  Conical space emerges inevitably as an outer space of any topological defect
of the vortex type. Quantum-mechanical scattering of a nonrelativistic particle
by a vortex centred in conical space is considered, and effects of the
transverse size of the vortex are taken into account. Paradoxical peculiarities
of scattering in the short-wavelength limit are discussed.


  Markov numbers are integers that appear in the solution triples of the
Diophantine equation, $x^2+y^2+z^2=3xyz$, called the Markov equation. A
classical topic in number theory, these numbers are related to many areas of
mathematics such as combinatorics, hyperbolic geometry, approximation theory
and cluster algebras.
  There is a natural map from the rational numbers between zero and one to the
Markov numbers. In this paper, we prove two conjectures seen in Martin Aigner's
book, Markov's theorem and 100 years of the uniqueness conjecture, that
determine an ordering on subsets of the Markov numbers based on their
corresponding rational.
  The proof relies on a relationship between Markov numbers and continuant
polynomials which originates in Frobenius' 1913 paper.


  Tackling pattern recognition problems in areas such as computer vision,
bioinformatics, speech or text recognition is often done best by taking into
account task-specific statistical relations between output variables. In
structured prediction, this internal structure is used to predict multiple
outputs simultaneously, leading to more accurate and coherent predictions.
Structural support vector machines (SSVMs) are nonprobabilistic models that
optimize a joint input-output function through margin-based learning. Because
SSVMs generally disregard the interplay between unary and interaction factors
during the training phase, final parameters are suboptimal. Moreover, its
factors are often restricted to linear combinations of input features, limiting
its generalization power. To improve prediction accuracy, this paper proposes:
(i) Joint inference and learning by integration of back-propagation and
loss-augmented inference in SSVM subgradient descent; (ii) Extending SSVM
factors to neural networks that form highly nonlinear functions of input
features. Image segmentation benchmark results demonstrate improvements over
conventional SSVM training methods in terms of accuracy, highlighting the
feasibility of end-to-end SSVM training with neural factors.


  We study the out of equilibrium dynamics of an elastic manifold in a random
potential using mean-field theory. We find two asymptotic time regimes: (i)
stationary dynamics, (ii) slow aging dynamics with violation of equilibrium
theorems. We obtain an analytical solution valid for all large times with
universal scalings of two-time quantities with space. A non-analytic scaling
function crosses over to ultrametricity when the correlations become
long-range. We propose procedures to test numerically or experimentally the
extent to which this scenario holds for a given system.


  We present two XMM-Newton observations of the luminous (L_x > 10^46 erg/s),
radio-quiet quasar, PG 1407+265, separated by eleven months. The data indicate
two distinct states: a highly variable, bright state (first epoch); and a
quiescent, low-flux one (second epoch). During the low-flux state the spectrum
is consistent with a single, unabsorbed power law. However, during the brighter
state a highly variable, steep component is statistically required.
Contemporaneous UV data from the Optical Monitor allow an estimate of the
optical-to-X-ray spectral index (alpha_ox), which appears typical of
radio-quiet quasars during the low-flux state, but extremely flat during the
high-flux state. The XMM-Newton data can be described as originating from a
combination of jet and accretion disc processes, in which the (relativistic)
X-ray jet only works intermittently. The scenario could help describe some of
the complexities seen in the broadband spectral energy distribution of PG
1407+265, such as weak high-ionisation emission lines, strong Fe II, unbeamed
continuum, and the weak radio emission relative to the optical.


  Sampling of sharp posteriors in high dimensions is a challenging problem,
especially when gradients of the likelihood are unavailable. In low to moderate
dimensions, affine-invariant methods, a class of ensemble-based gradient-free
methods, have found success in sampling concentrated posteriors. However, the
number of ensemble members must exceed the dimension of the unknown state in
order for the correct distribution to be targeted. Conversely, the
preconditioned Crank-Nicolson (pCN) algorithm succeeds at sampling in high
dimensions, but samples become highly correlated when the posterior differs
significantly from the prior. In this article we combine the above methods in
two different ways as an attempt to find a compromise. The first method
involves inflating the proposal covariance in pCN with that of the current
ensemble, whilst the second performs approximately affine-invariant steps on a
continually adapting low-dimensional subspace, while using pCN on its
orthogonal complement.


  We give a systematic treatment of lattice Green functions (LGF) on the
$d$-dimensional diamond, simple cubic, body-centred cubic and face-centred
cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three
lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there
is a close connection between the LGF of the $d$-dimensional hypercubic lattice
and that of the $(d-1)$-dimensional diamond lattice. We give constant-term
formulations of LGFs for all lattices and dimensions. Through a still
under-developed connection with Mahler measures, we point out an unexpected
connection between the coefficients of the s.c., b.c.c. and diamond LGFs and
some Ramanujan-type formulae for $1/\pi.$


  In recent years, wireless ad hoc sensor network becomes popular both in civil
and military jobs. However, security is one of the significant challenges for
sensor network because of their deployment in open and unprotected environment.
As cryptographic mechanism is not enough to protect sensor network from
external attacks, intrusion detection system needs to be introduced. Though
intrusion prevention mechanism is one of the major and efficient methods
against attacks, but there might be some attacks for which prevention method is
not known. Besides preventing the system from some known attacks, intrusion
detection system gather necessary information related to attack technique and
help in the development of intrusion prevention system. In addition to
reviewing the present attacks available in wireless sensor network this paper
examines the current efforts to intrusion detection system against wireless
sensor network. In this paper we propose a hierarchical architectural design
based intrusion detection system that fits the current demands and restrictions
of wireless ad hoc sensor network. In this proposed intrusion detection system
architecture we followed clustering mechanism to build a four level
hierarchical network which enhances network scalability to large geographical
area and use both anomaly and misuse detection techniques for intrusion
detection. We introduce policy based detection mechanism as well as intrusion
response together with GSM cell concept for intrusion detection architecture.


  We demonstrate a deep-learning-based scatterer density estimator (SDE) that
processes local speckle patterns of optical coherence tomography (OCT) images
and estimates the scatterer density behind each speckle pattern. The SDE is
trained using large quantities of numerically simulated OCT images and their
associated scatterer densities. The numerical simulation uses a noise model
that incorporates the spatial properties of three types of noise, i.e., shot
noise, relative-intensity noise, and non-optical noise. The SDE's performance
was evaluated numerically and experimentally using two types of scattering
phantom and in vitro tumor spheroids. The results confirmed that the SDE
estimates scatterer densities accurately. The estimation accuracy improved
significantly when compared with our previous deep-learning-based SDE, which
was trained using numerical speckle patterns generated from a noise model that
did not account for the spatial properties of noise.


  The Lick Observatory's Shane 3-meter telescope has been upgraded with a new
infrared instrument (ShARCS - Shane Adaptive optics infraRed Camera and
Spectrograph) and dual-deformable mirror adaptive optics (AO) system (ShaneAO).
We present first-light measurements of imaging sensitivity in the Ks band. We
compare measured results to predicted signal-to-noise ratio and magnitude
limits from modeling the emissivity and throughput of ShaneAO and ShARCS. The
model was validated by comparing its results to the Keck telescope adaptive
optics system model and then by estimating the sky background and limiting
magnitudes for IRCAL, the previous infra-red detector on the Shane telescope,
and comparing to measured, published results. We predict that the ShaneAO
system will measure lower sky backgrounds and achieve 20\% higher throughput
across the $JHK$ bands despite having more optical surfaces than the current
system. It will enable imaging of fainter objects (by 1-2 magnitudes) and will
be faster to reach a fiducial signal-to-noise ratio by a factor of 10-13. We
highlight the improvements in performance over the previous AO system and its
camera, IRCAL.


  We consider the initial value problem associated to the low dispersion
fractionary Benjamin-Bona-Mahony equation, fBBM. Our aim is to establish local
persistence results in weighted Sobolev spaces and to obtain unique
continuation results that imply that those results above are sharp. Hence,
arbitrary polynomial type decay is not preserved by the fBBM flow.


  Multiple spatial zero formations for Stokes and Navier-Stokes equations in
three dimensions are shown to occur according to nodal sets of solenoidal
Hermite polynomials. Extensions to well-posed Burnett equations with the
bi-harmonic viscosity operator are also discussed.


  It has previously been shown that the excess of events reported by the CoGeNT
collaboration could be generated by elastically scattering dark matter
particles with a mass of approximately 5-15 GeV. This mass range is very
similar to that required to generate the annual modulation observed by
DAMA/LIBRA and the gamma rays from the region surrounding the Galactic Center
identified within the data of the Fermi Gamma Ray Space Telescope. To
confidently conclude that CoGeNT's excess is the result of dark matter,
however, further data will likely be needed. In this paper, we make projections
for the first full year of CoGeNT data, and for its planned upgrade. Not only
will this body of data more accurately constrain the spectrum of nuclear recoil
events, and corresponding dark matter parameter space, but will also make it
possible to identify seasonal variations in the rate. In particular, if the
CoGeNT excess is the product of dark matter, then one year of CoGeNT data will
likely reveal an annual modulation with a significance of 2-3$\sigma$. The
planned CoGeNT upgrade will not only detect such an annual modulation with high
significance, but will be capable of measuring the energy spectrum of the
modulation amplitude. These measurements will be essential to irrefutably
confirming a dark matter origin of these events.


  Using high-resolution data of the $^{12}$CO and $^{13}$CO ($J$=1-0}) line
emission from The Mopra Southern Galactic Plane CO Survey in conjunction with
neutral hydrogen observations from the Southern Galactic Plane Survey (SGPS)
and mid-infrared Spitzer data, we have explored the large-scale environment of
the supernova remnant Kes 41. On the basis of these data, we identified for the
first time the parent cloud of Kes 41 in its whole extension and surveyed the
HII regions, masers, and the population of massive young stellar objects in the
cloud. The whole unveiled giant cloud, located at the kinematic distance of
12.0 $\pm$ 3.6 kpc, whose average total mass and size are $\sim$10-30
$\times10^5$ M$_\odot$ and $\sim$$26^{\prime}$, also shines in $\gamma$-rays,
as revealed by the Large Area Telescope on board the Fermi satellite. We
determined a high average proton density $\sim$500-1000~cm$^{-3}$ in the large
molecular complex, of which protons from the neutral atomic and ionised gases
comprise only $\sim$15%.


  Classification of the non-equilibrium quantum many-body dynamics is a
challenging problem in condensed matter physics and statistical mechanics. In
this work, we study the basic question that whether a (1+1) dimensional
conformal field theory (CFT) is stable or not under a periodic driving with $N$
non-commuting Hamiltonians. Previous works showed that a Floquet (or
periodically driven) CFT driven by certain $SL_2$ deformed Hamiltonians exhibit
both non-heating (stable) and heating (unstable) phases. In this work, we show
that the phase diagram depends on the types of driving Hamiltonians. In
general, the heating phase is generic, but the non-heating phase may be absent
in the phase diagram. For the existence of the non-heating phases, we give
sufficient and necessary conditions for $N=2$, and sufficient conditions for
$N>2$. These conditions are composed of $N$ layers of data, with each layer
determined by the types of driving Hamiltonians. Our results also apply to the
single quantum quench problem with $N=1$.


  We extend the Serre-Tate theory of canonical lifts of ordinary abelian
varieties to arbitrary unpolarised families of ordinary abelian varieties
parameterised by a $p$-adic formal scheme $S$. We show that the canonical lift
is the unique lift to $W(S)$ which admits a $\delta$-structure in the sense of
Joyal, Buium, and Bousfield. We prove analogous statements for families of
ordinary $p$-groups and $p$-divisible groups.


  Muography or muon radiography is a non-invasive emerging image technology
relying on high energy atmospheric muons, which complements other standard
geophysical tools to understand the Earth's subsurface. This work discusses a
geophysical inversion methodology for volcanic muography, based on the
Simulated Annealing algorithm, using a semi-empirical model of the muon flux to
reach the volcano topography and a framework for the energy loss of muons in
rock. The Metropolis-Simulated-Annealing algorithm starts from an 'observed'
muon flux and obtains the best associated inner density distribution function
inside a synthetic model of the Cerro Machin Volcano (Tolima-Colombia). The
estimated initial density model was obtained with GEOMODELER, adapted to the
volcano topography. We improved this model by including rock densities from
samples taken from the crater, the dome and the areas associated with
fumaroles. In this paper, we determined the minimum muon energy (a function of
the arrival direction) needed to cross the volcanic building, the emerging
integrated flux of muons, and the density profile inside a model of Cerro
Machin. The present inversion correctly reconstructed the density differences
inside the Machin, within a 1 percent error concerning our initial simulation
model, giving a remarkable density contrast between the volcanic duct, the
encasing rock and the fumaroles area.


  We systematically study the interaction between two quantized optical fields
and a cyclic atomic ensemble driven by a classic optical field. This so-called
atomic cyclic ensemble consists of three-level atoms with Delta-type
transitions due to the symmetry breaking, which can also be implemented in the
superconducting quantum circuit by Yu-xi Liu et al. [Phys. Rev. Lett. 95,
087001 (2005)]. We explore the dynamic mechanisms to creating the quantum
entanglements among photon states, and between photons and atomic collective
excitations by the coherent manipulation of the atom-photon system. It is shown
that the quantum information can be completely transferred from one quantized
optical mode to another, and the quantum information carried by the two
quantized optical fields can be stored in the collective modes of this atomic
ensemble by adiabatically controlling the classic field Rabi frequencies.


  Advances in high energy physics have created the need to increase
computational capacity. Project HEPGAME was composed to address this challenge.
One of the issues is that numerical integration of expressions of current
interest have millions of terms and takes weeks to compute. We have
investigated ways to simplify these expressions, using Horner schemes and
common subexpression elimination. Our approach applies MCTS, a search procedure
that has been successful in AI. We use it to find near-optimal Horner schemes.
Although MCTS finds better solutions, this approach gives rise to two further
challenges. (1) MCTS (with UCT) introduces a constant, $C_p$ that governs the
balance between exploration and exploitation. This constant has to be tuned
manually. (2) There should be more guided exploration at the bottom of the
tree, since the current approach reduces the quality of the solution towards
the end of the expression. We investigate NMCS (Nested Monte Carlo Search) to
address both issues, but find that NMCS is computationally unfeasible for our
problem. Then, we modify the MCTS formula by introducing a dynamic
exploration-exploitation parameter $T$ that decreases linearly with the
iteration number. Consequently, we provide a performance analysis. We observe
that a variable $C_p$ solves our domain: it yields more exploration at the
bottom and as a result the tuning problem has been simplified. The region in
$C_p$ for which good values are found is increased by more than a tenfold. This
result encourages us to continue our research to solve other prominent problems
in High Energy Physics.


  We investigate full strongly exceptional collections on smooth, com- plete
toric varieties. We obtain explicit results for a large family of varieties
with Picard number three, containing many of the families already known. We
also describe the relations between the collections and the split of the push
forward of the trivial line bundle by the toric Frobenius morphism.


  The state of the art in music source separation employs neural networks
trained in a supervised fashion on multi-track databases to estimate the
sources from a given mixture. With only few datasets available, often extensive
data augmentation is used to combat overfitting. Mixing random tracks, however,
can even reduce separation performance as instruments in real music are
strongly correlated. The key concept in our approach is that source estimates
of an optimal separator should be indistinguishable from real source signals.
Based on this idea, we drive the separator towards outputs deemed as realistic
by discriminator networks that are trained to tell apart real from separator
samples. This way, we can also use unpaired source and mixture recordings
without the drawbacks of creating unrealistic music mixtures. Our framework is
widely applicable as it does not assume a specific network architecture or
number of sources. To our knowledge, this is the first adoption of adversarial
training for music source separation. In a prototype experiment for singing
voice separation, separation performance increases with our approach compared
to purely supervised training.


  This paper presents simulations of the state vector dynamics for a pair of
atomic samples which are being probed by phase shift measurements on an optical
beam passing through both samples. We show how measurements, which are
sensitive to different atomic components, serve to prepare states which are
close to being maximally entangled.


  The Ethereum blockchain platform supports the execution of decentralised
applications or smart contracts. These typically hold and transfer digital
currency to other parties on the platform; however, they have been subject to
numerous attacks due to the unintentional introduction of bugs. Over a billion
dollars worth of currency has been stolen since its release in July 2015. As
smart contracts cannot be updated after deployment, it is imperative that the
programming language supports the development of robust contracts.
  We propose Flint, a new statically-typed programming language specifically
designed for writing robust smart contracts. Flint's features enforce the
writing of safe and predictable code. To encourage good practices, we introduce
protection blocks. Protection blocks restrict who can run code and when (using
typestate) it can be executed. To prevent vulnerabilities relating to the
unintentional loss of currency, Flint Asset traits provide safe atomic
operations, ensuring the state of contracts is always consistent. Writes to
state are restricted, simplifying reasoning about smart contracts.


  A logarithmic type modulus of continuity is established for weak solutions to
a two-phase Stefan problem, up to the parabolic boundary of a cylindrical
space-time domain. For the Dirichlet problem, we merely assume that the spatial
domain satisfies a measure density property, and the boundary datum has a
logarithmic type modulus of continuity. For the Neumann problem, we assume that
the lateral boundary is smooth, and the boundary datum is bounded. The proofs
are measure theoretical in nature, exploiting De Giorgi's iteration and
refining DiBenedetto's approach. Based on the sharp quantitative estimates,
construction of continuous weak (physical) solutions is also indicated. The
logarithmic type modulus of continuity has been conjectured to be optimal as a
structural property for weak solutions to such partial differential equations.


  Based on the form-invariant of Maxwell's equations under coordinate
transformations, we extend the theory of transformation optics to
transformation magneto-statics, which can design magnets through coordinate
transformations. Some novel DC magnetic field illusions created by magnets
(e.g. shirking magnets, cancelling magnets and overlapping magnets) are
designed and verified by numerical simulations. Our research will open a new
door to designing magnets and controlling DC magnetic fields.


  Graph-structured data are the commonly used and have wide application
scenarios in the real world. For these diverse applications, the vast variety
of learning tasks, graph domains, and complex graph learning procedures present
challenges for human experts when designing versatile graph learning
approaches. Facing these challenges, large language models (LLMs) offer a
potential solution due to the extensive knowledge and the human-like
intelligence. This paper proposes a novel conceptual prototype for designing
versatile graph learning methods with LLMs, with a particular focus on the
"where" and "how" perspectives. From the "where" perspective, we summarize four
key graph learning procedures, including task definition, graph data feature
engineering, model selection and optimization, deployment and serving. We then
explore the application scenarios of LLMs in these procedures across a wider
spectrum. In the "how" perspective, we align the abilities of LLMs with the
requirements of each procedure. Finally, we point out the promising directions
that could better leverage the strength of LLMs towards versatile graph
learning methods.


  The research and teaching efficiencies of 45 Turkish state universities are
evaluated by using Multi-Activity Data Envelopment Analysis (MA-DEA) model
developed by Beasley (1995). Universities are multi-purpose institutions,
therefore they face multiple production functions simultaneously associated
with research and teaching activities. MA-DEA allows assigning priorities and
allocating shared resources to these activities.


  We present a light-front determination of the pionic contribution to the
nucleon self-energy, $\Sigma_\pi$, to second-order in pion-baryon coupling
constants that allows the pion-nucleon vertex function to be treated in a
model-independent manner constrained by experiment. The pion mass $\mu$
dependence of $\Sigma_\pi$ is consistent with chiral perturbation theory
results for small values of $\mu$ and is also linearly dependent on $\mu$ for
larger values, in accord with the results of lattice QCD calculations. The
derivative of $\Sigma_\pi$ with respect to $\mu^2$ yields the dominant
contribution to the pion content, which is consistent with the
$\bar{d}-\bar{u}$ difference observed experimentally in the violation of the
Gottfried sum rule.


  In calculations of the elementary scalar spectra of spontaneously broken
gauge theories there is a number of subtleties which, though often unnecessary
to deal with in the order-of-magnitude type of calculations, have to be taken
into account if fully consistent results are sought for. Within the "canonical"
effective-potential approach these are, for instance: the need to handle
infinite series of nested commutators of derivatives of field-dependent mass
matrices, the need to cope with spurious IR divergences emerging in the
consistent leading-order approximation and, in particular, the need to account
for the fine interplay between the renormalization effects in the one- and
two-point Green's functions which, indeed, is essential for the proper stable
vacuum identification and, thus, for the correct interpretation of the results.
In this note we illustrate some of these issues in the realm of the minimal
abelian Higgs model and two of its simplest extensions including extra heavy
scalars in the spectrum in attempt to exemplify the key aspects of the usual
"hierarchy problem" lore in a very specific and simple setting. We emphasise
that, regardless of the omnipresent polynomial cut-off dependence in the
one-loop corrections to the scalar two-point function, the physical Higgs boson
mass is always governed by the associated symmetry-breaking VEV and, as such,
it is generally as UV-robust as all other VEV-driven masses in the theory.


  The main goal of this work is to investigate the possibility of finding the
supersymmetric version of the U(1)-global string model which behaves as a
vortex-superfluid. To describe the superfluid phase, we introduce a
Lorentz-symmetry breaking background that, in an approach based on
supersymmetry, leads to a discussion on the relation between the violation of
Lorentz symmetry and explicit soft supersymmetry breakings. We also study the
relation between the string configuration and the vortex-superfluid phase. In
the framework we settle down in terms of superspace and superfields, we
actually establish a duality between the vortex degrees of freedom and the
component fields of the Kalb-Ramond superfield. We make also considerations
about the fermionic excitations that may appear in connection with the vortex
formation.


  Dropped into an unknown environment, what should an agent do to quickly learn
about the environment and how to accomplish diverse tasks within it? We address
this question within the goal-conditioned reinforcement learning paradigm, by
identifying how the agent should set its goals at training time to maximize
exploration. We propose "Planning Exploratory Goals" (PEG), a method that sets
goals for each training episode to directly optimize an intrinsic exploration
reward. PEG first chooses goal commands such that the agent's goal-conditioned
policy, at its current level of training, will end up in states with high
exploration potential. It then launches an exploration policy starting at those
promising states. To enable this direct optimization, PEG learns world models
and adapts sampling-based planning algorithms to "plan goal commands". In
challenging simulated robotics environments including a multi-legged ant robot
in a maze, and a robot arm on a cluttered tabletop, PEG exploration enables
more efficient and effective training of goal-conditioned policies relative to
baselines and ablations. Our ant successfully navigates a long maze, and the
robot arm successfully builds a stack of three blocks upon command. Website:
https://penn-pal-lab.github.io/peg/


  We report nuclear magnetic resonance (NMR) studies in the antiferromagnetic
state of the quasi-two-dimensional (CuBr)LaNb2O7. The NMR spectra at zero
magnetic field and 4.2 K indicate a unique Cu and Br sites with an internal
field of 5.7 T (at Cu) and 16.4 T (at Br), confirming a magnetic order. For the
large internal field at the Br sites to be compatible with the collinear
antiferromagnetic order observed by neutron diffraction experiments (N. Oba et
al., J. Phys. Soc. Jpn. 75, (2006) 113601), the Br atoms must move
significantly off the center of the square of the Cu sublattice so that the Br
nuclei couple predominantly to two parallel Cu moments. While invalidating the
frustrated J1-J2 model defined on a C4-symmetric square lattice, our results
are compatible with the structural model proposed for (CuCl)LaNb2O7 by Yoshida
et al. (J. Phys. Soc. Jpn. 76 (2007) 104703).


  We study the class of two-field inflationary Universe models \lambda\phi^4/4
+ g^2\chi^2\phi^2/2, in which parametric resonance during the initial stages of
reheating can lead to an exponential amplification of the amplitude of
cosmological fluctuations. Employing both analytical arguments and numerical
simulations, we determine the time at which backreaction of fluctuations on the
background fields shuts off the exponential growth, making use of the Hartree
approximation, and including scalar metric perturbations. For the case
g^2/\lambda=2, we find that the amplitude of fluctuations after preheating will
exceed the observational upper bound independent of the value of \lambda,
unless the duration of inflation is very long. Cosmological fluctuations are
acceptably small for g^2/\lambda>=8. We also find that the addition of
\chi-field self-interaction can limit the growth of fluctuations, and in the
negative-coupling case the system can become effectively single-field, removing
the resonance.


  Weakly attractive interactions between the tips of rod-like colloidal
particles affect their liquid-crystal phase behaviour due to a subtle interplay
between enthalpy and entropy. Here, we employ molecular dynamics simulations on
semi-flexible, repulsive bead-spring chains of which one of the two end beads
attract each other. We calculate the phase diagram as a function of both the
volume fraction of the chains and the strength of the attractive potential. We
identify a large number of phases that include isotropic, nematic, smectic A,
smectic B and crystalline states. For tip attraction energies lower than the
thermal energy, our results are qualitatively consistent with experimental
findings: we find that an increase of the attraction strength shifts the
nematic to smectic A phase transition to lower volume fractions, with only
minor effect on the stability of the other phases. For sufficiently strong tip
attraction, the nematic phase disappears completely, in addition leading to the
destabilisation of the isotropic phase. In order to better understand the
underlying physics of these phenomena, we also investigate the clustering of
the particles at their attractive tips and the effective molecular field
experienced by the particles in the smectic A phase. Based on these results, we
argue that the clustering of the tips only affects the phase stability if
lamellar structures (``micelles'') are formed. We find that an increase of the
attraction strength increases the degree of order in the layered
phases.Interestingly, we also find evidence for the existence of an
anti-ferroelectric smectic A phase transition induced by the interaction
between the tips. A simple Maier-Saupe-McMillan model confirms our findings.


  The nuclear region of M87 was observed with the Faint Object Spectrograph
(FOS) on the Hubble Space Telescope (HST) at 6 epochs, spanning 18 months,
after the HST image quality was improved with the deployment of the corrective
optics (COSTAR) in December 1993. From the FOS target acquisition data, we have
established that the flux from the optical nucleus of M87 varies by a factor ~2
on time scales of ~2.5 months and by as much as 25% over 3 weeks, and remains
unchanged (<= 2.5%) on time scales of ~1 day. The changes occur in an
unresolved central region <= 5 pc in diameter, with the physical size of the
emitting region limited by the observed time scales to a few hundred
gravitational radii. The featureless continuum spectrum becomes bluer as it
brightens while emission lines remain unchanged. This variability combined with
the observations of the continuum spectral shape, strong relativistic boosting
and the detection of significant superluminal motions in the jet, strongly
suggest that M87 belongs to the class of BL Lac objects but is viewed at an
angle too large to reveal the classical BL Lac properties.


  Let $A=\{a_1,a_2,\dots, a_m\}$ be a subset of a finite abelian group $G$. We
call $A$ {\it $t$-independent} in $G$, if whenever
$$\lambda_1a_1+\lambda_2a_2+\cdots +\lambda_m a_m=0$$ for some integers
$\lambda_1, \lambda_2, \dots , \lambda_m$ with $$|\lambda_1|+|\lambda_2|+\cdots
+|\lambda_m| \leq t,$$ we have $\lambda_1=\lambda_2= \cdots = \lambda_m=0$, and
we say that $A$ is {\it $s$-spanning} in $G$, if every element $g$ of $G$ can
be written as $$g=\lambda_1a_1+\lambda_2a_2+\cdots +\lambda_m a_m$$ for some
integers $\lambda_1, \lambda_2, \dots , \lambda_m$ with
$$|\lambda_1|+|\lambda_2|+\cdots +|\lambda_m| \leq s.$$ In this paper we give
an upper bound for the size of a $t$-independent set and a lower bound for the
size of an $s$-spanning set in $G$, and determine some cases when this extremal
size occurs. We also discuss an interesting connection to spherical
combinatorics.


  The transport properties of certain strongly coupled thermal gauge theories
can be determined from their effective description in terms of gravity or
superstring theory duals. Here we provide a short summary of the results for
the shear and bulk viscosity, charge diffusion constant, and the speed of sound
in supersymmetric strongly interacting plasmas. We also outline a general
algorithm for computing transport coefficients in any gravity dual. The
algorithm relates the transport coefficients to the coefficients in the
quasinormal spectrum of five-dimensional black holes in asymptotically anti de
Sitter space.


  We discuss a test of a recently proposed approach to determine average
pairing matrix elements within a given interval of single-particle states (sp)
around the Fermi level $\lambda$ as obtained in the so-called uniform gap
method (UGM). It takes stock of the crucial role played by the averaged sp
level density $\tilde{\rho}(e)$. These matrix elements are deduced within the
UGM approach, from microscopically calculated $\tilde{\rho}(e)$ and gaps
obtained from analytical formulae of a semi-classical nature. Two effects
generally ignored in similar fits have been taken care of. They are: (a) the
correction for a systematic bias in choosing to fit pairing gaps corresponding
to equilibrium deformation solutions as discussed by M\"{o}ller and Nix [Nucl.
Phys. A 476, 1 (1992)] and (b) the correction for a systematic spurious
enhancement of $\tilde{\rho}(e)$ for protons in the vicinity of $\lambda$,
because of the local Slater approximation used for the treatment of the Coulomb
exchange terms in most calculations (see e.g. [Phys. Rev C 84, 014310 (2011)]).
This approach has been deemed to be very efficient upon performing Hartree-Fock
+ BCS (with seniority force and self-consistent blocking when dealing with odd
nuclei) calculations of a large sample of well and rigidly deformed even-even
rare-earth nuclei. The reproduction of their experimental moments of inertia
has been found to be at least of the same quality as what has been obtained in
a direct fit of these data [Phys. Rev C 99, 064306 (2019)]. We extend here the
test of our approach to the reproduction, in the same region, of three-point
odd-even mass differences centered on odd-$N$ or odd-$Z$ nuclei. The agreement
with the data is again roughly of the same quality as what has been obtained in
a direct fit, as performed in [Phys. Rev C 99, 064306 (2019)].


  The description of the early stage of microfracture growth in a quasibrittle
solid with thermodynamic positions is considered. From the most general
thermodynamic performances the "principle" of minimization of free energy is
received. The account high (down to thirds) degrees in expansion of free energy
concerning parameters of a mechanical field and average microcrack energy has
allowed to write down the state equation for solids with microcracks, to find
equilibrium and nonequilibrium values of their average energy. From positions
of a developed formalism the reason of high stability of work developments on
small depths and mechanism of loss of their stability on the large depths is
explained. From the fact of presence of qualitatively various behaviour of a
material on the large depths the additional estimated connection between
parameters of the theory is established.


  We recalculate the pion electromagnetic form factor based on the perturbative
QCD formalism that includes the Sudakov resummation. We take into account the
evolution of the pion wave function in $b$, which represents the transverse
extent of the pion. An infrared enhancement is observed when $1/b$ approaches
$\Lambda_{QCD}$. We propose to freeze the evolution of the wave function at
some scale above $\Lambda_{QCD}$, such that perturbative contributions are
stablized. Our predictions are consistent with experimental data, and
insensitive to the variation of relevant parameters.


  Morphoelasticity describes a family of nonlinear PDE system and has been
widely applied to understand growth and morphogenesis in living and nonliving
structures. Most previous studies depend on locally linearizing either the PDE
system or its discretized numerical counterpart. This involves conducting a
linear stability analysis for a trivial solution or utilizing Newton-Raphson
iteration on the force residual equations derived from finite element
approximation, respectively. The paper presents a numerical approach that
frames the search for solutions as the optimization of a discretized energy
functional, similar to Tallinen et al., PRL, 2013. In contrast to Tallinen et
al., we utilize the Hessian matrix of the energy to develop a gradient descent
algorithm that ensures energy stability, which allows us to search solutions
robustly in different types of bifurcations. The solutions are further refined
locally by Newton-Raphson iterations. We showcase the effectiveness of our
approach by studying shape transitions induced by the growth in the interior
layer of a bilayer annulus, with the outer layer constrained at its outermost
boundary. By investigating three cases with varying elastic-moduli ratios
between the two layers, we illustrate that our new method can not only identify
and characterize supercritical bifurcations leading to smooth wrinkles but also
capture subcritical transitions from smooth solutions to non-smooth
crease-forming solutions. Moreover, it reveals aperiodic solutions, both smooth
and non-smooth, that have not been previously reported.


  Let $Y_{1}, \ldots, Y_{q}$ be closed subschemes which are located in
$\ell$-subgeneral position with index $\kappa$ in a complex projective variety
$X$ of dimension $n.$ Let $A$ be an ample Cartier divisor on $X.$ We obtain
that if a holomorphic curve $f:\mathbb C \to X$ is Zariski-dense, then for
every $\epsilon >0,$ \begin{eqnarray*}
\sum^{q}_{j=1}\epsilon_{Y_{j}}(A)m_{f}(r,Y_{j})\leq_{exc}
\left(\frac{(\ell-n+\kappa)(n+1)}{\kappa}+\epsilon\right)T_{f,A}(r).
\end{eqnarray*}This generalizes the second main theorems for general position
case due to Heier-Levin [AM J. Math. 143(2021), no. 1, 213-226] and subgeneral
position case due to He-Ru [J. Number Theory 229(2021), 125-141]. In
particular, whenever all the $Y_j$ are reduced to Cartier divisors, we also
give a second main theorem with the distributive constant. The corresponding
Schmidt's subspace theorem for closed subschemes in Diophantine approximation
is also given.


  Within the class of ontological interpretations of quantum theory where a
physical system comprises a particle and a field (wavefunction) guiding it, an
empty wave is a segment of the wavefunction not containing the particle. We
examine the impact of this concept on the debate between the epistemological
and ontological viewpoints. The theoretical merits of the empty wave in
avoiding the wavefunction collapse hypothesis, and in supplying conceptual
precision in the application of quantum mechanics, are emphasized. Particular
reference is made to path detection in interferometry and it is shown how a
consistent application of the particle and empty wave concepts dispels the
suggestion that this is a <surrealist> theory. The problem of how the reality
of an empty wave might be demonstrated by its effect on other systems is
examined and general arguments advanced against this possibility. However,
these arguments are not conclusive and we describe how the technique of
protective measurement suggests a method to probe the empirical implications of
empty waves and potentially distinguish between the epistemological and
ontological perspectives.


  The possible methodologies to handle the uncertain parameter are reviewed.
The core idea of the desensitized Kalman filter is introduced. A new cost
function consisting of a posterior covariance trace and trace of a weighted
norm of the state error sensitivities matrix is minimizing to obtain a
well-known analytical gain matrix, which is different from the gain of the
desensitized Kalman filter. The pre-estimated uncertain parameter covariance is
set as a referential sensitivity-weighting matrix in the new framework, and the
rationality and validity of the covariance are tested. Then, these results are
extended to the linear continuous system.


  Three-dimensional del Pezzo varieties of degree 2 are double covers of
projective space $\mathbb{P}^{3}$ branced in a quadric. In this paper we prove
that if a del Pezzo variety of degree 2 has exactly 15 nodes then the
corresponding quadric is a hyperplane section of the Igusa quartic or,
equivalently, all such del Pezzo varieties are members of one particular linear
system on the Coble fourfold. Their automorphism groups are induced from the
automorphism group of Coble fourfold. Also we classify all $G$-birationally
rigid varieties of such type.


  In this paper, we study a cell-free multiple-input multiple-output network
equipped with integrated sensing and communication (ISAC) access points (APs).
The distributed APs are used to jointly serve the communication needs of user
equipments (UEs) while sensing a target, assumed to be an eavesdropper (Eve).
To increase the system's robustness towards said Eve, we develop an ISAC
waveform model that includes artificial noise (AN) aimed at degrading the Eve
channel quality. The central processing unit receives the observations from
each AP and calculates the optimal precoding and AN covariance matrices by
solving a semi-definite relaxation of a constrained Cramer-Rao bound (CRB)
minimization problem. Simulation results highlight an underlying trade-off
between sensing and communication performances: in particular, the UEs
signal-to-noise and interference ratio and the maximum Eve's signal to noise
ratio are directly proportional to the CRB. Furthermore, the optimal AN
covariance matrix is rank-1 and has a peak in the eve's direction, leading to a
surprising inverse-proportionality between the UEs-Eve distance and optimal-CRB
magnitude.


  We assess the status of big-bang nucleosynthesis (BBN) in light of the final
Planck data release and other recent developments, and in anticipation of
future measurements. Planck data fix the cosmic baryon density to 0.9%
precision, and determine the helium abundance and effective number of neutrinos
with precision approaching that of astronomical and BBN determinations
respectively. In addition, new high-redshift measurements give D/H to better
precision than theoretical predictions, and new Li/H data reconfirm the lithium
problem. We present new ${}^{7}{\rm Be}(n,p){}^{7}{\rm Li}$ rates using new
neutron capture measurements; we have also examined the effect of proposed
changes in the $d(p,\gamma){}^{3}{\rm He}$ rates. Using these results we
perform a series of likelihood analyses. We assess BBN/CMB consistency, with
attention to how our results depend on the choice of Planck data, as well as
how the results depend on the choice of non-BBN, non-Planck data sets. Most
importantly the lithium problem remains, and indeed is more acute given the
very tight D/H observational constraints; new neutron capture data reveals
systematics that somewhat increases uncertainty and thus slightly reduces but
does not essentially change the problem. We confirm that $d(p,\gamma){}^{3}{\rm
He}$ theoretical rates brings D/H out of agreement and slightly increases 7Li;
new experimental data are needed at BBN energies. Setting the lithium problem
aside, we find the effective number of neutrino species at BBN is $N_\nu = 2.86
\pm 0.15$. Future CMB Stage-4 measurements promise substantial improvements in
BBN parameters: helium abundance determinations will be competitive with the
best astronomical determinations, and $N_{\rm eff}$ will approach sensitivities
capable of detecting the effects of Standard Model neutrino heating of the
primordial plasma. (Abridged)


  In this paper, we present a formulation of the classical theory of Fermionic
(anticommuting) fields, which fits into the general framework proposed by
K.Fredenhagen, M.Duetsch and R.Brunetti. It was inspired by the recent
developments in perturbative algebraic quantum field theory and allows for a
deeper structural understanding also on the classical level. We propose a
modification of this formalism that allows to treat also Fermionic fields. In
contrast to other formulations of classical theory of anticommuting variables,
we don't introduce additional Grassman degrees of freedom. Instead the
anticommutativity is introduced in a natural way on the level of functionals.
Moreover our construction incorporates the functional-analytic and topological
aspects, which is usually neglected in the treatments of anticommuting fields.
We also give an example of an interacting model where our framework can be
applied.


  There is increasing appetite for analysing populations of network data due to
the fast-growing body of applications demanding such methods. While methods
exist to provide readily interpretable summaries of heterogeneous network
populations, these are often descriptive or ad hoc, lacking any formal
justification. In contrast, principled analysis methods often provide results
difficult to relate back to the applied problem of interest. Motivated by two
complementary applied examples, we develop a Bayesian framework to
appropriately model complex heterogeneous network populations, whilst also
allowing analysts to gain insights from the data, and make inferences most
relevant to their needs. The first application involves a study in Computer
Science measuring human movements across a University. The second analyses data
from Neuroscience investigating relationships between different regions of the
brain. While both applications entail analysis of a heterogeneous population of
networks, network sizes vary considerably. We focus on the problem of
clustering the elements of a network population, where each cluster is
characterised by a network representative. We take advantage of the Bayesian
machinery to simultaneously infer the cluster membership, the representatives,
and the community structure of the representatives, thus allowing intuitive
inferences to be made. The implementation of our method on the human movement
study reveals interesting movement patterns of individuals in clusters, readily
characterised by their network representative. For the brain networks
application, our model reveals a cluster of individuals with different network
properties of particular interest in Neuroscience. The performance of our
method is additionally validated in extensive simulation studies.


  The aim of the present study is to analyze the effect of the electron
cyclotron heating (ECH) on the linear stability of Alfven Eigenmodes (AE) and
energetic particle modes (EPM) triggered by energetic ions in Heliotron J
plasma. The analysis is performed using the FAR3d code that solves a reduced
MHD model to describe the thermal plasma coupled with a gyrofluid model for the
energetic particles (EP) species. The simulations reproduce the AE/EPM
stability trends observed in the experiments as the electron temperature (Te)
increases, modifying the thermal plasma beta, EP beta and EP slowing down time.
Particularly, the n/m=1/2 EPM and 2/4 Global AE (GAE) are stabilized in the low
bumpiness (LB) configuration due to an enhancement of the continuum, Finite
Larmor radius (FLR) and e-i Landau damping effects as the thermal beta
increases. On the other hand, a larger ECH injection power cannot stabilize the
AE/EPM in Medium (MB) and High bumpiness (HB) configurations because the
damping effects are weaker compared to the LB case, unable to balance the
further destabilization induced by an enhanced EP resonance as the EP slowing
down time and EP beta increases with Te


  We study the nonclassicality of photon-added squeezed vacuum (PASV) and its
decoherence in thermal environment in terms of the sub-Poissonian statistics
and the negativity of Wigner function (WF). By converting the PASV to a
squeezed Hermite polynomial excitation state, we derive a compact expression
for the normalization factor of m-PASV, which is an m-order Legendre polynomial
of squeezing parameter r. We also derive the explicit expression of WF of
m-PASV and find the negative region of WF in phase space. We show that there is
an upper bound value of r for this state to exhibit sub-Poissonian statistics
increasing as m increases. Then we derive the explicit analytical expression of
time evolution of WF of m-PASV in the thermal channel and discuss the loss of
nonclassicality using the negativity of WF. The threshold value of decay time
is presented for the single PASV.


  Prosopography is an investigation of the common characteristics of a group of
people in history, by a collective study of their lives. It involves a study of
biographies to solve historical problems. If such biographies are unavailable,
surviving documents and secondary biographical data are used. Quantitative
prosopography involves analysis of information from a wide variety of sources
about "ordinary people". In this paper, we present a machine learning framework
for automatically designing a people gazetteer which forms the basis of
quantitative prosopographical research. The gazetteer is learnt from the noisy
text of newspapers using a Named Entity Recognizer (NER). It is capable of
identifying influential people from it by making use of a custom designed
Influential Person Index (IPI). Our corpus comprises of 14020 articles from a
local newspaper, "The Sun", published from New York in 1896. Some influential
people identified by our algorithm include Captain Donald Hankey (an English
soldier), Dame Nellie Melba (an Australian operatic soprano), Hugh Allan (a
Canadian shipping magnate) and Sir Hugh John McDonald (the first Prime Minister
of Canada).


  Small ions are part of the atmospheric aerosol spectrum, and study of
ion-aerosol interactions is fundamental in atmospheric physics. Air ion physics
and instrumentation are reviewed, including the historical context. A
miniaturised Gerdien condenser for ion measurement, operating in situ to
minimise inlet errors, is described. Two operating modes using independent
current and voltage decay measurements are employed. A more sophisticated
self-calibrating and fully programmable ion mobility spectrometer (PIMS) based
on the same principles, is also discussed. Detailed analysis of error terms and
application of new technology is demonstrated to greatly improve its
capability. Self-consistent experimental approaches, including ionisation and
ion concentration instruments, are used for calibration. In developing and
characterising the individual components of the PIMS, favourable and
unfavourable operating regimes are identified: this approach can also be
applied to other aspiration ion counting techniques. Use of a sophisticated
programmable electrometer permits compensation for leakage terms.
Electrically-charged aerosol particles have been found to complicate the ion
measurements. Consequently, conventional ion-aerosol theory, which neglects the
particulate concentration, is thought to be incomplete. The polymodal ion
mobility spectrum is also found to influence the instrument's operation.
Development of the novel programmable ion instrumentation, in conjunction with
consideration of the ion mobility spectrum yields an improved and flexible
approach to in situ atmospheric ion measurements.


  We investigate parity violation in neutron-nucleus collisions at very low
energy region $(E \leq 100 \ev)$, including resonance states. We use the
coupled channel formalism for resonances with radiative emission. The parity
mixing between resonances with opposite parities is taken into account.
Finally, our theory is applied to $n-^{139}$La collision and relevant remarks
are given.


  We consider a six-dimensional $U(1)$ gauge theory compactified on
two-dimensional manifolds. The number of chiral fermions is determined by the
flux quantization number on the two-dimensional compact manifolds. Using the
Swampland Conjectures, we find constraints among the parameters of the theory:
the flux quantization number, the compactification scale, and the string scale.
Specifically, the Weak Gravity Conjecture and the Trans-Planckian Censorship
Conjecture give non-trivial bounds.


  In the theory of hyperplane arrangements, the most important and difficult
problem is the combinatorial dependency of several properties. In this atricle,
we prove that Terao's celebrated addition-deletion theorem for free
arrangements is combinatorial, i.e., whether you can apply it depends only on
the intersection lattice of arrangements. The proof is based on a classical
technique. Since some parts are already completed recently, we prove the rest
part, i.e., the combinatoriality of the addition theorem. As a corollary, we
can define a new class of free arrangements called the additionally free
arrangement of hyperplanes, which can be constructed from the empty arrangement
by using only the addition theorem. Then we can show that Terao's conjecture is
true in this class. As an application, we can show that every ideal-Shi
arrangement is additionally free, implying that their freeness is
combinatorial.


  In this article dedicated to the memory of Igor D. Chueshov, I first
summarize in a few words the joint results that we obtained over a period of
six years regarding the long-time behavior of solutions to a class of
semilinear stochastic parabolic partial differential equations. Then, as the
beautiful interplay between partial differential equations and probability
theory always was close to Igor's heart, I present some new results concerning
the time evolution of certain Markovian Bernstein processes naturally
associated with a class of deterministic linear parabolic partial differential
equations. Particular instances of such processes are certain conditioned
Ornstein-Uhlenbeck processes, generalizations of Bernstein bridges and
Bernstein loops, whose laws may evolve in space in a non trivial way.
Specifically, I examine in detail the time development of the probability of
finding such processes within two-dimensional geometric shapes exhibiting
spherical symmetry. I also define a Faedo-Galerkin scheme whose ultimate goal
is to allow approximate computations with controlled error terms of the various
probability distributions involved.


  There has been a significant interest in the last years in finding fractional
quantum Hall physics in lattice models, but it is not always clear how these
models connect to the corresponding models in continuum systems. Here we
introduce a family of models that is able to interpolate between a recently
proposed set of lattice models with Laughlin-like ground states constructed
from conformal field theory and models with ground states that are practically
the usual bosonic/fermionic Laughlin states in the continuum. Both the ground
state and the Hamiltonian are known analytically, and we find that the
Hamiltonian in the continuum limit does not coincide with the usual delta
interaction Hamiltonian for the Laughlin states. We introduce quasiholes into
the models and show analytically that their braiding properties are as expected
if the quasiholes are screened. We demonstrate screening numerically for the
1/3 Laughlin model and find that the quasiholes are slightly smaller in the
continuum than in the lattice. Finally, we compute the effective magnetic field
felt by the quasiholes and show that it is close to uniform when approaching
the continuum limit. The techniques presented here to interpolate between the
lattice and the continuum can also be applied to other fractional quantum Hall
states that are constructed from conformal field theory.


  We performed resonant soft X-ray diffraction on known charge density wave
(CDW) compounds, rare earth tri-tellurides. Near the $M_5$ (3d - 4f) absorption
edge of rare earth ions, an intense diffraction peak is detected at a
wavevector identical to that of CDW state hosted on Te$_2$ planes, indicating a
CDW-induced modulation on the rare earth ions. Surprisingly, the temperature
dependence of the diffraction peak intensity demonstrates an exponential
increase at low temperatures, vastly different than that of the CDW order
parameter. Assuming 4f multiplet splitting due to the CDW states,we present a
model to calculate X-ray absorption spectrum and resonant profile of the
diffraction peak, agreeing well with experimental observations. Our results
demonstrate a situation where the temperature dependence of resonant X-ray
diffraction peak intensity is not directly related to the intrinsic behavior of
the order parameter associated with the electronic order, but is dominated by
the thermal occupancy of the valence states.


  We study experimentally the interaction of a soliton with a nonlinear
lattice. We observe the formation of a novel type of composite soliton created
by strong coupling of mutually incoherent periodic and localized beam
components. By imposing an initial transverse momentum on the soliton stripe,
we observe the effect of lattice compression and deformation.


  The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy
algorithm for finding the balanced minimum evolution (BME) tree associated to a
dissimilarity map. From this point of view, NJ is ``optimal'' when the
algorithm outputs the tree which minimizes the balanced minimum evolution
criterion. We use the fact that the NJ tree topology and the BME tree topology
are determined by polyhedral subdivisions of the spaces of dissimilarity maps
${\R}_{+}^{n \choose 2}$ to study the optimality of the neighbor-joining
algorithm. In particular, we investigate and compare the polyhedral
subdivisions for $n \leq 8$. A key requirement is the measurement of volumes of
spherical polytopes in high dimension, which we obtain using a combination of
Monte Carlo methods and polyhedral algorithms. We show that highly unrelated
trees can be co-optimal in BME reconstruction, and that NJ regions are not
convex. We obtain the $l_2$ radius for neighbor-joining for $n=5$ and we
conjecture that the ability of the neighbor-joining algorithm to recover the
BME tree depends on the diameter of the BME tree.


  We present an implementation of an efficient algorithm for the calculation of
the spectrum of one-dimensional quantum systems with periodic boundary
conditions. This algorithm is based on a matrix product representation for
quantum states (MPS), and a similar representation for Hamiltonians and other
operators (MPO). It is significantly more efficient for systems of about 100
sites and more than for small quantum systems. We apply the formalism to
calculate the ground state and first excited state of a spin-1 Heisenberg ring
and deduce the size of the Haldane gap. The results are compared to previous
high-precision DMRG calculations. Furthermore, we study spin-1 systems with a
biquadratic nearest-neighbor interaction and show first results of an
application to a mesoscopic Hubbard ring of spinless Fermions which carries a
persistent current.


  A Gaussian measurement error assumption, i.e., an assumption that the data
are observed up to Gaussian noise, can bias any parameter estimation in the
presence of outliers. A heavy tailed error assumption based on Student's t
distribution helps reduce the bias. However, it may be less efficient in
estimating parameters if the heavy tailed assumption is uniformly applied to
all of the data when most of them are normally observed. We propose a mixture
error assumption that selectively converts Gaussian errors into Student's t
errors according to latent outlier indicators, leveraging the best of the
Gaussian and Student's t errors; a parameter estimation can be not only robust
but also accurate. Using simulated hospital profiling data and astronomical
time series of brightness data, we demonstrate the potential for the proposed
mixture error assumption to estimate parameters accurately in the presence of
outliers.


  We propose to incorporate neural architecture search (NAS) into
general-purpose multi-task learning (GP-MTL). Existing NAS methods typically
define different search spaces according to different tasks. In order to adapt
to different task combinations (i.e., task sets), we disentangle the GP-MTL
networks into single-task backbones (optionally encode the task priors), and a
hierarchical and layerwise features sharing/fusing scheme across them. This
enables us to design a novel and general task-agnostic search space, which
inserts cross-task edges (i.e., feature fusion connections) into fixed
single-task network backbones. Moreover, we also propose a novel single-shot
gradient-based search algorithm that closes the performance gap between the
searched architectures and the final evaluation architecture. This is realized
with a minimum entropy regularization on the architecture weights during the
search phase, which makes the architecture weights converge to near-discrete
values and therefore achieves a single model. As a result, our searched model
can be directly used for evaluation without (re-)training from scratch. We
perform extensive experiments using different single-task backbones on various
task sets, demonstrating the promising performance obtained by exploiting the
hierarchical and layerwise features, as well as the desirable generalizability
to different i) task sets and ii) single-task backbones. The code of our paper
is available at https://github.com/bhpfelix/MTLNAS.


  An Italian dominating function (IDF) of a graph G is a function $ f: V(G)
\rightarrow \{0,1,2\} $ satisfying the condition that for every $ v\in V $ with
$ f(v) = 0$, $\sum_{ u\in N(v)} f(u) \geq 2. $ The weight of an IDF on $G$ is
the sum $ f(V)= \sum_{v\in V}f(v) $ and the Italian domination number, $
\gamma_I(G) $, is the minimum weight of an IDF. An IDF is a perfect Italian
dominating function (PID) on $G$, if for every vertex $ v \in V(G) $ with $
f(v) = 0 $ the total weight assigned by $f$ to the neighbours of $ v $ is
exactly 2, i.e., all the neighbours of $u$ are assigned the weight 0 by $f$
except for exactly one vertex $v$ for which $ f(v) = 2 $ or for exactly two
vertices $v$ and $w$ for which $ f(v) = f(w) = 1 $. The weight of a PID-
function is $f(V)=\sum_{u \in V(G)}f(u)$. The perfect Italian domination number
of $G$, denoted by $ \gamma^{p}_{I}(G), $ is the minimum weight of a
PID-function of $G$. In this paper we obtain the Italian domination number and
perfect Italian domination number of Sierpi\'{n}ski graphs.


  We study the problem of stochastic bandits with adversarial corruptions in
the cooperative multi-agent setting, where $V$ agents interact with a common
$K$-armed bandit problem, and each pair of agents can communicate with each
other to expedite the learning process. In the problem, the rewards are
independently sampled from distributions across all agents and rounds, but they
may be corrupted by an adversary. Our goal is to minimize both the overall
regret and communication cost across all agents. We first show that an additive
term of corruption is unavoidable for any algorithm in this problem. Then, we
propose a new algorithm that is agnostic to the level of corruption. Our
algorithm not only achieves near-optimal regret in the stochastic setting, but
also obtains a regret with an additive term of corruption in the corrupted
setting, while maintaining efficient communication. The algorithm is also
applicable for the single-agent corruption problem, and achieves a high
probability regret that removes the multiplicative dependence of $K$ on
corruption level. Our result of the single-agent case resolves an open question
from Gupta et al. [2019].


  Realistic quantum mechanical systems are always exposed to an external
environment. The presence of the environment often gives rise to a Markovian
process in which the system loses information to its surroundings. However,
many quantum systems exhibit a pronounced non-Markovian behavior in which there
is a flow of information from the environment back to the system, signifying
the presence of quantum memory effects [1-5]. The environment is usually
composed of a large number of degrees of freedom which are difficult to
control, but some sophisticated schemes for modifying the environment have been
developed [6]. The physical realization and control of dynamical processes in
open quantum systems plays a decisive role, for example, in recent proposals
for the generation of entangled states [7-9], for schemes of dissipative
quantum computation [10], for the design of quantum memories [11] and for the
enhancement of the efficiency in quantum metrology [12]. Here we report an
experiment which allows through selective preparation of the initial
environmental states to drive the open system from the Markovian to the
non-Markovian regime, to control the information flow between the system and
the environment, and to determine the degree of non-Markovianity by direct
measurements on the open system.


  The aim of this work is to study the effects of environment on the growth in
size of galaxies. We examine the stellar mass-size relation for a sample of
isolated galaxies interpreted as stellar systems where evolution has been
mainly governed by internal processes. Effects of environment on the stellar
mass-size relation are evaluated by comparing our results with samples of less
isolated early- and late-type galaxies, as well as, for the first time,
different spiral subtypes. We find no difference in the stellar mass-size
relation for very isolated and less isolated early-type galaxies. We find that
late-type isolated galaxies are ~1.2 times larger than less isolated objects
with similar mass. Isolated galaxies and comparison samples were divided into 6
morphological ranges (E/S0, Spirals, Sb, Sbc, Sc, and Scd-Sdm) and 5 stellar
mass bins between log(M*)=[9,11.5]. In all cases the relation is better defined
and has less scatter for the isolated galaxies. We find that as the
morphological type becomes later the galaxy size (for a fixed stellar mass)
becomes larger. For the lowest stellar mass bins log(M*)=[9,10] we find good
agreement between sizes of AMIGA and comparison spirals. The isolated spiral
galaxies in the high stellar mass bins log(M*)=[10,11] tend to be larger than
less isolated galaxies. This difference in size is found for all spiral
subtypes and becomes larger when we compare fully isolated galaxies with
galaxies having 2 or more satellites (neighbors within 3 magnitudes of
difference at a distance less than 250 kpc from the galaxy). Our results
suggest that massive spiral galaxies located in low density environments, both
in terms of major companions and satellites, have larger sizes than samples of
less isolated galaxies. Hence the environment has played a role in the growth
in size of massive spiral galaxies.


  A categorical framework for modeling and analyzing systems in a broad sense
is proposed. These systems should be thought of as `machines' with inputs and
outputs, carrying some sort of signal that occurs through some notion of time.
Special cases include continuous and discrete dynamical systems (e.g. Moore
machines). Additionally, morphisms between the different types of systems allow
their translation in a common framework. A central goal is to understand the
systems that result from arbitrary interconnection of component subsystems,
possibly of different types, as well as establish conditions that ensure
totality and determinism compositionally. The fundamental categorical tools
used here include lax monoidal functors, which provide a language of
compositionality, as well as sheaf theory, which flexibly captures the crucial
notion of time.


  The computation of the amplitude, $\alpha$, of asymptotic standing wave tails
of weakly delocalized, stationary solutions in a fifth-order Korteweg-de Vries
equation is revisited. Assuming the coefficient of the fifth order derivative
term, $\epsilon^2\ll1$, a new derivation of the ``beyond all orders in
$\epsilon$'' amplitude, $\alpha$, is presented. It is shown by asymptotic
matching techniques, extended to higher orders in $\epsilon$, that the value of
$\alpha$ can be obtained from the asymmetry at the center of the unique
solution exponentially decaying in one direction. This observation,
complemented by some fundamental results of Hammersley and Mazzarino [Proc. R.
Soc. Lond. A 424, 19 (1989)], not only sheds new light on the computation of
$\alpha$, but also greatly facilitates its numerical determination to a
remarkable precision for so small values of $\epsilon$, which are beyond the
capabilities of standard numerical methods.


  This paper has been withdrawn because there is a fundamental error in the
computations; with the right computational scheme it seems to be just a version
of the Jones polynomial


  Let G be a compact connected Lie group with maximal torus T, and H a closed
subgroup containing T . We work out the Atiyah--Bott--Berline--Vergne
localization formula for the homogeneous space G/H under the natural action of
the maximal torus T. The computation gives explicit formulas for the ordinary
and equivariant characteristic numbers of a homogeneous space.


  We study a unification model for dark energy, dark matter, and inflation with
a single scalar field with non canonical kinetic term. In this model the
kinetic term of the Lagrangian accounts for the dark matter and dark energy,
and at early epochs a quadratic potential accounts for slow roll inflation. The
present work is an extension to the work by Bose and Majumdar [1] with a more
general kinetic term that was proposed by Chimento in [2]. We demonstrate that
the model is viable at the background and linear perturbation levels.


  We show that images of TeV blazars in the GeV energy band should contain,
along with point-like sources, degree-scale jet-like extensions. These GeV
extensions are the result of electromagnetic cascades initiated by TeV
gamma-rays interacting with extragalactic background light and the deflection
of the cascade electrons/positrons in extragalactic magnetic fields (EGMF).
Using Monte-Carlo simulations, we study the spectral and timing properties of
the degree-scale extensions in simulated GeV band images of TeV blazars. We
show that the brightness profile of such degree-scale extensions can be used to
infer the lightcurve of the primary TeV gamma-ray source over the past 1e7 yr,
i.e. over a time scale comparable to the life-time of the parent active
galactic nucleus. This implies that the degree-scale jet-like GeV emission
could be detected not only near known active TeV blazars, but also from "TeV
blazar remnants", whose central engines were switched off up to ten million
years ago. Since the brightness profile of the GeV "jets" depends on the
strength and the structure of the EGMF, their observation provides additionally
information about the EGMF.


  Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain
conditions and obtain some classes of algebras whose finitistic dimensions are
finite.


  Temporal data (such as news articles or Twitter feeds) often consists of a
mixture of long-lasting trends and popular but short-lasting topics of
interest. A truly successful topic modeling strategy should be able to detect
both types of topics and clearly locate them in time. In this paper, we first
show that nonnegative CANDECOMP/PARAFAC decomposition (NCPD) is able to
discover topics of variable persistence automatically. Then, we propose
sparseness-constrained NCPD (S-NCPD) and its online variant in order to
actively control the length of the learned topics effectively and efficiently.
Further, we propose quantitative ways to measure the topic length and
demonstrate the ability of S-NCPD (as well as its online variant) to discover
short and long-lasting temporal topics in a controlled manner in semi-synthetic
and real-world data including news headlines. We also demonstrate that the
online variant of S-NCPD reduces the reconstruction error more rapidly than
S-NCPD.


  In the last two decades, a number of methods have been proposed for
forecasting based on fuzzy time series. Most of the fuzzy time series methods
are presented for forecasting of car road accidents. However, the forecasting
accuracy rates of the existing methods are not good enough. In this paper, we
compared our proposed new method of fuzzy time series forecasting with existing
methods. Our method is based on means based partitioning of the historical data
of car road accidents. The proposed method belongs to the kth order and
time-variant methods. The proposed method can get the best forecasting accuracy
rate for forecasting the car road accidents than the existing methods.


  We analyze a deterministic form of the random walk on the integer line called
the {\em liar machine}, similar to the rotor-router model, finding
asymptotically tight pointwise and interval discrepancy bounds versus random
walk. This provides an improvement in the best-known winning strategies in the
binary symmetric pathological liar game with a linear fraction of responses
allowed to be lies. Equivalently, this proves the existence of adaptive binary
block covering codes with block length $n$, covering radius $\leq fn$ for
$f\in(0,1/2)$, and cardinality $O(\sqrt{\log \log n}/(1-2f))$ times the sphere
bound $2^n/\binom{n}{\leq \lfloor fn\rfloor}$.


  We study two different actions on the moduli spaces of logarithmic
connections over smooth complex projective curves. Firstly, we establish a
dictionary between logarithmic orbifold connections and parabolic logarithmic
connections over the quotient curve. Secondly, we prove that fixed points on
the moduli space of connections under the action of finite order line bundles
are exactly the push-forward of logarithmic connections on a certain unramified
Galois cover of the base curve. In the coprime case, this action of finite
order line bundles on the moduli space is cohomologically trivial.


  Extreme-mass-ratio inspirals consist of binary systems of compact objects,
with orders of magnitude differences in their masses, in the regime where the
dynamics are driven by gravitational wave emission. The unique nature of
extreme-mass-ratio inspirals facilitates the exploration of diverse and
stimulating tests related to various aspects of black holes and General
Relativity. These tests encompass investigations into the spacetime geometry,
the dissipation of the binary system energy and angular momentum, and the
impact of the intrinsic non-linear effects of the gravitational interaction.
This review accounts for the manifold opportunities for testing General
Relativity, ranging from examinations of black hole properties to cosmological
and multimessenger tests.


  We introduce the operator fidelity and propose to use its susceptibility for
characterizing the sensitivity of quantum systems to perturbations. Two typical
models are addressed: one is the transverse Ising model exhibiting a quantum
phase transition, and the other is the one dimensional Heisenberg spin chain
with next-nearest-neighbor interactions, which has the degeneracy. It is
revealed that the operator fidelity susceptibility is a good indicator of
quantum criticality regardless of the system degeneracy.


  Growing concern that most published results, including those widely agreed
upon, may be false are rarely examined against rapidly expanding research
production. Replications have only occurred on small scales due to prohibitive
expense and limited professional incentive. We introduce a novel,
high-throughput replication strategy aligning 51,292 published claims about
drug-gene interactions with high-throughput experiments performed through the
NIH LINCS L1000 program. We show (1) that unique claims replicate 19% more
frequently than at random, while those widely agreed upon replicate 45% more
frequently, manifesting collective correction mechanisms in science; but (2)
centralized scientific communities perpetuate claims that are less likely to
replicate even if widely agreed upon, demonstrating how centralized,
overlapping collaborations weaken collective understanding. Decentralized
research communities involve more independent teams and use more diverse
methodologies, generating the most robust, replicable results. Our findings
highlight the importance of science policies that foster decentralized
collaboration to promote robust scientific advance.


  Coulomb final-state interaction of positive charged kaons in heavy ion
reactions and its impact on the kaon transverse flow and the kaon azimuthal
distribution are investigated within the framework of QMD (Quantum Molecular
Dynamics) model. The Coulomb interaction is found to tend to draw the flow of
kaons away from that of nucleons and lead to a more isotropic azimuthal
distribution of kaons in the target rapidity region. The recent FOPI data have
been analyzed by taking into accout both the Coulomb interaction and a kaon
in-medium potential of the strong interaction. It is found that both the
calculated kaon flows with only the Coulomb interaction and with both the
Coulomb interaction and the strong potential agree within the error bars with
the data. The kaon azimuthal distribution exhibits asymmetries of similar
magnitude in both theoretical approaches. This means, the inclusion of the
Coulomb potential makes it more difficult to extract information of the kaon
mean field potential in nuclear matter from the kaon flow and azimuthal
distribution data.


  The famous $k$-means++ algorithm of Arthur and Vassilvitskii [SODA 2007] is
the most popular way of solving the $k$-means problem in practice. The
algorithm is very simple: it samples the first center uniformly at random and
each of the following $k-1$ centers is then always sampled proportional to its
squared distance to the closest center so far. Afterward, Lloyd's iterative
algorithm is run. The $k$-means++ algorithm is known to return a $\Theta(\log
k)$ approximate solution in expectation.
  In their seminal work, Arthur and Vassilvitskii [SODA 2007] asked about the
guarantees for its following \emph{greedy} variant: in every step, we sample
$\ell$ candidate centers instead of one and then pick the one that minimizes
the new cost. This is also how $k$-means++ is implemented in e.g. the popular
Scikit-learn library [Pedregosa et al.; JMLR 2011].
  We present nearly matching lower and upper bounds for the greedy $k$-means++:
We prove that it is an $O(\ell^3 \log^3 k)$-approximation algorithm. On the
other hand, we prove a lower bound of $\Omega(\ell^3 \log^3 k / \log^2(\ell\log
k))$. Previously, only an $\Omega(\ell \log k)$ lower bound was known
[Bhattacharya, Eube, R\"oglin, Schmidt; ESA 2020] and there was no known upper
bound.


  Let $A \subset \mathbb R$ and $G \subset A \times A$. We prove that, for any
$\lambda \in \mathbb R \setminus \{-1,0,1\}$, \[ \max \{|A+_G A|, |A+_G \lambda
A|, |A\cdot_G A|\} \gg |G|^{6/11}. \]


  We investigate the following generalisation of the 'multiplication table
problem' of Erd\H{o}s: given a bipartite graph with $m$ edges, how large is the
set of sizes of its induced subgraphs? Erd\H{o}s's problem of estimating the
number of distinct products $ab$ with $a,b \le n$ is precisely the problem
under consideration when the graph in question is the complete bipartite graph
$K_{n,n}$. In this note, we prove that the set of sizes of the induced
subgraphs of any bipartite graph with $m$ edges contains $\Omega(m/(\log
m)^{12})$ distinct elements.


  Harmonic stator-rotor coupling offers a promising approach for the
interconnection of rotating subsystems in the simulation of electric machines.
This paper studies the stability of discretization schemes based on harmonic
coupling in the framework of mortar methods for Poisson-like problems. A
general criterion is derived that allows to ensure the relevant inf-sup
stability condition for a variety of specific discretization approaches,
including finite-element methods and isogeometric analysis with harmonic mortar
coupling. The validity and sharpness of the theoretical results is demonstrated
by numerical tests.


  Spin textures such as skyrmions and magnetic vortices are good candidates for
a variety of applications, such as magnetic memories, oscillators and
neuromorphic computing. Understanding the magnetic process of these systems is
important, as it determines the system's response in field and frequency. In
this work, we investigated the magnetization process of single microdisks by
measuring their magnetotransport properties as a function of temperature. The
strong dependence of resistance on the disks magnetic state helped us
understand the magnetization configurations of a single microdisk for different
temperatures and fields. We determined the thermal barriers for the nucleation
and annihilation processes by fitting the nucleation and annihilation fields to
an exponential model. Moreover, we observed and characterized the domain wall
depinning effect for temperatures below 100 K. This effect prevents the
formation of a magnetic vortex during the nucleation process.


  We present a Dalitz plot analysis of charmless B+- decays to the final state
pi+-pi+-pi-+ using a sample of (465+-5)x10^-6 BBbar pairs collected by the
BABAR experiment at \sqrt{s} = 10.58 GeV. We measure the branching fractions
BF(B+- --> pi+-pi+-pi-+) = (15.2+-0.6+-1.2+-0.4)x10^-6, BF(B+- -->
rho0(770)pi+-) = (8.1+-0.7+-1.2^{+0.4}_{-1.1})x10^-6, BF(B+- --> f2(1270)pi+-)
= (1.57+-0.42+-0.16^{+0.53}_{-0.19})x10^-6, and BF(B+- --> pi+-pi+-pi-+
nonresonant) = (5.3+-0.7+-0.6^{+1.1}_{-0.5})x10^-6, where the uncertainties are
statistical, systematic, and model-dependent, respectively. Measurements of
branching fractions for the modes B+- --> rho0(1450)pi+- and B+- -->
f0(1370)pi+- are also presented. We observe no significant direct CP
asymmetries for the above modes, and there is no evidence for the decays B+-
--> chiC0 pi+-, or B+- --> chiC2 pi+-.


  Fully Homomorphic Encryption (FHE) has made it possible to perform addition
and multiplication operations on encrypted data. Using FHE in control thus has
the advantage that control effort for a plant can be calculated remotely
without ever decrypting the exchanged information. FHE in its current form is
however not practically applicable for real-time control as its computational
load is very high compared to traditional encryption methods. In this paper a
reformulation of the Gentry FHE scheme is proposed and applied on an FPGA to
solve this problem. It is shown that the resulting FHE scheme can be
implemented for real-time stabilization of an inverted double pendulum using
discrete time control.


  Machine learning (ML) models are known to be vulnerable to a number of
attacks that target the integrity of their predictions or the privacy of their
training data. To carry out these attacks, a black-box adversary must typically
possess the ability to query the model and observe its outputs (e.g., labels).
In this work, we demonstrate, for the first time, the ability to enhance such
decision-based attacks. To accomplish this, we present an approach that
exploits a novel side channel in which the adversary simply measures the
execution time of the algorithm used to post-process the predictions of the ML
model under attack. The leakage of inference-state elements into algorithmic
timing side channels has never been studied before, and we have found that it
can contain rich information that facilitates superior timing attacks that
significantly outperform attacks based solely on label outputs. In a case
study, we investigate leakage from the non-maximum suppression (NMS) algorithm,
which plays a crucial role in the operation of object detectors. In our
examination of the timing side-channel vulnerabilities associated with this
algorithm, we identified the potential to enhance decision-based attacks. We
demonstrate attacks against the YOLOv3 detector, leveraging the timing leakage
to successfully evade object detection using adversarial examples, and perform
dataset inference. Our experiments show that our adversarial examples exhibit
superior perturbation quality compared to a decision-based attack. In addition,
we present a new threat model in which dataset inference based solely on timing
leakage is performed. To address the timing leakage vulnerability inherent in
the NMS algorithm, we explore the potential and limitations of implementing
constant-time inference passes as a mitigation strategy.


  We revisit the construction in four-dimensional gauged $Spin(4)$ supergravity
of the holographic duals to topologically twisted three-dimensional
$\mathcal{N}=4$ field theories. Our focus in this paper is to highlight some
subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion
of finite counterterms and the necessity of a Legendre transformation to find
the dual to the field theory generating functional. Studying the geometry of
these supergravity solutions, we conclude that the gravitational free energy is
indeed independent from the metric of the boundary, and it vanishes for any
smooth solution.


  The presence of small neutrino masses and flavour mixings can be accounted
for naturally in various models about extensions of the standard model,
particularly in the seesaw mechanism models. In this work, we present a
minimally extended seesaw framework with two right-handed neutrinos, where the
active neutrino masses are derived in the radiative regime. Using the framework
it can be shown that within certain mass limits, the light neutrino mass term
can approach a form that is similar to its form under the type-I seesaw
mechanism. Apart from this, we show that the decay width of right-handed
neutrinos (produced through the decay of W boson in a particle collider) is
short enough to cause a sufficiently long lifetime for the particles, thus
ensuring an observable displacement in the LHC between the production and decay
vertices. We comment on the fact that these displaced vertex signatures thus
can serve as a means to verify the existence of these right-handed neutrinos in
future experiments. Lastly, we line up the possibility of our future work where
the vertex signatures of particles greater than the mass of W boson can be
worked upon.


  The orbital period of the eclipsing cataclysmic variable SDSS
J170213.26+322954.1 has been measured as 0.10008215+/-0.00000001d using
observations of eclipses during the first recorded superoutburst in October
2005 together with eclipses observed in quiescence in July 2003. This period
puts the system in the centre of the period gap. Observation of superhumps
during the October 2005 outburst with a period of 0.10496+/-0.00015d confirms
this to be a UGSU-type system with a period excess of 4.9%.


  In this paper, we apply the idea of T-duality to projective spaces. From a
connection on a line bundle on $\mathbb P^n$, a Lagrangian in the mirror
Landau-Ginzburg model is constructed. Under this correspondence, the full
strong exceptional collection $\mathcal O_{\mathbb P^n}(-n-1),...,\mathcal
O_{\mathbb P^n}(-1)$ is mapped to standard Lagrangians in the sense of
\cite{nz}. Passing to constructible sheaves, we explicitly compute the quiver
structure of these Lagrangians, and find that they match the quiver structure
of this exceptional collection of $\mathbb P^n$. In this way, T-duality
provides quasi-equivalence of the Fukaya category generated by these
Lagrangians and the category of coherent sheaves on $\mathbb P^n$, which is a
kind of homological mirror symmetry.


  One of the fundamental concepts of quantum information theory is that of
entanglement purification; that is, the transformation of a partially entangled
state into a smaller-dimensional, more completely entangled state. Of
particular interest are protocols for entanglement purification (EPPs) that
alternate purely local operations with one- or two-way classical communication.
In the present work, we consider a more general, but simpler, class of
transformations, called separable superoperators. Since every EPP is a
separable superoperator, bounds on separable superoperators apply as well to
EPPs; we use this fact to give a new upper bound on the rate of EPPs on
Bell-diagonal states, and thus on the capacity of Bell-diagonal channels.


  Abell 1689 is a galaxy cluster at $z=0.183$ where previous measurements of
its mass using various techniques gave discrepant results. We present a new
detailed measurement of the mass with the data based on X-ray observations with
the European Photon Imaging Camera aboard the XMM-Newton Observatory,
determined by using an unparameterized deprojection technique. Fitting the
total mass profile to a Navarro-Frenk-White model yields halo concentration
$c=7.2^{+1.6}_{-2.4}$ and $r_{200}=1.13 \pm 0.21 h^{-1} \mathrm{Mpc}$,
corresponding to a mass which is less than half of what is found from
gravitational lensing. Adding to the evidence of substructure from optical
observations, X-ray analysis shows a highly asymmetric temperature profile and
a non-uniform redshift distribution implying large scale relative motion of the
gas. A lower than expected gas mass fraction $f_{gas}=0.072 \pm 0.008$ (for a
flat $\Lambda$CDM cosmology) suggests a complex spatial and/or dynamical
structure. We also find no signs of any additional absorbing component
previously reported on the basis of the Chandra data, confirming the XMM low
energy response using data from ROSAT.


  The cosmic abundance of hydrides depends critically on high-energy UV, X-ray,
and particle irradiation. Here we study hydrides in star-forming regions where
irradiation by the young stellar object can be substantial, and density and
temperature can be much enhanced over interstellar values. Lines of OH, CH, NH,
SH and their ions OH+, CH+, NH+, SH+, H2O+, and H3O+ were observed in
star-forming regions by the HIFI spectrometer onboard the Herschel Space
Observatory. Molecular column densities are derived from observed ground-state
lines, models, or rotational diagrams. We report here on two prototypical
high-mass regions, AFGL 2591 and W3 IRS5, and compare them to chemical
calculations making assumptions on the high-energy irradiation. A model
assuming no ionizing protostellar emission is compared with (i) a model
assuming strong protostellar X-ray emission and (ii) a two-dimensional (2D)
model including emission in the far UV (FUV, 6 -- 13.6 eV) irradiating the
outflow walls that separate the outflowing gas and infalling envelope material.
We confirm that the effect of FUV in two dimensional models with enlarged
irradiated surfaces is clearly noticeable. A molecule that is very sensitive to
FUV irradiation is CH+, enhanced in abundance by more than 5 orders of
magnitude. The HIFI observations of CH+ lines agree with the two-dimensional
FUV model by Bruderer et al. which computes abundances, non-LTE excitation and
line radiative transfer.{Ref 20} It is concluded that CH+ is a good FUV tracer
in star-forming regions. The effect of potential X-ray irradiation is not
excluded, but cannot be demonstrated by the present data.


  We consider a single impurity with spin $S$ embedded in a three-dimensional
antiferromagnetic system which is close to the quantum critical point (QCP),
separating magnetically ordered and disordered phases. Approaching the QCP from
the disordered phase we study the spatial distribution of spin density and
staggered magnetization induced by the impurity. Using two methods
(self-consistent Born approximation and renormalization group) we found a power
law decay of the spin density $\propto 1/r^3$, and of the staggered
magnetization $\propto 1/r$ with relevant logarithmic corrections. We
demonstrate that the local spin at the impurity site $r=0$ approaches to zero
at the QCP. We show that in the semiclassical limit of large $S$ the problem is
equivalent to the exactly solvable independent boson model. Our results
demonstrate existence of spin-charge separation in the three dimensional
systems in the vicinity of the QCP.


  The role of charge order in the phase diagram of high temperature cuprate
superconductors has been recently re-emphasized by the experimental discovery
of an incipient bi-directional charge density wave (CDW) phase in a class of
underdoped cuprates. In a subset of the experiments, the CDW has been found to
be accompanied by a d-wave intra-unit-cell form factor, indicating modulation
of charge density on the oxygen orbitals sandwiched between neighboring Cu
atoms on the CuO planes (the so-called bond-density wave (BDW) phase). Here we
take a mean field Q_1=(2\pi/3,0) and Q_2=(0,2\pi/3) bi-directional BDW phase
with a d-wave form factor, which closely resembles the experimentally observed
charge ordered states in underdoped cuprates, and calculate the Fermi surface
topology and the resulting quasiparticle Nernst coefficient as a function of
temperature and doping. We establish that, in the appropriate doping ranges
where the low temperature phase (in the absence of superconductivity) is a BDW,
the Fermi surface consists of an electron and a hole pocket, resulting in a low
temperature negative Nernst coefficient as observed in experiments.


  We give an update on the ongoing effort of the RC$^\star$ collaboration to
generate fully dynamical QCD+QED configurations with C$^\star$ boundary
conditions using the openQ$^\star$D code. The simulations are tuned to the
U-symmetric point ($m_d=m_s$) with pions at $m_{\pi^\pm}\approx 400$ MeV. The
splitting of the light mesons is used as one of three tuning observables and
fixed to $m_{K^0} - m_{K^\pm} \approx 5$ MeV and $m_{K^0} - m_{K^\pm} \approx
25$ MeV on ensembles with renormalized electromagnetic coupling
$\alpha_\mathrm{R} \approx \alpha_\mathrm{phys.}$ and $\alpha_\mathrm{R}\approx
5.5 \alpha_\mathrm{phys.}$ respectively. We will discuss some details
concerning our tuning strategy and present the calculation of the meson and
baryon masses. Finally, we will also present a cost analysis for our
simulations. More technical details on finite-volume effects and the tuning can
be found in A. Cotellucci's proceedings.


  We report on an exploratory study of domain wall fermions (DWF) as a lattice
regularisation for heavy quarks. Within the framework of quenched QCD with the
tree-level improved Symanzik gauge action we identify the DWF parameters which
minimise discretisation effects. We find the corresponding effective 4$d$
overlap operator to be exponentially local, independent of the quark mass. We
determine a maximum bare heavy quark mass of $am_h\approx 0.4$, below which the
approximate chiral symmetry and O(a)-improvement of DWF are sustained. This
threshold appears to be largely independent of the lattice spacing. Based on
these findings, we carried out a detailed scaling study for the heavy-strange
meson dispersion relation and decay constant on four ensembles with lattice
spacings in the range $2.0-5.7\,\mathrm{GeV}$. We observe very mild $a^2$
scaling towards the continuum limit. Our findings establish a sound basis for
heavy DWF in dynamical simulations of lattice QCD with relevance to Standard
Model phenomenology.


  Metric facility location is a well-studied problem for which linear
programming methods have been used with great success in deriving approximation
algorithms. The capacity-constrained generalizations, such as capacitated
facility location (CFL) and lower-bounded facility location (LBFL), have proved
notorious as far as LP-based approximation is concerned: while there are
local-search-based constant-factor approximations, there is no known linear
relaxation with constant integrality gap. According to Williamson and Shmoys
devising a relaxation-based approximation for \cfl\ is among the top 10 open
problems in approximation algorithms.
  This paper advances significantly the state-of-the-art on the effectiveness
of linear programming for capacity-constrained facility location through a host
of impossibility results for both CFL and LBFL. We show that the relaxations
obtained from the natural LP at $\Omega(n)$ levels of the Sherali-Adams
hierarchy have an unbounded gap, partially answering an open question of
\cite{LiS13, AnBS13}. Here, $n$ denotes the number of facilities in the
instance. Building on the ideas for this result, we prove that the standard CFL
relaxation enriched with the generalized flow-cover valid inequalities
\cite{AardalPW95} has also an unbounded gap. This disproves a long-standing
conjecture of \cite{LeviSS12}. We finally introduce the family of proper
relaxations which generalizes to its logical extreme the classic star
relaxation and captures general configuration-style LPs. We characterize the
behavior of proper relaxations for CFL and LBFL through a sharp threshold
phenomenon.