title:
Large Unidirectional Magnetoresistance in a Magnetic Topological
  Insulator

abstract:
  We report current-direction dependent or unidirectional magnetoresistance
(UMR) in magnetic/nonmagnetic topological insulator (TI) heterostructures,
Cr$_x$(Bi$_{1-y}$Sb$_y$)$_{2-x}$Te$_3$/(Bi$_{1-y}$Sb$_y$)$_2$Te$_3$, that is
several orders of magnitude larger than in other reported systems. From the
magnetic field and temperature dependence, the UMR is identified to originate
from the asymmetric scattering of electrons by magnons. In particular, the
large magnitude of UMR is an outcome of spin-momentum locking and a small Fermi
wavenumber at the surface of TI. In fact, the UMR is maximized around the Dirac
point with the minimal Fermi wavenumber.


title:
Gluon fusion and $b\bar{b}$ corrections to $H W^+ W^- / H Z Z$
  production in the POWHEG-BOX

abstract:
  The study of the Higgs boson properties is one of the most important tasks to
be accomplished in the next years, at the Large Hadron Collider (LHC) and at
future colliders such as the Future Circular Collider in hadron-hadron mode
(FCC-hh), the potential 100 TeV follow-up of the LHC machine. In this view the
precise study of the Higgs couplings to weak gauge bosons is crucial and
requires as much information as possible. After the recent calculation of the
next-to-leading order QCD corrections to the production cross sections and
differential distributions of a Standard Model Higgs boson in association with
a pair of weak bosons, matched with parton shower in the POWHEG-BOX framework,
we present the gluon fusion correction $g g\to H W^+_{} W^-_{} ( H Z Z)$ to the
process $p p \to H W^+_{} W^-_{} (H Z Z)$. This correction can be sizeable and
amounts to $+3\,\%$ ($+10\,\%$) in the $H W^+_{} W^-_{}$ process and $+5\,\%$
($+18\,\%$) in the $H Z Z$ process at the LHC (FCC-hh). We also present the
first study of the impact of the bottom--quark initiated channels $b\bar{b}\to
H W^+_{} W^-_{} / H Z Z$ and find that they induce a significant $+18\,\%$
correction in the $H W^+_{} W^-_{}$ channel at the FCC-hh. We present results
on total cross sections and distributions at the LHC and at the FCC-hh.


title:
The effects of supernovae on the dynamical evolution of binary stars and
  star clusters

abstract:
  In this chapter I review the effects of supernovae explosions on the
dynamical evolution of (1) binary stars and (2) star clusters.
  (1) Supernovae in binaries can drastically alter the orbit of the system,
sometimes disrupting it entirely, and are thought to be partially responsible
for `runaway' massive stars - stars in the Galaxy with large peculiar
velocities. The ejection of the lower-mass secondary component of a binary
occurs often in the event of the more massive primary star exploding as a
supernova. The orbital properties of binaries that contain massive stars mean
that the observed velocities of runaway stars (10s - 100s km s$^{-1}$) are
consistent with this scenario.
  (2) Star formation is an inherently inefficient process, and much of the
potential in young star clusters remains in the form of gas. Supernovae can in
principle expel this gas, which would drastically alter the dynamics of the
cluster by unbinding the stars from the potential. However, recent numerical
simulations, and observational evidence that gas-free clusters are observed to
be bound, suggest that the effects of supernova explosions on the dynamics of
star clusters are likely to be minimal.


title: Barred galaxies in the EAGLE cosmological hydrodynamical simulation

abstract:
  We examine the properties of barred disc galaxies in a LCDM cosmological
hydrodynamical simulation from the EAGLE project. Our study follows the
formation of 269 discs identified at z = 0 in the stellar mass range 10.6 < log
Mstr /M < 11. These discs show a wide range of bar strengths, from unbarred
discs to weak bars to strongly barred systems (= 20%). Bars in these systems
develop after redshift = 1.3, on timescales that depend sen- sitively on the
strength of the pattern. Strong bars develop relatively quickly (in a few Gyr,
= 10 disc rotation periods) in systems that are disc dominated, gas poor, and
have declining rotation curves. Weak bars develop more slowly in systems where
the disc is less gravitation- ally important, and are still growing at z = 0.
Unbarred galaxies are comparatively gas-rich discs whose rotation speeds do not
exceed the maximum circular velocity of the halos they inhabit. Bar lengths
compare favourably with observations, ranging from 0.2 to 0.8 times the radius
containing 90% of the stars. Bars slow down remarkably quickly as they grow,
causing the inner regions of the surrounding dark halo to expand. At z = 0
strong bars have corota- tion radii roughly ten times the bar length. Such slow
bars are inconsistent with the few cases where pattern speeds have been
measured or inferred observationally, a discrepancy that, if confirmed, might
prove a challenge for disc galaxy formation in LCDM.


title:
Structure of the thermodynamic arrow of time in classical and quantum
  theories

abstract:
  In this work we analyse the structure of the thermodynamic arrow of time,
defined by transformations that leave the thermal equilibrium state unchanged,
in classical (incoherent) and quantum (coherent) regimes. We note that in the
infinite-temperature limit the thermodynamic ordering of states in both regimes
exhibits a lattice structure. This means that when energy does not matter and
the only thermodynamic resource is given by information, the thermodynamic
arrow of time has a very specific structure. Namely, for any two states at
present there exists a unique state in the past consistent with them and with
all possible joint pasts. Similarly, there also exists a unique state in the
future consistent with those states and with all possible joint futures. We
also show that the lattice structure in the classical regime is broken at
finite temperatures, i.e., when energy is a relevant thermodynamic resource.
Surprisingly, however, we prove that in the simplest quantum scenario of a
two-dimensional system, this structure is preserved at finite temperatures. We
provide the physical interpretation of these results by introducing and
analysing the history erasure process, and point out that quantum coherence may
be a necessary resource for the existence of an optimal erasure process.


title:
The link between turbulence, magnetic fields, filaments, and star
  formation in the Central Molecular Zone cloud G0.253+0.016

abstract:
  Star formation is primarily controlled by the interplay between gravity,
turbulence, and magnetic fields. However, the turbulence and magnetic fields in
molecular clouds near the Galactic Center may differ substantially from
spiral-arm clouds. Here we determine the physical parameters of the central
molecular zone (CMZ) cloud G0.253+0.016, its turbulence, magnetic field and
filamentary structure. Using column-density maps based on dust-continuum
emission observations with ALMA+Herschel, we identify filaments and show that
at least one dense core is located along them. We measure the filament width
W_fil=0.17$\pm$0.08pc and the sonic scale {\lambda}_sonic=0.15$\pm$0.11pc of
the turbulence, and find W_fil~{\lambda}_sonic. A strong velocity gradient is
seen in the HNCO intensity-weighted velocity maps obtained with ALMA+Mopra,
which is likely caused by large-scale shearing of G0.253+0.016, producing a
wide double-peaked velocity PDF. After subtracting the gradient to isolate the
turbulent motions, we find a nearly Gaussian velocity PDF typical for
turbulence. We measure the total and turbulent velocity dispersion,
8.8$\pm$0.2km/s and 3.9$\pm$0.1km/s, respectively. Using magnetohydrodynamical
simulations, we find that G0.253+0.016's turbulent magnetic field
B_turb=130$\pm$50$\mu$G is only ~1/10 of the ordered field component. Combining
these measurements, we reconstruct the dominant turbulence driving mode in
G0.253+0.016 and find a driving parameter b=0.22$\pm$0.12, indicating
solenoidal (divergence-free) driving. We compare this to spiral-arm clouds,
which typically have a significant compressive (curl-free) driving component
(b>0.4). Motivated by previous reports of strong shearing motions in the CMZ,
we speculate that shear causes the solenoidal driving in G0.253+0.016 and show
that this reduces the star formation rate (SFR) by a factor of 6.9 compared to
typical nearby clouds.


title:
Generalized Hill-Stability Criteria for Hierarchical Three-Body Systems
  at Arbitrary Inclinations

abstract:
  A fundamental aspect of the three-body problem is its stability. Most
stability studies have focused on the co-planar three-body problem, deriving
analytic criteria for the dynamical stability of such pro/retrograde systems.
Numerical studies of inclined systems phenomenologically mapped their stability
regions, but neither complement it by theoretical framework, nor provided
satisfactory fit for their dependence on mutual inclinations. Here we present a
novel approach to study the stability of hierarchical three-body systems at
arbitrary inclinations, which accounts not only for the instantaneous stability
of such systems, but also for the secular stability and evolution through
Lidov-Kozai cycles and evection. We generalize the Hill-stability criteria to
arbitrarily inclined triple systems, explain the existence of quasi-stable
regimes and characterize the inclination dependence of their stability. We
complement the analytic treatment with an extensive numerical study, to test
our analytic results. We find excellent correspondence up to high inclinations
$(\sim120^{\circ}$), beyond which the agreement is marginal. At such high
inclinations the stability radius is larger, the ratio between the outer and
inner periods becomes comparable, and our secular averaging approach is no
longer strictly valid. We therefore combine our analytic results with
polynomial fits to the numerical results to obtain a generalized stability
formula for triple systems at arbitrary inclinations. Besides providing a
generalized secular-based physical explanation for the stability of non
co-planar systems, our results have direct implications for any triple systems,
and in particular binary planets and moon/satellite systems; we briefly discuss
the latter as a test case for our models.


title:
Optical archival spectra of blazar candidates of uncertain type in the
  3$^{rd}$ Fermi Large Area Telescope Catalog

abstract:
  Despite the fact that blazars constitute the rarest class among active
galactic nuclei (AGNs) they are the largest known population of associated
$\gamma$-ray sources. Many of the $\gamma$-ray objects listed in the
Fermi-Large Area Telescope Third Source catalog (3FGL) are classified as blazar
candidates of uncertain type (BCUs), either because they show multifrequency
behaviour similar to blazars but lacking optical spectra in the literature, or
because the quality of such spectra is too low to confirm their nature. Here we
select, out of 585 BCUs in the 3FGL, 42 BCUs which we identify as probable
blazars by their WISE infrared colors and which also have optical spectra that
are available in the Sloan Digital Sky Survey (SDSS) and/or Six-Degree Field
Galaxy Survey Database (6dFGS). We confirm the blazar nature of all of the
sources. We furthermore conclude that 28 of them are BL Lacs, 8 are radio-loud
quasars with flat radio spectrum and 6 are BL Lac whose emission is dominated
by their host galaxy.


title: BPS relations from spectral problems and blowup equations

abstract:
  Recently an exact duality between topological string and the spectral theory
of operators constructed from mirror curves to toric Calabi-Yau threefolds has
been proposed. At the same time an exact quantization condition for the cluster
integrable systems associated to these geometries has been conjectured. The
consistency between the two approaches leads to an infinite set of constraints
for the refined BPS invariants of the toric Calabi-Yau threefolds. We prove
these constraints for the $Y^{N,m}$ geometries using the $K$-theoretic blowup
equations for $SU(N)$ SYM with generic Chern-Simons invariant $m$.


title:
Secular precessing compact binary dynamics, spin and orbital angular
  momentum flip-flops

abstract:
  We derive the conservative secular evolution of precessing compact binaries
to second post-Newtonian order accuracy, with leading-order spin-orbit,
spin-spin and mass quadrupole-monopole contributions included. The emerging
closed system of first-order differential equations evolves the pairs of polar
and azimuthal angles of the spin and orbital angular momentum vectors together
with the periastron angle. In contrast with the instantaneous dynamics, the
secular dynamics is autonomous. This secular dynamics reliably characterizes
the system over timescales starting from a few times the radial period to
several precessional periods, but less than the radiation reaction timescale.
We numerically compare the instantaneous and secular evolutions and estimate
the number of periods for which dissipation has no significant effect, e.g. the
conservative timescale. We apply the analytic equations to study the spin
flip-flop effect, recently found by numerical relativity methods. Our
investigations show that the effect does not generalize beyond its original
parameter settings, although we reveal distinct configurations exhibiting one
half flip-flops. In addition, we find a flip-flopping evolution of the orbital
angular momentum vector, which ventures from one pole to another through
several precessional periods. This is a new effect, occurring for mass ratios
much less than one.


title:
Illuminating Black Hole Binary Formation Channels with Spins in Advanced
  LIGO

abstract:
  The recent detections of the binary black hole mergers GW150914 and GW151226
have inaugurated the field of gravitational-wave astronomy. For the two main
formation channels that have been proposed for these sources, isolated binary
evolution in galactic fields and dynamical formation in dense star clusters,
the predicted masses and merger rates overlap significantly, complicating any
astrophysical claims that rely on measured masses alone. Here, we examine the
distribution of spin- orbit misalignments expected for binaries from the field
and from dense star clusters. Under standard assumptions for black-hole natal
kicks, we find that black-hole binaries similar to GW150914 could be formed
with significant spin-orbit misalignment only through dynamical processes. In
particular, these heavy-black-hole binaries can only form with a significant
spin-orbit anti-alignment in the dynamical channel. Our results suggest that
future detections of merging black hole binaries with measurable spins will
allow us to identify the main formation channel for these systems.


title: The Radial Acceleration Relation in Rotationally Supported Galaxies

abstract:
  We report a correlation between the radial acceleration traced by rotation
curves and that predicted by the observed distribution of baryons. The same
relation is followed by 2693 points in 153 galaxies with very different
morphologies, masses, sizes, and gas fractions. The correlation persists even
when dark matter dominates. Consequently, the dark matter contribution is fully
specified by that of the baryons. The observed scatter is small and largely
dominated by observational uncertainties. This radial acceleration relation is
tantamount to a natural law for rotating galaxies.


title:
SMASH 1: a very faint globular cluster disrupting in the outer reaches
  of the LMC?

abstract:
  We present the discovery of a very faint stellar system, SMASH 1, that is
potentially a satellite of the Large Magellanic Cloud. Found within the Survey
of the MAgellanic Stellar History (SMASH), SMASH 1 is a compact ($r_h =
9.1^{+5.9}_{-3.4}$ pc) and very low luminosity (M_V = -1.0 +/- 0.9,
$L_V=10^{2.3 +/- 0.4}$ Lsun) stellar system that is revealed by its sparsely
populated main sequence and a handful of red-giant-branch candidate member
stars. The photometric properties of these stars are compatible with a
metal-poor ([Fe/H]=-2.2) and old (13 Gyr) isochrone located at a distance
modulus of ~18.8, i.e. a distance of ~57 kpc. Situated at 11.3$^\circ$ from the
LMC in projection, its 3-dimensional distance from the Cloud is ~13 kpc,
consistent with a connection to the LMC, whose tidal radius is at least 16 kpc.
Although the nature of SMASH 1 remains uncertain, its compactness favors it
being a stellar cluster and hence dark-matter free. If this is the case, its
dynamical tidal radius is only <19 pc at this distance from the LMC, and
smaller than the system's extent on the sky. Its low luminosity and apparent
high ellipticity ($\epsilon=0.62^{+0.17}_{-0.21}$) with its major axis pointing
toward the LMC may well be the tell-tale sign of its imminent tidal demise.


title:
Buttiker Probe Based Modeling of TDDB: Application to Dielectric
  Breakdown in MTJs and MOS Devices

abstract:
  Dielectric layers are gradually being down-scaled in different electronic
devices like MOSFETs and Magnetic Tunnel Junctions (MTJ) with shrinking device
sizes. As a result, time dependent dielectric breakdown (TDDB) has become a
major issue in such devices. In this paper we propose a generalized way of
modeling the stress induced leakage current (SILC) and post breakdown current
(PBC) due to time dependent wear-out of the dielectric layer. We model the
traps formed in dielectric layer using Buttiker probe and incorporate the
Buttiker probe self-energies in standard self-consistent Non-Equilibrium Green
Function (NEGF) formalism in order to determine SILC and PBC. In addition, we
have shown the impact of break down in the dielectric layer on the spin current
and spin filtering characteristics of an MTJ. The proposed model is generic in
nature. It can be extended from MTJs and conventional CMOS technology to any
other devices with any type of single and multiple layers of dielectric
material(s).


title: Line Search For Generalized Alternating Projections

abstract:
  This paper is about line search for the generalized alternating projections
(GAP) method. This method is a generalization of the von Neumann alternating
projections method, where instead of performing alternating projections,
relaxed projections are alternated. The method can be interpreted as an
averaged iteration of a nonexpansive mapping. Therefore, a recently proposed
line search method for such algorithms is applicable to GAP. We evaluate this
line search and show situations when the line search can be performed with
little additional cost. We also present a variation of the basic line search
for GAP - the projected line search. We prove its convergence and show that the
line search condition is convex in the step length parameter. We show that
almost all convex optimization problems can be solved using this approach and
numerical results show superior performance with both the standard and the
projected line search, sometimes by several orders of magnitude, compared to
the nominal method.


title:
Guaranteed Model-Based Fault Detection in Cyber-Physical Systems: A
  Model Invalidation Approach

abstract:
  This paper presents a sound and complete fault detection approach for
cyber-physical systems represented by hidden-mode switched affine models with
time varying parametric uncertainty. The fault detection approach builds upon
techniques from model invalidation. In particular, a set-membership approach is
taken where the noisy input-output data is compared to the set of behaviors of
a nominal model. As we show, this set-membership check can be reduced to the
feasibility of a mixed-integer linear programming (MILP) problem, which can be
solved efficiently by leveraging the state-of-the-art MILP solvers. In the
second part of the paper, given a system model and a fault model, the concept
of T-detectability is introduced. If a pair of system and fault models
satisfies T-detectability property for a finite T, this allows the model
invalidation algorithm to be implemented in a receding horizon manner, without
compromising detection guarantees. In addition, the concept of
weak-detectability is introduced which extends the proposed approach to a more
expressive class of fault models that capture language constraints on the mode
sequences. Finally, the efficiency of the approach is illustrated with
numerical examples motivated by smart building radiant systems.


title: The RG-improved Twin Higgs effective potential at NNLL

abstract:
  We present the Renormalization Group improvement of the Twin Higgs effective
potential at cubic order in logarithmic accuracy. We first introduce a
model-independent low-energy effective Lagrangian that captures both the
pseudo-Nambu-Goldstone boson nature of the Higgs field and the twin light
degrees of freedom charged under a copy of the Standard Model. We then apply
the background field method to systematically re-sum all the one loop diagrams
contributing to the potential. We show how this technique can be efficient to
implicitly renormalize the higher-dimensional operators in the twin sector
without classifying all of them. A prediction for the Higgs mass in the Twin
Higgs model is derived and found to be of the order of $M_H \sim 120
~\text{GeV}$ with an ultraviolet cut-off $m_*\sim 10-20 ~\text{TeV}$.
Irrespective of any possible ultraviolet completion of the low-energy
Lagrangian, the infrared degrees of freedom alone are therefore enough to
account for the observed value of the Higgs mass through running effects.


title:
Astrometry with MCAO: HST-GeMS proper motions in the globular cluster
  NGC 6681

abstract:
  Aims: for the first time the astrometric capabilities of the Multi-Conjugate
Adaptive Optics (MCAO) facility GeMS with the GSAOI camera on Gemini-South are
tested to quantify the accuracy in determining stellar proper motions in the
Galactic globular cluster NGC 6681. Methods: proper motions from HST/ACS for a
sample of its stars are already available, and this allows us to construct a
distortion-free reference at the epoch of GeMS observations that is used to
measure and correct the temporally changing distortions for each GeMS exposure.
In this way, we are able to compare the corrected GeMS images with a
first-epoch of HST/ACS images to recover the relative proper motion of the
Sagittarius dwarf spheroidal galaxy with respect to NGC 6681. Results: we find
this to be (\mu_{\alpha}cos\delta, \mu_{\delta}) = (4.09,-3.41) mas/yr, which
matches previous HST/ACS measurements with a very good accuracy of 0.03 mas/yr
and with a comparable precision (r.m.s of 0.43 mas/yr). Conclusions: this study
successfully demonstrates that high-quality proper motions can be measured for
quite large fields of view (85 arcsec X 85 arcsec) with MCAO-assisted,
ground-based cameras and provides a first, successful test of the performances
of GeMS on multi-epoch data.


title: Equivalent Resistance from the Quantum to the Classical Transport Limit

abstract:
  We generalize the concept of equivalent resistance to the entire range from
coherent quantum to diffusive classical transport by introducing the notion of
transport equivalent networks. We show that this novel concept presents us with
a platform to simplify the structure of quantum networks while preserving their
global and local transport properties, even in the presence of electron-phonon
or electron-electron interactions. This allows us to describe the evolution of
equivalent quantum networks to equivalent classical resistor networks with
increasing interaction strength.


title:
Surgery for partially hyperbolic dynamical systems I. Blow-ups of
  invariant submanifolds

abstract:
  We suggest a method to construct new examples of partially hyperbolic
diffeomorphisms. We begin with a partially hyperbolic diffeomorphism $f\colon
M\to M$ which leaves invariant a submanifold $N\subset M$. We assume that $N$
is an Anosov submanifold for $f$, that is, the restriction $f|_N$ is an Anosov
diffeomorphism and the center distribution is transverse to $TN\subset TM$. By
replacing each point in $N$ with the projective space (real or complex) of
lines normal to $N$ we obtain the blow-up $\hat M$. Replacing $M$ with $\hat M$
amounts to a surgery on the neighborhood of $N$ which alters the topology of
the manifold. The diffeomorphism $f$ induces a canonical diffeomorphism $\hat
f\colon \hat M\to \hat M$. We prove that under certain assumptions on the local
dynamics of $f$ at $N$ the diffeomorphism $\hat f$ is also partially
hyperbolic. We also present some modifications such as the connected sum
construction which allows to "paste together" two partially hyperbolic
diffeomorphisms to obtain a new one. Finally, we present several examples to
which our results apply.


title:
Ising spin model using Spin-Hall Effect (SHE) induced magnetization
  reversal in Magnetic-Tunnel-Junction

abstract:
  Ising spin model is considered as an efficient computing method to solve
combinatorial optimization problems based on its natural tendency of
convergence towards low energy state. The underlying basic functions
facilitating the Ising model can be categorized into two parts, "Annealing and
Majority vote". In this paper, we propose an Ising cell based on Spin Hall
Effect (SHE) induced magnetization switching in a Magnetic Tunnel Junction
(MTJ). The stochasticity of our proposed Ising cell based on SHE induced MTJ
switching, can implement the natural annealing process by preventing the system
from being stuck in solutions with local minima. Further, by controlling the
current through the Heavy-Metal (HM) underlying the MTJ, we can mimic the
majority vote function which determines the next state of the individual spins.
By solving coupled \textit{Landau-Lifshitz-Gilbert} (LLG) equations, we
demonstrate that our Ising cell can be replicated to map certain combinatorial
problems. We present results for two representative problems - Maximum-cut and
Graph coloring - to illustrate the feasibility of the proposed device-circuit
configuration in solving combinatorial problems. Our proposed solution using a
Heavy Metal (HM) based MTJ device can be exploited to implement compact, fast,
and energy efficient Ising spin model.


title: Quasidecoupled state for dark matter in nonstandard thermal histories

abstract:
  Dark matter drops out of kinetic equilibrium with standard model particles
when the momentum-transfer rate equals the expansion rate. In a
radiation-dominated universe, this occurs at essentially the same time as dark
matter kinetically decouples from the plasma. Dark matter may also fall out of
kinetic equilibrium with standard model particles during an early
matter-dominated era (EMDE), which occurs when the energy content of the
Universe is dominated by either a decaying oscillating scalar field or a
semistable massive particle before big bang nucleosynthesis. Until now, it has
been assumed that kinetic decoupling during an EMDE happens similarly to the
way it does in a radiation-dominated era. We show that this is not the case. By
studying the evolution of the dark matter temperature, we establish a
quasidecoupled state for dark matter in an EMDE, during which the dark matter
temperature cools faster than the plasma temperature but slower than it would
cool if the dark matter were fully decoupled. The dark matter does not fully
decouple until the EMDE ends and the Universe becomes radiation dominated. We
also extend the criteria for quasidecoupling to other nonstandard thermal
histories and consider how quasidecoupling affects the free-streaming length of
dark matter.


title: The Symmetricity of Normal Modes in Symmetric Complexes

abstract:
  In this work, we look at the symmetry of normal modes in symmetric
structures, particularly structures with cyclic symmetry. We show that normal
modes of symmetric structures have different levels of symmetry, or
symmetricity. One novel theoretical result of this work is that, for a ring
structure with $m$ subunits, the symmetricity of the normal modes falls into
$m$ groups of equal size, with normal modes in each group having the same
symmetricity. The normal modes in each group can be computed separately, using
a much smaller amount of memory and time (up to $m^3$ less), thus making it
applicable to larger complexes. We show that normal modes with perfect symmetry
or anti-symmetry have no degeneracy while the rest of the modes have a
degeneracy of two. We show also how symmetry in normal modes correlates with
symmetry in structure. While a broken symmetry in structure generally leads to
a loss of symmetricity in symmetric normal modes, the symmetricity of some
symmetric normal modes is preserved even when symmetry in structure is broken.
This work suggests a deeper reason for the existence of symmetric complexes:
that they may be formed not only for structural purpose, but likely also for a
dynamical reason, that certain symmetry is needed by a given complex to obtain
certain symmetric motions that are functionally critical.


title:
Model reduction of cavity nonlinear optics for photonic logic: A
  quasi-principal components approach

abstract:
  Kerr nonlinear cavities displaying optical thresholding have been proposed
for the realization of ultra-low power photonic logic gates. In the ultra-low
photon number regime, corresponding to energy levels in the attojoule scale,
quantum input-output models become important to study the effect of unavoidable
quantum fluctuations on the performance of such logic gates. However, being a
quantum anharmonic oscillator, a Kerr-cavity has an infinite dimensional
Hilbert space spanned by the Fock states of the oscillator. This poses a
challenge to simulate and analyze photonic logic gates and circuits composed of
multiple Kerr nonlinearities. For simulation, the Hilbert of the oscillator is
typically truncated to the span of only a finite number of Fock states. This
paper develops a quasi-principal components approach to identify important
subspaces of a Kerr-cavity Hilbert space and exploits it to construct an
approximate reduced model of the Kerr-cavity on a smaller Hilbert space. Using
this approach, we find a reduced dimension model with a Hilbert space dimension
of 15 that can closely match the magnitudes of the mean transmitted and
reflected output fields of a conventional truncated Fock state model of
dimension 75, when driven by an input coherent field that switches between two
levels. For the same input, the reduced model also closely matches the
magnitudes of the mean output fields of Kerr-cavity-based AND and NOT gates and
a NAND latch obtained from simulation of the full 75 dimension model.


title:
A picture is worth a thousand words: an empirical study on the influence
  of content visibility on diffusion processes within a virtual world

abstract:
  Studying information diffusion and the spread of goods in the real world and
in many digital services can be extremely difficult since information about the
information flows is challenging to accurately track. How information spreads
has commonly been analysed from the perspective of homophily, social influence,
and initial seed selection. However, in virtual worlds and virtual economies,
the movements of information and goods can be precisely tracked. Therefore,
these environments create laboratories for the accurate study of information
diffusion characteristics that have been difficult to study in prior research.
In this paper, we study how content visibility as well as sender and receiver
characteristics, the relationship between them, and the types of multilayer
social network layers affect content absorption and diffusion in virtual world.
The results show that prior visibility of distributed content is the strongest
predictor of content adoption and its further spread across networks. Among
other analysed factors, the mechanics of diffusion, content quality, and
content adoption by users neighbours on the social activity layer had very
strong influences on the adoption of new content.


title: The Log Log Prior for the Frequency of Extraterrestrial Intelligences

abstract:
  It is unclear how frequently life and intelligence arise on planets. I
consider a Bayesian prior for the probability P(ETI) that intelligence evolves
at a suitable site, with weight distributed evenly over ln(1 - ln P(ETI)). This
log log prior can handle a very wide range of P(ETI) values, from 1 to
10^(-10^122), while remaining responsive to evidence about extraterrestrial
societies. It is motivated by our uncertainty in the number of conditions that
must be fulfilled for intelligence to arise, and it is related to
considerations of information, entropy, and state space dimensionality. After
setting a lower limit to P(ETI) from the number of possible genome sequences, I
calculate a Bayesian confidence of 18% that aliens exist within the observable
Universe. With different assumptions about the minimum P(ETI) and the number of
times intelligence can appear on a planet, this value falls between 1.4% and
47%. Overall, the prior leans towards our being isolated from extraterrestrial
intelligences, but indicates that we should not be confident of this
conclusion. I discuss the implications of the prior for the Search for
Extraterrestrial Intelligence, concluding that searches for interstellar probes
from nearby societies seem relatively effective. I also discuss the possibility
of very small probabilities allowed by the prior for the origin of life and the
Fermi Paradox, and note that similar priors might be constructed for
interesting complex phenomena in general.


title:
Semiclassical theory of nonlinear magneto-optical responses with
  applications to topological Dirac/Weyl semimetals

abstract:
  We study nonlinear magneto-optical responses of metals by a semiclassical
Boltzmann equation approach. We derive general formulas for linear and second
order nonlinear optical effects in the presence of magnetic fields that include
both Berry curvature and orbital magnetic moment. Applied to Weyl fermions, the
semiclassical approach (i) captures the directional anisotropy of linear
conductivity under magnetic field as a consequence of an anisotropic $B^2$
contribution, which may explain the low-field regime of recent experiments;
(ii) predicts strong second harmonic generation proportional to $B$ that is
enhanced as the Fermi energy approaches the Weyl point, leading to large
nonlinear Kerr rotation. Moreover, we show that the semiclassical formula for
the circular photogalvanic effect arising from the Berry curvature dipole is
reproduced by a full quantum calculation using a Floquet approach.


title: Complete waveform model for compact binaries on eccentric orbits

abstract:
  We present a time domain waveform model that describes the
inspiral-merger-ringdown (IMR) of compact binary systems whose components are
non-spinning, and which evolve on orbits with low to moderate eccentricity. The
inspiral evolution is described using third order post-Newtonian equations both
for the equations of motion of the binary, and its far-zone radiation field.
This latter component also includes instantaneous, tails and tails-of-tails
contributions, and a contribution due to non-linear memory. This framework
reduces to the post-Newtonian approximant TaylorT4 at third post-Newtonian
order in the zero eccentricity limit. To improve phase accuracy, we incorporate
higher-order post-Newtonian corrections for the energy flux of quasi-circular
binaries and gravitational self-force corrections to the binding energy of
compact binaries. This enhanced inspiral evolution prescription is combined
with an analytical prescription for the merger-ringdown evolution using a
catalog of numerical relativity simulations. This IMR waveform model reproduces
effective-one-body waveforms for systems with mass-ratios between 1 to 15 in
the zero eccentricity limit. Using a set of eccentric numerical relativity
simulations, not used during calibration, we show that our eccentric model
accurately reproduces the features of eccentric compact binary coalescence
throughout the merger. Using this model we show that the gravitational wave
transients GW150914 and GW151226 can be effectively recovered with template
banks of quasi-circular, spin-aligned waveforms if the eccentricity $e_0$ of
these systems when they enter the aLIGO band at a gravitational wave frequency
of 14 Hz satisfies $e_0^{\rm GW150914}\leq0.15$ and $e_0^{\rm
GW151226}\leq0.1$.


title:
A simple algorithm for sampling colourings of $G(n,d/n)$ up to Gibbs
  Uniqueness Threshold

abstract:
  Approximate random $k$-colouring of a graph $G$ is a well studied problem in
computer science and statistical physics. It amounts to constructing a
$k$-colouring of $G$ which is distributed close to {\em Gibbs distribution} in
polynomial time. Here, we deal with the problem when the underlying graph is an
instance of Erd\H{o}s-R\'enyi random graph $G(n,d/n)$, where $d$ is a
sufficiently large constant.
  We propose a novel efficient algorithm for approximate random $k$-colouring
$G(n,d/n)$ for any $k\geq (1+\epsilon)d$. To be more specific, with probability
at least $1-n^{-\Omega(1)}$ over the input instances $G(n,d/n)$ and for $k\geq
(1+\epsilon)d$, the algorithm returns a $k$-colouring which is distributed
within total variation distance $n^{-\Omega(1)}$ from the Gibbs distribution of
the input graph instance.
  The algorithm we propose is neither a MCMC one nor inspired by the message
passing algorithms proposed by statistical physicists. Roughly the idea is as
follows: Initially we remove sufficiently many edges of the input graph. This
results in a "simple graph" which can be $k$-coloured randomly efficiently. The
algorithm colours randomly this simple graph. Then it puts back the removed
edges one by one. Every time a new edge is put back the algorithm updates the
colouring of the graph so that the colouring remains random.
  The performance of the algorithm depends heavily on certain spatial
correlation decay properties of the Gibbs distribution.


title: Advances in All-Neural Speech Recognition

abstract:
  This paper advances the design of CTC-based all-neural (or end-to-end) speech
recognizers. We propose a novel symbol inventory, and a novel iterated-CTC
method in which a second system is used to transform a noisy initial output
into a cleaner version. We present a number of stabilization and initialization
methods we have found useful in training these networks. We evaluate our system
on the commonly used NIST 2000 conversational telephony test set, and
significantly exceed the previously published performance of similar systems,
both with and without the use of an external language model and decoding
technology.


title: Two limitations of our knowledge of quality

abstract:
  This article develops a quality notion that is complementary to the system
notion. As a major consequence, it becomes clear why quality can be measured
only to a certain extend based on the issues of validity and incompleteness.
First, there is an inherent conflict between the applicability and validity of
quality measures and second, quality considerations almost always refer to
high-dimensional spaces with only sparse knowledge also known as "curse of
dimensionality". The resulting gap of knowledge has to be filled by experienced
based heuristics. To deal with the curse of dimensionality, the heuristics of
categorizing qualities into strategic and necessary is proposed. Strategic
qualities provide contrast, while necessary qualities rather diminish contrast.
In an economic context the presence of strategic qualities motivate a
buy-decision and the absence of necessary qualities motivate a
don't-buy-decision.


title: Glue spin and helicity in proton from lattice QCD

abstract:
  We report the first lattice QCD calculation of the glue spin in the nucleon.
The lattice calculation is carried out with valence overlap fermions on 2+1
flavor DWF gauge configurations on four lattice spacings and four volumes
including an ensemble with physical values for the quark masses. The glue spin
$S_{G}$ in the Coulomb gauge in the $\overline{\text{MS}}$ scheme is obtained
with the 1-loop perturbative matching. We find the results fairly insensitive
to lattice spacing and quark masses. We also find that the proton momentum
dependence of $S_G$ in the range $0\leq |\vec{p}| < 1.5$ GeV is very mild, and
we determine it in the large momentum limit to be $S_{G}=0.251(47)(16)$ at the
physical pion mass in the $\overline{\text{MS}}$ scheme at $\mu^2=10$ GeV$^2$.
If the matching procedure in large momentum effective theory is neglected,
$S_G$ is equal to the glue helicity measured in high-energy scattering
experiments.


title:
Discrete self-similarity in interfacial hydrodynamics and the formation
  of iterated structures

abstract:
  The formation of iterated structures, such as satellite and sub-satellite
drops, filaments and bubbles, is a common feature in interfacial hydrodynamics.
Here we undertake a computational and theoretical study of their origin in the
case of thin films of viscous fluids that are destabilized by long-range
molecular or other forces. We demonstrate that iterated structures appear as a
consequence of discrete self-similarity, where certain patterns repeat
themselves, subject to rescaling, periodically in a logarithmic time scale. The
result is an infinite sequence of ridges and filaments with similarity
properties. The character of these discretely self-similar solutions as the
result of a Hopf bifurcation from ordinarily self-similar solutions is also
described.


title: Crises and Physical Phases of a Bipartite Market Model

abstract:
  We analyze the linear response of a market network to shocks based on the
bipartite market model we introduced in an earlier paper, which we claimed to
be able to identify the time-line of the 2009-2011 Eurozone crisis correctly.
We show that this model has three distinct phases that can broadly be
categorized as "stable" and "unstable". Based on the interpretation of our
behavioral parameters, the stable phase describes periods where investors and
traders have confidence in the market (e.g. predict that the market rebounds
from a loss). We show that the unstable phase happens when there is a lack of
confidence and seems to describe "boom-bust" periods in which changes in prices
are exponential. We analytically derive these phases and where the phase
transition happens using a mean field approximation of the model. We show that
the condition for stability is $\alpha \beta <1$ with $\alpha$ being the
inverse of the "price elasticity" and $\beta$ the "income elasticity of
demand", which measures how rash the investors make decisions. We also show
that in the mean-field limit this model reduces to the Langevin model by
Bouchaud et al. for price returns.


title: An Accurate Flux Density Scale from 50 MHz to 50 GHz

abstract:
  The flux density scale of Perley and Butler (2013) is extended downwards to
~50 MHz by utilizing recent observations with the Karl G. Jansky Very Large
Array (VLA) of 20 sources between 220 MHz and 48.1 GHz, and legacy VLA
observations at 73.8 MHz. The derived spectral flux densities are placed on an
absolute scale by utilizing the Baars et al. (1977) values of Cygnus A (3C405)
for frequencies below 2 GHz, and the Mars-based polynomials for 3C286, 3C295,
and 3C196 from Perley and Butler (2013) above 2 GHz. Polynomial expressions are
presented for all 20 sources, with accuracy limited by the primary standards to
3 -- 5% over the entire frequency range. Corrections to the scales proposed by
Perley and Butler (2013) and by Scaife and Heald (2012) are given.


title:
The Herschel Virgo Cluster Survey. XX. Dust and gas in the foreground
  Galactic cirrus

abstract:
  We study the correlation between far-infared/submm dust emission and atomic
gas column density in order to derive the properties of the high Galactic
latitude, low density, Milky Way cirrus in the foreground of the Virgo cluster
of galaxies. Dust emission maps from 60 to 850 um are obtained from SPIRE
observations carried out within the Herschel Virgo Cluster Survey, complemented
by IRAS-IRIS and Planck-HFI maps. Data from the Arecibo legacy Fast ALFA Survey
is used to derive atomic gas column densities for two broad velocity
components, low and intermediate velocity clouds. Dust emissivities are derived
for each gas component and each far-infared/submm band. For the low velocity
clouds, we measure an average emissivity 0.79 +/- 0.08 times 1E-20 MJy sr^-1
cm^2 at 250 um. After fitting a modified blackbody to the available bands, we
estimated a dust absorption cross-section 0.49 +/- 0.13 times 1E-25 cm^2 H^-1
at 250 um (with dust temperature T = 20.4 +/- 1.5 K and spectral index beta =
1.53 +/- 0.17). The results are in excellent agreement with those obtained by
Planck over a much larger coverage of the high Galactic latitude cirrus (50% of
the sky vs 0.2% in our work). For dust associated with intermediate velocity
gas, we confirm earlier Planck results and find a higher temperature and lower
emissivity and cross-section. After subtracting the modelled components, we
find regions at scales smaller than 20' where the residuals deviate
significantly from the average, cosmic-infrared-background dominated, scatter.
These large residuals are most likely due to local variations in the cirrus
dust properties (and/or the dust/atomic-gas correlation) or to high-latitude
molecular clouds with average N_H2 <~ 1E20 cm^-2. We find no conclusive
evidence for intracluster dust emission in Virgo.


title:
On the relative power of reduction notions in arithmetic circuit
  complexity

abstract:
  We show that the two main reduction notions in arithmetic circuit complexity,
p-projections and c-reductions, differ in power. We do so by showing
unconditionally that there are polynomials that are VNP-complete under
c-reductions but not under p-projections. We also show that the question of
which polynomials are VNP-complete under which type of reductions depends on
the underlying field.


title:
Entropy methods and convergence to equilibrium for volume-surface
  reaction-diffusion systems

abstract:
  We consider two volume-surface reaction-diffusion systems arising from cell
biology. The first system describes the localisation of the protein Lgl in the
asymmetric division of Drosophila SOP stem cells, while the second system
models the JAK2/STAT5 signalling pathway. Both model systems have in common
that i) different species are located in different spatial compartments, ii)
the involved chemical reaction kinetics between the species satisfies a complex
balance condition and iii) that the associated complex balance equilibrium is
spatially inhomogeneous. By using recent advances on the entropy method for
complex balanced reaction-diffusion systems, we show for both systems
exponential convergence to the equilibrium with constants and rates, which can
be explicitly estimated.


title: On the Convex Geometry of Weighted Nuclear Norm Minimization

abstract:
  Low-rank matrix approximation, which aims to construct a low-rank matrix from
an observation, has received much attention recently. An efficient method to
solve this problem is to convert the problem of rank minimization into a
nuclear norm minimization problem. However, soft-thresholding of singular
values leads to the elimination of important information about the sensed
matrix. Weighted nuclear norm minimization (WNNM) has been proposed, where the
singular values are assigned different weights, in order to treat singular
values differently. In this paper the solution for WNNM is analyzed under a
particular weighting condition using the connection between convex geometry and
compressed sensing algorithms. It is shown that the WNNM is convex where the
weights are in non-descending order and there is a unique global minimizer for
the minimization problem.


title: On the invariance of the total Monge-Ampere volume of Hermitian metrics

abstract:
  In this note, we describe the Hermitian metrics that leave the total
Monge-Ampere volume invariant. In particular, we give several characterizations
of the Hermitian metrics which satisfy the comparison principle for the complex
Monge-Ampere operator


title: Generic Multilinear Multipliers Associated to Degenerate Simplexes

abstract:
  For each $1 \leq p \leq \infty$, let $W_{p}(\mathbb{R}) = \left\{ f \in
L^p(\mathbb{R}): \hat{f} \in L^{p^\prime}(\mathbb{R}) \right\}$ with norm
$||f||_{W_{p}(\mathbb{R})} = ||\hat{f}||_{L^{p^\prime}(\mathbb{R})}$. Moreover,
let $ \Gamma = \left\{ \xi_1 + \xi_2 =0\right\} \subset \mathbb{R}^2$ and
$a_1,a_2 : \mathbb{R}^2 \rightarrow \mathbb{C}$ satisfy the
H\"{o}rmander-Mikhlin condition
  \begin{eqnarray*}
  \left| \partial^{\vec{\alpha}} a_j \left(\vec{\xi}\right) \right|
\lesssim_{\vec{\alpha}} \frac{1}{dist(\vec{\xi},
\Gamma)^{|\vec{\alpha}|}}~~~\forall \vec{\xi} \in \mathbb{R}^2, j \in \{1, 2\}
  \end{eqnarray*} for sufficiently many multi-indices $\vec{\alpha} \in
(\mathbb{N} \bigcup \{0\})^2$. Our main result is that the generic degenerate
trilinear simplex multiplier defined on $ \mathcal{S}^3(\mathbb{R})$ by
  \begin{eqnarray*}
  B[a_1, a_2] : (f_1, f_2, f_3) \rightarrow \int_{\mathbb{R}^3} a_1(\xi_1,
\xi_2) a_2(\xi_2, \xi_3) \left[ \prod_{j=1}^3 \hat{f_j} (\xi_j) e^{2 \pi ix
\xi_j} \right] d\xi_1 d\xi_2 d\xi_3
  \end{eqnarray*} extends to a map $L^{p_1}(\mathbb{R}) \times
W_{p_2}(\mathbb{R}) \times L^{p_3}(\mathbb{R}) \rightarrow
L^{\frac{1}{\frac{1}{p_1} + \frac{1}{p _2} +\frac{1}{p_3}}}(\mathbb{R})$
provided
  \begin{eqnarray*} 1 < p_1, p_3 \leq \infty, \frac{1}{p_1} + \frac{1}{p_2} <1,
\frac{1}{p_2} + \frac{1}{p_3} <1, 2 < p_2 <\infty.
  \end{eqnarray*}


title:
Investigation of Dependence between Time-zero and Time-dependent
  Variability in High-k NMOS Transistors

abstract:
  Bias Temperature Instability (BTI) is a major reliability concern in CMOS
technology, especially with High dielectric constant (High-\k{appa}/HK) metal
gate (MG) transistors. In addition, the time independent process induced
variation has also increased because of the aggressive scaling down of devices.
As a result, the faster devices at the lower threshold voltage distribution
tail experience higher stress, leading to additional skewness in the BTI
degradation. Since time dependent dielectric breakdown (TDDB) and
stress-induced leakage current (SILC) in NMOS devices are correlated to BTI, it
is necessary to investigate the effect of time zero variability on all these
effects simultaneously. To that effect, we propose a simulation framework to
model and analyze the impact of time-zero variability (in particular, random
dopant fluctuations) on different aging effects. For small area devices (~1000
nm2) in 30nm technology, we observe significant effect of Random Dopant
Fluctuation (RDF) on BTI induced variability ({\sigma}{\Delta}Vth). In
addition, the circuit analysis reveals similar trend on the performance
degradation. However, both TDDB and SILC show weak dependence on RDF. We
conclude that the effect of RDF on Vth degradation cannot be disregarded in
scaled technology and needs to be considered for variation tolerant circuit
design.


title: A non grid-based interpolation scheme for the eigenvalue problem

abstract:
  We propose a non grid-based interpolation scheme based on the information
from the data collected from the vicinity of the query point. As a
non-grid-based interpolation, the data points can be distributed randomly in a
small region, and the interpolation is constructed so that it naturally makes
use of the information not only on the function value but also on its higher
order derivatives. The main advantage of the present approach is that the
precision of the interpolation can be adjusted in accordance to the quantity of
the data, in other words, a balance between the precision and the computational
cost can be achieved by properly choosing the size of the neighborhood where
the data points are collected. The method is applicable to univariate as well
as multivariate functions. We show that the proposed scheme is efficient and
precise. The present approach is then employed to study the eigenvalue problem.


title:
Composite-boson approach to molecular Bose-Einstein condensates in
  mixtures of ultracold Fermi gases

abstract:
  We show that an ansatz based on independent composite bosons [Phys. Rep. 463,
215 (2008)] accurately describes the condensate fraction of molecular
Bose-Einstein condensates in ultracold Fermi gases. The entanglement between
the fermionic constituents of a single Feshbach molecule then governs the
many-particle statistics of the condensate, from the limit of strong
interaction to close to unitarity. This result strengthens the role of
entanglement as the indispensable driver of composite-boson behavior. The
condensate fraction of fermion pairs at zero temperature that we compute
matches excellently previous results obtained by means of fixed-node diffusion
Monte Carlo methods and the Bogoliubov depletion approximation. This paves the
way towards the exploration of the BEC-BCS crossover physics in mixtures of
cold Fermi gases with an arbitrary number of fermion pairs as well as the
implementation of Hong-Ou-Mandel-like interference experiments proposed within
coboson theory.


title:
Arithmetic Properties of Integers in Chains and Reflections of $g$-ary
  Expansions

abstract:
  Recently, there has been a sharp rise of interest in properties of digits
primes. Here we study yet another question of this kind. Namely, we fix an
integer base $g \ge 2$ and then for every infinite sequence $${\mathcal D} =
\{d_i\}_{i=0}^\infty \in \{0, \ldots, g-1\}^\infty $$ of $g$-ary digits we
consider the counting function $\varpi_{{\mathcal D},g}(N)$ of integers $n \le
N$ for which $\sum_{i=0}^{n-1} d_i g^i$ is prime.
  We construct sequences ${\mathcal D}$ for which $\varpi_{{\mathcal D},g}(N)$
grows fast enough, and show that for some constant $\vartheta_g< g$ there are
at most $O(\vartheta_g^N)$ initial elements $(d_0, \ldots, d_{N-1})$ of
${\mathcal D}$ for which $\varpi_{{\mathcal D},g}(N)=N+O(1)$. We also discuss
joint arithmetic properties of integers and mirror reflections of their $g$-ary
expansions.


title: Ramsey growth in some NIP structures

abstract:
  We investigate bounds in Ramsey's theorem for relations definable in NIP
structures. Applying model-theoretic methods to finitary combinatorics, we
generalize a theorem of Bukh and Matousek [B. Bukh, J. Matou\v{s}ek.
"Erd\H{o}s-Szekeres-type statements: Ramsey function and decidability in
dimension $1$", Duke Mathematical Journal 163.12 (2014): 2243-2270] from the
semialgebraic case to arbitrary polynomially bounded $o$-minimal expansions of
$\mathbb{R}$, and show that it doesn't hold in $\mathbb{R}_{\exp}$. This
provides a new combinatorial characterization of polynomial boundedness for
$o$-minimal structures. We also prove an analog for relations definable in
$P$-minimal structures, in particular for the field of the $p$-adics.
Generalizing [D. Conlon, J. Fox, J. Pach, B. Sudakov, A. Suk "Ramsey-type
results for semi-algebraic relations", Transactions of the American
Mathematical Society 366.9 (2014): 5043-5065], we show that in distal
structures the upper bound for $k$-ary definable relations is given by the
exponential tower of height $k-1$.


title:
Window Parity Games: An Alternative Approach Toward Parity Games with
  Time Bounds (Full Version)

abstract:
  Classical objectives in two-player zero-sum games played on graphs often deal
with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in
the quantitative setting, or parity in the qualitative one (a canonical way to
encode omega-regular properties). Those objectives offer powerful abstraction
mechanisms and often yield nice properties such as memoryless determinacy.
However, their very nature provides no guarantee on time bounds within which
something good can be witnessed. In this work, we consider two approaches
toward inclusion of time bounds in parity games. The first one, parity-response
games, is based on the notion of finitary parity games [CHH09] and parity games
with costs [FZ14,WZ16]. The second one, window parity games, is inspired by
window mean-payoff games [CDRR15]. We compare the two approaches and show that
while they prove to be equivalent in some contexts, window parity games offer a
more tractable alternative when the time bound is given as a parameter (P-c.
vs. PSPACE-C.). In particular, it provides a conservative approximation of
parity games computable in polynomial time. Furthermore, we extend both
approaches to the multi-dimension setting. We give the full picture for both
types of games with regard to complexity and memory bounds.
  [CHH09] K. Chatterjee, T.A. Henzinger, F. Horn (2009): Finitary winning in
omega-regular games. ACM Trans. Comput. Log. 11(1). [FZ14] N. Fijalkow, M.
Zimmermann (2014): Parity and Streett Games with Costs. LMCS 10(2). [WZ16] A.
Weinert, M. Zimmermann (2016): Easy to Win, Hard to Master: Optimal Strategies
in Parity Games with Costs. Proc. of CSL, LIPIcs 62, pp. 31:1-31:17, Schloss
Dagstuhl - LZI. [CDRR15] K. Chatterjee, L. Doyen, M. Randour, J.-F. Raskin
(2015): Looking at mean-payoff and total-payoff through windows. Information
and Computation 242, pp. 25-52.


title:
Superconductivity and spin-orbit coupling in non-centrosymmetric
  materials: a review

abstract:
  In non-centrosymmetric superconductors, where the crystal structure lacks a
centre of inversion, parity is no longer a good quantum number and an
electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by
symmetry. If this ASOC is sufficiently large, it has profound consequences on
the superconducting state. For example, it generally leads to a superconducting
pairing state which is a mixture of spin-singlet and spin-triplet components.
The possibility of such novel pairing states, as well as the potential for
observing a variety of unusual behaviours, led to intensive theoretical and
experimental investigations. Here we review the experimental and theoretical
results for superconducting systems lacking inversion symmetry. Firstly we give
a conceptual overview of the key theoretical results. We then review the
experimental properties of both strongly and weakly correlated bulk materials,
as well as two dimensional systems. Here the focus is on evaluating the effect
of ASOC on the superconducting properties and the extent to which there is
evidence for singlet-triplet mixing. This is followed by a more detailed
overview of theoretical aspects of non-centrosymmetric superconductivity. This
includes the effects of the ASOC on the pairing symmetry and the
superconducting magnetic response, magneto-electric effects, superconducting
finite momentum pairing states, and the potential of non-centrosymmetric
superconductors to display topological superconductivity.


title: Unboundedness Theorems for Symbols Adapted to Large Subspaces

abstract:
  For every integer $n \geq 3$, we prove that the n-sublinear generalization of
the Bi-Carleson operator of Muscalu, Tao, and Thiele given by nC^{\vec{\alpha}}
:(f_1,..., f_n) \mapsto \sup_{M} \left| \int_{\vec{\xi} \cdot \vec{\alpha} >0,
\xi_n < M} \left[\prod_{j=1}^n \hat{f}_j(\xi_j) e^{2 \pi i x \xi_j
}\right]d\vec{\xi} ~\right|satisfies no $L^p$ estimates provided $\vec{\alpha}
\in \mathbb{Q}^n$ with distinct, non-zero entries. Furthermore, if $n \geq 5$
and $\vec{\alpha} \in \mathbb{Q}^n$ has distinct, non-zero entries, it is shown
that there is a symbol $m:\mathbb{R}^n \rightarrow \mathbb{C}$ adapted to the
hyperplane $\Gamma^{\vec{a}}=\left\{ \vec{\xi} \in \mathbb{R}^n: \sum_{j=1}^n
\xi_j \cdot a_j =0 \right\} $ and supported in $\left\{ \vec{\xi} :
dist(\vec{\xi}, \Gamma^{\vec{\alpha}}) \lesssim 1 \right\}$ for which the
associated $n$-linear multiplier also satisfies no $L^p$ estimates. Next, we
construct a H\"{o}rmander-Marcinkiewicz symbol $\Pi: \mathbb{R}^2 \rightarrow
\mathbb{C}$, which is a paraproduct of $(\phi, \psi)$ type, such that the
trilinear operator $T_m$ whose symbol $m$ is $ sgn(\xi_1 + \xi_2) \Pi(\xi_2,
\xi_3)$ satisfies no $L^p$ estimates. Finally, we state a converse to a theorem
of Muscalu, Tao, and Thiele using Riesz kernels in the spirit of Muscalu's
recent work: for every pair of integers $(\mathfrak{d},n) $ s.t. $
\frac{n}{2}+\frac{3}{2} \leq \mathfrak{d}<n$ there is an explicit collection
$\mathfrak{C}$ of uncountably many $\mathfrak{d}$-dimensional non-degenerate
subspaces of $\mathbb{R}^n$ such that for each $\Gamma \in \mathcal{C}$ there
is an associated symbol $m_\Gamma$ adapted to $\Gamma$ in the
Mikhlin-H\"{o}rmander sense and supported in $\left\{ \vec{\xi} :
dist(\vec{\xi}, \Gamma) \lesssim 1 \right\}$ for which the associated
multilinear multiplier $T_{m_\Gamma}$ is unbounded.


title:
Ground states of a Bose-Einstein Condensate in a one-dimensional
  laser-assisted optical lattice

abstract:
  We study the ground-state behavior of a Bose-Einstein Condensate (BEC) in a
Raman-laser-assisted one-dimensional (1D) optical lattice potential forming a
multilayer system. We find that, such system can be described by an effective
model with spin-orbit coupling (SOC) of pseudospin $(N-1)/2$, where $N$ is the
number of layers. Due to the intricate interplay between atomic interactions,
SOC and laser-assisted tunnelings, the ground-state phase diagrams generally
consist of three phases -- a stripe, a plane wave and a normal phase with
zero-momentum, touching at a quantum tricritical point. More important, even
though the single-particle states only minimize at zero-momentum for odd $N$,
the many-body ground states may still develop finite momenta. The underlying
mechanisms are elucidated. Our results provide an alternative way to realize an
effective spin-orbit coupling of Bose gas with the Raman-laser-assisted optical
lattice, and would also be beneficial to the studies on SOC effects in spinor
Bose systems with large spin.


title:
Mixed Motives and Geometric Representation Theory in Equal
  Characteristic

abstract:
  Let $\mathbb{k}$ be a field of characteristic $p$. We introduce a formalism
of mixed sheaves with coefficients in $\mathbb{k}$ and showcase its use in
representation theory. More precisely, we construct for all quasi-projective
schemes $X$ over an algebraic closure of $\mathbb{F}_p$ a $\mathbb{k}$-linear
triangulated category of motives on $X$. Using work of Ayoub (2007),
Cisinski-Deglise (2012) and Geisser-Levine (2000), we show that this system of
categories has a six functors formalism and computes higher Chow groups.
Indeed, it behaves similarly to other categories of sheaves that one is used
to. We attempt to make its construction also accessible to non-experts. We then
consider the subcategory of stratified mixed Tate motives defined for affinely
stratified varieties $X$, discuss perverse and parity motives and prove
formality results. As an example, we combine these results and Soergel (2000)
to construct a geometric and graded version of Soergel's modular category
$\mathscr O(G)$, consisting of rational representations of a split semisimple
group $G/\mathbb{k}$, and thereby equip it with a full six functor formalism
(see Riche-Soergel-Williamson (2014) and Achar-Riche (2016) for other
approaches). The main idea of using motives in geometric representation theory
in this way as well as many results about stratified mixed Tate motives are
directly borrowed from Soergel and Wendt, who tell the story in characteristic
zero.


title:
Leggett-Garg test of superconducting qubit addressing the clumsiness
  loophole

abstract:
  The Leggett-Garg inequality holds for any macrorealistic system that is being
measured noninvasively. A violation of the inequality can signal that a system
does not conform to our primal intuition about the physical world.
Alternatively, a violation can simply indicate that "clumsy" experimental
technique led to invasive measurements. Here, we consider a recent Leggett-Garg
test designed to try to rule out the mundane second possibility. We tailor this
Leggett-Garg test to the IBM 5Q Quantum Experience system and find compelling
evidence that qubit $Q_2$ of the system cannot be described by noninvasive
macrorealism.


title: Rational curves on complete intersections in positive characteristic

abstract:
  We study properties of rational curves on complete intersections in positive
characteristic. It has long been known that in characteristic 0, smooth
Calabi-Yau and general type varieties are not uniruled. In positive
characteristic, however, there are well-known counterexamples to this
statement. We will show that nevertheless, a \emph{general} Calabi-Yau or
general type complete intersection in projective space is not uniruled. We will
also show that the space of complete intersections of degree $(d_1, \cdots,
d_k)$ containing a rational curve has codimension at least $\sum_{i=1}^k d_i -
2n + 2$ in the moduli space of all complete intersections of given multidegree
and dimension.


title: Conformalized Kernel Ridge Regression

abstract:
  General predictive models do not provide a measure of confidence in
predictions without Bayesian assumptions. A way to circumvent potential
restrictions is to use conformal methods for constructing non-parametric
confidence regions, that offer guarantees regarding validity. In this paper we
provide a detailed description of a computationally efficient conformal
procedure for Kernel Ridge Regression (KRR), and conduct a comparative
numerical study to see how well conformal regions perform against the Bayesian
confidence sets. The results suggest that conformalized KRR can yield
predictive confidence regions with specified coverage rate, which is essential
in constructing anomaly detection systems based on predictive models.


title:
Incremental Sampling-based Motion Planners Using Policy Iteration
  Methods

abstract:
  Recent progress in randomized motion planners has led to the development of a
new class of sampling-based algorithms that provide asymptotic optimality
guarantees, notably the RRT* and the PRM* algorithms. Careful analysis reveals
that the so-called "rewiring" step in these algorithms can be interpreted as a
local policy iteration (PI) step (i.e., a local policy evaluation step followed
by a local policy improvement step) so that asymptotically, as the number of
samples tend to infinity, both algorithms converge to the optimal path almost
surely (with probability 1). Policy iteration, along with value iteration (VI)
are common methods for solving dynamic programming (DP) problems. Based on this
observation, recently, the RRT$^{\#}$ algorithm has been proposed, which
performs, during each iteration, Bellman updates (aka "backups") on those
vertices of the graph that have the potential of being part of the optimal path
(i.e., the "promising" vertices). The RRT$^{\#}$ algorithm thus utilizes
dynamic programming ideas and implements them incrementally on randomly
generated graphs to obtain high quality solutions. In this work, and based on
this key insight, we explore a different class of dynamic programming
algorithms for solving shortest-path problems on random graphs generated by
iterative sampling methods. These class of algorithms utilize policy iteration
instead of value iteration, and thus are better suited for massive
parallelization. Contrary to the RRT* algorithm, the policy improvement during
the rewiring step is not performed only locally but rather on a set of vertices
that are classified as "promising" during the current iteration. This tends to
speed-up the whole process. The resulting algorithm, aptly named Policy
Iteration-RRT$^{\#}$ (PI-RRT$^{\#}$) is the first of a new class of DP-inspired
algorithms for randomized motion planning that utilize PI methods.


title: Optical trimer: A theoretical physics approach to waveguide couplers

abstract:
  We study electromagnetic field propagation through an ideal, passive,
triangular three-waveguide coupler using a symmetry based approach to take
advantage of the underlying $SU(3)$ symmetry. The planar version of this
platform has proven valuable in photonic circuit design providing optical
sampling, filtering, modulating, multiplexing, and switching. We show that a
group-theory approach can readily provide a starting point for design
optimization of the triangular version. Our analysis is presented as a
practical tutorial on the use of group theory to study photonic lattices for
those not familiar with abstract algebra methods. In particular, we study the
equilateral trimer to show the relation of pearl-necklace arrays with the
Discrete Fourier Transform due to their cyclic group symmetry, and the
isosceles trimer to show its relation with the golden ratio and its ability to
provide stable output at a single waveguide. We also study the propagation
dependent case of an equilateral trimer that linearly increases or decreases
its effective coupling with the propagation distance. For the sake of
completeness, we go beyond the standard optical-quantum analogy to show that it
is possible to derive coupled-mode equations for intensity and phase, and that
it is also possible to calculate envelopes for the propagation of all possible
inputs belonging to an energy class, as well as individual input field
amplitudes, without the need of point-to-point propagation.


title:
Katz Centrality of Markovian Temporal Networks: Analysis and
  Optimization

abstract:
  Identifying important nodes in complex networks is a fundamental problem in
network analysis. Although a plethora of measures has been proposed to identify
important nodes in static (i.e., time-invariant) networks, there is a lack of
tools in the context of temporal networks (i.e., networks whose connectivity
dynamically changes over time). The aim of this paper is to propose a
system-theoretic approach for identifying important nodes in temporal networks.
In this direction, we first propose a generalization of the popular Katz
centrality measure to the family of Markovian temporal networks using tools
from the theory of Markov jump linear systems. We then show that Katz
centrality in Markovian temporal networks can be efficiently computed using
linear programming. Finally, we propose a convex program for optimizing the
Katz centrality of a given node by tuning the weights of the temporal network
in a cost-efficient manner. Numerical simulations illustrate the effectiveness
of the obtained results.


title:
Scalar Quasinormal Modes of Anti-de Sitter Static Spacetime in
  Horava-Lifshitz Gravity with $U(1)$ Symmetry

abstract:
  In this paper, we investigate the scalar quasinormal modes of
Ho\v{r}ava-Lifshitz theory with $U(1)$ symmetry in static Anti-de Sitter
spacetime. The static planar and spherical black hole solutions in lower energy
limit are derived in non-projectable Ho\v{r}ava-Lifshitz gravity. The equation
of motion of a scalar field is obtained, and is utilized to study the
quasinormal modes of massless scalar particles. We find that the effect of
Ho\v{r}ava-Lifshitz correction is to increase the quasinormal period as well as
to slow down the decay of the oscillation magnitude. Besides, the scalar field
could be unstable when the correction becomes too large.


title: L^p Estimates for Semi-Degenerate Simplex Multipliers

abstract:
  Muscalu, Tao, and Thiele prove $L^p$ estimates for the "Biest" operator
defined on Schwartz functions by the map
  \begin{align*} \hspace{5mm} C^{1,1,1}:& (f_1, f_2, f_3) \mapsto \int_{\xi_1 <
\xi_2< \xi_3} \left[ \prod_{j=1}^3 \hat{f}_j (\xi_j) e^{2 \pi i x \xi_j }
\right] d \vec{\xi} \end{align*} via a time-frequency argument that produces
bounds for all multipliers with non-degenerate trilinear simplex symbols. In
this article we prove $L^p$ estimates for a pair of simplex multipliers for
which the non-degeneracy condition fails and which are defined on Schwartz
functions by the maps \begin{align*} C^{1,1,-2}:& (f_1, f_2, f_3) \mapsto
\int_{\xi_1 <\xi_2 < -\frac{\xi_3}{2}}\left[ \prod_{j=1}^3 \hat{f}_j (\xi_j)
e^{2 \pi i x \xi_j } \right] d \vec{\xi} \end{align*} \begin{align*}
C^{1,1,1,-2}:& (f_1, f_2, f_3, f_4) \mapsto \int_{\xi_1 <\xi_2 < \xi_3<
-\frac{\xi_4}{2}} \left[\prod_{j=1}^4 \hat{f}_j (\xi_j) e^{2 \pi i x \xi_j}
\right] d \vec{\xi}. \end{align*}
  Our argument combines the standard $\ell^2$-based energy with an
$\ell^1$-based energy in order to enable summability over various size
parameters. As a consequence, we obtain that $C^{1,1,-2}$ maps into $L^p$ for
all $1/2< p < \infty$ and $C^{1,1,1,-2}$ maps into $L^p$ for all $1/3 < p <
\infty$. Both target $L^p$ ranges are shown to be sharp.


title:
Dynamic behavior of the roots of the Taylor polynomials of the Riemann
  xi function with growing degree

abstract:
  We establish a uniform approximation result for the Taylor polynomials of the
xi function of Riemann which is valid in the entire complex plane as the degree
grows. In particular, we identify a domain growing with the degree of the
polynomials on which they converge to Riemann's xi function. Using this
approximation we obtain an estimate of the number of "spurious zeros" of the
Taylor polynomial which are outside of the critical strip, which leads to a
Riemann - von Mangoldt type of formula for the number of zeros of the Taylor
polynomials within the critical strip. Super-exponential convergence of Hurwitz
zeros of the Taylor polynomials to bounded zeros of the xi function are
established along the way, and finally we explain how our approximation
techniques can be extended to a collection of analytic L-functions.


title:
Extracting Flexibility of Heterogeneous Deferrable Loads via Polytopic
  Projection Approximation

abstract:
  Aggregation of a large number of responsive loads presents great power
flexibility for demand response. An effective control and coordination scheme
of flexible loads requires an accurate and tractable model that captures their
aggregate flexibility. This paper proposes a novel approach to extract the
aggregate flexibility of deferrable loads with heterogeneous parameters using
polytopic projection approximation. First, an exact characterization of their
aggregate flexibility is derived analytically, which in general contains
exponentially many inequality constraints with respect to the number of loads.
In order to have a tractable solution, we develop a numerical algorithm that
gives a sufficient approximation of the exact aggregate flexibility.
Geometrically, the flexibility of each individual load is a polytope, and their
aggregation is the Minkowski sum of these polytopes. Our method originates from
an alternative interpretation of the Minkowski sum as projection. The aggregate
flexibility can be viewed as the projection of a high-dimensional polytope onto
the subspace representing the aggregate power. We formulate a robust
optimization problem to optimally approximate the polytopic projection with
respect to the homothet of a given polytope. To enable efficient and parallel
computation of the aggregate flexibility for a large number of loads, a
muti-stage aggregation strategy is proposed. The scheduling policy for
individual loads is also derived. Finally, an energy arbitrage problem is
solved to demonstrate the effectiveness of the proposed method.


title:
It\^o's formula, the stochastic exponential and change of measure on
  general time scales

abstract:
  We provide an It\^{o}'s formula for stochastic dynamical equation on general
time scales. Based on this It\^{o}'s formula we give a closed form expression
for stochastic exponential on general time scales. We then demonstrate a
Girsanov's change of measure formula in the case of general time scales. Our
result is being applied to a Brownian motion on the quantum time scale (q-time
scale).


title: Chemical abundances of damped Lyman alpha systems in the XQ-100 survey

abstract:
  The XQ-100 survey has provided high signal-noise spectra of 100 redshift
3-4.5 quasars with the X-Shooter spectrograph. The metal abundances for 13
elements in the 41 damped Lyman alpha systems (DLAs) identified in the XQ-100
sample are presented, and an investigation into abundances of a variety of DLA
classes is conducted. The XQ-100 DLA sample contains five DLAs within 5000 km/s
of their host quasar (proximate DLAs; PDLAs) as well as three sightlines which
contain two DLAs within 10,000 km/s of each other along the same line-of-sight
(multiple DLAs; MDLAs). Combined with previous observations in the literature,
we demonstrate that PDLAs with logN(HI)<21.0 show lower [S/H] and [Fe/H]
(relative to intervening systems with similar redshift and N(HI)), whilst
higher [S/H] and [Si/H] are seen in PDLAs with logN(HI)>21.0. These abundance
discrepancies are independent of their line-of-sight velocity separation from
the host quasar, and the velocity width of the metal lines (v90). Contrary to
previous studies, MDLAs show no difference in [alpha/Fe] relative to single
DLAs matched in metallicity and redshift. In addition, we present follow-up
UVES data of J0034+1639, a sightline containing three DLAs, including a
metal-poor DLA with [Fe/H]=-2.82 (the third lowest [Fe/H] in DLAs identified to
date) at z=4.25. Lastly we study the dust-corrected [Zn/Fe], emphasizing that
near-IR coverage of X-Shooter provides unprecedented access to MgII, CaII and
TiII lines (at redshifts 3-4) to provide additional evidence for subsolar
[Zn/Fe] ratio in DLAs.


title:
The reproductive number of Zika in municipalities of Antioquia,
  Colombia: stratifying the potential transmission of an ongoing epidemic

abstract:
  Introduction: Zika epidemic in America was declared a public health emergency
of international concern after the rapid spread in the region. Stratification
of the potential transmission of the disease is needed to address the efforts
surveillance and disease control. The goal of this research is to compare the
basic reproductive number of Zika in different municipalities, from an SIR
model with implicit vector dynamics, based on the daily case reporting data of
Antioquia, Colombia, the second most affected country after Brazil. Methods: An
simple SIR model with implicit vector dynamics was derived and used. The
approximate solution of the model in terms of individuals recovered in each
time unit, allowed to obtain estimate of the model parameters including the
basic reproduction number (Ro) and its 95% confidence intervals. These
parameters were estimated via fitting the solution of the model to the daily
reported cumulative cases data from the regional surveillance system. Results:
Ro was estimated for 20 municipalities, all located at less than 2200 meters
above sea level. From January to April 2016, between 17 and 347 cases were
reported from these municipalities. Of these, 15 municipalities had a high
potential for transmission (Ro>1) and 5 had less potential (Ro<1), although in
3 of these, transmission was later possible because its upper confidence
interval of Ro was greater than one. Conclusion: Surveillance and control of
Zika should be directed primarily to municipalities with Ro>1. Furthermore,
strategies that will strengthen the detection and management of cases in the
remaining municipalities should be beneficial to the whole Antioquia region.


title:
Many-body topological invariants in fermionic symmetry protected
  topological phases: Cases of point group symmetries

abstract:
  We propose the definitions of many-body topological invariants to detect
symmetry-protected topological phases protected by point group symmetry, using
partial point group transformations on a given short-range entangled quantum
ground state. Partial point group transformations $g_D$ are defined by point
group transformations restricted to a spatial subregion $D$, which is closed
under the point group transformations and sufficiently larger than the bulk
correlation length $\xi$. By analytical and numerical calculations,we find that
the ground state expectation value of the partial point group transformations
behaves generically as $\langle GS | g_D | GS \rangle \sim \exp \Big[ i \theta+
\gamma - \alpha \frac{{\rm Area}(\partial D)}{\xi^{d-1}} \Big]$. Here, ${\rm
Area}(\partial D)$ is the area of the boundary of the subregion $D$, and
$\alpha$ is a dimensionless constant. The complex phase of the expectation
value $\theta$ is quantized and serves as the topological invariant, and
$\gamma$ is a scale-independent topological contribution to the amplitude. The
examples we consider include the $\mathbb{Z}_8$ and $\mathbb{Z}_{16}$
invariants of topological superconductors protected by inversion symmetry in
$(1+1)$ and $(3+1)$ dimensions, respectively, and the lens space topological
invariants in $(2+1)$-dimensional fermionic topological phases. Connections to
topological quantum field theories and cobordism classification of
symmetry-protected topological phases are discussed.


title:
A Multiband OFDMA Heterogeneous Network for Millimeter Wave 5G Wireless
  Applications

abstract:
  Emerging fifth generation (5G) wireless networks require massive bandwidth in
higher frequency bands, extreme network densities, and flexibility of
supporting multiple wireless technologies in order to provide higher data rates
and seamless coverage. It is expected that utilization of the large bandwidth
in the millimeter-wave (mmWave) band and deployment of heterogeneous networks
(HetNets) will help address the data rate requirements of 5G networks. However,
high pathloss and shadowing in the mmWave frequency band, strong interference
in the HetNets due to massive network densification, and coor- dination of
various air interfaces are challenges that must be addressed. In this paper, we
consider a relay-based multiband orthogonal frequency division multiple access
(OFDMA) HetNet in which mmWave small cells are deployed within the service area
of macro cells. Specifically, we attempt to exploit the distinct propagation
characteristics of mmWave bands (i.e., 60 GHz- the V-band - and 70-80 GHz -the
E-band-) and the Long Term Evolution (LTE) band to maximize overall data rate
of the network via efficient resource allocation. The problem is solved using a
modified dual decomposition approach and then a low complexity greedy solution
based on iterative activity selection algorithm is presented. Simulation
results show that the proposed approach outperforms conventional schemes.


title: Robust Gaussian Teleportation with Attenuations and Non-unity Gain

abstract:
  The average fidelity of the teleportation of a coherent state is calculated
for general Gaussian bipartite systems shared by the partners of the protocol,
Alice and Bob. It is considered that the shared Gaussian bipartite modes suffer
independent attenuations before the processing of Alice and Bob. Moreover the
classical communication between the partners can be controlled by a gain not
necessarily unitary. Comparing with the classical fidelity threshold of
measure-and-prepare methods, we establish several genuinely quantum
teleportation conditions which depend on the gain and the local attenuations.
Considering that the gain can be tuned to maximize the bipartite state set able
to genuinely quantum teleportation, a condition for teleportation robust to
local attenuations is found. This condition is demonstrated to be essentially
equivalent to the condition of robust Gaussian bipartite entanglement, obtained
in previous articles, showing that the attenuation robustness is an
entanglement property relevant for characterization and application of
bipartite systems. For the derivation of the robust teleportation conditions,
the Gaussian operations onto the bipartite system are thoroughly studied, so
that the transformations that maintain the fidelity invariant are found. Some
scenarios for different Gaussian bipartite states are presented and discussed.


title: The Million Optical - Radio/X-ray Associations (MORX) Catalogue

abstract:
  This automated catalogue combines all the largest published optical, radio
and X-ray sky catalogues to find probable radio/X-ray associations to optical
objects, plus double radio lobes, using uniform processing against all input
data. The total count is 1002855 optical objects so presented. Each object is
displayed with J2000 astrometry, optical and radio/X-ray identifiers, red and
blue photometry, and calculated probabilities and optical field solutions of
the associations. This is the third and final edition of this method.


title:
Phase transition for the SIR model with random transition rates on
  complete graphs

abstract:
  In this paper we are concerned with the Susceptible-Infective-Removed model
with random transition rates on complete graphs $C_n$ with $n$ vertices. We
assign i. i. d. copies of a positive random variable $\xi$ on each vertex as
the recovery rates and i. i. d copies of a positive random variable $\rho$ on
each edge as the edge infection weights. We assume that a susceptible vertex is
infected by an infective one at rate proportional to the edge weight on the
edge connecting these two vertices while an infective vertex becomes removed
with rate equals the recovery rate on it, then we show that the model performs
the following phase transition when at $t=0$ one vertex is infective and others
are susceptible. When $\lambda<\lambda_c$, the proportion of vertices which
have ever been infective converges to $0$ weakly as $n\rightarrow+\infty$ while
when $\lambda>\lambda_c$, there exist $c(\lambda)>0$ and $b(\lambda)>0$ such
that for each $n\geq 1$ with probability at least $b(\lambda)$ the proportion
of vertices which have ever been infective is at least $c(\lambda)$.
Furthermore, we prove that $\lambda_c$ is the inverse of the production of the
mean of $\rho$ and the mean of the inverse of $\xi$.


title: The chain-level intersection pairing for PL pseudomanifolds revisited

abstract:
  We generalize the PL intersection product for chains on PL manifolds and for
intersection chains on PL stratified pseudomanifolds to products of locally
finite chains on non-compact spaces that are natural with respect to
restriction to open sets. This is necessary to sheafify the intersection
product, an essential step in proving duality between the Goresky-MacPherson
intersection homology product and the intersection cohomology cup product
pairing recently defined by the author and McClure.
  We also provide a correction to the Goresky-MacPherson proof of a version of
Poincar\'e duality on pseudomanifolds that is used in the construction of the
intersection product.


title: Tangled Closure Algebras

abstract:
  The tangled closure of a collection of subsets of a topological space is the
largest subset in which each member of the collection is dense. This operation
models a logical `tangle modality' connective, of significance in finite model
theory. Here we study an abstract equational algebraic formulation of the
operation which generalises the McKinsey-Tarski theory of closure algebras. We
show that any dissectable tangled closure algebra, such as the algebra of
subsets of any metric space without isolated points, contains copies of every
finite tangled closure algebra. We then exhibit an example of a tangled closure
algebra that cannot be embedded into any complete tangled closure algebra, so
it has no MacNeille completion and no spatial representation.


title:
On the role of $\rm CD8^+$ T cells in determining recovery time from
  influenza virus infection

abstract:
  Myriad experiments have identified an important role for $\rm CD8^+$ T cell
response mechanisms in determining recovery from influenza A virus infection.
Animal models of influenza infection further implicate multiple elements of the
immune response in defining the dynamical characteristics of viral infection.
To date, influenza virus models, while capturing particular aspects of the
natural infection history, have been unable to reproduce the full gamut of
observed viral kinetic behaviour in a single coherent framework. Here, we
introduce a mathematical model of influenza viral dynamics incorporating all
major immune components (innate, humoral and cellular) and explore its
properties with a particular emphasis on the role of cellular immunity.
Calibrated against a range of murine data, our model is capable of
recapitulating observed viral kinetics from a multitude of experiments.
Importantly, the model predicts a robust exponential relationship between the
level of effector $\rm CD8^+$ T cells and recovery time, whereby recovery time
rapidly decreases to a fixed minimum recovery time with an increasing level of
effector $\rm CD8^+$ T cells. We find support for this relationship in recent
clinical data from influenza A(H7N9) hospitalised patients. The exponential
relationship implies that people with a lower level of naive $\rm CD8^+$ T
cells may receive significantly more benefit from induction of additional
effector $\rm CD8^+$ T cells arising from immunological memory, itself
established through either previous viral infection or T cell-based vaccines.


title:
FAST-PT II: an algorithm to calculate convolution integrals of general
  tensor quantities in cosmological perturbation theory

abstract:
  Cosmological perturbation theory is a powerful tool to predict the statistics
of large-scale structure in the weakly non-linear regime, but even at 1-loop
order it results in computationally expensive mode-coupling integrals. Here we
present a fast algorithm for computing 1-loop power spectra of quantities that
depend on the observer's orientation, thereby generalizing the FAST-PT
framework (McEwen et al., 2016) that was originally developed for scalars such
as the matter density. This algorithm works for an arbitrary input power
spectrum and substantially reduces the time required for numerical evaluation.
We apply the algorithm to four examples: intrinsic alignments of galaxies in
the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB
polarization due to baryon flows; and the 1-loop matter power spectrum in
redshift space. Code implementing this algorithm and these applications is
publicly available at https://github.com/JoeMcEwen/FAST-PT .


title: Evanescent single-molecule biosensing with quantum limited precision

abstract:
  Sensors that are able to detect and track single unlabelled biomolecules are
an important tool both to understand biomolecular dynamics and interactions at
nanoscale, and for medical diagnostics operating at their ultimate detection
limits. Recently, exceptional sensitivity has been achieved using the strongly
enhanced evanescent fields provided by optical microcavities and nano-sized
plasmonic resonators. However, at high field intensities photodamage to the
biological specimen becomes increasingly problematic. Here, we introduce an
optical nanofibre based evanescent biosensor that operates at the fundamental
precision limit introduced by quantisation of light. This allows a four
order-of-magnitude reduction in optical intensity whilst maintaining
state-of-the-art sensitivity. It enable quantum noise limited tracking of
single biomolecules as small as 3.5 nm, and surface-molecule interactions to be
monitored over extended periods. By achieving quantum noise limited precision,
our approach provides a pathway towards quantum-enhanced single-molecule
biosensors.


title:
Nonlinear inhomogeneous Fokker-Planck equations: entropy and free-energy
  time evolution

abstract:
  We extend a recently introduced free-energy formalism for homogeneous
Fokker-Planck equations to a wide, and physically appealing, class of
inhomogeneous nonlinear Fokker-Planck equations. In our approach, the
free-energy functional is expressed in terms of an entropic functional and an
auxiliary potential, both derived from the coefficients of the equation. With
reference to the introduced entropic functional, we discuss the entropy
production in a relaxation process towards equilibrium. The properties of the
stationary solutions of the considered Fokker-Planck equations are also
discussed.


title:
Unfolding of acyclic sign-skew-symmetric cluster algebras and
  applications to positivity and $F$-polynomials

abstract:
  In this paper, we build the unfolding approach from acyclic
sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of
infinite rank, which can be regard as an improvement of that in the
skew-symmetrizable case. Using this approach, we give a positive answer to the
problem by Berenstein, Fomin and Zelevinsky in \cite{fz3} which asks whether an
acyclic sign-skew-symmetric matrix is always totally sign-skew-symmetric. As
applications, the positivity for cluster algebras in acyclic
sign-skew-symmetric case is given; further, the $F$-polynomials of cluster
algebras are proved to have constant term 1 in acyclic sign-skew-symmetric
case.


title: The Kalman Decomposition for Linear Quantum Stochastic Systems

abstract:
  The Kalman decomposition for Linear Quantum Stochastic Systems in the real
quadrature operator representation, that was derived indirectly in [1] by the
authors, is derived here directly, using the "one-sided symplectic" SVD-like
factorization of [2] on the observability matrix of the system.


title: A Stochastic Model of Optimal Debt Management and Bankruptcy

abstract:
  A problem of optimal debt management is modeled as a noncooperative game
between a borrower and a pool of lenders, in infinite time horizon with
exponential discount. The yearly income of the borrower is governed by a
stochastic process. When the debt-to-income ratio $x(t)$ reaches a given size
$x^*$, bankruptcy instantly occurs. The interest rate charged by the
risk-neutral lenders is precisely determined in order to compensate for this
possible loss of their investment.
  For a given bankruptcy threshold $x^*$, existence and properties of optimal
feedback strategies for the borrower are studied, in a stochastic framework as
well as in a limit deterministic setting. The paper also analyzes how the
expected total cost to the borrower changes, depending on different values of
$x^*$, changes, depending on different values of $x^*$?.


title: List approximation for increasing Kolmogorov complexity

abstract:
  It is impossible to effectively modify a string in order to increase its
Kolmogorov complexity. But is it possible to construct a few strings, not
longer than the input string, so that most of them have larger complexity? We
show that the answer is yes. We present an algorithm that on input a string $x$
of length $n$ returns a list with $O(n^2)$ many strings, all of length $n$,
such that 99\% of them are more complex than $x$, provided the complexity of
$x$ is less than $n - \log \log n - O(1)$. We obtain similar results for other
parameters, including a polynomial-time construction.


title: A Note on Local Unitary Equivalence of Isotropic-like States

abstract:
  We consider the local unitary equivalence of a class of quantum states in
bipartite case and multipartite case. The necessary and sufficient condition is
presented. As special cases, the local unitary equivalent classes of isotropic
state and werner state are provided. Then we study the local unitary similar
equivalence of this class of quantum states and analyze the necessary and
sufficient condition.


title: Intrinsic sound of anti-de Sitter manifolds

abstract:
  As is well-known for compact Riemann surfaces, eigenvalues of the
Laplacianbare distributed discretely and most of eigenvalues vary viewed as
functions on the Teichmuller space.
  We discuss a new feature in the Lorentzian geometry, or more generally, in
pseudo-Riemannian geometry. One of the distinguished features is that
$L^2$-eigenvalues of the Laplacian may be distributed densely in R in
pseudo-Riemannian geometry. For three-dimensional anti-de Sitter manifolds, we
also explain another feature proved in joint with F. Kassel [Adv. Math. 2016]
that there exist countably many $L^2$-eigenvalues of the Laplacian that are
stable under any small deformation of anti-de Sitter structure.


title: Criterion for SLOCC Equivalence of Multipartite Quantum States

abstract:
  We study the stochastic local operation and classical communication (SLOCC)
equivalence for arbitrary dimensional multipartite quantum states. For
multipartite pure states, we present a necessary and sufficient criterion in
terms of their coefficient matrices. This condition can be used to classify
some SLOCC equivalent quantum states with coefficient matrices having the same
rank. For multipartite mixed state, we provide a necessary and sufficient
condition by means of the realignment of matrix. Some detailed examples are
given to identify the SLOCC equivalence of multipartite quantum states.


title: Lagrange Inversion

abstract:
  We give a survey of the Lagrange inversion formula, including different
versions and proofs, with applications to combinatorial and formal power series
identities.


title:
Macro-optimization of email recommendation response rates harnessing
  individual activity levels and group affinity trends

abstract:
  Recommendation emails are among the best ways to re-engage with customers
after they have left a website. While on-site recommendation systems focus on
finding the most relevant items for a user at the moment (right item), email
recommendations add two critical additional dimensions: who to send
recommendations to (right person) and when to send them (right time). It is
critical that a recommendation email system not send too many emails to too
many users in too short of a time-window, as users may unsubscribe from future
emails or become desensitized and ignore future emails if they receive too
many. Also, email service providers may mark such emails as spam if too many of
their users are contacted in a short time-window. Optimizing email
recommendation systems such that they can yield a maximum response rate for a
minimum number of email sends is thus critical for the long-term performance of
such a system. In this paper, we present a novel recommendation email system
that not only generates recommendations, but which also leverages a combination
of individual user activity data, as well as the behavior of the group to which
they belong, in order to determine each user's likelihood to respond to any
given set of recommendations within a given time period. In doing this, we have
effectively created a meta-recommendation system which recommends sets of
recommendations in order to optimize the aggregate response rate of the entire
system. The proposed technique has been applied successfully within
CareerBuilder's job recommendation email system to generate a 50\% increase in
total conversions while also decreasing sent emails by 72%