  Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces
over some `one particle space' $\K$ are formed by certain symmetrization
procedures performed on the full Fock space. We investigate alternative ways of
symmetrization by building on Joyal's notion of a combinatorial species. Any
such species $F$ gives rise to an endofunctor $\G_F$ of the category of Hilbert
spaces with contractions mapping a Hilbert space $\K$ to a symmetric Hilbert
space $\G_F(\K)$ with the same symmetry as the species $F$. A general framework
for annihilation and creation operators on these spaces is developed, and
compared to the generalised Brownian motions of R. Speicher and M. Bo\.zejko.
As a corollary we find that the commutation relation
$a_ia_j^*-a_j^*a_i=f(N)\delta_{ij}$ with $Na_i^*-a_i^*N=a_i^*$ admits a
realization on a symmetric Hilbert space whenever $f$ has a power series with
infinite radius of convergence and positive coefficients.


  Cognitive decline is a natural process that occurs as individuals age. Early
diagnosis of anomalous decline is crucial for initiating professional treatment
that can enhance the quality of life of those affected. To address this issue,
we propose a multimodal model capable of predicting Mild Cognitive Impairment
and cognitive scores. The TAUKADIAL dataset is used to conduct the evaluation,
which comprises audio recordings of clinical interviews. The proposed model
demonstrates the ability to transcribe and differentiate between languages used
in the interviews. Subsequently, the model extracts audio and text features,
combining them into a multimodal architecture to achieve robust and generalized
results. Our approach involves in-depth research to implement various features
obtained from the proposed modalities.


  The physics case for a possible fixed target polarized nucleon-nucleon
collision experiment at HERA is described. The experiment named HERA-N could be
realized using an internal polarized gas target in the HERA
polarized/unpolarized proton beam. A wide spectrum of nucleon spin structure
problems could be investigated and the experiment would constitute a fixed
target complement to the RHIC spin physics program with competitive statistical
accuracy.


  Making and using polaritonic states (i.e., hybrid electron-photon states) for
chemical applications have recently become one of the most prominent and active
fields that connects the communities of chemistry and quantum optics. Modeling
of such polaritonic phenomena using ab initio approaches calls for new
methodologies, leading to the reinvention of many commonly used electronic
structure methods, such as Hartree-Fock, density functional, and coupled
cluster theories. In this work, we explore the formally exact diffusion quantum
Monte Carlo approach (DQMC) to obtain numerical solutions to the polaritonic
ground state during the dissociation of the H$_2$ molecular system. We examine
various electron-nuclear-photon properties throughout the dissociation, such as
changes to the minimum of the cavity Born-Oppenheimer surface, the localization
of the electronic wavefunction, and the average mode occupation. Finally, we
directly compare our results to that obtained with state-of-the-art, yet
approximate, polaritonic coupled cluster approaches.


  Holomorphic 2-forms on K\"{a}hler surfaces lead to "Local Gromov-Witten
invariants" of spin curves. This paper shows how to derive sum formulas for
such local GW invariants from the sum formula for GW invariants of certain
ruled surfaces. These sum formulas also verify the Maulik-Pandharipande
formulas that were recently proved by Kiem and Li.


  In many online social networks (e.g., Facebook, Google+, Twitter, and
Instagram), users prefer to hide her/his partial or all relationships, which
makes such private relationships not visible to public users or even friends.
This leads to a new graph model called public-private networks, where each user
has her/his own perspective of the network including the private connections.
Recently, public-private network analysis has attracted significant research
interest in the literature. A great deal of important graph computing problems
(e.g., shortest paths, centrality, PageRank, and reachability tree) has been
studied. However, due to the limited data sources and privacy concerns,
proposed approaches are not tested on real-world datasets, but on synthetic
datasets by randomly selecting vertices as private ones. Therefore, real-world
datasets of public-private networks are essential and urgently needed for such
algorithms in the evaluation of efficiency and effectiveness.
  In this paper, we generate four public-private networks from real-world DBLP
records, called PPDBLP. We take published articles as public information and
regard ongoing collaborations as the hidden information, which is only known by
the authors. Our released datasets of PPDBLP offer the prospects for verifying
various kinds of efficient public-private analysis algorithms in a fair way. In
addition, motivated by widely existing attributed graphs, we propose an
advanced model of attributed public-private graphs where vertices have not only
private edges but also private attributes. We also discuss open problems on
attributed public-private graphs. Preliminary experimental results on our
generated real-world datasets verify the effectiveness and efficiency of
public-private models and state-of-the-art algorithms.


  Combining a precise ab initio electron band structure calculation of the TiO2
rutile structure with the temperature evolution of the Ti mean-square
displacements, we reproduce a puzzling temperature increase of the electric
field gradient at Ti sites in TiO2, observed experimentally. Our method employs
a procedure of averaging two quadrupole electron density components (L = 2)
inside a sphere vibrating with the Ti nucleus at its center, where the key
factor introducing the temperature dependence is the square root of the
Debye-Waller factor. Although the Debye-Waller factor always reduces the
corresponding Fourier component, in TiO2 due to the interplay between terms of
opposite signs, it results in a net increase of the whole sum with temperature,
leading to the growth of the electric field gradient. Quantitatively, we find
that the increase of electric field gradient is only half of the experimental
value, which we ascribe to anharmonic effects or a strong oxygen position
influence. In addition, our method reproduces the unusual temperature
dependence of the asymmetry parameter eta, which first decreases with
temperature, goes to zero and then increases.


  In this work we show the equivalence between Hamiltonian mechanics and
conservation of information entropy. We will show that distributions with
coordinate independent values for information entropy require that the manifold
on which the distribution is defined is charted by conjugate pairs (i.e. it is
a symplectic manifold). We will also show that further requiring that the
information entropy is conserved during the evolution yields Hamilton's
equations.


  The Wheeler-DeWitt equation for a class of Kantowski-Sachs like models is
completely solved. The generalized models include the Kantowski-Sachs model
with cosmological constant and pressureless dust. Likewise contained is a
joined model which consists of a Kantowski-Sachs cylinder inserted between two
FRW half--spheres. The (second order) WKB approximation is exact for the wave
functions of the complete set and this facilitates the product structure of the
wave function for the joined model. In spite of the product structure the wave
function can not be interpreted as admitting no correlations between the
different regions. This problem is due to the joining procedure and may
therefore be present for all joined models. Finally, the {s}ymmetric {i}nitial
{c}ondition (SIC) for the wave function is analyzed and compared with the ``no
bouindary'' condition. The consequences of the different boundary conditions
for the arrow of time are briefly mentioned.


  This paper presents an extension of the concept of NR-clean introduced in
[12] to graded ring theory. We define and explore graded NR-clean rings, which
generalize the class of graded U-nil clean previously studied in [15]. We
provide examples and basic properties of such rings, and investigate their
extensions to including matrix rings, group rings, as well as trivial ring
extensions.


  Neural collapse (NC) refers to the surprising structure of the last layer of
deep neural networks in the terminal phase of gradient descent training.
Recently, an increasing amount of experimental evidence has pointed to the
propagation of NC to earlier layers of neural networks. However, while the NC
in the last layer is well studied theoretically, much less is known about its
multi-layered counterpart - deep neural collapse (DNC). In particular, existing
work focuses either on linear layers or only on the last two layers at the
price of an extra assumption. Our paper fills this gap by generalizing the
established analytical framework for NC - the unconstrained features model - to
multiple non-linear layers. Our key technical contribution is to show that, in
a deep unconstrained features model, the unique global optimum for binary
classification exhibits all the properties typical of DNC. This explains the
existing experimental evidence of DNC. We also empirically show that (i) by
optimizing deep unconstrained features models via gradient descent, the
resulting solution agrees well with our theory, and (ii) trained networks
recover the unconstrained features suitable for the occurrence of DNC, thus
supporting the validity of this modeling principle.


  Several benchmarks have been proposed to holistically measure quantum
computing performance. While some have focused on the end user's perspective
(e.g., in application-oriented benchmarks), the real industrial value taking
into account the physical footprint of the quantum processor are not discussed.
Different use-cases come with different requirements for size, weight, power
consumption, or data privacy while demanding to surpass certain thresholds of
fidelity, speed, problem size, or precision. This paper aims to incorporate
these characteristics into a concept coined quantum utility, which demonstrates
the effectiveness and practicality of quantum computers for various
applications where quantum advantage -- defined as either being faster, more
accurate, or demanding less energy -- is achieved over a classical machine of
similar size, weight, and cost. To successively pursue quantum utility, a
level-based classification scheme -- constituted as application readiness
levels (ARLs) -- as well as extended classification labels are introduced.
These are demonstratively applied to different quantum applications from the
fields of quantum chemistry, quantum simulation, quantum machine learning, and
data analysis followed by a brief discussion.


  In [13], K. Roth showed that the expected value of the $L^2$ discrepancy of
the cyclic shifts of the $N$ point van der Corput set is bounded by a constant
multiple of $\sqrt{\log N}$, thus guaranteeing the existence of a shift with
asymptotically minimal $L^2$ discrepancy, [11]. In the present paper, we
construct a specific example of such a shift.


  Large language models are now tuned to align with the goals of their
creators, namely to be "helpful and harmless." These models should respond
helpfully to user questions, but refuse to answer requests that could cause
harm. However, adversarial users can construct inputs which circumvent attempts
at alignment. In this work, we study adversarial alignment, and ask to what
extent these models remain aligned when interacting with an adversarial user
who constructs worst-case inputs (adversarial examples). These inputs are
designed to cause the model to emit harmful content that would otherwise be
prohibited. We show that existing NLP-based optimization attacks are
insufficiently powerful to reliably attack aligned text models: even when
current NLP-based attacks fail, we can find adversarial inputs with brute
force. As a result, the failure of current attacks should not be seen as proof
that aligned text models remain aligned under adversarial inputs.
  However the recent trend in large-scale ML models is multimodal models that
allow users to provide images that influence the text that is generated. We
show these models can be easily attacked, i.e., induced to perform arbitrary
un-aligned behavior through adversarial perturbation of the input image. We
conjecture that improved NLP attacks may demonstrate this same level of
adversarial control over text-only models.


  The single-particle superconducting Green's functions of a Luther-Emery
liquid is computed by bosonization techniques. Using a formulation introduced
by Poilblanc and Scalapino [Phys. Rev. B v. 66, art. 052513 (2002)], an
asymptotic expression of the superconducting gap is deduced in the long
wavelength and small frequency limit. Due to superconducting phase
fluctuations, the gap exhibits as a function of size L a (1/L)^{1/2K_\rho}
power-law decay as well as an interesting singularity at the spectral gap
energy. Similarities and differences with the 2-leg t-J ladder are outlined.


  We present a local convergence analysis of the Gauss-Newton-Kurchatov method
for solving nonlinear least squares problems with a decomposition of the
operator. The method uses the sum of the derivative of the differentiable part
of the operator and the divided difference of the nondifferentiable part
instead of computing the full Jacobian. A theorem, which establishes the
conditions of convergence, radius and the convergence order of the proposed
method, is proved (Shakhno 2017). However, the radius of convergence is small
in general limiting the choice of initial points. Using tighter estimates on
the distances, under weaker hypotheses (Argyros et al. 2013), we provide an
analysis of the Gauss-Newton-Kurchatov method with the following advantages
over the corresponding results (Shakhno 2017): extended convergence region;
finer error distances, and an at least as precise information on the location
of the solution. The numerical examples illustrate the theoretical results.


  We present the design, implementation and experimental validation of a
supervisory predictive control approach for an electrical heating system
featuring a phase change slurry as heat storage and transfer medium. The
controller optimizes the energy flows that are used as set points for the heat
generation and energy distribution components. The optimization handles the
thermal and electrical subsystems simultaneously and is able to switch between
different objectives. We show the control can be implemented on low-cost
embedded hardware and validate it with an experimental test bed comprising an
installation of the complete heating system, including all hydraulic and all
electrical components. Experimental results demonstrate the feasibility of
both, a heat pump heating system with a phase change slurry, and the optimal
control approach. The main control objectives, i.e., thermal comfort and
maximum self-consumption of solar energy, can be met. In addition, the system
and its controller provide a load shifting potential.


  A search for the decays $B^0_s\to e^+e^-$ and $B^0\to e^+e^-$ is performed
using data collected with the LHCb experiment in proton-proton collisions at
center-of-mass energies of $7$, $8$ and $13\,\text{TeV}$, corresponding to
integrated luminosities of $1$, $2$ and $2\,\text{fb}^{-1}$, respectively. No
signal is observed. Assuming no contribution from $B^0\to e^+e^-$ decays, an
upper limit of $\mathcal{B}(B^0_s\to e^+e^-)<9.4\,(11.2)\times10^{-9}$ is
obtained at $90\,(95)\,\%$ confidence level. If no $B^0_s\to e^+e^-$
contribution is assumed, a limit of $\mathcal{B}(B^0\to
e^+e^-)<2.5\,(3.0)\times10^{-9}$ is determined at $90\,(95)\,\%$ confidence
level. These upper limits are more than one order of magnitude lower than the
previous values.


  In the past 40 years a considerable effort has been focused in determining
the age of the Universe at zero redshift using several stellar clocks. In this
review I will describe the best theoretical methods to determine the age of the
oldest Galactic Globular Clusters (GC). I will also argue that a more accurate
age determination may come from passively evolving high-redshift ellipticals.
In particular, I will review two new methods to determine the age of GC. These
two methods are more accurate than the classical isochrone fitting technique.
The first method is based on the morphology of the horizontal branch and is
independent of the distance modulus of the globular cluster. The second method
uses a careful binning of the stellar luminosity function which determines
simultaneously the distance and age of the GC. It is found that the oldest GCs
have an age of $13.5 \pm 2$ Gyr. The absolute minimum age for the oldest GCs is
10.5 Gyr and the maximum is 16.0 Gyr (with 99% confidence). Therefore, an
Einstein-De Sitter Universe ($\Omega=1$) is not totally ruled out if the Hubble
constant is about $65 \pm 10$ km s$^{-1}$ Mpc$^{-1}$. On the other hand, the
newly discovered red elliptical 53W069 ($z=1.43$) provides an stronger
constraint since its minimun age is 3.2 Gyr, thus ruling out an Einstein-De
Sitter Universe unless the Hubble constant is $\leq 45 \pm 10$ km s$^{-1}$.
Using 53W069 we find an age at $z=0$ of $13 \pm 2$ Gyr, in excellent agreement
with the GC determination.


  The rolling motion of a rigid cylinder on an inclined flat viscous surface is
investigated and the nonlinear resistance force against rolling, $F_R(v)$, is
derived. For small velocities $F_R(v)$ increases with velocity due to
increasing deformation rate of the surface material. For larger velocity it
decreases with velocity due to decreasing contact area between the rolling
cylinder and the deformed surface. The cylinder is, moreover, subjected to a
viscous drag force and stochastic fluctuations due to a surrounding medium
(air). For this system, in a wide range of parameters we observe bistability of
the rolling motion. Depending on the material parameters, increasing the noise
level may lead to increasing or decreasing average velocity.


  We perform an exhaustive analysis of all possible breaking patterns arising
from $S_4\rtimes H_{CP}$ in a new {\it tri-direct CP approach} to the minimal
seesaw model with two right-handed neutrinos, and construct a realistic flavour
model along these lines. According to this approach, separate residual flavour
and CP symmetries persist in the charged lepton, `atmospheric' and `solar'
right-handed neutrino sectors, i.e. we have {\it three} symmetry sectors rather
than the usual two of the {\it semi-direct CP approach} (charged leptons and
neutrinos). Following the {\it tri-direct CP approach}, we find twenty-six
kinds of independent phenomenologically interesting mixing patterns. Eight of
them predict a normal ordering (NO) neutrino mass spectrum and the other
eighteen predict an inverted ordering (IO) neutrino mass spectrum. For each
phenomenologically interesting mixing pattern, the corresponding predictions
for the PMNS matrix, the lepton mixing parameters, the neutrino masses and the
effective mass in neutrinoless double beta decay are given in a model
independent way. One breaking pattern with NO spectrum and two breaking
patterns with IO spectrum corresponds to form dominance. We find that the
lepton mixing matrices of three kinds of breaking patterns with NO spectrum and
one form dominance breaking pattern with IO spectrum preserve the first column
of the tri-bimaximal (TB) mixing matrix, i.e. yield a TM1 mixing matrix.


  Email responses often contain items-such as a file or a hyperlink to an
external document-that are attached to or included inline in the body of the
message. Analysis of an enterprise email corpus reveals that 35% of the time
when users include these items as part of their response, the attachable item
is already present in their inbox or sent folder. A modern email client can
proactively retrieve relevant attachable items from the user's past emails
based on the context of the current conversation, and recommend them for
inclusion, to reduce the time and effort involved in composing the response. In
this paper, we propose a weakly supervised learning framework for recommending
attachable items to the user. As email search systems are commonly available,
we constrain the recommendation task to formulating effective search queries
from the context of the conversations. The query is submitted to an existing IR
system to retrieve relevant items for attachment. We also present a novel
strategy for generating labels from an email corpus---without the need for
manual annotations---that can be used to train and evaluate the query
formulation model. In addition, we describe a deep convolutional neural network
that demonstrates satisfactory performance on this query formulation task when
evaluated on the publicly available Avocado dataset and a proprietary dataset
of internal emails obtained through an employee participation program.


  Let K be a number field, and let E be an elliptic curve over K. A famous
result by Faltings of 1983 can be reformulated for elliptic curves as follows:
if S is a set of primes of good reduction for E having density one, then the
K-isogeny class of E is determined by the function which maps a prime in S to
the size of the group of points over the residue field. In this paper, we prove
that it suffices to look at the radical of the size.


  In this paper we compute the quantity which is truly measured in a large
galaxy survey. We take into account the effects coming from the fact that we
actually observe galaxy redshifts and sky positions and not true spatial
positions. Our calculations are done within linear perturbation theory for both
the metric and the observer velocities but they can be used for non-linear
matter power spectra. We shall see that the complications due to the fact that
we only observe on our background lightcone and that we do not truly know the
distance of the observed galaxy, but only its redshift is not only an
additional difficulty, but even more a new opportunity for future galaxy
surveys.


  Psi-calculi is a parametric framework for process calculi similar to popular
pi-calculus extensions such as the explicit fusion calculus, the applied
pi-calculus and the spi calculus. Mechanised proofs of standard algebraic and
congruence properties of bisimilarity apply to all calculi within the
framework. A limitation of psi-calculi is that communication channels must be
symmetric and transitive. In this paper, we give a new operational semantics to
psi-calculi that allows us to lift these restrictions and simplify some of the
proofs. The key technical innovation is to annotate transitions with a
provenance -- a description of the scope and channel they originate from. We
give mechanised proofs that our extension is conservative, and that the
standard algebraic and congruence properties of strong and weak bisimilarity
are maintained. We show correspondence with a reduction semantics and barbed
bisimulation. We show how a pi-calculus with preorders that was previously
beyond the scope of psi-calculi can be captured, and how to encode mixed choice
under very strong quality criteria.


  I address the effect that a temperature dependent potential has on the
suppression of heavy quarkonia states in deconfined hadronic matter. I focus on
a simple medium: a homogenous, fixed temperature and deconfined system with a
finite lifetime (QGP-brick). Assuming that all the interactions of a heavy
quark anti-quark ($Q-\bar Q$) pair with the medium can be recast into an
in-medium potential, I solve the time dependent Schr\"odinger equation to
evolve the density matrix which describes the hard pair production and its
connection to the final distribution of hadrons after the medium disappears.
For those temperatures in which bound states survive in the medium, I find a
non-trivial dependence of the production of excited quarkonia states on the
in-medium levels, due to the mixing of vacuum and in-medium wave functions.
This mixing leads, in particular, to the enhancement of the relative abundance
of 2S to 1S states for those systems in which the in-medium ground state of the
$Q-\bar Q$ system is dissolved or close to threshold. I also explore quarkonia
production in a non-homogeneous expanding medium and find that the finite
formation time effects arising from the low binding energies of in-medium
states lead to the insensitivity of the heavy mesons yield to the hottest part
of the system evolution.


  Prior work on human motion forecasting has mostly focused on predicting the
future motion of single subjects in isolation from their past pose sequence. In
the presence of closely interacting people, however, this strategy fails to
account for the dependencies between the different subject's motions. In this
paper, we therefore introduce a motion prediction framework that explicitly
reasons about the interactions of two observed subjects. Specifically, we
achieve this by introducing a pairwise attention mechanism that models the
mutual dependencies in the motion history of the two subjects. This allows us
to preserve the long-term motion dynamics in a more realistic way and more
robustly predict unusual and fast-paced movements, such as the ones occurring
in a dance scenario. To evaluate this, and because no existing motion
prediction datasets depict two closely-interacting subjects, we introduce the
LindyHop600K dance dataset. Our results evidence that our approach outperforms
the state-of-the-art single person motion prediction techniques.


  Nanoscale inhomogeneities are typical for numerous metallic alloys and
crucially important for their practical applications. At the same time,
stabilization mechanisms of such a state are poorly understood. We present a
general overview of the problem, together with a more detailed discussion of
the prototype example, namely, Guinier-Preston zones in Al-based alloys. It is
shown that coherent strain due to a misfit between inclusion and host crystal
lattices plays a decisive role in the emergence of the inhomogeneous state. We
suggest a model explaining formation of ultrathin plates (with the thickness of
a few lattice constants) typical for Al-Cu alloys. Discreteness of the array of
misfit dislocations and long-ranged elastic interactions between them are the
key ingredients of the model. This opens a way to a general understanding of
the nature of (meta)stable embedded nanoparticles in practically important
systems.


  In this paper we consider random linear under-determined systems with
block-sparse solutions. A standard subvariant of such systems, namely,
precisely the same type of systems without additional block structuring
requirement, gained a lot of popularity over the last decade. This is of course
in first place due to the success in mathematical characterization of an
$\ell_1$ optimization technique typically used for solving such systems,
initially achieved in \cite{CRT,DOnoho06CS} and later on perfected in
\cite{DonohoPol,DonohoUnsigned,StojnicCSetam09,StojnicUpper10}. The success
that we achieved in \cite{StojnicCSetam09,StojnicUpper10} characterizing the
standard sparse solutions systems, we were then able to replicate in a sequence
of papers
\cite{StojnicCSetamBlock09,StojnicUpperBlock10,StojnicICASSP09block,StojnicJSTSP09}
where instead of the standard $\ell_1$ optimization we utilized its an
$\ell_2/\ell_1$ variant as a better fit for systems with block-sparse
solutions. All of these results finally settled the so-called threshold/phase
transitions phenomena (which naturally assume the asymptotic/large dimensional
scenario). Here, in addition to a few novel asymptotic considerations, we also
try to raise the level a bit, step a bit away from the asymptotics, and
consider the finite dimensions scenarios as well.


  Quantum optical states which have no coherent amplitude, such as squeezed
vacuum states, can not rely on standard readout techniques to generate error
signals for control of the quadrature phase. Here we investigate the use of
asymmetry in the quadrature variances to obtain a phase-sensitive readout and
to lock the phase of a squeezed vacuum state, a technique which we call noise
locking (NL). We carry out a theoretical derivation of the NL error signal and
the associated stability of the squeezed and anti-squeezed lock points.
Experimental data for the NL technique both in the presence and absence of
coherent fields are shown, including a comparison with coherent locking
techniques. Finally, we use NL to enable a stable readout of the squeezed
vacuum state on a homodyne detector.


  To measure node importance, network scientists employ centrality scores that
typically take a microscopic or macroscopic perspective, relying on node
features or global network structure. However, traditional centrality measures
such as degree centrality, betweenness centrality, or PageRank neglect the
community structure found in real-world networks. To study node importance
based on network flows from a mesoscopic perspective, we analytically derive a
community-aware information-theoretic centrality score based on network flow
and the coding principles behind the map equation: map equation centrality. Map
equation centrality measures how much further we can compress the network's
modular description by not coding for random walker transitions to the
respective node, using an adapted coding scheme and determining node importance
from a network flow-based point of view. The information-theoretic centrality
measure can be determined from a node's local network context alone because
changes to the coding scheme only affect other nodes in the same module. Map
equation centrality is agnostic to the chosen network flow model and allows
researchers to select the model that best reflects the dynamics of the process
under study. Applied to synthetic networks, we highlight how our approach
enables a more fine-grained differentiation between nodes than node-local or
network-global measures. Predicting influential nodes for two different
dynamical processes on real-world networks with traditional and other
community-aware centrality measures, we find that activating nodes based on map
equation centrality scores tends to create the largest cascades in a linear
threshold model.


  In this paper, we extend the work of Pollington and Velani in \cite{PV} to an
$S$-arithmetic set-up, where $S$ is a finite set of valuations of $\mathbb{Q}$.
In particular, for an `absolutely friendly' measure supported on a compact set
in $\mathbb{Q}_S^d$, we give a summation condition on approximating function
$\psi$ such that $\mu$ almost no point in the compact set is $\psi$
approximable. The crucial ingredient is a version of the simplex lemma that we
prove dynamically.


  Machine learning photo-z methods, trained directly on spectroscopic
redshifts, provide a viable alternative to traditional template fitting methods
but may not generalise well on new data that deviates from that in the training
set. In this work, we present a Hybrid Algorithm for WI(Y)de-range photo-z
estimation with Artificial neural networks and TEmplate fitting (HAYATE), a
novel photo-z method that combines template fitting and data-driven approaches
and whose training loss is optimised in terms of both redshift point estimates
and probability distributions. We produce artificial training data from
low-redshift galaxy SEDs at z<1.3, artificially redshifted up to z=5. We test
the model on data from the ZFOURGE surveys, demonstrating that HAYATE can
function as a reliable emulator of EAZY for the broad redshift range beyond the
region of sufficient spectroscopic completeness. The network achieves precise
photo-z estimations with smaller errors ($\sigma_{NMAD}$) than EAZY in the
initial low-z region (z<1.3), while being comparable even in the high-z
extrapolated regime (1.3<z<5). Meanwhile, it provides more robust photo-z
estimations than EAZY with the lower outlier rate ($\eta_{0.2}\lesssim 1\%$)
but runs $\sim100$ times faster than the original template fitting method. We
also demonstrate HAYATE offers more reliable redshift PDFs, showing a flatter
distribution of Probability Integral Transform scores than EAZY. The
performance is further improved using transfer learning with spec-z samples. We
expect that future large surveys will benefit from our novel methodology
applicable to observations over a wide redshift range.


  We consider a Riemannian submersion from a 3-manifold $\mathbb{E}$ to a
surface $M$, both connected and orientable, whose fibers are the integral
curves of a Killing vector field without zeros, not necessarily unitary. We
solve the Jenkins-Serrin problem for the minimal surface equation in
$\mathbb{E}$ over a relatively compact open domain $\Omega\subset M$ with
prescribed finite or infinite values on some arcs of the boundary under the
only assumption that the same value $+\infty$ or $-\infty$ cannot be prescribed
on two adjacent components of $\partial\Omega$ forming a convex angle. The
domain $\Omega$ can have reentrant corners as well as closed curves in its
boundary. We show that the solution exists if and only if some generalized
Jenkins-Serrin conditions (in terms of a conformal metric in $M$) are
fulfilled. We develop further the theory of divergence lines to study the
convergence of a sequence of minimal graphs. We also provide maximum principles
that guarantee the uniqueness of the solution. Finally, we obtain new examples
of minimal surfaces in $\mathbb{R}^3$ and in other homogeneous $3$-manifolds.


  An Overview of the status and results from the relativistic heavy ion program
at the AGS and SPS; perspective for future colliders.


  We extend the necessity part of Lucas Lehmer iteration for testing Mersenne
prime to all base and uniformly for both generalized Mersenne and Wagstaff
numbers(the later correspond to negative base). The role of the quadratic
iteration $x \rightarrow x^2-2$ is extended by Chebyshev polynomial $T_n(x)$
with an implied iteration algorithm because of the compositional identity
$T_n(T_m(x))=T_{nm}(x)$. This results from a Chebyshev polynomial primality
test based essentially on the Lucas pair $(\omega_a,\overline{\omega}_a)$,
$\omega_a=a+\sqrt{a^2-1}$, where $a \neq 0 \pm 1$. It seems interesting that
the arithmetic are all coded in the Chebyshev polynomials $T_n(x)$.


  We classify thick subcategories in a Paquette-Y\i ld\i r\i m completion
$\overline{\mathcal{C}}$ of a discrete cluster category of Dynkin type
$A_{\infty}$. To do this we introduce the notion of homologically connected
objects, and the hc (=homologically connected) decomposition of an object into
homologically connected objects in a $\mathrm{Hom}$-finite, Krull-Schmidt
triangulated category. We show that any object in a $\overline{\mathcal{C}}$
has a hc decomposition, and that the hc decomposition determines the thick
closure of an object. Moreover, we use this result to classify the classical
generators of $\overline{\mathcal{C}}$ as homologically connected objects
satisfying a maximality condition.
  Every homologically connected object has an invariant, known as the
homological length, and we show that in $\overline{\mathcal{C}}$ this
homological length is an upper bound for the generation time of a classical
generator. This allows us to provide an upper bound for the Orlov spectrum of
$\overline{\mathcal{C}}$, as well as giving the Rouquier dimension.


  The CFHTLS presents a unique data set for weak lensing studies, having high
quality imaging and deep multi-band photometry. We have initiated an XMM-CFHTLS
project to provide X-ray observations of the brightest X-ray selected clusters
within the wide CFHTLS area. Performance of these observations and the high
quality of CFHTLS data, allows us to revisit the identification of X-ray
sources, introducing automated reproducible algorithms, based on the
multi-color red sequence finder. We have also introduced a new optical mass
proxy. We provide the calibration of the red sequence observed in the CFHT
filters and compare the results with the traditional single color red sequence
and photoz. We test the identification algorithm on the subset of highly
significant XMM clusters and identify 100% of the sample. We find that the
integrated z-band luminosity of the red sequence galaxies correlates well with
the X-ray luminosity with a surprisingly small scatter of 0.20 dex. We further
use the multi-color red sequence to reduce spurious detections in the full XMM
and RASS data sets, resulting in catalogs of 196 and 32 clusters, respectively.
We made spectroscopic follow-up observations of some of these systems with
HECTOSPEC and in combination with BOSS DR9 data. We also describe the
modifications needed to the source detection algorithm in order to keep high
purity of extended sources in the shallow X-ray data. We also present the
scaling relation between X-ray luminosity and velocity dispersion.


  An engineering technique using continuous quantum measurement together with a
change detection algorithm is proposed to improve the probability of single
photon emission for a quantum-dot based single-photon source. The technique
involves continuous monitoring of the emitter, integrating the measured signal,
and a simple change detection circuit to decide when to stop pumping. The idea
is to pump just long enough such that the emitter $+$ cavity system is in a
state that can emit at most one photon with high probability. Continuous
monitoring provides partial information on the state of the emitter. This
technique is useful when the system is operating in the weak coupling regime,
and the rate of pumping is smaller than, or comparable to, the emitter-cavity
coupling strength, as can be the case for electrical pumping.


  We study the compactification of 4D $\mathcal{N}=3$ superconformal field
theories (SCFTs) on $S^1$, focusing on the relation between the 4D
superconformal index and 3D partition function on the squashed sphere $S^3_b$.
Since the center $\mathfrak{u}(1)$ of the $\mathfrak{u}(3)$ R-symmetry of the
4D theory can mix with an $\mathcal{N}=6$ abelian flavor symmetry in three
dimensions, the precise 4D/3D relation for the global symmetry is not obvious.
Focusing on the case in which the 3D theory is the ABJM theory, we demonstrate
that the above R-symmetry mixing can be precisely identified by considering the
Schur limit (and/or its $\mathcal{N}=3$ cousin) of the 4D index. As a result,
we generalize to the ABJM theories recent discussions on the connection between
supersymmetry enhancement of the 4D index and squashing independence of the
$S^3_b$ partition function.


  In this paper, we introduce a comprehensive framework for developing a
machine learning-based SOAP (Subjective, Objective, Assessment, and Plan)
classification system without manually SOAP annotated training data or with
less manually SOAP annotated training data. The system is composed of the
following two parts: 1) Data construction, 2) A neural network-based SOAP
classifier, and 3) Transfer learning framework. In data construction, since a
manual construction of a large size training dataset is expensive, we propose a
rule-based weak labeling method utilizing the structured information of an EHR
note. Then, we present a SOAP classifier composed of a pre-trained language
model and bi-directional long-short term memory with conditional random field
(Bi-LSTM-CRF). Finally, we propose a transfer learning framework that re-uses
the trained parameters of the SOAP classifier trained with the weakly labeled
dataset for datasets collected from another hospital. The proposed weakly
label-based learning model successfully performed SOAP classification (89.99
F1-score) on the notes collected from the target hospital. Otherwise, in the
notes collected from other hospitals and departments, the performance
dramatically decreased. Meanwhile, we verified that the transfer learning
framework is advantageous for inter-hospital adaptation of the model increasing
the models' performance in every cases. In particular, the transfer learning
approach was more efficient when the manually annotated data size was smaller.
We showed that SOAP classification models trained with our weakly labeling
algorithm can perform SOAP classification without manually annotated data on
the EHR notes from the same hospital. The transfer learning framework helps
SOAP classification model's inter-hospital migration with a minimal size of the
manually annotated dataset.


  We analyze a sample of optical light curves for 100 quasars, 70 of which have
black hole mass estimates. Our sample is the largest and broadest used yet for
modeling quasar variability. The sources in our sample have z < 2.8 and 10^6 <
M_BH < 10^10. We model the light curves as a continuous time stochastic
process, providing a natural means of estimating the characteristic time scale
and amplitude of quasar variations. We employ a Bayesian approach to estimate
the characteristic time scale and amplitude of flux variations; our approach is
not affected by biases introduced from discrete sampling effects. We find that
the characteristic time scales strongly correlate with black hole mass and
luminosity, and are consistent with disk orbital or thermal time scales. In
addition, the amplitude of short time scale variations is significantly
anti-correlated with black hole mass and luminosity. We interpret the optical
flux fluctuations as resulting from thermal fluctuations that are driven by an
underlying stochastic process, such as a turbulent magnetic field. In addition,
the intranight variations in optical flux implied by our empirical model are <
0.02 mag, consistent with current microvariability observations of radio-quiet
quasars. Our stochastic model is therefore able to unify both long and short
time scale optical variations in radio-quiet quasars as resulting from the same
underlying process, while radio-loud quasars have an additional variability
component that operates on time scales < 1 day.


  The ongoing globalisation of science has undisputedly a major impact on how
and where scientific research is being conducted nowadays. Yet, the big picture
remains blurred. It is largely unknown where this process is heading, and at
which rate. Which countries are leading or lagging? Many of its key features
are difficult if not impossible to capture in measurements and comparative
statistics. Our empirical study measures the extent and growth of scientific
globalisation in terms of physical distances between co-authoring researchers.
Our analysis, drawing on 21 million research publications across all countries
and fields of science, reveals that contemporary science has globalised at a
fairly steady rate during recent decades. The average collaboration distance
per publication has increased from 334 kilometres in 1980 to 1553 in 2009.
Despite significant differences in globalisation rates across countries and
fields of science, we observe a pervasive process in motion, moving towards a
truly interconnected global science system.


  For epitaxial trilayers of the magnetic rare-earth metals Gd and Tb, exchange
coupled through a non-magnetic Y spacer layer, element-specific hysteresis
loops were recorded by the x-ray magneto-optical Kerr effect at the rare-earth
$M_5$ thresholds. This allowed us to quantitatively determine the strength of
interlayer exchange coupling (IEC). In addition to the expected oscillatory
behavior as a function of spacer-layer thickness $d_Y$, a temperature-induced
sign reversal of IEC was observed for constant $d_Y$, arising from
magnetization-dependent electron reflectivities at the magnetic interfaces.


  The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic
symmetry group of all asymptotically flat Lorentzian space-times. As such, B is
the best candidate for the universal symmetry group of General Relativity.
However, in studying quantum gravity, space-times with signatures other than
the usual Lorentzian one, and complex space-times, are frequently considered.
Generalisations of B appropriate to these other signatures have been defined
earlier. In particular, the generalisation HB, a BMS group appropriate to the
ultrahyperbolic signature (+,+,-,-), has been defined in a previous paper where
it was shown that all the strongly continuous unitary irreducible
representations (IRs) of HB can be obtained with the Wigner-Mackey's inducing
method and that all the little groups of HB are compact. Here we describe in
detail all the infinite little groups of HB and we find the IRs of HB induced
by them.


  In this paper we present a continuous time dynamical model of heterogeneous
agents interacting in a financial market where transactions are cleared by a
market maker. The market is composed of fundamentalist, trend following and
contrarian agents who process information from the market with different time
delays. Each class of investor is characterized by path dependent risk
aversion. We also allow for the possibility of evolutionary switching between
trend following and contrarian strategies. We find that the system shows
periodic, quasi-periodic and chaotic dynamics as well as synchronization
between technical traders. Furthermore, the model is able to generate time
series of returns that exhibit statistical properties similar to those of the
S&P500 index, which is characterized by excess kurtosis, volatility clustering
and long memory


  An analytical model was developped to describe the current induced DW
dynamics of a Bloch DW in the presence of an external transverse magnetic
field. The model takes into account the DW deformation and the magnetization
tilting in the domain. The model is compared to the results of micromagnetic
simulation and an excellent agreement is obtained. In the steady state regime,
the model shows that the domain tilting does not change the DW mobility. An
external or current induced transverse magnetic field such as the Oersted or
Rashba field can prevent the Walker breakdown leading to a higher domain wall
velocity.


  Despite great progress in supervised semantic segmentation,a large
performance drop is usually observed when deploying the model in the wild.
Domain adaptation methods tackle the issue by aligning the source domain and
the target domain. However, most existing methods attempt to perform the
alignment from a holistic view, ignoring the underlying class-level data
structure in the target domain. To fully exploit the supervision in the source
domain, we propose a fine-grained adversarial learning strategy for class-level
feature alignment while preserving the internal structure of semantics across
domains. We adopt a fine-grained domain discriminator that not only plays as a
domain distinguisher, but also differentiates domains at class level. The
traditional binary domain labels are also generalized to domain encodings as
the supervision signal to guide the fine-grained feature alignment. An analysis
with Class Center Distance (CCD) validates that our fine-grained adversarial
strategy achieves better class-level alignment compared to other
state-of-the-art methods. Our method is easy to implement and its effectiveness
is evaluated on three classical domain adaptation tasks, i.e., GTA5 to
Cityscapes, SYNTHIA to Cityscapes and Cityscapes to Cross-City. Large
performance gains show that our method outperforms other global feature
alignment based and class-wise alignment based counterparts. The code is
publicly available at https://github.com/JDAI-CV/FADA.


  In this article we obtain asymptotic formulas for eigenvalues and
eigenfunctions of the operator generated by a system of ordinary differential
equations with summable coefficients and quasiperiodic boundary conditions.
Then using these asymptotic formulas, we find conditions on the coefficients
for which the number of gaps in the spectrum of the self-adjoint differential
operator with the periodic matrix coefficients is finite.


  Current neutrino oscillation data indicate that the 3x3 lepton flavor mixing
matrix V is likely to be symmetric about its V_{e3}-V_{\mu 2}-V_{\tau 1} axis.
This off-diagonal symmetry corresponds to three pairs of {\it congruent}
unitarity triangles in the complex plane. Terrestrial matter effects can
substantially modify the genuine CP-violating parameter and off-diagonal
asymmetries of V in realistic long-baseline experiments of neutrino
oscillations.


  Let $p$ and $q$ be odd prime numbers. In this paper we study non-abelian
pq-fold regular covers of the projective line, determine algebraic models for
some special cases and provide a general isogeny decomposition of the
corresponding Jacobian varieties. We also give a classification and description
of the one-dimensional families of compact Riemann surfaces as before.


  Deep neural networks are known to be vulnerable to adversarial examples,
where a perturbation in the input space leads to an amplified shift in the
latent network representation. In this paper, we combine canonical supervised
learning with self-supervised representation learning, and present
Self-supervised Online Adversarial Purification (SOAP), a novel defense
strategy that uses a self-supervised loss to purify adversarial examples at
test-time. Our approach leverages the label-independent nature of
self-supervised signals and counters the adversarial perturbation with respect
to the self-supervised tasks. SOAP yields competitive robust accuracy against
state-of-the-art adversarial training and purification methods, with
considerably less training complexity. In addition, our approach is robust even
when adversaries are given knowledge of the purification defense strategy. To
the best of our knowledge, our paper is the first that generalizes the idea of
using self-supervised signals to perform online test-time purification.


  Let $M$ be a $3$-manifold, compact with boundary and $\Gamma$ its fundamental
group. Consider a complex reductive algebraic group G. The character variety
$X(\Gamma,G)$ is the GIT quotient $\mathrm{Hom}(\Gamma,G)//G$ of the space of
morphisms $\Gamma\to G$ by the natural action by conjugation of $G$. In the
case $G=\mathrm{SL}(2,\mathbb C)$ this space has been thoroughly studied.
  Following work of Thurston, as presented by Culler-Shalen, we give a lower
bound for the dimension of irreducible components of $X(\Gamma,G)$ in terms of
the Euler characteristic $\chi(M)$ of $M$, the number $t$ of torus boundary
components of $M$, the dimension $d$ and the rank $r$ of $G$. Indeed, under
mild assumptions on an irreducible component $X_0$ of $X(\Gamma,G)$, we prove
the inequality $$\mathrm{dim}(X_0)\geq t \cdot r - d\chi(M).$$


  We consider weakly-coupled theories of massive higher-spin particles. This
class of models includes, for instance, tree-level String Theory and Large-N
Yang-Mills theory. The S-matrix in such theories is a meromorphic function
obeying unitarity and crossing symmetry. We discuss the (unphysical) regime
$s,t \gg 1$, in which we expect the amplitude to be universal and exponentially
large. We develop methods to study this regime and show that the amplitude
necessarily coincides with the Veneziano amplitude there. In particular, this
implies that the leading Regge trajectory, $j(t)$, is asymptotically linear in
Yang-Mills theory. Further, our analysis shows that any such theory of
higher-spin particles has stringy excitations and infinitely many
asymptotically parallel subleading trajectories. More generally, we argue that,
under some assumptions, any theory with at least one higher-spin particle must
have strings.


  In a multi-user millimeter (mm) wave communication system, we consider the
problem of estimating the channel response between the central node (base
station) and each of the user equipments (UE). We propose three different
strategies: 1) Each UE estimates its channel separately, 2) Base station
estimates all the UEs channels jointly, and 3) Two stage process with
estimation done at both UE and base station. Exploiting the low rank nature of
the mm wave channels, we propose a generalized block orthogonal matching
pursuit (G.BOMP) framework for channel estimation in all the three strategies.
Our simulation results show that, the average beamforming gain of the G.BOMP
algorithm is higher than that of the conventional OMP algorithm and other
existing works on the multi-user mm wave system.


  In this work, we study the four form-factors $f_1(Q^2)$, $f_2(Q^2)$,
$g_1(Q^2)$ and $g_2(Q^2)$ of the $\Sigma \to n$ in the framework of the
light-cone QCD sum rules approach up to twist-6 three valence quark light-cone
distribution amplitudes. The $f_1(0)$ is the basic input parameter in
extracting the CKM matrix element $|V_{us}|$ from the hyperon decays.
  The four form-factors $f_1(Q^2)$, $f_2(Q^2)$, $g_1(Q^2)$ and $g_2(Q^2)$ at
intermediate and large momentum transfers with $Q^2> 3 GeV^2$ have significant
contributions from the end-point (soft) terms. The numerical values of the four
form-factors $f_1(0)$, $f_2(0)$, $g_1(0)$ and $g_2(0)$ are compatible with the
experimental data and theoretical calculations (in magnitude); although the
uncertainties are large.


  The multi-frequency `Sedentary Survey' is a deep, statistically complete,
radio flux limited sample comprising 150 BL Lacertae objects distinguished by
their extremely high X-ray to radio flux ratio, ranging from five hundred to
over five thousand times that of typical BL Lacs discovered in radio surveys.
This paper presents the final, 100% identified, catalog together with the
optical, X-ray and broad-band SEDs constructed combining literature
multi-frequency data with non-simultaneous optical observations and BeppoSAX
X-ray data, when available. The SEDs confirm that the peak of the synchrotron
power in these objects is located at very high energies. BeppoSAX wide band
X-ray observations show that, in most cases, the X-ray spectra are convex and
well described by a logarithmic parabola model peaking (in a E f(E) vs E
representation) between 0.02 to several keV. Owing to the high synchrotron
energies involved most of the sources in the catalog are likely to be TeV
emitters, with the closest and brightest ones probably detectable by the
present generation of Cherenkov telescopes. The optical spectrum of about one
fourth of the sources is totally featureless. Because this implies that the
non-thermal emission must be well above that of the host galaxy, these objects
are likely to be the most powerful sources in the survey and therefore be
examples of the yet unreported high radio luminosity-high energy peaked BL
Lacs.


  We generalize our earlier results concerning meshfree collocation methods for
semilinear elliptic second order problems to the quasilinear case. The
stability question, however, is treated differently, namely by extending a
paper on uniformly stable discretizations of well-posd linear problems to the
nonlinear case. These two ingredients allow a proof that all well-posed
quasilinear elliptic second-order problems can be discretized in a uniformly
stable way by using sufficient oversampling, and then the error of the
numerical solution behaves like the error obtainable by direct approximation of
the true solution by functions from the chosen trial space, up to a factor
induced by being forced to use a H\"older-type theory for the nonlinear PDE. We
apply our general technique to prove convergence of meshfree methods for
quasilinear elliptic equations with Dirichlet and non-Dirichlet boundary
conditions. This is achieved for bifurcation and center manifolds of elliptic
partial differential equations and their numerical methods as well.


  In this note we give some sufficient conditions for an analytic function
$f(z)$ normalized by $f'(0)=1$ to belong to certain subfamilies of the class of
Bazilevic functions. In earlier works, the closure property of many classes of
functions under the Bernardi integral have been considered. The converse of
this problem is also considered here.


  We combine ultraviolet to near-infrared photometry with HI 21cm line
observations for a complete volume-limited sample of nearby galaxies in
different environments (from isolated galaxies to Virgo cluster members), to
study the migration of spirals from the blue to the red sequence. Although our
analysis confirms that, in the transition region between the two sequences, a
high fraction of spirals host active galactic nuclei (AGN), it clearly shows
that late-types with quenched star formation are mainly HI deficient galaxies
preferentially found in the Virgo cluster. This not only suggests that
environmental effects could play a significant role in driving the migration of
local galaxies from the blue sequence, but it also implies that a physical link
between AGN feedback and quenching may not be assumed from a correlation
between nuclear activity and colour.


  In an experimental study of single enzyme reactions, it has been proposed
that the rate constants of the enzymatic reactions fluctuate randomly,
according to a given distribution. To quantify the uncertainty arising from
random rate constants, it is necessary to investigate how one can simulate such
a biochemical system. To do this, we will take the Gillespie's stochastic
simulation algorithm for simulating the evolution of the state of a chemical
system, and study a modification of the algorithm that incorporates the random
rate constants. In addition to simulating the waiting time of each reaction
step, the modified algorithm also involves simulating the random fluctuation of
the rate constant at each reaction time. We consider the modified algorithm in
a general framework, then specialize it to two contrasting physical models, one
in which the fluctuations occur on a much faster time scale than the reaction
step, and the other in which the fluctuations occur much more slowly. The
latter case was applied to the single enzyme reaction system, using in part the
Metropolis-Hastings algorithm to enact the given distribution on the random
rate constants. The modified algorithm is shown to produce simulation outputs
that are corroborated by the experimental results. It is hoped that this
modified algorithm can subsequently be used as a tool for the estimation or
calibration of parameters in the system using experimental data.


  Based on generalized quantum Langevin equations for the tight-binding wave
function amplitudes and lattice displacements, electron and phonon quantum
transport are obtained exactly using molecular dynamics (MD) in the ballistic
regime. The electron-phonon interactions can be handled with a quasi-classical
approximation. Both charge and energy transport and their interplay can be
studied. We compare the MD results with that of a fully quantum mechanical
nonequilibrium Green's function (NEGF) approach for the electron currents. We
find a ballistic to diffusive transition of the electron conduction in one
dimensional chains as the chain length increases.


  During the recent years experiments with neutral kaons have yielded
remarkably sensitive results which are pertinent to such fundamental phenomena
as CPT invariance (protecting causality), time-reversal invariance violation,
coherence of wave functions, and entanglement of kaons in pair states. We
describe the phenomenological developments and the theoretical conclusions
drawn from the experimental material. An outlook to future experimentation is
indicated. An overview of formal similarities in fields outside neutral kaons
is included.


  Starting from the tri-Hamiltonian formulation of the Lagrange top in a
six-dimensional phase space, we discuss the reduction of the vector field and
of the Poisson tensors. We show explicitly that, after the reduction on each
one of the symplectic leaves, the vector field of the Lagrange top is separable
in the sense of Hamilton-Jacobi.


  The paper demonstrates the prospects of Spark Plasma Sintering (SPS) for the
high-speed diffusion welding of the high-strength ultrafine-grained (UFG)
near-a Ti-5Al-2V alloy. The effect of increased diffusion welding intensity in
the UFG Ti alloys is discussed also. The welds of the UFG near-a-Ti-5Al-2V
alloy obtained by SPS are featured by high density, strength, and corrosion
resistance. The rate of weld sealing in the UFG alloys has been shown to depend
on the heating rate non-monotonously (with a pronounced maximum). At the stage
of continuous heating and isothermic holding, the kinetics of the weld sealing
was found to be determined by the exponential creep rate, the intensity of
which in the coarse-grained (CG) alloys is limited by the diffusion rate in the
crystal lattice whereas in the UFG alloys it is limited by the grain boundary
diffusion rate.


  Internal dynamical evolution can drive stellar systems into states of high
central density. For many star clusters and galactic nuclei, the time scale on
which this occurs is significantly less than the age of the universe. As a
result, such systems are expected to be sites of frequent interactions among
stars, binary systems, and stellar remnants, making them efficient factories
for the production of compact binaries, intermediate-mass black holes, and
other interesting and eminently observable astrophysical exotica. We describe
some elements of the competition among stellar dynamics, stellar evolution, and
other mechanisms to control the dynamics of stellar systems, and discuss
briefly the techniques by which these systems are modeled and studied.
Particular emphasis is placed on pathways leading to massive black holes in
present-day globular clusters and other potentially detectable sources of
gravitational radiation.


  A large class of two-dimensional dilaton-gravity theories in asymptotically
AdS$_2$ spacetimes are holographically dual to a matrix integral, interpreted
as an ensemble average over Hamiltonians. Viewing these theories as
Jackiw-Teitelboim gravity with a gas of defects, we extend this duality to a
broader class of dilaton potentials compared to previous work by including
conical defects with small deficit angles. In order to do this we show that
these theories are equal to the large $p$ limit of a natural deformation of the
$(2,p)$ minimal string theory.


  The category of representations with a strongly typical central character of
a basic classical Lie superalgebra is proven to be equivalent to the category
of representations of its even part corresponding to an appropriate central
character.
  For a Lie superalgebra $osp(1,2l)$ the category of representations with a
"generic" weakly atypical central character is described.


  We propose a response-based method of knowledge distillation (KD) for the
head pose estimation problem. A student model trained by the proposed KD
achieves results better than a teacher model, which is atypical for the
response-based method. Our method consists of two stages. In the first stage,
we trained the base neural network (NN), which has one regression head and four
regression via classification (RvC) heads. We build the convolutional ensemble
over the base NN using offsets of face bounding boxes over a regular grid. In
the second stage, we perform KD from the convolutional ensemble into the final
NN with one RvC head. The KD improves the results by an average of 7.7\%
compared to base NN. This feature makes it possible to use KD as a booster and
effectively train deeper NNs. NNs trained by our KD method partially improved
the state-of-the-art results. KD-ResNet152 has the best results, and
KD-ResNet18 has a better result on the AFLW2000 dataset than any previous
method.We have made publicly available trained NNs and face bounding boxes for
the 300W-LP, AFLW, AFLW2000, and BIWI datasets.Our method potentially can be
effective for other regression problems.


  The equilibrium conditions for charges and currents, apparent in exact
solutions of the field equations, lead one to regard the Hermitian theory of
relativity as the theory of a field endowed with two sources: electromagnetic
and colour four-currents.


  We investigate the fusion cross sections of light nuclei in the presence of
linearly polarized intense laser fields. By combining the Coulomb-Volkov
solutions with the complex spherical square-well nuclear potential, we derive
an explicit formulation of the multiphoton cross section in a self-consistent
manner. Our analysis is specifically focused on deuteron-triton (DT) and
proton-boron (p$^{11}{\rm B}$) fusion reactions, both of which have garnered
widespread attention. The theoretical results reveal that, under conditions of
longer laser wavelengths and lower incident particle kinetic energies, a few
thousands of photons can participate in the fusion reactions, resulting in a
substantial enhancement of fusion cross sections by almost ten orders of
magnitude. We elucidate the multiphoton mechanism underlying these findings and
discuss their implications.


  We suggested a one-fluid model of a turbulent dilute suspension which
accounts for the ``two-way'' fluid-particle interactions by $k$-dependent
effective density of suspension and additional damping term in the
Navier-Stokes equation. We presented analytical description of the particle
modification of turbulence including scale invariant suppression of a small $k$
part of turbulent spectrum (independent of the particle response time) and
possible enhancemenent of large $k$ region [up to the factor $(1+\phi)^{2/3}$].
Our results are in agreement with qualitative picture of isotropic homogeneous
turbulence of dilute suspensions previously observed in laboratory and
numerical experiments.


  We are interested in a variation of the SIR (Susceptible/Infected/Recovered)
dynamics on the complete graph, in which infected individuals may only spread
to neighboring susceptible individuals at fixed rate $\lambda>0$ while
recovered individuals may only spread to neighboring infected individuals at
fixed rate $1$. This is also a variant of the so-called chase-escape process
introduced by Kordzakhia and then Bordenave & Ganesan. Our work is the first
study of this dynamics on complete graphs. Starting with one infected and one
recovered individuals on the complete graph with $N+2$ vertices, and stopping
the process when one type of individuals disappears, we study the asymptotic
behavior of the probability that the infection spreads to the whole graph as
$N\rightarrow\infty$ and show that for $\lambda\in (0,1)$ (resp. for
$\lambda>1$), the infection dies out (resp. does not die out) with probability
tending to one as $N\rightarrow\infty$, and that the probability that the
infection dies out tends to $1/2$ for $\lambda=1$. We also establish limit
theorems concerning the asymptotic state of the system in all regimes and show
that two additional phase transitions occur in the subcritical phase
$\lambda\in (0,1)$: at $\lambda=1/2$ the behavior of the expected number of
remaining infected individuals changes, while at $\lambda=(\sqrt {5}-1)/2$ the
behavior of the expected number of remaining recovered individuals changes. We
also study the outbreak sizes of the infection, and show that the outbreak
sizes are small if $\lambda \in(0,1/2]$, exhibit a power-law behavior for
$1/2<\lambda<1$, and are pandemic for $\lambda\geq 1$. Our method relies on
different couplings: we first couple the dynamics with two independent Yule
processes by using an Athreya-Karlin embedding, and then we couple the Yule
processes with Poisson processes thanks to Kendall's representation of Yule
processes.


  We discuss high-order calculations in perturbative effective field theory for
fermions at low energy scales. The Fermi-momentum or $k_{\rm F} a_s$ expansion
for the ground-state energy of the dilute Fermi gas is calculated to fourth
order, both in cutoff regularization and in dimensional regularization. For the
case of spin one-half fermions we find from a Bayesian analysis that the
expansion is well-converged at this order for ${| k_{\rm F} a_s | \lesssim
0.5}$. Further, we show that Pad{\'e}-Borel resummations can improve the
convergence for ${| k_{\rm F} a_s | \lesssim 1}$. Our results provide important
constraints for nonperturbative calculations of ultracold atoms and dilute
neutron matter.


  We study the anisotropic Ginzburg-Landau and Lawrence-Doniach models
describing a layered superfluid ultracold Fermi gas in optical lattices. We
derive the coefficients of the anisotropic Ginzburg-Landau and the mass tensor
as a function of anisotropy, filling and interaction, showing that near the
unitary limit the effective anisotropy of the masses is significantly reduced.
The anisotropy parameter is shown to vary in realistic setups in a wide range
of values. We also derive the Lawrence-Doniach model - often used to describe
the 2D-3D dimensional crossover in layered superconductors - for a layered
ultracold Fermi gas, obtaining a relation between the interlayer Josephson
couplings and the Ginzburg-Landau masses. Comparing to the Ginzburg-Landau
description, we find that the region of validity of the Lawrence-Doniach model
is near the unitary limit.


  Stellar flares have been extensively studied in soft X-rays (SXR) by
basically every X-ray mission. Hard X-ray (HXR) emission from stellar
superflares, however, have only been detected from a handful of objects over
the past years. One very extreme event was the superflare from the young
M-dwarf DG CVn binary star system, which triggered Swift/BAT as if it was a
$\gamma$-ray burst (GRB). In this work, we estimate the expected $\gamma$-ray
emission from DG CVn and the most extreme stellar flares by extrapolating from
solar flares based on measured solar energetic particles (SEPs), as well as
thermal and non-thermal emission properties. We find that ions are plausibly
accelerated in stellar superflares to 100 GeV energies, and possibly up to TeV
energies in the associated coronal mass ejections. The corresponding
$\pi^0$-decay $\gamma$-ray emission could be detectable from stellar
superflares with ground-based $\gamma$-ray telescopes. On the other hand, the
detection of $\gamma$-ray emission implies particle densities high enough that
ions suffer significant losses due to inelastic proton-proton scattering. The
next-generation Cherenkov Telescope Array (CTA) should be able to probe
superflares from M-dwarfs in the solar neighbourhood and constrain the energy
in interacting cosmic rays and/or their maximum energy. The detection of
$\gamma$-ray emission from stellar flares would open a new window for the study
of stellar physics, the underlying physical processes in flares and their
impact on habitability of planetary systems.


  In this work, the sixth of a series, we use the ASTRAEUS (semi-numerical
rAdiative tranSfer coupling of galaxy formaTion and Reionization in N-body dark
matter simUlationS) framework to investigate the nature of the sources that
reionized the Universe. We extend ASTRAEUS, which already couples a galaxy
formation semi-analytical model with a detailed semi-numerical reionization
scheme, to include a model for black hole formation, growth, and the production
of ionizing radiation from associated AGN (active galactic nuclei). We
calibrate our fiducial AGN model to reproduce the bolometric luminosity
function at z ~ 5, and explore the role of the resulting AGN population in
reionizing the Universe. We find that in all the models yielding a reasonable
AGN luminosity function, galaxies dominate overwhelmingly the ionizing budget
during the Epoch of Reionization, with AGN accounting for 1-10% of the ionizing
budget at z=6 and starting to play a role only below z < 5.


  The motion of a particle in a ring of length L is influenced by a dirty metal
environment whose fluctuations are characterized by a short correlation
distance $\ell << L$. We analyze the induced decoherence process, and compare
the results with those obtained in the opposing Caldeira-Leggett limit ($\ell
>> L$). A proper definition of the dephasing factor that does not depend on a
vague semiclassical picture is employed. Some recent Monte-Carlo results about
the effect of finite temperatures on "mass renormalization" in this system are
illuminated.


  We calculate the gluon structure function of a color dipole in a new approach
evaluating the matrix elements of SU(2) gluon field operators separated along a
direction close to the light cone. As vacuum state in the pure glue sector, we
use a variational ground state of the near-light-cone Hamiltonian. With a mean
momentum fraction of the gluons fixed to the "experimental value" in a proton,
the resulting gluon structure function for a dipole state with four links is
compared qualitatively to the NLO \emph{MRST} 2002 parameterization at $Q^2=1.5
\mathrm{GeV}^2$.


  The ordinary Bayes estimator based on the posterior density suffers from the
potential problems of non-robustness under data contamination or outliers. In
this paper, we consider the general set-up of independent but non-homogeneous
(INH) observations and study a robustified pseudo-posterior based estimation
for such parametric INH models. In particular, we focus on the
$R^{(\alpha)}$-posterior developed by Ghosh and Basu (2016) for IID data and
later extended by Ghosh and Basu (2017) for INH set-up, where its usefulness
and desirable properties have been numerically illustrated. In this paper, we
investigate the detailed theoretical properties of this robust pseudo Bayes
$R^{(\alpha)}$-posterior and associated $R^{(\alpha)}$-Bayes estimate under the
general INH set-up with applications to fixed-design regressions. We derive a
Bernstein von-Mises types asymptotic normality results and Laplace type
asymptotic expansion of the $R^{(\alpha)}$-posterior as well as the asymptotic
distributions of the expected $R^{(\alpha)}$-posterior estimators. The required
conditions and the asymptotic results are simplified for linear regressions
with known or unknown error variance and logistic regression models with fixed
covariates. The robustness of the $R^{(\alpha)}$-posterior and associated
estimators are theoretically examined through appropriate influence function
analyses under general INH set-up; illustrations are provided for the case of
linear regression. A high breakdown point result is derived for the expected
$R^{(\alpha)}$-posterior estimators of the location parameter under a
location-scale type model. Some interesting real life data examples illustrate
possible applications.


  Domain-independent planning is one of the foundational areas in the field of
Artificial Intelligence. A description of a planning task consists of an
initial world state, a goal, and a set of actions for modifying the world
state. The objective is to find a sequence of actions, that is, a plan, that
transforms the initial world state into a goal state. In optimal planning, we
are interested in finding not just a plan, but one of the cheapest plans. A
prominent approach to optimal planning these days is heuristic state-space
search, guided by admissible heuristic functions. Numerous admissible
heuristics have been developed, each with its own strengths and weaknesses, and
it is well known that there is no single "best heuristic for optimal planning
in general. Thus, which heuristic to choose for a given planning task is a
difficult question. This difficulty can be avoided by combining several
heuristics, but that requires computing numerous heuristic estimates at each
state, and the tradeoff between the time spent doing so and the time saved by
the combined advantages of the different heuristics might be high. We present a
novel method that reduces the cost of combining admissible heuristics for
optimal planning, while maintaining its benefits. Using an idealized search
space model, we formulate a decision rule for choosing the best heuristic to
compute at each state. We then present an active online learning approach for
learning a classifier with that decision rule as the target concept, and employ
the learned classifier to decide which heuristic to compute at each state. We
evaluate this technique empirically, and show that it substantially outperforms
the standard method for combining several heuristics via their pointwise
maximum.


  For any $n\geq 3$ and $ q\geq 3$, we prove that the {\sc Equality} function
$(=_n)$ on $n$ variables over a domain of size $q$ cannot be realized by
matchgates under holographic transformations. This is a consequence of our
theorem on the structure of blockwise symmetric matchgate signatures. %due to
the rank of the matrix form of the blockwise symmetric standard signatures,
%where $(=_n)$ is an equality signature on domain $\{0, 1, \cdots, q-1\}$. This
has the implication that the standard holographic algorithms based on
matchgates, a methodology known to be universal for \#CSP over the Boolean
domain, cannot produce P-time algorithms for planar \#CSP over any higher
domain $q\geq 3$.


  We introduce a measure called width, quantifying the amount of nondeterminism
in automata. Width generalises the notion of good-for-games (GFG) automata,
that correspond to NFAs of width 1, and where an accepting run can be built
on-the-fly on any accepted input. We describe an incremental determinisation
construction on NFAs, which can be more efficient than the full powerset
determinisation, depending on the width of the input NFA. This construction can
be generalised to infinite words, and is particularly well-suited to coB\"uchi
automata. For coB\"uchi automata, this procedure can be used to compute either
a deterministic automaton or a GFG one, and it is algorithmically more
efficient in the last case. We show this fact by proving that checking whether
a coB\"uchi automaton is determinisable by pruning is NP-complete. On finite or
infinite words, we show that computing the width of an automaton is
EXPTIME-complete. This implies EXPTIME-completeness for multipebble simulation
games on NFAs.


  Traditional methods for inference in change point detection often rely on a
large number of observed data points and can be inaccurate in non-asymptotic
settings. With the rise of mobile health and digital phenotyping studies, where
patients are monitored through the use of smartphones or other digital devices,
change point detection is needed in non-asymptotic settings where it may be
important to identify behavioral changes that occur just days before an adverse
event such as relapse or suicide. Furthermore, analytical and computationally
efficient means of inference are necessary for the monitoring and online
analysis of large-scale digital phenotyping cohorts. We extend the result for
asymptotic tail probabilities of the likelihood ratio test to the multivariate
change point detection setting, and demonstrate through simulation its
inaccuracy when the number of observed data points is not large. We propose a
non-asymptotic approach for inference on the likelihood ratio test, and compare
the efficiency of this estimated p-value to the popular empirical p-value
obtained through simulation of the null distribution. The accuracy and power of
this approach relative to competing methods is demonstrated through simulation
and through the detection of a change point in the behavior of a patient with
schizophrenia in the week prior to relapse.


  Unique measurement of the proton structure function F2 in a wide
two-dimensional region of x and Q**2 has been reported. The accessible
kinematics covers entire resonance region up to W=2.5 GeV in the Q**2 interval
from 0.1 to 4.5 GeV**2. Obtained data allowed for the first time an evaluation
of moments of the structure function F2 directly from experimental data as well
as an intensive study of the Bloom-Gilman duality phenomenon.


  In this paper, we apply the geometric Hamilton--Jacobi theory to obtain
solutions of classical hamiltonian systems that are either compatible with a
cosymplectic or a contact structure. As it is well known, the first structure
plays a central role in the theory of time-dependent hamiltonians, whilst the
second is here used to treat classical hamiltonians including dissipation
terms.
  The interest of a geometric Hamilton--Jacobi equation is the primordial
observation that if a hamiltonian vector field $X_{H}$ can be projected into a
configuration manifold by means of a 1-form $dW$, then the integral curves of
the projected vector field $X_{H}^{dW}$ can be transformed into integral curves
of $X_{H}$ provided that $W$ is a solution of the Hamilton--Jacobi equation. In
this way, we use the geometric Hamilton--Jacobi theory to derive solutions of
physical systems with a time-dependent hamiltonian formulation or including
dissipative terms. Explicit, new expressions for a geometric Hamilton--Jacobi
equation are obtained on a cosymplectic and a contact manifold. These equations
are later used to solve physical examples containing explicit time dependence,
as it is the case of a unidimensional trigonometric system, and two dimensional
nonlinear oscillators as Winternitz--Smorodinsky oscillators. For explicit
dissipative behavior, we solve the example of a unidimensional damped
oscillator.


  We introduce the concept of a quantum background and a functor QFT. In the
case that the QFT moduli space is smooth formal, we construct a flat quantum
superconnection on a bundle over QFT which defines algebraic structures
relevant to correlation functions in quantum field theory. We go further and
identify chain level generalizations of correlation functions which should be
present in all quantum field theories.


  Consider a graph G with n nodes and m edges, which represents a social
network, and assume that initially each node is blue or white. In each round,
all nodes simultaneously update their color to the most frequent color in their
neighborhood. This is called the Majority Model (MM) if a node keeps its color
in case of a tie and the Random Majority Model (RMM) if it chooses blue with
probability 1/2 and white otherwise.
  We prove that there are graphs for which RMM needs exponentially many rounds
to reach a stable configuration in expectation, and such a configuration can
have exponentially many states (i.e., colorings). This is in contrast to MM,
which is known to always reach a stable configuration with one or two states in
$O(m)$ rounds. For the special case of a cycle graph C_n, we prove the stronger
and tight bounds of $\lceil n/2\rceil-1$ and $O(n^2)$ in MM and RMM,
respectively. Furthermore, we show that the number of stable colorings in MM on
C_n is equal to $\Theta(\Phi^n)$, where $\Phi = (1+\sqrt{5})/2$ is the golden
ratio, while it is equal to 2 for RMM.
  We also study the minimum size of a winning set, which is a set of nodes
whose agreement on a color in the initial coloring enforces the process to end
in a coloring where all nodes share that color. We present tight bounds on the
minimum size of a winning set for both MM and RMM.
  Furthermore, we analyze our models for a random initial coloring, where each
node is colored blue independently with some probability $p$ and white
otherwise. Using some martingale analysis and counting arguments, we prove that
the expected final number of blue nodes is respectively equal to
$(2p^2-p^3)n/(1-p+p^2)$ and pn in MM and RMM on a cycle graph C_n.
  Finally, we conduct some experiments which complement our theoretical
findings and also lead to the proposal of some intriguing open problems and
conjectures to be tackled in future work.


  Perhaps the quantum state represents information about reality, and not
reality directly. Wave function collapse is then possibly no more mysterious
than a Bayesian update of a probability distribution given new data. We
consider models for quantum systems with measurement outcomes determined by an
underlying physical state of the system but where several quantum states are
consistent with a single underlying state---i.e., probability distributions for
distinct quantum states overlap. Significantly, we demonstrate by example that
additional assumptions are always necessary to rule out such a model.


  Parkinson's disease is a neuro-degenerative disorder affecting tens of
millions of people worldwide. Lately, there has been considerable interest in
systems for at-home monitoring of patients, using wearable devices which
contain inertial measurement units. We present a new wavelet-based approach for
analysis of data from single wrist-worn smart-watches, and show high detection
performance for tremor, bradykinesia, and dyskinesia, which have been the major
targets for monitoring in this context. We also discuss the implication of our
controlled-experiment results for uncontrolled home monitoring of freely
behaving patients.


  We report results of systematic measurements of charge transport properties
of the 20.5nm wide HgTe-based quantum well in perpendicular magnetic field,
performed under hydrostatic pressures up to 15.1 kbar. At ambient pressure
transport is well described by the two-band semiclassical model.In contrast, at
elevated pressure, we observed non-monotonic pressure dependence of resistivity
at CNP. For pressures lower than $\approx9$ kbar, resistivity grows with
pressure, in accord with expectations from the band structure calculations and
the model incorporating effects of disorder on transport in 2D semimetals with
indirect band overlap. For higher pressures, the resistivity saturates and
starts decreasing upon further increase of pressure. Above $\approx14$ kbar the
resistance and hopping transport character sharply change, which may indicate
formation of the excitonic insulator state. The data also reveals strong
influence of disorder on transport in 2D electron-hole system with a small band
overlap.


  We constrain the deceleration-acceleration epoch, namely the transition
redshift $z_{tr}$, adopting model-independent techniques that utilize a
calibrated $E_{\rm p}$-$E_{\rm iso}$ correlation for gamma-ray bursts (GRBs).
To do so, in addition to real data points, we employ up to $1000$ simulated
observational Hubble data (OHD) points. We then calibrate the $E_{\rm
p}$-$E_{\rm iso}$ correlation by means of the well-consolidate B\'ezier
polynomial technique, interpolating OHD up to the second order. Once GRB data
have been calibrated, we consider two strategies of cosmographic expansions,
i.e., first we take a direct Hubble rate expansion around $z_{tr}$, and second
the expansion of the deceleration parameter around the same redshift, but with
a different order. Employing type Ia supernovae, baryonic acoustic oscillations
and GRB data sets, from Monte Carlo analyses we infer tight constraints on
$z_{tr}$ and the jerk parameters at $z=z_{tr}$, namely $j_{tr}$. Our results
are extremely compatible with previous outcomes and confirm the $\Lambda$CDM
predictions, being slightly different in terms of the jerk parameter. In this
respect, we conjecture which extensions of the concordance paradigm are
possible and we compare our findings with expectations provided by generic dark
energy models.


  We consider functionals of the form
$$\mathcal{F}(u):=\int_\Omega\!F(x,u,\nabla u)\,\mathrm{d} x,$$ where
$\Omega\subseteq\mathbb{R}^n$ is open and bounded. The integrand
$F\colon\Omega\times\mathbb{R}^N\times\mathbb{R}^{N\times n}\to\mathbb{R}$ is
assumed to satisfy the classical assumptions of a power $p$-growth and the
corresponding strong quasiconvexity. In addition, $F$ is H\"older continuous
with exponent $2\beta\in(0,1)$ in its first two variables uniformly with
respect to the third variable, and bounded below by a quasiconvex function
depending only on $z\in\mathbb{R}^{N\times n}$. We establish that strong local
minimizers of $\mathcal{F}$ are of class $\mathrm{C}^{1,\beta}$ in an open
subset $\Omega_0\subseteq\Omega$ with
$\mathcal{L}^n(\Omega\setminus\Omega_0)=0$. This partial regularity also holds
for a certain class of weak local minimizers at which the second variation is
strongly positive and satisfying a $\mathrm{BMO}$-smallness condition. This
extends the partial regularity result for local minimizers by Kristensen and
Taheri (2003) to the case where the integrand depends also on $u$. Furthermore,
we provide a direct strategy for this result, in contrast to the blow-up
argument used for the case of homogeneous integrands.


  In this work, we report an atomic scale study on the ferromagnetic insulator
manganite LaMnO$_{3.12}$ using $\gamma-\gamma$ PAC spectroscopy. Data analysis
reveals a nanoscopic transition from an undistorted to a Jahn-Teller-distorted
local environment upon cooling. The percolation thresholds of the two local
environments enclose a macroscopic structural transition
(Rhombohedric-Orthorhombic). Two distinct regimes of JT-distortions were found:
a high temperature regime where uncorrelated polaron clusters with severe
distortions of the Mn$^{3+}$O$_{6}$ octahedra survive up to $T \approx 800 K$
and a low temperature regime where correlated regions have a weaker
JT-distorted symmetry.


  A very accurate, (HF)$_2$ potential energy surface (PES) is constructed based
on \ai\ calculations performed using the MOLPRO package at the CCSD(T) level of
theory with an aug-cc-pvQz-F12 basis set at about 161~000 points. a higher
correlation correction is computed at CCSDT(Q) level for 2000 points and is
considered alongside other more minor corrections due to relativity,
core-valence correlation and Born-Oppenheimer failure. The analytical surface
constructed uses 500 constants to reproduce the \ai\ points with a standard
deviation of 0.3 \cm. Vibration-rotation-inversion energy levels of the HF
dimer are computed for this PES by variational solution of the nuclear-motion
Schr\"{o}dinger using program WAVR4. Calculations over an extended range of
rotationally excited states show very good agreement with the experimental
data. In particular the known empirical rotational constants $B$ for the ground
vibrational states are predicted to better than about 2 MHz. $B$ constants for
excited vibrational states are reproduced several times more accurately than by
previous calculations. The experimental dissociation energy of the HF dimer is
reproduced \ai\ within the experimental accuracy of about 1 \cm\ for the first
time. This level of accuracy is shown to extend to higher excited
inter-molecular vibrational states $v$ and higher excited rotational quantum
numbers $(J,K_a)$.


  A comprehensive study of the structural properties of the heavily
investigated rare-earth A2Ir2O7 series under extreme conditions is presented.
The series is covered by studying iridates with A = Pr, Sm, Dy-Lu. Temperature-
and pressure-dependent synchrotron X-ray powder diffraction experiments reveal
robustness of the pyrochlore structure throughout the rare-earth series, down
to 4 K and up to 20 GPa. The thermal expansivity and pressure compressibility
are determined, including Debye temperature, bulk modulus and Gr\"uneisen
parameter. Temperature and pressure evolution of the fractional coordinate of
oxygen at 48f Wyckoff position, the sole free atomic position parameter, is
investigated and discussed regarding the antiferromagnetic ordering of the Ir
magnetic moments. In addition, the pressure evolution of the crystal structure
of an IrO2 minority phase is followed. The tetragonal rutile-type structure is
orthorhombically distorted at 15 GPa, and the orthorhombic structure is not
fully stabilised up to 20 GPa.


  Lack of nonreciprocity is one of the major drawbacks of solid-state acoustic
devices, which has hindered the development of microwave-frequency acoustic
isolators and circulators. Here we report giant nonreciprocal transmission of
shear-horizontal surface acoustic waves (SH-SAWs) on a LiTaO3 substrate coated
with a negative-positive magnetostrictive bilayer structure of Ni/Ti/FeCoSiB.
Although the static magnetic moments of two layers are parallel, SH-SAWs can
excite optical-mode spin waves much stronger than acoustic-mode ones at
relatively low frequencies via magnetoelastic coupling. The measured magnitude
nonreciprocity exceeds 40 dB (or 80 dB/mm) at 2.333 GHz. In addition, maximum
nonreciprocal phase accumulation reaches 188{\deg} (376{\deg}/mm), which is
desired for an effective SAW circulator. Our theoretical model and calculations
provide an insight into the observed phenomena and demonstrate a pathway for
further improvement of nonreciprocal acoustic devices.


  High-quality low-dimensional layered and van der Waals materials are
typically exfoliated, with sample cross sectional areas on the order of tens to
hundreds of microns. The small size of flakes makes the experimental
characterization of their dielectric properties unsuitable with conventional
spectroscopic ellipsometry, due to beam-sample size mismatch and
non-uniformities of the crystal axes. Previously, the experimental measurement
of the dielectrirc permittivity of such microcrystals was carried out with
near-field tip-based scanning probes. These measurements are sensitive to
external conditions like vibrations and temperature, and require
non-deterministic numerical fitting to some a priori known model. We present an
alternative method to extract the in-plane dielectric permittivity of van der
Waals microcrystals, based on identifying reflectance minima in spectroscopic
measurements. Our method does not require complex fitting algorithms nor near
field tip-based measurements and accommodates for small-area samples. We
demonstrate the robustness of our method using hexagonal boron nitride and
{\alpha}-MoO3, and recover their dielectric permittivities that are close to
literature values.


  The ever growing need for energy-efficient and fast communications is driving
the development of highly integrated photonic circuits where controlling light
at the nanoscale becomes the most critical aspect of information transfer .
Directional couplers, two interacting optical waveguides placed in close
proximity, are important building blocks in these integrated photonics circuits
and have been employed as optical modulators and switches for high speed
communication, data processing and integrated quantum operations. However,
active control over the coupling between closely packed waveguides is highly
desirable and yet remains a critical barrier towards ultra small footprint
devices. A general approach to achieve active control in waveguide systems is
to exploit optical nonlinearities enabled by a strong control pulse. However
these devices suffer from the nonlinear absorption induced by the intense
control pulse as the signal and its control propagate in the same waveguide.
Here we experimentally demonstrate a unique scheme based on adiabatic
elimination (AE) concept that effectively manipulates the coupling between
densely packed waveguides. We demonstrate active coupling control between two
closely packed waveguides by tuning the mode index of an in-between decoupled
waveguide. This is achieved via a dark mode and thus leaves the signal
unaffected by the induced losses. Such a scheme is a promising candidate for
ultra-dense integrated nano-photonics such as on-chip ultrafast modulators and
tunable filters for optical communication and quantum computing.


  Molecular dynamics simulations have been extensively used to predict thermal
properties, but simulating different phases with similar precision using a
unified force field is often difficult, due to the lack of accurate and
transferrable interatomistic potential fields. As a result, this issue has
become a major barrier to predicting the phase change of materials and their
transport properties with atomistic-level modeling techniques. Recently,
machine learning based algorithms have emerged as promising tools to develop
accurate potentials for molecular dynamics simulations. In this work, we
approach the problem of predicting the thermal conductivity of silicon in
different phases by performing molecular dynamics simulations with a deep
neural network potential. This neural network potential is trained with
ab-initio data of silicon in the crystalline, liquid and amorphous phases. The
accuracy of our potential is first validated through reproducing the atomistic
structures during the phase transition, where other empirical potentials
usually fail. The thermal conductivity of different phases is then calculated,
showing a good agreement with the experimental results and ab-initio
calculation results. Our work shows that a unified neural network-based
potential can be a promising tool for studying phase change and thermal
transport of materials with high accuracy.


  Horizontal gene transfer consists in exchanging genetic materials between
microorganisms during their lives. This is a major mechanism of bacterial
evolution and is believed to be of main importance in antibiotics resistance.
We consider a stochastic model for the evolution of a discrete population
structured by a trait taking finitely many values, with density-dependent
competition. Traits are vertically inherited unless a mutation occurs, and can
also be horizontally transferred by unilateral conjugation with frequency
dependent rate. Our goal is to analyze the trade-off between natural evolution
to higher birth rates on one side, and transfer which drives the population
towards lower birth rates on the other side. Simulations show that evolutionary
outcomes include evolutionary suicide or cyclic re-emergence of small
populations with well-adapted traits. We focus on a parameter scaling where
individual mutations are rare but the global mutation rate tends to infinity.
This implies that negligible sub-populations may have a strong contribution to
evolution. Our main result quantifies the asymptotic dynamics of subpopulation
sizes on a logarithmic scale. We characterize the possible evolutionary
outcomes with explicit criteria on the model parameters. An important
ingredient for the proofs lies in comparisons of the stochastic population
process with linear or logistic birth-death processes with immigration. For the
latter processes, we derive several results of independent interest.