title:
On Bochner's and Polya's Characterizations of Positive-Definite Kernels
  and the Respective Random Feature Maps

abstract:
  Positive-definite kernel functions are fundamental elements of kernel methods
and Gaussian processes. A well-known construction of such functions comes from
Bochner's characterization, which connects a positive-definite function with a
probability distribution. Another construction, which appears to have attracted
less attention, is Polya's criterion that characterizes a subset of these
functions. In this paper, we study the latter characterization and derive a
number of novel kernels little known previously.
  In the context of large-scale kernel machines, Rahimi and Recht (2007)
proposed a random feature map (random Fourier) that approximates a kernel
function, through independent sampling of the probability distribution in
Bochner's characterization. The authors also suggested another feature map
(random binning), which, although not explicitly stated, comes from Polya's
characterization. We show that with the same number of random samples, the
random binning map results in an Euclidean inner product closer to the kernel
than does the random Fourier map. The superiority of the random binning map is
confirmed empirically through regressions and classifications in the
reproducing kernel Hilbert space.


title:
Galactic Archaeology with TESS: Prospects for Testing the Star Formation
  History in the Solar Neighbourhood

abstract:
  A period of quenching between the formation of the thick and thin disks of
the Milky Way has been recently proposed to explain the observed
age-[{\alpha}/Fe] distribution of stars in the solar neighbourhood. However,
robust constraints on stellar ages are currently available for only a limited
number of stars. The all-sky survey TESS (Transiting Exoplanet Survey
Satellite) will observe the brightest stars in the sky and thus can be used to
investigate the age distributions of stars in these components of the Galaxy
via asteroseismology, where previously this has been difficult using other
techniques. The aim of this preliminary study was to determine whether TESS
will be able to provide evidence for quenching periods during the star
formation history of the Milky Way. Using a population synthesis code, we
produced populations based on various stellar formation history models and
limited the analysis to red-giant-branch stars. We investigated the
mass-Galactic-disk-height distributions, where stellar mass was used as an age
proxy, to test for whether periods of quenching can be observed by TESS. We
found that even with the addition of 15% noise to the inferred masses, it will
be possible for TESS to find evidence for/against quenching periods suggested
in the literature (e.g. between 7 and 9 Gyr ago), therefore providing stringent
constraints on the formation and evolution of the Milky Way.


title: Linear spaces on hypersurfaces over number fields

abstract:
  We establish an analytic Hasse principle for linear spaces of affine
dimension m on a complete intersection over an algebraic field extension K of
Q. The number of variables required to do this is no larger than what is known
for the analogous problem over Q. As an application we show that any smooth
hypersurface over K whose dimension is large enough in terms of the degree is
K-unirational, provided that either the degree is odd or K is totally
imaginary.


title:
The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory
  Compactifications

abstract:
  We study seven-branes in $O(10^{15})$ four-dimensional F-theory
compactifications where seven-brane moduli must be tuned in order to achieve
non-abelian gauge symmetry. The associated compact spaces $B$ are the set of
all smooth weak Fano toric threefolds. By a study of fine star regular
triangulations of three dimensional reflexive polytopes, the number of such
spaces is estimated to be $5.8\times 10^{14}\lesssim N_\text{bases}\lesssim
1.8\times 10^{17}$. Typically hundreds or thousands of moduli must be tuned to
achieve symmetry for $h^{11}(B)<10$, but the average number drops sharply into
the range $O(25)$-$O(200)$ as $h^{11}(B)$ increases. For some low rank groups,
such as $SU(2)$ and $SU(3)$, there exist examples where only a few moduli must
be tuned in order to achieve seven-brane gauge symmetry.


title: Hit-and-Run for Sampling and Planning in Non-Convex Spaces

abstract:
  We propose the Hit-and-Run algorithm for planning and sampling problems in
non-convex spaces. For sampling, we show the first analysis of the Hit-and-Run
algorithm in non-convex spaces and show that it mixes fast as long as certain
smoothness conditions are satisfied. In particular, our analysis reveals an
intriguing connection between fast mixing and the existence of smooth
measure-preserving mappings from a convex space to the non-convex space. For
planning, we show advantages of Hit-and-Run compared to state-of-the-art
planning methods such as Rapidly-Exploring Random Trees.


title:
Khovanov homology in characteristic two and involutive monopole Floer
  homology

abstract:
  We study the conjugation involution in Seiberg-Witten theory in the context
of the Ozsv\'ath-Szab\'o and Bloom's spectral sequence for the branched double
cover of a link $L$ in $S^3$. We prove that there exists a spectral sequence of
$\mathbb{F}[Q]/Q^2$-modules (where $Q$ has degree $-1$) which converges to
$\widetilde{\mathit{HMI}}_*(\Sigma(L))$, an involutive version of the monopole
Floer homology of the branched double cover, and whose $E^2$-page is a version
of Bar Natan's characteristic two Khovanov homology of the mirror of $L$. We
conjecture that an analogous result holds in the setting of
$\mathrm{Pin}(2)$-monopole Floer homology.


title: Constant mean curvature foliation of domains of dependence in $AdS_{3}$

abstract:
  We prove that, given an acausal curve $\Gamma$ in the boundary at infinity of
$AdS_{3}$ which is the graph of a quasi-symmetric homeomorphism $\phi$, there
exists a unique foliation of its domain of dependence $D(\Gamma)$ by constant
mean curvature surfaces with bounded second fundamental form. Moreover, these
surfaces provide a family of quasi-conformal extensions of $\phi$.


title:
Preheating after multifield inflation with nonminimal couplings, II:
  Resonance Structure

abstract:
  This is the second in a series of papers on preheating in inflationary models
comprised of multiple scalar fields coupled nonminimally to gravity. In this
paper, we work in the rigid-spacetime approximation and consider field
trajectories within the single-field attractor, which is a generic feature of
these models. We construct the Floquet charts to find regions of parameter
space in which particle production is efficient for both the adiabatic and
isocurvature modes, and analyze the resonance structure using analytic and
semi-analytic techniques. Particle production in the adiabatic direction is
characterized by the existence of an asymptotic scaling solution at large
values of the nonminimal couplings, $\xi_I \gg 1$, in which the dominant
instability band arises in the long-wavelength limit, for comoving wavenumbers
$k \rightarrow 0$. However, the large-$\xi_I$ regime is not reached until
$\xi_I \geq {\cal O} (100)$. In the intermediate regime, with $\xi_I \sim {\cal
O}(1 - 10)$, the resonance structure depends strongly on wavenumber and
couplings. The resonance structure for isocurvature perturbations is distinct
and more complicated than its adiabatic counterpart. An intermediate regime,
for $\xi_I \sim {\cal O} (1 - 10)$, is again evident. For large values of
$\xi_I$, the Floquet chart consists of densely spaced, nearly parallel
instability bands, suggesting a very efficient preheating behavior. The
increased efficiency arises from features of the nontrivial field-space
manifold in the Einstein frame, which itself arises from the fields' nonminimal
couplings in the Jordan frame, and has no analogue in models with minimal
couplings. Quantitatively, the approach to the large-$\xi_I$ asymptotic
solution for isocurvature modes is slower than in the case of the adiabatic
modes.


title: Magnonic Analogs of Topological Dirac Semimetals

abstract:
  In electronic topological Dirac semimetals the conduction and valence bands
touch at discrete points in the Brillouin zone and form Dirac cones. They are
robust against spin-orbit interaction (SOI) and protected by crystal
symmetries. They can be driven to different topological phases by breaking the
symmetries. In the low-temperature quantum magnetic systems the magnon
dispersions have similar band structures as the electron dispersions, but with
positive definite energies. In these magnetic systems SOI manifests in the form
of the Dzyaloshinskii-Moriya interaction (DMI). In this Communication, we
identify two types of {\it magnonic Dirac semimetals} in quasi-two-dimensional
quantum magnets. The first type is a consequence of topological phase
transition between trivial and topological magnon insulators and the second
type is intrinsic and protected by crystal symmetries. They are robust against
DMI and can be driven to a topological magnon phase by breaking the symmetries.
They can be manipulated by an external magnetic field and accessible by the
bulk sensitive inelastic neutron scattering experiments.


title:
Uniform continuity bounds for information characteristics of quantum
  channels depending on input dimension and on input energy

abstract:
  We obtain continuity bounds for basic information characteristics of quantum
channels depending on their input dimension (if it is finite) and on the input
energy bound (if the input dimension is infinite). We pay a special attention
to the case of a multi-mode quantum oscillator as an input system.
  First we prove continuity bounds for the output conditional mutual
information for a single channel and for $n$ copies of a channel.
  Then we obtain estimates for variation of the output Holevo quantity with
respect to simultaneous variations of a channel and of an input ensemble.
  As a result tight and close-to-tight continuity bounds for basic capacities
of quantum channels depending on the input dimension are obtained. They
complement the Leung-Smith continuity bounds depending on the output dimension.
  Finally, we obtain tight and close-to-tight continuity bounds for basic
capacities of infinite-dimensional energy-constrained channels with respect to
the energy-constrained Bures distance generating the strong convergence of
quantum channels.


title: Detecting People in Artwork with CNNs

abstract:
  CNNs have massively improved performance in object detection in photographs.
However research into object detection in artwork remains limited. We show
state-of-the-art performance on a challenging dataset, People-Art, which
contains people from photos, cartoons and 41 different artwork movements. We
achieve this high performance by fine-tuning a CNN for this task, thus also
demonstrating that training CNNs on photos results in overfitting for photos:
only the first three or four layers transfer from photos to artwork. Although
the CNN's performance is the highest yet, it remains less than 60\% AP,
suggesting further work is needed for the cross-depiction problem. The final
publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-46604-0_57


title: More about a successful vector-tensor theory of gravitation

abstract:
  The vector-tensor (VT) theory of gravitation revisited in this article was
studied in previous papers, where it was proved that VT works and deserves
attention. New observational data and numerical codes have motivated further
development which is presented here. New research has been planed with the
essential aim of proving that current cosmological observations, including
Planck data, baryon acoustic oscillations (BAO), and so on, may be explained
with VT, a theory which accounts for a kind of dark energy which has the same
equation of state as vacuum. New versions of the codes CAMB and COSMOMC have
been designed for applications to VT, and the resulting versions have been used
to get the cosmological parameters of the VT model at suitable confidence
levels. The parameters to be estimated are the same as ingeneral relativity
(GR), plus a new parameter $D$. For $D=0$, VT linear cosmological perturbations
reduces to those of GR, but the VT background may explain dark energy. The fits
between observations and VT predictions lead to non vanishing $|D|$ upper
limits at the $1\sigma $ confidence level. The value $D=0$ is admissible at
this level, but this value is not that of the best fit in any case. Results
strongly suggest that VT may explain current observations, at least, as well as
GR; with the advantage that, as it is proved in this paper, VT has an
additional parameter which facilitates adjustments to current observational
data.}


title: A rough calculus approach to level sets in the Heisenberg group

abstract:
  We introduce novel equations, in the spirit of rough path theory, that
parametrize level sets of intrinsically regular maps on the Heisenberg group
with values in $\mathbb{R}^2$. These equations can be seen as a sub-Riemannian
counterpart to classical ODEs arising from the implicit function theorem. We
show that they enjoy all the natural well-posedness properties, thus allowing
for a "good calculus" on nonsmooth level sets. We apply these results to prove
an area formula for the intrinsic measure of level sets, along with the
corresponding coarea formula.


title:
Quantum to classical transition in the work distribution for chaotic
  systems

abstract:
  The work distribution is a fundamental quantity in nonequilibrium
thermodynamics mainly due to its connection with fluctuations theorems. Here we
develop a semiclassical approximation to the work distribution for a quench
process in chaotic systems. The approach is based on the dephasing
representation of the quantum Loschmidt echo and on the quantum ergodic
conjecture, which states that the Wigner function of a typical eigenstate of a
classically chaotic Hamiltonian is equidistributed on the energy shell. We show
that our semiclassical approximation is accurate in describing the quantum
distribution as we increase the temperature. Moreover, we also show that this
semiclassical approximation provides a link between the quantum and classical
work distributions.


title:
Effect of 2 MeV Fe3+ irradiation on Fe atom site population in a
  sigma-phase Fe-Cr compound

abstract:
  A sigma-Fe54.5Cr45.5 samples irradiated in vacuum with 2 MeV Fe3+ ions at
300, 400, 475 and 700 deg C to the maximum dose of 12.5 dpa were studied with
the conversion electron M\"ossbauer spectroscopy (CEMS). The analysis of the
room temperature CEMS spectra revealed an irradiation-induced redistribution of
Fe atoms viz. their number on B and D sites decreased while on A, C and E sites
increased. The degree of the redistribution was found to be proportional to the
number of Fe atoms present on the lattice sites in the non-irradiated samples.
The highest degree of the redistribution was revealed in the sample irradiated
at 300 deg C. No change in the site occupancy was found in the sample
irradiated at 700 deg C.


title:
Some Computational and Theoretical Aspects of the Exponentiated
  Generalized Nadarajah-Haghighi Distribution

abstract:
  Real data from applications in the survival context have required the use of
more flexible models. A new four-parameter model called the Exponentiated
Generalized Nadarajah-Haghighi (EGNH) distribution has been introduced in order
to verify this requirement.


title:
Experimental Observation of Three-Component 'New Fermions' in
  Topological Semimetal MoP

abstract:
  Condensed matter systems can host quasiparticle excitations that are
analogues to elementary particles such as Majorana, Weyl, and Dirac fermions.
Recent advances in band theory have expanded the classification of fermions in
crystals, and revealed crystal symmetry-protected electron excitations that
have no high-energy counterparts. Here, using angle-resolved photoemission
spectroscopy, we demonstrate the existence of a triply degenerate point in the
electronic structure of MoP crystal, where the quasiparticle excitations are
beyond the Majorana-Weyl-Dirac classification. Furthermore, we observe pairs of
Weyl points in the bulk electronic structure coexisting with the 'new
fermions', thus introducing a platform for studying the interplay between
different types of fermions.


title: Asymptotics for rough stochastic volatility models

abstract:
  Using the large deviation principle (LDP) for a re-scaled fractional Brownian
motion $B^H_t$ where the rate function is defined via the reproducing kernel
Hilbert space, we compute small-time asymptotics for a correlated fractional
stochastic volatility model of the form $dS_t=S_t\sigma(Y_t) (\bar{\rho} dW_t
+\rho dB_t), \,dY_t=dB^H_t$ where $\sigma$ is $\alpha$-H\"{o}lder continuous
for some $\alpha\in(0,1]$; in particular, we show that $t^{H-\frac{1}{2}} \log
S_t $ satisfies the LDP as $t\to0$ and the model has a well-defined implied
volatility smile as $t \to 0$, when the log-moneyness $k(t)=x
t^{\frac{1}{2}-H}$. Thus the smile steepens to infinity or flattens to zero
depending on whether $H\in(0,\frac{1}{2})$ or $H\in(\frac{1}{2},1)$. We also
compute large-time asymptotics for a fractional local-stochastic volatility
model of the form: $dS_t= S_t^{\beta} |Y_t|^p dW_t,dY_t=dB^H_t$, and we
generalize two identities in Matsumoto&Yor05 to show that $\frac{1}{t^{2H}}\log
\frac{1}{t}\int_0^t e^{2 B^H_s} ds$ and $\frac{1}{t^{2H}}(\log \int_0^t
e^{2(\mu s+B^H_s)} ds-2 \mu t)$ converge in law to $ 2\mathrm{max}_{0 \le s \le
1} B^H_{s}$ and $2B_1$ respectively for $H \in (0,\frac{1}{2})$ and $\mu>0$ as
$t \to \infty$.


title: Coupled mass-momenta balance for modeling material failure

abstract:
  Cracks are created by massive breakage of molecular or atomic bonds. The
latter, in its turn, leads to the highly localized loss of material, which is
the reason why even closed cracks are visible by a naked eye. Thus, fracture
can be interpreted as the local material sink. Mass conservation is violated
locally in the area of material failure. We consider a theoretical formulation
of the coupled mass and momenta balance equations for a description of
fracture. Our focus is on brittle fracture and we propose a finite strain
hyperelastic thermodynamic framework for the coupled mass-flow-elastic boundary
value problem. The attractiveness of the proposed framework as compared to the
traditional continuum damage theories is that no internal parameters (like
damage variables, phase fields etc.) are used while the regularization of the
failure localization is provided by the physically sound law of mass balance.


title:
Controlled Electrode Magnetization Alignment in Planar Elliptical
  Ferromagnetic Break Junction Devices

abstract:
  Controlling the magnetization reversal process of magnetic elements is
important for a wide range of applications that make use of magnetoresistive
effects, but is difficult to achieve for devices that require adjacent thin
film structures capable of contacting an individual molecule or quantum dot. We
report on the fabrication and measurement of ferromagnetic break junction
devices with planar, elliptical leads to address the particular challenge of
controlling the relative magnetization alignment between neighboring
electrodes. Low temperature transport measurements, supported by finite-element
micromagnetic simulations, are used to characterize the magnetoresistance
response across a range of conductance levels. We demonstrate that an in-plane
external field applied parallel to the hard axis of the ellipses may be used to
controllably switch the magnetization of the source and drain electrodes
between monodomain-like parallel and antiparallel configurations for devices in
the tunneling regime.


title:
A Revisit of Block Power Methods for Finite State Markov Chain
  Applications

abstract:
  In this paper, we revisit the generalized block power methods for
approximating the eigenvector associated with $\lambda_1 = 1$ of a Markov chain
transition matrix. Our analysis of the block power method shows that when $s$
linearly independent probability vectors are used as the initial block, the
convergence of the block power method to the stationary distribution depends on
the magnitude of the $(s+1)$th dominant eigenvalue $\lambda_{s+1}$ of $P$
instead of that of $\lambda_2$ in the power method. Therefore, the block power
method with block size $s$ is particularly effective for transition matrices
where $|\lambda_{s+1}|$ is well separated from $\lambda_1 = 1$ but
$|\lambda_2|$ is not. This approach is particularly useful when visiting the
elements of a large transition matrix is the main computational bottleneck over
matrix--vector multiplications, where the block power method can effectively
reduce the total number of times to pass over the matrix. To further reduce the
overall computational cost, we combine the block power method with a sliding
window scheme, taking advantage of the subsequent vectors of the latest $s$
iterations to assemble the block matrix. The sliding window scheme correlates
vectors in the sliding window to quickly remove the influences from the
eigenvalues whose magnitudes are smaller than $|\lambda_{s}|$ to reduce the
overall number of matrix--vector multiplications to reach convergence. Finally,
we compare the effectiveness of these methods in a Markov chain model
representing a stochastic luminal calcium release site.


title: Cosmology on all scales: a two-parameter perturbation expansion

abstract:
  We propose and construct a two-parameter perturbative expansion around a
Friedmann-Lema\^{i}tre-Robertson-Walker geometry that can be used to model
high-order gravitational effects in the presence of non-linear structure. This
framework reduces to the weak-field and slow-motion post-Newtonian treatment of
gravity in the appropriate limits, but also includes the low-amplitude
large-scale fluctuations that are important for cosmological modelling. We
derive a set of field equations that can be applied to the late Universe, where
non-linear structure exists on supercluster scales, and perform a detailed
investigation of the associated gauge problem. This allows us to identify a
consistent set of perturbed quantities in both the gravitational and matter
sectors, and to construct a set of gauge-invariant quantities that correspond
to each of them. The field equations, written in terms of these quantities,
take on a relatively simple form, and allow the effects of small-scale
structure on the large-scale properties of the Universe to be clearly
identified. We find that inhomogeneous structures source the global expansion,
that there exist new field equations at new orders, and that there is vector
gravitational potential that is a hundred times larger than one might naively
expect from cosmological perturbation theory. Finally, we expect our formalism
to be of use for calculating relativistic effects in upcoming ultra-large-scale
surveys, as the form of the gravitational coupling between small and large
scales depends on the non-linearity of Einstein's equations, and occurs at what
is normally thought of as first order in cosmological perturbations.


title:
PandaX-III: Searching for Neutrinoless Double Beta Decay with High
  Pressure $^{136}$Xe Gas Time Projection Chambers

abstract:
  Searching for the Neutrinoless Double Beta Decay (NLDBD) is now regarded as
the topmost promising technique to explore the nature of neutrinos after the
discovery of neutrino masses in oscillation experiments. PandaX-III (Particle
And Astrophysical Xenon Experiment III) will search for the NLDBD of $^{136}$Xe
at the China Jin Ping underground Laboratory (CJPL). In the first phase of the
experiment, a high pressure gas Time Projection Chamber (TPC) will contain 200
kg, 90% $^{136}$Xe enriched gas operated at 10 bar. Fine pitch micro-pattern
gas detector (Microbulk Micromegas) will be used at both ends of the TPC for
the charge readout with a cathode in the middle. Charge signals can be used to
reconstruct tracks of NLDBD events and provide good energy and spatial
resolution. The detector will be immersed in a large water tank to ensure
$\sim$5 m of water shielding in all directions. The second phase, a ton-scale
experiment, will consist of five TPCs in the same water tank, with improved
energy resolution and better control over backgrounds.


title: Recognizing IC-Planar and NIC-Planar Graphs

abstract:
  We prove that triangulated IC-planar and NIC-planar graphs can be recognized
in cubic time.
  A graph is 1-planar if it can be drawn in the plane with at most one crossing
per edge. A drawing is IC-planar if, in addition, each vertex is incident to at
most one crossing edge and NIC-planar if two pairs of crossing edges share at
most one vertex. In a triangulated drawing each face is a triangle. In
consequence, planar-maximal and maximal IC-planar and NIC-planar graphs can be
recognized in O(n^5) time and maximum and optimal ones in O(n^3) time. In
contrast, recognizing 3-connected IC-planar and NIC-planar graphs is
NP-complete, even if the graphs are given with a rotation system which
describes the cyclic ordering of the edges at each vertex. Our results
complement similar ones for 1-planar graphs.


title: Optimal actuator placement for minimizing the worst-case control energy

abstract:
  We consider the actuator placement problem for linear systems. Specifically,
we aim to identify an actuator which requires the least amount of control
energy to drive the system from an arbitrary initial condition to the origin in
the worst case. Said otherwise, we investigate the minimax problem of
minimizing the control energy over the worst possible initial conditions.
Recall that the least amount of control energy needed to drive a linear
controllable system from any initial condition on the unit sphere to the origin
is upper-bounded by the inverse of the smallest eigenvalue of the associated
controllability Gramian, and moreover, the upper-bound is sharp. The minimax
problem can be thus viewed as the optimization problem of minimizing the
upper-bound via the placement of an actuator. In spite of its simple and
natural formulation, this problem is difficult to solve. In fact, properties
such as the stability of the system matrix, which are not related to
controllability, now play important roles. We focus in this paper on the
special case where the system matrix is positive definite. Under this
assumption, we are able to provide a complete solution to the optimal actuator
placement problem and highlight the difficulty in solving the general problem.


title:
Purification of an unpolarized spin ensemble into entangled singlet
  pairs

abstract:
  Dynamical polarization of nuclear spin ensembles is of central importance for
magnetic resonance studies, precision sensing and for applications in quantum
information theory. Here we propose a scheme to generate long-lived singlet
pairs in an unpolarized nuclear spin ensemble which is dipolar coupled to the
electron spins of a Nitrogen Vacancy center in diamond. The quantum mechanical
back-action induced by frequent spin-selective readout of the NV centers allows
the nuclear spins to pair up into maximally entangled singlet pairs.
Counterintuitively, the robustness of the pair formation to dephasing noise
improves with increasing size of the spin ensemble. We also show how the paired
nuclear spin state allows for enhanced sensing capabilities of NV centers in
diamond.

categories: quant-ph cond-mat.mes-hall cond-mat.str-el physics.chem-ph


title: How to project onto extended second order cones

abstract:
  The extended second order cones were introduced by S. Z. N\'emeth and G.
Zhang in [S. Z. N\'emeth and G. Zhang. Extended Lorentz cones and variational
inequalities on cylinders. J. Optim. Theory Appl., 168(3):756-768, 2016] for
solving mixed complementarity problems and variational inequalities on
cylinders. R. Sznajder in [R. Sznajder. The Lyapunov rank of extended second
order cones. Journal of Global Optimization, 66(3):585-593, 2016] determined
the automorphism groups and the Lyapunov or bilinearity ranks of these cones.
S. Z. N\'emeth and G. Zhang in [S.Z. N\'emeth and G. Zhang. Positive operators
of Extended Lorentz cones. arXiv:1608.07455v2, 2016] found both necessary
conditions and sufficient conditions for a linear operator to be a positive
operator of an extended second order cone. This note will give formulas for
projecting onto the extended second order cones. In the most general case the
formula will depend on a piecewise linear equation for one real variable which
will be solved by using numerical methods.


title:
Influence of multiorbitals and anisotropic Coulomb interactions on
  isotope effect coefficient in doped Fe-based superconductors

abstract:
  The present work describes the theoretical analysis of isotope effect
coefficient as a function of transition temperature in two orbital per site
model Hamiltonian in iron based superconducting system. The expression of
isotope effect coefficient has been computed numerically and self-consistently
by employing Green's function technique within the BCS-mean-field
approximation. It is observed that the isotope effect coefficient increases
with the increase of the hybridization while with the increase in Coulomb
interaction it starts decreasing. On increasing the carrier density per site in
two orbital per site iron pnictide system, isotope effect coefficient
($\alpha$) exhibits large values (much higher than BCS limit) at lower
temperatures. While in the underdoped case, isotope effect coefficient shows
minimum value in superconducting states of the iron based systems. Furthermore,
it has been found that the large value of the isotope effect coefficient is the
indication of the fact that the contribution of phonon alone is inadequate as
the origin of superconductivity in these systems. Finally, the obtained
theoretical results have been compared with experimental and existing
theoretical observations in iron based superconductors.


title: 3D sensors for the HL-LHC

abstract:
  In order to increase its discovery potential, the Large Hadron Collider (LHC)
accelerator will be upgraded in the next decade. The high luminosity LHC
(HL-LHC) period demands new sensor technologies to cope with increasing
radiation fluences and particle rates. The ATLAS experiment will replace the
entire inner tracking detector with a completely new silicon-only system. 3D
pixel sensors are promising candidates for the innermost layers of the Pixel
detector due to their excellent radiation hardness at low operation voltages
and low power dissipation at moderate temperatures. Recent developments of 3D
sensors for the HL-LHC are presented.


title: An algorithm and software for establishing heterogeneous parking prices

abstract:
  Parking prices in cities are uniform over large areas and do not reflect
spatially heterogeneous parking supply and demand. Underpricing results in high
parking occupancy in the subareas where the demand exceeds supply and long
search for the vacant parking, whereas overpricing leads to low occupancy and
hampered economic vitality. We present Nearest Pocket for Prices Algorithm
(NPPA), a spatially explicit algorithm for establishing on-and off-street
parking prices that guarantee a predetermined uniform level of occupation over
the entire parking space. We apply NPPA for establishing heterogeneous parking
prices that guarantee 90% parking occupancy in the Israeli city of Bat Yam.


title: Bound states of a light atom and two heavy dipoles in two dimensions

abstract:
  We study a three-body system, formed by a light particle and two identical
heavy dipoles, in two dimensions in the Born-Oppenheimer approximation. We
present the analytic light-particle wave function resulting from an attractive
zero-range potential between the light and each of the heavy particles. It
expresses the large-distance universal properties which must be reproduced by
all realistic short-range interactions. We calculate the three-body spectrum
for zero heavy-heavy interaction as a function of light to heavy mass ratio. We
discuss the relatively small deviations from Coulomb estimates and the
degeneracies related to radial nodes and angular momentum quantum numbers. We
include a repulsive dipole-dipole interaction and investigate the three-body
solutions as functions of strength and dipole direction. Avoided crossings
occur between levels localized in the emerging small and large-distance minima,
respectively. The characteristic exchange of properties such as mean square
radii are calculated. Simulation of quantum information transfer is suggested.
For large heavy-heavy particle repulsion all bound states have disappeared into
the continuum. The corresponding critical strength is inversely proportional to
the square of the mass ratio, far from the linear dependence from the Landau
criterion.


title: Overdetermined elliptic problems in topological disks

abstract:
  We introduce a method, based on the Poincare-Hopf index theorem, to classify
solutions to overdetermined problems for fully nonlinear elliptic equations in
domains diffeomorphic to a closed disk. Applications to some well-known
nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of
Hopf's uniqueness theorem for constant mean curvature spheres, but for the
general analytic context of overdetermined elliptic problems.


title: Characteristic classes as complete obstructions

abstract:
  In the first part of this paper, we propose a uniform interpretation of
characteristic classes as obstructions to the reduction of the structure group
and to the existence of an equivariant extension of a certain homomorphism
defined a priori only on a single fiber of the bundle. By plugging in the
correct parameters, we recover several classical theorems. Afterwards, we
define a family of invariants of principal bundles that detect the number of
group reductions that a principal bundle admits. We prove that they fit into a
long exact sequence of abelian groups, together with the cohomology of the base
space and the cohomology of the classifying space of the structure group.


title: Detailed VHE Studies of the Pulsar Wind Nebula HESS J1825-137

abstract:
  The pulsar wind nebula (PWN) HESS~J1825-137, known to exhibit strong energy
dependent morphology, was discovered by HESS in 2005. Powered by the pulsar
PSR~B1823-13, the TeV gamma-ray emitting nebula is significantly offset from
the pulsar. The asymmetric shape and 21~kyr characteristic age of the pulsar
suggest that HESS~J1825-137 is in an evolved state, having possibly already
undergone reverse shock interactions from the progenitor supernova. Given its
large angular extent, despite its 4~kpc distance, it may have the largest
intrinsic size of any TeV PWN so far detected. A rich dataset is currently
available with H.E.S.S., including H.E.S.S. II data with a low energy
threshold, enabling detailed studies of the source properties and environment.
We present new views of the changing nature of the PWN with energy, including
maps of the region and spectral studies.


title:
A randomised primal-dual algorithm for distributed radio-interferometric
  imaging

abstract:
  Next generation radio telescopes, like the Square Kilometre Array, will
acquire an unprecedented amount of data for radio astronomy. The development of
fast, parallelisable or distributed algorithms for handling such large-scale
data sets is of prime importance. Motivated by this, we investigate herein a
convex optimisation algorithmic structure, based on primal-dual
forward-backward iterations, for solving the radio interferometric imaging
problem. It can encompass any convex prior of interest. It allows for the
distributed processing of the measured data and introduces further flexibility
by employing a probabilistic approach for the selection of the data blocks used
at a given iteration. We study the reconstruction performance with respect to
the data distribution and we propose the use of nonuniform probabilities for
the randomised updates. Our simulations show the feasibility of the
randomisation given a limited computing infrastructure as well as important
computational advantages when compared to state-of-the-art algorithmic
structures.


title: Quantitative quasisymmetric uniformization of compact surfaces

abstract:
  Bonk and Kleiner showed that any metric sphere which is Ahlfors 2-regular and
linearly locally contractible is quasisymmetrically equivalent to the standard
sphere, in a quantitative way. We extend this result to arbitrary metric
compact orientable surfaces.


title: Construction of $\Phi^4_3$ diagrams for pedestrians

abstract:
  We aim to give a pedagogic and essentially self-contained presentation of the
construction of various stochastic objects appearing in the dynamical
$\Phi^4_3$ model. The construction presented here is based on the use of
paraproducts. The emphasis is on describing the stochastic objects themselves
rather than introducing a solution theory for the equation.


title: Phase Separation Transition in a Nonconserved Two Species Model

abstract:
  A one dimensional stochastic exclusion process with two species of particles,
$+$ and $-$, is studied where density of each species can fluctuate but the
total particle density is conserved. From the exact stationary state weights we
show that, in the limiting case where density of negative particles vanishes,
the system undergoes a phase separation transition where a macroscopic domain
of vacancies form in front of a single surviving negative particle. We also
show that the phase separated state is associated with a diverging correlation
length for any density and the critical exponents characterizing the behaviour
in this region are different from those at the transition line. The static and
the dynamical critical exponents are obtained from the exact solution and
numerical simulations, respectively.


title:
Estimation of heterogeneous individual treatment effects with endogenous
  treatments

abstract:
  This paper estimates individual treatment effects in a triangular model with
binary--valued endogenous treatments. Following the identification strategy
established in Vuong and Xu (2014), we propose a two--stage estimation
approach. First, we estimate the counterfactual outcome and hence the
individual treatment effect (ITE) for every observational unit in the sample.
Second, we estimate the density of individual treatment effects in the
population. Our estimation method does not suffer from the ill--posed inverse
problem associated with inverting a non--linear functional. Asymptotic
properties of the proposed method are established. We study its finite sample
properties in Monte Carlo experiments. We also illustrate our approach with an
empirical application assessing the effects of 401(k) retirement programs on
personal savings. Our results show that there exists a small but statistically
significant proportion of individuals who experience negative effects, although
the majority of ITEs is positive.


title:
Optimal renormalization and the extraction of the strange quark mass
  from moments of the $\tau$-decay spectral function

abstract:
  We introduce an optimal renormalization group analysis pertinent to the
analysis of polarization functions associated with the $s$-quark mass relevant
in $\tau$-decay. The technique is based on the renormalization group invariance
constraints which lead to closed form summation of all the leading and
next-to-leading logarithms at each order in perturbation theory. The new
perturbation series exhibits reduced sensitivity to the renormalization scale
and improved behavior in the complex plane along the integration contour. Using
improved experimental and theory inputs, we have extracted the value of the
strange quark mass $m_s(2{\rm GeV}) = 106.70 \pm 9.36~{\rm MeV}$ and $m_s(2{\rm
GeV}) = 74.47 \pm 7.77~{\rm MeV}$ from presently available ALEPH and OPAL data
respectively. These determinations are in agreement with the determinations in
other phenomenological methods and from the lattice.


title: Spin Currents and Magnon Dynamics in Insulating Magnets

abstract:
  Nambu-Goldstone theorem provides gapless modes to both relativistic and
nonrelativistic systems. The Nambu-Goldstone bosons in insulating magnets are
called magnons or spin-waves and play a key role in magnetization transport. We
review here our past works on magnetization transport in insulating magnets and
also add new insights, with a particular focus on magnon transport. We
summarize in detail the magnon counterparts of electron transport, such as the
Wiedemann-Franz law, the Onsager reciprocal relation between the Seebeck and
Peltier coefficients, the Hall effects, the superconducting state, the
Josephson effects, and the persistent quantized current in a ring to list a
few. Focusing on the electromagnetism of moving magnons, i.e., magnetic
dipoles, we theoretically propose a way to directly measure magnon currents. As
a consequence of the Mermin-Wagner-Hohenberg theorem, spin transport is
drastically altered in one-dimensional antiferromagnetic (AF) spin-1/2 chains;
where the N\'eel order is destroyed by quantum fluctuations and a quasiparticle
magnon-like picture breaks down. Instead, the low-energy collective excitations
of the AF spin chain are described by a Tomonaga-Luttinger liquid (TLL) which
provides the spin transport properties in such antiferromagnets some universal
features at low enough temperature. Finally, we enumerate open issues and
provide a platform to discuss the future directions of magnonics.

categories: cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.quant-gas cond-mat.stat-mech cond-mat.str-el


title: Off- and on-shell harmonic superspaces for 6D SYM theories

abstract:
  It is a brief account of the harmonic superspace formulations of {\cal
N}=(1,0) and {\cal N}=(1,1) SYM theories in six dimensions. The on-shell {\cal
N}=(1,1) harmonic superspace is argued to provide an efficient tool of
constructing candidate counterterms and other invariants of {\cal N}=(1,1) SYM.
It allows one, e.g., to find out an essential difference between the single-
and double-trace dimension d=10 invariants, which could be capable to explain
the absence of the three-loop double-trace (non-planar) counterterms in this
theory. The defining superspace constraints of {\cal N}=(1,1) SYM are solved in
terms of {\cal N}=(1,0) harmonic superfields.


title: Social Interactions in Large Networks: A Game Theoretic Approach

abstract:
  This paper studies social interactions in a game theoretic model with players
in a large social network. We consider observations from one single equilibrium
of a large network game with asymmetric information, in which each player
chooses an action from a finite set and is subject to interactions with her
friends. Simple assumptions about the structure are made to establish the
existence and uniqueness of equilibrium. In particular, we show that the
equilibrium strategies satisfy a network decaying dependence (NDD) condition
requiring that dependence between any two players' decisions decays with their
network distance. The formulation of such an NDD property is novel and serves
as the basis for statistical inference. Further, we establish the
identification of the structural model and introduce a computationally feasible
and efficient estimation method. We illustrate the estimation method with an
actual application to college attendance, as well as in Monte Carlo
experiments.


title: Local Similarity-Aware Deep Feature Embedding

abstract:
  Existing deep embedding methods in vision tasks are capable of learning a
compact Euclidean space from images, where Euclidean distances correspond to a
similarity metric. To make learning more effective and efficient, hard sample
mining is usually employed, with samples identified through computing the
Euclidean feature distance. However, the global Euclidean distance cannot
faithfully characterize the true feature similarity in a complex visual feature
space, where the intraclass distance in a high-density region may be larger
than the interclass distance in low-density regions. In this paper, we
introduce a Position-Dependent Deep Metric (PDDM) unit, which is capable of
learning a similarity metric adaptive to local feature structure. The metric
can be used to select genuinely hard samples in a local neighborhood to guide
the deep embedding learning in an online and robust manner. The new layer is
appealing in that it is pluggable to any convolutional networks and is trained
end-to-end. Our local similarity-aware feature embedding not only demonstrates
faster convergence and boosted performance on two complex image retrieval
datasets, its large margin nature also leads to superior generalization results
under the large and open set scenarios of transfer learning and zero-shot
learning on ImageNet 2010 and ImageNet-10K datasets.


title: Curvature Instability of Membranes near Rigid Inclusions

abstract:
  In multicomponent membranes, internal scalar fields may couple to membrane
curvature, thus renormalizing the membrane elastic constants and destabilizing
the flat membranes. Here, a general elasticity theory of membranes is
considered that employs a quartic curvature expansion. The shape of the
membrane and its deformation energy near a long rod-like inclusion are studied
analytically. In the limit where one can neglect the end-effects, the nonlinear
response of the membrane to such inclusions is found in exact form. Notably,
new shape solutions are found when the membrane is curvature unstable,
manifested by a negative rigidity. Near the instability point (i.e. at
vanishing rigidity), the membrane is stabilized by the quartic term, giving
rise to a new length scale and new scale exponents for the shape and its energy
profile. The contact angle induced by an applied force at the inclusion
provides a method to experimentally determine the quartic curvature modulus.


title:
Logarithmic Query Complexity for Approximate Nash Computation in Large
  Games

abstract:
  We investigate the problem of equilibrium computation for "large" $n$-player
games. Large games have a Lipschitz-type property that no single player's
utility is greatly affected by any other individual player's actions. In this
paper, we mostly focus on the case where any change of strategy by a player
causes other players' payoffs to change by at most $\frac{1}{n}$. We study
algorithms having query access to the game's payoff function, aiming to find
$\epsilon$-Nash equilibria. We seek algorithms that obtain $\epsilon$ as small
as possible, in time polynomial in $n$.
  Our main result is a randomised algorithm that achieves $\epsilon$
approaching $\frac{1}{8}$ for 2-strategy games in a {\em completely uncoupled}
setting, where each player observes her own payoff to a query, and adjusts her
behaviour independently of other players' payoffs/actions. $O(\log n)$
rounds/queries are required. We also show how to obtain a slight improvement
over $\frac{1}{8}$, by introducing a small amount of communication between the
players.
  Finally, we give extension of our results to large games with more than two
strategies per player, and alternative largeness parameters.


title:
Mass Generation, the Cosmological Constant Problem, Conformal Symmetry,
  and the Higgs Boson

abstract:
  In 2013 the Nobel Prize in Physics was awarded to Francois Englert and Peter
Higgs for their work in 1964 along with the late Robert Brout on the mass
generation mechanism (the Higgs mechanism) in local gauge theories. This
mechanism requires the existence of a massive scalar particle, the Higgs boson,
and in 2012 the Higgs boson was finally discovered at the Large Hadron Collider
after being sought for almost half a century. In this article we review the
work that led to the discovery of the Higgs boson and discuss its implications.
We approach the topic from the perspective of a dynamically generated Higgs
boson that is a fermion-antifermion bound state rather than an elementary field
that appears in an input Lagrangian. In particular, we emphasize the connection
with the Barden-Cooper-Schrieffer theory of superconductivity. We identify the
double-well Higgs potential not as a fundamental potential but as a mean-field
effective Lagrangian with a dynamical Higgs boson being generated through a
residual interaction that accompanies the mean-field Lagrangian. We discuss
what we believe to be the key challenge raised by the discovery of the Higgs
boson, namely determining whether it is elementary or composite, and through
study of a conformal invariant field theory model as realized with critical
scaling and anomalous dimensions, suggest that the width of the Higgs boson
might serve as a suitable diagnostic for discriminating between an elementary
Higgs boson and a composite one. We show that the contribution to the
cosmological constant due to a composite Higgs boson is more tractable and
under control than the contribution due to an elementary Higgs boson, and is
potentially completely under control if there is an underlying conformal
symmetry not just in a critical scaling matter sector, but equally in the
gravity sector to which the matter sector couples.


title:
The Einstein-Vlasov system in spherical symmetry: reduction of the
  equations of motion and classification of single-shell static solutions, in
  the limit of massless particles

abstract:
  We express the Einstein-Vlasov system in spherical symmetry in terms of a
dimensionless momentum variable $z$ (radial over angular momentum). This
regularises the limit of massless particles, and in that limit allows us to
obtain a reduced system in independent variables $(t,r,z)$ only. Similarly, in
this limit the Vlasov density function $f$ for static solutions depends on a
single variable $Q$ (energy over angular momentum). This reduction allows us to
show that any given static metric which has vanishing Ricci scalar, is vacuum
at the centre and for $r>3M$ and obeys certain energy conditions uniquely
determines a consistent $f=\bar k(Q)$ (in closed form). Vice versa, any $\bar
k(Q)$ within a certain class uniquely determines a static metric (as the
solution of a system of two first-order quasilinear ODEs). Hence the space of
static spherically symmetric solutions of Einstein-Vlasov is locally a space of
functions of one variable. For a simple 2-parameter family of functions $\bar
k(Q)$, we construct the corresponding static spherically symmetric solutions,
finding that their compactness is in the interval $0.7\lesssim \rm
max_r(2M/r)\le 8/9$. This class of static solutions includes one that agrees
with the approximately universal type-I critical solution recently found by
Akbarian and Choptuik (AC) in numerical time evolutions. We speculate on what
singles it out as the critical solution found by fine-tuning generic data to
the collapse threshold, given that AC also found that {\em all} static
solutions are one-parameter unstable and sit on the threshold of collapse.


title: Rationalization and Identification of Binary Games with Correlated Types

abstract:
  This paper studies the rationalization and identification of binary games
where players have correlated private types. Allowing for correlation is
crucial in global games and in models with social interactions as it represents
correlated information and homophily, respectively. Our approach is fully
nonparametric in the joint distribution of types and the strategic effects in
the payoffs. First, under monotone pure Bayesian Nash Equilibrium strategy, we
characterize all the restrictions if any on the distribution of players'
choices imposed by the game-theoretic model as well as restrictions associated
with two assumptions frequently made in the empirical analysis of discrete
games. Namely, we consider exogeneity of payoff shifters relative to private
information, and mutual independence of private information given payoff
shifters. Second, we study the nonparametric identification of the payoff
functions and types distribution. We show that the model with exogenous payoff
shifters is fully identified up to a single location--scale normalization under
some exclusion restrictions and rank conditions. Third, we discuss partial
identification under weaker conditions and multiple equilibria. Lastly, we
briefly point out the implications of our results for model testing and
estimation.


title: Perfect Memory Context Trees in time series modeling

abstract:
  The Stochastic Context Tree (SCOT) is a useful tool for studying infinite
random sequences generated by an m-Markov Chain (m-MC). It captures the
phenomenon that the probability distribution of the next state sometimes
depends on less than m of the preceding states. This allows compressing the
information needed to describe an m-MC. The SCOT construction has been earlier
used under various names: VLMC, VOMC, PST, CTW. In this paper we study the
possibility of reducing the m-MC to a 1-MC on the leaves of the SCOT. Such
context trees are called perfect-memory. We give various combinatorial
characterizations of perfect-memory context trees and an efficient algorithm to
find the minimal perfect-memory extension of a SCOT.


title: Toward Mining Visual Log of Software

abstract:
  In this paper, we define visual log of a software system as data capturing
the interactions between its users and its graphic user interface (GUI), such
as screen-shots and screen recordings. We vision that mining such visual log
could be useful for bug reproducing and debugging, automated GUI testing, user
interface designing, question answering of common usages in software support,
etc. Toward that vision, we propose a core framework for mining visual log of
software. This framework focuses on detecting GUI elements and changes in
visual log, removing users' private data, recognizing user interactions with
GUI elements, and learning GUI usage patterns. We also performed a small study
on the characteristics of GUI elements in mobile apps. The findings from this
study suggested several heuristics to design techniques for recognizing GUI
elements and interactions.


title:
Ground state energy of the $\delta$-Bose and Fermi gas at weak coupling
  from double extrapolation

abstract:
  We consider the ground state energy of the Lieb-Liniger gas with $\delta$
interaction in the weak coupling regime $\gamma\to0$. For bosons with repulsive
interaction, previous studies gave the expansion
$e_{\text{B}}(\gamma)\simeq\gamma-4\gamma^{3/2}/3\pi+(1/6-1/\pi^{2})\gamma^{2}$.
Using a numerical solution of the Lieb-Liniger integral equation discretized
with $M$ points and finite strength $\gamma$ of the interaction, we obtain very
accurate numerics for the next orders after extrapolation on $M$ and $\gamma$.
The coefficient of $\gamma^{5/2}$ in the expansion is found approximately equal
to $-0.00158769986550594498929$, accurate within all digits shown. This value
is supported by a numerical solution of the Bethe equations with $N$ particles
followed by extrapolation on $N$ and $\gamma$. It was identified as
$(3\zeta(3)/8-1/2)/\pi^{3}$ by G. Lang. The next two coefficients are also
guessed from numerics. For balanced spin $1/2$ fermions with attractive
interaction, the best result so far for the ground state energy was
$e_{\text{F}}(\gamma)\simeq\pi^{2}/12-\gamma/2+\gamma^{2}/6$. An analogue
double extrapolation scheme leads to the value $-\zeta(3)/\pi^{4}$ for the
coefficient of $\gamma^{3}$.


title: Lattice points counting and bounds on periods of Maass forms

abstract:
  We provide a "soft" proof for non-trivial bounds on spherical, hyperbolic and
unipotent Fourier coefficients of a fixed Maass form for a general co-finite
lattice $\Gamma$ in $PGL(2,R)$. We use the amplification method based on the
Airy type phenomenon for corresponding matrix coefficients and an effective
Selberg type pointwise asymptotic for the lattice points counting in various
homogeneous spaces for $PGL(2,R)$.


title: Ex Machina: Personal Attacks Seen at Scale

abstract:
  The damage personal attacks cause to online discourse motivates many
platforms to try to curb the phenomenon. However, understanding the prevalence
and impact of personal attacks in online platforms at scale remains
surprisingly difficult. The contribution of this paper is to develop and
illustrate a method that combines crowdsourcing and machine learning to analyze
personal attacks at scale. We show an evaluation method for a classifier in
terms of the aggregated number of crowd-workers it can approximate. We apply
our methodology to English Wikipedia, generating a corpus of over 100k high
quality human-labeled comments and 63M machine-labeled ones from a classifier
that is as good as the aggregate of 3 crowd-workers, as measured by the area
under the ROC curve and Spearman correlation. Using this corpus of
machine-labeled scores, our methodology allows us to explore some of the open
questions about the nature of online personal attacks. This reveals that the
majority of personal attacks on Wikipedia are not the result of a few malicious
users, nor primarily the consequence of allowing anonymous contributions from
unregistered users.


title:
Comparison of the dislocation density obtained by HR-EBSD and X-ray
  profile analysis

abstract:
  Based on the cross correlation analysis of the Kikuchi diffraction patterns
high-resolution EBSD is a well established method to determine the internal
stress in deformed crystalline materials. In many cases, however, the stress
values obtained at the different scanning points have a large (in the order of
GPa) scatter. As it was first demonstrated by Wilkinson and co-workers this is
due to the long tail of the probability distribution of the internal stress
($P(\sigma)$) generated by the dislocations present in the system. According to
the theoretical investigations of Groma and co-workers the tail of $P(\sigma)$
is inverse cubic with prefactor proportional to the total dislocation density
$<\rho>$. In this paper we present a direct comparison of the X-ray line
broadening and $P(\sigma)$ obtained by EBSD on deformed Cu single crystals. It
is shown that $<\rho>$ can be determined from $P(\sigma)$. This opens new
perspectives for the application of EBSD in determining mesoscale parameters in
a heterogeneous sample.


title:
Preheating after multifield inflation with nonminimal couplings, III:
  Dynamical spacetime results

abstract:
  This paper concludes our semi-analytic study of preheating in inflationary
models comprised of multiple scalar fields coupled nonminimally to gravity.
Using the covariant framework of paper I in this series, we extend the
rigid-spacetime results of paper II by considering both the expansion of the
universe during preheating, as well as the effect of the coupled metric
perturbations on particle production. The adiabatic and isocurvature
perturbations are governed by different effective masses that scale differently
with the nonminimal couplings and evolve differently in time. The effective
mass for the adiabatic modes is dominated by contributions from the coupled
metric perturbations immediately after inflation. The metric perturbations
contribute an oscillating tachyonic term that enhances an early period of
significant particle production for the adiabatic modes, which ceases on a
time-scale governed by the nonminimal couplings $\xi_I$. The effective mass of
the isocurvature perturbations, on the other hand, is dominated by
contributions from the fields' potential and from the curvature of the
field-space manifold (in the Einstein frame), the balance between which shifts
on a time-scale governed by $\xi_I$. As in papers I and II, we identify
distinct behavior depending on whether the nonminimal couplings are small
($\xi_I \lesssim {\cal O} (1)$), intermediate ($\xi_I \sim {\cal O} (1 - 10)$),
or large ($\xi_I \geq 100$).


title: Supersymmetric SYK models

abstract:
  We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model.
These are quantum mechanical models involving $N$ Majorana fermions. The
supercharge is given by a polynomial expression in terms of the Majorana
fermions with random coefficients. The Hamiltonian is the square of the
supercharge. The ${\cal N}=1$ model with a single supercharge has unbroken
supersymmetry at large $N$, but non-perturbatively spontaneously broken
supersymmetry in the exact theory. We analyze the model by looking at the large
$N$ equation, and also by performing numerical computations for small values of
$N$. We also compute the large $N$ spectrum of "singlet" operators, where we
find a structure qualitatively similar to the ordinary SYK model. We also
discuss an ${\cal N}=2$ version. In this case, the model preserves
supersymmetry in the exact theory and we can compute a suitably weighted Witten
index to count the number of ground states, which agrees with the large $N$
computation of the entropy. In both cases, we discuss the supersymmetric
generalizations of the Schwarzian action which give the dominant effects at low
energies.


title:
Income and wealth distribution of the richest Norwegian individuals: An
  inequality analysis

abstract:
  Using the empirical data from the Norwegian tax office, we analyse the wealth
and income of the richest individuals in Norway during the period 2010--2013.
We find that both annual income and wealth level of the richest individuals are
describable using the Pareto law. We find that the robust mean Pareto exponent
over the four-year period to be $\approx 2.3$ for income and $\approx 1.5$ for
wealth.


title:
Exotic domain walls in Bose-Einstein condensates with double-well
  dispersion

abstract:
  We study the domain walls which form when Bose condensates acquire a
double-well dispersion. Experiments have observed such domain walls in
condensates driven across a $\mathbb{Z}_2$ symmetry-breaking phase transition
in a shaken optical lattice. We derive a generic model to describe the
dispersion and to compute the wavefunctions and energies of the domain walls.
We find two distinct regimes which demand different physical pictures. In the
weak coupling regime, where interactions are weak compared to the kinetic
energy barrier, "density wave domain walls" form that support an extended
density wave and a series of phase steps. These features can be understood as
the quantum interference between domains with distinct momenta. In the strong
coupling regime where interaction dominates, the system forms "phase domain
walls" which have the minimum width allowed by the uncertainty principle and
suppressed density modulation. Analytic results for the domain wall
wavefunctions are obtained in the two regimes. The energy of domain walls
behaves similarly to that of topological defects in paradigmatic field
theories.


title:
Determination of the Walk Dimension of the Sierpi\'nski Gasket Without
  Using Diffusion

abstract:
  We determine the walk dimension of the Sierpi\'nski gasket without using
diffusion. We construct non-local regular Dirichlet forms on the Sierpi\'nski
gasket from regular Dirichlet forms on the Sierpi\'nski graph whose suitable
boundary is the Sierpi\'nski gasket.


title: Theory of earthquakes interevent times applied to financial markets

abstract:
  We analyze the probability density function (PDF) of waiting times between
financial loss exceedances. The empirical PDFs are fitted with the self-excited
Hawkes conditional Poisson process with a long power law memory kernel. The
Hawkes process is the simplest extension of the Poisson process that takes into
account how past events influence the occurrence of future events. By analyzing
the empirical data for 15 different financial assets, we show that the
formalism of the Hawkes process used for earthquakes can successfully model the
PDF of interevent times between successive market losses.


title: Electron Ion Collider: Physics and Prospects

abstract:
  We give an outline of the anticipated physics program for a future electron
ion collider. The status and prospects for construction of such a device are
discussed.


title:
Rank bounds for design matrices with block entries and geometric
  applications

abstract:
  Design matrices are sparse matrices in which the supports of different
columns intersect in a few positions. Such matrices come up naturally when
studying problems involving point sets with many collinear triples. In this
work we consider design matrices with block (or matrix) entries. Our main
result is a lower bound on the rank of such matrices, extending the bounds
proved in {BDWY12,DSW12} for the scalar case. As a result we obtain several
applications in combinatorial geometry. The first application involves
extending the notion of structural rigidity (or graph rigidity) to the setting
where we wish to bound the number of `degrees of freedom' in perturbing a set
of points under collinearity constraints (keeping some family of triples
collinear). Other applications are an asymptotically tight Sylvester-Gallai
type result for arrangements of subspaces (improving {DH16}) and a new
incidence bound for high dimensional line/curve arrangements.
  The main technical tool in the proof of the rank bound is an extension of the
technique of matrix scaling to the setting of block matrices. We generalize the
definition of doubly stochastic matrices to matrices with block entries and
derive sufficient conditions for a doubly stochastic scaling to exist.


title: Linear Inviscid Damping for Couette Flow in Stratified Fluid

abstract:
  We study the inviscid damping of Couette flow with an exponentially
stratified density. The optimal decay rates of the velocity field and the
density are obtained for general perturbations with minimal regularity. For
Boussinesq approximation model, the decay rates we get are consistent with the
previous results in the literature. We also study the decay rates for the full
Euler equations of stratified fluids, which were not studied before. For both
models, the decay rates depend on the Richardson number in a very similar way.
Besides, we also study the dispersive decay due to the exponential
stratification when there is no shear.


title:
An improved bound for quantum speed limit time in open quantum systems
  by introducing an alternative fidelity

abstract:
  In this paper, we introduce a new alternative quantum fidelity for quantum
states which perfectly satisfies all Jozsas axioms and is zero for orthogonal
states. By employing this fidelity, we derive an improved bound for quantum
speed limit time in open quantum systems in which the initial states can be
chosen as either pure or mixed. This bound leads to the well-known
Mandelstamm-Tamm type bound for nonunitary dynamics in the case of initial pure
states. However, in the case of initial mixed states, the bound provided by the
introduced fidelity is tighter and sharper than the obtained bounds in the
previous works.


title: An alternative Explanation for the Fermi GeV Gamma-Ray Excess

abstract:
  The "GeV-excess" of the diffuse gamma-rays in the halo is studied with a
template fit based on energy spectra for each possible process of gamma-ray
emission. Such a fit allows to determine the background and signal
simultaneously, so the Galactic Disk can be included in the analysis. We find
evidence that the "excess", characterised by a gamma-ray spectrum peaking at 2
GeV, is much stronger in Molecular Clouds in the disk than the "GeV-excess"
observed up to now in the halo. The possible reason why the emissivity of
Molecular Clouds peaks at 2 GeV are the energy losses and magnetic cutoffs
inside MCs, thus depleting the low energy part of the CR spectra and shifting
the maximum of the gamma-ray spectra to higher energies. This peaking of the
emissivity in Molecular Clouds at 2 GeV was clearly observed from the spectrum
of the Central Molecular Zone, which dominates the emission in the inner few
degrees of the Galactic Centre.
  Although the spectrum of the Central Molecular Zone peaks at 2 GeV, it cannot
be responsible for the "GeV-excess" observed in the halo, since the latitude
extension of the Zone is below $\rm |b|<0.5^\circ$. However, lines-of-sight
into the halo cross Molecular Clouds in the disk, so the emissivity of clouds
in the disk will be observed in the halo as an apparent "GeV-excess". The fact,
that this "GeV-excess" has the same morphology in the disk {\it and} in the
halo as the column density of Molecular Clouds, as traced by the CO map from
the Planck satellite resembling an NFW-like latitude profile, and the fact the
MCs have an emissivity peaking at 2 GeV shows that the "GeV-excess" originates
from Molecular Clouds in the disk, not from a process surrounding the Galactic
Centre.


title: Voice Conversion using Convolutional Neural Networks

abstract:
  The human auditory system is able to distinguish the vocal source of
thousands of speakers, yet not much is known about what features the auditory
system uses to do this. Fourier Transforms are capable of capturing the pitch
and harmonic structure of the speaker but this alone proves insufficient at
identifying speakers uniquely. The remaining structure, often referred to as
timbre, is critical to identifying speakers but we understood little about it.
In this paper we use recent advances in neural networks in order to manipulate
the voice of one speaker into another by transforming not only the pitch of the
speaker, but the timbre. We review generative models built with neural networks
as well as architectures for creating neural networks that learn analogies. Our
preliminary results converting voices from one speaker to another are
encouraging.


title:
Rapid Posterior Exploration in Bayesian Non-negative Matrix
  Factorization

abstract:
  Non-negative Matrix Factorization (NMF) is a popular tool for data
exploration. Bayesian NMF promises to also characterize uncertainty in the
factorization. Unfortunately, current inference approaches such as MCMC mix
slowly and tend to get stuck on single modes. We introduce a novel approach
using rapidly-exploring random trees (RRTs) to asymptotically cover regions of
high posterior density. These are placed in a principled Bayesian framework via
an online extension to nonparametric variational inference. On experiments on
real and synthetic data, we obtain greater coverage of the posterior and higher
ELBO values than standard NMF inference approaches.


title: Locally Adaptive Confidence Bands

abstract:
  We develop honest and locally adaptive confidence bands for probability
densities. They provide substantially improved confidence statements in case of
inhomogeneous smoothness, and are easily implemented and visualized. The
article contributes conceptual work on locally adaptive inference as a
straightforward modification of the global setting imposes severe obstacles for
statistical purposes. Among others, we introduce a statistical notion of local
H\"older regularity and prove a correspondingly strong version of local
adaptivity. We substantially relax the straightforward localization of the
self-similarity condition in order not to rule out prototypical densities. The
set of densities permanently excluded from the consideration is shown to be
pathological in a mathematically rigorous sense. On a technical level, the
crucial component for the verification of honesty is the identification of an
asymptotically least favorable stationary case by means of Slepian's comparison
inequality.


title:
Groomed jets in heavy-ion collisions: sensitivity to medium-induced
  bremsstrahlung

abstract:
  We argue that contemporary jet substructure techniques might facilitate a
more direct measurement of hard medium-induced gluon bremsstrahlung in
heavy-ion collisions, and focus specifically on the "soft drop declustering"
procedure that singles out the two leading jet substructures. Assuming coherent
jet energy loss, we find an enhancement of the distribution of the energy
fractions shared by the two substructures at small subjet energy caused by hard
medium-induced gluon radiation. Departures from this approximation are
discussed, in particular, the effects of colour decoherence and the
contamination of the grooming procedure by soft background. Finally, we propose
a complementary observable, that is the ratio of the two-pronged probability in
Pb-Pb to proton-proton collisions and discuss its sensitivity to various energy
loss mechanisms.


title: Absence of Many-Body Localization in a Single Landau Level

abstract:
  The dynamics of the highly excited states of a system projected into a single
Landau level are analyzed. An analysis of level spacing ratios for finite size
systems shows a clear crossover from extend (GUE) to localized (Poisson)
statistics, indicating a many body localization transition. However, the
location of this transition depends very strongly on system size, and appears
to scale to infinite disorder in the thermodynamic limit. This result does not
depend on the properties of the ground state (such as whether the ground state
exhibits topological order), as expected for a transition of highly-excited
eigenstates. We therefore conclude that many body localization does not exist
in these systems. Our results demonstrate that a sub-thermodynamic number of
single particle effectively extended states is sufficient to cause all many
body states to become extended.


title: On the number and boundedness of log minimal models of general type

abstract:
  We show that the number of marked minimal models of an n-dimensional smooth
complex projective variety of general type can be bounded in terms of its
volume, and, if n=3, also in terms of its Betti numbers. For an n-dimensional
projective klt pair (X,D) with $K_X+D$ big, we show more generally that the
number of its weak log canonical models can be bounded in terms of the
coefficients of D and the volume of $K_X+D$. We further show that all
n-dimensional projective klt pairs (X,D), such that $K_X+D$ is big and nef of
fixed volume and such that the coefficients of D are contained in a given DCC
set, form a bounded family. It follows that in any dimension, minimal models of
general type and bounded volume form a bounded family.


title: Asymptotic behavior of flows by powers of the Gaussian curvature

abstract:
  We consider a one-parameter family of strictly convex hypersurfaces in
$\mathbb{R}^{n+1}$ moving with speed $- K^\alpha \nu$, where $\nu$ denotes the
outward-pointing unit normal vector and $\alpha \geq \frac{1}{n+2}$. For
$\alpha > \frac{1}{n+2}$, we show that the flow converges to a round sphere
after rescaling. In the affine invariant case $\alpha=\frac{1}{n+2}$, our
arguments give an alternative proof of the fact that the flow converges to an
ellipsoid after rescaling.


title:
On the junction physics of Schottky contact of (10, 10) MX2 (MoS2, WS2)
  nanotube and (10, 10) carbon nanotube (CNT): an atomistic study

abstract:
  Armchair nanotubes of MoS2 and WS2 offer a sizeable band gap, with the
advantage of a one dimensional (1D) electronic material, but free from edge
roughness and thermodynamic instability of nanoribbons. Use of such
semiconducting MX2 (MoS2, WS2) armchair nanotubes (NTs) in conjunction with
metallic carbon nanotubes (CNT) could prove useful for nanoelectronics and
photonics applications. In this work atomistic simulations of MoS2 NT-CNT and
WS2 NT-CNT junctions are carried out to study the physics of such junctions.
With density functional theory (DFT) we study the carrier density distribution,
effective potential, electron difference density, electron localization
function, electrostatic difference potential and projected local density of
states of such MX2 NT-CNT 1D junctions. Thereafter the conductance of such a
junction under moderate bias is studied with non-equilibrium Greens function
(NEGF) method. From the forward bias characteristics simulated from NEGF, we
extract diode parameters of the junction. The electrostatic simulations from
DFT show the formation of an inhomogeneous Schottky barrier with a tendency
towards charge transfer from metal and chalcogen atoms towards the C atoms. For
low bias conditions, the ideality factor was calculated to be 1.1322 for MoS2
NT-CNT junction and 1.2526 for the WS2 NT-CNT junction. The Schottky barrier
heights displayed significant bias dependent modulation and are calculated to
be in the range 0.697 - 0.664eV for MoS2 NT-CNT and 0.669-0.610 eV for the WS2
NT-CNT respectively.


title:
ANI-1: An extensible neural network potential with DFT accuracy at force
  field computational cost

abstract:
  Deep learning is revolutionizing many areas of science and technology,
especially image, text and speech recognition. In this paper, we demonstrate
how a deep neural network (NN) trained on quantum mechanical (QM) DFT
calculations can learn an accurate and fully transferable potential for organic
molecules. We introduce ANAKIN-ME (Accurate NeurAl networK engINe for Molecular
Energies) or ANI in short. ANI is a new method and procedure for training
neural network potentials that utilizes a highly modified version of the Behler
and Parrinello symmetry functions to build single-atom atomic environment
vectors as a molecular representation. We utilize ANI to build a potential
called ANI-1, which was trained on a subset of the GDB databases with up to 8
heavy atoms to predict total energies for organic molecules containing four
atom types: H, C, N, and O. To obtain an accelerated but physically relevant
sampling of molecular potential surfaces, we also propose a Normal Mode
Sampling (NMS) method for generating molecular configurations. Through a series
of case studies, we show that ANI-1 is chemically accurate compared to
reference DFT calculations on much larger molecular systems (up to 54 atoms)
than those included in the training data set, with root mean square errors as
low as 0.56 kcal/mol.


title: Learning Scalable Deep Kernels with Recurrent Structure

abstract:
  Many applications in speech, robotics, finance, and biology deal with
sequential data, where ordering matters and recurrent structures are common.
However, this structure cannot be easily captured by standard kernel functions.
To model such structure, we propose expressive closed-form kernel functions for
Gaussian processes. The resulting model, GP-LSTM, fully encapsulates the
inductive biases of long short-term memory (LSTM) recurrent networks, while
retaining the non-parametric probabilistic advantages of Gaussian processes. We
learn the properties of the proposed kernels by optimizing the Gaussian process
marginal likelihood using a new provably convergent semi-stochastic gradient
procedure and exploit the structure of these kernels for scalable training and
prediction. This approach provides a practical representation for Bayesian
LSTMs. We demonstrate state-of-the-art performance on several benchmarks, and
thoroughly investigate a consequential autonomous driving application, where
the predictive uncertainties provided by GP-LSTM are uniquely valuable.


title:
(Re)solving Mysteries of Convection and Mass Loss of AGB Stars: What New
  Models and Observations Tell Us About Long-Standing Problems

abstract:
  The recent progress in high-spatial-resolution techniques, spanning
wavelengths from the visual to the radio regime, is leading to new valuable
insights into the complex dynamical atmospheres of Asymptotic Giant Branch
(AGB) stars and their wind forming regions. Striking examples are images of
asymmetries and inhomogeneities in the photospheric and dust-forming layers
which vary on time-scales of months. These features are probably related to
large-scale convective flows predicted by 3D star-in-a-box models. Furthermore,
high-resolution observations make it possible to measure dust condensation
distances, and they give information about the chemical composition and sizes
of dust grains in the close vicinity of cool giants. These are essential
constraints for building realistic models of wind acceleration and developing a
predictive theory of mass loss for AGB stars, which is a crucial ingredient of
stellar and galactic chemical evolution models.


title:
Perturbations d'exemples de Latt\`es et dimension de Hausdorff du lieu
  de bifurcation

abstract:
  We give an estimate for the Hausdorff dimension of the bifurcation locus of a
family of endomorphisms of $\mathbb{P}^k (\mathbb{C})$. This dimension is
maximal near isolated Latt\`es examples.


title: Three radial gaps in the disk of TW Hydrae imaged with SPHERE

abstract:
  We present scattered light images of the TW Hya disk performed with SPHERE in
PDI mode at 0.63, 0.79, 1.24 and 1.62 micron. We also present H2/H3-band ADI
observations. Three distinct radial depressions in the polarized intensity
distribution are seen, around 85, 21, and 6~au. The overall intensity
distribution has a high degree of azimuthal symmetry; the disk is somewhat
brighter than average towards the South and darker towards the North-West. The
ADI observations yielded no signifiant detection of point sources in the disk.
  Our observations have a linear spatial resolution of 1 to 2au, similar to
that of recent ALMA dust continuum observations. The sub-micron sized dust
grains that dominate the light scattering in the disk surface are strongly
coupled to the gas. We created a radiative transfer disk model with
self-consistent temperature and vertical structure iteration and including
grain size-dependent dust settling. This method may provide independent
constraints on the gas distribution at higher spatial resolution than is
feasible with ALMA gas line observations.
  We find that the gas surface density in the "gaps" is reduced by 50% to 80%
relative to an unperturbed model. Should embedded planets be responsible for
carving the gaps then their masses are at most a few 10 Mearth. The observed
gaps are wider, with shallower flanks, than expected for planet-disk
interaction with such low-mass planets. If forming planetary bodies have
undergone collapse and are in the "detachted phase" then they may be directly
observable with future facilities such as METIS at the E-ELT.


title:
Vortex-antivortex proliferation from an obstacle in thin film
  ferromagnets

abstract:
  Magnetization dynamics in thin film ferromagnets can be studied using a
dispersive hydrodynamic formulation. The equations describing the
magnetodynamics map to a compressible fluid with broken Galilean invariance
parametrized by the longitudinal spin density and a magnetic analog of the
fluid velocity that define spin-density waves. A direct consequence of these
equations is the determination of a magnetic Mach number. Micromagnetic
simulations reveal nucleation of nonlinear structures from an impenetrable
object realized by an applied magnetic field spot or a defect. In this work,
micromagnetic simulations demonstrate vortex-antivortex pair nucleation from an
obstacle. Their interaction establishes either ordered or irregular
vortex-antivortex complexes. Furthermore, when the magnetic Mach number exceeds
unity (supersonic flow), a Mach cone and periodic wavefronts are observed,
which can be well-described by solutions of the steady, linearized equations.
These results are reminiscent of theoretical and experimental observations in
Bose-Einstein condensates, and further supports the analogy between the
magnetodynamics of a thin film ferromagnet and compressible fluids. The
nucleation of nonlinear structures and vortex-antivortex complexes using this
approach enables the study of their interactions and effects on the stability
of spin-density waves.


title:
Robust manipulation of light using topologically protected plasmonic
  modes

abstract:
  We propose a topological plasmonic crystal structure composed of an array of
parallel nanowires with unequal spacing. In the paraxial approximation, the
Helmholtz equation that describes the propagation of light along the nanowires
maps onto the Schr\"{o}dinger equation of the Su-Schrieffer-Heeger (SSH) model.
Using full three-dimensional finite difference time domain solution of the
Maxwell equations we demonstrate the existence of topological defect modes,
with sub-wavelength localization, bound to kinks of the plasmonic crystal.
Furthermore, we show that by manipulating kinks we can construct spatial mode
filters, that couple bulk modes to topological defect modes, and topological
beam-splitters that couple two topological defect modes. Finally, we show that
the structures are robust to fabrication errors with inverse length-scale
smaller than the topological band gap.


title:
Lifetime and mass of rho meson in correlation with magnetic-dimensional
  reduction

abstract:
  It is simply anticipated that in a strong magnetic configuration, the Landau
quantization ceases the neutral rho meson to decay to the charged pion pair, so
the neutral rho meson will be long-lived. To closely access this naive
observation, we explicitly compute the charged pion-loop in the magnetic field
at the one-loop level, to evaluate the magnetic dependence of the lifetime for
the neutral rho meson as well as its mass.Due to the dimensional reduction
induced by the magnetic field (violation of the Lorentz invariance), the
polarization (spin $s_z=-1,0,+1$) modes of the rho meson, as well as the
corresponding pole mass and width, are decomposed in a nontrivial manner
compared to the vacuum case. To see the significance of the reduction effect,
we simply take the lowest-Landau level approximation to analyze the
spin-dependent rho masses and widths. We find that the "fate" of the rho meson
may be more complicated because of the magnetic-dimensional reduction: as the
magnetic field increases, the rho width for the spin $s_z=0$ starts to develop,
reach a peak, to be vanishing at the critical magnetic field to which the
folklore refers. On the other side, the decay rates of the other rhos for
$s_z=-1,+1$ monotonically increase as the magnetic field develops. The
correlation between the polarization dependence and the Landau-level truncation
is also addressed.


title: Partial Regularity for Symmetric-Convex Functionals of Linear Growth

abstract:
  We establish partial regularity of BD-minima for variational integrals of
linear growth which depend on the symmetric gradients and satisfy a weak
ellipticity condition. Since there is no Korn Inequality in the $L^{1}$-Setup,
the result does not follow from the respective result on BV due to Anzellotti
and Giaquinta.


title:
Discovery and Modeling of a Flattening of the Positive Cyclotron
  Line/Luminosity Relation in GX 304-1 with RXTE

abstract:
  The RXTE observed four outbursts of the accreting X-ray binary transient
source, GX 304-1 in 2010 and 2011. We present results of detailed 3-100 keV
spectral analysis of 69 separate observations, and report a positive
correlation between cyclotron line parameters, as well as other spectral
parameters, with power law flux. The cyclotron line energy, width and depth
versus flux, and thus luminosity, correlations show a flattening of the
relationships with increasing luminosity, which are well described by
quasi-spherical or disk accretion that yield the surface magnetic field to be
~60 keV. Since HEXTE cluster A was fixed aligned with the PCA field of view and
cluster B was fixed viewing a background region 1.5 degrees off of the source
direction during these observations near the end of the RXTE mission, the
cluster A background was estimated from cluster B events using HEXTEBACKEST.
This made possible the detection of the ~55 keV cyclotron line and an accurate
measurement of the continuum. Correlations of all spectral parameters with the
primary 2-10 keV power law flux reveal it to be the primary driver of the
spectral shape. The accretion is found to be in the collisionless shock braking
regime.


title: Constructing MASAs with prescribed properties

abstract:
  We consider an iterative procedure for constructing maximal abelian
$^*$-subalgebras (MASAs) satisfying prescribed properties in II$_1$ factors.
This method pairs well with the intertwining by bimodules technique and with
properties of the MASA and of the ambient factor that can be described locally.
We obtain such a local characterization for II$_1$ factors $M$ that have an
{\it s-MASA}, $A\subset M$ (i.e., for which $A \vee JAJ$ is maximal abelian in
$\Cal B(L^2M)$), and use this strategy to prove that any factor in this class
has uncountably many non-intertwinable singular (respectively semiregular)
s-MASAs.


title: Symmetric-Convex Functionals of Linear Growth

abstract:
  We give a survey of results regarding existence and regularity for autonomous
functionals of linear growth that depend on the symmetric rather than the full
gradients.


title: Affine cubic surfaces and character varieties of knots

abstract:
  It is known that the fundamental group homomorphism $\pi_1(T^2) \to
\pi_1(S^3\setminus K)$ induced by the inclusion of the boundary torus into the
complement of a knot $K$ in $S^3$ is a complete knot invariant. Many classical
invariants of knots arise from the natural (restriction) map induced by the
above homomorphism on the $\mathrm{SL}_2$-character varieties of the
corresponding fundamental groups. In our earlier work [BS16], we proposed a
conjecture that the classical restriction map admits a canonical 2-parameter
deformation into a smooth cubic surface. In this paper, we show that (modulo
some mild technical conditions) our conjecture follows from a known conjecture
of Brumfiel and Hilden [BH95] on the algebraic structure of the peripheral
system of a knot. We then confirm the Brumfiel-Hilden conjecture for an
infinite class of knots, including all torus knots, 2-bridge knots, and certain
pretzel knots. We also show the class of knots for which the Brumfiel-Hilden
conjecture holds is closed under taking connect sums and certain knot
coverings.


title: A Galaxy-Halo Model for Multiple Cosmological Tracers

abstract:
  The information extracted from large galaxy surveys with the likes of DES,
DESI, Euclid, LSST, SKA, and WFIRST will be greatly enhanced if the resultant
galaxy catalogues can be cross-correlated with one another. Predicting the
nature of the information gain, and developing the tools to realise it, depends
on establishing a consistent model of how the galaxies detected by each survey
trace the same underlying matter distribution. Existing analytic methods, such
as halo occupation distribution (HOD) modelling, are not well-suited for this
task, and can suffer from ambiguities and tuning issues when applied to
multiple tracers. In this paper, we take the first steps towards constructing
an alternative that provides a common model for the connection between galaxies
and dark matter halos across a wide range of wavelengths (and thus tracer
populations). This is based on a chain of parametrised statistical
distributions that model the connection between (a) halo mass and bulk physical
properties of galaxies, such as star-formation rate; and (b) those same
physical properties and a variety of emission processes. The result is a
flexible parametric model that allows analytic halo model calculations of
1-point functions to be carried out for multiple tracers, as well as providing
semi-realistic galaxy properties for fast mock catalogue generation.


title: Cavity type problems ruled by infinity Laplacian operator

abstract:
  We study a singularly perturbed problem related to infinity Laplacian
operator with prescribed boundary values in a region. We prove that solutions
are locally (uniformly) Lipschitz continuous, they grow as a linear function,
are strongly non-degenerate and have porous level surfaces. Moreover, for some
restricted cases we show the finiteness of the (n-1)-dimensional Hausdorff
measure of level sets. The analysis of the asymptotic limits is carried out as
well.


title:
A Tunable Waveguide-Coupled Cavity Design for Efficient Spin-Photon
  Interfaces in Photonic Integrated Circuits

abstract:
  A solid state emitter coupled to a photonic crystal cavity exhibits increased
photon emission into a single frequency mode. However, current designs for
photonic crystal cavities coupled to quantum emitters have three main problems:
emitters are placed near surfaces that can degrade their optical properties,
the cavity fluorescence cannot be collected into a single useful mode for
further routing, and post-fabrication tuning is not currently possible in a
stable and reversible manner for each node individually. In this paper, we
introduce a hybrid cavity design with minimal fabrication of the host material
that keeps the emitter $\geq100\,$nm from all surfaces. This cavity has an
unloaded quality factor ($Q$) larger than $1\times10^6$ and a loaded $Q$ of
$5.5\times10^4$ with more than 75% of the emission coupled directly into an
underlying photonic integrated circuit built from a convenient material that
provides low loss waveguides. Finally this design can be actively and
reversibly tuned onto resonance with the emitter, allowing tuning over more
than 10 times the cavity linewidth while maintaining $\geq50$% of the $Q$
factor with no effects to other cavities on the same chip.


title:
Spin-one-half particles in strong electromagnetic fields: spin effects
  and radiation reaction

abstract:
  Various classical models of electrons including their spin degrees of freedom
are commonly applied to describe the electron dynamics in strong
electromagnetic fields. We demonstrate that different models can lead to
different or even contradicting predictions regarding how the spin degree of
freedom modifies the electron's orbital motion when the electron moves in
strong electromagnetic fields. This discrepancy is rooted in the model-specific
energy dependency of the spin-induced Stern-Gerlach force acting on the
electron. The Frenkel model and the classical Foldy-Wouthuysen model are
compared exemplarily in the nonrelativistic and the relativistic limits in
order to identify parameter regimes where these classical models make different
predictions. This allows for experimental tests of these models. In ultrastrong
laser setups in parameter regimes where effects of the Stern-Gerlach force
become relevant, radiation-reaction effects are also expected to set in. We
incorporate the radiation reaction classically via the Landau-Lifshitz equation
and demonstrate that although radiation-reaction effects can have a significant
effect on the electron trajectory, the Frenkel model and the classical
Foldy-Wouthuysen model remain distinguishable also if radiation-reaction
effects are taken into account. Our calculations are also suitable to verify
the Landau-Lifshitz equation for the radiation reaction of electrons and other
spin-1/2 particles.


title: Bulk fields from the boundary OPE

abstract:
  Previous work has established an equality between the geodesic integral of a
free bulk field in AdS and the contribution of the conformal descendants of its
dual CFT primary operator to the OPE of two other operators inserted at the
endpoints of the geodesic. Working in the context of the AdS$_3$/CFT$_2$
correspondence, we extend this relation to include the $1/N$ corrections to the
bulk field obtained by dressing it with i) a $U(1)$ current and ii) the CFT
stress tensor. In the former case, we argue that the contribution of the
Ka\v{c}-Moody descendants to the respective boundary OPE equals the geodesic
integral of a particular $U(1)$-dressed bulk field, which is framed to the
boundary via a split Wilson line. In the latter case, we compute the
gravitational $1/N$ corrections to the bulk field in various gauges, and then
write a CFT expression for a putative bulk field whose geodesic integral
captures the contribution of Virasoro descendants to the OPE of interest. We
comment on the bulk interpretation of this expression.


title: Einstein--Weyl Spaces and Near-Horizon Geometry

abstract:
  We show that a class of solutions of minimal supergravity in five dimensions
is given by lifts of three--dimensional Einstein--Weyl structures of hyper-CR
type. We characterise this class as most general near--horizon limits of
supersymmetric solutions to the five--dimensional theory. In particular, we
deduce that a compact spatial section of a horizon can only be a Berger sphere,
a product metric on $S^1\times S^2$ or a flat three-torus. We then consider the
problem of reconstructing all supersymmetric solutions from a given
near--horizon geometry. By exploiting the ellipticity of the linearised field
equations we demonstrate that the moduli space of transverse infinitesimal
deformations of a near--horizon geometry is finite--dimensional.


title:
Particle-number projection in the finite-temperature mean-field
  approximation

abstract:
  Calculation of statistical properties of nuclei in a finite-temperature
mean-field theory requires projection onto good particle number, since the
theory is formulated in the grand canonical ensemble. This projection is
usually carried out in a saddle-point approximation. Here we derive formulas
for an exact particle-number projection of the finite-temperature mean-field
solution. We consider both deformed nuclei, in which the pairing condensate is
weak and the Hartree-Fock (HF) approximation is the appropriate mean-field
theory, and nuclei with strong pairing condensates, in which the appropriate
theory is the Hartree-Fock-Bogoliubov (HFB) approximation, a method that
explicitly violates particle-number conservation. For the HFB approximation, we
present a general projection formula for a condensate that is time-reversal
invariant and a simpler formula for the Bardeen-Cooper-Schrieffer (BCS) limit,
which is realized in nuclei with spherical condensates. We apply the method to
three heavy nuclei: a typical deformed nucleus $^{162}$Dy, a typical spherical
nucleus $^{148}$Sm, and a transitional nucleus $^{150}$Sm in which the pairing
condensate is deformed. We compare the results of this projection with results
from the saddle-point approximation and exact shell model Monte Carlo
calculations. We find that the approximate canonical HF entropy in the
particle-number projection decreases monotonically to zero in the limit when
the temperature goes to zero. However, in a nucleus with a strong pairing
condensate, the approximate canonical HFB entropy in the particle-number
projection decreases monotonically to a negative value, reflecting the
violation of particle-number conservation. Computationally, the exact
particle-number projection is more efficient than calculating the derivatives
required in the saddle-point approximation.


title:
Singular solutions with vorticity control for a nonlocal system of
  evolution equations

abstract:
  We investigate a system of nonlocal transport equations in one spatial
dimension. The system can be regarded as a model for the 3D Euler equations in
the hyperbolic flow scenario. We construct blowup solutions with control up to
the blowup time.