  The entanglement between photon pairs generated from the biexciton cascade
transition in a semi- conductor quantum dot located in the vicinity of a metal
nanoparticle is theoretically investigated. In the model scheme, the
biexciton-exciton and exciton-ground state transitions are assumed to be
coupled to two principal plasmon modes of orthogonal polarizations. For a broad
spectral window, because the horizontal and vertical spectra are overlapped,
the biexciton and exciton photons are degenerate in energy. This allows us to
overcome the natural splitting between the intermediate exciton states.
Moreover, the degree of entanglement depends on the geometrical parameters of
the system. i.e., the radius of the metal nanoparticle and the distance between
the quantum dot and the nanoparticle. The results reveal that such a hybrid
system profoundly modifies the photon entanglement even in the absence of
strong coupling between the emitter and the metal nanosphere.


  We propose a new acceleration mechanism for charged particles by using
cylindrical or spherical non-linear acoustic waves propagating in ion-electron
plasma. The acoustic wave, which is described by the cylindrical or spherical
Kortweg-de Vries equation, grows in its wave height as the wave shrinks to the
center. Charged particles confined by the electric potential accompanied with
the shrinking wave get energy by repetition of reflections. We obtain power law
spectrums of energy for accelerated particles. As an application, we discuss
briefly that high energy particles coming from the Sun are produced by the
present mechanism.


  We demonstrate a novel technique for the measurement of the charge carried by
a colloidal particle. The technique uses the phenomenon of the resonance of a
particle held in an optical tweezers trap and driven by a sinusoidal electric
field. The trapped particle forms a strongly damped harmonic oscillator whose
fluctuations are a function of $\gamma$, the ratio of the root-mean square
average of the electric and thermal forces on the particle. At low applied
fields, where $\gamma \ll 1$, the particle is confined to the optical axis
while at high fields ($\gamma \gg 1$) the probability distribution of the
particle is double-peaked. The periodically-modulated thermal fluctuations are
measured with nanometer sensitivity using an interferometric position detector.
Charges, as low as a few elementary charges, can be measured with an
uncertainty of about 0.25 $e$. This is significantly better than previous
techniques and opens up new possibilities for the study of nonpolar
suspensions.


  Type-I quantum defects are considered in the context of the gl_N spin chain.
The type-I defects are associated to the generalized harmonic oscillator
algebra, and the chosen defect matrix is the one of the vector non-linear
Schrodinger (NLS) model. The transmission matrices relevant to this particular
type of defects are computed via the Bethe ansatz methodology.


  We propose a definition of symplectic 2-groupoid which includes integrations
of Courant algebroids that have been recently constructed. We study in detail
the simple but illustrative case of constant symplectic 2-groupoids. We show
that the constant symplectic 2-groupoids are, up to equivalence, in one-to-one
correspondence with a simple class of Courant algebroids that we call constant
Courant algebroids. Furthermore, we find a correspondence between certain Dirac
structures and Lagrangian sub-2-groupoids.


  Transfer learning is crucial in training deep neural networks on new target
tasks. Current transfer learning methods always assume at least one of (i)
source and target task label spaces overlap, (ii) source datasets are
available, and (iii) target network architectures are consistent with source
ones. However, holding these assumptions is difficult in practical settings
because the target task rarely has the same labels as the source task, the
source dataset access is restricted due to storage costs and privacy, and the
target architecture is often specialized to each task. To transfer source
knowledge without these assumptions, we propose a transfer learning method that
uses deep generative models and is composed of the following two stages: pseudo
pre-training (PP) and pseudo semi-supervised learning (P-SSL). PP trains a
target architecture with an artificial dataset synthesized by using conditional
source generative models. P-SSL applies SSL algorithms to labeled target data
and unlabeled pseudo samples, which are generated by cascading the source
classifier and generative models to condition them with target samples. Our
experimental results indicate that our method can outperform the baselines of
scratch training and knowledge distillation.


  Within the framework of the Lovelock gravity theory, we propose a new
rank-four divergenceless tensor consisting of the Riemann curvature tensor and
inheriting its algebraic symmetry characters. Such a tensor can be adopted to
define conserved charges of the Lovelock gravity theory in asymptotically
anti-de Sitter (AdS) spacetimes. Besides, inspired with the case of the
Lovelock gravity, we put forward another general fourth-rank tensor in the
context of an arbitrary diffeomorphism invariant theory of gravity described by
the Lagrangian constructed out of the curvature tensor. On basis of the
newly-constructed tensor, we further suggest a Komar-like formula for the
conserved charges of this generic gravity theory.


  Collective many-body dynamics for time-dependent quantum Hamiltonian
functions is investigated for a dynamical system that exhibits multiple degrees
of freedom, in this case a combined (Paul and Penning) trap. Quantum stability
is characterized by a discrete quasienergy spectrum, while the quasienergy
states are symplectic coherent states. We introduce the generators of the Lie
algebra of the symplectic group ${\cal {SL}}(2, \mathbb R)$, which we use to
build the coherent states (CS) associated to the system under investigation.
The trapped ion is treated as a harmonic oscillator (HO) to which we associate
the quantum Hamilton function. We obtain the kinetic and potential energy
operators as functions of the Lie algebra generators and supply the expressions
for the classical coordinate, momentum, kinetic and potential energy, as well
as the total energy. In addition, we also infer the dispersions for the
coordinate and momentum, together with the asymmetry and the flatness parameter
for the distribution. The system interaction with laser radiation is also
examined for a system of identical two-level atoms. The Hamilton function for
the Dicke model is derived. The optical system is modelled as a HO (trapped
ion) that undergoes interaction with an external laser field and we use it to
engineer a squeezed state of the electromagnetic (EM) field. We consider
coherent and squeezed states associated to both ion dynamics and to the EM
field. Such an approach enables one to build CS in a compact and smart manner
by use of the group theory.


  An efficient finite element method (FEM) for calculating eigenvalues and
eigenfunctions of quantum billiard systems is presented. We consider the FEM
based on triangular $C_1$ continuity quartic interpolation. Various shapes of
quantum billiards including an integrable unit circle are treated. The
numerical results show that the applied method provides accurate set of
eigenvalues exceeding a thousand levels for any shape of quantum billiards on a
personal computer. Comparison with the results from the FEM based on well-known
$C_0$ continuity quadratic interpolation proves the efficiency of the method.


  The crossing of a transition state in a multidimensional reactive system is
mediated by invariant geometric objects in phase space: An invariant
hyper-sphere that represents the transition state itself and invariant
hyper-cylinders that channel the system towards and away from the transition
state. The existence of these structures can only be guaranteed if the
invariant hyper-sphere is normally hyperbolic, i.e., the dynamics within the
transition state is not too strongly chaotic. We study the dynamics within the
transition state for the hydrogen exchange reaction in three degrees of
freedom. As the energy increases, the dynamics within the transition state
becomes increasingly chaotic. We find that the transition state first looses
and then, surprisingly, regains its normal hyperbolicity. The important phase
space structures of transition state theory will therefore exist at most
energies above the threshold.


  In this paper, a geometric framework for neural networks is proposed. This
framework uses the inner product space structure underlying the parameter set
to perform gradient descent not in a component-based form, but in a
coordinate-free manner. Convolutional neural networks are described in this
framework in a compact form, with the gradients of standard --- and
higher-order --- loss functions calculated for each layer of the network. This
approach can be applied to other network structures and provides a basis on
which to create new networks.


  In this short note I present a simple calculation of the top quark and Higgs
masses, based on the idea that in the standard model without elementary Higgs,
the fact that the $U(1)_Y$ coupling becomes of the order of unity at the Landau
scale $\lambda$ leads to spontaneous symmetry breaking and generation of
masses.


  This paper proposes a method for testing the delay lines of Blade
asynchronous timing resilience template. It consists of an offline test method,
with low area overhead, for measuring the internal propagation delay of the
delay lines with external testers.


  Three recent results on weak measurements are presented. They are: i)
repeated measurements on a single copy can not provide any information on it
and further, that in the limit of very large such measurements, weak
measurements have exactly the same characterstics as strong measurements, ii)
the apparent non-invasiveness of weak measurements is \emph{illusory} and they
are no more advantageous than strong measurements even in the specific context
of establishing Leggett-Garg inequalities, when errors are properly taken into
account, and, finally, iii) weak value measurements are optimal, in the precise
sense of Wootters and Fields, when the post-selected states are mutually
unbiased with respect to the eigenstates of the observable whose weak values
are being measured. Notion of weak value coordinates for state spaces are
introduced and elaborated.


  The Ising model has become a popular psychometric model for analyzing item
response data. The statistical inference of the Ising model is typically
carried out via a pseudo-likelihood, as the standard likelihood approach
suffers from a high computational cost when there are many variables (i.e.,
items). Unfortunately, the presence of missing values can hinder the use of
pseudo-likelihood, and a listwise deletion approach for missing data treatment
may introduce a substantial bias into the estimation and sometimes yield
misleading interpretations. This paper proposes a conditional Bayesian
framework for Ising network analysis with missing data, which integrates a
pseudo-likelihood approach with iterative data imputation. An asymptotic theory
is established for the method. Furthermore, a computationally efficient
{P{\'o}lya}-Gamma data augmentation procedure is proposed to streamline the
sampling of model parameters. The method's performance is shown through
simulations and a real-world application to data on major depressive and
generalized anxiety disorders from the National Epidemiological Survey on
Alcohol and Related Conditions (NESARC).


  We show that the reduced motive of a smooth affine quadric is invertible as
an object of the triangulated category of motives DM(k, ZZ[1/e]) (where k is a
perfect field of exponential characteristic e). We also establish a motivic
version of the conjectures of Po Hu on products of certain affine Pfister
quadrics. Both of these results are obtained by studying a novel conservative
functor on (a subcategory of) DM(k, ZZ[1/e]), the construction of which
constitutes the main part of this work.


  We propose that Borcherds' Fake Monster Lie algebra is a broken symmetry of
heterotic string theory compactified on $T^7 \times T^2$. As evidence, we study
the fully flavored counting function for BPS instantons contributing to a
certain loop amplitude. The result is controlled by $\Phi_{12}$, an automorphic
form for $O(2, 26, \mathbb{Z})$. The degeneracies it encodes in its Fourier
coefficients are graded dimensions of a second-quantized Fock space for this
large symmetry algebra. This construction provides a concrete realization of
Harvey and Moore's proposed relationship between Generalized Kac-Moody
symmetries and supersymmetric string vacua.


  In this paper, we introduce a collaborative training algorithm of balanced
random forests with convolutional neural networks for domain adaptation tasks.
In real scenarios, most domain adaptation algorithms face the challenges from
noisy, insufficient training data and open set categorization. In such cases,
conventional methods suffer from overfitting and fail to successfully transfer
the knowledge of the source to the target domain. To address these issues, the
following two techniques are proposed. First, we introduce the optimized
decision tree construction method with convolutional neural networks, in which
the data at each node are split into equal sizes while maximizing the
information gain. It generates balanced decision trees on deep features because
of the even-split constraint, which contributes to enhanced discrimination
power and reduced overfitting problem. Second, to tackle the domain
misalignment problem, we propose the domain alignment loss which penalizes
uneven splits of the source and target domain data. By collaboratively
optimizing the information gain of the labeled source data as well as the
entropy of unlabeled target data distributions, the proposed CoBRF algorithm
achieves significantly better performance than the state-of-the-art methods.


  Dihadron and isolated direct photon-hadron angular correlations are measured
in $p$$+$$p$ collisions at $\sqrt{s}=510$ GeV. Correlations of charged hadrons
of $0.7<p_T<10$ GeV/$c$ with $\pi^0$ mesons of $4<p_T<15$ GeV/$c$ or isolated
direct photons of $7<p_T<15$ GeV/$c$ are used to study nonperturbative effects
generated by initial-state partonic transverse momentum and final-state
transverse momentum from fragmentation. The nonperturbative behavior is
characterized by measuring the out-of-plane transverse momentum component
$p_{\rm out}$ perpendicular to the axis of the trigger particle, which is the
high-$p_T$ direct photon or $\pi^0$. Nonperturbative evolution effects are
extracted from Gaussian fits to the away-side inclusive-charged-hadron yields
for different trigger-particle transverse momenta ($p_T^{\rm trig}$). The
Gaussian widths and root mean square of $p_{\rm out}$ are reported as a
function of the interaction hard scale $p_T^{\rm trig}$ to investigate possible
transverse-momentum-dependent evolution differences between the $\pi^0$-h$^\pm$
and direct photon-h$^\pm$ correlations and factorization breaking effects. The
widths are found to decrease with $p_T^{\rm trig}$, which indicates that the
Collins-Soper-Sterman soft factor is not driving the evolution with the hard
scale in nearly back-to-back dihadron and direct photon-hadron production in
$p$$+$$p$ collisions. This behavior is in contrast to Drell-Yan and
semi-inclusive deep-inelastic scattering measurements.


  Consider a first-order autoregressive process $X_i=\beta
X_{i-1}+\varepsilon_i,$ where $\varepsilon_i=G(\eta_i,\eta_{i-1},\ldots)$ and
$\eta_i,i\in\mathbb{Z}$ are i.i.d. random variables. Motivated by two important
issues for the inference of this model, namely, the quantile inference for
$H_0: \beta=1$, and the goodness-of-fit for the unit root model, the notion of
the marked empirical process
$\alpha_n(x)=\frac{1}{n}\sum_{i=1}^ng(X_i/a_n)I(\varepsilon_i\leq
x),x\in\mathbb{R}$ is investigated in this paper. Herein, $g(\cdot)$ is a
continuous function on $\mathbb{R}$ and $\{a_n\}$ is a sequence of
self-normalizing constants. As the innovation $\{\varepsilon_i\}$ is usually
not observable, the residual marked empirical process $\hat
{\alpha}_n(x)=\frac{1}{n}\sum_{i=1}^ng(X_i/a_n)I(\hat{\varepsilon}_i\l eq
x),x\in\mathbb{R},$ is considered instead, where
$\hat{\varepsilon}_i=X_i-\hat{\beta}X_{i-1}$ and $\hat{\beta}$ is a consistent
estimate of $\beta.$ In particular, via the martingale decomposition of
stationary process and the stochastic integral result of Jakubowski (Ann.
Probab. 24 (1996) 2141-2153), the limit distributions of $\alpha_n(x)$ and
$\hat{\alpha}_n(x)$ are established when $\{\varepsilon_i\}$ is a short-memory
process. Furthermore, by virtue of the results of Wu (Bernoulli 95 (2003)
809-831) and Ho and Hsing (Ann. Statist. 24 (1996) 992-1024) of empirical
process and the integral result of Mikosch and Norvai\v{s}a (Bernoulli 6 (2000)
401-434) and Young (Acta Math. 67 (1936) 251-282), the limit distributions of
$\alpha_n(x)$ and $\hat{\alpha}_n(x)$ are also derived when $\{\varepsilon_i\}$
is a long-memory process.


  Motivated by the recent discovery of 30 new millisecond pulsars in Terzan 5,
made using the Green Bank Telescope's S-band receiver and the Pulsar Spigot
spectrometer, we have set out to use the same observing system in a systematic
search for pulsars in other globular clusters. Here we report on the discovery
of five new pulsars in NGC 6440 and three in NGC 6441; each cluster previously
had one known pulsar. Using the most recent distance estimates to these
clusters, we conclude that there are as many potentially observable pulsars in
NGC 6440 and NGC 6441 as in Terzan 5. We present timing solutions for all of
the pulsars in these globular clusters. Four of the new discoveries are in
binary systems; one of them, PSR J1748-2021B (NGC 6440B), has a wide (P_b =
20.5 d) and eccentric (e = 0.57) orbit. This allowed a measurement of its rate
of advance of periastron: 0.00391(18) degrees per year. If due to the effects
of general relativity, the total mass of this binary system is 2.92 +/- 0.20
solar masses (1 sigma), implying a median pulsar mass of 2.74 +/- 0.21 solar
masses. There is a 1 % probability that the inclination is low enough that
pulsar mass is below 2 solar masses, and 0.10 % probability that it is between
1.20 and 1.44 solar masses. If confirmed, this anomalously large mass would
strongly constrain the equation of state for dense matter. The other highly
eccentric binary, PSR J1750-37A, has e = 0.71, and periastron advance of
0.0055(3) degrees per year, implying a total system mass of 1.97 +/-0.15 solar
masses and, along with the mass function, maximum and median pulsar masses of
1.65 and 1.26 solar masses respectively.


  Upper and lower estimates are obtained for the Schatten-von Neumann norms of
the Hardy-Steklov operator in Lebesgue function spaces on the semi-axis.


  In the nearby (D=14 Mpc) AGN-starburst composite galaxy NGC 1068, it has been
found that the molecular gas in the Circum-nuclear Disk (CND) is outflowing,
which is a manifestation of ongoing AGN feedback. The outflowing gas has a
large spread of velocities, which likely drive different shock chemistry
signatures at different locations in the CND. We perform a multi-line molecular
study using two shock tracers, SiO and HNCO, with the aim to determine the gas
properties traced by these two species, and explore the possibility of
reconstructing the shock history in the CND. Five SiO transitions and three
HNCO transitions were imaged at high resolution $0''.5-0''.8$ with the Atacama
Large Millimeter/submillimeter Array (ALMA). We performed both LTE and non-LTE
radiative transfer analysis coupled with Bayesian inference process in order to
characterize the gas properties, such as molecular gas density and gas
temperature. We found clear evidence of chemical differentiation between SiO
and HNCO, with the SiO/HNCO ratio ranging from greater than one on the east of
CND to lower than one on the west side. The non-LTE radiative transfer analysis
coupled with Bayesian inference confirms that the gas traced by SiO has
different densities - and possibly temperatures - than that traced by HNCO. We
find that SiO traces gas affected by fast shocks while the gas traced by HNCO
is either just affected by slow shocks or not shocked at all. A distinct
differentiation between SiO and HNCO has been revealed in our observations and
the further analysis of the gas properties traced by both species, which
confirms the results from previous chemical modelings.


  We propose an experimental study of adaptive time-stepping methods for
efficient modeling of the aggregation-fragmentation kinetics. Precise modeling
of this phenomena usually requires utilization of the large systems of
nonlinear ordinary differential equations and intensive computations. We
concentrate on performance of three explicit Runge-Kutta time-integration
methods and provide simulations for two types of problems: finding of
equilibrium solutions and simulations for kinetics with periodic solutions. The
first class of problems may be analyzed through the relaxation of the solution
to the stationary state after large time. In this case, the adaptive
time-stepping may help to reach it using big steps reducing cost of the
calculations without loss of accuracy. In the second case, the problem becomes
numerically unstable at certain points of the phase space and may require tiny
steps making the simulations very time-consuming. Adaptive criteria allows to
increase the steps for most of points and speedup simulations significantly.


  We present a calculation of the NNLO QCD corrections to Z-boson pair
production at hadron colliders, based on the N-jettiness method for the real
radiation parts. We discuss the size and shape of the perturbative corrections
along with their associated scale uncertainties and compare our results to
recent LHC data at $\sqrt{s}=13$ TeV.


  Graph are a ubiquitous data representation, as they represent a flexible and
compact representation. For instance, the 3D structure of RNA can be
efficiently represented as $\textit{2.5D graphs}$, graphs whose nodes are
nucleotides and edges represent chemical interactions. In this setting, we have
biological evidence of the similarity between the edge types, as some chemical
interactions are more similar than others.
  Machine learning on graphs have recently experienced a breakthrough with the
introduction of Graph Neural Networks. This algorithm can be framed as a
message passing algorithm between graph nodes over graph edges. These messages
can depend on the edge type they are transmitted through, but no method
currently constrains how a message is altered when the edge type changes.
  Motivated by the RNA use case, in this project we introduce a graph neural
network layer which can leverage prior information about similarities between
edges. We show that despite the theoretical appeal of including this similarity
prior, the empirical performance is not enhanced on the tasks and datasets we
include here.


  In recent years there has been growing evidence that even after teaching
designed to address the learning difficulties dictated by literature, many
physics learners fail to create the proper reasoning chains that connect the
fundamental principles and lead to reasoned predictions. Even though students
have the required knowledge and skills, they are often based on a variety of
intuitive reasoning that leads them to wrong conclusions. This paper studies
students' reasoning on science problems through heuristic - analytical thought
processes (System 1 - System 2). System 1 operates automatically and quickly
with little or no effort and no sense of voluntary control, while System 2
focuses on the demanding mental activities that require it and is slow based on
rules.


  We present new Herschel/PACS images at 70, 100, and 160 micron of the
well-known, nearby, carbon-rich asymptotic giant branch star IRC+10216
revealing multiple dust shells in its circumstellar envelope. For the first
time, dust shells (or arcs) are detected until 320 arcsec. The almost spherical
shells are non-concentric and have an angular extent between 40 deg and 200
deg. The shells have a typical width of 5 arcsec - 8 arcsec, and the shell
separation varies in the range of 10 arcsec - 35 arcsec, corresponding to
500-1700 yr. Local density variations within one arc are visible. The
shell/intershell density contrast is typically 4, and the arcs contain some 50%
more dust mass than the smooth envelope. The observed (nested) arcs record the
mass-loss history over the past 16 000 yr, but Rayleigh-Taylor and
Kelvin-Helmholtz instabilities in the turbulent astropause and astrosheath will
erase any signature of the mass-loss history for at least the first 200 000 yr
of mass loss. Accounting for the bowshock structure, the envelope mass around
IRC+10216 contains >2Msun of gas and dust mass. It is argued that the origin of
the shells is related to non-isotropic mass-loss events and clumpy dust
formation.


  Using the index theorem of Dubson, Le, Ginsburg and Sabbah for the vanishing
cycle functor, we give a short proof of formula of Brasselet, Le and Seade for
the Euler obstruction.


  One of the major challenges in realizing antiferromagnetic and superfluid
phases in optical lattices is the ability to cool fermions. We determine
constraints on the entropy for observing these phases in two-dimensional
Hubbard models. We investigate antiferromagnetic correlations in the repulsive
model at half filling and superfluidity of s-wave pairs in the attractive case
away from half filling using determinantal quantum Monte Carlo simulations that
are free of the fermion sign problem. We find that an entropy per particle
~log(2) is sufficient to observe the charge gap in the repulsive Hubbard model
or the pairing pseudogap in the attractive case. Observing antiferromagnetic
correlations or superfluidity in 2D systems requires a further reduction in
entropy by a factor of three or more. In contrast to higher dimensions, we find
that adiabatic cooling is not useful to achieve the required low temperatures.
We also show that double occupancy measurements are useful for thermometry for
temperatures greater than the nearest-neighbor hopping.


  We study the asymptotics of the natural $L^2$ metric on the Hitchin moduli
space with group $G = \mathrm{SU}(2)$. Our main result, which addresses a
detailed conjectural picture made by Gaiotto, Neitzke and Moore \cite{gmn13},
is that on the regular part of the Hitchin system, this metric is
well-approximated by the semiflat metric from \cite{gmn13}. We prove that the
asymptotic rate of convergence for gauged tangent vectors to the moduli space
has a precise polynomial expansion, and hence that the the difference between
the two sets of metric coefficients in a certain natural coordinate system also
has polynomial decay. Very recent work by Dumas and Neitzke indicates that the
convergence rate for the metric is exponential, at least in certain directions.


  We present both theory and numerical-computation results for the transmission
and reflection probability currents of a charged particle across a potential
step in the presence of a Rashba spin-orbit interaction. By varying kinetic
energy and angle of incident electrons or barrier height, different features
associated with tunneling and reflection of electrons are revealed by
inter-spin-channel electron tunnelings and reflections. These unique properties
are further accompanied by spin-state quantum interference of either a
reflected or transmitted pairs of spin-correlated electrons with the same
kinetic energy but in different spin-orbital states. Such distinctive features
are expected to give rise to a lot of applications in both spintronics and
quantum-computation devices.


  We present maps of 14.4 deg^2 of the Ophiuchus dark clouds observed by the
Spitzer Space Telescope Multiband Imaging Photometer for Spitzer (MIPS). These
high quality maps depict both numerous point sources as well as extended dust
emission within the star-forming and non-star-forming portions of these clouds.
Using PSF-fitting photometry, we detect 5779 sources at 24 um and 81 sources at
70 um at the 10 sigma level of significance. Three hundred twenty-three
candidate young stellar objects (YSOs) were identified according to their
positions on the MIPS/2MASS K versus K$-$[24] color-magnitude diagrams as
compared to 24 um detections in the SWIRE extragalactic survey. We find that
more than half of the YSO candidates, and almost all the ones with protostellar
Class I spectral energy distributions, are confined to the known cluster and
aggregates.


  Habitability of exoplanet's deepest oceans could be limited by the presence
of high-pressure ices at their base. New work demonstrates that efficient
chemical transport within deep planetary ice mantles is possible through
significant salt incorporation within the high-pressure ice.


  Generalising in the sense of Hahn's spin echo, we completely characterise
those unitary propagators of effective multi-qubit interactions that can be
inverted solely by {\em local} unitary operations on $n$ qubits
(spins-$\tfrac{1}{2}$). The subset of $U\in \mathbf{SU}(2^n)$ satisfying
$U^{-1}=K_1 U K_2$ with pairs of local unitaries $K_1,
K_2\in\mathbf{SU}(2)^{\otimes n}$ comprises two classes: in type-I, $K_1$ and
$K_2$ are inverse to one another, while in type-II they are not. {Type-I}
consists of one-parameter groups that can jointly be inverted for all times
$t\in\R{}$ because their Hamiltonian generators satisfy $K H K^{-1} = \Ad K (H)
= -H$. As all the Hamiltonians generating locally invertible unitaries of
type-I are spanned by the eigenspace associated to the eigenvalue -1 of the
{\em local} conjugation map $\Ad K$, this eigenspace can be given in closed
algebraic form. The relation to the root space decomposition of
$\mathfrak{sl}(N,\C{})$ is pointed out. Special cases of type-I invertible
Hamiltonians are of $p$-quantum order and are analysed by the transformation
properties of spherical tensors of order $p$. Effective multi-qubit interaction
Hamiltonians are characterised via the graphs of their coupling topology.
  {Type-II} consists of pointwise locally invertible propagators, part of which
can be classified according to the symmetries of their matrix representations.
Moreover, we show gradient flows for numerically solving the decision problem
whether a propagator is type-I or type-II invertible or not by driving the
least-squares distance $\norm{K_1 e^{-itH} K_2 - e^{+itH}}^2_2$ to zero.


  Formation of base pairs between the nucleotides of an RNA sequence gives rise
to a complex and often highly branched RNA structure. While numerous studies
have demonstrated the functional importance of the high degree of RNA branching
-- for instance, for its spatial compactness or interaction with other
biological macromolecules -- RNA branching topology remains largely unexplored.
Here, we use the theory of randomly branching polymers to explore the scaling
properties of RNAs by mapping their secondary structures onto planar tree
graphs. Focusing on random RNA sequences of varying lengths, we determine the
two scaling exponents related to their topology of branching. Our results
indicate that ensembles of RNA secondary structures are characterized by
annealed random branching and scale similarly to self-avoiding trees in three
dimensions. We further show that the obtained scaling exponents are robust upon
changes in nucleotide composition, tree topology, and folding energy
parameters. Finally, in order to apply the theory of branching polymers to
biological RNAs, whose length cannot be arbitrarily varied, we demonstrate how
both scaling exponents can be obtained from the distributions of the related
topological quantities of individual RNA molecules with fixed length. In this
way, we establish a framework to study the branching properties of RNA and
compare them to other known classes of branched polymers. By understanding the
scaling properties of RNA related to its branching structure we aim to improve
our understanding of the underlying principles and open up the possibility to
design RNA sequences with desired topological properties.


  We compute analytically the dominant contribution to the tree-level
bispectrum in the Starobinsky model of inflation. In this model, the potential
is vacuum energy dominated but contains a subdominant linear term which changes
the slope abruptly at a point. We show that on large scales compared with the
transition scale $k_0$ and in the equilateral limit the analogue of the
non-linearity parameter scales as $(k/k_0)^2$, that is its amplitude decays for
larger and larger scales until it becomes subdominant with respect to the usual
slow-roll suppressed corrections. On small scales we show that the
non-linearity parameter oscillates with angular frequency given by $3/k_0$ and
its amplitude grows linearly towards smaller scales and can be large depending
on the model parameters. We also compare our results with previous results in
the literature.


  We report on strong renormalization encountered in periodically driven
interacting quantum dots in the non-adiabatic regime. Correlations between lead
and dot electrons enhance or suppress the amplitude of driving depending on the
sign of the interaction. Employing a newly developed flexible renormalization
group based approach for periodic driving to an interacting resonant level we
show analytically that the magnitude of this effect follows a power law. Our
setup can act as a non-Markovian, single-parameter quantum pump.


  In this paper two issues are addressed. First, we discuss renormalization
properties of a class of gauged linear sigma models (GLSM) which reduce to
$\mathbb{WCP}(N,\tilde{N})$ non-linear sigma models (NLSM) in the low-energy
limit. Sometimes they are referred to as the Hanany-Tong models. If
supersymmetry is ${\cal N} =(2,2)$ the ultraviolet-divergent logarithm in LGSM
appears, in the renormalization of the Fayet-Iliopoulos parameter, and is
exhausted by a single tadpole graph. This is not the case in the daughter
NLSMs. As a result, the one-loop renormalizations are different in GLSMs and
their daughter NLSMs We explain this difference and identify its source.
  In particular, we show why at $N=\tilde N$ there is no UV logarithms in the
parent GLSM, while they do appear on the corresponding NLSM does not vanish. In
the second part of the paper we discuss the same problem for a class of ${\cal
N} =(0,2)$ GLSMs considered previously. In this case renormalization is not
limited to one loop; all-orders exact $\beta$ functions for GLSMs are known. We
discuss divergent loops at one and two-loop levels.


  We analyze the stability properties of a linear thermoelastic
Timoshenko-Gurtin-Pipkin system with thermal coupling acting on both the shear
force and the bending moment. Under either the mixed Dirichlet-Neumann or else
the full Dirichlet boundary conditions, we show that the associated solution
semigroup in the history space framework of Dafermos is exponentially stable
independently of the values of the structural parameters of the model.


  Measurements of the star formation efficiency (SFE) of giant molecular clouds
(GMCs) in the Milky Way generally show a large scatter, which could be
intrinsic or observational. We use magnetohydrodynamic simulations of GMCs
(including feedback) to forward-model the relationship between the true GMC SFE
and observational proxies. We show that individual GMCs trace broad ranges of
observed SFE throughout collapse, star formation, and disruption. Low measured
SFEs (<<1%) are "real" but correspond to early stages, the true "per-freefall"
SFE where most stars actually form can be much larger. Very high (>>10%) values
are often artificially enhanced by rapid gas dispersal. Simulations including
stellar feedback reproduce observed GMC-scale SFEs, but simulations without
feedback produce 20x larger SFEs. Radiative feedback dominates among mechanisms
simulated. An anticorrelation of SFE with cloud mass is shown to be an
observational artifact. We also explore individual dense "clumps" within GMCs
and show that (with feedback) their bulk properties agree well with
observations. Predicted SFEs within the dense clumps are ~2x larger than
observed, possibly indicating physics other than feedback from massive (main
sequence) stars is needed to regulate their collapse.


  We study the problem of parameters estimation in Indirect Observability
contexts, where $X_t \in R^r$ is an unobservable stationary process
parametrized by a vector of unknown parameters and all observable data are
generated by an approximating process $Y^{\varepsilon}_t$ which is close to
$X_t$ in $L^4$ norm. We construct consistent parameter estimators which are
smooth functions of the sub-sampled empirical mean and empirical lagged
covariance matrices computed from the observable data. We derive explicit
optimal sub-sampling schemes specifying the best paired choices of sub-sampling
time-step and number of observations. We show that these choices ensure that
our parameter estimators reach optimized asymptotic $L^2$-convergence rates,
which are constant multiples of the $L^4$ norm $|| Y^{\varepsilon}_t - X_t ||$.


  In this study, we explored the progression trajectories of artificial
intelligence (AI) systems through the lens of complexity theory. We challenged
the conventional linear and exponential projections of AI advancement toward
Artificial General Intelligence (AGI) underpinned by transformer-based
architectures, and posited the existence of critical points, akin to phase
transitions in complex systems, where AI performance might plateau or regress
into instability upon exceeding a critical complexity threshold. We employed
agent-based modelling (ABM) to simulate hypothetical scenarios of AI systems'
evolution under specific assumptions, using benchmark performance as a proxy
for capability and complexity. Our simulations demonstrated how increasing the
complexity of the AI system could exceed an upper criticality threshold,
leading to unpredictable performance behaviours. Additionally, we developed a
practical methodology for detecting these critical thresholds using simulation
data and stochastic gradient descent to fine-tune detection thresholds. This
research offers a novel perspective on AI advancement that has a particular
relevance to Large Language Models (LLMs), emphasising the need for a tempered
approach to extrapolating AI's growth potential and underscoring the importance
of developing more robust and comprehensive AI performance benchmarks.


  The nuclear multiple chirality in $A\sim60$ mass region is explored by the
adiabatic and configuration-fixed constrained covariant density functional
theory for cobalt isotopes. The potential-energy curves and triaxiality
parameters $\gamma$ as functions of the deformation parameter $\beta$ in
$^{54,56,57,58,59,60}$Co are obtained. It is found that there are high-$j$
particle(s) and hole(s) configurations with prominent triaxially deformed
shapes in these isotopes. This points towards that the existence of chirality
or multiple chirality in $A\sim60$ mass region are highly anticipated.


  The dynamic structure factor of a harmonically trapped Bose gas has been
calculated well above the Bose-Einstein condensation temperature by treating
the gas cloud as a canonical ensemble of noninteracting classical particles.
The static structure factor is found to vanish as wavenumber squared in the
long-wavelength limit. We also incorporate a relaxation mechanism
phenomenologically by including a stochastic friction force to study the
dynamic structure factor. A significant temperature dependence of the
density-fluctuation spectra is found. The Debye-Waller factor has been
calculated for the trapped thermal cloud as function of wavenumber and of
particle number. A substantial difference is found between clouds of small and
large particle number.


  We show that for a family of randomly kicked Hamilton-Jacobi equations, the
unique global minimizer is hyperbolic, almost surely. Furthermore, we prove the
unique forward and backward viscosity solutions, though in general only
Lipshitz, are smooth in a neighbourhood of the global minimizer. Our result
generalizes the result of E, Khanin, Mazel and Sinai (\cite{EKMS00}) to
dimension $d\ge 2$, and extends the result of Iturriaga and Khanin in
\cite{IK03}.


  The lightest superdeformed nuclei of the mass-60 region are described using
the Projected Shell Model. In contrast to the heaviest superdeformed nuclei
where a coherent motion of nucleons often dominates the physics, it is found
that alignment of $g_{9/2}$ proton and neutron pairs determines the high spin
behavior for superdeformed rotational bands in this mass region. It is
predicted that, due to the systematics of shell fillings along the even--even
Zn isotopic chain, observation of a regular superdeformed yrast band sequence
will be unlikely for certain nuclei in this mass region.


  High-precision pulsar timing observations are limited in their accuracy by
the jitter noise that appears in the arrival time of pulses. Therefore, it is
important to systematically characterise the amplitude of the jitter noise and
its variation with frequency. In this paper, we provide jitter measurements
from low-frequency wideband observations of PSR J0437$-$4715 using data
obtained as part of the Indian Pulsar Timing Array experiment. We were able to
detect jitter in both the 300 - 500 MHz and 1260 - 1460 MHz observations of the
upgraded Giant Metrewave Radio Telescope (uGMRT). The former is the first
jitter measurement for this pulsar below 700 MHz, and the latter is in good
agreement with results from previous studies. In addition, at 300 - 500 MHz, we
investigated the frequency dependence of the jitter by calculating the jitter
for each sub-banded arrival time of pulses. We found that the jitter amplitude
increases with frequency. This trend is opposite as compared to previous
studies, indicating that there is a turnover at intermediate frequencies. It
will be possible to investigate this in more detail with uGMRT observations at
550 - 750 MHz and future high sensitive wideband observations from next
generation telescopes, such as the Square Kilometre Array. We also explored the
effect of jitter on the high precision dispersion measure (DM) measurements
derived from short duration observations. We find that even though the DM
precision will be better at lower frequencies due to the smaller amplitude of
jitter noise, it will limit the DM precision for high signal-to-noise
observations, which are of short durations. This limitation can be overcome by
integrating for a long enough duration optimised for a given pulsar.


  A graphene bilayer is known to perfectly reflect normally incident electrons
due to their chirality. This is similar to Klein tunneling, which, in a
monolayer, is instead responsible for perfect transmission at normal incidence.
Stacking defaults turn each parabolic band crossing of a bilayer into pairs of
Dirac cones. Here we show that, surprisingly, a stacking default (or shift) in
a bilayer can result in perfect {\it transmission} at normal incidence as a
result of Fabry-P\'erot type resonances {\it at zero-energy}. These
constructive interferences only happen for a specific orientation of the Dirac
cones with respect to the incident electron and for quantized values of their
separation in reciprocal space. Our results provide a way to control
transmission resonances in undoped graphene bilayer structure by adjusting the
layer stacking.


  This paper presents a novel boundary integral equation (BIE) formulation for
the two-dimensional time-harmonic water-waves problem. It utilizes a
complex-scaled Laplace's free-space Green's function, resulting in a BIE posed
on the infinite boundaries of the domain. The perfectly matched layer (PML)
coordinate stretching that is used to render propagating waves exponentially
decaying, allows for the effective truncation and discretization of the BIE
unbounded domain. We show through a variety of numerical examples that, despite
the logarithmic growth of the complex-scaled Laplace's free-space Green's
function, the truncation errors are exponentially small with respect to the
truncation length. Our formulation uses only simple function evaluations (e.g.
complex logarithms and square roots), hence avoiding the need to compute the
involved water-wave Green's function. Finally, we show that the proposed
approach can also be used to find complex resonances through a \emph{linear}
eigenvalue problem since the Green's function is frequency-independent.


  This paper introduces Dual Interior Point Learning (DIPL) and Dual
Supergradient Learning (DSL) to learn dual feasible solutions to parametric
linear programs with bounded variables, which are pervasive across many
industries. DIPL mimics a novel dual interior point algorithm while DSL mimics
classical dual supergradient ascent. DIPL and DSL ensure dual feasibility by
predicting dual variables associated with the constraints then exploiting the
flexibility of the duals of the bound constraints. DIPL and DSL complement
existing primal learning methods by providing a certificate of quality. They
are shown to produce high-fidelity dual-feasible solutions to large-scale
optimal power flow problems providing valid dual bounds under 0.5% optimality
gap.


  Given a separable, locally compact Hausdorff space $X$ and a positive Radon
measure $m(dx)$ on it, we study the problem of finding the potential $V(x) \ge
0$ that maximizes the first eigenvalue of the Schr\"odinger-type operator
$L+V(x)$; $L$ is the generator of a local Dirichlet form $(a, D[a])$ on $L^2(X,
m(dx))$.


  Inspired by our recent paper "reshuffled SIMP dark matter", we notice that
the reaction rate of the two-loop induced $2 \to 2$ process may dominate over
or be comparable with that of the $3 \to 2$ process at the chemical freezeout
of Co-SIMP dark matter [Phys. Rev. Lett. 125, 131301 (2020)], especially when
the Co-SIMP mass is close to the standard model particle mass (called the edge
case). To check our point, we then derive the Boltzmann equation with all
relevant annihilation cross sections in an electrophilic model and numerically
solve it to obtain the cosmological evolution of Co-SIMP dark matter. Our
result shows that the two-loop induced $2 \to 2$ process does modify the
parameter space of the coupling for the edge case in the Co-SIMP mechanism and
has to be taken into account in UV completion models.


  We report on an "anti-Gleason" phenomenon in classical mechanics: in contrast
with the quantum case, the algebra of classical observables can carry a
non-linear quasi-state, a monotone functional which is linear on all subspaces
generated by Poisson-commutative functions. We present an example of such a
quasi-state in the case when the phase space is the 2-sphere. This example lies
in the intersection of two seemingly remote mathematical theories - symplectic
topology and the theory of topological quasi-states. We use this quasi-state to
estimate the error of the simultaneous measurement of non-commuting
Hamiltonians.


  In our previous paper we describe the Galois module structures of $p$th-power
class groups $K^\times/{K^{\times p}}$, where $K/F$ is a cyclic extension of
degree $p$ over a field $F$ containing a primitive $p$th root of unity. Our
description relies upon arithmetic invariants associated with $K/F$. Here we
construct field extensions $K/F$ with prescribed arithmetic invariants, thus
completing our classification of Galois modules $K^{\times}/K^{\times p}$.


  In this work, we study quantum fluctuations in the stress energy tensor of
spinor fields evolving in general FRW spacetimes. We quantify these
fluctuations by the noise kernel of spinor fields. For the particular case of
de Sitter spacetime, we place the spinor field in what is called the fermionic
Bunch Davies vacuum and study the variation of the noise kernel with the mass
of the field. We then make use of the conformal invariance of massless spinor
fields and employ an equivalence that relates a massless spinor field in any
given FRW spacetime with a corresponding massless spinor field in de Sitter
spacetime. Using this equivalence, we study the behaviour of the noise kernel
of massless spinor fields in general FRW spacetimes while placing the fields in
the Bunch Davies vacuum of the corresponding massless spinor field of the de
Sitter spacetime. We extend this analysis to the coordinate invariant quantity
of the energy energy correlator. We compare these results for spinor fields in
considered spacetimes with the analogous results for scalar fields. This study
helps us better understand whether the spin 1/2 fermionic matter remains
strongly correlated in considered spacetimes leading to considerable
backreaction or not.


  We propose a simple generalization of standard and empirically successful
decision tree learning algorithms such as ID3, C4.5, and CART. These
algorithms, which have been central to machine learning for decades, are greedy
in nature: they grow a decision tree by iteratively splitting on the best
attribute. Our algorithm, Top-$k$, considers the $k$ best attributes as
possible splits instead of just the single best attribute. We demonstrate,
theoretically and empirically, the power of this simple generalization. We
first prove a {\sl greediness hierarchy theorem} showing that for every $k \in
\mathbb{N}$, Top-$(k+1)$ can be dramatically more powerful than Top-$k$: there
are data distributions for which the former achieves accuracy $1-\varepsilon$,
whereas the latter only achieves accuracy $\frac1{2}+\varepsilon$. We then
show, through extensive experiments, that Top-$k$ outperforms the two main
approaches to decision tree learning: classic greedy algorithms and more recent
"optimal decision tree" algorithms. On one hand, Top-$k$ consistently enjoys
significant accuracy gains over greedy algorithms across a wide range of
benchmarks. On the other hand, Top-$k$ is markedly more scalable than optimal
decision tree algorithms and is able to handle dataset and feature set sizes
that remain far beyond the reach of these algorithms.


  In this paper, we consider a generalized second order nonlinear ordinary
differential equation of the form
$\ddot{x}+(k_1x^q+k_2)\dot{x}+k_3x^{2q+1}+k_4x^{q+1}+\lambda_1x=0$, where
$k_i$'s, $i=1,2,3,4$, $\lambda_1$ and $q$ are arbitrary parameters, which
includes several physically important nonlinear oscillators such as the simple
harmonic oscillator, anharmonic oscillator, force-free Helmholtz oscillator,
force-free Duffing and Duffing-van der Pol oscillators, modified Emden type
equation and its hierarchy, generalized Duffing-van der Pol oscillator equation
hierarchy and so on and investigate the integrability properties of this rather
general equation. We identify several new integrable cases for arbitrary value
of the exponent $q, q\in R$. The $q=1$ and $q=2$ cases are analyzed in detail
and the results are generalized to arbitrary $q$. Our results show that many
classical integrable nonlinear oscillators can be derived as sub-cases of our
results and significantly enlarge the list of integrable equations that exist
in the contemporary literature. To explore the above underlying results we use
the recently introduced generalized extended Prelle-Singer procedure applicable
to second order ODEs. As an added advantage of the method we not only identify
integrable regimes but also construct integrating factors, integrals of motion
and general solutions for the integrable cases, wherever possible, and bring
out the mathematical structures associated with each of the integrable cases.


  A precise definition of an adiabaticity parameter $\nu$ of a time-dependent
Hamiltonian is proposed. A variation of the time-dependent perturbation theory
is presented which yields a series expansion of the evolution operator
$U(\tau)=\sum_\ell U^{(\ell)}(\tau)$ with $U^{(\ell)}(\tau)$ being at least of
the order $\nu^\ell$. In particular $U^{(0)}(\tau)$ corresponds to the
adiabatic approximation and yields Berry's adiabatic phase. It is shown that
this series expansion has nothing to do with the $1/\tau$-expansion of
$U(\tau)$. It is also shown that the non-adiabatic part of the evolution
operator is generated by a transformed Hamiltonian which is off-diagonal in the
eigenbasis of the initial Hamiltonian. Some related issues concerning the
geometric phase are also discussed.


  We review the Exact Renormalization Group equations of Wegner and Houghton in
an approximation which permits both numerical and analytical studies of
nonperturbative renormalization flows. We obtain critical exponents numerically
and with the local polynomial approximation (LPA), and discuss the advantages
and shortcomings of these methods, and compare our results with the literature.
In particular, convergence of the LPA is discussed in some detail. We finally
integrate the flows numerically and find a $c$-function which determines these
flows to be gradient in this approximation.


  We introduce the notion of the full quiver of a representation of an algebra,
which is a cover of the (classical) quiver, but which captures properties of
the representation itself. Gluing of vertices and of arrows enables one to
study subtle combinatorial aspects of algebras which are lost in the classical
quiver. Full quivers of representations apply especially well to \Zcd\
algebras, which have properties very like those of finite dimensional algebras
over fields. By choosing the representation appropriately, one can restrict the
gluing to two main types: {\it Frobenius} (along the diagonal) and, more
generally {\it proportional} Frobenius gluing (above the diagonal), and our
main result is that any representable algebra has a faithful representation
described completely by such a full quiver. Further reductions are considered,
which bear on the polynomial identities.


  The appearance of monojets is among the most striking signature of jet
quenching in the context of ultrarelativistic heavy-ion collisions at the Large
Hadron Collider. Experimentally, the asymmetry of back-to-back jets is
quantified in terms of the dijet imbalance distribution by the ATLAS and CMS
collaborations. Recently, the CMS collaboration has also studied the trigger
jet momentum (P_T) dependence of the imbalance in the range between 120 and 500
GeV which is found to decrease with jet P_T. In this work, results from the
in-medium shower code YaJEM are compared with this data set. These results
suggest that the main effects observed in the data are the kinematical
collimation of jets and the increase in the probability to produce more
collimated quark jets with jet P_T, whereas there is no indication for any
non-trivial energy dependence of the shower-medium interaction mechanism
itself. The data furthermore can rule out models in which the jet shape is
collimated due to the medium modification.


  A new nano--material in the form of a double gyroid has motivated us to study
(non-commutative $C^*$ geometry of periodic wire networks and the associated
graph Hamiltonians. Here we present the general abstract framework, which is
given by certain quiver representations, with special attention to the original
case of the gyroid as well as related cases, such as graphene. In these
geometric situations, the non- commutativity is introduced by a constant
magnetic field and the theory splits into two pieces: commutative and
non-commutative, both of which are governed by a $C^*$ geometry.
  In the non-commutative case, we can use tools such as K-theory to make
statements about the band structure. In the commutative case, we give geometric
and algebraic methods to study band intersections; these methods come from
singularity theory and representation theory. We also provide new tools in the
study, using $K$-theory and Chern classes. The latter can be computed using
Berry connection in the momentum space. This brings monopole charges and issues
of topological stability into the picture.


  Customized built-in elements in HTML5 significantly transform web
development. These elements enable developers to create unique HTML components
tailored with specific design and purpose. Customized built-in elements enable
developers to address the unique needs of web applications more quickly,
supporting consistent user interfaces and experiences across diverse digital
platforms. This study investigates the role of these features in
Component-Based Software Engineering (CBSE) and Design Systems, emphasizing the
benefits of code modularity, reusability, and scalability in web development.
Customized built-in elements enable developers to address the unique needs of
web applications more quickly, supporting consistent user interfaces and
experiences across diverse digital platforms. The paper also discusses the
difficulties and concerns that must be addressed when creating customized
built-in elements, such as browser compatibility, performance optimization,
accessibility, security, styling, and interoperability. It emphasizes the
importance of standardization, developer tooling, and community interaction in
order to fully realize the potential of these features. Looking ahead,
customized built-in elements have potential in a variety of applications,
including the Internet of Things (IoT), e-commerce, and educational
technologies. Their incorporation into Progressive Web Apps (PWAs) is expected
to further improve web experiences. While obstacles remain, the article
concludes that HTML5 customized built-in elements are a driver for web
development innovation, allowing the production of efficient, adaptive, and
user-centric web applications in an ever-changing digital context.


  Matrix rank and inertia optimization problems are a class of discontinuous
optimization problems in which the decision variables are matrices running over
certain matrix sets, while the ranks and inertias of the variable matrices are
taken as integer-valued objective functions. In this paper, we establish a
group of explicit formulas for calculating the maximal and minimal values of
the rank and inertia objective functions of the Hermitian matrix expression
$A_1 - B_1XB_1^{*}$ subject to the common Hermitian solution of a pair of
consistent matrix equations $B_2XB^{*}_2 = A_2$ and $B_3XB_3^{*} = A_3$, and
Hermitian solution of the consistent matrix equation $B_4X= A_4$, respectively.
Many consequences are obtained, in particular, necessary and sufficient
conditions are established for the triple matrix equations $B_1XB^{*}_1 =A_1$,
$B_2XB^{*}_2 = A_2$ and $B_3XB^{*}_3 = A_3$ to have a common Hermitian
solution, as necessary and sufficient conditions for the two matrix equations
$B_1XB^{*}_1 =A_1$ and $B_4X = A_4$ to have a common Hermitian solution.


  We present a two dimensional map of the gas temperature distribution in the
Centaurus cluster, based on ASCA observations derived using a novel approach to
account for the energy dependent point spread function. Along with a cool
region, centered on NGC4696, asymmetric temperature variations of moderate
amplitude are detected. The hottest region roughly coincides with the position
of the second brightest galaxy NGC4709, known to be the dominant galaxy of one
of the subgroups in the Centaurus cluster. ROSAT images show faint surface
brightness emission also centered on this galaxy. The imaging and spectral
results suggest that a subcluster, centered on NGC4709 is merging with the main
cluster centered on NGC4696, in agreement with the earlier suggestion by Lucey
et al. (1986) that these two systems are located at the same distance despite
their different line-of-sight velocities.


  Separation Logic is a widely used formalism for describing dynamically
allocated linked data structures, such as lists, trees, etc. The decidability
status of various fragments of the logic constitutes a long standing open
problem. Current results report on techniques to decide satisfiability and
validity of entailments for Separation Logic(s) over lists (possibly with
data). In this paper we establish a more general decidability result. We prove
that any Separation Logic formula using rather general recursively defined
predicates is decidable for satisfiability, and moreover, entailments between
such formulae are decidable for validity. These predicates are general enough
to define (doubly-) linked lists, trees, and structures more general than
trees, such as trees whose leaves are chained in a list. The decidability
proofs are by reduction to decidability of Monadic Second Order Logic on graphs
with bounded tree width.


  In medicine, reference curves serve as an important tool for everyday
clinical practice. Pediatricians assess the growth process of children with the
help of percentile curves serving as norm references. The mathematical methods
for the construction of these reference curves are sophisticated and often
require technical knowledge beyond the scope of physicians. An easy-to-use
software for life scientists and physicians is missing. As a consequence, most
medical publications do not document the construction properly. This project
aims to develop a software that enables non-technical users to apply modern
statistical methods to create and analyze reference curves. In this paper, we
present RefCurv, a software that facilitates the construction of reference
curves. The software comprises functionalities to select and visualize data.
Users can fit models to the data and graphically present them as percentile
curves. Furthermore, the software provides features to highlight possible
outliers, perform model selection, and analyze the sensitivity. RefCurv is an
open-source software with a graphical user interface (GUI) written in Python.
It uses R and the gamlss add-on package (Rigby and Stasinopoulos (2005)) as the
underlying statistical engine. In summary, RefCurv is the first software based
on the gamlss package, which enables practitioners to construct and analyze
reference curves in a user-friendly GUI. In broader terms, the software brings
together the fields of statistical learning and medical application.
Consequently, RefCurv can help to establish the construction of reference
curves in other medical fields.


  We present a construction of Hermitian operators and quantum states labelled
by strings from a finite field. The distance between these operators or states
is then simply related (typically, proportional) to the Hamming distance
between their corresponding strings. This allows a straightforward application
of classical coding theory to find arrangements of operators or states with a
given distance distribution. Using the simplex or extended Reed-Solomon code in
our construction recovers the discrete Wigner function, which has important
applications in quantum information theory.


  The odd-even staggering of the yield of final reaction products has been
studied as a function of proton (Z) and neutron (N) numbers for the collisions
84 Kr+112 Sn and 84 Kr+124 Sn at 35 MeV/nucleon, in a wide range of elements
(up to Z ~ 20). The experimental data show that staggering effects rapidly
decrease with increasing size of the fragments. Moreover the staggering in N is
definitely larger than the one in Z. Similar general features are qualitatively
reproduced by the GEMINI code. Concerning the comparison of the two systems,
the staggering in N is in general rather similar, being slightly larger only
for the lightest fragments produced in the n-rich system. In contrast the
staggering in Z, although smaller than that in N, is sizably larger for the
n-poor system with respect to the n-rich one.


  Games have benchmarked AI methods since the inception of the field, with
classic board games such as Chess and Go recently leaving room for video games
with related yet different sets of challenges. The set of AI problems
associated with video games has in recent decades expanded from simply playing
games to win, to playing games in particular styles, generating game content,
modeling players etc. Different games pose very different challenges for AI
systems, and several different AI challenges can typically be posed by the same
game. In this article we analyze the popular collectible card game Hearthstone
(Blizzard 2014) and describe a varied set of interesting AI challenges posed by
this game. Collectible card games are relatively understudied in the AI
community, despite their popularity and the interesting challenges they pose.
Analyzing a single game in-depth in the manner we do here allows us to see the
entire field of AI and Games through the lens of a single game, discovering a
few new variations on existing research topics.


  This article describes a procedure to generate a snapshot of the structure of
a specific scientific community and their outputs based on the information
available in Google Scholar Citations (GSC). We call this method MADAP
(Multifaceted Analysis of Disciplines through Academic Profiles). The
international community of researchers working in Bibliometrics,
Scientometrics, Informetrics, Webometrics, and Altmetrics was selected as a
case study. The records of the top 1,000 most cited documents by these authors
according to GSC were manually processed to fill any missing information and
deduplicate fields like the journal titles and book publishers. The results
suggest that it is feasible to use GSC and the MADAP method to produce an
accurate depiction of the community of researchers working in Bibliometrics
(both specialists and occasional researchers) and their publication habits
(main publication venues such as journals and book publishers). Additionally,
the wide document coverage of Google Scholar (specially books and book
chapters) enables more comprehensive analyses of the documents published in a
specific discipline than were previously possible with other citation indexes,
finally shedding light on what until now had been a blind spot in most citation
analyses.


  The transition from Population III to Population II stars is determined by
the presence of a sufficient amount of metals, in particular, oxygen and
carbon. The vastly different yields of these relevant metals between different
initial stellar mass functions would then cause such a transition to occur at
different times. We show that the transition from Pop III to Pop II stars is
likely to occur before the universe can be reionized, if the IMF is entirely
very massive stars (M > 140 M_sun). A factor of about 10 more ionizing photons
would be produced in the case with normal top-heavy IMF (e.g., M ~ 10-100
M_sun), when such a transition occurs. Thus, a high Thomson optical depth
(tau_e >= 0.11-0.14) may be indication that the Population III stars possess a
more conventional top-heavy IMF.


  We prove that Lefschetz's principle of approximating the cohomology of a
possibly singular affine scheme of finite type over a field by the cohomology
of a suitable (thickening of a) hyperplane section can be made uniform: in the
affine case, we can choose the hyperplane section independently of the
cohomology. Using Jouanolou's trick, this gives a new way to bound the Betti
numbers of quasi-projective schemes over a field, independently of the
cohomology. This is achieved through a motivic version of Deligne's generic
base change formula and an axiomatic presentation of the theory of perverse
sheaves. These methods produce generating families of Voevodsky motivic sheaves
that are realized in perverse sheaves over any base of equal characteristic.


  Moir\'e superlattices provide a powerful way to engineer properties of
electrons and excitons in two-dimensional van der Waals heterostructures. The
moir\'e effect can be especially strong for interlayer excitons, where
electrons and holes reside in different layers and can be addressed separately.
In particular, it was recently proposed that the moir\'e superlattice potential
not only localizes interlayer exciton states at different superlattice
positions, but also hosts an emerging moir\'e quasi-angular momentum (QAM) that
periodically switches the optical selection rules for interlayer excitons at
different moir\'e sites. Here we report the observation of multiple interlayer
exciton states coexisting in a WSe2/WS2 moir\'e superlattice and unambiguously
determine their spin, valley, and moir\'e QAM through novel resonant optical
pump-probe spectroscopy and photoluminescence excitation spectroscopy. We
demonstrate that interlayer excitons localized at different moir\'e sites can
exhibit opposite optical selection rules due to the spatially-varying moir\'e
QAM. Our observation reveals new opportunities to engineer interlayer exciton
states and valley physics with moir\'e superlattices for optoelectronic and
valleytronic applications.


  In this paper, we present the Semantic Boundary Conditioned Backbone (SBCB)
framework, a simple yet effective training framework that is model-agnostic and
boosts segmentation performance, especially around the boundaries. Motivated by
the recent development in improving semantic segmentation by incorporating
boundaries as auxiliary tasks, we propose a multi-task framework that uses
semantic boundary detection (SBD) as an auxiliary task. The SBCB framework
utilizes the nature of the SBD task, which is complementary to semantic
segmentation, to improve the backbone of the segmentation head. We apply an SBD
head that exploits the multi-scale features from the backbone, where the model
learns low-level features in the earlier stages, and high-level semantic
understanding in the later stages. This head perfectly complements the common
semantic segmentation architectures where the features from the later stages
are used for classification. We can improve semantic segmentation models
without additional parameters during inference by only conditioning the
backbone. Through extensive evaluations, we show the effectiveness of the SBCB
framework by improving various popular segmentation heads and backbones by 0.5%
~ 3.0% IoU on the Cityscapes dataset and gains 1.6% ~ 4.1% in boundary Fscores.
We also apply this framework on customized backbones and the emerging vision
transformer models and show the effectiveness of the SBCB framework.


  XML database query languages have been studied extensively, but XML database
updates have received relatively little attention, and pose many challenges to
language design. We are developing an XML update language called Flux, which
stands for FunctionaL Updates for XML, drawing upon ideas from functional
programming languages. In prior work, we have introduced a core language for
Flux with a clear operational semantics and a sound, decidable static type
system based on regular expression types.
  Our initial proposal had several limitations. First, it lacked support for
recursive types or update procedures. Second, although a high-level source
language can easily be translated to the core language, it is difficult to
propagate meaningful type errors from the core language back to the source.
Third, certain updates are well-formed yet contain path errors, or ``dead''
subexpressions which never do any useful work. It would be useful to detect
path errors, since they often represent errors or optimization opportunities.
  In this paper, we address all three limitations. Specifically, we present an
improved, sound type system that handles recursion. We also formalize a source
update language and give a translation to the core language that preserves and
reflects typability. We also develop a path-error analysis (a form of dead-code
analysis) for updates.


  The original topological Aharonov-Casher (AC) effect is due to the
interaction of the anomalous magnetic dipole moment (MDM) with certain
configurations of electric field. Naively one would not expect an AC effect for
a scalar particle for which no anomalous MDM can be defined in the usual sense.
In this letter we study the AC effect in supersymmetric systems. In this
framework there is the possibility of deducing the AC effect of a scalar
particle from the corresponding effect for a spinor particle. In 3+1 dimensions
such a connection is not possible because the anomalous MDM is zero if
supersymmetry is an exact symmetry. However, in 2+1 dimensions it is possible
to have an anomalous MDM even with exact supersymmetry.
  Having demonstrated the relationship between the spinor and the scalar MDM,
we proceed to show that the scalar AC effect is uniquely defined. We then
compute the anomalous MDM at the one loop level, showing how the scalar form
arises in 2+1 dimensions from the coupling of the scalar to spinors. This model
shows how an AC effect for a scalar can be generated for non-supersymmetric
theories, and we construct such a model to illustrate the mechanism.


  In addition to the dielectric and magnetic permeability constants, another
constant is generally needed to describe the electrodynamic properties of a
linear isotropic medium. We discuss why the need for the third constant arises
and what sort of physical situations can give rise to a non-zero value for it.
This additional constant, which we call the {\em ``Activity Constant''} and
denote by $\zeta$, can explain optical activity and other phenomena from a
purely macroscopic and phenomenological point of view.


  We construct uncountably generated algebras inside the following sets of
special functions: Sierpi\'nski-Zygmund functions, perfectly everywhere
surjective functions and nowhere continuous Darboux functions. All conclusions
obtained in this paper are improvements of some already known results.


  When two identical (coherent) beams are injected at a semi-infinite
non-Hermitian medium from left and right, we show that both reflection
$(r_L,r_R)$ and transmission $(t_L,t_R)$ amplitudes are non-reciprocal. In a
parametric domain, there exists Spectral Singularity (SS) at a real energy
$E=E_*$ and the determinant of the time-reversed two port S-matrix i.e.,
$|\det(S)|=|t_L t_R-r_L r_R|$ vanishes sharply at $E=E_*$ displaying the
phenomenon of Coherent Perfect Absorption (CPA). In the complimentary
parametric domain, the potential becomes either left or right reflectionless at
$E=E_z$. But we rule out the existence of Invisibility despite $r_R(E_i)=0$ and
$t_R(E_i)=1$ in these new models. We present two simple exactly solvable models
where the expressions for $E_*$, $E_z$, $E_i$ and the parametric conditions on
the potential have been obtained in explicit and simple forms. Earlier, the
novel phenomena of SS and CPA have been found to occur only in the scattering
complex potentials which are spatially localized (vanish asymptotically) and
having $t_L=t_R$.


  Numerical error induced by the "ghost forces" in the quasicontinuum method is
studied in the context of dynamic problems. The error in the ({W}^{1,\infty})
norm is analyzed for the time scale (\mc{O}(\eps)) and the time scale
(\mc{O}(1)) with $\eps$ being the lattice spacing.


  We unveil the existence of two-particle bound state in the continuum (BIC) in
a one-dimensional interacting nonreciprocal lattice with a generalized boundary
condition. By applying the Bethe-ansatz method, we can exactly solve the
wavefunction and eigenvalue of the bound state in the continuum band, which
enable us to precisely determine the phase diagrams of BIC. Our results
demonstrate that the non-reciprocal hopping can delocalize the bound state and
thus shrink the region of BIC. By analyzing the wavefunction, we identify the
existence of two types of BICs with different spatial distributions and
analytically derive the corresponding threshold values for the breakdown of
BICs. The BIC with similar properties is also found to exist in another system
with an impurity potential.


  We present simulation results on the structure and dynamics of micromagnetic
point singularities with atomistic resolution. This is achieved by embedding an
atomistic computational region into a standard micromagnetic algorithm. Several
length scales are bridged by means of an adaptive mesh refinement and a
seamless coupling between the continuum theory and a Heisenberg formulation for
the atomistic region. The code operates on graphical processing units and is
able to detect and track the position of strongly inhomogeneous magnetic
regions. This enables us to reliably simulate the dynamics of Bloch points,
which means that a fundamental class of micromagnetic switching processes can
be analyzed with unprecedented accuracy. We test the code by comparing it with
established results and present its functionality with the example of a
simulated field-driven Bloch point motion in a soft-magnetic cylinder.


  We propose a method for synthesizing cardiac magnetic resonance (MR) images
with plausible heart pathologies and realistic appearances for the purpose of
generating labeled data for the application of supervised deep-learning (DL)
training. The image synthesis consists of label deformation and label-to-image
translation tasks. The former is achieved via latent space interpolation in a
VAE model, while the latter is accomplished via a label-conditional GAN model.
We devise three approaches for label manipulation in the latent space of the
trained VAE model; i) \textbf{intra-subject synthesis} aiming to interpolate
the intermediate slices of a subject to increase the through-plane resolution,
ii) \textbf{inter-subject synthesis} aiming to interpolate the geometry and
appearance of intermediate images between two dissimilar subjects acquired with
different scanner vendors, and iii) \textbf{pathology synthesis} aiming to
synthesize a series of pseudo-pathological synthetic subjects with
characteristics of a desired heart disease. Furthermore, we propose to model
the relationship between 2D slices in the latent space of the VAE prior to
reconstruction for generating 3D-consistent subjects from stacking up 2D
slice-by-slice generations. We demonstrate that such an approach could provide
a solution to diversify and enrich an available database of cardiac MR images
and to pave the way for the development of generalizable DL-based image
analysis algorithms. We quantitatively evaluate the quality of the synthesized
data in an augmentation scenario to achieve generalization and robustness to
multi-vendor and multi-disease data for image segmentation. Our code is
available at https://github.com/sinaamirrajab/CardiacPathologySynthesis.


  White Matter Hyperintensities (WMH) are the most common manifestation of
cerebral small vessel disease (cSVD) on the brain MRI. Accurate WMH
segmentation algorithms are important to determine cSVD burden and its clinical
consequences. Most of existing WMH segmentation algorithms require both fluid
attenuated inversion recovery (FLAIR) images and T1-weighted images as inputs.
However, T1-weighted images are typically not part of standard clinicalscans
which are acquired for patients with acute stroke. In this paper, we propose a
novel brain atlas guided attention U-Net (BAGAU-Net) that leverages only FLAIR
images with a spatially-registered white matter (WM) brain atlas to yield
competitive WMH segmentation performance. Specifically, we designed a dual-path
segmentation model with two novel connecting mechanisms, namely multi-input
attention module (MAM) and attention fusion module (AFM) to fuse the
information from two paths for accurate results. Experiments on two publicly
available datasets show the effectiveness of the proposed BAGAU-Net. With only
FLAIR images and WM brain atlas, BAGAU-Net outperforms the state-of-the-art
method with T1-weighted images, paving the way for effective development of WMH
segmentation. Availability:https://github.com/Ericzhang1/BAGAU-Net


  When the motion of electrons is restricted to a plane under a perpendicular
magnetic field B, a variety of quantum phases emerge at low temperatures whose
properties are dictated by the Coulomb interaction and its interplay with
disorder. At very strong B, the sequence of fractional quantum Hall (FQH)
liquid phases terminates in an insulating phase, which is widely believed to be
due to the solidification of electrons into domains possessing Wigner crystal
(WC) order. The existence of such WC domains is signaled by the emergence of
microwave pinning-mode resonances, which reflect the mechanical properties
characteristic of a solid. However, the most direct manifestation of the broken
translational symmetry accompanying the solidification - the spatial modulation
of particles' probability amplitude - has not been observed yet. Here, we
demonstrate that nuclear magnetic resonance (NMR) provides a direct probe of
the density topography of electron solids in the integer and fractional quantum
Hall regimes. The data uncover quantum and thermal fluctuation of lattice
electrons resolved on the nanometre scale. Our results pave the way to studies
of other exotic phases with non-trivial spatial spin/charge order.


  Richomme asked the following question: what is the infimum of the real
numbers $\alpha$ > 2 such that there exists an infinite word that avoids
$\alpha$-powers but contains arbitrarily large squares beginning at every
position? We resolve this question in the case of a binary alphabet by showing
that the answer is $\alpha$ = 7/3.


  This paper reviews some of the phenomenological models which have been
introduced to incorporate the scaling properties of financial data. It also
illustrates a microscopic model, based on heterogeneous interacting agents,
which provides a possible explanation for the complex dynamics of markets'
returns. Scaling and multi-scaling analysis performed on the simulated data is
in good quantitative agreement with the empirical results.


  Define a gamma-reflected process
W_\gamma(t)=Y_H(t)-\gamma\inf_{s\in[0,t]}Y_H(s), t\ge0 with input process
{Y_H(t), t\ge 0} which is a fractional Brownian motion with Hurst index H\in
(0,1) and a negative linear trend. In risk theory {u-W_\gamma(t), t\ge 0} is
referred to as the risk process with tax payments of a loss-carry-forward type.
For various risk processes numerous results are known for the approximation of
the first and last passage times to 0 (ruin times) when the initial reserve $u$
goes to infinity. In this paper we show that for the gamma-reflected process
the conditional (standardized) first and last passage times are jointly
asymptotically Gaussian and completely dependent. An important contribution of
this paper is that it links ruin problems with extremes of non-homogeneous
Gaussian random fields defined by Y_H which are also investigated in this
contribution.


  This paper considers an aggregator of Electric Vehicles (EVs) who aims to
learn the aggregate power of his/her fleet while also participating in the
electricity market. The proposed approach is based on a data-driven inverse
optimization (IO) method, which is highly nonlinear. To overcome such a caveat,
we use a two-step estimation procedure which requires solving two convex
programs. Both programs depend on penalty parameters that can be adjusted by
using grid search. In addition, we propose the use of kernel regression to
account for the nonlinear relationship between the behaviour of the pool of EVs
and the explanatory variables, i.e., the past electricity prices and EV fleet's
driving patterns. Unlike any other forecasting method, the proposed IO
framework also allows the aggregator to derive a bid/offer curve, i.e. the
tuple of price-quantity to be submitted to the electricity market, according to
the market rules. We show the benefits of the proposed method against the
machine-learning techniques that are reported to exhibit the best forecasting
performance for this application in the technical literature.


  Non-Bloch topological invariants preserve the bulk-boundary correspondence in
non-Hermitian topological systems, and are a key concept in the contemporary
study of non-Hermitian topology. Here we report the dynamic detection of
non-Bloch topological invariants in single-photon quantum walks, revealed
through the biorthogonal chiral displacement, and crosschecked with the dynamic
spin textures in the generalized quasimomentum-time domain following a quantum
quench. Both detection schemes are robust against symmetry-preserving
disorders, and yield consistent results with theoretical predictions. Our
experiments are performed far away from any boundaries, and therefore underline
non-Bloch topological invariants as intrinsic properties of the system that
persist in the thermodynamic limit. Our work sheds new light on the
experimental investigation of non-Hermitian topology.


  It has been demonstrated recently that supercooled liquids sharing simple
structural features (e.g. pair distribution functions) may exhibit strikingly
distinct dynamical behavior. Here we show that a more subtle structural feature
correlates with relaxation times in three simulated systems that have nearly
identical radial distribution functions but starkly different dynamical
behavior. In particular, for the first time we determine the thermodynamic
"point-to-set" length scale in several canonical model systems and demonstrate
the quantitative connection between this length scale and the growth of
relaxation times. Our results provide clues necessary for distinguishing
competing theories of the glass transition.


  In modern electronic medical records (EMR) much of the clinically important
data - signs and symptoms, symptom severity, disease status, etc. - are not
provided in structured data fields, but rather are encoded in clinician
generated narrative text. Natural language processing (NLP) provides a means of
"unlocking" this important data source for applications in clinical decision
support, quality assurance, and public health. This chapter provides an
overview of representative NLP systems in biomedicine based on a unified
architectural view. A general architecture in an NLP system consists of two
main components: background knowledge that includes biomedical knowledge
resources and a framework that integrates NLP tools to process text. Systems
differ in both components, which we will review briefly. Additionally,
challenges facing current research efforts in biomedical NLP include the
paucity of large, publicly available annotated corpora, although initiatives
that facilitate data sharing, system evaluation, and collaborative work between
researchers in clinical NLP are starting to emerge.


  Type Ia supernovae play a significant role in the evolution of the Universe
and have a wide range of applications. It is widely believed that these events
are the thermonuclear explosions of carbon-oxygen white dwarfs close to the
Chandrasekhar mass (1.38 M\odot). However, CO white dwarfs are born with masses
much below the Chandrasekhar limit and thus require mass accretion to become
Type Ia supernovae. There are two main scenarios for accretion. First, the
merger of two white dwarfs and, second, a stable mass accretion from a
companion star. According to predictions, this companion star (also referred to
as donor star) survives the explosion and thus should be visible in the center
of Type Ia remnants. In this paper we scrutinize the central stars (79 in
total) of the SN 1006 remnant to search for the surviving donor star as
predicted by this scenario. We find no star consistent with the traditional
accretion scenario in SN1006.


  We study the formation and evolution of topological defects that arise in the
post-recombination phase transition predicted by the gravitational neutrino
mass model in [Dvali, Funcke, Phys. Rev. D 93, 113002 (2016)]. In the
transition, global skyrmions, monopoles, strings, and domain walls form due to
the spontaneous breaking of the neutrino flavor symmetry. These defects are
unique in their softness and origin; as they appear at a very low energy scale,
they only require Standard Model particle content, and they differ
fundamentally depending on the Majorana or Dirac nature of the neutrinos. One
of the observational signatures is the time dependence and space dependence of
the neutrino mass matrix, which could be observable in future neutrino
experiments. Already existing data rule out parts of the parameter space in the
Majorana case. The detection of this effect could shed light onto the open
question of the Dirac versus Majorana neutrino nature.


  X-ray spectra of active galactic nuclei (AGN) consist of several different
emission and absorption components, which are often fitted manually with models
chosen on a case-by-case basis. However, it becomes very hard for a survey with
a large number of sources. In addition, when the signal-to-noise ratio (S/N) is
low, there is a tendency to adopt an overly simplistic model, biasing the
parameters and making their uncertainties unrealistic. We developed a Bayesian
method for automatically fitting XMM-Newton AGN X-ray spectra with a consistent
and physically motivated model including all spectral components, even when the
data quality is low. An empirical model is used for the non-X-ray background.
Noninformative priors were applied on the photon index (Gamma) and the hydrogen
column density (N_H), while informative priors obtained from deep surveys were
used to marginalize the remaining parameters. We tested this method using a
realistically simulated sample of 5000 spectra reproducing typical population
properties. Spectral parameters were randomly drawn from the priors, taking the
luminosity function into account. Meaningful posterior probability density
distributions were obtained for, for instance, N_H, Gamma, and L_X, even at low
S/N, but in this case, we were unable to constrain the parameters of secondary
components such as the reflection and soft excess. As a comparison, a
maximum-likelihood approach with model selection among six models of different
complexities was also applied to this sample. We find clear failures in the
measurement of Gamma in most cases, and of N_H when the source is unabsorbed
(N_H < 10^22 cm-2). The results can hardly be used to reconstruct the parent
distributions of the spectral parameters, while our Bayesian method provides
meaningful multidimensional posteriors that will be used in a subsequent paper
to infer the population. (abridged)


  We study the behavior of $p$-Dirichlet optimal design problem with volume
constraint for $p$ large. As the limit as $p$ goes to infinity, we find a
limiting free boundary problem governed by the infinity-Laplacian operator. We
establish a necessary and sufficient condition for uniqueness of the limiting
problem and, under such a condition, we determine precisely the optimal
configuration for the limiting problem. Finally, we establish convergence
results for the free boundaries.


  We study point particles in 2+1 dimensional first order gravity using a
triangulation to fix the connection and frame-field. The Hamiltonian is reduced
to a boundary term which yields the total mass. The triangulation is dynamical
with non-trivial transitions occurring when a particle meets an edge. This
framework facilitates a description in terms of the loop gravity phase space.


  Operadic Lax representations for the harmonic oscillator are used to
construct the quantum counterparts of 3d real Lie algebras. The Jacobians of
the corresponding quantum algebras are calculated.


  Modern processors deploy a variety of weak memory models, which for
efficiency reasons may (appear to) execute instructions in an order different
to that specified by the program text. The consequences of instruction
reordering can be complex and subtle, and can impact on ensuring correctness.
Previous work on the semantics of weak memory models has focussed on the
behaviour of assembler-level programs. In this paper we utilise that work to
extract some general principles underlying instruction reordering, and apply
those principles to a wide-spectrum language encompassing abstract data types
as well as low-level assembler code. The goal is to support reasoning about
implementations of data structures for modern processors with respect to an
abstract specification.
  Specifically, we define an operational semantics, from which we derive some
properties of program refinement, and encode the semantics in the rewriting
engine Maude as a model-checking tool. The tool is used to validate the
semantics against the behaviour of a set of litmus tests (small assembler
programs) run on hardware, and also to model check implementations of data
structures from the literature against their abstract specifications.


  In the present work, we investigate the case of Directed Polymer in a Random
Environment (DPRE), when the increments of the random walk are heavy-tailed
with tail-exponent equal to zero ($\mathbf{P}[|X_1|\geq n]$ decays slower than
any power of $n$). This case has not yet been studied in the context of
directed polymers and present key differences with the simple symmetric random
walk case and the cases where the increments belong to the domain of attraction
of an $\alpha$-stable law, where $\alpha \in (0, 2]$. We establish the absence
of a very strong disorder regime - that is, the free energy equals zero at
every temperature - for every disorder distribution. We also prove that a
strong disorder regime (partition function converging to zero at low
temperature) may exist or not depending on finer properties of the random walk:
we establish non-matching necessary and sufficient conditions for having a
phase transition from weak to strong disorder. In particular our results imply
that for this directed polymer model, very strong disorder is not equivalent to
strong disorder, shedding a new light on a long standing conjecture concerning
the original nearest-neighbor DPRE.


  Motivated by a question of Stover, we discuss an example of a Zariski-dense
finitely generated subgroup of $\mathrm{SL}_5(\mathbb{Z})$ that is not finitely
presented.


  In order to study how outflows from protostars influence the physical and
chemical conditions of the parent molecular cloud, we have observed Barnard 1
(B1) main core, which harbors four Class 0 and three Class I sources, in the CO
(J=1-0), CH3OH (J_K=2_K-1_K), and the SiO (J=1-0) lines using the Nobeyama 45 m
telescope. We have identified three CO outflows in this region; one is an
elongated (~ 0.3 pc) bipolar outflow from a Class 0 protostar B1-c in the
submillimeter clump SMM 2, another is a rather compact (~ 0.1 pc) outflow from
a Class I protostar B1 IRS in the clump SMM 6, and the other is an extended
outflow from a Class I protostar in SMM 11. In the western lobe of the SMM 2
outflow, both the SiO and CH3OH lines show broad redshifted wings with the
terminal velocities of 25 km/s and 13 km/s, respectively. It is likely that the
shocks caused by the interaction between the outflow and ambient gas enhance
the abundance of SiO and CH3OH in the gas phase. The total energy input rate by
the outflows (1.1x10^{-3} Lsun) is smaller than the energy loss rate
(8.5x10^{-3} Lsun$) through the turbulence decay in B1 main core, which
suggests that the outflows can not sustain the turbulence in this region. Since
the outflows are energetic enough to compensate the dissipating turbulence
energy in the neighboring, more evolved star forming region NGC 1333, we
suggest that the turbulence energy balance depends on the evolutionary state of
the star formation in molecular clouds.


  We show that, within the AdS/CFT correspondence, recent formulations of the
information paradox can be reduced to a question about the existence of certain
kinds of operators in the CFT. We describe a remarkably simple construction of
these operators on a given state of the CFT. Our construction leads to a smooth
horizon, addresses the strong subadditivity paradox, while preserving locality
within effective field theory, and reconciles the existence of the interior
with the growth of states with energy in the CFT. We also extend our
construction to non-equilibrium states.


  The ALICE Muon Trigger is currently yielded by a detector currently composed
of 72 Bakelite single-gap Resistive Plate Chambers operated in maxi-avalanche
mode, arranged in four 5.5x6.5 m2 detection planes. In order to meet the
requirements posed by the forthcoming LHC high luminosity runs starting from
2021 onwards, in which ALICE will be read out in continuous mode, the Muon
Trigger will become a Muon Identifier and will undergo a major upgrade. In the
current setup, signals from about 21k strips are discriminated by 2400
non-amplified Front End (FEE) cards, whose thresholds are provided by external
analog voltages (one for each chamber side). All these cards will be replaced
with discriminators equipped with a pre-amplification stage which will allow a
reduction in the operating high voltage of the detectors, thus prolonging their
lifetime. Furthermore, their reference thresholds will be passed via wireless
(and I2C chained per chamber side) allowing the tuning of the values at the
single card level. Moreover, the 24 most exposed chambers will be replaced with
new ones, equipped with high-quality (i.e. smoother surface) Bakelite
laminates. The tests performed on the new FEE cards, used both in a test bench
and on detectors, and on the new RPC chambers (with cosmic rays) are reported.


  Raw data on the cumulative number of deaths at a country level generally
indicate a spatially variable distribution of the incidence of COVID-19
disease. An important issue is to determine whether this spatial pattern is a
consequence of environmental heterogeneities, such as the climatic conditions,
during the course of the outbreak. Another fundamental issue is to understand
the spatial spreading of COVID-19. To address these questions, we consider four
candidate epidemiological models with varying complexity in terms of initial
conditions, contact rates and non-local transmissions, and we fit them to
French mortality data with a mixed probabilistic-ODE approach. Using standard
statistical criteria, we select the model with non-local transmission
corresponding to a diffusion on the graph of counties that depends on the
geographic proximity, with time-dependent contact rate and spatially constant
parameters. This original spatially parsimonious model suggests that in a
geographically middle size centralized country such as France, once the
epidemic is established, the effect of global processes such as restriction
policies, sanitary measures and social distancing overwhelms the effect of
local factors. Additionally, this modeling approach reveals the latent
epidemiological dynamics including the local level of immunity, and allows us
to evaluate the role of non-local interactions on the future spread of the
disease. In view of its theoretical and numerical simplicity and its ability to
accurately track the COVID-19 epidemic curves, the framework we develop here,
in particular the non-local model and the associated estimation procedure, is
of general interest in studying spatial dynamics of epidemics.