formation of excess current on the IVC of PC based on SL and HTS.
The values of the energy gap $\Delta_0$ at low temperatures in units of $kT_c$
are found to be anomalously large for SL and HTS. For anisotropic
three-dimensional SL with a strong bond between two-dimensional SC planes, two
gaps emerge from the MD. For quasi-two-dimensional SL with a weak bond between
two-dimensional SC planes, the $\Delta(T)$ dependence is nonmonotonic, and the
fluctuation region for these SL and for HTS reveals a gap that is practically
independent of temperature. The IVC derivatives of a $Cu$-SL PC reveal an
oscillating structure which is restricted to an energy of $90\ meV$ and is
apparently associated with the electron-phonon interaction. It is assumed that
there is a similarity between the SC mechanisms in SL and HTS. pacs 73.40.Jn,
74.25.Kc, 74.45.+c, 74.50.+r., 73.40.-c, 74.78.-w, 74.78.Fk, 74.20.Mn,
74.40.+k.-n, 74.45.+c, 74.62.Dn, 74.70.Ad


title:
On Storage Allocation in Cache-Enabled Interference Channels with Mixed
  CSIT

abstract:
  Recently, it has been shown that in a cache-enabled interference channel, the
storage at the transmit and receive sides are of equal value in terms of
Degrees of Freedom (DoF). This is derived by assuming full Channel State
Information at the Transmitter (CSIT). In this paper, we consider a more
practical scenario, where a training/feedback phase should exist for obtaining
CSIT, during which instantaneous channel state is not known to the
transmitters. This results in a combination of delayed and current CSIT
availability, called mixed CSIT. In this setup, we derive DoF of a
cache-enabled interference channel with mixed CSIT, which depends on the memory
available at transmit and receive sides as well as the training/feedback phase
duration. In contrast to the case of having full CSIT, we prove that, in our
setup, the storage at the receive side is more valuable than the one at the
transmit side. This is due to the fact that cooperation opportunities granted
by transmitters' caches are strongly based on instantaneous CSIT availability.
However, multi-casting opportunities provided by receivers' caches are robust
to such imperfection.


title: Efficient Stochastic Inference of Bitwise Deep Neural Networks

abstract:
  Recently published methods enable training of bitwise neural networks which
allow reduced representation of down to a single bit per weight. We present a
method that exploits ensemble decisions based on multiple stochastically
sampled network models to increase performance figures of bitwise neural
networks in terms of classification accuracy at inference. Our experiments with
the CIFAR-10 and GTSRB datasets show that the performance of such network
ensembles surpasses the performance of the high-precision base model. With this
technique we achieve 5.81% best classification error on CIFAR-10 test set using
bitwise networks. Concerning inference on embedded systems we evaluate these
bitwise networks using a hardware efficient stochastic rounding procedure. Our
work contributes to efficient embedded bitwise neural networks.


title:
Novel picture of the soft modes at the QCD critical point based on the
  FRG method

abstract:
  We investigate the soft mode at the QCD critical point (CP) on the basis of
the functional renormalization group. We calculate the spectral functions in
the meson channels in the two-flavor quark--meson model. Our result shows that
the energy of the peak position of the particle--hole mode in the sigma channel
becomes vanishingly small as the system approaches the QCD CP, which is a
manifestation of the softening of the phonon mode. We also extract the
dispersion curves of the mesonic and the phonon mode, a hydrodynamic mode which
leads to a finding that the dispersion curve of the sigma-mesonic mode crosses
the light-cone into the space-like momentum region, and then eventually merges
into the phonon mode as the system approaches further close to the CP. This may
suggest that the sigma-mesonic mode forms the soft mode together with the
hydrodynamic mode at the CP.


title: Koszul duality between Higgs and Coulomb categories $\mathcal{O}$

abstract:
  We prove a Koszul duality theorem between the category of weight modules over
the quantized Coulomb branch (as defined by Braverman, Finkelberg and Nakajima)
attached to a group $G$ and representation $V$ and a category of
$G$-equivariant D-modules on the vector space $V$. This is proven by relating
both categories to an explicit, combinatorially presented category.
  These categories are related to generalized categories $\mathcal{O}$ for
symplectic singularities. Letting $\mathcal{O}_{\operatorname{Coulomb}}$ and
$\mathcal{O}_{\operatorname{Higgs}}$ be these categories for the Coulomb and
Higgs branches associated to $V$ and $G$, we obtain a functor
$\mathcal{O}_{\operatorname{Coulomb}}^!\to \mathcal{O}_{\operatorname{Higgs}}$
from the Koszul dual of one to the other. This functor is an equivalence in the
special cases where the hyperk\"ahler quotient of $T^*V$ by $G$ is a Nakajima
quiver variety or smooth hypertoric variety. This includes as special cases the
parabolic-singular Koszul duality of category $\mathcal{O}$ in type A, the
categorified rank-level duality proposed by Chuang and Miyachi and proven by
Shan, Vasserot and Varagnolo, and the hypertoric Koszul duality proven by
Braden, Licata, Proudfoot and the author.
  We also show that this equivalence intertwines so-called twisting and
shuffling functors. This together with the duality discussed confirms the most
important components of the symplectic duality conjecture of Braden, Licata,
Proudfoot and the author in this case.


title:
SU(3) Yang-Mills Hamiltonian in the flux-tube gauge: Strong coupling
  expansion and glueball dynamics

abstract:
  It is shown that the formulation of the SU(3) Yang-Mills quantum Hamiltonian
in the "flux-tube gauge" $A_{a1}=0$ for all a=1,2,4,5,6,7 and $A_{a2}=0$ for
all a=5,7 allows for a systematic and practical strong coupling expansion of
the Hamiltonian in $\lambda\equiv g^{-2/3}$, equivalent to an expansion in the
number of spatial derivatives. Introducing an infinite spatial lattice with box
length a, the "free part" is the sum of Hamiltonians of Yang-Mills quantum
mechanics of constant fields for each box, and the "interaction terms" contain
higher and higher number of spatial derivatives connecting different boxes. The
Faddeev-Popov operator, its determinant and inverse, are rather simple, but
show a highly non-trivial periodic structure of six Gribov-horizons separating
six Weyl-chambers. The energy eigensystem of the gauge reduced Hamiltonian of
SU(3) Yang-Mills mechanics of spatially constant fields can be calculated in
principle with arbitrary high precision using the orthonormal basis of all
solutions of the corresponding harmonic oscillator problem, which turn out to
be made of orthogonal polynomials of the 45 components of eight irreducible
symmetric spatial tensors. First results for the low-energy glueball spectrum
are obtained which substantially improve those by Weisz and Ziemann using the
constrained approach. Thus, the gauge reduced approach using the flux-tube
gauge proposed here, is expected to enable one to obtain valuable
non-perturbative information about low-energy glueball dynamics, using
perturbation theory in $\lambda$.


title: Rings of non-spherical, axisymmetric bodies

abstract:
  We investigate the dynamical behavior of rings around bodies whose shapes
depart considerably from that of a sphere. To this end, we have developed a new
self-gravitating discrete element N-body code, and employed a local simulation
method to simulate a patch of the ring. The central body is modeled as a
symmetric (oblate or prolate) ellipsoid, or defined through the characteristic
frequencies (circular, vertical, epicyclic) that represent its gravitational
field. Through our simulations we explore how a ring's behavior --
characterized by dynamical properties like impact frequency, granular
temperature, number density, vertical thickness and radial width -- varies with
the changing gravitational potential of the central body. We also contrast
properties of rings about large central bodies (e.g. Saturn) with those of
smaller ones (e.g. Chariklo). Finally, we investigate how the characteristic
frequencies of a central body, restricted to being a solid of revolution with
an equatorial plane of symmetry, affect the ring dynamics. The latter process
may be employed to qualitatively understand the dynamics of rings about any
symmetric solids of revolution.


title: Stochastic Agent-Based Models of Intimate Partner Violence

abstract:
  Intimate partner violence (IPV) is a significant public health problem and
social issue that involves couples from all socioeconomic and cultural
contexts. IPV may affect women and men, but these latter are the most common
perpetrators of IPV. We developed stochastic Agent-Based models of IPV focused
on the couple dynamics, determined by the parallel, individual behaviour of
partners. Based on the psychological theory of the Cycle of Violence, we have
developed a model based on four discrete states: passivity, normal situation,
upset and physical assault. The individual transition probability depends on
the previous state of the subject and that of the partner, and on a control
parameter, the aggressiveness. We then let this parameter evolve depending on
the perceived violence from past experiences (polarisation) or from the support
received from the environment (social influence). From the analysis of the
phase diagrams we observe the emergence of characteristic patterns, in
agreement with the observations of IPV in the literature.


title: Stop the tests: Opinion bias and statistical tests

abstract:
  When statisticians quarrel about hypothesis testing, the debate usually focus
on which method is the correct one. The fundamental question of whether we
should test hypothesis at all tends to be forgotten. This lack of debate has
its roots on our desire to have ideas we believe and defend. But cognitive
experiments have been showing that, when we do choose ideas, we become prey to
a large number of biases. Several of our biases can be grouped together in a
single description, an opinion bias. This opinion bias is nothing more than our
desire to believe in something and to defend it. Also, despite our feelings,
believing has no solid logical or philosophical grounds. In this paper, I will
show that if we combine the fact that even logic can never prove an idea right
or wrong and the problems our brains cause when we pick ideas, hypothesis
testing and its terminology are a recipe for disaster. Testing should have no
place when we are thinking about hypothesis.


title: A characterisation of elementary abelian 3-groups

abstract:
  Tarnauceanu [Archiv der Mathematik, 102 (1), (2014), 11--14] gave a
characterisation of elementary abelian $2$-groups in terms of their maximal
sum-free sets. His theorem states that a finite group $G$ is an elementary
abelian $2$-group if and only if the set of maximal sum-free sets coincides
with the set of complements of the maximal subgroups. A corollary is that the
number of maximal sum-free sets in an elementary abelian $2$-group of finite
rank $n$ is $2^n-1$. Regretfully, we show here that the theorem is wrong. We
then prove a correct version of the theorem from which the desired corollary
can be deduced. Moreover, we give a characterisation of elementary abelian
$3$-groups in terms of their maximal sum-free sets. A corollary to our result
is that the number of maximal sum-free sets in an elementary abelian $3$-group
of finite rank $n$ is $3^n-1$. Finally, for prime $p>3$ and $n\in \mathbb{N}$,
we show that there is no direct analogue of this result for elementary abelian
$p$-groups of finite rank $n$.


title: A critical comparative analysis of five world university rankings

abstract:
  To provide users insight into the value and limits of world university
rankings, a comparative analysis is conducted of 5 ranking systems: ARWU,
Leiden, THE, QS and U-Multirank. It links these systems with one another at the
level of individual institutions, and analyses the overlap in institutional
coverage, geographical coverage, how indicators are calculated from raw data,
the skewness of indicator distributions, and statistical correlations between
indicators. Four secondary analyses are presented investigating national
academic systems and selected pairs of indicators. It is argued that current
systems are still one-dimensional in the sense that they provide finalized,
seemingly unrelated indicator values rather than offering a data set and tools
to observe patterns in multi-faceted data. By systematically comparing
different systems, more insight is provided into how their institutional
coverage, rating methods, the selection of indicators and their normalizations
influence the ranking positions of given institutions.


title:
A note about "Faster algorithms for computing Hong's bound on absolute
  positiveness" by K. Mehlhorn and S. Ray

abstract:
  We show that a linear-time algorithm for computing Hong's bound for positive
roots of a univariate polynomial, described by K. Mehlhorn and S. Ray in an
article "Faster algorithms for computing Hong's bound on absolute
positiveness", is incorrect. We present a corrected version.


title:
High critical temperature nodal superconductors as building block for
  time-reversal invariant topological superconductivity

abstract:
  We study possible applications of high critical temperature nodal
superconductors for the search for Majorana bound states in the DIII class. We
propose a microscopic analysis of the proximity effect induced by d-wave
superconductors on a semiconductor wire with strong spin-orbit coupling. We
characterize the induced superconductivity on the wire employing a numerical
self-consistent tight-binding Bogoliubov-de Gennes approach, and analytical
considerations on the Green's function. The order parameter induced on the
wire, the pair correlation function, and the renormalization of the Fermi
points are analyzed in detail, as well as the topological phase diagram in the
case of weak coupling. We highlight optimal Hamiltonian parameters to access
the nontrivial topological phase which could display time-reversal invariant
Majorana doublets at the boundaries of the wire.


title:
Noncritical generation of nonclassical frequency combs via spontaneous
  rotational symmetry breaking

abstract:
  Synchronously pumped optical parametric oscillators (SPOPOs) are optical
cavities containing a nonlinear crystal capable of down-converting a frequency
comb to lower frequencies. These have received a lot of attention lately,
because their intrinsic multimode nature makes them compact sources of quantum
correlated light with promising applications in modern quantum information
technologies. In this work we show that SPOPOs are also capable of accessing
the challenging but interesting regime where spontaneous symmetry breaking
plays a crucial role in the quantum properties of the emitted light, difficult
to access with any other nonlinear optical cavity. Apart from opening the
possibility of studying experimentally this elusive regime of dissipative phase
transitions, our predictions will have a practical impact, since we show that
spontaneous symmetry breaking provides a specific spatiotemporal mode with
perfect squeezing for any value of the system parameters, turning SPOPOs into
robust sources of highly nonclassical light above threshold.


title:
Consistency of nonlinear interacting ghost dark energy with recent
  observations

abstract:
  In this paper we investigate ghost dark energy model in the presence of
non-linear interaction between dark energy and dark matter. We also extend the
analysis to the so called generalized ghost dark energy (GGDE) which
$\rho_D=\alpha H+\beta H^2$. The model contains three free parameters as
$\Omega_D, \zeta(=\frac{8\pi G \beta}{3})$ and $b^2$ (the coupling coefficient
of interactions). We propose three kinds of non-linear interaction terms and
discuss the behavior of equation of state, deceleration and dark energy density
parameters of the model. We also find the squared sound speed and search for
signs of stability of the model. To compare the interacting GGDE model with
observational data sets, we use more recent observational outcomes, namely SNIa
from JLA catalog, Hubble parameter, baryonic acoustic oscillation and the most
relevant CMB parameters including, the position of acoustic peaks, shift
parameters and redshift to recombination. For GGDE with the first non-linear
interaction, the joint analysis indicates that $\Omega_D=0.7192\pm0.0062$,
$b^2=0.146^{+0.030}_{-0.026}$ and $\zeta=0.104\pm0.047$ at 1 optimal variance
error. For the second interaction, the best fit values at $1\sigma$ confidence
are $\Omega_D=0.72091\pm0.0065$, $b^2=0.0395\pm0.0080$ and $\zeta\le0.0173$.
According to combination of all observational data sets considered in this
paper the best fit values for third non-linearly interacting model are
$\Omega_D=0.7287\pm0.0062$, $b^2=0.0109\pm0.0023$ and $\zeta\le0.00764$ at
$1\sigma$ confidence interval. Finally we found that the presence of
interaction is compatible in mentioned models via current observational data
sets.


title:
The statistical properties of the q-deformed Dirac oscillator in one and
  two-dimensions

abstract:
  In this paper, we study the behavior of the eigenvalues of the one and two
dimensions of q-deformed Dirac oscillator. The eigensolutions have been
obtained by using a method based on the q-deformed creation and annihilation
operators in both dimensions. For a two-dimensional case, we have used the
complex formalism which reduced the problem to the problem of one dimensional
case. The influence of the q-numbers on the eigenvalues has been well analyzed.
Also, the connection between the q-oscillator and a quantum optics is well
established. Finally, for very small deformation \eta, we have mentioned to
existence of well-known q-deformed version of Zitterbewegung in relativistic
quantum dynamics, and calculated the partition function and all thermal
quantities such as the free energy, total energy, entropy and specific heat:
here we consider only the case of a pure phase (q=e^{i\eta}). The extension to
the case of graphene has been discussed


title:
Spin-Dependent Weakly-Interacting-Massive-Particle--Nucleon Cross
  Section Limits from First Data of PandaX-II Experiment

abstract:
  New constraints are presented on the spin-dependent WIMP-nucleon interaction
from the PandaX-II experiment, using a data set corresponding to a total
exposure of 3.3$\times10^4$ kg-days. Assuming a standard axial-vector
spin-dependent WIMP interaction with $^{129}$Xe and $^{131}$Xe nuclei, the most
stringent upper limits on WIMP-neutron cross sections for WIMPs with masses
above 10 GeV/c$^{2}$ are set in all dark matter direct detection experiments.
The minimum upper limit of $4.1\times 10^{-41}$ cm$^2$ at 90\% confidence level
is obtained for a WIMP mass of 40 GeV/c$^{2}$. This represents more than a
factor of two improvement on the best available limits at this and higher
masses. These improved cross-section limits provide more stringent constraints
on the effective WIMP-proton and WIMP-neutron couplings.


title:
Spin-polarized quasiparticle control in a double spin-filter tunnel
  junction

abstract:
  Spin-polarized quasiparticles can be easily created during spin-filtering
through a ferromagnetic insulator (FI) in contact with a superconductor due to
pair breaking effects at the interface. A combination FI-N-FI sandwiched
between two superconductors can be used to create and analyze such
spin-polarized quasiparticles through their nonequilibrium accumulation in the
middle metallic (N) layer. We report spin-polarized quasiparticle regulation in
a double spin-filter tunnel junction in the configuration NbN-GdN1-Ti-GdN2-NbN.
The middle Ti layer provides magnetic decoupling between two ferromagnetic GdN
and a place for nonequilibrium quasiparticle accumulation. The two GdN(1,2)
layers were deposited under different conditions to introduce coercive
contrast. The quasiparticle tunneling spectra has been measured at different
temperatures to understand the tunneling mechanism in these double spin-filter
junctions. The conductance spectra were found to be comparable to an asymmetric
SINI'S-type tunnel junction. A hysteretic R-H loop with higher resistance for
the antiparallel configuration compared to parallel state was observed
asserting the spin-polarized nature of quasiparticles. The hysteresis in the
R-H loop was found to disappear for sub-gap bias current. This difference can
be understood by considering suppression of the interlayer coupling due to
nonequilibrium spin-polarized quasiparticle accumulation in the Ti layer.


title: The bound states of the massless Dirac equation on the torus

abstract:
  The Dirac equation on the toroidal surface is studied. The non-constant Fermi
velocity functions are used in the Dirac Hamiltonian to get trigonometric Scarf
and Rosen-Morse potentials using the method given in [19], then, the exact
solutions are written. On the other hand, consecutive mappings are used to get
a trigonometric Scarf I-like potential model and the solutions are obtained in
the second part of the paper.


title: Fuzzy soft numbers

abstract:
  In this paper, we introduce the notion of fuzzy soft numbers. Here defined
fuzzy soft number and four arithmetic operations $ \tilde{+}, \tilde{-},
\tilde{\times}, \tilde{\div} $ and related properties. Also introduce Hausdorff
distance, Fuzzy soft metric space, convergence sequence, Cauchy sequence,
Continuity, and uniform continuity of fuzzy soft numbers. At starting of this
paper, we study convex and concave fuzzy soft sets and some of their
properties.


title: A lower bound on the zero forcing number

abstract:
  In this note, we study a dynamic vertex coloring for a graph $G$. In
particular, one starts with a certain set of vertices black, and all other
vertices white. Then, at each time step, a black vertex with exactly one white
neighbor forces its white neighbor to become black. The initial set of black
vertices is called a \emph{zero forcing set} if by iterating this process, all
of the vertices in $G$ become black. The \emph{zero forcing number} of $G$ is
the minimum cardinality of a zero forcing set in $G$, and is denoted by $Z(G)$.
Davila and Kenter have conjectured in 2015 that $Z(G)\geq
(g-3)(\delta-2)+\delta$ where $g$ and $\delta$ denote the girth and the minimum
degree of $G$, respectively. This conjecture has been proven for graphs with
girth $g \leq 10$. In this note, we present a proof for $g \geq 5$, $\delta
\geq 2$, thereby settling the conjecture.


title:
Bounded perturbations of Bernstein functions of several operator
  variables

abstract:
  The paper deals with (multidimensional and one-dimensional) Bochner-Phillips
functional calculus. Bounded perturbations of Bernstein functions of (one or
several commuting) semigroup generators on Banach spaces are considered,
conditions for Lipschitzness and Frechet-differentiability of such functions
are obtained, estimates for the norm of commutators are proved, and a
generalization of Livschits-Kre\u{\i}n trace formula derived.


title:
A sufficient condition for global operator monotonicity for functions in
  several variables

abstract:
  The note contains two remarks to the authors note (Mathematical Notes, Vol.
94, 2013, p. 154 -- 156; in Russian) which was also devoted to sufficient
conditions of global operator monotonicity.


title:
Some topics in the perturbation theory for a functional calculus of
  closed operators on Banach spaces

abstract:
  The wark is a contribution to the functional calculus constructed by of the
author and A. A. Atvinovskii of closed operators on Banach spaces. The calculus
is based on Markov and related functions as symbols. Estimates of bounded
perturbations of operator functions with respect to general operator ideal
norms, operator Lipschitzness, moment inequality, Freshet operator
differentiability, and Livshitz-Krein trace formulae have been considered.


title: Latest results from lattice N=4 supersymmetric Yang--Mills

abstract:
  We present some of the latest results from our numerical investigations of
N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based
on a construction that exactly preserves a single supersymmetry at non-zero
lattice spacing, we recently developed an improved lattice action that is now
being employed in large-scale calculations. Here we update our studies of the
static potential using this new action, also applying tree-level lattice
perturbation theory to improve the analysis of the potential itself.
Considering relatively weak couplings, we obtain results for the Coulomb
coefficient that are consistent with continuum perturbation theory.


title:
Controlling plasmonic orbital angular momentum by combining geometric
  and dynamic phases

abstract:
  Tunable orbit angular momentum (OAM) of surface plasmon polaritons (SPPs) is
theoretically studied with appropriately designed metasurfaces. By controlling
both the orientation angle and spatial position of nano aperture array on an
ultrathin gold film, the field distributions of the surface waves can be
engineered to contain both spin dependent and independent OAM components.
Simultaneous control over the geometric phase and optical path difference
induced phase (dynamic phase) provides extra degrees of freedom for
manipulating OAM of SPPs. We show that arbitrary combination of OAM numbers can
be realized for the SPPs excited by incident light of different circular
polarizations. The results provides powerful control over the OAM of SPPs,
which will have potential applications on optical trapping, imaging,
communications and quantum information processing.


title: Curvature-Driven Morphing of Non-Euclidean Shells

abstract:
  We investigate how thin structures change their shape in response to
non-mechanical stimuli that can be interpreted as variations in the structure's
natural curvature. Starting from the theory of non-Euclidean plates and shells,
we derive an effective model that reduces a three-dimensional stimulus to the
natural fundamental forms of the mid-surface of the structure, incorporating
expansion, or growth, in the thickness. Then, we apply the model to a variety
of thin bodies, from flat plates to spherical shells, obtaining excellent
agreement between theory and numerics. We show how cylinders and cones can
either bend more or unroll, and eventually snap and rotate. We also study the
nearly-isometric deformations of a spherical shell and describe how this shape
change is ruled by the geometry of a spindle. As the derived results stem from
a purely geometrical model, they are general and scalable.


title: Hankel Operators over Compact Abelian Groups

abstract:
  Two variants of generalizations of Hankel operators to the case of linearly
ordered abelian groups are considered, criteria of the boundedness and
compactness of these operators are given, among them in terms of functions of
bounded mean oscillation, the nonfredholmness of generalized Hankel operators
is proved. Some applications to the theory of Toeplitz operators on groups are
given.


title: Deep Tensor Convolution on Multicores

abstract:
  Deep convolutional neural networks (ConvNets) of 3-dimensional kernels allow
joint modeling of spatiotemporal features. These networks have improved
performance of video and volumetric image analysis, but have been limited in
size due to the low memory ceiling of GPU hardware. Existing CPU
implementations overcome this constraint but are impractically slow. Here we
extend and optimize the faster Winograd-class of convolutional algorithms to
the $N$-dimensional case and specifically for CPU hardware. First, we remove
the need to manually hand-craft algorithms by exploiting the relaxed
constraints and cheap sparse access of CPU memory. Second, we maximize CPU
utilization and multicore scalability by transforming data matrices to be
cache-aware, integer multiples of AVX vector widths. Treating 2-dimensional
ConvNets as a special (and the least beneficial) case of our approach, we
demonstrate a 5 to 25-fold improvement in throughput compared to previous
state-of-the-art.


title:
Asymptotic properties of functionals of increments of a continuous
  semimartingale with stochastic sampling times

abstract:
  This paper is concerned with asymptotic behavior of a variety of functionals
of increments of continuous semimartingales. Sampling times are assumed to
follow a rather general discretization scheme. If an underlying semimartingale
is thought of as a financial asset price process, a general sampling scheme
like the one employed in this paper is capable of reflecting what happens
whenever the financial trading data are recorded in a tick-by-tick fashion. A
law of large numbers and a central limit theorem are proved after an
appropriate normalization. One application of our result is an extension of the
realized kernel estimator of integrated volatility to the case of random
sampling times.


title: Breathing dissipative solitons in optical microresonators

abstract:
  Dissipative solitons are self-localized structures resulting from a double
balance between dispersion and nonlinearity as well as dissipation and a
driving force. They occur in a wide variety of fields ranging from optics,
hydrodynamics to chemistry and biology. Recently, significant interest has
focused on their temporal realization in driven optical microresonators, known
as dissipative Kerr solitons. They provide access to coherent, chip-scale
optical frequency combs, which have already been employed in optical metrology,
data communication and spectroscopy. Such Kerr resonator systems can exhibit
numerous localized intracavity patterns and provide rich insights into
nonlinear dynamics. A particular class of solutions consists of breathing
dissipative solitons, representing pulses with oscillating amplitude and
duration, for which no comprehensive understanding has been presented to date.
Here, we observe and study single and multiple breathing dissipative solitons
in two different microresonator platforms: crystalline $\mathrm{MgF_2}$
resonator and $\mathrm{Si_3N_4}$ integrated microring. We report a
deterministic route to access the breathing state, which allowed for a detailed
exploration of the breathing dynamics. In particular, we establish the link
between the breathing frequency and two system control parameters - effective
pump laser detuning and pump power. Using a fast detection, we present a direct
observation of the spatiotemporal dynamics of individual solitons, revealing
irregular oscillations and switching. An understanding of breathing solitons is
not only of fundamental interest concerning nonlinear systems close to critical
transition, but also relevant for applications to prevent breather-induced
instabilities in soliton-based frequency combs.


title: Left-right symmetric extensions of 3-3-1 models

abstract:
  We propose four left-right symmetric extensions of several chiral 3-3-1
models. Although they have some common features they also have important
difference due to different representation content.


title: On finite $P\sigma T$-groups

abstract:
  Let $\sigma =\{\sigma_{i} | i\in I\}$ be some partition of the set of all
primes $\Bbb{P}$ and $G$ a finite group. $G$ is said to be
\emph{$\sigma$-soluble} if every chief factor $H/K$ of $G$ is a
$\sigma_{i}$-group for some $i=i(H/K)$. A set ${\cal H}$ of subgroups of $G$ is
said to be a \emph{complete Hall $\sigma $-set} of $G$ if every member $\ne 1$
of ${\cal H}$ is a Hall $\sigma_{i}$-subgroup of $G$ for some $\sigma_{i}\in
\sigma $ and ${\cal H}$ contains exact one Hall $\sigma_{i}$-subgroup of $G$
for every $i \in I$ such that $\sigma_{i}\cap \pi (G)\ne \emptyset$. A subgroup
$A$ of $G$ is said to be \emph{${\sigma}$-permutable} or
\emph{${\sigma}$-quasinormal} in $G$ if $G$ has a complete Hall $\sigma$-set
$\cal H$ such that $AH^{x}=H^{x}A$ for all $x\in G$ and all $H\in \cal H$. We
obtain a characterization of finite $\sigma$-soluble groups $G$ in which
$\sigma$-quasinormality is a transitive relation in $G$.


title: Square of a Hamilton cycle in a random graph

abstract:
  We show that the threshold for the random graph $G_{n,p}$ to contain the
square of a Hamilton cycle is $p=\frac{1}{\sqrt{n}}$. This improves the
previous results of K\"uhn and Osthus and also Nenadov and \v{S}kori\'c. In
addition we consider how many random edges need to be added to a graph of order
$n$ with minimum degree $\alpha n$ in order that it contains the square of a
Hamilton cycle w.h.p.


title: Hirzebruch manifolds and positive holomorphic sectional curvature

abstract:
  This paper is the first step in a systematic project to study examples of
K\"ahler manifolds with positive holomorphic sectional curvature ($H > 0$).
Previously Hitchin proved that any compact K\"ahler surface with $H>0$ must be
rational and he constructed such examples on Hirzebruch surfaces $M_{2,
k}=\mathbb{P}(H^{k}\oplus 1_{\mathbb{CP}^1})$. We generalize Hitchin's
construction and prove that any Hirzebruch manifold $M_{n,
k}=\mathbb{P}(H^{k}\oplus 1_{\mathbb{CP}^{n-1}})$ admits a K\"ahler metric of
$H>0$ in each of its K\"ahler classes. We demonstrate that the pinching
behaviors of holomorphic sectional curvatures of new examples differ from those
of Hitchin's which were studied in the recent work of Alvarez-Chaturvedi-Heier.
Some connections to recent works on the K\"ahler-Ricci flow on Hirzebruch
manifolds are also discussed.
  It seems interesting to study the space of all K\"ahler metrics of $H>0$ on a
given K\"ahler manifold. We give higher dimensional examples such that some
K\"ahler classes admit K\"ahler metrics with $H>0$ and some do not.


title: Manifolds with conullity at most two as graph manifolds

abstract:
  We find necessary and sufficient conditions for a complete $n$-dimensional
Riemannian manifold of finite volume, whose curvature tensor has nullity at
least $n-2$, to be a geometric graph manifold. In the process, we show that
Nomizu's conjecture, well known to be false in general, is true for manifolds
with finite volume.


title:
Dynamical friction and the evolution of Supermassive Black hole
  Binaries: the final hundred-parsec problem

abstract:
  The supermassive black holes originally in the nuclei of two merging galaxies
will form a binary in the remnant core. The early evolution of the massive
binary is driven by dynamical friction before the binary becomes "hard" and
eventually reaches coalescence through gravitational wave emission. { We
consider the dynamical friction evolution of massive binaries consisting of a
secondary hole orbiting inside a stellar cusp dominated by a more massive
central black hole.} In our treatment we include the frictional force from
stars moving faster than the inspiralling object which is neglected in the
standard Chandrasekhar's treatment. We show that the binary eccentricity
increases if the stellar cusp density profile rises less steeply than
$\rho\propto r^{-2}$. In cusps shallower than $\rho\propto r^{-1}$ the
frictional timescale can become very long due to the deficit of stars moving
slower than the massive body. Although including the fast stars increases the
decay rate, low mass-ratio binaries ($q\lesssim 10^{-3}$) in sufficiently
massive galaxies have decay timescales longer than one Hubble time. During such
minor mergers the secondary hole stalls on an eccentric orbit at a distance of
order one tenth the influence radius of the primary hole (i.e., $\approx
10-100\rm pc$ for massive ellipticals). We calculate the expected number of
stalled satellites as a function of the host galaxy mass, and show that the
brightest cluster galaxies should have $\gtrsim 1$ of such satellites orbiting
within their cores. Our results could provide an explanation to a number of
observations, which include multiple nuclei in core ellipticals, off-center
AGNs and eccentric nuclear disks.


title:
Meet-reducible submaximal clones determined by nontrivial equivalence
  relations

abstract:
  The structure of the lattice of clones on a finite set has been proven to be
very complex. To better understand the top of this lattice, it is important to
provide a characterization of submaximal clones in the lattice of clones. It is
known that the clones $Pol(\theta)$ and $Pol(\rho)$ (where $\theta$ is a
nontrivial equivalence relation on $E_k = \{0,\dots, k-1\}$, and $\rho$ is
among the six types of relations which characterize maximal clones) are maximal
clones. In this paper, we provide a classification of relations (of Rosenberg's
List) on $E_k$ such that the clone $Pol(\theta) \cap Pol(\rho)$ is maximal in
$Pol(\theta)$.


title:
A maximum smoothed likelihood based estimation for two component
  semiparametric density mixtures with a known component

abstract:
  We consider a semiparametric mixture of two univariate density functions
where one of them is known while the weight and the other function are unknown.
Such mixtures have a history of application to the problem of detecting
differentially expressed genes under two or more conditions in microarray data.
Until now, some additional knowledge about the unknown component (e.g. the fact
that it belongs to a location family) has been assumed. As opposed to this
approach, we do not assume any additional structure on the unknown density
function. For this mixture model, we derive a new sufficient identifiability
condition and pinpoint a specific class of distributions describing the unknown
component for which this condition is mostly satisfied. Our approach to
estimation of this model is based on an idea of applying a maximum smoothed
likelihood to what would otherwise have been an ill-posed problem. We introduce
an iterative MM (Majorization-Minimization) algorithm that estimates all of the
model parameters. We establish that the algorithm possesses a descent property
with respect to a log-likelihood objective functional and prove that the
algorithm converges to a minimizer of such an objective functional. Finally, we
also illustrate the performance of our algorithm in a simulation study and
using a real dataset.


title: Distributed Nonconvex Optimization for Sparse Representation

abstract:
  We consider a non-convex constrained Lagrangian formulation of a fundamental
bi-criteria optimization problem for variable selection in statistical
learning; the two criteria are a smooth (possibly) nonconvex loss function,
measuring the fitness of the model to data, and the latter function is a
difference-of-convex (DC) regularization, employed to promote some extra
structure on the solution, like sparsity. This general class of nonconvex
problems arises in many big-data applications, from statistical machine
learning to physical sciences and engineering. We develop the first unified
distributed algorithmic framework for these problems and establish its
asymptotic convergence to d-stationary solutions. Two key features of the
method are: i) it can be implemented on arbitrary networks (digraphs) with
(possibly) time-varying connectivity; and ii) it does not require the
restrictive assumption that the (sub)gradient of the objective function is
bounded, which enlarges significantly the class of statistical learning
problems that can be solved with convergence guarantees.


title: Shifted Character Sums with Multiplicative Coefficients, II

abstract:
  Let $f(n)$ be a multiplicative function with $|f(n)|\leq 1, q$ be a prime
number and $a$ be an integer with $(a, q)=1, \chi$ be a non-principal Dirichlet
character modulo $q$. Let $\varepsilon$ be a sufficiently small positive
constant, $A$ be a large constant, $q^{\frac12+\varepsilon}\ll N\ll q^A$. In
this paper, we shall prove that $$ \sum_{n\leq N}f(n)\chi(n+a)\ll
N\frac{\log\log q}{\log q} $$ and that $$ \sum_{n\leq
N}f(n)\chi(n+a_1)\cdots\chi(n+a_t)\ll N\frac{\log\log q}{\log q}, $$ where
$t\geq 2, a_1, \ldots, a_t$ are distinct integers modulo $q$.


title: H$_2$ in low-ionization structures of planetary nebulae

abstract:
  We report the detection of near-IR H$_2$ emission from the low-ionization
structures (knots) in two planetary nebulae. The deepest ever, high-angular
resolution H$_2$ 1-0 S(1) at 2.122$\mu$, H$_2$ 2-1 S(1) at 2.248$\mu$ and
Br$\gamma$ images of K 4-47 and NGC 7662, obtained using the Near InfraRed
Imager and Spectrometer (NIRI) at Gemini-North, are analyzed here. K 4-47
reveals a remarkable highly collimated bipolar structure not only in the
optical but also in the molecular hydrogen emission. The H$_2$ emission
emanates from the walls of the bipolar outflows and also from the pair of knots
at the tip of the outflows. The H$_2$ 1-0 S(1)/2-1 S(1) line ratio ranges from
~7 to ~10 suggesting the presence of shock interactions. Our findings can be
explained by the interaction of a jet/bullet ejected from the central star with
the surrounding asymptotic giant branch material. The strongest H$_2$ line,
v=1-0 S(1) is also detected in several low-ionization knots located at the
periphery of the elliptical planetary nebula NGC 7662, but only four of these
knots are detected in the H$_2$ v=2-1 S(1) line. These four knots exhibit an
H$_2$ line ratio between 2 and 3.5, which suggests that the emission is caused
by the UV ionizing flux of the central star. Our data confirms the presence of
H$_2$ gas in both fast- and slow-moving low-ionization knots, which has only
been confirmed before in the nearby Helix nebula and Hu 1-2. Overall, the
low-ionization structures of planetary nebulae are found to share similar
traits to photodissociation regions.


title: High Energy Polarimetry of Prompt GRB Emission

abstract:
  Evidence of polarized $\gamma$-ray emission ($>$ 50 keV) from Gamma-Ray
Bursts (GRBs) has been accumulated in recent years. Measurements have been
reported with levels in the range of 30-80\%, typically with limited
statistical significance. No clear picture has yet emerged with regards to the
polarization properties of GRBs. Taken at face value, the data suggest that
most GRBs have a relatively large level of polarization (typically, $> 50\%$),
which may suggest synchrotron emission associated with an ordered magnetic
field structure within the GRB jet. But these results are far from conclusive.
Here, we review the observations that have been made, concentrating especially
on the instrumental issues and the lessons that might be learned from these
data.


title:
Convective heat transport in stratified atmospheres at low and high Mach
  number

abstract:
  We study fully compressible convection in the context of plane-parallel,
polytropically stratified atmospheres. We perform a suite of 2D and 3D
simulations in which we vary the initial superadiabaticity ($\epsilon$) and the
Rayleigh number (Ra) while fixing the initial density stratification, aspect
ratio, and Prandtl number. The evolved heat transport, quantified by the
Nusselt number (Nu), follows scaling relationships similar to those found in
the well-studied, incompressible Rayleigh-B\'{e}nard problem. This scaling
holds up in both 2D and 3D and is not appreciably affected by the magnitude of
$\epsilon$.


title: The Dynamics of Flat Surface Internal Geophysical Waves with Currents

abstract:
  A two-dimensional water wave system is examined consisting of two discrete
incompressible fluid domains separated by a free common interface. In a
geophysical context this is a model of an internal wave, formed at a pycnocline
or thermocline in the ocean. The system is considered as being bounded at the
bottom and top by a flatbed and wave-free surface respectively. A current
profile with depth-dependent currents in each domain is considered. The
Hamiltonian of the system is determined and expressed in terms of canonical
wave-related variables. Limiting behaviour is examined and compared to that of
other known models. The linearised equations as well as long-wave
approximations are presented.


title: High-Throughput Atomic Force Microscopes Operating in Parallel

abstract:
  Atomic force microscopy (AFM) is an essential nanoinstrument technique for
several applications such as cell biology and nanoelectronics metrology and
inspection. The need for statistically significant sample sizes means that data
collection can be an extremely lengthy process in AFM. The use of a single AFM
instrument is known for its very low speed and not being suitable for scanning
large areas, resulting in very-low-throughput measurement. We address this
challenge by parallelizing AFM instruments. The parallelization is achieved by
miniaturizing the AFM instrument and operating many of them simultaneously.
This nanoinstrument has the advantages that each miniaturized AFM can be
operated independently and that the advances in the field of AFM, both in terms
of speed and imaging modalities, can be implemented more easily. Moreover, a
parallel AFM instrument also allows one to measure several physical parameters
simultaneously; while one instrument measures nano-scale topography, another
instrument can measure mechanical, electrical or thermal properties, making it
a Lab-on-an-Instrument. In this paper, a proof of principle (PoP) of such a
parallel AFM instrument has been demonstrated by analyzing the topography of
large samples such as semiconductor wafers. This nanoinstrument provides new
research opportunities in the nanometrology of wafers and nanolithography masks
by enabling real die-to-die and wafer-level measurements and in cell biology by
measuring the nano-scale properties of a large number of cells.


title:
Analyzing student conceptual understanding of resistor networks using
  binary, descriptive, and computational questions

abstract:
  This paper presents a case-study assessing and analyzing student engagement
with and responses to binary, descriptive, and computational questions testing
the concepts underlying resistor networks (series and parallel combinations).
The participants of the study were undergraduate students enrolled in a
university in Pakistan. The majority of students struggled with the descriptive
question, even when successfully answering the binary and computational ones,
failed to build an expectation for the answer, and betrayed significant lack of
conceptual understanding in the process. The data collected was also used to
analyze the relative efficacy of the three questions as means of assessing
conceptual understanding. The three questions were revealed to be uncorrelated
and unlikely to be testing the same construct. The ability to answer the binary
or computational question was observed to be divorced from a deeper
understanding of the concepts involved.


title: The Markov-Stieltjes transform as an operator

abstract:
  We prove that the Markov-Stieltjes transform is a bounded non compact Hankel
operator on Hardy space $H^p$ with Hilbert matrix with respect to the standard
Schauder basis of $H^p$ and a bounded non compact operator on Lebesgue space
$L^p[0,1]$ for $p\in(1,\infty)$ and obtain estimates for its norm in this
spaces. It is shown that the Markov-Stieltjes transform on $L^2(0,1)$ is
unitary equivalent to the Markov-Stieltjes transform on $H^2$. Inverse formulas
and operational properties for this transform are obtained.


title: Variational Boosting: Iteratively Refining Posterior Approximations

abstract:
  We propose a black-box variational inference method to approximate
intractable distributions with an increasingly rich approximating class. Our
method, termed variational boosting, iteratively refines an existing
variational approximation by solving a sequence of optimization problems,
allowing the practitioner to trade computation time for accuracy. We show how
to expand the variational approximating class by incorporating additional
covariance structure and by introducing new components to form a mixture. We
apply variational boosting to synthetic and real statistical models, and show
that resulting posterior inferences compare favorably to existing posterior
approximation algorithms in both accuracy and efficiency.


title:
High-$E_{\rm T}$ isolated-photon plus jets production in $pp$ collisions
  at $\sqrt s=$ 8 TeV with the ATLAS detector

abstract:
  The dynamics of isolated-photon plus one-, two- and three-jet production in
$pp$ collisions at a centre-of-mass energy of 8 TeV are studied with the ATLAS
detector at the LHC using a data set with an integrated luminosity of 20.2
fb$^{-1}$. Measurements of isolated-photon plus jets cross sections are
presented as functions of the photon and jet transverse momenta. The cross
sections as functions of the azimuthal angle between the photon and the jets,
the azimuthal angle between the jets, the photon-jet invariant mass and the
scattering angle in the photon-jet centre-of-mass system are presented. The
pattern of QCD radiation around the photon and the leading jet is investigated
by measuring jet production in an annular region centred on each object;
enhancements are observed around the leading jet with respect to the photon in
the directions towards the beams. The experimental measurements are compared to
several different theoretical calculations, and overall a good description of
the data is found.


title:
Wellformedness Properties in Euler Diagrams: An Eye Tracking Study for
  Visualisation Evaluation

abstract:
  In the field of information visualisation, Euler diagrams are an important
tool used in various application areas such as engineering, medicine and social
analysis. To effectively use Euler diagrams, some of the wellformedness
properties needs to be avoided, as they are considered to reduce user
comprehension. From the previous empirical studies, we know some properties are
swappable but there is no clear justification which property would be the best
to use. In this paper, we considered two main wellformedness properties
(duplicated curve labels and disconnected zones) to test which among the two
affect user comprehension the most, based on the task performance (accuracy and
response time), preference and eye movements of the users. Twelve participants
performed three different types of tasks with nine diagrams of each property
(so, in total eighteen diagrams) and the results showed that duplicated curve
labels property slows down and trigger extra eye movements, causing delays for
the tasks. Though there is no significant difference in the accuracy but the
insights obtained from the response time, preference and eye movements will be
useful for software developers on the optimal way to visualise Euler diagrams
in real world application areas.


title: Drift of suspended ferromagnetic particles due to the Magnus effect

abstract:
  A minimal system of equations is introduced and applied to study the drift
motion of ferromagnetic particles suspended in a viscous fluid and subjected to
a time-periodic driving force and a nonuniformly rotating magnetic field. It is
demonstrated that the synchronized translational and rotational oscillations of
these particles are accompanied by their drift in a preferred direction, which
occurs under the action of the Magnus force. We calculate both analytically and
numerically the drift velocity of particles characterized by single-domain
cores and nonmagnetic shells and show that there are two types of drift,
unidirectional and bidirectional, which can be realized in suspensions composed
of particles with different core-shell ratios. The possibility of using the
effect of bidirectional drift for the separation of core-shell particles in
suspensions is also discussed.


title: Fair Division via Social Comparison

abstract:
  In the classical cake cutting problem, a resource must be divided among
agents with different utilities so that each agent believes they have received
a fair share of the resource relative to the other agents. We introduce a
variant of the problem in which we model an underlying social network on the
agents with a graph, and agents only evaluate their shares relative to their
neighbors' in the network. This formulation captures many situations in which
it is unrealistic to assume a global view, and also exposes interesting
phenomena in the original problem.
  Specifically, we say an allocation is locally envy-free if no agent envies a
neighbor's allocation and locally proportional if each agent values her own
allocation as much as the average value of her neighbor's allocations, with the
former implying the latter. While global envy-freeness implies local
envy-freeness, global proportionality does not imply local proportionality, or
vice versa. A general result is that for any two distinct graphs on the same
set of nodes and an allocation, there exists a set of valuation functions such
that the allocation is locally proportional on one but not the other.
  We fully characterize the set of graphs for which an oblivious single-cutter
protocol-- a protocol that uses a single agent to cut the cake into pieces
--admits a bounded protocol with $O(n^2)$ query complexity for locally
envy-free allocations in the Robertson-Webb model. We also consider the price
of envy-freeness, which compares the total utility of an optimal allocation to
the best utility of an allocation that is envy-free. We show that a lower bound
of $\Omega(\sqrt{n})$ on the price of envy-freeness for global allocations in
fact holds for local envy-freeness in any connected undirected graph. Thus,
sparse graphs surprisingly do not provide more flexibility with respect to the
quality of envy-free allocations.


title:
The Sommerfeld Enhancement in the Scotogenic Model with Large
  Electroweak Scalar Multiplets

abstract:
  We investigate the Sommerfeld enhancement (SE) in the generalized scotogenic
model with large electroweak multiplets. We focus on scalar dark matter (DM)
candidate of the model and compare DM annihilation cross sections to $WW$,
$ZZ$, $\gamma\gamma$ and $\gamma Z$ at present day in the galactic halo for
scalar doublet and its immediate generalization, the quartet in their
respective viable regions of parameter space. We find that larger multiplet has
sizable Sommerfeld enhanced annihilation cross section compared to the doublet
and because of that it is more likely to be constrained by the current H.E.S.S.
results and future CTA sensitivity limits.


title: Coded Caching with Distributed Storage

abstract:
  Content delivery networks store information distributed across multiple
servers, so as to balance the load and avoid unrecoverable losses in case of
node or disk failures. Coded caching has been shown to be a useful technique
which can reduce peak traffic rates by pre-fetching popular content at the end
users and encoding transmissions so that different users can extract different
information from the same packet. On one hand, distributed storage limits the
capability of combining content from different servers into a single message,
causing performance losses in coded caching schemes. But, on the other hand,
the inherent redundancy existing in distributed storage systems can be used to
improve the performance of those schemes through parallelism.
  This paper designs a scheme combining distributed storage of the content in
multiple servers and an efficient coded caching algorithm for delivery to the
users. This scheme is shown to reduce the peak transmission rate below that of
state-of-the-art algorithms.


title:
A Generalized Read-Shockley Model and Large Scale Simulations for the
  Energy and Structure of Graphene Grain Boundaries

abstract:
  The grain boundary (GB) energy is a quantity of fundamental importance for
understanding several key properties of graphene. Here we present a
comprehensive theoretical and numerical study of the entire space of symmetric
and asymmetric graphene GBs. We have simulated over 79,000 graphene GBs to
explore the configuration space of GBs in graphene. We use a generalized
Read-Shockley theory and the Frank-Bilby relation to develop analytical
expressions for the GB energy as a function of the misorientation angle and the
line angle, and elucidate the salient structural features of the low energy GB
configurations.


title:
Characterizing Polytopes Contained in the $0/1$-Cube with Bounded
  Chv\'atal-Gomory Rank

abstract:
  Let $S \subseteq \{0,1\}^n$ and $R$ be any polytope contained in $[0,1]^n$
with $R \cap \{0,1\}^n = S$. We prove that $R$ has bounded Chv\'atal-Gomory
rank (CG-rank) provided that $S$ has bounded notch and bounded gap, where the
notch is the minimum integer $p$ such that all $p$-dimensional faces of the
$0/1$-cube have a nonempty intersection with $S$, and the gap is a measure of
the size of the facet coefficients of $\mathsf{conv}(S)$.
  Let $H[\bar{S}]$ denote the subgraph of the $n$-cube induced by the vertices
not in $S$. We prove that if $H[\bar{S}]$ does not contain a subdivision of a
large complete graph, then both the notch and the gap are bounded. By our main
result, this implies that the CG-rank of $R$ is bounded as a function of the
treewidth of $H[\bar{S}]$. We also prove that if $S$ has notch $3$, then the
CG-rank of $R$ is always bounded. Both results generalize a recent theorem of
Cornu\'ejols and Lee, who proved that the CG-rank is bounded by a constant if
the treewidth of $H[\bar{S}]$ is at most $2$.


title:
Search for heavy resonances decaying to tau lepton pairs in
  proton-proton collisions at sqrt(s) = 13 TeV

abstract:
  A search for heavy resonances that decay to tau lepton pairs is performed
using proton-proton collisions at sqrt(s) = 13 TeV. The data were collected
with the CMS detector at the CERN LHC and correspond to an integrated
luminosity of 2.2 inverse femtobarns. The observations are in agreement with
standard model predictions. An upper limit at 95% confidence level on the
product of the production cross section and branching fraction into tau lepton
pairs is calculated as a function of the resonance mass. For the sequential
standard model, the presence of Z' bosons decaying into tau lepton pairs is
excluded for Z' masses below 2.1 TeV, extending previous limits for this final
state. For the topcolor-assisted technicolor model, which predicts Z' bosons
that preferentially couple to third-generation fermions, Z' masses below 1.7
TeV are excluded, representing the most stringent limit to date.


title: Equation for self-similar singularity of Euler 3D

abstract:
  The equations for a self-similar solution of an inviscid incompressible fluid
are mapped into an integral equation which hopefully can be solved by
iteration. It is argued that the exponent of the similarity are ruled by
Kelvin's theorem of conservation of circulation. The end result is an iteration
with a nonlinear term entering in a kernel given by a 3D integral (in general
3D flow) or 2D (for swirling flows), which seems to be within reach of present
day computational power. Because of the slow decay of the similarity solution
at large distances the total energy is diverging and recent mathematical
results excluding a solution of the self-similar solution of Euler equation do
not apply.


title: Object Recognition with and without Objects

abstract:
  While recent deep neural networks have achieved a promising performance on
object recognition, they rely implicitly on the visual contents of the whole
image. In this paper, we train deep neural net- works on the foreground
(object) and background (context) regions of images respectively. Consider- ing
human recognition in the same situations, net- works trained on the pure
background without ob- jects achieves highly reasonable recognition performance
that beats humans by a large margin if only given context. However, humans
still outperform networks with pure object available, which indicates networks
and human beings have different mechanisms in understanding an image.
Furthermore, we straightforwardly combine multiple trained networks to explore
different visual cues learned by different networks. Experiments show that
useful visual hints can be explicitly learned separately and then combined to
achieve higher performance, which verifies the advantages of the proposed
framework.


title: Effective SU(2) theory for the pseudogap state

abstract:
  This paper exposes in a detailed manner the recent findings about the SU(2)
scenario for the underdoped phase of the Cuprate superconductors. The SU(2)
symmetry is formulated as a rotation between the $d$-wave SC phase and a
$d$-wave charge order. We define the operators responsible for the SU(2)
rotations and we derive the non-linear $\sigma$-model associated with it. In
this framework, we demonstrate that SU(2) fluctuations are massless in finite
portions of the Brillouin Zone corresponding to the anti-nodal regions
($0,$$\pi$), ($\pi,0$). We argue that the presence of SU(2) fluctuations in the
anti-nodal region leads to the opening of Fermi arcs around the Fermi surface
and to the formation of the pseudo-gap. Moreover, we show that SU(2)
fluctuations lead, in turn, to the emergence of a finite momentum SC order -or
Pair Density Wave (PDW)- and more importantly to a new kind of excitonic
particle-hole pairs liquid, the Resonant Excitonic State (RES), which is made
of patches of preformed particle-hole pairs with multiple momenta. When the RES
liquid becomes critical, we demonstrate that electronic scattering through the
critical modes leads to anomalous transport properties. This new finding can
account for the Strange Metal (SM) phase at finite temperature, on the right
hand side of the SC dome, shedding light on another notoriously mysterious part
of the phase diagram of the Cuprates.


title: Cumulants for finite free convolution

abstract:
  In this paper we define cumulants for finite free convolution. We give a
moment-cumulant formula and show that these cumulants satisfy desired
properties: they are additive with respect to finite free convolution and they
approach free cumulants as the dimension goes to infinity.


title:
The effect of dynamical compressive and shear strain on magnetic
  anisotropy in low symmetry ferromagnetic film

abstract:
  Dynamical strain generated upon excitation of a metallic film by a
femtosecond laser pulse may become a versatile tool enabling control of
magnetic state of thin films and nanostructures via inverse magnetostriction on
a picosecond time scale. Here we explore two alternative approaches to
manipulate magnetocrystalline anisotropy and excite magnetization precession in
a low-symmetry film of a magnetic metallic alloy galfenol (Fe,Ga) either by
injecting picosecond strain pulse into it from a substrate or by generating
dynamical strain of complex temporal profile in the film directly. In the
former case we realize ultrafast excitation of magnetization dynamics solely by
strain pulses. In the latter case optically-generated strain emerged abruptly
in the film modifies its magnetocrystalline anisotropy, competing with
heat-induced change of anisotropy parameters. We demonstrate that the
optically-generated strain remains efficient for launching magnetization
precession, when the heat-induced changes of anisotropy parameters do not
trigger the precession anymore. We emphasize that in both approaches the
ultrafast change of magnetic anisotropy mediating the precession excitation
relies on mixed, compressive and shear, character of the dynamical strain,
which emerges due to low-symmetry of the metallic film under study.


title: Monoid actions and ultrafilter methods in Ramsey theory

abstract:
  First, we prove a theorem on dynamics of actions of monoids by endomorphisms
of semigroups. Second, we introduce algebraic structures suitable for
formalizing infinitary Ramsey statements and prove a theorem that such
statements are implied by existence of appropriate homomorphisms between the
algebraic structures. We make a connection between the two themes above, which
allows us to prove some general Ramsey theorems for sequences. We give a new
proof of the Furstenberg--Katznelson Ramsey theorem; in fact, we obtain a
version of this theorem that is stronger than the original one. We answer in
the negative a question of Lupini on possible extensions of Gowers' Ramsey
theorem.


title: Long distance part of $\epsilon_K$ from lattice QCD

abstract:
  We demonstrate the lattice QCD calculation of the long distance contribution
to $\epsilon_K$. Due to the singular, short-distance structure of $\epsilon_K$,
we must perform a short-distance subtraction and introduce a corresponding
low-energy constant determined from perturbation theory, which we calculate at
Next Leading Order (NLO). We perform the calculation on a $24^3 \times 64$
lattice with a pion mass of 329 MeV. This work is a complete calculation, which
includes all connected and disconnected diagrams.


title:
Sub-leading flow modes in PbPb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
  from HYDJET++ model

abstract:
  Recent LHC results on the appearance of sub-leading flow modes in PbPb
collisions at 2.76~TeV, related to initial-state fluctuations, are analyzed and
interpreted within the HYDJET++ model. Using the newly introduced Principal
Component Analysis (PCA) method applied to two-particle azimuthal correlations
extracted from the model calculations, the leading and the sub-leading flow
modes are studied as a function of the transverse momentum ($p_{T}$) over a
wide centrality range. The leading modes of the elliptic ($v^{(1)}_{2}$) and
triangular ($v^{(1)}_{3}$) flow calculated within the HYDJET++ model reproduce
rather well the $v_{2}\{2\}$ and $v_{3}\{2\}$ coefficients experimentally
measured using the two-particle correlations. Within the $p_{T} \le $~3~GeV/c
range where hydrodynamics dominates, the sub-leading flow effects are greatest
at the highest $p_{T}$ of around 3~GeV/c. The sub-leading elliptic flow mode
($v^{(2)}_{2}$), which corresponds to $n = 2$ harmonic, has a small non-zero
value and slowly increases from central to peripheral collisions, while the
sub-leading triangular flow mode ($v^{(2)}_{3}$), which corresponds to $n = 3$
harmonic, is even smaller and does not depend on centrality. For $n = $~2, the
relative magnitude of the effect measured with respect to the leading flow mode
shows a shallow minimum for semi-central collisions and increases for very
central and for peripheral collisions. For $n = $~3 case, there is no
centrality dependence. The sub-leading flow mode results obtained from the
HYDJET++ model are in a rather good agreement with the experimental
measurements of the CMS Collaboration.


title: Rigidity of eigenvalues for $\beta$ ensemble in multi-cut regime

abstract:
  We prove the rigidity of eigenvalues in the bulk for $\beta$ ensemble in the
multi-cut regime. We study the model for general $\beta>0$ and real analytic
potential. The main method is to decompose the $\beta$ ensemble in multi-cut
regime to be a product of $\beta$ ensembles in one-cut regime.


title:
Search for supersymmetry in events with photons and missing transverse
  energy in pp collisions at 13 TeV

abstract:
  The results of a search for new physics in final states with photons and
missing transverse energy are reported. The study is based on a sample of
proton-proton collisions collected at a center-of-mass energy of 13 TeV with
the CMS detector in 2015, corresponding to an integrated luminosity of 2.3
inverse femtobarns. Final states with two photons and significant missing
transverse energy are used to search for supersymmetric particles in models of
supersymmetry (SUSY) with general gauge-mediated (GGM) supersymmetry breaking.
No excess is observed with respect to the standard model expectation, and the
results are used to set limits on gluino pair production and squark pair
production in the GGM SUSY framework. Gluino masses below 1.65 TeV and squark
masses below 1.37 TeV are excluded at a 95% confidence level.


title: Algorithmic and Hardness Results for the Hub Labeling Problem

abstract:
  There has been significant success in designing highly efficient algorithms
for distance and shortest-path queries in recent years; many of the
state-of-the-art algorithms use the hub labeling framework. In this paper, we
study the approximability of the Hub Labeling problem. We prove a hardness of
$\Omega(\log n)$ for Hub Labeling, matching known approximation guarantees. The
hardness result applies to graphs that have multiple shortest paths between
some pairs of vertices. No hardness of approximation results were known
previously.
  Then, we focus on graphs that have a unique shortest path between each pair
of vertices. This is a very natural family of graphs, and much research on the
Hub Labeling problem has studied such graphs. We give an $O(\log D)$
approximation algorithm for graphs of diameter $D$ with unique shortest paths.
In particular, we get an $O(\log \log n)$ approximation for graphs of
polylogarithmic diameter, while previously known algorithms gave an $O(\log n)$
proximation. Finally, we present a polynomial-time approximation scheme (PTAS)
and quasi-polynomial time algorithms for Hub Labeling on trees; additionally,
we analyze a simple combinatorial heuristic for Hub Labeling on trees, proposed
by Peleg in 2000. We show that this heuristic gives an approximation factor of
2.


title:
Cosmological dynamics of a class of non-minimally coupled models of
  gravity

abstract:
  In this work a new non-minimally coupled model is presented, where a generic
function $f(R)$ of the scalar curvature factors the usual Einstein-Hilbert
action functional, motivated by relevant results obtained from similar models.
Its cosmological dynamics are derived and the possibility of attaining a phase
of accelerated expansion is assessed. To further probe the possible
implications of the model, a dynamical system formulation is established, and
used to assess the scenarios where $f(R)$ assumes a power-law or exponential
form.


title: A Hierarchical Approach for Generating Descriptive Image Paragraphs

abstract:
  Recent progress on image captioning has made it possible to generate novel
sentences describing images in natural language, but compressing an image into
a single sentence can describe visual content in only coarse detail. While one
new captioning approach, dense captioning, can potentially describe images in
finer levels of detail by captioning many regions within an image, it in turn
is unable to produce a coherent story for an image. In this paper we overcome
these limitations by generating entire paragraphs for describing images, which
can tell detailed, unified stories. We develop a model that decomposes both
images and paragraphs into their constituent parts, detecting semantic regions
in images and using a hierarchical recurrent neural network to reason about
language. Linguistic analysis confirms the complexity of the paragraph
generation task, and thorough experiments on a new dataset of image and
paragraph pairs demonstrate the effectiveness of our approach.


title:
Analytical solutions for the Schr\"odinger equation subjected to a
  deformable hyperbolic potential

abstract:
  In this work we discuss in detail the known solutions of the stationary
Schr\"odinger equation subject to a deformable hyperbolic tangent potential
exactly soluble $ V(x) = \frac {V_0} {2} (1+ \tanh (\delta x)) $. We find the
analytical solutions in terms of Gauss hypergeometric functions for the
scattering states with energy greater than the maximum value of the potential.
We also discussed the case for the energy lower than the maximum and the
similarities and differences with the abrupt step potential in both cases. We
graphically illustrate the relevant physical situations to the problem.


title: MAC Protocols for IEEE 802.11ax: Avoiding Collisions on Dense Networks

abstract:
  Wireless networks have become the main form of Internet access. Statistics
show that the global mobile Internet penetration should exceed 70\% until 2019.
Wi-Fi is an important player in this change. Founded on IEEE 802.11, this
technology has a crucial impact in how we share broadband access both in
domestic and corporate networks. However, recent works have indicated
performance issues in Wi-Fi networks, mainly when they have been deployed
without planning and under high user density. Hence, different collision
avoidance techniques and Medium Access Control protocols have been designed in
order to improve Wi-Fi performance. Analyzing the collision problem, this work
strengthens the claims found in the literature about the low Wi-Fi performance
under dense scenarios. Then, in particular, this article overviews the MAC
protocols used in the IEEE 802.11 standard and discusses solutions to mitigate
collisions. Finally, it contributes presenting future trends in MAC protocols.
This assists in foreseeing expected improvements for the next generation of
Wi-Fi devices.


title:
Throughput Efficient Large M2M Networks through Incremental Redundancy
  Combining

abstract:
  In this paper, we investigate the performance of incremental redundancy
combining as a new cooperative relaying protocol for large M2M networks with
opportunistic relaying. The nodes in the large M2M network are modeled by a
Poisson Point Process, experience Rayleigh fading and utilize slotted ALOHA as
the MAC protocol. The progress rate density (PRD) of the M2M network is used to
quantify the performance of proposed relaying protocol and compare it to
conventional multihop relaying with no cooperation. It is shown that
incremental redundancy combining in a large M2M network provides substantial
throughput improvements over conventional relaying with no cooperation at all
practical values of the network parameters.