title: The Road to Popularity: The Dilution of Growing Audience on Twitter

abstract:
  On social media platforms, like Twitter, users are often interested in
gaining more influence and popularity by growing their set of followers, aka
their audience. Several studies have described the properties of users on
Twitter based on static snapshots of their follower network. Other studies have
analyzed the general process of link formation. Here, rather than investigating
the dynamics of this process itself, we study how the characteristics of the
audience and follower links change as the audience of a user grows in size on
the road to user's popularity.
  To begin with, we find that the early followers tend to be more elite users
than the late followers, i.e., they are more likely to have verified and expert
accounts. Moreover, the early followers are significantly more similar to the
person that they follow than the late followers. Namely, they are more likely
to share time zone, language, and topics of interests with the followed user.
To some extent, these phenomena are related with the growth of Twitter itself,
wherein the early followers tend to be the early adopters of Twitter, while the
late followers are late adopters. We isolate, however, the effect of the growth
of audiences consisting of followers from the growth of Twitter's user base
itself. Finally, we measure the engagement of such audiences with the content
of the followed user, by measuring the probability that an early or late
follower becomes a retweeter.


title:
Fast and High-Fidelity Entangling Gate through Parametrically Modulated
  Longitudinal Coupling

abstract:
  We investigate an approach to universal quantum computation based on the
modulation of longitudinal qubit-oscillator coupling. We show how to realize a
controlled-phase gate by simultaneously modulating the longitudinal coupling of
two qubits to a common oscillator mode. In contrast to the more familiar
transversal qubit-oscillator coupling, the magnitude of the effective
qubit-qubit interaction does not rely on a small perturbative parameter. As a
result, this effective interaction strength can be made large, leading to short
gate times and high gate fidelities. We moreover show how the gate infidelity
can be exponentially suppressed with squeezing and how the entangling gate can
be generalized to qubits coupled to separate oscillators. Our proposal can be
realized in multiple physical platforms for quantum computing, including
superconducting and spin qubits.


title:
Distinguishing between Topical and Non-topical Information Diffusion
  Mechanisms in Social Media

abstract:
  A number of recent studies of information diffusion in social media, both
empirical and theoretical, have been inspired by viral propagation models
derived from epidemiology. These studies model the propagation of memes, i.e.,
pieces of information, between users in a social network similarly to the way
diseases spread in human society. Importantly, one would expect a meme to
spread in a social network amongst the people who are interested in the topic
of that meme. Yet, the importance of topicality for information diffusion has
been less explored in the literature.
  Here, we study empirical data about two different types of memes (hashtags
and URLs) spreading through the Twitter's online social network. For every
meme, we infer its topics and for every user, we infer her topical interests.
To analyze the impact of such topics on the propagation of memes, we introduce
a novel theoretical framework of information diffusion. Our analysis identifies
two distinct mechanisms, namely topical and non-topical, of information
diffusion. The non-topical information diffusion resembles disease spreading as
in simple contagion. In contrast, the topical information diffusion happens
between users who are topically aligned with the information and has
characteristics of complex contagion. Non-topical memes spread broadly among
all users and end up being relatively popular. Topical memes spread narrowly
among users who have interests topically aligned with them and are diffused
more readily after multiple exposures. Our results show that the topicality of
memes and users' interests are essential for understanding and predicting
information diffusion.


title: Holography on Non-Orientable Surfaces

abstract:
  We consider the holographic computation of two dimensional conformal field
theory partition functions on non-orientable surfaces. We classify the three
dimensional geometries that give bulk saddle point contributions to the
partition function, and find that there are fewer saddles than in the
orientable case. For example, for the Klein bottle there is a single smooth
saddle and a single additional saddle with an orbifold singularity. We argue
that one must generally include singular bulk saddle points in order to
reproduce the CFT results. We also discuss loop corrections to these partition
functions for the Klein bottle.


title:
Fermion Parity Flips and Majorana Bound States at twist defects in
  Superconducting Fractional Topological Phases

abstract:
  In this paper we consider a layered heterostructure of an Abelian
topologically ordered state (TO), such as a fractional Chern insulator/quantum
Hall state with an s-wave superconductor in order to explore the existence of
non-Abelian defects. In order to uncover such defects we must augment the
original TO by a $\mathbb{Z}_2$ gauge theory sector coming from the s-wave SC.
We first determine the extended TO for a wide variety of fractional quantum
Hall or fractional Chern insulator heterostructures. We prove the existence of
a general anyon permutation symmetry (AS) that exists in any fermionic Abelian
TO state in contact with an s-wave superconductor. Physically this permutation
corresponds to adding a fermion to an odd flux vortices (in units of $h/2e$) as
they travel around the associated topological (twist) defect. As such, we call
it a fermion parity flip AS. We consider twist defects which mutate anyons
according to the fermion parity flip symmetry and show that they can be
realized at domain walls between distinct gapped edges or interfaces of the TO
superconducting state. We analyze the properties of such defects and show that
fermion parity flip twist defects are always associated with Majorana zero
modes. Our formalism also reproduces known results such as
Majorana/parafermionic bound states at superconducting domain walls of
topological/Fractional Chern insulators when twist defects are constructed
based on charge conjugation symmetry. Finally, we briefly describe more exotic
twist liquid phases obtained by gauging the AS where the twist defects become
deconfined anyonic excitations.


title: On possible memory effects in tests of Bell inequalities

abstract:
  It is shown that memory effects in experiments measuring correlations in
entangled photon pairs are not able to produce a relevant loophole for the test
of local hidden variables theories.


title: Birdsong dialect patterns explained using magnetic domains

abstract:
  The songs and calls of many bird species, like human speech, form distinct
regional dialects. We suggest that the process of dialect formation is
analogous to the physical process of magnetic domain formation. We take the
coastal breeding grounds of the Puget Sound white crowned sparrow as an
example. Previous field studies suggest that birds of this species learn
multiple songs early in life, and when establishing a territory for the first
time, retain one of these dialects in order to match the majority of their
neighbours. We introduce a simple lattice model of the process, showing that
this matching behaviour can produce single dialect domains provided the death
rate of adult birds is sufficiently low. We relate death rate to thermodynamic
temperature in magnetic materials, and calculate the critical death rate by
analogy with the Ising model. Using parameters consistent with the known
behavior of these birds we show that coastal dialect domain shapes may be
explained by viewing them as low temperature "stripe states".


title: Probing a Gravitational Cat State: Experimental Possibilities

abstract:
  This is a progress report on a preliminary feasibility study of experimental
setups for preparing and probing a gravitational cat state [1].


title: A remark on analytic Fredholm alternative

abstract:
  We apply a recent result of Borichev-Golinskii-Kupin on the Blaschke-type
conditions for zeros of analytic functions on the complex plane with a cut
along the positive semi-axis to the problem of the eigenvalues distribution of
the Fredholm-type analytic operator-valued functions.


title: Rydberg-Stark deceleration of atoms and molecules

abstract:
  The large electric dipole moments associated with highly excited Rydberg
states of atoms and molecules make gas-phase samples in these states very well
suited to deceleration and trapping using inhomogeneous electric fields. The
methods of Rydberg-Stark deceleration with which this can be achieved are
reviewed here. Using these techniques, the longitudinal motion of beams of
atoms and molecules moving at speeds as high as 2500~m/s have been manipulated,
with changes in kinetic energy of up to $|\Delta
E_{\mathrm{kin}}|=1.3\times10^{-20}$~J ($|\Delta E_{\mathrm{kin}}|/e=80$~meV or
$|\Delta E_{\mathrm{kin}}|/hc=650$~cm$^{-1}$) achieved, while decelerated and
trapped samples with number densities of $10^6$--$10^7$~cm$^{-3}$ and
translational temperatures of $\sim150$~mK have been prepared. Applications of
these samples in areas of research at the interface between physics and
physical chemistry are discussed.


title:
Determination of the total absorption peak in an electromagnetic
  calorimeter

abstract:
  A physically-motivated function was developed to accurately determine the
total absorption peak in an electromagnetic calorimeter and to overcome biases
present in many commonly used methods. The function is the convolution of a
detector resolution function with the sum of a delta function, which represents
the complete absorption of energy, and a tail function, which describes the
partial absorption of energy and depends on the detector materials and
structures. Its performance was tested with the simulation of three typical
cases. The accuracy of the extracted peak value, resolution, and peak area was
improved by an order of magnitude on average, relative to the Crystal Ball
function.


title: Two analogs of Thue-Morse sequence

abstract:
  We introduce and study two analogs of one of the best known sequence in
Mathematics : Thue-Morse sequence. The first analog is concerned with the
parity of number of runs of 1's in the binary representation of nonnegative
integers. The second one is connected with the parity of number of 1's in the
representation of nonnegative integers in so-called negabinary (or in base
$-2).$ We give for them some recurrent and structure formulas and prove that
the second $(0,1)$-sequence is cube-free, while the first one is quint-free.
Finally we consider several interesting unsolved problems.


title: Extreme AO Observations of Two Triple Asteroid Systems with SPHERE

abstract:
  We present the discovery of a new satellite of asteroid (130) Elektra -
S/2014 (130) 1 - in differential imaging and in integral field spectroscopy
data over multiple epochs obtained with SPHERE/VLT. This new (second) moonlet
of Elektra is about 2 km across, on an eccentric orbit and about 500 km away
from the primary. For a comparative study, we also observed another triple
asteroid system (93) Minerva. For both systems, component-resolved reflectance
spectra of the satellites and primary were obtained simultaneously. No
significant spectral difference was observed between the satellites and the
primary for either triple system. We find that the moonlets in both systems are
more likely to have been created by sub-disruptive impacts as opposed to having
been captured.


title: Precision Islands in the Ising and $O(N)$ Models

abstract:
  We make precise determinations of the leading scaling dimensions and operator
product expansion (OPE) coefficients in the 3d Ising, $O(2)$, and $O(3)$ models
from the conformal bootstrap with mixed correlators. We improve on previous
studies by scanning over possible relative values of the leading OPE
coefficients, which incorporates the physical information that there is only a
single operator at a given scaling dimension. The scaling dimensions and OPE
coefficients obtained for the 3d Ising model, $(\Delta_{\sigma},
\Delta_{\epsilon},\lambda_{\sigma\sigma\epsilon},
\lambda_{\epsilon\epsilon\epsilon}) = (0.5181489(10), 1.412625(10),
1.0518537(41), 1.532435(19))$, give the most precise determinations of these
quantities to date.


title: The Ubiquity of Coeval Starbursts in Massive Galaxy Cluster Progenitors

abstract:
  The Universe's largest galaxy clusters likely built the majority of their
massive $>10^{11} M_\odot$ galaxies in simultaneous, short-lived bursts of
activity well before virialization. This conclusion is reached from emerging
datasets on $z>2$ proto-clusters and the characteristics of their member
galaxies, in particular, rare starbursts and ultraluminous active galactic
nuclei (AGN). The most challenging observational hurdle in identifying such
structures is their very large volumes, $\sim10^{4}$ comoving Mpc$^3$ at $z>2$,
subtending areas $\sim$half a degree on the sky. Thus the contrast afforded by
an overabundance of very rare galaxies in comparison to the background can more
easily distinguish overdense structures from the surrounding, normal density
field. Five $2<z<3$ proto-clusters from the literature are discussed in detail
and are found to contain up to 12 dusty starbursts or luminous AGN galaxies
each, a phenomenon that is unlikely to occur by chance even in overdense
environments. Measurements of gas depletion times suggest that they are indeed
short-lived on $\sim$100 Myr timescales, and the probability of finding a
structure containing more than 8 such systems is $\sim$0.2\%, unless their
`triggering' is correlated on very large spatial scales, $\sim$10 Mpc across.
The volume density of starburst-rich proto-clusters is found to be comparable
to all $>10^{15} M_\odot$ galaxy clusters in the nearby Universe, a factor of
five larger than expected in some simulations. Some tension yet exists between
measurements of their volume density of starburst-rich proto-clusters and the
expectation that they are generated via short-lived episodes. However, improved
observations of proto-clusters over large regions of sky will certainly shed
more light on the assembly of galaxy clusters, and whether or not they build
their galaxies through episodic bursts as suggested here. [abridged]


title:
FR II radio galaxies at low frequencies I: morphology, magnetic field
  strength and energetics

abstract:
  Due to their steep spectra, low-frequency observations of FR II radio
galaxies potentially provide key insights in to the morphology, energetics and
spectrum of these powerful radio sources. However, limitations imposed by the
previous generation of radio interferometers at metre wavelengths has meant
that this region of parameter space remains largely unexplored. In this paper,
the first in a series examining FR IIs at low frequencies, we use LOFAR
observations between 50 and 160 MHz, along with complementary archival radio
and X-ray data, to explore the properties of two FR II sources, 3C452 and
3C223. We find that the morphology of 3C452 is that of a standard FR II rather
than of a double-double radio galaxy as had previously been suggested, with no
remnant emission being observed beyond the active lobes. We find that the
low-frequency integrated spectra of both sources are much steeper than expected
based on traditional assumptions and, using synchrotron/inverse-Compton model
fitting, show that the total energy content of the lobes is greater than
previous estimates by a factor of around 5 for 3C452 and 2 for 3C223. We go on
to discuss possible causes of these steeper than expected spectra and provide
revised estimates of the internal pressures and magnetic field strengths for
the intrinsically steep case. We find that the ratio between the equipartition
magnetic field strengths and those derived through synchrotron/inverse-Compton
model fitting remains consistent with previous findings and show that the
observed departure from equipartition may in some cases provide a solution to
the spectral versus dynamical age disparity.


title: SaxiGUTs and their Predictions

abstract:
  We introduce a class of unified supersymmetric axion theories with unified
and PQ symmetries broken by the same set of fields at a scale $\sim 2\times
10^{16}$ GeV. A typical domain wall number of order 30 leads to an axion decay
constant $f_a$ of order $10^{15}$ GeV. Inflation generates a large saxion
condensate giving a reheat temperature $T_R$ below the QCD scale for
supersymmetry breaking of order $1-10$ TeV. Axion field oscillations commence
in the saxion matter-dominated era near the QCD scale, and recent lattice
computations of the temperature dependence of the axion mass in this era allow
a controlled calculation of the axion dark matter abundance. A successful
prediction of this abundance results for an initial axion misalignment angle of
order unity, $\theta_i \sim 1$. A highly correlated set of predictions is
discussed for $f_a$, $T_R$, the supersymmetric Higgs mass parameter $\mu$, the
amount of dark radiation $\Delta N_{eff}$, the proton decay rate $\Gamma(p
\rightarrow e^+ \pi^0)$, isocurvature density perturbations and the $B$-mode of
the cosmic microwave background. The last two are particularly interesting when
the energy scale of inflation is also of order $10^{16}$ GeV.


title: Field Theory Aspects of non-Abelian T-duality and N=2 Linear Quivers

abstract:
  In this paper we propose a linear quiver with gauge groups of increasing rank
as field theory dual to the AdS_5 background constructed by Sfetsos and
Thompson through non-Abelian T-duality. The formalism to study 4d N=2 SUSY CFTs
developed by Gaiotto and Maldacena is essential for our proposal. We point out
an interesting relation between (Hopf) Abelian and non-Abelian T-dual
backgrounds that allows to see both backgrounds as different limits of a
solution constructed by Maldacena and Nunez. This suggests different
completions of the long quiver describing the CFT dual to the non-Abelian
T-dual background that match different observables.


title:
Revealing the z~2.5 Cosmic Web With 3D Lyman-Alpha Forest Tomography: A
  Deformation Tensor Approach

abstract:
  Studies of cosmological objects should take into account their positions
within the cosmic web of large-scale structure. Unfortunately, the cosmic web
has only been extensively mapped at low-redshifts ($z<1$), using galaxy
redshifts as tracers of the underlying density field. At $z>1$, the required
galaxy densities are inaccessible for the foreseeable future, but 3D
reconstructions of Lyman-$\alpha$ forest absorption in closely-separated
background QSOs and star-forming galaxies already offer a detailed window into
$z\sim2-3$ large-scale structure. We quantify the utility of such maps for
studying the cosmic web by using realistic $z=2.5$ Ly$\alpha$ forest
simulations matched to observational properties of upcoming surveys. A
deformation tensor-based analysis is used to classify voids, sheets, filaments
and nodes in the flux, which is compared to those determined from the
underlying dark matter field. We find an extremely good correspondence, with
$70\%$ of the volume in the flux maps correctly classified relative to the dark
matter web, and $99\%$ classified to within 1 eigenvalue. This compares
favorably to the performance of galaxy-based classifiers with even the highest
galaxy densities at low-redshift. We find that narrow survey geometries can
degrade the cosmic web recovery unless the survey is $\gtrsim
60\,h^{-1}\,\mathrm{Mpc}$ or $\gtrsim 1\,\mathrm{deg}$ on the sky. We also
examine halo abundances as a function of the cosmic web, and find a clear
dependence as a function of flux overdensity, but little explicit dependence on
the cosmic web. These methods will provide a new window on cosmological
environments of galaxies at this very special time in galaxy formation, "high
noon", and on overall properties of cosmological structures at this epoch.


title: Fracton Topological Order, Generalized Lattice Gauge Theory and Duality

abstract:
  We introduce a generalization of conventional lattice gauge theory to
describe fracton topological phases, which are characterized by immobile,
point-like topological excitations, and sub-extensive topological degeneracy.
We demonstrate a duality between fracton topological order and interacting spin
systems with symmetries along extensive, lower-dimensional subsystems, which
may be used to systematically search for and characterize fracton topological
phases. Commutative algebra and elementary algebraic geometry provide an
effective mathematical toolset for our results. Our work paves the way for
identifying possible material realizations of fracton topological phases.


title:
Knowing the unknowns: uncertainties in simple estimators of galactic
  dynamical masses

abstract:
  The observed stellar kinematics of dispersion-supported galaxies are often
used to measure dynamical masses. Recently, several analytical relationships
between the stellar line-of-sight velocity dispersion, the projected (2D) or
deprojected (3D) half-light radius, and the total mass enclosed within the
half-light radius, relying on the spherical Jeans equation, have been proposed.
Here, we make use of the APOSTLE cosmological hydrodynamical simulations of the
Local Group to test the validity and accuracy of such mass estimators for both
dispersion and rotation-supported galaxies, for field and satellite galaxies,
and for galaxies of varying masses, shapes, and velocity dispersion
anisotropies. We find that the mass estimators of Walker et al. and Wolf et al.
are able to recover the masses of dispersion-dominated systems with little
systematic bias, but with a 1-sigma scatter of 25 and 23 percent, respectively.
The error on the estimated mass is dominated by the impact of the 3D shape of
the stellar mass distribution, which is difficult to constrain observationally.
This intrinsic scatter becomes the dominant source of uncertainty in the masses
estimated for galaxies like the dwarf spheroidal (dSph) satellites of the Milky
Way, where the observational errors in their sizes and velocity dispersions are
small. Such scatter may also affect the inner density slopes of dSphs derived
from multiple stellar populations, relaxing the significance with which
Navarro-Frenk-White profiles may be excluded, depending on the degree to which
the relevant properties of the different stellar populations are correlated.
Finally, we derive a new optimal mass estimator that removes the residual
biases and achieves a statistically significant reduction in the scatter to 20
percent overall for dispersion-dominated galaxies, allowing more precise and
accurate mass estimates.


title: The Random-Bond Ising Model in 2.01 and 3 Dimensions

abstract:
  We consider the Ising model between 2 and 4 dimensions perturbed by quenched
disorder in the strength of the interaction between nearby spins. In the
interval 2<d<4 this disorder is a relevant perturbation that drives the system
to a new fixed point of the renormalization group. At d=2 such disorder is
marginally irrelevant and can be studied using conformal perturbation theory.
Combining conformal perturbation theory with recent results from the conformal
bootstrap we compute some scaling exponents in an expansion around d=2. If one
trusts these computations also in d=3, one finds results consistent with
experimental data and Monte Carlo simulations. In addition, we perform a direct
uncontrolled computation in d=3 using new results for low-lying operator
dimensions and OPE coefficients in the 3d Ising model. We compare these new
methods with previous studies. Finally, we comment about the $O(2)$ model in
d=3, where we predict a large logarithmic correction to the infrared scaling of
disorder.

categories: hep-th cond-mat.dis-nn cond-mat.stat-mech cond-mat.str-el


title: Speed limit to the Abrikosov lattice in mesoscopic superconductors

abstract:
  We study the instability of the superconducting state in a mesoscopic
geometry for the low pinning material Mo$_3$Ge characterized by a large
Ginzburg-Landau parameter. We observe that in the current driven switching to
the normal state from a nonlinear region of the Abrikosov flux flow, the mean
critical vortex velocity reaches a limiting maximum velocity as a function of
the applied magnetic field. Based on time dependent Ginzburg-Landau simulations
we argue that the observed behavior is due to the high velocity vortex dynamics
confined on a mesoscopic scale. We build up a general phase diagram which
includes all possible dynamic configurations of Abrikosov lattice in a
mesoscopic superconductor.


title:
Multiple negative differential conductance regions and inelastic phonon
  assisted tunneling in graphene-hBN-graphene structures

abstract:
  In this paper we study in detail the effect of the rotational alignment
between a hexagonal boron nitride (hBN) slab and the graphene layers in the
vertical current of a a graphene-hBN-graphene device. We show how for small
rotational angles, the transference of momentum by the hBN crystal lattice
leads to multiple peaks in the I-V curve of the device, giving origin to
multiple regions displaying negative differential conductance. We also study
the effect of scattering by phonons in the vertical current an see how the
opening up of inelastic tunneling events allowed by spontaneous emission of
optical phonons leads to sharp peaks in the second derivative of the current.


title: On the Efficiency of the Information Networks in Social Media

abstract:
  Social media sites are information marketplaces, where users produce and
consume a wide variety of information and ideas. In these sites, users
typically choose their information sources, which in turn determine what
specific information they receive, how much information they receive and how
quickly this information is shown to them. In this context, a natural question
that arises is how efficient are social media users at selecting their
information sources.
  In this work, we propose a computational framework to quantify users'
efficiency at selecting information sources. Our framework is based on the
assumption that the goal of users is to acquire a set of unique pieces of
information. To quantify user's efficiency, we ask if the user could have
acquired the same pieces of information from another set of sources more
efficiently. We define three different notions of efficiency -- link, in-flow,
and delay -- corresponding to the number of sources the user follows, the
amount of (redundant) information she acquires and the delay with which she
receives the information. Our definitions of efficiency are general and
applicable to any social media system with an underlying information network,
in which every user follows others to receive the information they produce.
  In our experiments, we measure the efficiency of Twitter users at acquiring
different types of information. We find that Twitter users exhibit sub-optimal
efficiency across the three notions of efficiency, although they tend to be
more efficient at acquiring non-popular than popular pieces of information. We
then show that this lack of efficiency is a consequence of the triadic closure
mechanism by which users typically discover and follow other users in social
media. Finally, we develop a heuristic algorithm that enables users to be
significantly more efficient at acquiring the same unique pieces of
information.


title:
Regimes of heating and dynamical response in driven many-body localized
  systems

abstract:
  We explore the response of many-body localized (MBL) systems to periodic
driving of arbitrary amplitude, focusing on the rate at which they exchange
energy with the drive. To this end, we introduce an infinite-temperature
generalization of the effective "heating rate" in terms of the spread of a
random walk in energy space. We compute this heating rate numerically and
estimate it analytically in various regimes. When the drive amplitude is much
smaller than the frequency, this effective heating rate is given by linear
response theory with a coefficient that is proportional to the optical
conductivity; in the opposite limit, the response is nonlinear and the heating
rate is a nontrivial power-law of time. We discuss the mechanisms underlying
this crossover in the MBL phase, and comment on its implications for the
subdiffusive thermal phase near the MBL transition.


title: The systematic spectral analysis of radio surveys

abstract:
  Current and future continuum surveys being undertaken by the new generation
of radio telescopes are now poised to address many important science questions,
ranging from the earliest galaxies, to the physics of nearby AGN, as well as
potentially providing new and unexpected discoveries. However, how to
efficiently analyse the large quantities of data collected by these studies in
order to maximise their scientific output remains an open question. In these
proceedings we present details of the surveys module for the Broadband Radio
Astronomy Tools (BRATS) software package which will combine new observations
with existing multi-frequency data in order to automatically analyse and select
sources based on their spectrum. We show how these methods can been applied to
investigate objects observed on a variety of spatial scales, and suggest a
pathway for how this can be used in the wider context of surveys and large
samples.


title: Space group constraints on weak indices in topological insulators

abstract:
  Lattice translation symmetry gives rise to a large class of "weak"
topological insulators (TIs), characterized by translation-protected gapless
surface states and dislocation bound states. In this work we show that space
group symmetries lead to constraints on the weak topological indices that
define these phases. In particular we show that screw rotation symmetry
enforces the Hall conductivity along the screw axis to be quantized in
multiples of the screw rank, which generally applies to interacting systems. We
further show that certain 3D weak indices associated with quantum spin Hall
effects (class AII) are forbidden by the Bravais-lattice and by glide or
even-fold screw symmetries. These results put a strong constraints on
candidates of weak TIs in the experimental and numerical search for topological
materials, based on the crystal structure alone.


title: The Quadratic Minimum Spanning Tree Problem and its Variations

abstract:
  The quadratic minimum spanning tree problem and its variations such as the
quadratic bottleneck spanning tree problem, the minimum spanning tree problem
with conflict pair constraints, and the bottleneck spanning tree problem with
conflict pair constraints are useful in modeling various real life
applications. All these problems are known to be NP-hard. In this paper, we
investigate these problems to obtain additional insights into the structure of
the problems and to identify possible demarcation between easy and hard special
cases. New polynomially solvable cases have been identified, as well as NP-hard
instances on very simple graphs. As a byproduct, we have a recursive formula
for counting the number of spanning trees on a $(k,n)$-accordion and a
characterization of matroids in the context of a quadratic objective function.


title: Parabolic BMO and the forward-in-time maximal operator

abstract:
  We study if the parabolic forward-in-time maximal operator is bounded on
parabolic BMO. It turns out that for non-negative functions the answer is
positive, but the behaviour of sign changing functions is more delicate. The
class parabolic BMO and the forward-in-time maximal operator originate from the
regularity theory of nonlinear parabolic partial differential equations. In
addition to that context, we also study the question in dimension one.


title:
Electronic vortex structure of Fe-based superconductors: application to
  LiFeAs

abstract:
  Detailed tunneling spectroscopy of vortex core states can provide important
insight to the momentum structure of the superconducting order parameter. We
present a theoretical study of vortex bound states in iron-based
superconductors by use of a realistic five-band model relevant to these
systems, and superconductivity stabilized by spin-fluctuation generated pairing
vertices yielding an $s\pm$ gap structure. The computed local density of states
agrees remarkably well with both the bias dependence of the local conductance
and the spatial structure of the low-bias conductance as obtained by scanning
tunneling microscopy measurements on LiFeAs [T. Hanaguri et al., Phys. Rev. B
85, 214505 (2012)].


title: Action principles for higher and fractional spin gravities

abstract:
  We review various off-shell formulations for interacting higher-spin systems
in dimensions 3 and 4. Associated with higher-spin systems in spacetime
dimension 4 is a Chern-Simons action for a superconnection taking its values in
a direct product of an infinite-dimensional algebra of oscillators and a
Frobenius algebra. A crucial ingredient of the model is that it elevates the
rigid closed and central two-form of Vasiliev's theory to a dynamical 2-form
and doubles the higher-spin algebra, thereby considerably reducing the number
of possible higher spin invariants and giving a nonzero effective functional
on-shell. The two action principles we give for higher-spin systems in 3D are
based on Chern-Simons and BF models. In the first case, the theory we give
unifies higher-spin gauge fields with fractional-spin fields and an internal
sector. In particular, Newton's constant is related to the coupling constant of
the internal sector. In the second case, the BF action we review gives the
fully nonlinear Prokushkin-Vasiliev, bosonic equations for matter-coupled
higher spins in 3D. We present the truncation to a single, real matter field
relevant in the Gaberdiel-Gopakumar holographic duality. The link between the
various actions we present is the fact that they all borrow ingredients from
Topological Field Theory. It has bee conjectured that there is an underlying
and unifying 2-dimensional first-quantised description of the previous
higher-spin models in 3D and 4D, in the form of a Cattaneo-Felder-like
topological action containing fermionic fields.


title: Laser Accelerated Ions from a Shock Compressed Gas Foil

abstract:
  We present results of energetic laser-ion acceleration from a tailored, near
solid density gas target. Colliding hydrodynamic shocks compress a pure
hydrogen gas jet into a 70 {\mu}m thick target prior to the arrival of the
ultra-intense laser pulse. A density scan reveals the transition from a regime
characterized by a wide angle, low energy beam to one of a more focused beam
with a high energy halo. In the latter case, three dimensional simulations show
the formation of a Z-pinch driven by the axial current resulting from laser
wakefield accelerated electrons. Ions at the rear of the target are then
accelerated by a combination of space charge fields from accelerated electrons
and Coulombic repulsion as the pinch dissipates.


title:
A posteriori error estimates for discontinuous Galerkin methods using
  non-polynomial basis functions. Part II: Eigenvalue problems

abstract:
  We present the first systematic work for deriving a posteriori error
estimates for general non-polynomial basis functions in an interior penalty
discontinuous Galerkin (DG) formulation for solving eigenvalue problems
associated with second order linear operators. Eigenvalue problems of such
types play important roles in scientific and engineering applications,
particularly in theoretical chemistry, solid state physics and material
science. Based on the framework developed in [{\it L. Lin, B. Stamm,
http://dx.doi.org/10.1051/m2an/2015069}] for second order PDEs, we develop
residual type upper and lower bound error estimates for measuring the a
posteriori error for eigenvalue problems. The main merit of our method is that
the method is parameter-free, in the sense that all but one solution-dependent
constants appearing in the upper and lower bound estimates are explicitly
computable by solving local and independent eigenvalue problems, and the only
non-computable constant can be reasonably approximated by a computable one
without affecting the overall effectiveness of the estimates in practice.
Compared to the PDE case, we find that a posteriori error estimators for
eigenvalue problems must neglect certain terms, which involves explicitly the
exact eigenvalues or eigenfunctions that are not accessible in numerical
simulations. We define such terms carefully, and justify numerically that the
neglected terms are indeed numerically high order terms compared to the
computable estimators. Numerical results for a variety of problems in 1D and 2D
demonstrate that both the upper bound and lower bound are effective for
measuring the error of eigenvalues and eigenfunctions.


title:
All-Optical Materials Design of Chiral Edge Modes in Transition-Metal
  Dichalcogenides

abstract:
  Manipulating materials properties far from equilibrium recently garnered
significant attention, with experimental emphasis on transient melting,
enhancement, or induction of electronic order. A more tantalizing aspect of the
matter-light interaction regards the possibility to access dynamical steady
states with distinct non-equilibrium phase transitions to affect electronic
transport. Here, we show that the interplay of crystal symmetry and optical
pumping of monolayer transition-metal dichalcogenides (TMDCs) provides a novel
avenue to engineer topologically-protected chiral edge modes. In stark contrast
to graphene and previously-discussed toy models, the underlying generic
mechanism relies on the intrinsic three-band nature of TMDCs near the band
edges. Photo-induced band inversions scale linearly in applied pump field and
exhibit a transition from one to two chiral edge modes upon sweeping from red
to blue detuning. We develop a strategy to understand non-equilibrium
Floquet-Bloch bands and topological transitions directly from ab initio
calculations, and illustrate for the example of WS$_2$ that control of chiral
edge modes can be dictated solely from symmetry principles and is not
qualitatively sensitive to microscopic materials details.


title: Phase Transition by 0-Branes of U(1) Lattice Gauge Theory

abstract:
  The site reduction of U(1) lattice gauge theory is used to model the 0-branes
in the dual theory. The reduced theory is the 1D plane-rotator model of the
angle-valued coordinates on discrete world-line. The energy spectrum is
obtained exactly via the transfer-matrix method, with a minimum in the lowest
energy as a direct consequence of compact nature of coordinates. Below the
critical coupling $g_c=1.125$ and temperature $T_c=0.335$ the system undergoes
a first order phase transition between coexistent phases with lower and higher
gauge couplings. The possible relation between the model and the proposed role
for magnetic monopoles in confinement mechanism based on dual Meissner effect
is pointed.


title:
Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer
  map

abstract:
  Let $K$ be a global function field and let $\phi\in K[x]$. For all wandering
basepoints $b\in K$, we show that there is a bound on the size of the elements
of the dynamical Zsigmondy set $\mathcal{Z}(\phi,b)$ that depends only on
$\phi$, the poles of the $b$, and $K$. Moreover, when we order
$b\in\mathcal{O}_{K,S}$ by height, we show that $\mathcal{Z}(\phi,b)$ is empty
on average. As an application, we prove that the inverse limit of the Galois
groups of iterates of $\phi(x)=x^d+f$ is a finite index subgroup of an iterated
wreath product of cyclic groups. Finally, we establish similar results on
Zsigmondy sets when $K$ is the field of rational numbers or $K$ is a quadratic
imaginary field subject to an added stipulation: either zero has finite orbit
under iteration of $\phi$ or the Vojta conjecture for algebraic points on
curves holds.


title: Levenberg-Marquardt dynamics associated to variational inequalities

abstract:
  In connection with the optimization problem $$\inf_{x\in argmin
\Psi}\{\Phi(x)+\Theta(x)\},$$ where $\Phi$ is a proper, convex and lower
semicontinuous function and $\Theta$ and $\Psi$ are convex and smooth functions
defined on a real Hilbert space, we investigate the asymptotic behavior of the
trajectories of the nonautonomous Levenberg-Marquardt dynamical system
\begin{equation*}\left\{ \begin{array}{ll} v(t)\in\partial\Phi(x(t))\\
\lambda(t)\dot x(t) + \dot v(t) + v(t) + \nabla \Theta(x(t))+\beta(t)\nabla
\Psi(x(t))=0, \end{array}\right.\end{equation*} where $\lambda$ and $\beta$ are
functions of time controlling the velocity and the penalty term, respectively.
We show weak convergence of the generated trajectory to an optimal solution as
well as convergence of the objective function values along the trajectories,
provided $\lambda$ is monotonically decreasing, $\beta$ satisfies a growth
condition and a relation expressed via the Fenchel conjugate of $\Psi$ is
fulfilled. When the objective function is assumed to be strongly convex, we can
even show strong convergence of the trajectories.


title:
Furiously Fast and Red: Sub-second Optical Flaring in V404 Cyg during
  the 2015 Outburst Peak

abstract:
  We present observations of rapid (sub-second) optical flux variability in
V404 Cyg during its 2015 June outburst. Simultaneous three-band observations
with the ULTRACAM fast imager on four nights show steep power spectra dominated
by slow variations on ~100-1000s timescales. Near the peak of the outburst on
June 26, a dramatic change occurs and additional, persistent sub-second optical
flaring appears close in time to giant radio and X-ray flaring. The flares
reach peak optical luminosities of ~few x 10^{36} erg/s. Some are unresolved
down to a time resolution of 24 milliseconds. Whereas the fast flares are
stronger in the red, the slow variations are bluer when brighter. The redder
slopes, emitted power, and characteristic timescales of the fast flares can be
explained as optically-thin synchrotron emission from a compact jet arising on
size scales ~140-500 Gravitational radii (with a possible additional
contribution by a thermal particle distribution). The origin of the slower
variations is unclear. The optical continuum spectral slopes are strongly
affected by dereddening uncertainties and contamination by strong H{alpha}
emission, but the variations of these slopes follow relatively stable loci as a
function of flux. Cross-correlating the slow variations between the different
bands shows asymmetries on all nights consistent with a small red skew (i.e.,
red lag). X-ray reprocessing and non-thermal emission could both contribute to
these. These data reveal a complex mix of components over five decades in
timescale during the outburst.


title:
Minimum vertex degree conditions for loose Hamilton cycles in
  $3$-uniform hypergraphs

abstract:
  We investigate minimum vertex degree conditions for $3$-uniform hypergraphs
which ensure the existence of loose Hamilton cycles. A loose Hamilton cycle is
a spanning cycle in which only consecutive edges intersect and these
intersections consist of precisely one vertex.
  We prove that every $3$-uniform $n$-vertex ($n$ even) hypergraph
$\mathcal{H}$ with minimum vertex degree $\delta_1(\mathcal{H})\geq
\left(\frac7{16}+o(1)\right)\binom{n}{2}$ contains a loose Hamilton cycle. This
bound is asymptotically best possible.


title:
Magnetic properties of restacked 2D spin $\frac{1}{2}$ honeycomb
  RuCl$_3$ nanosheets

abstract:
  Spin $\frac{1}{2}$ honeycomb materials have gained substantial interest due
to their exotic magnetism and possible application in quantum computing.
However, in all current materials out-of-plane interactions are interfering
with the in-plane order, hence a true 2D magnetic honeycomb system is still of
demand. Here, we report the exfoliation of the magnetic semiconductor
$\alpha$-RuCl$_3$ into the first halide monolayers and the magnetic
characterization of the spin $\frac{1}{2}$ honeycomb arrangement of
turbostratically stacked RuCl$_3$ monolayers. The exfoliation is based on a
reductive lithiation/hydration approach, which gives rise to a loss of
cooperative magnetism due to the disruption of the spin $\frac{1}{2}$ state by
electron injection into the layers. After an oxidative treatment, cooperative
magnetism similar to the bulk is restored. The oxidized pellets of restacked
single layers feature a magnetic transition at T$_N$ = 7 K in the in-plane
direction, while the magnetic properties in the out-of-plane direction vastly
differ from bulk $\alpha$-RuCl$_3$. The macroscopic pellets of RuCl$_3$
therefore behave like a stack of monolayers without any symmetry relation in
the stacking direction. The deliberate introduction of turbostratic disorder to
manipulate the spin structure of RuCl$_3$ is of interest for research in
frustrated magnetism and complex magnetic order as predicted by the
Kitaev-Heisenberg model.


title: Threshold enhancement of diphoton resonances

abstract:
  The data collected by the LHC collaborations at an energy of 13 TeV indicates
the presence of an excess in the diphoton spectrum that would correspond to a
resonance of a 750 GeV mass. The apparently large production cross section is
nevertheless very difficult to explain in minimal models. We consider the
possibility that the resonance is a pseudoscalar boson $A$ with a two--photon
decay mediated by a charged and uncolored fermion having a mass at the $\frac12
M_A$ threshold and a very small decay width, $\ll 1$ MeV; one can then generate
a large enhancement of the $A\gamma\gamma$ amplitude which explains the excess
without invoking a large multiplicity of particles propagating in the loop,
large electric charges and/or very strong Yukawa couplings. The implications of
such a threshold enhancement are discussed in two explicit scenarios: i) the
Minimal Supersymmetric Standard Model in which the $A$ state is produced via
the top quark mediated gluon fusion process and decays into photons
predominantly through loops of charginos with masses close to $\frac12 M_A$ and
ii) a two Higgs doublet model in which $A$ is again produced by gluon fusion
but decays into photons through loops of vector--like charged heavy leptons. We
also comment on a minimal scenario in which the $A$ state couples only to
photons through a heavy lepton loop and is both produced and decays through
this coupling. In all these scenarios, while the mass of the charged fermion
has to be adjusted to be extremely close to half of the $A$ resonance mass, the
small total widths are naturally obtained if only suppressed three-body decay
channels occur. Finally, the implications of some of these scenarios for dark
matter are discussed.


title: Propagation of quantum fluctuations in quantum Ising model

abstract:
  We investigate the entanglement dynamics between two distant qubits by
analyzing correlations in the quantum Ising model. Starting from the spin
system in a paramagnetic regime enforced by the external magnetic field $B$, we
then switch on the ferromagnetic spin-spin coupling $J$. Using the large
coordination number expansion, we consider two limiting switching regimes: (1)
adiabatic, which monitors the evolution of the ground state through the quantum
transition to an ordered state; and (2) instantaneous (quench) which monitors
instead the propagation of quantum fluctuations and simulates the generation of
long range correlations. In particular, we find that quantum fluctuations
propagate with twice the group speed of excitations in the equilibrium state of
the system.


title:
Sequential Voting Promotes Collective Discovery in Social Recommendation
  Systems

abstract:
  One goal of online social recommendation systems is to harness the wisdom of
crowds in order to identify high quality content. Yet the sequential voting
mechanisms that are commonly used by these systems are at odds with existing
theoretical and empirical literature on optimal aggregation. This literature
suggests that sequential voting will promote herding---the tendency for
individuals to copy the decisions of others around them---and hence lead to
suboptimal content recommendation. Is there a problem with our practice, or a
problem with our theory? Previous attempts at answering this question have been
limited by a lack of objective measurements of content quality. Quality is
typically defined endogenously as the popularity of content in absence of
social influence. The flaw of this metric is its presupposition that the
preferences of the crowd are aligned with underlying quality. Domains in which
content quality can be defined exogenously and measured objectively are thus
needed in order to better assess the design choices of social recommendation
systems. In this work, we look to the domain of education, where content
quality can be measured via how well students are able to learn from the
material presented to them. Through a behavioral experiment involving a
simulated massive open online course (MOOC) run on Amazon Mechanical Turk, we
show that sequential voting systems can surface better content than systems
that elicit independent votes.


title:
TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed
  Systems

abstract:
  TensorFlow is an interface for expressing machine learning algorithms, and an
implementation for executing such algorithms. A computation expressed using
TensorFlow can be executed with little or no change on a wide variety of
heterogeneous systems, ranging from mobile devices such as phones and tablets
up to large-scale distributed systems of hundreds of machines and thousands of
computational devices such as GPU cards. The system is flexible and can be used
to express a wide variety of algorithms, including training and inference
algorithms for deep neural network models, and it has been used for conducting
research and for deploying machine learning systems into production across more
than a dozen areas of computer science and other fields, including speech
recognition, computer vision, robotics, information retrieval, natural language
processing, geographic information extraction, and computational drug
discovery. This paper describes the TensorFlow interface and an implementation
of that interface that we have built at Google. The TensorFlow API and a
reference implementation were released as an open-source package under the
Apache 2.0 license in November, 2015 and are available at www.tensorflow.org.


title: Limits on CPT violation from solar neutrinos

abstract:
  Violations of CPT invariance can induce neutrino-to-antineutrino transitions.
We study this effect for solar neutrinos and use the upper bound on the solar
neutrino-to-antineutrino transition probability from the KamLAND experiment to
constrain CPT-symmetry-violating coefficients of the general Standard-Model
Extension. The long propagation distance from the Sun to the Earth allows us to
improve existing limits by factors ranging from about a thousand to $10^{11}$.


title: Binary black hole shadows, chaotic scattering and the Cantor set

abstract:
  We investigate the qualitative features of binary black hole shadows using
the model of two extremally charged black holes in static equilibrium (a
Majumdar--Papapetrou solution). Our perspective is that binary spacetimes are
natural exemplars of chaotic scattering, because they admit more than one
fundamental null orbit, and thus an uncountably-infinite set of perpetual null
orbits which generate scattering singularities in initial data. Inspired by the
three-disc model, we develop an appropriate symbolic dynamics to describe
planar null geodesics on the double black hole spacetime. We show that a
one-dimensional (1D) black hole shadow may constructed through an iterative
procedure akin to the construction of the Cantor set; thus the 1D shadow is
self-similar. Next, we study non-planar rays, to understand how angular
momentum affects the existence and properties of the fundamental null orbits.
Taking slices through 2D shadows, we observe three types of 1D shadow: regular,
Cantor-like, and highly chaotic. The switch from Cantor-like to regular occurs
where outer fundamental orbits are forbidden by angular momentum. The highly
chaotic part is associated with an unexpected feature: stable and bounded null
orbits, which exist around two black holes of equal mass $M$ separated by $a_1
< a < \sqrt{2} a_1$, where $a_1 = 4M/\sqrt{27}$. To show how this possibility
arises, we define a certain potential function and classify its stationary
points. We conjecture that the highly chaotic parts of the 2D shadow possess
the Wada property. Finally, we consider the possibility of following null
geodesics through event horizons, and chaos in the maximally-extended
spacetime.


title: Holographic Effective Field Theories

abstract:
  We derive the four-dimensional low-energy effective field theory governing
the moduli space of strongly coupled superconformal quiver gauge theories
associated with D3-branes at Calabi-Yau conical singularities in the
holographic regime of validity. We use the dual supergravity description
provided by warped resolved conical geometries with mobile D3-branes.
Information on the baryonic directions of the moduli space is also obtained by
using wrapped Euclidean D3-branes. We illustrate our general results by
discussing in detail their application to the Klebanov-Witten model.


title:
Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM
  Theory

abstract:
  We incorporate gauge-invariant local composite operators into the
twistor-space formulation of $\mathcal{N}=4$ Super Yang-Mills theory. In this
formulation, the interactions of the elementary fields are reorganized into
infinitely many interaction vertices and we argue that the same applies to
composite operators. To test our definition of the local composite operators in
twistor space, we compute several corresponding form factors, thereby also
initiating the study of form factors using the position twistor-space
framework. Throughout this letter, we use the composite operator built from two
identical complex scalars as a pedagogical example; we treat the general case
in a follow-up paper.


title:
On uniform distribution for invariant extensions of the linear Lebesgue
  measure

abstract:
  The concept of uniform distribution in $[0,1]$ is extended for a certain
strictly separated maximal (in the sense of cardinality) family $(\lambda_t)_{t
\in [0,1]}$ of invariant extensions of the linear Lebesgue measure $\lambda$ in
$[0.1]$, and it is shown that the $\lambda_t^{\infty}$ measure of the set of
all $\lambda_t$-uniformly distributed sequences is equal to $1$, where
$\lambda_t^{\infty}$ denotes the infinite power of the measure $\lambda_t$.
This is an analogue of Hlawka's (1956) theorem for $\lambda_t$-uniformly
distributed sequences. An analogy of Weyl's (1916) theorem is obtained in
similar manner.


title: Distance distribution in configuration model networks

abstract:
  We present analytical results for the distribution of shortest path lengths
between random pairs of nodes in configuration model networks. The results,
which are based on recursion equations, are shown to be in good agreement with
numerical simulations for networks with degenerate, binomial and power-law
degree distributions. The mean, mode and variance of the distribution of
shortest path lengths are also evaluated. These results provide expressions for
central measures and dispersion measures of the distribution of shortest path
lengths in terms of moments of the degree distribution, illuminating the
connection between the two distributions.


title:
The IAC Stripe 82 Legacy Project: a wide-area survey for faint surface
  brightness astronomy

abstract:
  We present new deep co-adds of data taken within Stripe 82 of the Sloan
Digital Sky Survey (SDSS), especially stacked to reach the faintest surface
brightness limits of this data set. Stripe 82 covers 275 square degrees within
-50 < RA < +60 and -1.25 < Dec. < +1.25. We discuss the steps of our reduction
which puts special emphasis on preserving the characteristics of the background
(sky + diffuse light) in the input images using a non-aggressive sky
subtraction strategy. Our reduction reaches a limit of ~28.5 mag/arcsec^2 (3
sigma, 10x10 arcsec^2) in the r band. The effective surface brightness limit
(50% completeness for exponential light distribution) lies at <mu_e(r)> ~ 25.5
mag/arcsec^2. For point sources, we reach 50% completeness limits (3 sigma
level) of (24.2,25.2,24.7,24.3,23.0) mag in (u,g,r,i,z). This is between 1.7
and 2.0 mag deeper than the single epoch SDSS releases. The co-adds show point
spread functions with median FWHM values ranging between 1 arcsec in i and z to
1.3 arcsec in the u band. The imaging data are made publicly available at
http://www.iac.es/proyecto/stripe82. The release includes deep co-adds and
representations of the PSF for each field. Additionally, we provide object
catalogues with stars and galaxies confidently separated until g~23 mag. The
IAC Stripe 82 coadds offer a rather unique possibility to study the low surface
brightness universe, exemplified by the discovery of stellar streams around
NGC0426 and NGC0936. We also discuss further science cases like stellar haloes
and disc truncations, low surface brightness galaxies, the intra-cluster light
in galaxy clusters and the diffuse emission of Galactic dust known as Galactic
Cirrus.


title:
A modified implementation of MINRES to monitor residual subvector norms
  for block systems

abstract:
  Saddle-point systems, i.e., structured linear systems with symmetric matrices
are considered. A modified implementation of (preconditioned) MINRES is derived
which allows to monitor the norms of the subvectors individually. Compared to
the implementation from the textbook of [Elman, Sylvester and Wathen, Oxford
University Press, 2014], our method requires one extra vector of storage and no
additional applications of the preconditioner. Numerical experiments are
included.


title:
Open Questions for operators related to Rectangular Catalan
  Combinatorics

abstract:
  We formulate many open questions regarding the Schur positivity of the effect
of interesting operators on symmetric functions, and give supporting evidence
for why one should expect such behavior.


title: Bifurcation of Transition Paths Induced by Coupled Bistable Systems

abstract:
  We discuss the transition paths in a coupled bistable system consisting of
interacting multiple identical bistable motifs. We propose a simple model of
coupled bistable gene circuits as an example, and show that its transition
paths are bifurcating. We then derive a criterion to predict the bifurcation of
transition paths in a generalized coupled bistable system. We confirm the
validity of the theory for the example system by numerical simulation. We also
demonstrate in the example system that, if the steady states of individual gene
circuits are not changed by the coupling, the bifurcation pattern is not
dependent on the number of gene circuits. We further show that the transition
rate exponentially decreases with the number of gene circuits when the
transition path does not bifurcate, while a bifurcation facilitates the
transition by lowering the quasi-potential energy barrier.


title: Supersymmetry on the lattice

abstract:
  We discuss the motivations, difficulties and progress in the study of
supersymmetric lattice gauge theories focusing in particular on ${\cal N}=1$
and ${\cal N}=4$ super Yang-Mills in four dimensions. Brief reviews of the
corresponding lattice formalisms are given and current results are presented
and discussed. We conclude with a summary of the main aspects of current work
and prospects for the future.


title:
Confronting dark matter with the diphoton excess from a parent resonance
  decay

abstract:
  A diphoton excess with an invariant mass of about 750 GeV has been recently
reported by both ATLAS and CMS experiments at LHC. While the simplest
interpretation requires the resonant production of a 750 GeV (pseudo)scalar,
here we consider an alternative setup, with an additional heavy parent particle
which decays into a pair of 750 GeV resonances. This configuration improves the
agreement between the 8 TeV and 13 TeV data. Moreover, we include a dark matter
candidate in the form of a Majorana fermion which interacts through the 750 GeV
portal. The invisible decays of the light resonance help to suppress additional
decay channels into Standard Model particles in association with the diphoton
signal. We realise our hierarchical framework in the context of an effective
theory, and we analyse the diphoton signal as well as the consistency with
other LHC searches. We finally address the interplay of the LHC results with
the dark matter phenomenology, namely the compatibility with the relic density
abundance and the indirect detection bounds.


title: The Halphen cubics of order two

abstract:
  For each $m\ge 1$, Roulleau and Urz\'ua give an implicit construction of a
configuration of $4(3m^2-1)$ complex plane cubic curves. This construction was
crucial for their work on surfaces of general type. We make this construction
explicit by proving that the Roulleau-Urz\'ua configuration consists precisely
of the Halphen cubics of order $m$, and we determine specific equations of the
cubics for $m=1$ (which were known) and for $m=2$ (which are new).


title: Flavors of Translative Coverings

abstract:
  We survey results on the problem of covering the space ${\mathbb R}^n$, or a
convex body in it, by translates of a convex body. Our main goal is to present
a diverse set of methods. A theorem of Rogers is a central result, according to
which, for any convex body $K$, the space ${\mathbb R}^n$ can be covered by
translates of $K$ with density around $n\ln n$. We outline four approaches to
proving this result. Then, we discuss the illumination conjecture,
decomposability of multiple coverings, Sudakov's inequality and some problems
concerning coverings by sequences of sets.


title: An approach towards debiasing user ratings

abstract:
  With increasing importance of e-commerce, many websites have emerged where
users can express their opinions about products, such as movies, books, songs,
etc. Such interactions can be modeled as bipartite graphs where the weight of
the directed edge from a user to a product denotes a rating that the user
imparts to the product. These graphs are used for recommendation systems and
discovering most reliable (trusted) products. For these applications, it is
important to capture the bias of a user when she is rating a product. Users
have inherent bias---many users always impart high ratings while many others
always rate poorly. It is necessary to know the bias of a reviewer while
reading the review of a product. It is equally important to compensate for this
bias while assigning a ranking for an object. In this paper, we propose an
algorithm to capture the bias of a user and then subdue it to compute the true
rating a product deserves. Experiments show the efficiency and effectiveness of
our system in capturing the bias of users and then computing the true ratings
of a product.


title:
Fast calculation of inverse square root with the use of magic constant
  $-$ analytical approach

abstract:
  We present a mathematical analysis of transformations used in fast
calculation of inverse square root for single-precision floating-point numbers.
Optimal values of the so called magic constants are derived in a systematic
way, minimizing either absolute or relative errors at subsequent stages of the
discussed algorithm.


title: Shape coexistence and the role of axial asymmetry in $^{72}$Ge

abstract:
  The quadrupole collectivity of low-lying states and the anomalous behavior of
the $0^+_2$ and $2^+_3$ levels in $^{72}$Ge are investigated via projectile
multi-step Coulomb excitation with GRETINA and CHICO-2. A total of forty six
$E2$ and $M1$ matrix elements connecting fourteen low-lying levels were
determined using the least-squares search code, gosia. Evidence for triaxiality
and shape coexistence, based on the model-independent shape invariants deduced
from the Kumar-Cline sum rule, is presented. These are interpreted using a
simple two-state mixing model as well as multistate mixing calculations carried
out within the framework of the triaxial rotor model. The results represent a
significant milestone towards the understanding of the unusual structure of
this nucleus.


title:
A Practical Approach to the Hamilton-Jacobi Formulation of Holographic
  Renormalization

abstract:
  We revisit the subject of holographic renormalization for asymptotically AdS
spacetimes. For many applications of holography, one has to handle the
divergences associated with the on-shell gravitational action. The brute force
approach uses the Fefferman-Graham (FG) expansion near the AdS boundary to
identify the divergences, but subsequent reversal of the expansion is needed to
construct the infinite counterterms. While in principle straightforward, the
method is cumbersome and application/reversal of FG is formally unsatisfactory.
Various authors have proposed an alternative method based on the
Hamilton-Jacobi equation. However, this approach may appear to be abstract,
difficult to implement, and in some cases limited in applicability. In this
paper, we clarify the Hamilton-Jacobi formulation of holographic
renormalization and present a simple algorithm for its implementation to
extract cleanly the infinite counterterms. While the derivation of the method
relies on the Hamiltonian formulation of general relativity, the actual
application of our algorithm does not. The work applies to any $D$-dimensional
holographic dual with asymptotic AdS boundary, Euclidean or Lorentzian, and
arbitrary slicing. We illustrate the method in several examples, including the
FGPW model, a holographic model of 3d ABJM theory, and cases with marginal
scalars such as a dilaton-axion system.


title:
Macroscopic coherent structures in a stochastic neural network: from
  interface dynamics to coarse-grained bifurcation analysis

abstract:
  We study coarse pattern formation in a cellular automaton modelling a
spatially-extended stochastic neural network. The model, originally proposed by
Gong and Robinson [36], is known to support stationary and travelling bumps of
localised activity. We pose the model on a ring and study the existence and
stability of these patterns in various limits using a combination of analytical
and numerical techniques. In a purely deterministic version of the model, posed
on a continuum, we construct bumps and travelling waves analytically using
standard interface methods from neural fields theory. In a stochastic version
with Heaviside firing rate, we construct approximate analytical probability
mass functions associated with bumps and travelling waves. In the full
stochastic model posed on a discrete lattice, where a coarse analytic
description is unavailable, we compute patterns and their linear stability
using equation-free methods. The lifting procedure used in the coarse
time-stepper is informed by the analysis in the deterministic and stochastic
limits. In all settings, we identify the synaptic profile as a mesoscopic
variable, and the width of the corresponding activity set as a macroscopic
variable. Stationary and travelling bumps have similar meso- and macroscopic
profiles, but different microscopic structure, hence we propose lifting
operators which use microscopic motifs to disambiguate between them. We provide
numerical evidence that waves are supported by a combination of high synaptic
gain and long refractory times, while meandering bumps are elicited by short
refractory times.


title: Quantum Memristors with Superconducting Circuits

abstract:
  Memristors are resistive elements retaining information of their past
dynamics. They have garnered substantial interest due to their potential for
representing a paradigm change in electronics, information processing and
unconventional computing. Given the advent of quantum technologies, a design
for a quantum memristor with superconducting circuits may be envisaged. Along
these lines, we introduce such a quantum device whose memristive behavior
arises from quasiparticle-induced tunneling when supercurrents are cancelled.
For realistic parameters, we find that the relevant hysteretic behavior may be
observed using current state-of-the-art measurements of the phase-driven
tunneling current. Finally, we develop suitable methods to quantify memory
retention in the system.


title:
750 GeV Di-photon Excess and Strongly First-Order Electroweak Phase
  Transition

abstract:
  A new scalar particle, coupled to photons and gluons via loops of vector-like
quarks, provides a simple theoretical interpretation of the 750 GeV diphoton
excess reported by the experiments at the Large Hadron Collider (LHC). In this
paper, we show that this model contains a large, phenomenologically viable
parameter space region in which the electroweak phase transition (EWPT) is
strongly first-order, opening the possibility that electroweak baryogenesis
mechanism can be realized in this context. A large coupling between the Higgs
doublet and the heavy scalar, required for a strongly first-order EWPT, can
arise naturally in composite Higgs models. The scenario makes robust
predictions that will be tested in near-future experiments. The cross section
of resonant di-Higgs production at the 13 TeV LHC is predicted to be at least
20 fb, while the Higgs cubic self-coupling is enhanced by 40% or more with
respect to its Standard Model (SM) value.


title: On the Waring-Goldbach Problem for tenth powers

abstract:
  Using sharper Weyl sum estimates, we show that $H(10)\le 105$, improving upon
the previous bound of $107$.


title: Lie algebroids, gauge theories, and compatible geometrical structures

abstract:
  The construction of gauge theories beyond the realm of Lie groups and
algebras leads one to consider Lie groupoids and algebroids equipped with
additional geometrical structures which, for gauge invariance of the
construction, need to satisfy particular compatibility conditions. This paper
analyzes these compatibilities from a mathematical perspective.
  In particular, we show that the compatibility of a connection with a Lie
algebroid that one finds is the Cartan condition, introduced previously by A.
Blaom. For the metric on the base M of a Lie algebroid equipped with any
connection, we show that the compatibility suggested from gauge theories
implies that the (possibly singular) foliation induced by the Lie algebroid
becomes a Riemannian foliation. Building upon a result of del Hoyo and
Fernandes, we prove furthermore that every Lie algebroid integrating to a
proper Lie groupoid admits a compatible Riemannian base. We also consider the
case where the base is equipped with a compatible symplectic or generalized
metric structure.


title: Cerenkov-Like Emission of Pions by Photons in a Lorentz-Violating Theory

abstract:
  In the presence of Lorentz violation, the Cerenkov-like process
$\gamma\rightarrow\gamma+\pi^{0}$ may become allowed for sufficiently energetic
photons. Photons above the threshold would lose energy rapidly through pion
emission. The fact that propagating photons with energies of up to 80 TeV
survive to be observed on Earth allows us to place a one-sided constraint on an
isotropic Lorentz violating parameter at the $7\times 10^{-13}$ level; this is
more than an order of magnitude better than best previous result.


title: General Methods of Elliptic Minimization

abstract:
  We provide new general methods in the calculus of variations for the
anisotropic Plateau problem in arbitrary dimension and codimension. A new
direct proof of Almgren's 1968 existence result is presented; namely, we
produce from a class of competing "surfaces," which span a given bounding set
in some ambient space, one with minimal anisotropically weighted area. In
particular, rectifiability of a candidate minimizer is proved without the
assumption of quasiminimality. Our ambient spaces are a class of Lipschitz
neighborhood retracts which includes manifolds with boundary and manifolds with
certain singularities. Our competing surfaces are rectifiable sets which
satisfy any combination of general homological, cohomological or homotopical
spanning conditions. An axiomatic spanning criterion is also provided. Our
boundaries are permitted to be arbitrary closed subsets of the ambient space,
providing a good setting for surfaces with sliding boundaries.


title: High quantum efficiency S-20 photocathodes in photon counting detectors

abstract:
  Based on conventional S-20 processes, a new series of high quantum efficiency
(QE) photocathodes has been developed that can be specifically tuned for use in
the ultraviolet, blue or green regions of the spectrum. The QE values exceed
30% at maximum response, and the dark count rate is found to be as low as 30
Hz/cm$^2$ at room temperature. This combination of properties along with a fast
temporal response makes these photocathodes ideal for application in photon
counting detectors, which is illustrated with an MCP photomultiplier tube for
single and multi-photoelectron detection.


title:
Front propagation directed by a line of fast diffusion: large diffusion
  and large time asymptotics

abstract:
  The system under study is a reaction-diffusion equation in a horizontal
strip, coupled to a diffusion equation on its upper boundary via an exchange
condition of the Robin type. This class of models was introduced by H.
Berestycki, L. Rossi and the second author in order to model biological
invasions directed by lines of fast diffusion. They proved, in particular, that
the speed of invasion was enhanced by a fast diffusion on the line, the
spreading velocity being asymptotically proportional to the square root of the
fast diffusion coefficient. These results could be reduced, in the logistic
case, to explicit algebraic computations. The goal of this paper is to prove
that the same phenomenon holds, with a different type of nonlinearity, which
precludes explicit computations. We discover a new transition phenomenon, that
we explain in detail.


title: Can the 750 GeV diphoton LHC excess be due to a radion-dominated state?

abstract:
  We discuss the possibility of interpreting the 125 GeV scalar boson and the
750 GeV diphoton excess recently reported by the ATLAS and CMS experiments as a
Higgs-dominated and a radion-dominated states respectively in a stabilized
brane-world model. It is shown that in the simplest variant of the model, where
only the gravitational degrees of freedom propagate in the bulk, the production
cross section of the radion-dominated state with mass 750 GeV turns out to be
too small in the allowed region of the model parameter space for explaining the
nature of the excess in this approach.


title: Electron Cyclotron Maser Emissions from Evolving Fast Electron Beams

abstract:
  Fast electron beams (FEBs) are common products of solar active phenomena.
Solar radio bursts are an important diagnostic tool in the understanding of
FEBs as well as the solar plasma environment in which they are propagating
along solar magnetic fields. In particular, the evolutions of the energy
spectrum and velocity distribution of FEBs due to the interaction with the
ambient plasma and field when propagating can significantly influence the
efficiency and property of their emissions. In this paper, we discuss some
possible evolutions of the energy spectrum and velocity distribution of FEBs
due to the energy loss processes and the pitch-angle effect caused by the
magnetic field inhomogeneity, and analyze the effects of these evolutions on
electron cyclotron maser (ECM) emission, which is one of the most important
mechanisms of producing solar radio bursts by FEBs. The results show that the
growth rates all decrease with the energy loss factor $Q$, but increase with
the magnetic mirror ratio $\sigma$ as well as with the steepness index
$\delta$. Moreover, the evolution of FEBs also can significantly influence the
fastest growing mode and the fastest growing phase angle. This leads to the
change of the polarization sense of ECM emission. In particular, our results
also reveal that FEB that undergoes different evolution processes will generate
different types of ECM emission. We believe the present results to be very
helpful on more comprehensive understanding of dynamic spectra of solar radio
bursts.


title: Towards Bottom-Up Analysis of Social Food

abstract:
  Social media provide a wealth of information for research into public health
by providing a rich mix of personal data, location, hashtags, and social
network information. Among these, Instagram has been recently the subject of
many computational social science studies. However despite Instagram's focus on
image sharing, most studies have exclusively focused on the hashtag and social
network structure. In this paper we perform the first large scale content
analysis of Instagram posts, addressing both the image and the associated
hashtags, aiming to understand the content of partially-labelled images taken
in-the-wild and the relationship with hashtags that individuals use as noisy
labels. In particular, we explore the possibility of learning to recognise food
image content in a data driven way, discovering both the categories of food,
and how to recognise them, purely from social network data. Notably, we
demonstrate that our approach to food recognition can often achieve accuracies
greater than 70% in recognising popular food-related image categories, despite
using no manual annotation. We highlight the current capabilities and future
challenges and opportunities for such data-driven analysis of image content and
the relation to hashtags.


title: Updated constraints on spatial variations of the fine-structure constant

abstract:
  Recent work by Webb {\it et al.} has provided indications of spatial
variations of the fine-structure constant, $\alpha$, at a level of a few parts
per million. Using a dataset of 293 archival measurements, they further show
that a dipole provides a statistically good fit to the data, a result
subsequently confirmed by other authors. Here we show that a more recent
dataset of dedicated measurements further constrains these variations: although
there are only 10 such measurements, their uncertainties are considerably
smaller. We find that a dipolar variation is still a good fit to the combined
dataset, but the amplitude of such a dipole must be somewhat smaller:
$8.1\pm1.7$ ppm for the full dataset, versus $9.4\pm2.2$ ppm for the Webb {\it
et al.} data alone, both at the $68.3\%$ confidence level. Constraints on the
direction on the sky of such a dipole are also significantly improved. On the
other hand the data can't yet discriminate between a pure spatial dipole and
one with an additional redshift dependence.


title: Efficient Containment of Exact SIR Markovian Processes on Networks

abstract:
  This paper introduces a theoretical framework for the analysis and control of
the stochastic susceptible-infected-removed (SIR) spreading process over a
network of heterogeneous agents. In our analysis, we analyze the exact
networked Markov process describing the SIR model, without resorting to
mean-field approximations, and introduce a convex optimization framework to
find an efficient allocation of resources to contain the expected number of
accumulated infections over time. Numerical simulations are presented to
illustrate the effectiveness of the obtained results.


title: Optimal designs for dose response curves with common parameters

abstract:
  A common problem in Phase II clinical trials is the comparison of dose
response curves corresponding to different treatment groups. If the effect of
the dose level is described by parametric regression models and the treatments
differ in the administration frequency (but not in the sort of drug) a
reasonable assumption is that the regression models for the different
treatments share common parameters. This paper develops optimal design theory
for the comparison of different regression models with common parameters. We
derive upper bounds on the number of support points of admissible designs, and
explicit expressions for $D$-optimal designs are derived for frequently used
dose response models with a common location parameter. If the location and
scale parameter in the different models coincide, minimally supported designs
are determined and sufficient conditions for their optimality in the class of
all designs derived. The results are illustrated in a dose-finding study
comparing monthly and weekly administration.


title: Resolving the structure of TiBe$_{12}$

abstract:
  There has been considerable controversy regarding the structure of
TiBe$_{12}$, which is variously reported as hexagonal and tetragonal. Lattice
dynamics simulations based on density functional theory show the tetragonal
phase space group $I4/mmm$ to be more stable over all temperatures, while the
hexagonal phase exhibits an imaginary phonon mode, which, if followed, would
lead to the cell adopting the tetragonal structure. We then report the
predicted ground state elastic constants and temperature dependence of the bulk
modulus and thermal expansion for the tetragonal phase.


title: On the gyrokinetic limit for the two-dimensional Vlasov-Poisson system

abstract:
  We investigate the gyrokinetic limit for the Vlasov-Poisson system in two
dimensions, in the regime studied by Golse and Saint-Raymond. We present
another proof of convergence to the Euler equation under several assumptions on
the energy and on the $L^\infty$ norms of the initial data.


title: Two-photon Rabi model: Analytic solutions and spectral collapse

abstract:
  The two-photon quantum Rabi model with quadratic coupling is studied using
extended squeezed states and we derive $G$-functions for Bargmann index $q=1/4$
and $3/4$. The simple singularity structure of the $G$-function allows to draw
conclusions about the distribution of eigenvalues along the real axis. The
previously found picture of the spectral collapse at critical coupling
$g_{\mathrm{c}}$ has to be modified regarding the low lying states, especially
the ground state: We obtain a finite gap between ground state and the continuum
of excited states at the collapse point. For large qubit splitting, also other
low lying states may be separated from the continuum at $g_{\mathrm{c}}$. We
have carried out a perturbative analysis allowing for explicit and simple
formulae of the eigenstates. Interestingly, a vanishing of the gap between
ground state and excited continuum at $g_{\mathrm{c}}$ is obtained in each
finite order of approximation. This demonstrates cleary the non-pertubative
nature of the excitation gap. We corroborate these findings with a variational
calculation for the ground state.


title: Segmented strings coupled to a B-field

abstract:
  In this paper we study segmented strings in AdS$_3$ coupled to a background
two-form whose field strength is proportional to the volume form. By changing
the coupling, the theory interpolates between the Nambu-Goto string and the
$SL(2)$ Wess-Zumino-Witten model. In terms of the kink momentum vectors, the
action is independent of the coupling and the classical theory reduces to a
single discrete-time Toda-type theory. The WZW model is a singular point in
coupling space where the map into Toda variables degenerates.


title: Eigenvector method for umbrella sampling enables error analysis

abstract:
  Umbrella sampling efficiently yields equilibrium averages that depend on
exploring rare states of a model by biasing simulations to windows of
coordinate values and then combining the resulting data with physical
weighting. Here, we introduce a mathematical framework that casts the step of
combining the data as an eigenproblem. The advantage to this approach is that
it facilitates error analysis. We discuss how the error scales with the number
of windows. Then, we derive a central limit theorem for averages that are
obtained from umbrella sampling. The central limit theorem suggests an
estimator of the error contributions from individual windows, and we develop a
simple and computationally inexpensive procedure for implementing it. We
demonstrate this estimator for simulations of the alanine dipeptide and show
that it emphasizes low free energy pathways between stable states in comparison
to existing approaches for assessing error contributions. We discuss the
possibility of using the estimator and, more generally, the eigenvector method
for umbrella sampling to guide adaptation of the simulation parameters to
accelerate convergence.


title: Conformal Predictors for Compound Activity Prediction

abstract:
  The paper presents an application of Conformal Predictors to a
chemoinformatics problem of identifying activities of chemical compounds. The
paper addresses some specific challenges of this domain: a large number of
compounds (training examples), high-dimensionality of feature space, sparseness
and a strong class imbalance. A variant of conformal predictors called
Inductive Mondrian Conformal Predictor is applied to deal with these
challenges. Results are presented for several non-conformity measures (NCM)
extracted from underlying algorithms and different kernels. A number of
performance measures are used in order to demonstrate the flexibility of
Inductive Mondrian Conformal Predictors in dealing with such a complex set of
data.
  Keywords: Conformal Prediction, Confidence Estimation, Chemoinformatics,
Non-Conformity Measure.


title: FOTOMCAp: a new quasi-automatic code for high-precision photometry

abstract:
  The search for Earth-like planets using the transit technique has encouraged
the development of strategies to obtain light curves with increasingly
precision. In this context we developed the FOTOMCAp program. This is an IRAF
quasi-automatic code which employs the aperture correction method and allows to
obtain high-precision light curves. In this contribution we describe how this
code works and show the results obtained for planetary transits light curves.


title:
Colossal Magnetocapacitance Effect and Multiferroism of Polycrystalline
  La0.2Pb0.7Fe12O19

abstract:
  The mutual control of the electric and magnetic properties of a multiferroic
solid is of fundamental and great technological importance. We report here on
the colossal magnetoelectric coupling effect of polycrystalline
La0.2Pb0.7Fe12O19. A large classic ferroelectric hysteresis loop with full
saturation and a strong magnetic hysteresis loop were observed simultaneously
in polycrystalline La0.2Pb0.7Fe12O19 due to the coexistence of an off-centered
FeO6 octahedron in its unit cell and electron spins in the partially filled 3d
orbits of the Fe3+ ions. The coupling voltage and capacity demonstrate giant
oscillations, along with magnetic field; the maximum magnetocapacitance ratio
exceeds 1.9E5 at 80 Hz. The substitution of La ions with Pb ions progressively
stabilized the conical spin structure, which gave rise to the spin-current
induced capacity oscillations upon magnetic field.


title: Quantum enhanced spectroscopy with entangled multi-photon states

abstract:
  Traditionally, spectroscopy is performed by examining the position of
absorption lines. However, at frequencies near the transition frequency,
additional information can be obtained from the phase shift. In this work we
consider the information about the transition frequency obtained from both the
absorption and the phase shift, as quantified by the Fisher information in an
interferometric measurement. We examine the use of multiple single-photon
states, NOON states, and numerically optimized states that are entangled and
have multiple photons. We find the optimized states that improve over the
standard quantum limit set by independent single photons for some atom number
densities.


title: Particle Gaussian Mixture (PGM) Filters

abstract:
  Recursive estimation of nonlinear dynamical systems is an important problem
that arises in several engineering applications. Consistent and accurate
propagation of uncertainties is important to ensuring good estimation
performance. It is well known that the posterior state estimates in nonlinear
problems may assume non-Gaussian multimodal densities. In the past, Gaussian
mixture filters and particle filters were introduced to handle non-Gaussianity
and nonlinearity. However, these methods have seen only limited success as most
mixture filters attempt to fix the number of mixture modes during estimation
process, and the particle filters suffer from the curse of dimensionality. In
this paper, we propose a particle based Gaussian mixture filtering approach for
the general nonlinear estimation problem that is free of the particle depletion
problem inherent to most particle filters. We employ an ensemble of randomly
sampled states for the propagation of state probability density. A Gaussian
mixture model of the propagated uncertainty is then recovered by clustering the
ensemble. The posterior density is obtained subsequently through a Kalman
measurement update of the mixture modes. We prove the weak convergence of the
PGM density to the true filter density assuming exponential forgetting of
initial conditions by the true filter. The estimation performance of the
proposed filtering approach is demonstrated through several test cases.


title:
Fidelity, entropy, and Poincar\'e sections as tools to study the polyad
  breaking phenomena

abstract:
  The correlation diagram of the vibrational energy spectra associated with the
stretching modes of triatomic molecules such as CO$_2$ and H$_2$O is analyzed
by means of two interacting Morse oscillators. By considering a linear
dependence of the structure and force constants ($x_g=g^o_{rr'}/g^o_{rr},
x_f=f_{rr'}/f_{rr}$) going from the water parameters to the carbon dioxide, it
is shown that the fidelity, entropy and Poincar\'e sections detect the polyad
breaking process manifested in the transition from local to normal mode
behaviors. Additionally Poincar\'e sections show a transition to chaos where
the polyad cannot be defined.


title:
Demonstration of a small programmable quantum computer with atomic
  qubits

abstract:
  Quantum computers can solve certain problems more efficiently than any
possible conventional computer. Small quantum algorithms have been demonstrated
on multiple quantum computing platforms, many specifically tailored in hardware
to implement a particular algorithm or execute a limited number of
computational paths. Here, we demonstrate a five-qubit trapped-ion quantum
computer that can be programmed in software to implement arbitrary quantum
algorithms by executing any sequence of universal quantum logic gates. We
compile algorithms into a fully-connected set of gate operations that are
native to the hardware and have a mean fidelity of 98 %. Reconfiguring these
gate sequences provides the flexibility to implement a variety of algorithms
without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ)
and Bernstein-Vazirani (BV) algorithms with average success rates of 95 % and
90 %, respectively. We also perform a coherent quantum Fourier transform (QFT)
on five trappedion qubits for phase estimation and period finding with average
fidelities of 62 % and 84 %, respectively. This small quantum computer can be
scaled to larger numbers of qubits within a single register, and can be further
expanded by connecting several such modules through ion shuttling or photonic
quantum channels.


title: Multichannel Variable-Size Convolution for Sentence Classification

abstract:
  We propose MVCNN, a convolution neural network (CNN) architecture for
sentence classification. It (i) combines diverse versions of pretrained word
embeddings and (ii) extracts features of multigranular phrases with
variable-size convolution filters. We also show that pretraining MVCNN is
critical for good performance. MVCNN achieves state-of-the-art performance on
four tasks: on small-scale binary, small-scale multi-class and largescale
Twitter sentiment prediction and on subjectivity classification.


title: Present Aspects and Future Prospects of Neutrino Mass and Oscillation

abstract:
  Neutrinos are neutral, spin-$\frac{1}{2}$ particles which undergo only weak
interactions. The experimentally observed phenomenon of neutrino oscillation
establishes the fact that neutrinos are massive and there is mixing between
different neutrino flavours. This constitutes the first unambiguous hint
towards the physics Beyond Standard Model (BSM). In the BSM theories, the
neutrino mass terms in the Lagrangian lead to the non-diagonal neutrino mass
matrix in the flavour basis which depends on neutrino mass and mixing
parameters. Thus knowledge of the neutrino oscillation parameters and
understanding the underlying symmetries of the neutrino mass matrix are very
important as they can give an insight to the new physics beyond Standard Model.
Therefore the measurement of different oscillation parameters and studying the
structure of the neutrino mass matrix are some of the main goals in neutrino
physics at present. In this thesis we have studied the potential of
present/future neutrino oscillation experiments and synergy between them to
determine the unknown parameters in the neutrino sector in the light of current
experimental results. We have also studied the phenomenological consequences of
texture zeros in the neutrino mass matrices in the presence of a sterile
neutrino.


title:
Electric Field-Induced Second Order Nonlinear Optical Effects in Silicon
  Waveguides

abstract:
  The demand for nonlinear effects within a silicon platform to support
photonic circuits requiring phase-only modulation, frequency doubling, and/or
difference frequency generation, is becoming increasingly clear. However, the
symmetry of the silicon crystal inhibits second order optical nonlinear
susceptibility, $\chi^{(2)}$. Here, we show that the crystalline symmetry is
broken when a DC field is present, inducing a $\chi^{(2)}$ in a silicon
waveguide that is proportional to the large $\chi^{(3)}$ of silicon. First,
Mach-Zehnder interferometers using the DC Kerr effect optical phase shifters in
silicon ridge waveguides with p-i-n junctions are demonstrated with a
$V_{\pi}L$ of $2.4Vcm$ in telecom bands $({\lambda}_{\omega}=1.58{\mu}m)$
without requiring to dope the silicon core. Second, the pump and second
harmonic modes in silicon ridge waveguides are quasi-phase matched when the
magnitude, spatial distribution of the DC field and $\chi^{(2)}$ are controlled
with p-i-n junctions. Using these waveguides, second harmonic generation at
multiple pump wavelengths are observed with a maximum efficiency of
$P_{2{\omega}}/P_{\omega}^2$=12%/W at ${\lambda}_{\omega}=2.29{\mu}m$ in a 1mm
long waveguide. This corresponds to a field-induced $\chi^{(2)}=41pm/V$,
comparable to non-centrosymmetric media (LiNbO3, GaAs, GaN). The field-induced
nonlinear silicon photonics will lead to a new class of CMOS compatible
integrated devices spanning from near to mid infrared spectrum.


title:
Holographic entanglement entropy in metal/superconductor phase
  transition with exponential nonlinear electrodynamics

abstract:
  We study the holographic entanglement entropy in metal/superconductor phase
transition with exponential nonlinear electrodynamics (ENE) in four and five
dimensional spacetimes. We find that the holographic entanglement entropy is
powerful tool in studying the properties of the holographic phase transition.
For the operator $\langle\mathcal{O}_{+}\rangle$, we observe that the
entanglement entropy in 4-dimensional spacetime decreases in metal phase but
changes non-monotonously in superconducting phase with the increase of the ENE
parameter. Interestingly, the change of the entanglement entropy in
5-dimensional spacetime for both the phases is monotonous as the ENE factor
alters. For the operator $\langle\mathcal{O}_{-}\rangle$, we show that the
behavior of entanglement entropy in four and five dimensions changes
monotonously for both phases as one tunes the strength of the ENE. Furthermore,
for both the operators the entanglement entropy in four or five dimensional
black hole increases with the increase of the width of the region.


title:
On the derivative at $t = 1$ of the skew-growth functions for Artin
  monoids

abstract:
  Let $G_{M}^{+}$ be the Artin monoid of finite type generated by the letters
$a_i, i\in I$ with respect to a Coxeter matrix $M$ that is equipped with the
degree map $\deg\!:\!G_{M}^{+} \to\!\Z_{\ge0}$ defined by assigning to each
equivalence class of words the length of the words, and let $N_{M,
\deg}(t)\!:=\!\!\sum_{J \subset I}(-1)^{\#J} t^{\deg(\Delta_{J})}$ be the
skew-growth function, where the summation index $J$ runs over all subsets of
$I$ and $\Delta_{J}$ is the fundamental element in $G_{M}^{+}$ associated to
the set $J$. In this article, we will calculate the derivative at $t = 1$ of
the polynomial $N_{M, \deg}(t)$. As a result, we show that the polynomial
$N_{M, \deg}(t)$ has a simple root at $t = 1$.