  The dilepton production from $pC$ and $pCu$ collisions at $T_{lab}=12$ GeV is
calculated using the semi-classical BUU transport model, that includes the
off-shell propagation of vector mesons nonperturbatively and calculates the
width of the vector mesons dynamically. It is found that the collisional
broadening of the vector meson width and dropping vector meson masses lead to a
small enhancement of the dilepton yield below the $\omega$ meson mass pole in
$p Cu$ collisions compared to $p C$, which is, however, not sufficient to
explain the enhanced production of dileptons as observed in the experiment by
the KEK-PS E325 collaboration. It is argued that such in-medium effects are
expected to be small due to kinematical reasons -- the dominant part of vector
mesons radiate dileptons and decay outside the nucleus due to the finite
formation time for $\rho$ and $\omega$ mesons, which is large by Lorentz
covariance since the produced vector mesons move with high velocity relative to
the target nucleus.


  We model s-wave and d-wave disordered granular superconductors with a
three-dimensional lattice of randomly distributed Josephson junctions with
finite self-inductance. The nonlinear ac resistivity of these systems was
calculated using Langevin dynamical equations. The current amplitude dependence
of the nonlinear resistivity at the peak position is found to be a power law
characterized by exponent $\alpha$. The later is not universal but depends on
the self-inductance and current regimes. In the weak current regime $\alpha$ is
independent of the self-inductance and equal to 0.5 or both of s- and d-wave
materials. In the strong current regime this exponent depends on the screening.
We find $\alpha \approx 1$ for some interval of inductance which agrees with
the experimental finding for d-wave ceramic superconductors.


  We investigate the spectral properties of a quasi-one-dimensional lattice in
two possible dimerisation configurations. Both configurations are characterized
by the same lattice topology and the identical spectra containing a flat band
at zero energy. We find that one of the dimerised configuration has similar
symmetry to a one-dimensional chain proposed by Su-Schrieffer-Heeger for
studying solitons in conjugated polymers. Whereas, the other dimerised
configuration only shows non-trivial topological properties in the presence of
chiral-symmetry breaking adiabatic pumping.


  Mitral regurgitation (MR) is a serious heart valve disease. Early and
accurate diagnosis of MR via ultrasound video is critical for timely clinical
decision-making and surgical intervention. However, manual MR diagnosis heavily
relies on the operator's experience, which may cause misdiagnosis and
inter-observer variability. Since MR data is limited and has large intra-class
variability, we propose an unsupervised out-of-distribution (OOD) detection
method to identify MR rather than building a deep classifier. To our knowledge,
we are the first to explore OOD in MR ultrasound videos. Our method consists of
a feature extractor, a feature reconstruction model, and a residual
accumulation amplification algorithm. The feature extractor obtains features
from the video clips and feeds them into the feature reconstruction model to
restore the original features. The residual accumulation amplification
algorithm then iteratively performs noise feature reconstruction, amplifying
the reconstructed error of OOD features. This algorithm is straightforward yet
efficient and can seamlessly integrate as a plug-and-play component in
reconstruction-based OOD detection methods. We validated the proposed method on
a large ultrasound dataset containing 893 non-MR and 267 MR videos.
Experimental results show that our OOD detection method can effectively
identify MR samples.


  We study the potential of the next $ep$ collider, namely LHeC, with two
options $\sqrt{s}=1.3$ TeV $\sqrt{s}=1.98$ TeV, to search for excited spin-1/2
and spin-3/2 neutrinos. We calculate the single production cross section of
excited spin-1/2 and spin-3/2 neutrinos according to their effective currents
describing their interactions between gauge bosons and SM leptons. We choose
the $\nu^{\star}\rightarrow eW$ decay mode of excited neutrinos and
$W\rightarrow jj$ decay mode of $W$-boson for the analysis. We put some
kinematical cuts for the final state detectable particles and plot the
invariant mass distributions for signal and the corresponding backgrounds. In
order to obtain accessible limits for excited neutrino couplings, we show the
$f-f^{\prime}$ and $c_{iV}-c_{iA}$ contour plots for excited spin-1/2 and
excited spin-3/2 neutrinos, respectively.


  Robertson and Seymour proved that the family of all graphs containing a fixed
graph $H$ as a minor has the Erd\H{o}s-P\'osa property if and only if $H$ is
planar. We show that this is no longer true for the edge version of the
Erd\H{o}s-P\'osa property, and indeed even fails when $H$ is an arbitrary
subcubic tree of large pathwidth or a long ladder. This answers a question of
Raymond, Sau and Thilikos.


  We simulate 4d simplicial gravity for three topologis S4, S3xS1, (S1)^4 and
show that the free energy for these three fixed topology ensembles is the same
in the thermodynamic limit. We show, that the next-to-leading order
corrections, at least away from the critical point, can be described by
kinematic sources.


  We recall the path breaking contributions of the nuclear theory group of the
Variable Energy Cyclotron Centre, Kolkata. From a beginning of just one person
in 1970s, the group has steadily developed into a leading group in the country
today, with seminal contributions to almost the entire range of nuclear
physics, viz., low energy nuclear reactions, nuclear structure, deep inelastic
collisions, fission, liquid to gas phase transitions, nuclear matter, equation
of state, mass formulae, neutron stars, relativistic heavy ion collisions,
medium modification of hadron properties, quark gluon plasma, and cosmology of
early universe.


  Inductive inference in supervised classification context constitutes to
methods and approaches to assign some objects or items into different
predefined classes using a formal rule that is derived from training data and
possibly some additional auxiliary information. The optimality of such an
assignment varies under different conditions due to intrinsic attributes of the
objects being considered for such a task. One of these cases is when all the
objects' features are discrete variables with a priori known categories. As
another example, one can consider a modification of this case with a priori
unknown categories. These two cases are the main focus of this thesis and based
on Bayesian inductive theories, de Finetti type exchangeability is a suitable
assumption that facilitates the derivation of classifiers in the former
scenario. On the contrary, this type of exchangeability is not applicable in
the latter case, instead, it is possible to utilise the partition
exchangeability due to John Kingman. These two types of exchangeabilities are
discussed and furthermore here I investigate inductive supervised classifiers
based on both types of exchangeabilities. I further demonstrate that the
classifiers based on de Finetti type exchangeability can optimally handle test
items independently of each other in the presence of infinite amounts of
training data while on the other hand, classifiers based on partition
exchangeability still continue to benefit from joint labelling of all the test
items. Additionally, it is shown that the inductive learning process for the
simultaneous classifier saturates when the amount of test data tends to
infinity.


  Bayesian Neural Networks (BNNs) that possess a property of uncertainty
estimation have been increasingly adopted in a wide range of safety-critical AI
applications which demand reliable and robust decision making, e.g.,
self-driving, rescue robots, medical image diagnosis. The training procedure of
a probabilistic BNN model involves training an ensemble of sampled DNN models,
which induces orders of magnitude larger volume of data movement than training
a single DNN model. In this paper, we reveal that the root cause for BNN
training inefficiency originates from the massive off-chip data transfer by
Gaussian Random Variables (GRVs). To tackle this challenge, we propose a novel
design that eliminates all the off-chip data transfer by GRVs through the
reversed shifting of Linear Feedback Shift Registers (LFSRs) without incurring
any training accuracy loss. To efficiently support our LFSR reversion strategy
at the hardware level, we explore the design space of the current DNN
accelerators and identify the optimal computation mapping scheme to best
accommodate our strategy. By leveraging this finding, we design and prototype
the first highly efficient BNN training accelerator, named Shift-BNN, that is
low-cost and scalable. Extensive evaluation on five representative BNN models
demonstrates that Shift-BNN achieves an average of 4.9x (up to 10.8x) boost in
energy efficiency and 1.6x (up to 2.8x) speedup over the baseline DNN training
accelerator.


  We consider a lightcone wrapped supermembrane compactified on 2-torus in the
matrix regularization. We examine the double dimensional reduction technique
and deduce the free matrix string of (p,q)-string in type IIB superstring
theory explicitly from the matrix-regularized wrapped supermembrane. In
addition we obtain the (2+1)-dimensional super Yang-Mills action in curved
background. We also examine the duality.


  We analyze the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process on a finite
lattice and with the most general open boundary conditions. We extend results
obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L.
Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We
determine the finite-size scaling of the spectral gap, which characterizes the
approach to stationarity at large times, in the low and high density regimes
and on the coexistence line. We observe boundary induced crossovers and discuss
possible interpretations of our results in terms of effective domain wall
theories.


  Neutron star properties, such as its mass, radius, and moment of inertia, are
calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations using the
ring-diagram equation of state (EOS) obtained from realistic low-momentum NN
interactions $V_{low-k}$. Several NN potentials (CDBonn, Nijmegen, Argonne V18
and BonnA) have been employed to calculate the ring-diagram EOS where the
particle-particle hole-hole ring diagrams are summed to all orders. The proton
fractions for different radial regions of a $\beta$-stable neutron star are
determined from the chemical potential conditions $\mu_n-\mu_p = \mu_e =
\mu_\mu$. The neutron star masses, radii and moments of inertia given by the
above potentials all tend to be too small compared with the accepted values.
Our results are largely improved with the inclusion of medium corrections based
on Brown-Rho scaling where the in-medium meson masses, particularly those of
$\omega$, $\rho$ and $\sigma$, are slightly decreased compared with their
in-vacuum values. Representative results using such medium corrected
interactions are neutron star mass $M\sim 1.8 M_{\odot}$, radius $R\sim 9$ km
and moment of inertia $\sim 60 M_{\odot}km^2$. The mass-radius trajectories
given by the above four realistic NN potentials are by and large overlapping.


  In this paper we prove in a rigorous mathematical way (using the Clifford
bundle formalism) that the energies and momenta of two distinct and arbitrary
free Maxwell fields (of finite energies and momenta) that are superposed are
additive and thus that there is no incompatibility between the principle of
superposition of fields and the principle of energy-momentum conservation,
contrary to some recent claims. Our proof depends on a noticeable formula for
the energy-momentum 1-form fields T^{a},namely Riesz formula, which is valid
for any electromagnetic field configuration F satisfying Maxwell equation.


  This paper describes the incremental generation of parse tables for the
LR-type parsing of Tree Adjoining Languages (TALs). The algorithm presented
handles modifications to the input grammar by updating the parser generated so
far. In this paper, a lazy generation of LR-type parsers for TALs is defined in
which parse tables are created by need while parsing. We then describe an
incremental parser generator for TALs which responds to modification of the
input grammar by updating parse tables built so far.


  An uncertainty relation for the R\'enyi entropies of conjugate quantum
observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE}
\geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error
of any estimate of a random optical phase shift in terms of average photon
number, where $f(\alpha)$ is maximised for non-Shannon entropies. Related
simple yet strong uncertainty relations linking phase uncertainty to the photon
number distribution, such as $\Delta\Phi\geq \max_n p_n$, are also obtained.
These results are significantly strengthened via upper and lower bounds on the
R\'enyi mutual information of quantum communication channels, related to
asymmetry and convolution, and applied to the estimation (with prior
information) of unitary shift parameters such as rotation angle and time, and
to obtain strong bounds on measures of coherence. Sharper R\'enyi entropic
uncertainty relations are also obtained, including time-energy uncertainty
relations for Hamiltonians with discrete spectra. In the latter case
almost-periodic R\'enyi entropies are introduced for nonperiodic systems.


  We present near-infrared and optical observations of the nova V496 Scuti 2009
covering various phases - pre-maximum, early decline and nebular - during the
first 10 months of its discovery followed by limited observations in early part
of 2011 April. The spectra follow the evolution of the nova when the lines had
strong P Cygni profiles to a phase dominated by prominent emission lines. The
notable feature of the near-IR spectra in the early decline phase is the rare
presence of first overtone bands of carbon monoxide in emission. Later about
150 days after the peak brightness the IR spectra show clear dust formation in
the expanding ejecta. Dust formation in V496 Sct is consistent with the
presence of lines of elements with low ionization potentials like Na and Mg in
the early spectra and the detection of CO bands in emission. The light curve
shows a slow rise to the maximum and a slow decline indicating a prolonged mass
loss. This is corroborated by the strengthening of P Cygni profiles during the
first 30 days. In the spectra taken close to the optical maximum brightness,
the broad and single absorption component seen at the time of discovery is
replaced by two sharper components. During the early decline phase two sharp
dips that show increasing outflow velocities are seen in the P Cygni absorption
components of Fe II and H I lines. The spectra in 2010 March showed the onset
of the nebular phase. Several emission lines display saddle-like profiles
during the nebular phase. In the nebular stage the observed fluxes of [O III]
and H-beta lines are used to estimate the electron number densities and the
mass of the ejecta. The optical spectra show that the nova evolved in the P_fe
A_o spectral sequence. The physical conditions in the ejecta are estimated. The
absolute magnitude and the distance to the nova are estimated to be M_V = -7.0
+/- 0.2 and d = 2.9 +/- 0.3 kpc respectively.


  A muon collider operating in the TeV energy range can be an ideal s-channel
Higgs boson factory. This is especially true for a heavy Higgs boson. The
non-perturbative dynamical aspects of such a Higgs boson were recently
investigated with large N expansion methods at next to leading order, and
reveal the existence of a mass saturation effect. Even at strong coupling, the
Higgs resonance remains always below 1 TeV. However, if the coupling is strong
enough, the resonance becomes impossible to be detected.


  We analyzed 5,484 close contacts of COVID-19 cases from Italy, all of them
tested for SARS-CoV-2 infection. We found an infection fatality ratio of 2.2%
(95%CI 1.69-2.81%) and identified male sex, age >70 years, cardiovascular
comorbidities, and infection early in the epidemics as risk factors for death.


  Linear regressions with period and group fixed effects are widely used to
estimate policies' effects: 26 of the 100 most cited papers published by the
American Economic Review from 2015 to 2019 estimate such regressions. It has
recently been shown that those regressions may produce misleading estimates, if
the policy's effect is heterogeneous between groups or over time, as is often
the case. This survey reviews a fast-growing literature that documents this
issue, and that proposes alternative estimators robust to heterogeneous
effects. We use those alternative estimators to revisit Wolfers (2006).


  We introduce a large-scale dataset of the complete texts of free/open source
software (FOSS) license variants. To assemble it we have collected from the
Software Heritage archive-the largest publicly available archive of FOSS source
code with accompanying development history-all versions of files whose names
are commonly used to convey licensing terms to software users and
developers.The dataset consists of 6.5 million unique license files that can be
used to conduct empirical studies on open source licensing, training of
automated license classifiers, natural language processing (NLP) analyses of
legal texts, as well as historical and phylogenetic studies on FOSS licensing.
Additional metadata about shipped license files are also provided, making the
dataset ready to use in various contexts; they include: file length measures,
detected MIME type, detected SPDX license (using ScanCode), example origin
(e.g., GitHub repository), oldest public commit in which the license
appeared.The dataset is released as open data as an archive file containing all
deduplicated license files, plus several portable CSV files for metadata,
referencing files via cryptographic checksums.


  By decomposing velocity dispersion into non-spin and spin-induced, mean flow
and dispersion are analytically solved for axisymmetric rotating and growing
halos. The polar flow can be neglected and azimuthal flow is directly related
to dispersion. The fictitious ("Reynolds") stress acts on mean flow to enable
energy transfer from mean flow to random motion and maximize system entropy.
For large halos (high peak height $\nu$ at early stage of halo life) with
constant concentration, there exists a self-similar radial flow (outward in
core and inward in outer region). Halo mass, size and specific angular momentum
increase linearly with time via fast mass accretion. Halo core spins faster
than outer region. Large halos rotate with an angular velocity proportional to
Hubble parameter and spin-induced dispersion is dominant. All specific energies
(radial/rotational/kinetic/potential) are time-invariant. Both halo spin
($\sim$0.031) and anisotropic parameters can be analytically derived. For
"small" halos with stable core and slow mass accretion (low peak height $\nu$
at late stage of halo life), radial flow vanishes. Small halos rotate with
constant angular velocity and non-spin axial dispersion is dominant. Small
halos are spherical in shape, incompressible, and isotropic. Radial and
azimuthal dispersion are comparable and greater than polar dispersion. Due to
finite spin, kinetic energy is not equipartitioned with the greatest energy
along azimuthal direction. Different from normal matter, small halos are hotter
with faster spin. Halo relaxation from early to late stage involves variation
of shape, density, mean flow, momentum, and energy. During relaxation, halo
isotopically "stretches" with conserved specific rotational kinetic energy,
increasing concentration and momentum of inertial. Halo "stretching" leads to
decreasing angular velocity, increasing angular momentum and spin parameter.


  Methods exploiting sparsity have been popular in imaging and signal
processing applications including compression, denoising, and imaging inverse
problems. Data-driven approaches such as dictionary learning and transform
learning enable one to discover complex image features from datasets and
provide promising performance over analytical models. Alternating minimization
algorithms have been particularly popular in dictionary or transform learning.
In this work, we study the properties of alternating minimization for
structured (unitary) sparsifying operator learning. While the algorithm
converges to the stationary points of the non-convex problem in general, we
prove rapid local linear convergence to the underlying generative model under
mild assumptions. Our experiments show that the unitary operator learning
algorithm is robust to initialization.


  In the prophet secretary problem, $n$ values are drawn independently from
known distributions, and presented in a uniformly random order. A
decision-maker must accept or reject each value when it is presented, and may
accept at most $k$ values in total. The objective is to maximize the expected
sum of accepted values.
  We analyze the performance of static threshold policies, which accept the
first $k$ values exceeding a fixed threshold (or all such values, if fewer than
$k$ exist). We show that an appropriate threshold guarantees $\gamma_k = 1 -
e^{-k}k^k/k!$ times the value of the offline optimal solution. Note that
$\gamma_1 = 1-1/e$, and by Stirling's approximation $\gamma_k \approx
1-1/\sqrt{2 \pi k}$. This represents the best-known guarantee for the prophet
secretary problem for all $k>1$, and is tight for all $k$ for the class of
static threshold policies.
  We provide two simple methods for setting the threshold. Our first method
sets a threshold such that $k \cdot \gamma_k$ values are accepted in
expectation, and offers an optimal guarantee for all $k$. Our second sets a
threshold such that the expected number of values exceeding the threshold is
equal to $k$. This approach gives an optimal guarantee if $k > 4$, but gives
sub-optimal guarantees for $k \le 4$. Our proofs use a new result for
optimizing sums of independent Bernoulli random variables, which extends a
classical result of Hoeffding (1956) and is likely to be of independent
interest. Finally, we note that our methods for setting thresholds can be
implemented under limited information about agents' values.


  We investigate the effect of aliasing when applied to the storage of
variables, and their reconstruction for the solution of conservation equations.
In particular, we investigate the effect on the error of storing primitives
versus conserved variables for the Navier-Stokes equations. It was found that
storing the conserved variables introduces less dissipation and that the
dissipation caused by constructing the conversed variable from the primitives
grows factorially with the order. Hence, this problem becomes increasingly
important with the continuing move towards higher orders. Furthermore, the
method of gradient calculation is investigated, as applied to the viscous
fluxes in the Navier-Stokes equations. It was found that in most cases the
difference was small, and that the product rule applied to the gradients of the
conserved variables should be used due to a lower operation count. Finally,
working precision is investigated and found to have a minimal impact on
free-stream-turbulence-like flows when the compressible equations are solved,
except at low Mach numbers.


  Recent data-privacy laws have sparked interest in machine unlearning, which
involves removing the effect of specific training samples from a learnt model
as if they were never present in the original training dataset. The challenge
of machine unlearning is to discard information about the ``forget'' data in
the learnt model without altering the knowledge about the remaining dataset and
to do so more efficiently than the naive retraining approach. To achieve this,
we adopt a projected-gradient based learning method, named as
Projected-Gradient Unlearning (PGU), in which the model takes steps in the
orthogonal direction to the gradient subspaces deemed unimportant for the
retaining dataset, so as to its knowledge is preserved. By utilizing Stochastic
Gradient Descent (SGD) to update the model weights, our method can efficiently
scale to any model and dataset size. We provide empirically evidence to
demonstrate that our unlearning method can produce models that behave similar
to models retrained from scratch across various metrics even when the training
dataset is no longer accessible. Our code is available at
https://github.com/hnanhtuan/projected_gradient_unlearning.


  We consider Vachaspati's primordial magnetic field which is generated at the
electroweak phase transition. Assuming that either the gradients of the Higgs
field or, alternatively, the magnetic field itself are stochastic variables
with a normal distribution, we find that the resulting magnetic field has an
{\em rms} value in the present-day universe which is fully consistent with what
is required for the galactic dynamo mechanism.


  This paper is a sequel (and contains a better treatment) of math.QA/0404032;
We construct some canonical bases for quantum toroidal algebras of types D_4,
E_6, E_7, E_8 using perverse sheaves on quot schemes parametrizing equivariant
coherent sheaves on elliptic curves. We also study some compatibility
properties of these bases with some natural filtrations and modules.


  This paper attempts to develop a graph-theoretic multi-agent perspective of
population games to study the \quotes{truncation} behavior. The proposed method
considers fitness of the population as a dynamical system to address the issue
of restrictive description of this behavior which pertains to the underlying
population dynamic. The fitness dynamic resembles an agreement protocol that
enables comments on the steady-state characteristics of the graph that
represents the population structure. The structural attributes of the
underlying graph and the truncation behavior are emphasized by exploiting the
spectral properties of the associated Laplacian matrix. The asymptotic
stability of the fitness agreement protocol has been shown to be sufficient in
concluding the stability of population dynamics. Simulation results validating
the proposed hypothesis have been discussed.


  We study moduli stabilization of the F-theory compactified on an elliptically
fibered Calabi-Yau fourfold. Our setup is based on the mirror symmetry
framework including brane deformations. The complex structure moduli dependence
of the resulting 4D N=1 effective theory is determined by the associated
fourfold period integrals. By turning on appropriate G-fluxes, we explicitly
demonstrate that all the complex structure moduli fields can be stabilized
around the large complex structure point of the F-theory fourfold.


  The semisimple bismash product Hopf algebra $J_n=k^{S_{n-1}}\#kC_n$ for an
algebraically closed field $k$ is constructed using the matched pair actions of
$C_n$ and $S_{n-1}$ on each other. In this work, we reinterpret these actions
and use an understanding of the involutions of $S_{n-1}$ to derive a new
Froebnius-Schur indicator formula for irreps of $J_n$ and show that for $n$
odd, all indicators of $J_n$ are nonnegative. We also derive a variety of
counting formulas including Theorem 6.2.2 which fully describes the indicators
of all $2$-dimensional irreps of $J_n$ and Theorem 6.1.2 which fully describes
the indicators of all odd-dimensional irreps of $J_n$ and use these formulas to
show that nonzero indicators become rare for large $n$.


  We continue our systematic statistical study of various components in
gamma-ray burst (GRB) optical lightcurves. We decompose the early onset bump
and the late re-brightening bump with empirical fits and analyze their
statistical properties. Among the 146 GRBs that have well-sampled optical
lightcurves, the onset and re-brightening bumps are observed in 38 and 26 GRBs,
respectively. It is found that the typical rising and decaying slopes for both
the onset and re-brightening bumps are ~1.5 and -1.15, respectively. No early
onset bumps in the X-ray band are detected to be associated with the optical
onset bumps, while an X-ray re-brightening bump is detected for half of the
re-brightening optical bumps. The peak luminosity is anti-correlated with the
peak time, L_p\propto t_{p}^{-1.81+/-0.32} and L_p\propto t_{p}^{-0.83+/-0.17}
for the onset and re-brightening bumps, respectively. Both L_p and the
isotropic energy release of the onset bumps are correlated with E_{\gamma,
iso}, whereas no similar correlation is found for the re-brightening bumps.
Taking the onset bumps as probes for the properties of the fireballs and their
ambient medium, we find that the typical power-law index of the relativistic
electrons is 2.5 and the medium density profile behaves as n\propto r^{-1}
within the framework of the synchrotron external shock models. With the medium
density profile obtained from our analysis, we also confirm the correlation
between initial Lorentz factor (\Gamma_0) and E_{\gamma, iso} in our previous
work. The jet component that produces the re-brightening bump seems to be
on-axis and independent of the prompt emission jet component. Its typical
kinetic energy budget would be about one order of magnitude larger than the
prompt emission component, but with a lower \Gamma_0, typically several tens.


  Core decomposition is a fundamental operator in network analysis. In this
paper, we study the problem of computing distance-generalized core
decomposition on a network. A distance-generalized core, also termed $(k,
h)$-core, is a maximal subgraph in which every vertex has at least $k$ other
vertices at distance no larger than $h$. The state-of-the-art algorithm for
solving this problem is based on a peeling technique which iteratively removes
the vertex (denoted by $v$) from the graph that has the smallest $h$-degree.
The $h$-degree of a vertex $v$ denotes the number of other vertices that are
reachable from $v$ within $h$ hops. Such a peeling algorithm, however, needs to
frequently recompute the $h$-degrees of $v$'s neighbors after deleting $v$,
which is typically very costly for a large $h$. To overcome this limitation, we
propose an efficient peeling algorithm based on a novel $h$-degree updating
technique. Instead of recomputing the $h$-degrees, our algorithm can
dynamically maintain the $h$-degrees for all vertices via exploring a very
small subgraph, after peeling a vertex. We show that such an $h$-degree
updating procedure can be efficiently implemented by an elegant bitmap
technique. In addition, we also propose a sampling-based algorithm and a
parallelization technique to further improve the efficiency. Finally, we
conduct extensive experiments on 12 real-world graphs to evaluate our
algorithms. The results show that, when $h\ge 3$, our exact and sampling-based
algorithms can achieve up to $10\times$ and $100\times$ speedup over the
state-of-the-art algorithm, respectively.


  We give a new construction of sheaves on a relative site associated to a
product $X\times S$ where $S$ plays the role of a parameter space, expanding
the previous construction by the same authors, where the subanalytic structure
on $S$ was required. Here we let this last condition fall. In this way the
construction becomes much easier to apply when dimension of $S$ is bigger than
one. We also study the functorial properties of base change with respect to the
parameter space.


  We show that the scale dependence of the fluctuations of the natural time
itself under time reversal provides a useful tool for the discrimination of
seismic electric signals (critical dynamics) from noises emitted from man made
sources as well as for the determination of the scaling exponent. We present
recent data of electric signals detected at the Earth's surface, which confirm
that the value of the entropy in natural time as well as its value under time
reversal are smaller than that of the entropy of a "uniform" distribution.


  We show the possible stable soliton generation for the dark-state polaritons
(DSPs) in an electromagnetic induced transparency (EIT) medium composed of
$\Lambda$-type atoms. Whether the solitons are dark or bright can be controlled
by the coupling field intensity and the one photon detuning of the probe field.
Besides, the velocity and time width of the solitons also can be adjusted by
the coupling light.


  Existing offline reinforcement learning (RL) algorithms typically assume that
training data is either: 1) generated by a known policy, or 2) of entirely
unknown origin. We consider multi-demonstrator offline RL, a middle ground
where we know which demonstrators generated each dataset, but make no
assumptions about the underlying policies of the demonstrators. This is the
most natural setting when collecting data from multiple human operators, yet
remains unexplored. Since different demonstrators induce different data
distributions, we show that this can be naturally framed as a domain
generalization problem, with each demonstrator corresponding to a different
domain. Specifically, we propose Domain-Invariant Model-based Offline RL
(DIMORL), where we apply Risk Extrapolation (REx) (Krueger et al., 2020) to the
process of learning dynamics and rewards models. Our results show that models
trained with REx exhibit improved domain generalization performance when
compared with the natural baseline of pooling all demonstrators' data. We
observe that the resulting models frequently enable the learning of superior
policies in the offline model-based RL setting, can improve the stability of
the policy learning process, and potentially enable increased exploration.


  Feature modeling has been a very popular approach for variability management
in software product lines. Building a feature model requires substantial domain
expertise, however, even experts cannot foresee all future possibilities.
Changing requirements can force a feature model to evolve in order to adapt to
the new conditions. Feather is a language to describe model transformations
that will evolve a feature model. This article presents the structure and
foundations of Feather. First, the language elements, which consist of
declarations to characterize the model to evolve and commands to manipulate its
structure, are introduced. Then, semantics grounding in feature model
properties are given for the commands in order to provide precise command
definitions. Next, an interpreter that can realize the transformations
described by the commands in a Feather script is presented. Finally,
effectiveness of the language is discussed using two realistic examples, where
one of the examples includes a system from a dynamic environment and the other
employs a system that has a large feature model containing 1,227 features.


  I describe a Bayesian persuasion problem where Receiver has a private type
representing a cutoff for choosing Sender's preferred action, and Sender has
maxmin preferences over all Receiver type distributions with known mean and
bounds. This problem can be represented as a zero-sum game where Sender chooses
a distribution of posterior mean beliefs that is a mean-preserving contraction
of the prior over states, and an adversarial Nature chooses a Receiver type
distribution with the known mean; the player with the higher realization from
their chosen distribution wins. I formalize the connection between maxmin
persuasion and similar games used to model political spending, all-pay
auctions, and competitive persuasion. In both a standard binary-state setting
and a new continuous-state setting, Sender optimally linearizes the prior
distribution over states to create a distribution of posterior means that is
uniform on a known interval with an atom at the lower bound of its support.


  We present the e-TidalGCs Project which aims at modeling and predicting the
extra-tidal features surrounding all Galactic globular clusters for which 6D
phase space information, masses and sizes are available (currently 159 globular
clusters). We focus the analysis and presentation of the results on the
distribution of extra-tidal material on the sky, and on the different
structures found at different heliocentric distances. We emphasize the wide
variety of morphologies found: beyond the canonical tidal tails, our models
reveal that the extra-tidal features generated by globular clusters take a wide
variety of shapes, from thin and elongated shapes, to thick, and complex
halo-like structures. We also compare some of the most well studied stellar
streams found around Galactic globular clusters to our model predictions,
namely those associated to the clusters NGC 3201, NGC 4590, NGC 5466 and Pal 5.
Additionally, we investigate how the distribution and extension in the sky of
the simulated streams vary with the Galactic potential by making use of three
different models, containing or not a central spheroid, or a stellar bar.
Overall, our models predict that the mass lost by the current globular cluster
population in the field from the last 5 Gyrs is between
$0.3-2.1\times10^{7}M_{\odot}$, an amount comparable between 7-55 % of current
mass. Most of this lost mass is found in the inner Galaxy, with the half-mass
radius of this population being between 4-6 kpc. The outputs of the simulations
will be publicly available, at a time when the ESA Gaia mission and
complementary spectroscopic surveys are delivering exquisite data to which
these models can be compared.


  In a decentralized environment, exchanging resources requires users to
bargain until an agreement is found. Moreover, human agreements involve a
combination of collaborative and selfish behavior and often induce circularity,
complicating the evaluation of exchange requests. We introduce MuAC, a policy
language that allows users to state in isolation under which conditions they
are open to grant their resources and what they require in return. In MuAC,
exchange requests are evaluated automatically with the guarantee that the only
exchanges that will take place are those that mutually satisfy users'
conditions. Moreover, MuAC can be used as an enforcement mechanism to prevent
users from cheating. As a proof of concept, we implement a blockchain smart
contract that allows users to exchange their non-fungible tokens.


  This thesis explores nuclear systems under extreme conditions of isospin
asymmetry and strong magnetic fields. Its first chapter is devoted to the phase
diagram of isospin-asymmetrical nuclear matter in the density-temperature
plane. Four competing phases of matter are included into the consideration: the
unpaired phase, the ordinary Bardeen-Cooper-Schrieffer (BCS) phase, a phase
where normal fluid and superfluid separate into distinct domains and the
superfluid phase with a non-zero total momentum of Cooper pairs. The evolution
of these phases from the weakly BCS limit to the strongly coupled
Bose-Einstein-Condensate limit is studied by varying the density from high to
low values at various temperatures and asymmetries. The emergence of
tri-critical points (including a Lifshitz point) and various intrinsic
properties of the condensate (pair wave-function, occupation numbers,
quasiparticle spectra) are discussed. The second chapter studies the nuclei
$^{12}$C, $^{16}$O, and $^{20}$Ne in a magnetic field $B\approx 10^{17}\,$G by
utilizing the SKY3D code, suitably extended to include the magnetic field. Our
solutions of time-independent Hartree-Fock equations on a Cartesian
three-dimensional grid with a Skyrme interaction demonstrate a number of
interesting phenomena, such as level splitting in the magnetic field,
spontaneous rearrangement of energy levels, changes in the nuclear shape, etc.
The third chapter studies the pairing in low-density neutron matter in the
presence of a strong magnetic field. In particular, we find the limiting field
for the destruction of the superfluidity of neutrons in the crust and outer
core of magnetars. This field is density-dependent but is generally of the
order of $B\geq 10^{17}\,$G. The phase diagram of spin-polarized neutron matter
is constructed in the case where only the BCS phase is allowed along with the
(spin-polarized) normal phase.


  Presented here are algorithms for converting between (decimal)
scientific-notation and (binary) IEEE-754 double-precision floating-point
numbers. By employing a rounding integer quotient operation these algorithms
are much simpler than those previously published. The values are stable under
repeated conversions between the formats. Unlike Java-1.8, the scientific
representations generated use only the minimum number of mantissa digits needed
to convert back to the original binary values.


  I review in a schematic way the current status of indirect searches for Dark
Matter: I list the main relevant experimental results of the recent years and I
discuss the excitements and disappointments that their phenomenological
interpretations in terms of almost-standard annihilating Dark Matter have
brought along. I then try to individuate the main directions which have emerged
from the recent very intense model-building activity. In passing, I list the
main sources of uncertainties that affect this kind of searches.


  We describe a new regime of magnetotransport in two dimensional electron
systems in the presence of a narrow potential barrier imposed by external
gates. In such systems, the Landau level states, confined to the barrier region
in strong magnetic fields, undergo a deconfinement transition as the field is
lowered. We present transport measurements showing Shubnikov-de Haas (SdH)
oscillations which, in the unipolar regime, abruptly disappear when the
strength of the magnetic field is reduced below a certain critical value. This
behavior is explained by a semiclassical analysis of the transformation of
closed cyclotron orbits into open, deconfined trajectories. Comparison to
SdH-type resonances in the local density of states is presented.


  We synthesized a series of K0.8Fe2-xCoxSe2 samples with nominal compositions
0\leq x\leq 0.035 and investigated their physical properties. The results show
that the superconductivity in K0.8Fe2-xCoxSe2 is quenched down to 5 K by 0.5
at. % Co doping, the fastest quenching rate ever-reported. The role played here
by Co is in contrast with the one in FeAs based superconductors where Co
usually induces superconductivity from parent compounds. Such a rapid quenching
favors a localized 3d model against the itinerant one for iron pnictide
superconductors.


  Triangular systems with nonadditively separable unobserved heterogeneity
provide a theoretically appealing framework for the modelling of complex
structural relationships. However, they are not commonly used in practice due
to the need for exogenous variables with large support for identification, the
curse of dimensionality in estimation, and the lack of inferential tools. This
paper introduces two classes of semiparametric nonseparable triangular models
that address these limitations. They are based on distribution and quantile
regression modelling of the reduced form conditional distributions of the
endogenous variables. We show that average, distribution and quantile
structural functions are identified in these systems through a control function
approach that does not require a large support condition. We propose a
computationally attractive three-stage procedure to estimate the structural
functions where the first two stages consist of quantile or distribution
regressions. We provide asymptotic theory and uniform inference methods for
each stage. In particular, we derive functional central limit theorems and
bootstrap functional central limit theorems for the distribution regression
estimators of the structural functions. These results establish the validity of
the bootstrap for three-stage estimators of structural functions, and lead to
simple inference algorithms. We illustrate the implementation and applicability
of all our methods with numerical simulations and an empirical application to
demand analysis.


  We have studied the transport properties of LaTiO3/SrTiO3 (LTO/STO)
heterostructures. In spite of 2D growth observed in reflection high energy
electron diffraction, Transmission Electron Microscopy images revealed that the
samples tend to amorphize. Still, we observe that the structures are
conducting, and some of them exhibit high conductance and/or superconductivity.
We established that conductivity arises mainly on the STO side of the
interface, and shows all the signs of the 2-dimensional electron gas usually
observed at interfaces between SrTiO3 and LaTiO3 or LaAlO3, including the
presence of two electron bands and tunability with a gate voltage. Analysis of
magnetoresistance (MR) and superconductivity indicates presence of a spatial
fluctuations of the electronic properties in our samples. That can explain the
observed quasilinear out-of-plane MR, as well as various features of the
in-plane MR and the observed superconductivity.


  We realized a potential energy gradient - a ramp - for indirect excitons
using a shaped electrode at constant voltage. We studied transport of indirect
excitons along the ramp and observed that the exciton transport distance
increases with increasing density and temperature.


  We provide a hand-checkable proof for Lemma 4.9 in the paper "Logical limit
laws for minor-closed classes of graphs" by Heinig, Muller, Noy and Taraz.


  Quantum repeaters with multiple quantum memories provide high throughput, low
latency, and high fidelity quantum state (qubit) transfer over long distances.
However, conventional quantum repeater protocols require full connections among
the multiple quantum memories in a repeater node, which is technically
challenging. Here, we propose a quantum repeater protocol based on backward
propagating photon emission and absorption, where the quantum memories are
multiplexed in the time-domain to speed up a single transmission channel
without requiring full connectivity, drastically facilitating physical
implementation. Although the protocol is described with nitrogen-vacancy (NV)
centers in diamond, it is applicable to various physical systems and opens up
the possibility of high-speed high-fidelity quantum networks for distributed
quantum computation and quantum Internet.


  In the deep learning era, improving the neural network performance in jet
physics is a rewarding task as it directly contributes to more accurate physics
measurements at the LHC. Recent research has proposed various network designs
in consideration of the full Lorentz symmetry, but its benefit is still not
systematically asserted, given that there remain many successful networks
without taking it into account. We conduct a detailed study on the
Lorentz-symmetric design. We propose two generalized approaches for modifying a
network - these methods are experimented on Particle Flow Network, ParticleNet,
and LorentzNet, and exhibit a general performance gain. We also reveal that the
notable improvement attributed to the "pairwise mass" feature in the network is
due to its introduction of a structure that fully complies with Lorentz
symmetry. We confirm that Lorentz-symmetry preservation serves as a strong
inductive bias of jet physics, hence calling for attention to such general
recipes in future network designs.


  In this article we consider a cascaded taxis model for two proliferating and
degrading species which thrive on the same nutrient but orient their movement
according to different schemes. In particular, we assume the first group, the
foragers, to orient their movement directly along an increasing gradient of the
food density, while the second group, the exploiters, instead track higher
densities of the forager group. Specifically, we will investigate an initial
boundary-value problem for a prototypical forager-exploiter model of the form
\begin{align*} \left\{ \begin{array}{r@{\,}c@{\,}l@{\quad
}l@{\quad}l@{\quad}l@{\,}c} u_{t}&=&\Delta u-\nabla\cdot\big(u\nabla
w\big)+f(u),\ &x\in\Omega,& t>0,\\ v_{t}&=&\Delta v-\nabla\cdot\big(v\nabla
u\big)+g(v),\ &x\in\Omega,& t>0,\\ w_{t}&=&\Delta w-(u+v)w-\mu w+r(x,t),\
&x\in\Omega,& t>0, \end{array}\right. \end{align*}%} in a smoothly bounded
domain $\Omega\subset\mathbb{R}^2$, where $\mu\geq 0$, $r\in\
C^1(\bar{\Omega}\times[0,\infty))\cap
L^\infty\!\left(\Omega\times(0,\infty)\right)$ is nonnegative and the functions
$f,g\in C^1\!\left([0,\infty)\right)$ are assumed to satisfy $f(0)\geq0$,
$g(0)\geq0$ as well as $$-k_f s^{\alpha} -l_f\leq f(s)\leq -K_f s^\alpha+L_f\
\text{ and }\ -k_g s^\beta -l_g\leq g(s)\leq -K_g s^\beta+L_g\quad\text{for
}s\geq0,$$ respectively, with constants $\alpha,\beta>1$, $k_f,K_f,k_g,K_g>0$
and $l_f,L_f,l_g,L_g\geq0$ and $\alpha,\beta>1$.
  Assuming that $\alpha>1+\sqrt{2}$,
$\min\{\alpha,\beta\}>\frac{\alpha+1}{\alpha-1}$ and that $r$ satisfies certain
structural conditions we establish the global solvability of this system with
respect to a suitable generalized solution concept and then, for the more
restrictive case of $\alpha,\beta>1+\sqrt{2}$ and $\mu>0$, investigate an
eventual regularity effect driven by the decay of the nutrient density $w$.


  We define a very general notion of regularity for functions taking values in
an alternative real $*$-algebra. Over Clifford numbers, this notion subsumes
the well-established notions of monogenic function and slice-monogenic
function. Over quaternions, in addition to subsuming the notions of
Fueter-regular function and of slice-regular function, it gives rise to an
entirely new theory, which we develop in some detail.


  The present work is devoted to an extension of the well-known Ehrling
inequalities, which quantitatively characterize compact embeddings of function
spaces, to more general operators. Firstly, a modified notion of continuity for
linear operators, named \emph{Ehrling continuity} and inspired by the classical
Ehrling inequality, is introduced, and then, a necessary and sufficient
condition for Ehrling continuity is provided via arguments based on general
topology. Secondly, general completely continuous operators between normed
spaces are characterized in terms of (generalized) Ehrling type inequalities.
To this end, the well-known local metrization of the weak topology (so to
speak, a \emph{very weak norm}) plays a crucial role. Thanks to these results,
a universal relation is observed among complete continuity, the very weak norm
and generalized Ehrling type inequality.


  Measurements of the production of muons from heavy-flavour hadron decays at
forward rapidity ($2.5 < y < 4.0$) in Pb--Pb collisions at $\sqrt{s_{\rm NN}} =
2.76$ and 5.02 TeV with the ALICE detector are presented along with the $R_{\rm
AA}$ measurements in different centrality intervals as a function of transverse
momentum, $p_{\rm T}$. Results of the measured $R_{\rm AA}$ at both energies
are shown and are compared to the different model predictions.


  The phase space of $N$ damped linear oscillators is endowed with a bilinear
map under which the evolution operator is symmetric. This analog of
self-adjointness allows properties familiar from conservative systems to be
recovered, e.g., eigenvectors are "orthogonal" under the bilinear map and obey
sum rules, initial-value problems are readily solved and perturbation theory
applies to the_complex_ eigenvalues. These concepts are conveniently
represented in a biorthogonal basis.


  We consider the linear stochastic wave equation with spatially homogenous
Gaussian noise, which is fractional in time with index $H>1/2$. We show that
the necessary and sufficient condition for the existence of the solution is a
relaxation of the condition obtained in \cite{dalang99}, when the noise is
white in time. Under this condition, we show that the solution is
$L^2(\Omega)$-continuous. Similar results are obtained for the heat equation.
Unlike the white noise case, the necessary and sufficient condition for the
existence of the solution in the case of the heat equation is {\em different}
(and more general) than the one obtained for the wave equation.


  We study the role of non-adiabatic Holstein electron-phonon coupling on the
neutral-ionic phase transition of charge transfer crystals which can be tuned
from continuous to discontinuous, using exact numerical diagonalization. The
variation of electronic properties through the transition is smoothed by
nonadiabaticity. Lattice properties are strongly affected, and we observe both
squeezing and antisqueezing, depending on details of the adiabatic potentials,
and identify the quantum uncertainty of the phonons as the most sensitive
measure of nonadiabaticity. The adiabatic limit is regular for a continuous
transition but turns out completely inadequate near a discontinuous transition.
The relevance of coherent state approaches is assessed critically.


  We obtain spinning boson star solutions and hairy black holes with
synchronised hair in the Einstein-Klein-Gordon model, wherein the scalar field
is massive, complex and with a non-minimal coupling to the Ricci scalar. The
existence of these hairy black holes in this model provides yet another
manifestation of the universality of the synchronisation mechanism to endow
spinning black holes with hair. We study the variation of the physical
properties of the boson stars and hairy black holes with the coupling parameter
between the scalar field and the curvature, showing that they are,
qualitatively, identical to those in the minimally coupled case. By discussing
the conformal transformation to the Einstein frame, we argue that the solutions
herein provide new rotating boson star and hairy black hole solutions in the
minimally coupled theory, with a particular potential, and that no spherically
symmetric hairy black hole solutions exist in the non-minimally coupled theory,
under a condition of conformal regularity.


  In this paper, we prove the problem of stabbing a set of disjoint bends by a
convex stabber to be NP-hard. We also consider the optimization version of the
convex stabber problem and prove this problem to be APX-hard for sets of line
segments.


  We use Faraday rotation measurements from the latest catalog LoTSS DR2 from
LOFAR to probe intergalactic magnetic fields. To identify the extragalactic
component of the observed rotation measure (RM) we use two different
techniques: residual rotation measure (RRM) and close radio pairs. For the RRM
approach, we conclude that, despite smaller measurement errors in the LOFAR
data, robust and conservative treatment of the systematic uncertainties in the
Galactic contribution to RM results in the constraint on a homogeneous
volume-filling magnetic field at the level 2.4 nG, slightly weaker than
previous constraints from NVSS data, and does not allow to probe the presence
of over-magnetized bubbles predicted by the AGN feedback model of the
IllustrisTNG. Analyzing close radio pairs we found that in only 0.5% of our
mock realizations of observed data, the expected contribution from the
over-magnetized bubbles does not exceed LoTSS DR2 data.


  Many real networks are complex and have power-law vertex degree distribution,
short diameter, and high clustering. We analyze the network model based on
thresholding of the summed vertex weights, which belongs to the class of
networks proposed by Caldarelli et al. (2002). Power-law degree distributions,
particularly with the dynamically stable scaling exponent 2, realistic
clustering, and short path lengths are produced for many types of weight
distributions. Thresholding mechanisms can underlie a family of real complex
networks that is characterized by cooperativeness and the baseline scaling
exponent 2. It contrasts with the class of growth models with preferential
attachment, which is marked by competitiveness and baseline scaling exponent 3.


  Skyrmions are present in many models of electroweak symmetry breaking where
the Higgs is a pseudo-Goldstone boson of some strongly interacting sector. They
are stable, composite objects whose mass lies in the range 10-100 TeV and can
be naturally abundant in the universe due to their small annihilation
cross-section. They represent therefore good dark matter candidates. We show
however in this work that the lightest skyrmion states are electrically charged
in most of the popular little Higgs models, and hence should have been directly
or indirectly observed in nature already. The charge of the skyrmion under the
electroweak gauge group is computed in a model-independent way and is related
to the presence of anomalies in the underlying theory via the
Wess-Zumino-Witten term.


  We construct a hyperbolic attractor of renormalization of bi-cubic circle
maps with bounded combinatorics, with a codimension-two stable foliation.


  While deep reinforcement learning techniques have led to agents that are
successfully able to learn to perform a number of tasks that had been
previously unlearnable, these techniques are still susceptible to the
longstanding problem of reward sparsity. This is especially true for tasks such
as training an agent to play StarCraft II, a real-time strategy game where
reward is only given at the end of a game which is usually very long. While
this problem can be addressed through reward shaping, such approaches typically
require a human expert with specialized knowledge. Inspired by the vision of
enabling reward shaping through the more-accessible paradigm of
natural-language narration, we develop a technique that can provide the
benefits of reward shaping using natural language commands. Our
narration-guided RL agent projects sequences of natural-language commands into
the same high-dimensional representation space as corresponding goal states. We
show that we can get improved performance with our method compared to
traditional reward-shaping approaches. Additionally, we demonstrate the ability
of our method to generalize to unseen natural-language commands.


  We propose fast O(N) preconditioning, where N is the number of gridpoints on
the prediction horizon, for iterative solution of (non)-linear systems
appearing in model predictive control methods such as forward-difference
Newton-Krylov methods. The Continuation/GMRES method for nonlinear model
predictive control, suggested by T. Ohtsuka in 2004, is a specific application
of the Newton-Krylov method, which uses the GMRES iterative algorithm to solve
a forward difference approximation of the optimality equations on every time
step.


  Dynamic mode decomposition (DMD) is an emerging methodology that has recently
attracted computational scientists working on nonintrusive reduced order
modeling. One of the major strengths that DMD possesses is having ground
theoretical roots from the Koopman approximation theory. Indeed, DMD may be
viewed as the data-driven realization of the famous Koopman operator.
Nonetheless, the stable implementation of DMD incurs computing the singular
value decomposition of the input data matrix. This, in turn, makes the process
computationally demanding for high dimensional systems. In order to alleviate
this burden, we develop a framework based on sketching methods, wherein a
sketch of a matrix is simply another matrix which is significantly smaller, but
still sufficiently approximates the original system. Such sketching or
embedding is performed by applying random transformations, with certain
properties, on the input matrix to yield a compressed version of the initial
system. Hence, many of the expensive computations can be carried out on the
smaller matrix, thereby accelerating the solution of the original problem. We
conduct numerical experiments conducted using the spherical shallow water
equations as a prototypical model in the context of geophysical flows. The
performance of several sketching approaches is evaluated for capturing the
range and co-range of the data matrix. The proposed sketching-based framework
can accelerate various portions of the DMD algorithm, compared to classical
methods that operate directly on the raw input data. This eventually leads to
substantial computational gains that are vital for digital twinning of high
dimensional systems.


  Carbon spectral features are ubiquitous in the ultraviolet (UV) and
far-infrared (FIR) spectra of galaxies in the epoch of reionization (EoR). We
probe the ionized carbon content of a blue compact dwarf galaxy Pox 186 using
the UV, optical, mid-infrared and FIR data taken with telescopes in space
(Hubble, Spitzer, Herschel) and on the ground (Gemini). This local
(z~0.0040705) galaxy is likely an analogue of EoR galaxies, as revealed by its
extreme FIR emission line ratio, [OIII] 88/[CII] 157 (>10). The UV spectra
reveal extreme CIII] 1907, 1909 emission with the strongest equivalent width
(EW) = 35.85 $\pm$ 0.73 \AA detected so far in the local (z~0) Universe, a
relatively strong CIV 1548, 1550 emission with EW = 7.95 $\pm$0.45\AA, but no
He II 1640 detection. Several scenarios are explored to explain the high EW of
carbon lines, including high effective temperature, high carbon-to-oxygen
ratio, slope and upper mass of top-heavy initial mass function, hard ionizing
radiation and in-homogeneous dust distribution. Both CIII] and CIV line
profiles are broadened with respect to the OIII] 1660 emission line. Each
emission line of CIV 1548, 1550 shows the most distinct double-peak structure
ever detected, which we model via two scenarios, firstly a double-peaked
profile that might emerge from resonant scattering and secondly, a single
nebular emission line along with a weaker interstellar absorption. The study
demonstrates that galaxies with extreme FIR emission line ratio may also show
extreme UV properties, hence paving a promising avenue of using FIR+UV in the
local (via HST+Herschel/SOFIA) and distant (via JWST+ALMA) Universe for
unveiling the mysteries of the EoR.


  We compute the large-$m_t$ contributions to the $Zb\overline b$ vertex in the
Standard Model non-perturbatively using both the $1/\nc$ and the $1/\nf$
expansions. Triviality and its consequences for the perturbative result are
systematically analyzed. In particular, we point out that the effect of
triviality is already important at the two-loop level for a heavy Higgs
($600\gev<M_H<1\tev$) even when the top mass is below $200\gev$.


  We show that the closed-form monotone solution linking two different vacuum
states, for the exterior Yang--Mills wave equation over the extremal
Reissner--Nordstr\"{o}m spacetime found in a recent work of Bizo\'{n} and Kahl,
is the unique solution to an associated domain-wall type energy minimization
problem. We also derive the accompanying interior Yang--Mills wave equation
within the same formalism. We obtain a few more closed-form solutions, regular
and singular, among other solutions of oscillatory behavior, and discuss
several interesting features of the solutions based on some energy
consideration.


  The human immune system protects the human body against various pathogens
like e.g. biological viruses and bacteria. Artificial immune systems reuse the
architecture, organization, and workflows of the human immune system for
various problems in computer science. In the network security, the artificial
immune system is used to secure a network and its nodes against intrusions like
viruses, worms, and trojans. However, these approaches are far away from
production where they are academic proof-of-concept implementations or use only
a small part to protect against a certain intrusion. This article discusses the
required steps to bring artificial immune systems into production in the
network security domain. It furthermore figures out the challenges and provides
the description and results of the prototype of an artificial immune system,
which is SANA called.


  We formalize a multivariate quantifier elimination (QE) algorithm in the
theorem prover Isabelle/HOL. Our algorithm is complete, in that it is able to
reduce any quantified formula in the first-order logic of real arithmetic to a
logically equivalent quantifier-free formula. The algorithm we formalize is a
hybrid mixture of Tarski's original QE algorithm and the Ben-Or, Kozen, and
Reif algorithm, and it is the first complete multivariate QE algorithm
formalized in Isabelle/HOL.


  We advocate the step change in properties of discrete $d$-level quantum
systems, between $d=2$ and $d\geq 3$. Qubit systems, or multipartite systems
containing qubit subsystem, are exceptional in their relative simplicity. One
faces a step in complexity in valuating measures of quantum correlations for
qutrits and then other higher dimensional qudits. There is a growing number of
arguments leading to such conclusion: recently found no-go theorem for
generalization of the Peres-Horodecki's PPT criterion \cite{sko}, change in
geometry of state spaces of qubit and higher degree qudits (the so called
'generalized Bloch ball' is not a ball anymore), restricted possibilities for
diagonalization of correlation matrices for bipartite systems, more difficult
way for handling the set of relevant families of orthogonal projectors.


  Addressing pedestrian safety at intersections is one of the paramount
concerns in the field of transportation research, driven by the urgency of
reducing traffic-related injuries and fatalities. With advances in computer
vision technologies and predictive models, the pursuit of developing real-time
proactive protection systems is increasingly recognized as vital to improving
pedestrian safety at intersections. The core of these protection systems lies
in the prediction-based evaluation of pedestrian's potential risks, which plays
a significant role in preventing the occurrence of accidents. The major
challenges in the current prediction-based potential risk evaluation research
can be summarized into three aspects: the inadequate progress in creating a
real-time framework for the evaluation of pedestrian's potential risks, the
absence of accurate and explainable safety indicators that can represent the
potential risk, and the lack of tailor-made evaluation criteria specifically
for each category of pedestrians. To address these research challenges, in this
study, a framework with computer vision technologies and predictive models is
developed to evaluate the potential risk of pedestrians in real time. Integral
to this framework is a novel surrogate safety measure, the Predicted
Post-Encroachment Time (P-PET), derived from deep learning models capable to
predict the arrival time of pedestrians and vehicles at intersections. To
further improve the effectiveness and reliability of pedestrian risk
evaluation, we classify pedestrians into distinct categories and apply specific
evaluation criteria for each group. The results demonstrate the framework's
ability to effectively identify potential risks through the use of P-PET,
indicating its feasibility for real-time applications and its improved
performance in risk evaluation across different categories of pedestrians.


  Differential privacy is the gold standard in the problem of privacy
preserving data analysis, which is crucial in a wide range of disciplines.
Vertex colouring is one of the most fundamental questions about a graph. In
this paper, we study the vertex colouring problem in the differentially private
setting.
  To be edge-differentially private, a colouring algorithm needs to be
defective: a colouring is d-defective if a vertex can share a colour with at
most d of its neighbours. Without defectiveness, the only differentially
private colouring algorithm needs to assign n different colours to the n
different vertices. We show the following lower bound for the defectiveness: a
differentially private c-edge colouring algorithm of a graph of maximum degree
{\Delta} > 0 has defectiveness at least d = {\Omega} (log n / (log c+log
{\Delta})).
  We also present an {\epsilon}-differentially private algorithm to {\Theta} (
{\Delta} / log n + 1 / {\epsilon})-colour a graph with defectiveness at most
{\Theta}(log n).


  It is well known that in a neutrally-stratified turbulent flow in a deep
constant-stress layer above a flat surface, the variation of the mean velocity
with respect to the distance from the surface obeys the logarithmic law (the
so-called ``law-of-the-wall''). More recently, the same logarithmic law has
been found also in the presence of non flat surfaces. It governs the dynamics
of the mean velocity (i.e. all the smaller scales are averaged out) and
involves renormalized effective parameters. Recent numerical simulations
analyzed by the authors of the present Letter show that a more intrinsic
logarithmic shape actually takes place also at smaller scales. Such a
generalized law-of-the-wall involves effective parameters smoothly depending on
the position along the underlying topography. Here, we present wind tunnel
experimental evidence confirming and corroborating this new-found property. New
results and their physical interpretation are also presented and discussed.


  Different schemes for the treatment of long-ranged electrostatic interactions
will be examined for water simulations using the polarizable fluctuating charge
potential. Several different methods are compared, including Ewald sums,
potential shifting, spherical truncation and reaction field corrections. For
liquid water, properties such as the energy, pressure, dynamics and structure
are more sensitive to the treatment of the long-ranged interactions with
polarizable than with non-polarizable potentials.


  Scalable frames are frames with the property that the frame vectors can be
rescaled resulting in tight frames. However, if a frame is not scalable, one
has to aim for an approximate procedure. For this, in this paper we introduce
three novel quantitative measures of the closeness to scalability for frames in
finite dimensional real Euclidean spaces. Besides the natural measure of
scalability given by the distance of a frame to the set of scalable frames,
another measure is obtained by optimizing a quadratic functional, while the
third is given by the volume of the ellipsoid of minimal volume containing the
symmetrized frame. After proving that these measures are equivalent in a
certain sense, we establish bounds on the probability of a randomly selected
frame to be scalable. In the process, we also derive new necessary and
sufficient conditions for a frame to be scalable.


  We consider \textit{anytime} linear prediction in the common machine learning
setting, where features are in groups that have costs. We achieve anytime (or
interruptible) predictions by sequencing the computation of feature groups and
reporting results using the computed features at interruption. We extend
Orthogonal Matching Pursuit (OMP) and Forward Regression (FR) to learn the
sequencing greedily under this group setting with costs. We theoretically
guarantee that our algorithms achieve near-optimal linear predictions at each
budget when a feature group is chosen. With a novel analysis of OMP, we improve
its theoretical bound to the same strength as that of FR. In addition, we
develop a novel algorithm that consumes cost $4B$ to approximate the optimal
performance of \textit{any} cost $B$, and prove that with cost less than $4B$,
such an approximation is impossible. To our knowledge, these are the first
anytime bounds at \textit{all} budgets. We test our algorithms on two
real-world data-sets and evaluate them in terms of anytime linear prediction
performance against cost-weighted Group Lasso and alternative greedy
algorithms.


  Bosonic encoding of quantum information into harmonic oscillators is a
hardware efficient approach to battle noise. In this regard,
oscillator-to-oscillator codes not only provide an additional opportunity in
bosonic encoding, but also extend the applicability of error correction to
continuous-variable states ubiquitous in quantum sensing and communication. In
this work, we derive the optimal oscillator-to-oscillator codes among the
general family of Gottesman-Kitaev-Preskill (GKP)-stablizer codes for
homogeneous noise. We prove that an arbitrary GKP-stabilizer code can be
reduced to a generalized GKP two-mode-squeezing (TMS) code. The optimal
encoding to minimize the geometric mean error can be constructed from GKP-TMS
codes with an optimized GKP lattice and TMS gains. For single-mode data and
ancilla, this optimal code design problem can be efficiently solved, and we
further provide numerical evidence that a hexagonal GKP lattice is optimal and
strictly better than the previously adopted square lattice. For the multimode
case, general GKP lattice optimization is challenging. In the two-mode data and
ancilla case, we identify the D4 lattice -- a 4-dimensional dense-packing
lattice -- to be superior to a product of lower dimensional lattices. As a
by-product, the code reduction allows us to prove a universal
no-threshold-theorem for arbitrary oscillators-to-oscillators codes based on
Gaussian encoding, even when the ancilla are not GKP states.


  This work is to continue the development of the general model, Multi-Average
Ion Collisional-Radiative Model (MAICRM), to calculate the plasma spectral
properties of hot dense plasmas. In this model, an average ion is used to
characterize the average orbital occupations and the total populations of the
configurations within a single charge state. The orbital occupations and
population of the average ion are obtained by solving two sets of rate
equations sequentially and iteratively. The calculated spectra of Xe and Au
plasmas under different plasma conditions are in good agreement with the
DCA/SCA calculations while the computational cost is much lower.


  We in this paper study the nonexpansive operators equipped with arbitrary
metric and investigate the connections between firm nonexpansiveness,
cocoerciveness and averagedness. The convergence of the associated fixed-point
iterations is discussed with particular focus on the case of degenerate metric,
since the degeneracy is often encountered when reformulating many existing
first-order operator splitting algorithms as a metric resolvent. This work
paves a way for analyzing the generalized proximal point algorithm with a
non-trivial relaxation step and degenerate metric.


  We establish new sufficient conditions for the existence of weak Besicovitch
quasiperiodic solutions for natural Lagrangian system on Riemannian manifold
with time-quasiperiodic force function


  The photometry of eclipse white-light (W-L) images showing a moving blob is
interpreted for the first time together with observations from space with the
PRoject for On Board Autonomy (PROBA-2) mission (ESA). An off-limb event seen
with great details in W-L was analyzed with the SWAP imager (Sun Watcher using
Active pixel system detector and image Processing) working in the EUV near 174
A. It is an elongated plasma blob structure of 25 Mm diameter moving above the
E-limb with coronal loops under. Summed and co-aligned SWAP images are
evaluated using a 20 hours sequence, in addition to the July 11, 2010 eclipse
W-L images taken from several sites. The Atmospheric Imaging Assembly (AIA)
instruments on board the Solar Dynamical Observatory (SDO) recorded the event
suggesting a magnetic reconnection near a high neutral point; accordingly, we
also call it a magnetic plasmoid. The measured proper motion of the blob shows
a velocity up to 12 km s^-1. Electron densities of the isolated condensation
(cloud or blob or plasmoid) is photometrically evaluated. The typical value is
10^8 cm^-3 at r=1.7 R, superposed on a background corona of 10^7 cm^-3 density.
The mass of the cloud near its maximum brightness is found to be 1.6x10^13 gr
which is typically 0.6x10^-4 of the overall mass of the corona. From the
extrapolated magnetic field the cloud evolves inside a rather broad open region
but decelerates, after reaching its maximum brightness. The influence of such
small events for supplying material to the ubiquitous slow wind is noticed. A
precise evaluation of the EUV photometric data after accurately removing the
stray light, suggests an interpretation of the weak 174 A radiation of the
cloud as due to resonance scattering in the Fe IX/X lines.


  It is known that if $x\in[0,1]$ is polynomial time random (i.e. no polynomial
time computable martingale succeeds on the binary fractional expansion of $x$)
then $x$ is normal in any integer base greater than one. We show that if $x$ is
polynomial time random and $\beta>1$ is Pisot, then $x$ is "normal in base
$\beta$", in the sense that the sequence $(x\beta^n)_{n\in\mathbb{N}}$ is
uniformly distributed modulo one. We work with the notion of "$P$-martingale",
a generalization of martingales to non-uniform distributions, and show that a
sequence over a finite alphabet is distributed according to an irreducible,
invariant Markov measure~$P$ if an only if no $P$-martingale whose betting
factors are computed by a deterministic finite automaton succeeds on it. This
is a generalization of Schnorr and Stimm's characterization of normal sequences
in integer bases. Our results use tools and techniques from symbolic dynamics,
together with automata theory and algorithmic randomness.


  Solar arrays are structures which are connected to satellites; during launch,
they are in a folded position and submitted to high vibrations. In order to
save mass, the flexibility of the panels is not negligible and they may strike
each other; this may damage the structure. To prevent this, rubber snubbers are
mounted at well chosen points of the structure; a prestress is applied to the
snubber; but it is quite difficult to check the amount of prestress and the
snubber may act only on one side; they will be modeled as one sided springs
(see figure 2). In this article, some analysis for responses (displacements) in
both time and frequency domains for a clamped-clamped Euler-Bernoulli beam
model with a spring are presented. This spring can be unilateral or bilateral
fixed at a point. The mounting (beam +spring) is fixed on a rigid support which
has a sinusoidal motion of constant frequency. The system is also studied in
the frequency domain by sweeping frequencies between two fixed values, in order
to save the maximum of displacements corresponding to each frequency. Numerical
results are compared with exact solutions in particular cases which already
exist in the literature. On the other hand, a numerical and theoretical
investigation of nonlinear normal mode (NNM) can be a new method to describe
nonlinear behaviors, this work is in progress.


  Systems, technologies, protocols, and infrastructures all face
interoperability challenges. It is among the most crucial parameters to give
real-world effectiveness. Organizations that achieve interoperability will be
able to identify, prevent, and provide appropriate protection on an
international scale, which can be relied upon. This paper aims to explain how
future technologies such as 6G mobile communication, Internet of Everything
(IoE), Artificial Intelligence (AI), and Smart Contract embedded WPA3
protocol-based WiFi-8 can work together to prevent known attack vectors and
provide protection against zero-day attacks, thus offering intelligent
solutions for smart cities. The phrase zero-day refers to an attack that occurs
on the day zero of the vulnerability's disclosure to the public or vendor.
Existing systems require an extra layer of security. In the security world,
interoperability enables disparate security solutions and systems to
collaborate seamlessly. AI improves cybersecurity by enabling improved
capabilities for detecting, responding, and preventing zero-day attacks. When
interoperability and Explainable Artificial Intelligence (XAI) are integrated
into cybersecurity, they form a strong protection against zero-day assaults.
Additionally, we evaluate a couple of parameters based on the accuracy and time
required for efficiently analyzing attack patterns and anomalies.


  Since the 1974 paper by Peskine and Szpiro, liaison theory via complete
intersections, and more generally via Gorenstein varieties, has become a
standard tool kit in commutative algebra and algebraic geometry, allowing to
compare algebraic features of linked varieties. In this paper we develop a
liaison theory via quasi-Gorenstein varieties, a much broader class than
Gorenstein varieties: it is not misleading to think that quasi-Gorenstein rings
are to Gorenstein rings as manifolds are to spheres. As applications, we derive
a connectedness property of quasi-Gorenstein subspace arrangements generalizing
previous results by Benedetti and the second author, and we deduce the
classical topological Lefschetz duality via the Stanley-Reisner correspondence.


  To describe the crossover from the bulk BCS superconductivity to a
fluctuation-dominated regime in ultrasmall metallic grains, new order
parameters and correlation functions, such as ``parity gap'' and ``pair-mixing
correlation function'', have been recently introduced. In this paper, we
discuss the small-grain behaviour of the Penrose-Onsager-Yang off-diagonal
long-range order (ODLRO) parameter in a pseudo-spin representation. Relations
between the ODLRO parameter and those mentioned above are established through
analytical and numerical calculations.


  For an integer $n>2$, a rank-$n$ matroid is called an $n$-spike if it
consists of $n$ three-point lines through a common point such that, for all
$k\in\{1, 2, ..., n - 1\}$, the union of every set of $k$ of these lines has
rank $k+1$. Spikes are very special and important in matroid theory. In 2003 Wu
found the exact numbers of $n$-spikes over fields with 2, 3, 4, 5, 7 elements,
and the asymptotic values for larger finite fields. In this paper, we prove
that, for each prime number $p$, a $GF(p$) representable $n$-spike $M$ is only
representable on fields with characteristic $p$ provided that $n \ge 2p-1$.
Moreover, $M$ is uniquely representable over $GF(p)$.


  Autonomous agents are promising in applications such as intelligent
transportation and smart manufacturing, and scheduling of agents has to take
their inertial constraints into consideration. Most current researches require
the obedience of all agents, which is hard to achieve in non-dedicated systems
such as traffic intersections. In this article, we establish a minimax
framework for the scheduling of two inertially constrained agents with no
cooperation assumptions. Specifically, we first provide a unified and
sufficient representation for various types of situation information, and
define a state value function characterizing the agent's preference of states
under a given situation. Then, the minimax control policy along with the
calculation methods is proposed which optimizes the worst-case state value
function at each step, and the safety guarantee of the policy is also
presented. Furthermore, several generalizations are introduced on the
applicable scenarios of the proposed framework. Numerical simulations show that
the minimax control policy can reduce the largest scheduling cost by $13.4\%$
compared with queueing and following policies. Finally, the effects of decision
period, observation period and inertial constraints are also numerically
discussed.


  We solve four out of the six open problems concerning critical cardinalities
of topological diagonalization properties involving tau-covers, show that the
remaining two cardinals are equal, and give a consistency result concerning
this remaining cardinal. Consequently, 21 open problems concerning potential
implications between these properties are settled. We also give structural
results based on the combinatorial techniques.


  Using an approach to the Jacobian Conjecture by L.M. Dru\.zkowski and K.
Rusek 12], G. Gorni and G. Zampieri [19], and A.V. Yagzhev[27], we describe a
correspondence between finite dimensional symmetric algebras and homogeneous
tuples of elements of polynomial algebras. We show that this correspondence
closely relates Albert's problem [10, Problem 1.1], in classical ring theory
and the homogeneous dependence problem [13, page 145, Problem 7.1.5], in affine
algebraic geometry related to the Jacobian Conjecture. We demonstrate these
relations in concrete examples and formulate some open questions.


  We introduce a general multisummability theory of formal power series in
Carleman ultraholomorphic classes. The finitely many levels of summation are
determined by pairwise comparable, nonequivalent weight sequences admitting
nonzero proximate orders and whose growth indices are distinct. Thus, we extend
the powerful multisummability theory for finitely many Gevrey levels, developed
by J.-P. Ramis, J. \'Ecalle and W. Balser, among others. We provide both the
analytical and cohomological approaches, and obtain a reconstruction formula
for the multisum of a multisummable series by means of iterated generalized
Laplace-like operators.


  The pressure-induced structural phase transition in the intermediate-valence
compound CeNi has been investigated by X-ray and neutron powder diffraction
techniques. For the first time it is shown that the structure of the
pressure-induced CeNi phase (phases) can be described in terms of the Pnma
space group. Equations of state for CeNi on both sides of the phase transition
are derived and an approximate P-T phase diagram is suggested for P < 8 GPa and
T < 300 K. The observed Cmcm -> Pnma structural transition is analyzed using
density functional theory (DFT) calculations, which successfully reproduce the
ground state volume, the phase transition pressure, and the volume collapse
associated with the phase transition.


  I present here a pedagogical introduction to the works by Rashel Tublin and
Yan V. Fyodorov on random linear systems with quadratic constraints, using
tools from Random Matrix Theory and replicas. These notes illustrate and
complement the material presented at the Summer School organised within the
Puglia Summer Trimester 2023 in Bari (Italy). Consider a system of $M$ linear
equations in $N$ unknowns, $\sum_{j=1}^N A_{kj}x_j=b_k$ for $k=1,\ldots,M$,
subject to the constraint that the solutions live on the $N$-sphere,
$x_1^2+\ldots + x_N^2=N$. Assume that both the coefficients $A_{ij}$ and the
parameters $b_i$ be independent Gaussian random variables with zero mean. Using
two different approaches -- based on Random Matrix Theory and on a replica
calculation -- it is possible to compute whether a large linear system subject
to a quadratic constraint is typically solvable or not, as a function of the
ratio $\alpha=M/N$ and the variance $\sigma^2$ of the $b_i$'s. This is done by
defining a quadratic loss function $H({\bf
x})=\frac{1}{2}\sum_{k=1}^M\left[\sum_{j=1}^NA_{kj} x_j-b_k\right]^2$ and
computing the statistics of its minimal value on the sphere,
$E_{min}=\min_{||\bf x||^2=N}H({\bf x})$, which is zero if the system is
compatible, and larger than zero if it is incompatible. One finds that there
exists a compatibility threshold $0<\alpha_c<1$, such that systems with
$\alpha>\alpha_c$ are typically incompatible. This means that even weakly
under-complete linear systems could become typically incompatible if forced to
additionally obey a quadratic constraint.


  Most micro- and macro-expression spotting methods in untrimmed videos suffer
from the burden of video-wise collection and frame-wise annotation.
Weakly-supervised expression spotting (WES) based on video-level labels can
potentially mitigate the complexity of frame-level annotation while achieving
fine-grained frame-level spotting. However, we argue that existing
weakly-supervised methods are based on multiple instance learning (MIL)
involving inter-modality, inter-sample, and inter-task gaps. The inter-sample
gap is primarily from the sample distribution and duration. Therefore, we
propose a novel and simple WES framework, MC-WES, using multi-consistency
collaborative mechanisms that include modal-level saliency, video-level
distribution, label-level duration and segment-level feature consistency
strategies to implement fine frame-level spotting with only video-level labels
to alleviate the above gaps and merge prior knowledge. The modal-level saliency
consistency strategy focuses on capturing key correlations between raw images
and optical flow. The video-level distribution consistency strategy utilizes
the difference of sparsity in temporal distribution. The label-level duration
consistency strategy exploits the difference in the duration of facial muscles.
The segment-level feature consistency strategy emphasizes that features under
the same labels maintain similarity. Experimental results on three challenging
datasets -- CAS(ME)$^2$, CAS(ME)$^3$, and SAMM-LV -- demonstrate that MC-WES is
comparable to state-of-the-art fully-supervised methods.


  The orbital decay of a perturber within a larger system plays a key role in
the dynamics of many astrophysical systems -- from nuclear star clusters or
globular clusters in galaxies, to massive black holes in galactic nuclei, to
dwarf galaxy satellites within the dark matter halos of more massive galaxies.
For many decades, there have been various attempts to determine the underlying
physics and time-scales of the drag mechanism, ranging from the local dynamical
friction approach to descriptions based on the back-reaction of global modes
induced in the background system. We present ultra-high-resolution $N$-body
simulations of massive satellites orbiting a Milky Way-like galaxy (with $>
10^8$ particles), that appear to capture both the local "wake" and the global
"mode" induced in the primary halo. We address directly the mechanism of
orbital decay from the combined action of local and global perturbations and
specifically analyze where the bulk of the torque originates.


  The spin-torque in magnetic tunnel junctions possesses two components that
both depend on the applied voltage. Here, we develop a new method for the
accurate extraction of this bias-dependence from experiments over large voltage
ranges. We study several junctions with different magnetic layer structures of
the top electrode. Our results obtained on junctions with symmetric CoFeB
electrodes agree well with theoretical calculations. The bias-dependences of
asymmetric samples, with top electrodes containing NiFe, however, are twisted
compared to the quadratic form generally assumed. Our measurements reveal the
complexity of spin-torque mechanisms at large bias.


  The paradigmatic spin-boson model considers a spin degree of freedom
interacting with an environment typically constituted by a continuum of bosonic
modes. This ubiquitous model is of relevance in a number of physical systems
where, in general, one has neither control over the bosonic modes, nor the
ability to tune distinct interaction mechanisms. Despite this apparent lack of
control, we present a suitable transformation that approximately maps the
spin-boson dynamics into that of a tunable multiphoton Jaynes-Cummings model
undergoing dissipation. Interestingly, the latter model describes the coherent
interaction between a spin and a single bosonic mode via the simultaneous
exchange of n bosons per spin excitation. Resorting to the so-called reaction
coordinate method, we identify a relevant collective bosonic mode in the
environment which is then used to generate multiphoton interactions following
the proposed theoretical framework. Moreover, we show that spin-boson models
featuring structured environments can lead into non-Markovian multiphoton
Jaynes-Cummings dynamics. We discuss the validity of the proposed method
depending on the parameters and analyze its performance, which is supported by
numerical simulations. In this manner, the spin-boson model serves as a good
analog quantum simulator for the inspection and realization of multiphoton
Jaynes-Cummings models as well as the interplay of non-Markovian effects, and
thus, as a simulator of light-matter systems with tunable interaction
mechanisms.


  We calculate the real-time-correlation function of the
Sherrington-Kirkpatrick spin-glass model in a transverse field. Using a careful
analysis of the perturbative expansion of the functional-integral
representation, we derive the asymptotic form of the correlation function. In
contrast to the previous works, we find for large transverse field a power-law
decay of the correlation with time $t$ as $t^{-3/2}$ at zero temperature and
$t^{-2}$ at infinite temperature. At the small field region, we also find a
significant change in the correlation which comes from the structural
difference between two paramagnetic phases.


  A long-term spectroscopic and photometric survey of the most luminous and
massive stars in the vicinity of the super-massive black hole Sgr A* revealed
two new binaries; a long-period Ofpe/WN9 binary, GCIRS 16NE, with a modest
eccentricity of 0.3 and a period of 224 days and an eclipsing Wolf-Rayet binary
with a period of 2.3 days. Together with the already identified binary GCIRS
16SW, there are now three confirmed OB/WR binaries in the inner 0.2\,pc of the
Galactic Center. Using radial velocity change upper limits, we were able to
constrain the spectroscopic binary fraction in the Galactic Center to $F_{\rm
SB}=0.27^{+0.29}_{-0.19}$ at a confidence level of 95%, a massive binary
fraction similar to that observed in dense clusters. The fraction of eclipsing
binaries with photometric amplitudes $\Delta m>0.4$ is $F^{\rm GC}_{\rm
EB}=3\pm2%$, which is consistent with local OB star clusters ($F_{\rm EB}=1%$).
Overall the Galactic Center binary fraction seems to be close to the binary
fraction in comparable young clusters.


  Local and nonlocal differential resistance measurements on Hall bars defined
in AlO$_x$/KTaO$_3$ heterostructures show anomalous behavior that depends on
the crystal orientation and the applied back gate voltage. The local
differential resistance is asymmetric in the dc bias current, with an
antisymmetric component that grows with decreasing gate voltage. More
surprisingly, a large nonlocal differential resistance is observed that extends
between measurement probes that are separated by 100s of microns. The potential
source of this anomalous behavior is discussed.


  It is known that the anomalous Chern-Simons (CS) coupling of O$_p$-plane is
not consistent with the T-duality transformations. Compatibility of this
coupling with the T-duality requires the inclusion of couplings involving one
R-R field strength. In this paper we find such couplings at order $\alpha'^2$.
  By requiring the R-R and NS-NS gauge invariances, we first find all
independent couplings at order $\alpha'^2$. There are $1,\, 6,\,28,\,20,\,
19,\, 2$ couplings corresponding to the R-R field strengths $F^{(p-4)}$,
$\,F^{(p-2)}$, $\,F^{(p)}$, $\,F^{(p+2)}$, $\,F^{(p+4)}$ and $F^{(p+6)}$,
respectively. We then impose the T-duality constraint on these couplings and on
the CS coupling $C^{(p-3)}\wedge R\wedge R$ at order $\alpha'^2$ to fix their
corresponding coefficients. The T-duality constraint fixes all coefficients in
terms of the CS coefficient. They are fully consistent with the partial
couplings that have been already found in the literature by the S-matrix
method.


  We present the results of a survey to detect low-mass companions of UMa group
members, carried out in 2003-2006 with NACO at the ESO VLT. While many
extra-solar planets and planetary candidates have been found in close orbits
around stars by the radial velocity and the transit method, direct detections
at wider orbits are rare. The Ursa Major (UMa) group, a young stellar
association at an age of about 200-600 Myr and an average distance of 25 pc,
has not yet been addressed as a whole although its members represent a very
interesting sample to search for and characterize sub-stellar companions by
direct imaging. Our goal was to find or to provide detection limits on wide
sub-stellar companions around nearby UMa group members using high-resolution
imaging. We searched for faint companions around 20 UMa group members within 30
pc. The primaries were placed below a semi-transparent coronagraph, a rather
rarely used mode of NACO, to increase the dynamic range of the images. In most
cases, second epoch images of companion candidates were taken to check whether
they share common proper motion with the primary. Our coronagraphic images rule
out sub-stellar companions around the stars of the sample. A dynamical range of
typically 13-15 mag in the Ks band was achieved at separations beyond 3" from
the star. Candidates as faint as Ks ~ 20 were securely identified and measured.
The survey is most sensitive between separations of 100 and 200 au but only on
average because of the very different target distance. Field coverage reaches
about 650 au for the most distant targets. Most of the 200 candidates are
visible in two epochs. All of those were rejected being distant background
objects.


  The field-free spin-orbit torque induced 180{\deg} reorientation of
perpendicular magnetization is beneficial for the high performance magnetic
memory. The antiferromagnetic material (AFM) can provide higher operation speed
than the ferromagnetic counterpart. In this paper, we propose a trilayer
AFM/Insulator/Heavy Metal structure as the AFM memory device. We show that the
field-free switching of the AFM with perpendicular N\'eel vector can be
achieved by using two orthogonal currents, which provide the uniform
damping-like torque and stagger field-like torque, respectively. The reversible
switching can be obtained by reversing either current. A current density of
1.79 10^11A/m^2 is sufficient to induce the switching. In addition, the two
magnetic moments become noncollinear during the switching. This enables an
ultrafast switching within 40 picoseconds. The device and switching mechanism
proposed in this work offer a promising approach to deterministically switch
the AFM with perpendicular N\'eel vector. It can also stimulate the development
of ultrafast AFM-based MRAM.


  Leading finite temperature effects on the neutrino decoupling temperature in
the early Universe have been studied. We have incorporated modifications of the
dispersion relation and the phase space distribution due to the presence of
particles in the heat bath at temperature around MeV. Since both the expansion
rate of the Universe and the interaction rate of a neutrino are reduced by
finite temperature effects, it is necessary to calculate thermal corrections as
precisely as possible in order to find the net effect on the neutrino
decoupling temperature. We have performed such a calculation by using the
finite temperature field theory. It has been shown that the finite temperature
effects increase the neutrino decoupling temperature by 4.4%, the largest
contribution coming from the modification of the phase space due to the thermal
bath.