  In the present paper we study two qubit entanglement in the most general
$XYZ$ Heisenberg magnetic chain with (non)homogeneous magnetic fields and the
DM anisotropic antisymmetric exchange interaction, arising from the spin-orbit
coupling . The model includes all known results as particular cases, for both
antiferromagnetic and ferromagnetic $XX, XY, XXX, XXZ, XYZ$ chains. The
concurrence of two qubit thermal entanglement and its dependence on anisotropic
parameters, external magnetic field and temperature are studied in details. We
found that in all cases, inclusion of the DM interaction, which is responsible
for weak ferromagnetism in mainly antiferromagnetic crystals and spin
arrangement in low symmetry magnets, creates (when it does not exist) or
strengthens (when it exists) entanglement in $XYZ$ spin chain. This implies
existence of a relation between arrangement of spins and entanglement, in which
the DM coupling plays an essential role. It suggests also that anisotropic
antisymmetric exchange interaction could be an efficient control parameter of
entanglement in the general $XYZ$ case.


  Square-root (loss) regularized models have recently become popular in linear
regression due to their nice statistical properties. Moreover, some of these
models can be interpreted as the distributionally robust optimization
counterparts of the traditional least-squares regularized models. In this
paper, we give a unified proof to show that any square-root regularized model
whose penalty function being the sum of a simple norm and a seminorm can be
interpreted as the distributionally robust optimization (DRO) formulation of
the corresponding least-squares problem. In particular, the optimal transport
cost in the DRO formulation is given by a certain dual form of the penalty. To
solve the resulting square-root regularized model whose loss function and
penalty function are both nonsmooth, we design a proximal point dual semismooth
Newton algorithm and demonstrate its efficiency when the penalty is the sparse
group Lasso penalty or the fused Lasso penalty. Extensive experiments
demonstrate that our algorithm is highly efficient for solving the square-root
sparse group Lasso problems and the square-root fused Lasso problems.


  With security threats increasing in frequency and severity, it is critical
that we consider the important role of threat hunters. These highly-trained
security professionals learn to see, identify, and intercept security threats.
Many recent works and existing tools in cybersecurity are focused on automating
the threat hunting process, often overlooking the critical human element. Our
study shifts this paradigm by emphasizing a human-centered approach to
understanding the lived experiences of threat hunters. By observing threat
hunters during hunting sessions and analyzing the rich insights they provide,
we seek to advance the understanding of their cognitive processes and the tool
support they need. Through an in-depth observational study of threat hunters,
we introduce a model of how they build and refine their mental models during
threat hunting sessions. We also present 23 themes that provide a foundation to
better understand threat hunter needs and five actionable design propositions
to enhance the tools that support them. Through these contributions, our work
enriches the theoretical understanding of threat hunting and provides practical
insights for designing more effective, human-centered cybersecurity tools.


  In this work, we use ~500 low-redshift (z ~ 0.1) X-ray AGNs observed by
XMM-Newton and SDSS to investigate the prevalence and nature of AGNs that
apparently lack optical emission lines (``optically dull AGNs''). Although 1/4
of spectra appear absorption-line dominated in visual assessment, line
extraction with robust continuum subtraction from the MPA/JHU catalog reveals
usable [OIII] measurements in 98% of the sample, allowing us to study
[OIII]-underluminous AGNs together with more typical AGNs in the context of the
L$_{\mathrm{[OIII]}}$--L$_{X}$ relation. We find that ``optically dull AGNs''
do not constitute a distinct population of AGNs. Instead, they are the
[OIII]-underluminous tail of a single, unimodal L$_{\mathrm{[OIII]}}$--L$_{X}$
relation that has substantial scatter (0.6 dex). We find the degree to which an
AGN is underluminous in [OIII] correlates with the specific SFR or D$_{4000}$
index of the host, which are both linked to the molecular gas fraction. Thus
the emerging physical picture for the large scatter seems to involve the gas
content of the narrow-line region. We find no significant role for previously
proposed scenarios for the presence of optically dull AGNs, such as host
dilution or dust obscuration. Despite occasionally weak lines in SDSS spectra,
>80% of X-ray AGNs are identified as such with the BPT diagram. >90% are
classified as AGNs based only on [NII]/H$\alpha$, providing more complete AGN
samples when [OIII] or H$\beta$ are weak. X-ray AGNs with LINER spectra obey
essentially the same \lxo\ relation as Seyfert 2s, suggesting their line
emission is produced by AGN activity.


  We present a general review of the bifurcation sequences of periodic orbits
in general position of a family of resonant Hamiltonian normal forms with
nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$
symmetry. The rich structure of these classical systems is investigated with
geometric methods and the relation with the singularity theory approach is also
highlighted. The geometric approach is the most straightforward way to obtain a
general picture of the phase-space dynamics of the family as is defined by a
complete subset in the space of control parameters complying with the symmetry
constraint. It is shown how to find an energy-momentum map describing the phase
space structure of each member of the family, a catastrophe map that captures
its global features and formal expressions for action-angle variables. Several
examples, mainly taken from astrodynamics, are used as applications.


  Active muscles are crucial for maintaining postural stability when seated in
a moving vehicle. Advanced active 3D non-linear full body models have been
developed for impact and comfort simulation, including large numbers of
individual muscle elements, and detailed non-linear models of the joint
structures. While such models have an apparent potential to provide insight
into postural stabilization, they are computationally demanding, making them
less practical in particular for driving comfort where long time periods are to
be studied. In vibrational comfort and in general biomechanical research,
linearized models are effectively used. This paper evaluates the effectiveness
of simplified 3D full-body human models to capture comfort provoked by
whole-body vibrations. An efficient seated human body model is developed and
validated using experimental data. We evaluate the required complexity in terms
of joints and degrees of freedom for the spine, and explore how well linear
spring-damper models can approximate reflexive postural stabilization. Results
indicate that linear stiffness and damping models can well capture the human
response. The results are improved by adding proportional integral derivative
(PID) and head-in-space (HIS) controllers to maintain the defined initial body
posture. The integrator is shown to be essential to prevent drift from the
defined posture. The joint angular relative displacement is used as the input
reference to each PID controller. With this model, a faster than real-time
solution is obtained when used with a simple seat model. The paper also
discusses the advantages and disadvantages of various models and provides
insight into which models are more appropriate for motion comfort analysis.


  In this letter we present, for the first time, the results for the
photoproduction of massive gauge bosons in proton -- proton, proton -- Lead and
Lead -- Lead collisions at the Large Hadron Collider (LHC), High -- Energy LHC
(HE -- LHC) and Future Circular Collider (FCC). Predictions for the rapidity
distributions and total cross sections are presented. We predict a large number
of events in the rapidity range probed by the LHC detectors, which implies that
this process can be used to probe the photoproduction of massive gauge bosons
as well to perform the search of Beyond Standard Model physics.


  In plane orientation of magnetic easy axis of sputtered strontium hexaferrite
thin films has been explained using classical Heisenberg Hamiltonian. The
variation of average value of in plane spin component with temperature was
plotted in order to determine the temperature at which easy axis is oriented in
the plane of the strontium ferrite film. The average value of in plane spin
component in this 2-D model reaches zero at one particular temperature. This
particular temperature obtained using our theoretical model agrees with the
experimental value of the temperature of rf sputtered polycrystalline strontium
ferrite thin films deposited on polycrystalline Al2O3 substrates (500 0C). This
spin reorientation temperature solely depends on the values of energy
parameters used in our modified Heisenberg Hamiltonian equation.


  A neural language model can be conditioned into generating descriptions for
images by providing visual information apart from the sentence prefix. This
visual information can be included into the language model through different
points of entry resulting in different neural architectures. We identify four
main architectures which we call init-inject, pre-inject, par-inject, and
merge.
  We analyse these four architectures and conclude that the best performing one
is init-inject, which is when the visual information is injected into the
initial state of the recurrent neural network. We confirm this using both
automatic evaluation measures and human annotation.
  We then analyse how much influence the images have on each architecture. This
is done by measuring how different the output probabilities of a model are when
a partial sentence is combined with a completely different image from the one
it is meant to be combined with. We find that init-inject tends to quickly
become less influenced by the image as more words are generated. A different
architecture called merge, which is when the visual information is merged with
the recurrent neural network's hidden state vector prior to output, loses
visual influence much more slowly, suggesting that it would work better for
generating longer sentences.
  We also observe that the merge architecture can have its recurrent neural
network pre-trained in a text-only language model (transfer learning) rather
than be initialised randomly as usual. This results in even better performance
than the other architectures, provided that the source language model is not
too good at language modelling or it will overspecialise and be less effective
at image description generation.
  Our work opens up new avenues of research in neural architectures,
explainable AI, and transfer learning.


  We report density functional theory calculations for Mo$_3$S$_7$(dmit)$_3$.
We derive an ab initio tight-binding model from overlaps of Wannier orbitals;
finding a layered model with interlayer hopping terms $\sim3/4$ the size of the
in-plane terms. The in-plane Hamiltonian interpolates the kagom\'e and
honeycomb lattices. It supports states localized to dodecahedral rings within
the plane, which populate one-dimensional (1D) bands and lead to a quasi-1D
spin-one model on a layered honeycomb lattice once interactions are included.
Two lines of Dirac cones also cross the Fermi energy.


  CG crowds have become increasingly popular this last decade in the VFX and
animation industry: formerly reserved to only a few high end studios and
blockbusters, they are now widely used in TV shows or commercials. Yet, there
is still one major limitation: in order to be ingested properly in crowd
software, studio rigs have to comply with specific prerequisites, especially in
terms of deformations. Usually only skinning, blend shapes and geometry caches
are supported preventing close-up shots with facial performances on crowd
characters. We envisioned two approaches to tackle this: either reverse
engineer the hundreds of deformer nodes available in the major DCCs/plugins and
incorporate them in our crowd package, or surf the machine learning wave to
compress the deformations of a rig using a neural network architecture.
Considering we could not commit 5+ man/years of development into this problem,
and that we were excited to dip our toes in the machine learning pool, we went
for the latter.
  From our first tests to a minimum viable product, we went through hopes and
disappointments: we hit multiple pitfalls, took false shortcuts and dead ends
before reaching our destination. With this paper, we hope to provide a valuable
feedback by sharing the lessons we learnt from this experience.


  For a reductive group G and a finite order Cartan-type automorphism \iota of
G, we construct an eigenvariety parameterizing \iota-invariant cuspidal Hecke
eigensystems of G. In particular, for G = Gln, we prove, any self-dual cuspidal
Hecke eigensystem can be deformed in a p-adic family of self-dual cuspidal
Hecke eigensystems containing a Zariski dense subset of classical points.


  In this paper we give sufficient conditions on a measurable function
$p:(0,\infty)^n\rightarrow [1,\infty)$ in order that harmonic analysis
operators (maximal operators, Riesz transforms, Littlewood--Paley functions and
multipliers) associated with $\alpha$-Laguerre polynomial expansions are
bounded on the variable Lebesgue space $L^{p(\cdot)} ((0,\infty)^n,
\mu_\alpha)$, where $d\mu_\alpha (x)=2^n\prod_{j=1}^n \frac{x_j^{2\alpha_j+1}
e^{-x_j^2}}{\Gamma(\alpha_j+1)} dx$, being $\alpha=(\alpha_1, \dots,
\alpha_n)\in [0,\infty)^n$ and $x=(x_1,\dots,x_n)\in (0,\infty)^n$.


  We study the late time dynamics of a single active Brownian particle in two
dimensions with speed $v_0$ and rotation diffusion constant $D_R$. We show that
at late times $t\gg D_R^{-1}$, while the position probability distribution
$P(x,y,t)$ in the $x$-$y$ plane approaches a Gaussian form near its peak
describing the typical diffusive fluctuations, it has non-Gaussian tails
describing atypical rare fluctuations when $\sqrt{x^2+y^2}\sim v_0 t$. In this
regime, the distribution admits a large deviation form, $P(x,y,t) \sim
\exp\left[-t\, D_R\, \Phi\left(\sqrt{x^2+y^2}/(v_0 t)\right)\right]$, where we
compute the rate function $\Phi(z)$ analytically and also numerically using an
importance sampling method. We show that the rate function $\Phi(z)$, encoding
the rare fluctuations, still carries the trace of activity even at late times.
Another way of detecting activity at late times is to subject the active
particle to an external harmonic potential. In this case we show that the
stationary distribution $P_\text{stat}(x,y)$ depends explicitly on the activity
parameter $D_R^{-1}$ and undergoes a crossover, as $D_R$ increases, from a ring
shape in the strongly active limit ($D_R\to 0$) to a Gaussian shape in the
strongly passive limit $(D_R\to \infty)$.


  Free floating Test Masses (TM) of inertial reference instruments accumulate
charge mainly through the triboelectric effect during separation from their
housings and, if in the space environment, from cosmic radiation. These charges
will degrade the accuracy of high sensitivity accelerometers and drag-free
sensors. We demonstrate in ground testing two passive bipolar charge management
systems using photoelectrons emitted from Au coated surfaces under illumination
by UV-LEDs of 255 nm, 275 nm, and 295 nm central wavelength. The first method
uses fast photoelectrons, generated by two 255 nm UV-LEDs with
adjustable-intensity (through fine-tuning of their excitation currents) and
illuminating the TM and its housing respectively. A second technique uses slow
photoelectrons generated by one UV LED, of either 275 nm or 295 nm, located on
the TM housing. Fast and slow electrons are defined as having kinetic energies
after photoemission above and below the maximum allowable potential above
ground, VTMmax, required for normal operation of the TM. In their optimized
configurations and following a 10 to 30 sec exposure to UV with initial TM
potentials of between -3 V and 3 V, both control systems converge to a TM
potential of about 10 mV with a drift of about 2 mV/day. For reference, VTMmax
is about 100mV for the LISA and LISA pathfinder sensors. Insight into the slow
photoelectrons charge control method is provided by our simple gaussian model
of the distribution of the photoemission sites of Au films: 4.6 eV center, 0.2
eV standard deviation, and 4.30 eV and 4.90 eV cutoffs. The lowest energy
photoemission is obtained with the 295 nm LED at about 4.35 eV or 285 nm;
equivalent to 2.5 times the standard deviation from its center wavelength and
at 4% of its maximum intensity.


  Co-addition of deep (rms about 30 microJy) 20 cm data obtained with the
Australia Telescope Compact Array at the location of Spitzer Wide field survey
(SWIRE) sources has yielded statistics of radio source counterparts to faint 24
micron sources in stacked images with rms < 1 microJy. We confirm that the
infrared-radio correlation extends to f(24micron) = 100 microJy but with a
significantly lower coefficient, f (20cm) = 0.039 f(24micron) (or q24 = 1.39)
than hitherto reported. We postulate that this may be due to a change in the
mean q24 value ratio for objects with f(24micron) < 1mJy.


  The multi-agent perception system collects visual data from sensors located
on various agents and leverages their relative poses determined by GPS signals
to effectively fuse information, mitigating the limitations of single-agent
sensing, such as occlusion. However, the precision of GPS signals can be
influenced by a range of factors, including wireless transmission and
obstructions like buildings. Given the pivotal role of GPS signals in
perception fusion and the potential for various interference, it becomes
imperative to investigate whether specific GPS signals can easily mislead the
multi-agent perception system. To address this concern, we frame the task as an
adversarial attack challenge and introduce \textsc{AdvGPS}, a method capable of
generating adversarial GPS signals which are also stealthy for individual
agents within the system, significantly reducing object detection accuracy. To
enhance the success rates of these attacks in a black-box scenario, we
introduce three types of statistically sensitive natural discrepancies:
appearance-based discrepancy, distribution-based discrepancy, and task-aware
discrepancy. Our extensive experiments on the OPV2V dataset demonstrate that
these attacks substantially undermine the performance of state-of-the-art
methods, showcasing remarkable transferability across different point cloud
based 3D detection systems. This alarming revelation underscores the pressing
need to address security implications within multi-agent perception systems,
thereby underscoring a critical area of research.


  The separating and reattaching turbulent flow past a rectangular cylinder is
studied to describe how small and large scales contribute to the sustaining
mechanism of the velocity fluctuations. The work is based on the Anisotropic
Generalised Kolmogorov Equations (AGKE), exact budget equations for the
second-order structure function tensor in the space of scales and in the
physical space. Scale-space energy fluxes show that forward and reverse energy
transfers simultaneously occur in the flow, with interesting modelling
implications.
  Over the longitudinal cylinder side, the Kelvin-Helmholtz instability of the
leading-edge shear layer generates large spanwise rolls, which get stretched
into hairpin-like vortices and eventually break down into smaller streamwise
vortices. Independent sources of velocity fluctuations act at different scales.
The flow dynamics is dominated by pressure-strain: the flow impingement on the
cylinder surface in the reattachment zone produces spanwise velocity
fluctuations very close to the wall and, at larger wall distances, reorients
them to feed streamwise-aligned vortices.
  In the near wake, large von K\`arm\`an-like vortices are shed from the
trailing edge and coexist with smaller turbulent structures, each with its own
independent production mechanism. At the trailing edge, the sudden
disappearance of the wall changes the structure of turbulence: streamwise
vortices progressively vanish, while spanwise structures close to the wall are
suddenly turned into vertical fluctuations by the pressure strain.


  Two flows are topologically almost commensurable if, up to removing finitely
many periodic orbits and taking finite coverings, they are topologically
equivalent. We prove that all suspensions of automorphisms of the 2-dimensional
torus and all geodesic flows on unit tangent bundles to hyperbolic 2-orbifolds
are pairwise almost commensurable.


  We study the behaviour of the 2-rank of the adjacency matrix of a graph under
Seidel and Godsil-McKay switching, and apply the result to graphs coming from
graphical Hadamard matrices of order $4^m$. Starting with graphs from known
Hadamard matrices of order $64$, we find (by computer) many Godsil-McKay
switching sets that increase the 2-rank. Thus we find strongly regular graphs
with parameters $(63,32,16,16)$, $(64,36,20,20)$, and $(64,28,12,12)$ for
almost all feasible 2-ranks. In addition we work out the behaviour of the
2-rank for a graph product related to the Kronecker product for Hadamard
matrices, which enables us to find many graphical Hadamard matrices of order
$4^m$ for which the related strongly regular graphs have an unbounded number of
different 2-ranks. The paper extends results from the article 'Switched
symplectic graphs and their 2-ranks' by the first and the last author.


  A new light-front formulation of Q.E.D. is developed, within the framework of
standard perturbation theory, in which $x^+$ plays the role of the evolution
parameter and the gauge choice is $A_+=0$ (light-front "temporal" gauge). It is
shown that this formulation leads to the Mandelstam-Leibbrandt causal
prescription for the non-covariant singularities in the photon propagator.
Furthermore, it is proved that the dimensionally regularized one loop off-shell
amplitudes exactly coincide with the correct ones, as computed within the
standard approach using ordinary space-time coordinates.


  We present the results of hydrodynamical simulations of nonaxisymmetric gas
flow past a gravitating compact object in two dimensions. Calculations were
performed with uniform flow as well as with transverse velocity and density
gradients. We find that the flow is highly nonsteady, exhibiting the
``flip-flop'' behavior seen in previous studies in which accretion disks form
with alternating directions of rotation. We investigate the periodicity of the
flip-flop behavior, and study the effects of spatial resolution on the results.
We find that the flip-flop motion creates accretion torques which, in some
cases, may be large enough to explain the erratic spin behavior observed in
some massive X-ray pulsars.


  We propose that the fermionic superpartner of a weak-scale Goldstone boson
can be a natural WIMP candidate. The p-wave annihilation of this `Goldstone
fermion' into pairs of Goldstone bosons automatically generates the correct
relic abundance, whereas the XENON100 direct detection bounds are evaded due to
suppressed couplings to the Standard Model. Further, it is able to avoid
indirect detection constraints because the relevant s-wave annihilations are
small. The interactions of the Goldstone supermultiplet can induce non-standard
Higgs decays and novel collider phenomenology.


  The semileptonic decay of the neutral K meson, KL -> pi e nu (Ke3), was used
to study the strangeness-changing weak interaction of hadrons. A sample of 5.6
million reconstructed events recorded by the NA48 experiment was used to
measure the Dalitz plot density. Admitting all possible Lorentz-covariant
couplings, the form factors for vector (f_+(q^2)), scalar (f_S) and tensor
(f_T) interactions were measured. The linear slope of the vector form factor
lambda_+ = 0.0284+-0.0007+-0.0013 and values for the ratios |f_S/f_+(0)| =
0.015^{+0.007}_{-0.010}+-0.012 and |f_T/f_+(0)| = 0.05^{+0.03}_{-0.04}+-0.03
were obtained. The values for f_S and f_T are consistent with zero. Assuming
only Vector-Axial vector couplings, lambda_+ = 0.0288+-0.0004+-0.0011 and a
good fit consistent with pure V-A couplings were obtained. Alternatively, a fit
to a dipole form factor yields a pole mass of M = 859+-18 MeV, consistent with
the K^*(892) mass.


  We show that a twistor construction of Hitchin and Ward can be adapted to
study unitons (harmonic spheres in a unitary group). Specifically, we show that
unitons are equivalent to holomorphic bundles with extra structure over a
rational ruled surface with energy given by Chern class. This equivalence
allows us to confirm the conjecture of Wood that unitons are rational. We also
construct an example of a two uniton in U(3) using this construction.


  Phonon-induced orbital and spin relaxation rates of single electron states in
lateral single and double quantum dots are obtained numerically for realistic
materials parameters. The rates are calculated as a function of magnetic field
and interdot coupling, at various field and quantum dot orientations. It is
found that orbital relaxation is due to deformation potential phonons at low
magnetic fields, while piezoelectric phonons dominate the relaxation at high
fields. Spin relaxation, which is dominated by piezoelectric phonons, in single
quantum dots is highly anisotropic due to the interplay of the Bychkov-Rashba
and Dresselhaus spin-orbit couplings. Orbital relaxation in double dots varies
strongly with the interdot coupling due to the cyclotron effects on the
tunneling energy. Spin relaxation in double dots has an additional anisotropy
due to anisotropic spin hot spots which otherwise cause giant enhancement of
the rate at useful magnetic fields and interdot couplings. Conditions for the
absence of the spin hot spots in in-plane magnetic fields (easy passages) and
perpendicular magnetic fields (weak passages) are formulated analytically for
different growth directions of the underlying heterostructure. It is shown that
easy passages disappear (spin hot spots reappear) if the double dot system
loses symmetry by an xy-like perturbation.


  An entire solution of the Allen-Cahn equation $\Delta u=f(u)$, where $f$ has
exactly three zeros at $\pm 1$ and 0, is balanced and odd, e.g.
$f(u)=u(u^2-1)$, is called a $2k$-ended solution if its nodal set is asymptotic
to $2k$ half lines, and if along each of these half lines the function $u$
looks like the one dimensional, heteroclinic solution. In this paper we
consider the family of four ended solutions whose ends are almost parallel at
$\infty$. We show that this family can be parametrized by the family of
solutions of the two component Toda system. As a result we obtain the
uniqueness of four ended solutions with almost parallel ends. Combining this
result with the classification of connected components in the moduli space of
the four ended solutions we can classify all such solutions. Thus we show that
four end solutions form, up to rigid motions, a one parameter family. This
family contains the saddle solution, for which the angle between the nodal
lines is $\frac{\pi}{2}$ as well as solutions for which the angle between the
asymptotic half lines of the nodal set is arbitrary small (almost parallel
nodal sets).


  The energy gradient theory is used to study the instability of Taylor-Couette
flow between concentric rotating cylinders. This theory has been proposed in
our previous works. In our previous studies, the energy gradient theory was
demonstrated to be applicable for wall-bounded parallel flows. It was found
that the critical value of the energy gradient parameter Kmax at turbulent
transition is about 370-389 for wall-bounded parallel flows (which include
plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow) below which
no turbulence occurs. In this paper, the detailed derivation for the
calculation of the energy gradient parameter in the flow between concentric
rotating cylinders is provided. The calculated results for the critical
condition of primary instability (with semi-empirical treatment) are found to
be in very good agreement with the experiments in the literature. A possible
mechanism of spiral turbulence generation observed for counter-rotation of two
cylinders can also be explained using the energy gradient theory. The energy
gradient theory can serve to relate the condition of transition in
Taylor-Couette flow to that in plane Couette flow. The latter reasonably
becomes the limiting case of the former when the radii of cylinders tend to
infinity. It is our contention that the energy gradient theory is possibly
fairly universal for analysis of flow instability and turbulent transition, and
is found valid for both pressure and shear driven flows in parallel and
rotating flow configurations.


  The transversal number $\tau(H)$ of a hypergraph $H$ is the minimum number of
vertices that intersect every edge of $H$. A linear hypergraph is one in which
every two distinct edges intersect in at most one vertex. A $k$-uniform
hypergraph has all edges of size $k$. It is known that $\tau(H) \le (n +
m)/(k+1)$ holds for all $k$-uniform, linear hypergraphs $H$ when $k \in
\{2,3\}$ or when $k \ge 4$ and the maximum degree of $H$ is at most two. It has
been conjectured that $\tau(H) \le (n+m)/(k+1)$ holds for all $k$-uniform,
linear hypergraphs $H$. We disprove the conjecture for large $k$, and show that
the best possible constant $c_k$ in the bound $\tau(H) \le c_k (n+m)$ has order
$\ln(k)/k$ for both linear (which we show in this paper) and non-linear
hypergraphs. We show that for those $k$ where the conjecture holds, it is tight
for a large number of densities if there exists an affine plane $AG(2,k)$ of
order $k \ge 2$. We raise the problem to find the smallest value, $k_{\min}$,
of $k$ for which the conjecture fails. We prove a general result, which when
applied to a projective plane of order $331$ shows that $k_{\min} \le 166$.
Even though the conjecture fails for large $k$, our main result is that it
still holds for $k=4$, implying that $k_{\min} \ge 5$. The case $k=4$ is much
more difficult than the cases $k \in \{2,3\}$, as the conjecture does not hold
for general (non-linear) hypergraphs when $k=4$. Key to our proof is the
completely new technique of the deficiency of a hypergraph introduced in this
paper.


  The question of whether Hawking evaporation violates unitarity, and therefore
results in the loss of information, remains unresolved since Hawking's seminal
discovery. So far the investigations remain mostly theoretical since it is
almost impossible to settle this paradox through direct astrophysical black
hole observations. Here we point out that relativistic plasma mirrors can be
accelerated drastically and stopped abruptly by impinging ultra intense x-ray
pulses on solid plasma targets with a density gradient. This is analogous to
the late time evolution of black hole Hawking evaporation. A conception of such
an experiment is proposed and a self-consistent set of physical parameters is
presented. Critical issues such as black hole unitarity may be addressed
through the measurement of the entanglement between the Hawking radiation and
their partner modes.


  We have detected the optical counterpart of the proposed double degenerate
polar RX J1914+24. The I band light curve is modulated on the 9.5 min period
seen in X-rays. There is no evidence for any other periods. No significant
modulation is seen in J. The infrared colours of RX J1914+24 are not consistent
with a main sequence dwarf secondary star. Our ASCA spectrum of RX J1914+24 is
typical of a heavily absorbed polar and our ASCA light curve also shows only
the 9.5 min period. We find that the folded I band and X-ray light curves are
out of phase. We attribute the I band flux to the irradiated face of the donor
star. The long term X-ray light curve shows a variation in the observed flux of
up to an order of magnitude. These observations strengthen the view that RX
J1914+24 is indeed the first double degenerate polar to be detected. In this
light, we discuss the synchronising mechanisms in such a close binary and other
system parameters.


  Aircraft failures alter dynamics, diminishing manoeuvrability. Such
manoeuvring flight envelope variations, governed by the aircraft's complex
nonlinear dynamics, are unpredictable by pilots and existing flight management
systems. To prevent in-flight Loss of Control, post-failure trajectories must
be optimal, planned in real-time, avoid terrain, and adhere to the impaired
aircraft's reduced manoeuvrability and dynamic constraints. This paper presents
a novel real-time trajectory optimization method for impaired aircraft based on
a combination of differential flatness theory, the pseudospectral method,
nonlinear programming, and inverse dynamics. In the proposed method, which
utilizes a high-fidelity nonlinear six degree-of-freedom model, to conform to
aircraft's altered dynamics a sequence of trim points is selected from the
impaired aircraft's manoeuvring flight envelope based on the chosen
optimization criteria, ensuring that the resulting three-dimensional trajectory
observes terrain avoidance. Then, the required control inputs are obtained for
each manoeuvre in less than a second. The method is applied to the NASA Generic
Transport Model with rudder failure near a complex mountainous terrain. Both an
optimal one-piece trajectory and a near-optimal piecewise path consisting of
several optimal trajectories, are generated in non-real-time and real-time,
respectively, and compared. Results show that the near-optimal real-time
trajectory retains up to 80% of the optimality.


  A robust prediction of $\Lambda{\rm CDM}$ cosmology is the halo circular
velocity function (CVF), a dynamical cousin of the halo mass function. The
correspondence between theoretical and observed CVFs is uncertain, however:
cluster galaxies are reported to exhibit a power-law CVF consistent with
$N$-body simulations, but that of the field is distinctly Schechter-like,
flattened relative to $\Lambda{\rm CDM}$ expectations at circular velocities
$v_c \lesssim 200\, {\rm km\, s^{-1}}$. Groups offer a powerful probe of the
role environment plays in this discrepancy as they bridge the field and
clusters. Here, we construct the CVF for a large, mass- and
multiplicity-complete sample of group galaxies from the Sloan Digital Sky
Survey. Using independent photometric $v_c$ estimators, we find no transition
from a field- to $\Lambda{\rm CDM}$-shaped CVF above $v_c = 50\, {\rm km\,
s^{-1}}$ as a function of group halo mass. All groups with $12.4 \lesssim \log
M_{\rm halo} / M_{\odot} \lesssim 15.1$ (Local Group analogs to rich clusters)
display similar Schechter-like CVFs marginally suppressed at low-$v_c$ compared
to that of the field. Conversely, some agreement with $N$-body results emerges
for samples saturated with late-type galaxies, with isolated late-types
displaying a CVF similar in shape to $\Lambda{\rm CDM}$ predictions. We
conclude that the flattening of the low-$v_c$ slope in groups is due to their
depressed late-type fractions -- environment affecting the CVF only to the
extent that it correlates with this quantity -- and that previous cluster
analyses may suffer from interloper contamination. These results serve as
useful benchmarks for cosmological simulations of galaxy formation.


  Motivated by a recent paper by Barrett and S\"uli [J.W. Barrett & E. S\"uli:
Existence of global weak solutions to compressible isentropic finitely
extensible bead-spring chain models for dilute polymers, Math. Models Methods
Appl. Sci., 26 (2016)], we consider the compressible Navier--Stokes system
coupled with a Fokker--Planck type equation describing the motion of polymer
molecules in a viscous compressible fluid occupying a bounded spatial domain,
with polymer-number-density-dependent viscosity coefficients. The model arises
in the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids,
where the polymer molecules are idealized as bead-spring chains with finitely
extensible nonlinear elastic (FENE) type spring potentials. The motion of the
solvent is governed by the unsteady, compressible, barotropic Navier--Stokes
system, where the viscosity coefficients in the Newtonian stress tensor depend
on the polymer number density. Our goal is to show that the existence theory
developed in the case of constant viscosity coefficients can be extended to the
case of polymer-number-density-dependent viscosities, provided that certain
technical restrictions are imposed, relating the behavior of the viscosity
coefficients and the pressure for large values of the solvent density. As a
first step in this direction, we prove here the weak sequential stability of
the family of dissipative (finite-energy) weak solutions to the system.


  For a relativistic charged particle moving in a constant electromagnetic
field, its velocity 4-vector has been well studied. However, despite the fact
that both the electromagnetic field and the equations of motion are purely
real, the resulting 4-velocity is seemingly due to a complex electromagnetic
field. This work shows that this is not due to some complex formalism used
(such as Clifford algebra) but is intrinsically due to the fact that the
$o(3,1)$ Lie algebra of the Lorentz group is equivalent to two commuting
complex $su(2)$ algebras. Expressing the complex $su(2)$ generators in terms of
the boost and rotation operators then naturally introduces a complex
electromagnetic field. This work solves the equation of motion not as a matrix
equation, but as an operator evolution equation in terms of the generators of
the Lorentz group. The factorization of the real evolution operator into two
commuting complex evolution operators then directly gives the time evolution of
the velocity 4-vector without any reference to an intermediate field.


  We give a bound on which singularities may appear on
Koll\'ar--Shepherd-Barron--Alexeev stable surfaces for a wide range of
topological invariants and use this result to describe all stable numerical
quintic surfaces (KSBA-stable surfaces with $K^2=\chi=5$) whose unique non Du
Val singularity is a Wahl singularity. We then extend the deformation theory of
Horikawa to the log setting in order to describe the boundary divisor of the
moduli space $\overline{\mathcal{M}}_{5,5}$ corresponding to these surfaces.
Quintic surfaces are the simplest examples of surfaces of general type and the
question of describing their moduli is a long-standing question in algebraic
geometry.


  Pre-trained multilingual language models (LMs) have achieved state-of-the-art
results in cross-lingual transfer, but they often lead to an inequitable
representation of languages due to limited capacity, skewed pre-training data,
and sub-optimal vocabularies. This has prompted the creation of an ever-growing
pre-trained model universe, where each model is trained on large amounts of
language or domain specific data with a carefully curated, linguistically
informed vocabulary. However, doing so brings us back full circle and prevents
one from leveraging the benefits of multilinguality. To address the gaps at
both ends of the spectrum, we propose MergeDistill, a framework to merge
pre-trained LMs in a way that can best leverage their assets with minimal
dependencies, using task-agnostic knowledge distillation. We demonstrate the
applicability of our framework in a practical setting by leveraging
pre-existing teacher LMs and training student LMs that perform competitively
with or even outperform teacher LMs trained on several orders of magnitude more
data and with a fixed model capacity. We also highlight the importance of
teacher selection and its impact on student model performance.


  We present some analytical results for the stochastic sandpile model, studied
earlier by Manna. In this model, the operators corresponding to particle
addition at different sites commute. The eigenvalues of operators satisfy a
system of coupled polynomial equations. For an L X L square, we construct a
nontrivial toppling invariant, and hence a ladder operator which acting on
eigenvectors of evolution operator gives new eigenvectors with different
eigenvalues. For periodic boundary conditions in one direction, one more
toppling invariant can be constructed. We show that there are many forbidden
subconfigurations, and only an exponentially small fraction of all stable
configurations are recurrent. We obtain rigorous lower and upper bounds for the
minimum number of particles in a recurrent configuration, and conjecture a
formula for its exact value for finite-size rectangles.


  We study the low T/W instability associated with the f-mode of differentially
rotating stars. Our stellar models are described by a polytropic equation of
state and the rotation profile is given by the standard j-constant law. The
properties of the relevant oscillation modes, including the instability growth
time, are determined from time evolutions of the linearised dynamical equations
in Newtonian gravity. In order to analyse the instability we monitor also the
canonical energy and angular momentum. Our results demonstrate that the l=m=2
f-mode becomes unstable as soon as a co-rotation point develops inside the star
(i.e. whenever there is a point where the mode's pattern speed matches the bulk
angular velocity). Considering various degrees of differential rotation, we
show that the instability grows faster deep inside the co-rotation region and
deduce an empirical relation that correlates the mode frequency and the star's
parameters, which captures the main features of the l=m=2 f-mode growth time.
This function is proportional to the product of the kinetic to gravitational
energy ratio and the gradient of the star's spin, strengthening further the
relationship between the co-rotation point and the low T/W instability. We
briefly consider also the l=m=2 r-mode and demonstrate that it never moves far
inside the co-rotation region even for significant differential rotation.


  Solving constrained optimization problems by multi-objective evolutionary
algorithms has scored tremendous achievements in the last decade. Standard
multi-objective schemes usually aim at minimizing the objective function and
also the degree of constraint violation simultaneously. This paper proposes a
new multi-objective method for solving constrained optimization problems. The
new method keeps two standard objectives: the original objective function and
the sum of degrees of constraint violation. But besides them, four more
objectives are added. One is based on the feasible rule. The other three come
from the penalty functions. This paper conducts an initial experimental study
on thirteen benchmark functions. A simplified version of CMODE is applied to
solving multi-objective optimization problems. Our initial experimental results
confirm our expectation that adding more helper functions could be useful. The
performance of SMODE with more helper functions (four or six) is better than
that with only two helper functions.


  The oxygen deficiency $\delta$ in YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) plays a
crucial role for affecting high-temperature superconductivity. We applied
(coincident) Doppler broadening spectroscopy of the electron-positron
annihilation line to study in situ the temperature dependence of the oxygen
concentration and its depth profile in single crystalline YBCO film grown on
SrTiO$_3$ (STO) substrates. The oxygen diffusion during tempering was found to
lead to a distinct depth dependence of $\delta$, which is not accessible using
X-ray diffraction. A steady-state reached within a few minutes is defined by
both, the oxygen exchange at the surface and at the interface to the STO
substrate. Moreover, we revealed the depth dependent critical temperature
$T_{\mathrm{c}}$ in the as prepared and tempered YBCO film.


  In active learning, acquisition functions define informativeness directly on
the representation position within the model manifold. However, for most
machine learning models (in particular neural networks) this representation is
not fixed due to the training pool fluctuations in between active learning
rounds. Therefore, several popular strategies are sensitive to experiment
parameters (e.g. architecture) and do not consider model robustness to
out-of-distribution settings. To alleviate this issue, we propose a grounded
second-order definition of information content and sample importance within the
context of active learning. Specifically, we define importance by how often a
neural network "forgets" a sample during training - artifacts of second order
representation shifts. We show that our definition produces highly accurate
importance scores even when the model representations are constrained by the
lack of training data. Motivated by our analysis, we develop Gaussian Switch
Sampling (GauSS). We show that GauSS is setup agnostic and robust to anomalous
distributions with exhaustive experiments on three in-distribution benchmarks,
three out-of-distribution benchmarks, and three different architectures. We
report an improvement of up to 5% when compared against four popular query
strategies.


  In high-dimensional regression, we attempt to estimate a parameter vector
$\beta_0\in\mathbb{R}^p$ from $n\lesssim p$ observations $\{(y_i,x_i)\}_{i\leq
n}$ where $x_i\in\mathbb{R}^p$ is a vector of predictors and $y_i$ is a
response variable. A well-established approach uses convex regularizers to
promote specific structures (e.g. sparsity) of the estimate $\widehat{\beta}$,
while allowing for practical algorithms. Theoretical analysis implies that
convex penalization schemes have nearly optimal estimation properties in
certain settings. However, in general the gaps between statistically optimal
estimation (with unbounded computational resources) and convex methods are
poorly understood.
  We show that when the statistican has very simple structural information
about the distribution of the entries of $\beta_0$, a large gap frequently
exists between the best performance achieved by any convex regularizer
satisfying a mild technical condition and either (i) the optimal statistical
error or (ii) the statistical error achieved by optimal approximate message
passing algorithms. Remarkably, a gap occurs at high enough signal-to-noise
ratio if and only if the distribution of the coordinates of $\beta_0$ is not
log-concave. These conclusions follow from an analysis of standard Gaussian
designs. Our lower bounds are expected to be generally tight, and we prove
tightness under certain conditions.


  In this paper it is shown how to obtain the simplest equations for the
Mukhanov-Sasaki variables describing quantum linear scalar perturbations in the
case of scalar fields without potential term. This was done through the
implementation of canonical transformations at the classical level, and unitary
transformations at the quantum level, without ever using any classical
background equation, and it completes the simplification initiated in
investigations by Langlois \cite{langlois}, and Pinho and Pinto-Neto
\cite{emanuel2} for this case. These equations were then used to calculate the
spectrum index $n_s$ of quantum scalar perturbations of a non-singular
inflationary quantum background model, which starts at infinity past from flat
space-time with Planckian size spacelike hypersurfaces, and inflates due to a
quantum cosmological effect, until it makes an analytical graceful exit from
this inflationary epoch to a decelerated classical stiff matter expansion
phase. The result is $n_s=3$, incompatible with observations.


  Gravity duals for a class of UV complete minimally supersymmetric
non-conformal gauge theories require deformed conifolds with fluxes. However
these manifolds do not allow for the standard Kahler or conformally Kahler
metrics on them, instead the metrics are fully non-Kahler. We take a generic
such configuration of a non-Kahler deformed conifold with fluxes and ask what
constraints do supersymmetry impose in the Baryonic branch. We study the
supersymmetry conditions and show that for the correct choices of the vielbeins
and the complex structure all the equations may be consistently solved. The
constraints now lead not only to the known cases in the literature but also to
some new backgrounds. We also show how geometric features of these backgrounds,
including the overall warp factor and the resolution parameters, can be seen on
the field theory side from perturbative `probe-brane' type calculations by
Higgsing the theory and studying one-loop 4-point functions of vector and
chiral multiplets. Finally we discuss how UV completions of these gauge
theories may be seen from our set-up, both from type IIB as well as from the
T-dual type IIA brane constructions.


  Recently, minimax optimization received renewed focus due to modern
applications in machine learning, robust optimization, and reinforcement
learning. The scale of these applications naturally leads to the use of
first-order methods. However, the nonconvexities and nonconcavities present in
these problems, prevents the application of typical Gradient Descent-Ascent,
which is known to diverge even in bilinear problems. Recently, it was shown
that the Proximal Point Method (PPM) converges linearly for a family of
nonconvex-nonconcave problems. In this paper, we study the convergence of a
damped version of Extra-Gradient Method (EGM) which avoids potentially costly
proximal computations, only relying on gradient evaluation. We show that EGM
converges linearly for smooth minimax optimization problem satisfying the same
nonconvex-nonconcave condition needed by PPM.


  Recent research has revealed that deep neural networks often take dataset
biases as a shortcut to make decisions rather than understand tasks, leading to
failures in real-world applications. In this study, we focus on the spurious
correlation between word features and labels that models learn from the biased
data distribution of training data. In particular, we define the word highly
co-occurring with a specific label as biased word, and the example containing
biased word as biased example. Our analysis shows that biased examples are
easier for models to learn, while at the time of prediction, biased words make
a significantly higher contribution to the models' predictions, and models tend
to assign predicted labels over-relying on the spurious correlation between
words and labels. To mitigate models' over-reliance on the shortcut (i.e.
spurious correlation), we propose a training strategy Less-Learn-Shortcut
(LLS): our strategy quantifies the biased degree of the biased examples and
down-weights them accordingly. Experimental results on Question Matching,
Natural Language Inference and Sentiment Analysis tasks show that LLS is a
task-agnostic strategy and can improve the model performance on adversarial
data while maintaining good performance on in-domain data.


  This is first of series papers on new two-side Gaussian bounds for the heat
kernel $H(x,y,t)$ on a complete manifold $(M,g)$. In this paper, on a complete
manifold $M$ with $Ric(M)\geq 0$, we obtain new two-side Gaussian bounds for
the heat kernel $H(x,y,t)$, which improve the well-known Li-Yau's two-side
bounds. As applications of our new two-side Gaussian bounds, We obtain a sharp
gradient estimate and a Laplacian estimate for the heat kernel on a complete
manifold with $Ric(M)\geq 0$, and we also give a simpler proof for the result
concerning the asymptotic behavior in the time variable for the heat kernel as
was proved in \cite{LiP-1} on a complete manifold $M$ with $Ric(M)\geq 0$ and
maximal volume growth.


  A photon emitted near a compact object at an angle $\alpha$ with respect to
the radial direction escapes to infinity at a different angle $\psi>\alpha$.
This bending of light is caused by a strong gravitational field. We show that,
in a Schwarzschild metric, the effect is described by
$1-\cos\alpha=(1-\cos\psi)(1-r_g/R)$ where $R/r_g$ is the emission radius in
Schwarzschild units. The formula is approximate and it applies at $R\geq 2r_g$
only, however at these radii it has amazing accuracy, fully sufficient in many
applications. As one application we develop a new formulation for the light
bending effects in pulsars. It reveals the simple character of these effects
and gives their quantitative description with practically no losses of accuracy
(for the typical radius of a neutron star $R=3r_g$ the error is 1%). The
visible fraction of a star surface is shown to be $S_v/4\pi
R^2=[2(1-r_g/R)]^{-1}$ which is 3/4 for $R=3r_g$. The instantaneous flux of a
pulsar comes from one or two antipodal polar caps that rotate in the visible
zone. The pulse produced by one blackbody cap is found to be sinusoidal (light
bending impacts the pulse amplitude but not its shape). When both caps are
visible, the pulse shows a plateau: the variable parts of the antipodal
emissions precisely cancel each other. The pulsed fraction of blackbody
emission with antipodal symmetry has an upper limit
$A_{max}=(R-2r_g)/(R+2r_g)$. Pulsars with $A>A_{max}$ must be asymmetric.


  While the sources of X-ray and radio emission in the different states of
low-mass X-ray binaries are relatively well understood, the origin of the
near-infrared (NIR) and optical emission is more often debated. It is likely
that the NIR/optical flux originates from an amalgam of different emission
regions, because it occurs at the intersecting wavelengths of multiple
processes. We aim to identify the NIR/optical emission region(s) of one such
low-mass X-ray binary and black hole candidate, XTE J1650-500, via photometric,
timing, and spectral analyses. We present unique NIR/optical images and
spectra, obtained with the ESO-New Technology Telescope, during the peak of the
2001 outburst of XTE J1650-500. The data suggest that the NIR/optical flux is
due to a combination of emission mechanisms including a significant
contribution from X-ray reprocessing and, at early times in the hard state, a
relativistic jet that is NIR/radio dim compared to similar sources.The jet of
XTE J1650-500 is relatively weak compared to that of other black hole low-mass
X-ray binaries, possibly because we observe as it is being "turned off" or
quenched at the state transition. While there are several outliers to the
radio--X-ray correlation of the hard state of low-mass X-ray binaries, XTE
J1650-500 is the first example of an outlier to the NIR/optical--X-ray
correlation.


  For the evaluation of carcinogenicity bioassays a new trend test is proposed
which is based on a maximum of arithmetic, ordinal, and logarithmic regression
scores as well as the Williams-type contrasts for either crude proportions or
more appropriate poly3-estimates for the tumor-by-time relationships. This test
provides an almost appropriate power for most shapes of dose-response
relationships (including for possible downturn effect at high(er) dose(s)),
common signs of significance (p-value, confidence limits) and the information
on the probable shape. Related software is easily available within the
CRAN-packages tukeytrend, MCPAN, multcomp.


  Massive parallelisation has lead to a dramatic increase in available
computational power. However, data transfer speeds have failed to keep pace and
are the major limiting factor in the development of exascale computing. New
algorithms must be developed which minimise the transfer of data. Patch
dynamics is a computational macroscale modelling scheme which provides a coarse
macroscale solution of a problem defined on a fine microscale by dividing the
domain into many nonoverlapping, coupled patches. Patch dynamics is readily
adaptable to massive parallelisation as each processor can evaluate the
dynamics on one, or a few, patches. However, patch coupling conditions
interpolate across the unevaluated parts of the domain between patches, and are
typically reevaluated at every microscale time step, thus requiring almost
continuous data transfer. We propose a modified patch dynamics scheme which
minimises data transfer by only reevaluating the patch coupling conditions at
`mesoscale' time scales which are significantly larger than the microscale time
of the microscale problem. We analyse the error arising from patch dynamics
with mesoscale temporal coupling as a function of the mesoscale time interval,
patch size, and ratio between the microscale and macroscale.


  Generating novel molecules with optimal properties is a crucial step in many
industries such as drug discovery. Recently, deep generative models have shown
a promising way of performing de-novo molecular design. Although graph
generative models are currently available they either have a graph size
dependency in their number of parameters, limiting their use to only very small
graphs or are formulated as a sequence of discrete actions needed to construct
a graph, making the output graph non-differentiable w.r.t the model parameters,
therefore preventing them to be used in scenarios such as conditional graph
generation. In this work we propose a model for conditional graph generation
that is computationally efficient and enables direct optimisation of the graph.
We demonstrate favourable performance of our model on prototype-based molecular
graph conditional generation tasks.


  Due to importance of reducing of time solution in numerical codes, we propose
an algorithm for parallel LU decomposition solver for dense and sparse matrices
on GPU. This algorithm is based on first bi-vectorizing a triangular matrices
of decomposed coefficient matrix and then equalizing vectors. So we improve
performance of LU decomposition on equal contributed scheme on threads. This
algorithm also is convenient for other parallelism method and multi devices.
Several test cases show advantage of this method over other familiar method.


  A young and energetic pulsar powers the well-known Crab Nebula. Here we
describe two separate gamma-ray (photon energy >100 MeV) flares from this
source detected by the Large Area Telescope on board the Fermi Gamma-ray Space
Telescope. The first flare occurred in February 2009 and lasted approximately
16 days. The second flare was detected in September 2010 and lasted
approximately 4 days. During these outbursts the gamma-ray flux from the nebula
increased by factors of four and six, respectively. The brevity of the flares
implies that the gamma rays were emitted via synchrotron radiation from PeV
(10^15 eV) electrons in a region smaller than 1.4 10^-2 pc. These are the
highest energy particles that can be associated with a discrete astronomical
source, and they pose challenges to particle acceleration theory.


  An asymptotic theory is developed for general non-integrable boundary quantum
field theory in 1+1 dimensions based on the Langrangean description. Reflection
matrices are defined to connect asymptotic states and are shown to be related
to the Green functions via the boundary reduction formula derived. The
definition of the $R$-matrix for integrable theories due to Ghoshal and
Zamolodchikov and the one used in the perturbative approaches are shown to be
related.


  The goal of this paper is to review some of the main ideas that emerged from
the attempts to confirm mathematically the predictions of the celebrated Parisi
ansatz in the Sherrington-Kirkpatrick model. We try to focus on the big picture
while sketching the proofs of only a few selected results, but an interested
reader can find most of the missing details in [31] and [44].


  In this paper, we answer a fundamental question: when the total number of
antennas per square kilometer is fixed, what is the optimal network deployment?
A denser network with a less number of antennas per base station (BS) or the
opposite case. To evaluate network performance, we consider a practical network
scenario with a fixed antennas density and multiuser
multiple-input-multiple-output (MU-MIMO) operations for single-antenna users.
The number of antennas in each BS is calculated by dividing the antenna density
by the BS density. With the consideration of several practical network models,
i.e., pilot contamination, a limited user equipment (UE) density and
probabilistic line-of-sight (LoS)/non-line-of-sight (NLoS) path loss model, we
evaluate the area spectral efficiency (ASE) performance. From our simulation
results, we conclude that there exists an optimal BS density for a certain UE
density to maximize the ASE performance when the antenna density is fixed. The
intuition is that (i) by densifying the network with more BSs, we can achieve a
receive power gain due to the smaller distance between the typical UE and its
serving BS; (ii) by installing more antennas in each BS, we can achieve a
beamforming gain for UEs using MU-MIMO, although such beamforming gain is
degraded by pilot contamination; (iii) thus, a trade-off exists between the
receive power gain and the beamforming gain, if we fix the antenna density in
the network.


  We give a sufficient condition for exponential stability of a network of
lossless telegrapher's equations, coupled by linear time-varying boundary
conditions. The sufficient conditions is in terms of dissipativity of the
couplings, which is natural for instance in the context of microwave circuits.
Exponential stability is with respect to any $L^p$-norm, $1\leq p\leq\infty$.
This also yields a sufficient condition for exponential stability to a special
class of linear time-varying difference delay systems which is quite explicit
and tractable. One ingredient of the proof is that $L^p$ exponential stability
for such difference delay systems is independent of $p$, thereby reproving in a
simpler way some results from [Y. Chitour, G. Mazanti, and M. Sigalotti, $\it
{Netw. Heterog. Media}$, 11 (2016), pp. 563--601].


  When describing an image, reading text in the visual scene is crucial to
understand the key information. Recent work explores the TextCaps task, i.e.
image captioning with reading Optical Character Recognition (OCR) tokens, which
requires models to read text and cover them in generated captions. Existing
approaches fail to generate accurate descriptions because of their (1) poor
reading ability; (2) inability to choose the crucial words among all extracted
OCR tokens; (3) repetition of words in predicted captions. To this end, we
propose a Confidence-aware Non-repetitive Multimodal Transformers (CNMT) to
tackle the above challenges. Our CNMT consists of a reading, a reasoning and a
generation modules, in which Reading Module employs better OCR systems to
enhance text reading ability and a confidence embedding to select the most
noteworthy tokens. To address the issue of word redundancy in captions, our
Generation Module includes a repetition mask to avoid predicting repeated word
in captions. Our model outperforms state-of-the-art models on TextCaps dataset,
improving from 81.0 to 93.0 in CIDEr. Our source code is publicly available.


  A review is given on phase-sensitive measurements, such as homodyne
detection, for radiation fields and material systems. Methods of quantum-state
reconstruction are considered for radiation fields, including multimode and
pulsed radiation. For matter systems, methods are reported for the
reconstruction of quantum states of molecular vibrations, the quantized motion
of trapped atoms, Bose-Einstein condensates, atomic matter waves, electron
motion, spin and angular momentum systems, and crystal lattices.


  We derive a formulation of molecular dynamics that generates only symmetric
configurations. We implement it for all 2D planar and 3D space groups. An atlas
of 2D Lennard-Jones crystals under all planar groups is created with symmetric
molecular dynamics.


  We call a connected Lie group endowed with a left-invariant Lorentzian flat
metric Lorentzian flat Lie group. In this Note, we determine all Lorentzian
flat Lie groups admitting a timelike left-invariant Killing vector field. We
show that these Lie groups are 2-solvable and unimodular and hence geodesically
complete. Moreover, we show that a Lorentzian flat Lie group $(\mathrm{G},\mu)$
admits a timelike left-invariant Killing vector field if and only if
$\mathrm{G}$ admits a left-invariant Riemannian metric which has the same
Levi-Civita connection of $\mu$. Finally, we give an useful characterization of
left-invariant pseudo-Riemannian flat metrics on Lie groups $\mathrm{G}$
satisfying the property: for any couple of left invariant vector fields $X$ and
$Y$ their Lie bracket $[X,Y]$ is a linear combination of $X$ and $Y$.


  Mahowald proved the height 1 telescope conjecture at the prime 2 as an
application of his seminal work on bo-resolutions. In this paper we study the
height 2 telescope conjecture at the prime 2 through the lens of
tmf-resolutions. To this end we compute the structure of the tmf-resolution for
a specifc type 2 complex Z. We find that, analogous to the height 1 case, the
E1-page of the tmf-resolution possesses a decomposition into a v2-periodic
summand, and an Eilenberg-MacLane summand which consists of bounded v2-torsion.
However, unlike the height 1 case, the E2-page of the tmf-resolution exhibits
unbounded v2-torsion. We compare this to the work of Mahowald-Ravenel-Shick,
and discuss how the validity of the telescope conjecture is connected to the
fate of this unbounded v2-torsion: either the unbounded v2-torsion kills itself
off in the spectral sequence, and the telescope conjecture is true, or it
persists to form v2-parabolas and the telescope conjecture is false. We also
study how to use the tmf-resolution to effectively give low dimensional
computations of the homotopy groups of Z. These computations allow us to prove
a conjecture of the second author and Egger: the E(2)-local Adams-Novikov
spectral sequence for Z collapses.


  We explore a novel mechanism to restrict TeV-scale leptoquark interactions
and render the proton exactly stable to all orders in the effective field
theory expansion. A scalar condensate breaks a lepton-flavoured
$\mathrm{U}(1)_X$ gauge symmetry in the ultraviolet and generates neutrino
masses, leaving a discrete $\mathbb{Z}_9$ or $\mathbb{Z}_{18}$ gauge symmetry
in the infrared, forbidding $\Delta B = 1$ processes. This provides an elegant
framework to address the flavour anomalies and can be adapted to many other
new-physics models. The $ \mathrm{U}(1)_X $ can emerge from a gauge-flavour
unified $ \mathrm{SU}(12) \times \mathrm{SU}(2) \times \mathrm{SU}(2) $ theory
at even higher energies.


  For topological dynamical systems $(X,T,\sigma)$ with abelian group $T$ which
admit an equicontinuous factor $\pi:(X,T,\sigma)\to (Y,T,\delta)$ the Ellis
semigroup $E(X)$ is an extension of $Y$ by its subsemigroup $E^{fib}(X)$ of
elements which preserve the fibres of $\pi$. We establish methods to compute
$E^{fib}(X)$ and use them to determine the Ellis semigroup of dynamical systems
arising from primitive aperiodic bijective substitutions. As an application we
show that for these substitution shifts, the virtual automorphism group is
isomorphic to the classical automorphism group.


  We study a wiretap channel model where the sender has $M$ transmit antennas
and there are two groups consisting of $J_1$ and $J_2$ receivers respectively.
Each receiver has a single antenna. We consider two scenarios. First we
consider the compound wiretap model -- group 1 constitutes the set of
legitimate receivers, all interested in a common message, whereas group 2 is
the set of eavesdroppers. We establish new lower and upper bounds on the secure
degrees of freedom. Our lower bound is based on the recently proposed
\emph{real interference alignment} scheme. The upper bound provides the first
known example which illustrates that the \emph{pairwise upper bound} used in
earlier works is not tight.
  The second scenario we study is the compound private broadcast channel. Each
group is interested in a message that must be protected from the other group.
Upper and lower bounds on the degrees of freedom are developed by extending the
results on the compound wiretap channel.


  Local electromagnetic field enhancement in resonant metamaterials is useful
for efficient generation of nonlinear phenomena; however, the field enhancement
is suppressed by losses of nonlinear elements in metamaterials. For overcoming
this issue, we investigate the nonlinear response of an electromagnetically
induced transparency like metasurface loaded with gas as the nonlinear element.
To induce nonlinearity in the gas associated with discharges, an
electromagnetic wave with a modulated amplitude is incident on the metasurface.
The measured waveform and spectrum of the transmitted electromagnetic wave,
along with light emission from the discharge microplasma, reveal that frequency
mixing can occur on the metasurface. The parameter dependence of the conversion
efficiency of the frequency mixing phenomenon shows that the efficiency is
determined almost entirely by the ratio of the duration of microplasma
generation to the modulation period of the incident wave amplitude. This result
implies that the frequency mixing is derived from a binary change in the
transmittance of the metasurface caused by the generation and quenching of the
microplasma.


  Nearly orthogonal lattices were formally defined in [4], where their
applications to image compression were also discussed. The idea of ``near
orthogonality" in $2$-dimensions goes back to the work of Gauss. In this paper,
we focus on well-rounded nearly orthogonal lattices in~$\mathbb R^n$ and
investigate their geometric and optimization properties. Specifically, we prove
that the sphere packing density function on the space of well-rounded lattices
in dimension $n\geq 3$ does not have any local maxima on the nearly orthogonal
set and has only one local minimum there: at the integer lattice~$\mathbb Z^n$.
Further, we show that the nearly orthogonal set cannot contain any perfect
lattices for~$n \geq 3$, although it contains multiple eutactic (and even
strongly eutactic) lattices in every dimension. This implies that eutactic
lattices, while always critical points of the packing density function, are not
necessarily local maxima or minima even among the well-rounded lattices. We
also prove that a (weakly) nearly orthogonal lattice in~$\mathbb R^n$ contains
no more than~$4n-2$ minimal vectors (with any smaller even number possible) and
establish some bounds on coherence of these lattices.


  Two experiments of four-photon interference are performed with two pairs of
photons from parametric down-conversion with the help of asymmetric beam
splitters. The first experiment is a generalization of the Hong-Ou-Mandel
interference effect to two pairs of photons while the second one utilizes this
effect to demonstrate a four-photon de Broglie wavelength of $\lambda/4$ by
projection measurement.


  In this paper, we consider a recently proposed model of Dark Energy (DE)
which contains three terms (one proportional to the squared Hubble parameter,
one to the first derivative with respect to the cosmic time of the Hubble
parameter and one proportional to the second derivative with respect to the
cosmic time of the Hubble parameter) in the light of the $f\left(R,T \right)$
model of modified gravity, considering the particular model $f\left(R,T \right)
= \mu R + \nu T$, with $\mu$ and $\nu$ two free positive constant parameters.
Here $R$ and $T$ are the curvature and torsion scalars, respectively. In this
work, we have found that the Hubble parameter $H$ exhibits a decaying behavior
until redshifts of the order of $z\approx-0.5$ (when it starts to increase) and
the time derivative of the Hubble parameter goes from negative to positive
values for different redshifts. The equation of state (EoS) parameter of DE and
the effective EoS parameter exhibit a transition from $\omega<-1$ to
$\omega>-1$ (then the EoS parameters have a quintom-like behavior). We have
also found that the said model can attain the late time accelerated phase of
the universe. Using the statefinder parameters $r$ and $s$, we derived that the
considered model can attaining the $\Lambda$CDM phase of the universe and can
interpolate between dust and $\Lambda$CDM phase of the universe. Finally,
studying the squared speed of sound $v_s^2$, we have seen that the model under
consideration is classically stable in the earlier stage of the universe, but
classically unstable in the current stage.


  Polymer representations of the Weyl algebra of linear systems provide the
simplest analogues of the representation used in loop quantum gravity. The
construction of these representations is algebraic, based on the
Gelfand-Naimark-Segal construction. Is it possible to understand these
representations from a Geometric Quantization point of view? We address this
question for the case of a two dimensional phase space.


  The geometry and interactions between the constituents of a liquid crystal,
which are responsible for inducing the partial order in the fluid, may locally
favor an attempted phase that could not be realized in $\mathbb{R}^3$. While
states that are incompatible with the geometry of $\mathbb{R}^3$ were
identified more than 50 years ago, the collection of compatible states remained
poorly understood and not well characterized. Recently, the compatibility
conditions for three-dimensional director fields were derived using the method
of moving frames. These compatibility conditions take the form of six
differential relations in five scalar fields locally characterizing the
director field. In this work, we rederive these equations using a more
transparent approach employing vector calculus. We then use these equations to
characterize a wide collection of compatible phases.


  Forecasting of weakly correlated time series of conversion rate by methods of
exponential smoothing, neural network and decision tree on the example of
conversion percent series for an electronic store is considered in the paper.
The advantages and disadvantages of each method are considered.


  The concept of bounded expansion provides a robust way to capture sparse
graph classes with interesting algorithmic properties. Most notably, every
problem definable in first-order logic can be solved in linear time on bounded
expansion graph classes. First-order interpretations and transductions of
sparse graph classes lead to more general, dense graph classes that seem to
inherit many of the nice algorithmic properties of their sparse counterparts.
In this paper, we show that one can encode graphs from a class with
structurally bounded expansion via lacon-, shrub- and parity-decompositions
from a class with bounded expansion. These decompositions are useful for
lifting properties from sparse to structurally sparse graph classes.


  We discuss the physics of backreaction-driven accelerated expansion. Using
the exact equations for the behaviour of averages in dust universes, we explain
how large-scale smoothness does not imply that the effect of inhomogeneity and
anisotropy on the expansion rate is small. We demonstrate with an analytical
toy model how gravitational collapse can lead to acceleration. We find that the
conjecture of the accelerated expansion being due to structure formation is in
agreement with the general observational picture of structures in the universe,
and more quantitative work is needed to make a detailed comparison.


  Several site-testing programs and observatories currently use combined
MASS-DIMM instruments for monitoring parameters of optical turbulence. The
instrument is described here. After a short recall of the measured quantities
and operational principles, the optics and electronics of MASS-DIMM,
interfacing to telescopes and detectors, and operation are covered in some
detail. Particular attention is given to the correct measurement and control of
instrumental parameters to ensure valid and well-calibrated data, to the data
quality and filtering. Examples of MASS-DIMM data are given, followed by the
list of present and future applications.


  Safely meeting Worst Case Energy Consumption (WCEC) criteria requires
accurate energy modeling of software. We investigate the impact of instruction
operand values upon energy consumption in cacheless embedded processors.
Existing instruction-level energy models typically use measurements from random
input data, providing estimates unsuitable for safe WCEC analysis.
  We examine probabilistic energy distributions of instructions and propose a
model for composing instruction sequences using distributions, enabling WCEC
analysis on program basic blocks. The worst case is predicted with statistical
analysis. Further, we verify that the energy of embedded benchmarks can be
characterised as a distribution, and compare our proposed technique with other
methods of estimating energy consumption.


  Recently, Donaldson proved asymptotic stability for a polarized algebraic
manifold $M$ with polarization class admitting a K\"ahler metric of constant
scalar curvature, essentially when the linear algebraic part $H$ of $Aut^0(M)$
is semisimple. The purpose of this paper is to give a generalization of
Donaldson's result to the case where the polarization class admits an extremal
K\"ahler metric, even when $H$ is not semisimple.


  Modern machine learning is transforming particle physics fast, bullying its
way into our numerical tool box. For young researchers it is crucial to stay on
top of this development, which means applying cutting-edge methods and tools to
the full range of LHC physics problems. These lecture notes lead students with
basic knowledge of particle physics and significant enthusiasm for machine
learning to relevant applications. They start with an LHC-specific motivation
and a non-standard introduction to neural networks and then cover
classification, unsupervised classification, generative networks, and inverse
problems. Two themes defining much of the discussion are well-defined loss
functions and uncertainty-aware networks. As part of the applications, the
notes include some aspects of theoretical LHC physics. All examples are chosen
from particle physics publications of the last few years.


  We present N2D+ 3-2 (IRAM) and H2D+ 1_11 - 1_10 and N2H+ 4-3 (JCMT) maps of
the small cluster-forming Ophiuchus B2 core in the nearby Ophiuchus molecular
cloud. In conjunction with previously published N2H+ 1-0 observations, the N2D+
data reveal the deuterium fractionation in the high density gas across Oph B2.
The average deuterium fractionation R_D = N(N2D+)/N(N2H+) ~ 0.03 over Oph B2,
with several small scale R_D peaks and a maximum R_D = 0.1. The mean R_D is
consistent with previous results in isolated starless and protostellar cores.
The column density distributions of both H2D+ and N2D+ show no correlation with
total H2 column density. We find, however, an anticorrelation in deuterium
fractionation with proximity to the embedded protostars in Oph B2 to distances
>= 0.04 pc. Destruction mechanisms for deuterated molecules require gas
temperatures greater than those previously determined through NH3 observations
of Oph B2 to proceed. We present temperatures calculated for the dense core gas
through the equating of non-thermal line widths for molecules (i.e., N2D+ and
H2D+) expected to trace the same core regions, but the observed complex line
structures in B2 preclude finding a reasonable result in many locations. This
method may, however, work well in isolated cores with less complicated velocity
structures. Finally, we use R_D and the H2D+ column density across Oph B2 to
set a lower limit on the ionization fraction across the core, finding a mean
x_e, lim >= few x 10^{-8}. Our results show that care must be taken when using
deuterated species as a probe of the physical conditions of dense gas in
star-forming regions.


  In the dynamic approximate maximum bipartite matching problem we are given
bipartite graph $G$ undergoing updates and our goal is to maintain a matching
of $G$ which is large compared the maximum matching size $\mu(G)$. We define a
dynamic matching algorithm to be $\alpha$ (respectively $(\alpha,
\beta)$)-approximate if it maintains matching $M$ such that at all times $|M |
\geq \mu(G) \cdot \alpha$ (respectively $|M| \geq \mu(G) \cdot \alpha -
\beta$).
  We present the first deterministic $(1-\epsilon )$-approximate dynamic
matching algorithm with $O(poly(\epsilon ^{-1}))$ amortized update time for
graphs undergoing edge insertions. Previous solutions either required
super-constant [Gupta FSTTCS'14, Bhattacharya-Kiss-Saranurak SODA'23] or
exponential in $1/\epsilon $
[Grandoni-Leonardi-Sankowski-Schwiegelshohn-Solomon SODA'19] update time. Our
implementation is arguably simpler than the mentioned algorithms and its
description is self contained. Moreover, we show that if we allow for additive
$(1, \epsilon \cdot n)$-approximation our algorithm seamlessly extends to also
handle vertex deletions, on top of edge insertions. This makes our algorithm
one of the few small update time algorithms for $(1-\epsilon )$-approximate
dynamic matching allowing for updates both increasing and decreasing the
maximum matching size of $G$ in a fully dynamic manner.


  Perturbative calculations with unstable particles require the inclusion of
their finite decay widths. A convenient, universal scheme for this purpose is
the complex-mass scheme. It fully respects gauge-invariance, is
straight-forward to apply, and has been successfully used for the calculation
of various tree-level processes and of the electroweak radiative corrections to
e+ e- -> 4f and H -> 4f.


  We evaluate the cross section for electron-positron pair production by a
single high energy photon in the space-time of a static, straight cosmic
string. Energy and momentum conservation precludes this process in empty
Minkowski space. It happens around a cosmic string, in spite of the local
flatness of the metric, as a consequence of the conical structure of space.
Previous results based on a simplified model with scalar fields are here
extended to the realistic QED case. Analytic expressions are found in three
different regimes: near the threshold, at energies much larger than the
electron rest mass M, and at ultrahigh energies, much larger than $M/\delta$,
with $\delta$ the string mass per unit length in Planck units.


  We calculate global $m=1$ modes with low pattern speed corresponding to
introducing a finite eccentricity into a protoplanetary disc. We consider disc
models which are either isolated or contain one or two protoplanets orbiting in
an inner cavity. Global modes that are strongly coupled to inner protoplanets
are found to have disc orbits which tend to have apsidal lines antialigned with
respect to those of the inner protoplanets. Other modes corresponding to free
disc modes may be global over a large range of length scales and accordingly be
long lived. We consider the motion of a protoplanet in the earth mass range
embedded in an eccentric disc and determine the equilibrium orbits which
maintain fixed apsidal alignment with respect to the disc gas orbits.
Equilibrium eccentricities are found to be comparable or possibly exceed the
disc eccentricity. We then approximately calculate the tidal interaction with
the disc in order to estimate the orbital migration rate. Results are found to
deviate from the case of axisymmetric disc with near circular protoplanet orbit
once eccentricities of protoplanet and disc orbits become comparable to the
disc aspect ratio in magnitude. Aligned protoplanet orbits with very similar
eccentricity to that of the gas disc are found to undergo litle eccentricity
change while undergoing inward migration in general. However, for significantly
larger orbital eccentricities, migration may be significantly reduced or even
reverse from inwards to outwards. Thus the existence of global non circular
motions in discs with radial excursions comparable to the semi-thickness may
have important consequences for the migration and survival of protoplanetary
cores in the earth mass range.


  Using the Argonne V18 interaction, renormalized with the Lee-Suzuki method,
we study nuclei around the $N=20$ island of inversion. We include 5 major
oscillator shells, in a no-core approach, using the Hybrid Multi-Determinant
method reaching up to few hundreds Slater determinants. Although qualitatively
in agreement with the experimental levels, the calculated BE2 do not show the
same amount of collectivity seen experimentally.


  DNA sequencing is revolutionising the field of medicine. DNA sequencers, the
machines which perform DNA sequencing, have evolved from the size of a fridge
to that of a mobile phone over the last two decades. The cost of sequencing a
human genome also has reduced from billions of dollars to hundreds of dollars.
Despite these improvements, DNA sequencers output hundreds or thousands of
gigabytes of data that must be analysed on computers to discover meaningful
information with biological implications. Unfortunately, the analysis
techniques have not kept the pace with rapidly improving sequencing
technologies. Consequently, even today, the process of DNA analysis is
performed on high-performance computers, just as it was a couple of decades
ago. Such high-performance computers are not portable. Consequently, the full
utility of an ultra-portable sequencer for sequencing in-the-field or at the
point-of-care is limited by the lack of portable lightweight analytic
techniques. This thesis proposes computer architecture-aware optimisation of
DNA analysis software. DNA analysis software is inevitably convoluted due to
the complexity associated with biological data. Modern computer architectures
are also complex. Performing architecture-aware optimisations requires the
synergistic use of knowledge from both domains, (i.e, DNA sequence analysis and
computer architecture). This thesis aims to draw the two domains together. In
this thesis, gold-standard DNA sequence analysis workflows are systematically
examined for algorithmic components that cause performance bottlenecks.
Identified bottlenecks are resolved through architecture-aware optimisations at
different levels, i.e., memory, cache, register and processor. The optimised
software tools are used in complete end-to-end analysis workflows and their
efficacy is demonstrated by running on prototypical embedded systems.


  Translucency is now a common design element in at least one popular mobile
operating system. This raises security concerns as it can make it harder for
users to correctly identify and interpret trusted interaction elements. In this
paper, we demonstrate this security problem using the example of the Safari
browser in the latest iOS version on Apple tablets and phones (iOS7), and
discuss technical challenges of an attack as well as solutions to these
challenges. We conclude with a survey-based user study, where we seek to
quantify the security impact, and find that further investigation is warranted.


  We report the temperature dependence of the resistivity and thermoelectric
power under hydrostatic pressure of the itinerant antiferromagnet BaFe2As2 and
the electron-doped superconductor Ba(Fe0.9Co0.1)2As2. We observe a hole-like
contribution to the thermopower below the structural-magnetic transition in the
parent compound that is suppressed in magnitude and temperature with pressure.
Pressure increases the contribution of electrons to transport in both the doped
and undoped compound. In the 10% Co-doped sample, we used a two-band model for
thermopower to estimate the carrier concentrations and determine the effect of
pressure on the band structure.


  We have proposed a new approach to search for axion dark matter with an
optical ring cavity [Phys. Rev. Lett. 121, 161301 (2018)]. The coupling of
photons to axions or axion-like particles makes a modulated difference in the
phase velocity between left- and right-handed photons. Our method is to measure
this phase velocity difference with a ring cavity, by measuring the resonant
frequency difference between two circular polarizations. Our estimation shows
that the sensitivity to axion-photon coupling constant $g_{a \gamma}$ for axion
mass $m \lesssim 10^{-10}$ eV can be improved by several orders of magnitude
compared with the current best limits. In this paper, we present the principles
of the Dark matter Axion search with riNg Cavity Experiment (DANCE) and the
status of the prototype experiment, DANCE Act-1.


  To explore the mechanism for the entropic force proposal in Entropic Gravity,
we propose a specific thermodynamic process for states thermalized in local
Hawking Temperature. We find when Casini's version of the Bekenstein bound is
saturated, the thermodynamic force derived in the entanglement first law
matches the local inertial force for the Schwarzschild solution, except for a
negligible statistics-dependent factor. We argue the gravity viewed by static
observers may have observable effects emerged from quantum statistics. The
successful detailed calculation in this simple model inspires and is in support
of the further development in our following research arXiv:2004.14059.


  Wilson lines in N=4SYM can be computed in terms of branes carrying electric
flux, i.e. F-strings dissolved in their worldvolumes. It is then natural to
think that those configurations are the effective description of strings
expanding due to dielectric effect to D-branes. In this note we explicitly show
this for a class of such configurations, namely those dual to Wilson lines
either in the symmetric or in the antisymmetric tensor product of fundamentals.


  In this study, a novel coordinative scheduling optimization approach is
proposed to enhance port efficiency by reducing average wait time and
turnaround time. The proposed approach consists of enhanced particle swarm
optimization (ePSO) as kernel and augmented firefly algorithm (AFA) as global
optimal search. Two paradigm methods of the proposed approach are investigated,
which are batch method and rolling horizon method. The experimental results
show that both paradigm methods of proposed approach can effectively enhance
port efficiency. The average wait time could be significantly reduced by 86.0%
- 95.5%, and the average turnaround time could eventually save 38.2% - 42.4%
with respect to historical benchmarks. Moreover, the paradigm method of rolling
horizon could reduce to 20 mins on running time over 3-month datasets, rather
than 4 hrs on batch method at corresponding maximum performance.


  We study the electron correlation effects in the calculations of isotope
shifts in Na and Mg+ using the relativistic coupled-cluster method. The trends
of the correlation effects are explicitly discussed and comparison of the
present results with the previously reported results are given. We also present
the fine structure constant variation coefficients for many states in the above
systems. From these results, it is possible to find out suitable transition
lines those can be used as anchor and probe lines in finding possible variation
in the fine structure constant.


  We present arguments suggesting that large size overlapping instantons are
the driving mechanism of the confinement-deconfinement phase transition at
nonzero chemical potential mu. The arguments are based on the picture that
instantons at very large chemical potential in the weak coupling regime are
localized configurations with finite size \rho\sim\mu^{-1}. At the same time,
the same instantons at smaller chemical potential in the strong coupling regime
are well represented by the so-called instanton-quarks with fractional
topological charge 1/N_c. We estimate the critical chemical potential mu_c(T)
where transition between these two regimes takes place. We identify this
transition with confinement- deconfinement phase transition.
  We also argue that the instanton quarks carry magnetic charges. As a
consequence of it, there is a relation between our picture and the standard
t'Hooft and Mandelstam picture of the confinement. We also comment on possible
relations of instanton-quarks with "periodic instantons", " center vortices",
and "fractional instantons" in the brane construction. We also argue that the
variation of the external parameter mu, which plays the role of the vacuum
expectation value of a "Higgs" field at mu >> \Lambda_{QCD}, allows to study
the transition from a "Higgs -like" gauge theory (weak coupling regime, mu>>
\Lambda_{QCD}) to ordinary QCD (strong coupling regime, mu<< \Lambda_{QCD}). We
also comment on some recent lattice results on topological charge density
distribution which support our picture.


  We derive a Born-Markov master equation describing the dissipation induced by
a bath of lossy but coherently driven two-level systems (TLS) coupled to a
bosonic system via Jaynes-Cummings interaction. We analytically derive all the
master equation rates. We characterize these rates for the particular case of a
single-mode system coupled to identical TLS. We study the steady state of the
system and its exotic properties stemming from the non-thermal stationary state
of the driven TLS bath. These properties include dissipative amplification,
bath-induced linear instability, and both coherent and dissipative squeezing.
The master equation is valid for arbitrarily strong TLS driving, and it can be
generalized to include multi-level systems or other system-bath interaction
terms, among others. Our work provides a tool to study and characterize
TLS-induced decoherence, a key limiting factor in quantum technological devices
based on, for instance, superconducting circuits, magnonic systems, or quantum
acoustics.


  We study the effects of low-$p_T$ collective flow on radiative energy loss
from high-$p_T$ partons traversing the QCD medium created in high-energy
nucleus-nucleus collisions. We illustrate this idea through three examples. Due
to longitudinal flow, jet profiles at the LHC present marked asymmetries in the
$\eta\times \phi$-plane, and widths in $\eta$ and $\phi$ of particle
distributions associated with a high-$p_T$ trigger at RHIC become different.
Finally, transverse flow implies an increase of high-$p_T$ $v_2$ at RHIC.


  We consider nonlinear Schr\"odinger equation with a Hartree-type nonlocal
nonlinearity. The case where a nonlinear interaction potential grows at the
spatial infinity is studied. By virtue of an effective decomposition of the
nonlinearity based on conservation of mass, this kind of growing nonlinear
interaction is known to contain an effect like a linear potential. In this
paper, a well-posedness result is obtained in a suitable energy space for a
class of interaction potential growing at the spatial infinity in at most the
quadratic order. If the growth rate of interaction potential is faster than the
linear order, a priori information on the center of mass plays a crucial role.
When the interaction potential is exactly in the quadratic order, solution are
written explicitly.


  We calculate the spectrum of collective excitations of the XY spiral state
prepared adiabatically or suddenly from a uniform ferromagnetic F=1 condensate.
For spiral wavevectors past a critical value, spin wave excitation energies
become imaginary indicating a dynamical instability. We construct phase
diagrams as functions of spiral wavevector and quadratic Zeeman energy.


  Recent experiments on nanoscale conductors coupled to microwave cavities put
in prospect transport investigations of electron-photon interplay in the deep
quantum regime. Here we propose a pump-probe scheme to investigate the
transient dynamics of individual electron-photon excitations in a double
quantum dot-cavity system. Excitations pumped into the system decay via charge
tunneling at the double dot, probed in real time. We investigate theoretically
the short-time charge transfer statistics at the dot, for periodic pumping, and
show that this gives access to vacuum Rabi oscillations as well as excitation
dynamics in the presence of double dot dephasing and relaxation.


  Motivated by several classic decision-theoretic paradoxes, and by analogies
with the paradoxes which in physics motivated the development of quantum
mechanics, we introduce a projective generalization of expected utility along
the lines of the quantum-mechanical generalization of probability theory. The
resulting decision theory accommodates the dominant paradoxes, while retaining
significant simplicity and tractability. In particular, every finite game
within this larger class of preferences still has an equilibrium.


  Small area estimation (SAE) entails estimating characteristics of interest
for domains, often geographical areas, in which there may be few or no samples
available. SAE has a long history and a wide variety of methods have been
suggested, from a bewildering range of philosophical standpoints. We describe
design-based and model-based approaches and models that are specified at the
area-level and at the unit-level, focusing on health applications and fully
Bayesian spatial models. The use of auxiliary information is a key ingredient
for successful inference when response data are sparse and we discuss a number
of approaches that allow the inclusion of covariate data. SAE for HIV
prevalence, using data collected from a Demographic Health Survey in Malawi in
2015-2016, is used to illustrate a number of techniques. The potential use of
SAE techniques for outcomes related to COVID-19 is discussed.


  Diamond displays a large variety of luminescence centers which define its
optical properties and can be either created or modified by irradiation. The
main purpose of the present work is to study the radiation hardness of several
of such centers in homoepitaxial single crystal CVD diamond by following the
evolution of photoluminescence and ionoluminescence upon 2 MeV proton
irradiation. Luminescence decays were observed with values of the fluence at
half of the starting luminescence (F1/2) of the order of 1014 cm-2. The 3H
center displayed a non monotonic behavior, with a growing behavior and a
subsequent decay with a rather high F1/2 value (in the order of few 1016 cm-2),
maintaining at the highest fluences an intensity significantly higher than the
blue A-band. A simple model based on a double-exponential trend was defined to
fit with satisfactory accuracy the evolution of the 3H center. Several PL
centers (namely: 3H, TR12, 491 nm, 494 nm) exhibited clear correlations and
anti-correlations in their fluence dependences, which were considered in the
attempt to acquire some insight into their possible alternative attributions.


  We describe the $C^*$-algebra associated with the finite sections
discretization of truncated Toeplitz operators on the model space $K^2_u$ where
$u$ is an infinite Blaschke product. As consequences, we get a stability
criterion for the finite sections discretization and results on spectral and
pseudospectral approximation.