  The extended Bose-Hubbard model for a double-well potential with pair
tunneling is studied through both exact diagonalization and mean field theory
(MFT). When pair tunneling is strong enough, the ground state wavefunction
predicted by the MFT is complex and doubly degenerate while the quantum ground
state wavefunction is always real and unique. The time reversal symmetry is
spontaneously broken when the system transfers from the quantum ground state
into one of the mean field ground states upon a small perturbation. As the gap
between the lowest two levels decreases exponentially with particle number, the
required perturbation inducing the spontaneous symmetry breaking (SSB) is
infinitesimal for particle number of typical cold atom systems. The quantum
ground state is further analyzed with the Penrose-Onsager criterion, and is
found to be a fragmented condensate. The state also develops the pair
correlation and has non-vanishing pair order parameter instead of the
conventional single particle order parameter. When this model is generalized to
optical lattice, a pair superfluid can be generated. The mean field ground
state can be regarded as effective ground state in this simple model. The
detailed computation for this model enables us to offer an in-depth discussion
of the relation between SSB and effective ground state, giving a glimpse on how
nonlinearity arises in the SSB of a quantum system.


  We consider a superconformal quantum mechanical system which has been chosen
on the basis of a local BRST topological invariance. We suggest that it truly
leads to topological observables which we compute. The absences of a ground
state and of a mass gap are special features of this system.


  We present a theoretical analysis of electronic structure evolution in the
highly-mismatched dilute carbide group-IV alloy Ge$_{1-x}$C$_{x}$. For ordered
alloy supercells, we demonstrate that C incorporation strongly perturbs the
conduction band (CB) structure by driving hybridisation of $A_{1}$-symmetric
linear combinations of Ge states lying close in energy to the CB edge. This
leads, in the ultra-dilute limit, to the alloy CB edge being formed primarily
of an $A_{1}$-symmetric linear combination of the L-point CB edge states of the
Ge host matrix semiconductor. Our calculations describe the emergence of a
"quasi-direct" alloy band gap, which retains a significant admixture of
indirect Ge L-point CB edge character. We then analyse the evolution of the
electronic structure of realistic (large, disordered) Ge$_{1-x}$C$_{x}$ alloy
supercells for C compositions up to $x = 2$%. We show that short-range alloy
disorder introduces a distribution of localised states at energies below the Ge
CB edge, with these states acquiring minimal direct ($\Gamma$) character. Our
calculations demonstrate strong intrinsic inhomogeneous energy broadening of
the CB edge Bloch character, driven by hybridisation between Ge host matrix and
C-related localised states. The trends identified by our calculations are
markedly different to those expected based on a recently proposed
interpretation of the CB structure based on the band anti-crossing model. The
implications of our findings for device applications are discussed.


  We study the convergence of the Augmented Decomposition Algorithm (ADA)
proposed in [32] for solving multi-block separable convex minimization problems
subject to linear constraints. We show that the global convergence rate of the
exact ADA is o(1/k) under the assumption that there exists a saddle point. We
consider the inexact Augmented Decomposition Algorithm (iADA) and establish
global and local convergence results under some mild assumptions, by providing
a stability result for the maximal monotone operator T associated with the
perturbation from both primal and dual perspectives. This result implies the
local linear convergence of the inexact ADA for many applications such as the
lasso, total variation reconstruction, exchange problem and many other problems
from statistics, machine learning and engineering with l1 regularization.


  While load balancing in distributed-memory computing has been well-studied,
we present an innovative approach to this problem: a unified, reduced-order
model that combines three key components to describe "work" in a distributed
system: computation, communication, and memory. Our model enables an optimizer
to explore complex tradeoffs in task placement, such as increased parallelism
at the expense of data replication, which increases memory usage. We propose a
fully distributed, heuristic-based load balancing optimization algorithm, and
demonstrate that it quickly finds close-to-optimal solutions. We formalize the
complex optimization problem as a mixed-integer linear program, and compare it
to our strategy. Finally, we show that when applied to an electromagnetics
code, our approach obtains up to 2.3x speedups for the imbalanced execution.


  We study the semiclassical limit of the $Sp(N)$ generalization of the
pyrochlore lattice Heisenberg antiferromagnet by expanding about the $N \to
\infty$ saddlepoint in powers of a generalized inverse spin. To leading order,
we write down an effective Hamiltonian as a series in loops on the lattice.
Using this as a formula for calculating the energy of any classical ground
state, we perform Monte-Carlo simulations and find a unique collinear ground
state. This state is not a ground state of linear spin-wave theory, and can
therefore not be a physical (N=1) semiclassical ground state.


  We study the thermodynamic properties of spin systems with bond-disorder on
small-world hypergraphs, obtained by superimposing a one-dimensional Ising
chain onto a random Bethe graph with p-spin interactions. Using transfer-matrix
techniques, we derive fixed-point equations describing the relevant order
parameters and the free energy, both in the replica symmetric and one step
replica symmetry breaking approximation. We determine the static and dynamic
ferromagnetic transition and the spinglass transition within replica symmetry
for all temperatures, and demonstrate corrections to these results when one
step replica symmetry breaking is taken into account. The results obtained are
in agreement with Monte-Carlo simulations.


  We study the interplay between spectrum, geometry and boundary conditions for
two distinguished self-adjoint realisations of the Laplacian on infinite metric
graphs, the so-called Friedrichs and Neumann extensions. We introduce a new
criterion for compactness of the resolvent and apply this to identify a
transition from purely discrete to non-empty essential spectrum among a class
of infinite metric graphs, a phenomenon that seems to have no known counterpart
for Laplacians on Euclidean domains of infinite volume. In the case of discrete
spectrum we then prove upper and lower bounds on eigenvalues, thus extending a
number of bounds previously only known in the compact setting to infinite
graphs. Some of our bounds, for instance in terms of the inradius, are new even
on compact graphs.


  The nonequilibrium thermodynamics of an open (classical or quantum) system in
strong contact with a single heat bath can be conveniently described in terms
of the Hamiltonian of mean force. However, the conventional formulation is
limited by the necessity to measure differences in equilibrium properties of
the system-bath composite. We make use of the freedom involved in defining
thermodynamic quantities, which leaves the thermodynamics unchanged, to show
that the Hamiltonian of mean force can be inferred from measurements on the
system alone, up to that irrelevant freedom. In doing so, we refute a key
criticism expressed in Phys. Rev. E 94, 022143 and arXiv:1911.11660. We also
discuss the remaining part of the criticism.


  The recently introduced backward Monte-Carlo method [Johan Carlsson,
arXiv:math.NA/0010118] is validated, benchmarked, and compared to the
conventional, forward Monte-Carlo method by analyzing the error in the
Monte-Carlo solutions to a simple model equation. In particular, it is shown
how the backward method reduces the statistical error in the common case where
the solution is of interest in only a small part of phase space. The forward
method requires binning of particles, and linear interpolation between the bins
introduces an additional error. Reducing this error by decreasing the bin size
increases the statistical error. The backward method is not afflicted by this
conflict. Finally, it is shown how the poor time convergence can be improved
for the backward method by a minor modification of the Monte-Carlo equation of
motion that governs the stochastic particle trajectories. This scheme does not
work for the conventional, forward method.


  We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on
it, as a three-dimensional geometric interpretation of the SM fermions. Each C
x /(R^3) describes an electroweak doublet. The Dirac equation has a
doubler-free staggered spatial discretization on the lattice space Aff(3) x C
(Z^3). This space allows a simple physical interpretation as a phase space of a
lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on
Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action
preserving E(3) symmetry and symplectic structure, which can be constructed
using two simple types of gauge-like lattice fields: Wilson gauge fields and
correction terms for lattice deformations. The lattice fermion fields we
propose to quantize as low energy states of a canonical quantum theory with
Z_2-degenerated vacuum state. We construct anticommuting fermion operators for
the resulting Z_2-valued (spin) field theory. A metric theory of gravity
compatible with this model is presented too.


  A new nonlinear 3+1 dimensional evolution equation admitting the Lax pair is
presented. In the case of one spatial dimension, the equation reduces to the
Burgers equation. A method of construction of exact solutions, based on a class
of discrete symmetries of the former equation is developed. These symmetries
reduce to the Cole-Hopf transformation in one-dimensional limit. Some exact
solutions are analyzed, in the physical context of spatial dissipative
structures and shock wave dressing.


  We consider mean-field dynamo models with fluctuating \alpha effect, both
with and without shear. The \alpha effect is chosen to be Gaussian white noise
with zero mean and given covariance. We show analytically that the mean
magnetic field does not grow, but, in an infinitely large domain, the
mean-squared magnetic field shows exponential growth of the fastest growing
mode at a rate proportional to the shear rate, which agrees with earlier
numerical results of Yousef et al (2008) and recent analytical treatment by
Heinemann et al (2011) who use a method different from ours. In the absence of
shear, an incoherent \alpha^2 dynamo may also be possible. We further show by
explicit calculation of the growth rate of third and fourth order moments of
the magnetic field that the probability density function of the mean magnetic
field generated by this dynamo is non-Gaussian.


  We study adsorption sites of a single Xe adatom on Nb(110) surface using a
density functional theory approach: The on-top site is the most favorable
position for the adsorption. We compare the binding features of the present
study to earlier studies of a Xe adatom on close-packed (111) surface of
face-centered cubic metals. The different features are attributed through a
microscopic picture to the less than half filled d-states in Nb.


  We prove that eigenfunctions of the Laplacian on a compact hyperbolic surface
delocalise in terms of a geometric parameter dependent upon the number of short
closed geodesics on the surface. In particular, we show that an $L^2$
normalised eigenfunction restricted to a measurable subset of the surface has
squared $L^2$-norm $\varepsilon>0$, only if the set has a relatively large size
-- exponential in the geometric parameter. For random surfaces with respect to
the Weil-Petersson probability measure, we then show, with high probability as
$g\to\infty$, that the size of the set must be at least the genus of the
surface to some power dependent upon the eigenvalue and $\varepsilon$.


  We consider a generalization of Einstein's general theory of relativity such
that it respects local scale invariance. This requires the introduction of a
scalar and a vector field in the action. We show that the theory naturally
displays both dark energy and dark matter. We solve the resulting equations of
motion assuming an FRW metric. The solutions are found to be almost identical
to those corresponding to the standard $\Lambda$CDM model


  We study the topological phase diagram of a setup composed of two nanowires
with strong Rashba spin-orbit interaction subjected to an external magnetic
field and brought into the proximity to a bulk $s$-wave superconductor in the
presence of a supercurrent flowing through it. The supercurrent reduces the
critical values of the Zeeman energy and crossed Andreev superconducting
pairing required to reach the topological phase characterized by the presence
of one Majorana bound state localized at each system end. We demonstrate that,
even in the regime of the crossed Andreev pairing being smaller than the direct
proximity pairing, a relatively weak magnetic field drives the system into the
topological phase due to the presence of the supercurrent.


  This paper presents pricing and hedging methods for rainbow options and
lookback options under Bayesian Markov-Switching Vector Autoregressive
(MS--VAR) process. Here we assumed that a regime-switching process is generated
by a homogeneous Markov process. An advantage of our model is it depends on
economic variables and simple as compared with previous existing papers.


  Geometric inequalities of classical differential geometry are used to extend
to higher dimensional spacetimes the Penrose-Gibbons isoperimetric inequalities
and the hoop conjecture of general reltivity.


  We extend a theorem of Kato on similarity for sequences of projections in
Hilbert spaces to the case of isomorphic Schauder decompositions in certain
Banach spaces. To this end we use $\ell_{\Psi}$-Hilbertian and
$\infty$-Hilbertian Schauder decompositions instead of orthogonal Schauder
decompositions, generalize the concept of an orthogonal Schauder decomposition
in a Hilbert space and introduce the class of spaces with Schauder-Orlicz
decompositions. Furthermore, we generalize the notions of type, cotype,
infratype and $M$-cotype of a Banach space and study the properties of
unconditional Schauder decompositions in spaces possessing certain geometric
structure.


  Recently, it has been considering robotics to face world population aging.
According to the WHO, in 2050 there will be about 2.1 billion people over 60
years old worldwide causing a persistent growing need of assistance and a
shortage of manpower for delivering congruous assistance. Therefore, seniors'
QoL is continuously threatened. Socially Assistive Robotics proposes itself as
a solution. To improve SARs acceptability, it is necessary to tailor the
system's characteristics with respect to the target needs and issues through
the analysis of previous and current studies in the HRI field. Through the
examination of the state of the art of social robotics in elderly care, past
case studies and paper research about SARs' efficiency, it has been proposed
two potential solution examples for two different scenarios, applying two
different SARs: Pepper and Nao robots.


  Graphene like 2D materials have attracted tremendous attention in the field
of photocatalytic water splitting. Indium Selenide (InSe) is one such potential
material. Here, we report the effect of Tellurium on InSe monolayer for the
photocatalytic water splitting by means of density functional calculations. The
calculated bandgaps fall within the visible region of the solar spectrum
indicating these materials could absorb a significant amount of solar light.
Density of states calculations show that the covalent character is present
between the atoms which is typical for the layered system. The band alignment
with respect to redox potentials show that Te doped InSe is more favorable for
the hydrogen reduction reaction than the pristine InSe monolayer. Our overall
results show that Te substitution improves the photocatalytic water splitting
ability in InSe monolayer.


  (Abridged) We present mass models of a sample of 14 spiral and 14 S0 galaxies
that constrain their stellar and dark matter content. For each galaxy we derive
the stellar mass distribution from near-infrared photometry under the
assumptions of axisymmetry and a constant Ks-band stellar mass-to-light ratio,
(M/L)_Ks. To this we add a dark halo assumed to follow a spherically symmetric
NFW profile and a correlation between concentration and dark mass within the
virial radius, M_DM. We solve the Jeans equations for the corresponding
potential under the assumption of constant anisotropy in the meridional plane,
beta_z. By comparing the predicted second velocity moment to observed long-slit
stellar kinematics, we determine the three best-fitting parameters of the
model: (M/L)_Ks, M_DM and beta_z. These simple axisymmetric Jeans models are
able to accurately reproduce the wide range of observed stellar kinematics,
which typically extend to ~2-3 Re or, equivalently, ~0.5-1 R_25. We find a
median stellar mass-to-light ratio at Ks-band of 1.09 (solar units) with an rms
scatter of 0.31. We present preliminary comparisons between this large sample
of dynamically determined stellar mass-to-light ratios and the predictions of
stellar population models. The stellar population models predict slightly lower
mass-to-light ratios than we measure. The mass models contain a median of 15
per cent dark matter by mass within an effective radius Re, and 49 per cent
within the optical radius R_25. Dark and stellar matter contribute equally to
the mass within a sphere of radius 4.1 Re or 1.0 R_25. There is no evidence of
any significant difference in the dark matter content of the spirals and S0s in
our sample.


  In this work, we deepen on the use of normalizing flows for causal reasoning.
Specifically, we first leverage recent results on non-linear ICA to show that
causal models are identifiable from observational data given a causal ordering,
and thus can be recovered using autoregressive normalizing flows (NFs). Second,
we analyze different design and learning choices for causal normalizing flows
to capture the underlying causal data-generating process. Third, we describe
how to implement the do-operator in causal NFs, and thus, how to answer
interventional and counterfactual questions. Finally, in our experiments, we
validate our design and training choices through a comprehensive ablation
study; compare causal NFs to other approaches for approximating causal models;
and empirically demonstrate that causal NFs can be used to address real-world
problems, where the presence of mixed discrete-continuous data and partial
knowledge on the causal graph is the norm. The code for this work can be found
at https://github.com/psanch21/causal-flows.


  We investigate observational constraints on the variable Chaplygin gas model
from the gold sample of type Ia supernova data and the recent measurements of
the X-ray gas mass fractions in galaxy clusters. Combining these databases, we
obtain a tight constraint on the two model parameters. Our results indicate
that the original Chaplygin gas model is ruled out by the data at 99.7%
confidence level.


  Using ideas of Ramakrishnan, we consider the icosahedral analogue of the
theorems of Sarnak and Brumley on Hecke-Maass newforms with Fourier
coefficients in a quadratic order. Although we are unable to conclude the
existence of an associated Galois representation in this case, we show that one
can deduce some implications of such an association, including weak automorphy
of all symmetric powers and the value distribution of Fourier coefficients
predicted by the Chebotarev density theorem.


  Classification of seizure type is a key step in the clinical process for
evaluating an individual who presents with seizures. It determines the course
of clinical diagnosis and treatment, and its impact stretches beyond the
clinical domain to epilepsy research and the development of novel therapies.
Automated identification of seizure type may facilitate understanding of the
disease, and seizure detection and prediction has been the focus of recent
research that has sought to exploit the benefits of machine learning and deep
learning architectures. Nevertheless, there is not yet a definitive solution
for automating the classification of seizure type, a task that must currently
be performed by an expert epileptologist. Inspired by recent advances in neural
memory networks (NMNs), we introduce a novel approach for the classification of
seizure type using electrophysiological data. We first explore the performance
of traditional deep learning techniques which use convolutional and recurrent
neural networks, and enhance these architectures by using external memory
modules with trainable neural plasticity. We show that our model achieves a
state-of-the-art weighted F1 score of 0.945 for seizure type classification on
the TUH EEG Seizure Corpus with the IBM TUSZ preprocessed data. This work
highlights the potential of neural memory networks to support the field of
epilepsy research, along with biomedical research and signal analysis more
broadly.


  In a nonrelativistic constituent quark model we find a constraint on the
mixing angle of the strange axial-vector mesons, $35^o\stackrel{<}{\sim }
\theta _K\stackrel{<}{\sim }55^o,$ determined solely by two parameters: the
mass difference of the $a_1$ and $b_1$ mesons and the ratio of the constituent
quark masses.


  We prove that any dominant morphism of algebraic varieties over a field k of
characteristic zero can be transformed into a toroidal (hence monomial)
morphism by projective birational modifications of source and target. This was
previously proved by the first and third author when k is algebraically closed.
Moreover we show that certain additional requirements can be satisfied.


  A zero-one matrix $M$ contains a zero-one matrix $A$ if one can delete some
rows and columns of $M$, and turn some 1-entries into 0-entries such that the
resulting matrix is $A$. The extremal number of $A$, denoted by $ex(n,A)$, is
the maximum number of $1$-entries in an $n\times n$ sized matrix $M$ that does
not contain $A$.
  A matrix $A$ is column-$t$-partite (or row-$t$-partite), if it can be cut
along the columns (or rows) into $t$ submatrices such that every row (or
column) of these submatrices contains at most one $1$-entry. We prove that if
$A$ is column-$t$-partite, then
$ex(n,A)<n^{2-\frac{1}{t}+\frac{1}{2t^{2}}+o(1)}$, and if $A$ is both column-
and row-$t$-partite, then $ex(n,A)<n^{2-\frac{1}{t}+o(1)}$. Our proof combines
a novel density-increment-type argument with the celebrated dependent random
choice method.
  Results about the extremal numbers of zero-one matrices translate into
results about the Tur\'an numbers of bipartite ordered graphs. In particular, a
zero-one matrix with at most $t$ 1-entries in each row corresponds to a
bipartite ordered graph with maximum degree $t$ in one of its vertex classes.
Our results are partially motivated by a well known result of F\"uredi (1991)
and Alon, Krivelevich, Sudakov (2003) stating that if $H$ is a bipartite graph
with maximum degree $t$ in one of the vertex classes, then
$ex(n,H)=O(n^{2-\frac{1}{t}})$. The aim of the present paper is to establish
similar general results about the extremal numbers of ordered graphs.


  We present a minimal model of charge transport in hybrid perovskites, which
provides an intuitive explanation for the recently proposed formation of
ferroelectric large polarons. We demonstrate that short-ranged charge--rotor
interactions lead to long-range ferroelectic ordering of rotors, which strongly
affects the carrier mobility. In the nonperturbative regime, where our theory
cannot be reduced to any of the earlier models, we predict polaron properties
in good agreement with experiment. This shows the potential of simple models to
reveal electronic properties of molecular materials.


  The equations of motion of a secularly precessing ellipse are developed using
time as the independent variable. The equations are useful when integrating
numerically the perturbations about a reference trajectory which is subject to
secular perturbations in the node, the argument of pericenter and the mean
motion. Usually this is done in connection with Encke's method to ensure
minimal rectification frequency. Similar equations are already available in the
literature, but they are either given based on the true anomaly as the
independent variable, or in mixed mode with respect to the time through the use
of a supporting equation to track the anomaly. The equations developed here
form a complete and independent set of six equations in the time.
Reformulations both of Escobal's and Kyner and Bennett's equations are also
provided which lead to a more concise form.


  We present a method to formulate algorithm discovery as program search, and
apply it to discover optimization algorithms for deep neural network training.
We leverage efficient search techniques to explore an infinite and sparse
program space. To bridge the large generalization gap between proxy and target
tasks, we also introduce program selection and simplification strategies. Our
method discovers a simple and effective optimization algorithm, $\textbf{Lion}$
($\textit{Evo$\textbf{L}$ved S$\textbf{i}$gn M$\textbf{o}$me$\textbf{n}$tum}$).
It is more memory-efficient than Adam as it only keeps track of the momentum.
Different from adaptive optimizers, its update has the same magnitude for each
parameter calculated through the sign operation. We compare Lion with widely
used optimizers, such as Adam and Adafactor, for training a variety of models
on different tasks. On image classification, Lion boosts the accuracy of ViT by
up to 2% on ImageNet and saves up to 5x the pre-training compute on JFT. On
vision-language contrastive learning, we achieve 88.3% $\textit{zero-shot}$ and
91.1% $\textit{fine-tuning}$ accuracy on ImageNet, surpassing the previous best
results by 2% and 0.1%, respectively. On diffusion models, Lion outperforms
Adam by achieving a better FID score and reducing the training compute by up to
2.3x. For autoregressive, masked language modeling, and fine-tuning, Lion
exhibits a similar or better performance compared to Adam. Our analysis of Lion
reveals that its performance gain grows with the training batch size. It also
requires a smaller learning rate than Adam due to the larger norm of the update
produced by the sign function. Additionally, we examine the limitations of Lion
and identify scenarios where its improvements are small or not statistically
significant. Lion is also successfully deployed in production systems such as
Google search ads CTR model.


  We compute the locations of satellite galaxies in the Two-Degree Field Galaxy
Redshift Survey using two sets of selection criteria and three sources of
photometric data. Using the SuperCOSMOS r_F photometry, we find that the
satellites are located preferentially near the major axes of their hosts, and
the anisotropy is detected at a highly-significant level (confidence levels of
99.6% to 99.9%). The locations of satellites that have high velocities relative
to their hosts are statistically indistinguishable from the locations of
satellites that have low velocities relative to their hosts. Additionally,
satellites with passive star formation are distributed anisotropically about
their hosts (99% confidence level), while the locations of star-forming
satellites are consistent with an isotropic distribution. These two
distributions are, however, statistically indistinguishable. Therefore it is
not correct to interpret this as evidence that the locations of the
star-forming satellites are intrinsically different from those of the passive
satellites.


  We present a unified analysis of single excitation vector models in 3D. We
show that there is a family of first order master actions related by duality
transformations which interpolate between the different models. We use a
Hamiltonian (2+1) analysis to show the equivalence of the self-dual and
topologically massive models with a covariant non local model which propagates
also a single massive excitation. It is shown how the non local terms appears
naturally in the path integral framework.


  In this paper we introduce techniques from complex harmonic analysis to prove
a weaker version of the Geometric Arveson-Douglas Conjecture for complex
analytic subsets that is smooth on the boundary of the unit ball and intersects
transversally with it. In fact, we prove that the projection operator onto the
corresponding quotient module is in the Toeplitz algebra
$\mathcal{T}(L^{\infty})$, which implies the essential normality of the
quotient module. Combining some other techniques we actually obtain the
$p$-essential normality for $p>2d$, where $d$ is the complex dimension of the
analytic subset. Finally, we show that our results apply for the closure of a
radical polynomial ideal $I$ whose zero variety satisfies the above conditions.
A key technique is defining a right inverse operator of the restriction map
from the unit ball to the analytic subset generalizing the result of Beatrous's
paper "$L^p$-estimates for extensions of holomorphic functions".


  Tied links in $S^3$ were introduced by Aicardi and Juyumaya as standard links
in $S^3$ equipped with some non-embedded arcs, called {\it ties}, joining some
components of the link. Tied links in the Solid Torus were then naturally
generalized by Flores. In this paper we study this new class of links in other
topological settings. More precisely, we study tied links in the lens spaces
$L(p,1)$, in handlebodies of genus $g$, and in the complement of the
$g$-component unlink. We introduce the tied braid groups $TB_{g, n}$ by
combining the algebraic mixed braid groups defined by Lambropoulou and the tied
braid monoid, and we state and prove Alexander's and Markov's theorems for tied
links in the 3-manifolds mentioned above. Finally, we emphasize on further
steps needed in order to study tied links in knot complements and c.c.o.
3-manifolds, which is the subject of a sequel paper.


  We study the relation between the age-specific prevalence, incidence and
mortality in an illness-death model consisting of the three states Healthy,
Ill, Dead. The dependency on three different time scales (age, calendar time,
disease duration) is considered. It is shown that Keiding's equation published
in 1991 is a generalisation of the solution of Brunet and Struchiner's partial
differential equation from 1999. In a special case, we propose a particularly
simple estimate of the incidence from prevalence data.


  Traditionally the Costa Rican historians and genealogists have interpreted
that the Spanish ruling elite emerged after the conquest was exclusively of
European origin. On the other side, recent technological advances in Genetics
give us the opportunity to approach the study of pedigrees from a new
perspective, examining alive people and simultaneously collating the historical
information of their ancestors. In this paper, a complete matrilineal genealogy
was reconstructed from nowadays "white" Costa Ricans to their ancestors in the
early Colonial society (XVI century). It was compared the correlation between
ethnic affiliations deduced from historical records with the genetic
inheritance from maternal lineages. The MtDNA lineage observed corresponds to a
Native American ancestry. These results show that some Amerindian gene flow
into the Spanish group must have occurred since the first generation of
Colonial society, a finding that contrasts with the prevailing ideas that the
Spanish elite avoided the intermarriage with other ethnic groups. Examples like
this one confirm that miscegenation began early in Costa Rica. So, those who
considered themselves "Spaniards" in the late colonial era, were actually
biologically mestizos. It is widely accepted, that the general Costa Rican
population is the result of an admixture process between Europeans, Amerindians
and Africans.


  We introduce a new entropy formula for Kerr black holes inspired by recent
results for 3-dimensional black holes and cosmologies with soft Heisenberg
hair. We show that also Kerr-Taub-NUT black holes obey the same formula.


  Distributed stochastic optimization has drawn great attention recently due to
its effectiveness in solving large-scale machine learning problems. Though
numerous algorithms have been proposed and successfully applied to general
practical problems, their theoretical guarantees mainly rely on certain
boundedness conditions on the stochastic gradients, varying from uniform
boundedness to the relaxed growth condition. In addition, how to characterize
the data heterogeneity among the agents and its impacts on the algorithmic
performance remains challenging. In light of such motivations, we revisit the
classical Federated Averaging (FedAvg) algorithm (McMahan et al., 2017) as well
as the more recent SCAFFOLD method (Karimireddy et al., 2020) for solving the
distributed stochastic optimization problem and establish the convergence
results under only a mild variance condition on the stochastic gradients for
smooth nonconvex objective functions. Almost sure convergence to a stationary
point is also established under the condition. Moreover, we discuss a more
informative measurement for data heterogeneity as well as its implications.


  We study the problem of joint load balancing and interference mitigation in
heterogeneous networks (HetNets) in which massive multiple-input
multiple-output (MIMO) macro cell base station (BS) equipped with a large
number of antennas, overlaid with wireless self-backhauled small cells (SCs)
are assumed. Self-backhauled SC BSs with full-duplex communication employing
regular antenna arrays serve both macro users and SC users by using the
wireless backhaul from macro BS in the same frequency band. We formulate the
joint load balancing and interference mitigation problem as a network utility
maximization subject to wireless backhaul constraints. Subsequently, leveraging
the framework of stochastic optimization, the problem is decoupled into dynamic
scheduling of macro cell users, backhaul provisioning of SCs, and offloading
macro cell users to SCs as a function of interference and backhaul links. Via
numerical results, we show the performance gains of our proposed framework
under the impact of small cells density, number of base station antennas, and
transmit power levels at low and high frequency bands. We further provide
insights into the performance analysis and convergence of the proposed
framework. The numerical results show that the proposed user association
algorithm outperforms other baselines. Interestingly, we find that even at
lower frequency band the performance of open access small cell is close to that
of closed access at some operating points, the open access full- duplex small
cell still yields higher gain as compared to the closed access at higher
frequency bands. With increasing the small cell density or the wireless
backhaul quality, the open access full- duplex small cells outperform and
achieve a 5.6x gain in terms of cell-edge performance as compared to the closed
access ones in ultra-dense networks with 350 small cell base stations per km2 .


  Coulomb blockade (CB) in a quantum dot (QD) with one anomalously broad level
is considered. In this case many consecutive pronounced CB peaks correspond to
occupation of one and the same broad level. Between the peaks the electron
jumps from this level to one of the narrow levels and the transmission through
the dot at the next resonance essentially repeats that at the previous one.
This offers a natural explanation to the recently observed behavior of the
transmission phase in an interferometer with a QD. Single particle resonances
of very different width are natural if the dot is not fully chaotic. This idea
is illustrated by the numerical simulations for a non-integrable QD whose
classical dynamics is intermediate between integrable and chaotic. Possible
manifestations for the Kondo experiments in the QD are discussed.


  The non-fungible token (NFT) market emerges as a recent trading innovation
leveraging blockchain technology, mirroring the dynamics of the cryptocurrency
market. The current study is based on the capitalization changes and
transaction volumes across a large number of token collections on the Ethereum
platform. In order to deepen the understanding of the market dynamics, the
collection-collection dependencies are examined by using the multivariate
formalism of detrended correlation coefficient and correlation matrix. It
appears that correlation strength is lower here than that observed in
previously studied markets. Consequently, the eigenvalue spectra of the
correlation matrix more closely follow the Marchenko-Pastur distribution,
still, some departures indicating the existence of correlations remain. The
comparison of results obtained from the correlation matrix built from the
Pearson coefficients and, independently, from the detrended cross-correlation
coefficients suggests that the global correlations in the NFT market arise from
higher frequency fluctuations. Corresponding minimal spanning trees (MSTs) for
capitalization variability exhibit a scale-free character while, for the number
of transactions, they are somewhat more decentralized.


  Bosonic and fermionic particle currents can be introduced in a more unified
way, with the cost of introducing a preferred spacetime foliation. Such a
unified treatment of bosons and fermions naturally emerges from an analogous
superstring current, showing that the preferred spacetime foliation appears
only at the level of effective field theory, not at the fundamental superstring
level. The existence of the preferred spacetime foliation allows an objective
definition of particles associated with quantum field theory in curved
spacetime. Such an objective definition of particles makes the Bohmian
interpretation of particle quantum mechanics more appealing. The superstring
current allows a consistent Bohmian interpretation of superstrings themselves,
including a Bohmian description of string creation and destruction in terms of
string splitting. The Bohmian equations of motion and the corresponding
probabilistic predictions are fully relativistic covariant and do not depend on
the preferred foliation.


  In 5D SUSY GUTs, wave-function localization permits to reproduce flavour
hierarchy. As this mechanism also acts on SUSY breaking parameters, it can
potentially solve the SUSY flavour problem. We carry out an analysis of the
Holographic Grand Unification framework, where we take properly into account
effects of matrix anarchy. In this contribution, we focus on brane-localized
SUSY breaking and its consequences.


  The recent detection of the anomalous X-ray pulsar (AXP) 4U 0142+61 in the
mid-infrared with the {\it Spitzer} observatory by Z.Wang and coworkers
constitutes the first instance of a disk around an AXP. We show, by analyzing
earlier optical and near-IR data together with the recent data, that the
overall broadband data set can be reproduced by a single model of an irradiated
and viscously heated disk.


  This paper has been removed by arXiv administrators because it plagiarizes
gr-qc/0411070, "Structure and stability of the Lukash plane-wave spacetime," by
John D. Barrow and Christos G. Tsagas; and gr-qc/0205028, "Gravitational Energy
of Kerr and Kerr Anti-de Sitter Space-times in the Teleparallel Geometry," by
J. F. da Rocha-neto and K. H. Castello-Branco.


  Nubmer of physically interesting processes is charachterized by the rapidity
gaps. In reality, this gaps is filled by uderlying events with high (more than
0.75 for higgs) probability. In this paper we purpose a way to detect this
shadowed events with aim to raise the number of rare events.


  Dialog is a natural modality for interaction between customers and businesses
in the service industry. As customers call up the service provider, their
interactions may be routine or extraordinary. We believe that these
interactions, when seen as dialogs, can be analyzed to obtain a better
understanding of customer needs and how to efficiently address them. We
introduce the idea of a dialog complexity measure to characterize multi-party
interactions, propose a general data-driven method to calculate it, use it to
discover insights in public and enterprise dialog datasets, and demonstrate its
beneficial usage in facilitating better handling of customer requests and
evaluating service agents.


  We construct new relativistic linear differential equation in $d$ dimensions
generalizing Dirac equation by employing the Clifford algebra of the cubic
polynomial associated to Klein-Gordon operator multiplied by the mass
parameter. Unlike the Dirac case where the spin content is unique and Lorentz
covariance is manifest, here the spin as well as Lorentz covariance of the
theory are related to the choice of representation of the Clifford algebra. One
of the considered explicit matrix representations gives rise to anyon-like
fields in $d=1+1$. Coupling to a U(1) gauge field is discussed and compared
with Dirac theory.


  We revisit the determination of the two-loop spectral function in the shear
channel of hot Yang-Mills theory. Correcting a technical error in an earlier
computation and extending the result with a leading order Hard Thermal Loop
resummation is seen to improve the infrared behavior of the quantity
significantly. This makes it possible to straightforwardly use the result in
the corresponding imaginary time correlator and the shear sum rule.


  In this paper, we study an asynchronous randomized gossip algorithm under
unreliable communication. At each instance, two nodes are selected to meet with
a given probability. When nodes meet, two unreliable communication links are
established with communication in each direction succeeding with a time-varying
probability. It is shown that two particularly interesting cases arise when
these communication processes are either perfectly dependent or independent.
Necessary and sufficient conditions on the success probability sequence are
proposed to ensure almost sure consensus or $\epsilon$-consensus. Weak
connectivity is required when the communication is perfectly dependent, while
double connectivity is required when the communication is independent.
Moreover, it is proven that with odd number of nodes, average preserving turns
from almost forever (with probability one for all initial conditions) for
perfectly dependent communication, to almost never (with probability zero for
almost all initial conditions) for the independent case. This average
preserving property does not hold true for general number of nodes. These
results indicate the fundamental role the node interactions have in randomized
gossip algorithms.


  For a class of Schrodinger Hamiltonians the supersymmetry transformations can
degenerate to simple coordinate displacements. We examine this phenomenon and
show that it distinguishes the Weierstrass potentials including the one-soliton
wells and periodic Lame functions. A supersymmetric sense of the addition
formula for the Weierstrass functions is elucidated.


  Understanding how large neural networks avoid memorizing training data is key
to explaining their high generalization performance. To examine the structure
of when and where memorization occurs in a deep network, we use a recently
developed replica-based mean field theoretic geometric analysis method. We find
that all layers preferentially learn from examples which share features, and
link this behavior to generalization performance. Memorization predominately
occurs in the deeper layers, due to decreasing object manifolds' radius and
dimension, whereas early layers are minimally affected. This predicts that
generalization can be restored by reverting the final few layer weights to
earlier epochs before significant memorization occurred, which is confirmed by
the experiments. Additionally, by studying generalization under different model
sizes, we reveal the connection between the double descent phenomenon and the
underlying model geometry. Finally, analytical analysis shows that networks
avoid memorization early in training because close to initialization, the
gradient contribution from permuted examples are small. These findings provide
quantitative evidence for the structure of memorization across layers of a deep
neural network, the drivers for such structure, and its connection to manifold
geometric properties.


  Most link prediction methods return estimates of the connection probability
of missing edges in a graph. Such output can be used to rank the missing edges
from most to least likely to be a true edge, but does not directly provide a
classification into true and non-existent. In this work, we consider the
problem of identifying a set of true edges with a control of the false
discovery rate (FDR). We propose a novel method based on high-level ideas from
the literature on conformal inference. The graph structure induces intricate
dependence in the data, which we carefully take into account, as this makes the
setup different from the usual setup in conformal inference, where data
exchangeability is assumed. The FDR control is empirically demonstrated for
both simulated and real data.


  Bangla Handwritten Digit recognition is a significant step forward in the
development of Bangla OCR. However, intricate shape, structural likeness and
distinctive composition style of Bangla digits makes it relatively challenging
to distinguish. Thus, in this paper, we benchmarked four rigorous classifiers
to recognize Bangla Handwritten Digit: K-Nearest Neighbor (KNN), Support Vector
Machine (SVM), Random Forest (RF), and Gradient-Boosted Decision Trees (GBDT)
based on three handcrafted feature extraction techniques: Histogram of Oriented
Gradients (HOG), Local Binary Pattern (LBP), and Gabor filter on four publicly
available Bangla handwriting digits datasets: NumtaDB, CMARTdb, Ekush and BDRW.
Here, handcrafted feature extraction methods are used to extract features from
the dataset image, which are then utilized to train machine learning
classifiers to identify Bangla handwritten digits. We further fine-tuned the
hyperparameters of the classification algorithms in order to acquire the finest
Bangla handwritten digits recognition performance from these algorithms, and
among all the models we employed, the HOG features combined with SVM model
(HOG+SVM) attained the best performance metrics across all datasets. The
recognition accuracy of the HOG+SVM method on the NumtaDB, CMARTdb, Ekush and
BDRW datasets reached 93.32%, 98.08%, 95.68% and 89.68%, respectively as well
as we compared the model performance with recent state-of-art methods.


  We prove a version for random measures of the celebrated
Kantorovich-Rubinstein duality theorem and we give an application to the
coupling of random variables which extends and unifies known results.


  We consider integrals of type $\int_{O_n}u_{11}^{a_1}...
u_{1n}^{a_n}u_{21}^{b_1}... u_{2n}^{b_n} du$, with respect to the Haar measure
on the orthogonal group. We establish several remarkable invariance properties
satisfied by such integrals, by using combinatorial methods. We present as well
a general formula for such integrals, as a sum of products of factorials.


  We consider a theoretical model for membranes with adhesive receptors, or
stickers, that are actively switched between two conformational states. In
their 'on'-state, the stickers bind to ligands in an apposing membrane, whereas
they do not interact with the ligands in their 'off'-state. We show that the
adhesiveness of the membranes depends sensitively on the rates of the
conformational switching process. This dependence is reflected in a resonance
at intermediate switching rates, which can lead to large membrane separations
and unbinding. Our results may provide insights into novel mechanisms for the
controlled adhesion of biological or biomimetic membranes.


  We revisit a classical graph-theoretic problem, the \textit{single-source
shortest-path} (SSSP) problem, in weighted unit-disk graphs. We first propose
an exact (and deterministic) algorithm which solves the problem in $O(n \log^2
n)$ time using linear space, where $n$ is the number of the vertices of the
graph. This significantly improves the previous deterministic algorithm by
Cabello and Jej\v{c}i\v{c} [CGTA'15] which uses $O(n^{1+\delta})$ time and
$O(n^{1+\delta})$ space (for any small constant $\delta>0$) and the previous
randomized algorithm by Kaplan et al. [SODA'17] which uses $O(n \log^{12+o(1)}
n)$ expected time and $O(n \log^3 n)$ space. More specifically, we show that if
the 2D offline insertion-only (additively-)weighted nearest-neighbor problem
with $k$ operations (i.e., insertions and queries) can be solved in $f(k)$
time, then the SSSP problem in weighted unit-disk graphs can be solved in $O(n
\log n+f(n))$ time. Using the same framework with some new ideas, we also
obtain a $(1+\varepsilon)$-approximate algorithm for the problem, using $O(n
\log n + n \log^2(1/\varepsilon))$ time and linear space. This improves the
previous $(1+\varepsilon)$-approximate algorithm by Chan and Skrepetos
[SoCG'18] which uses $O((1/\varepsilon)^2 n \log n)$ time and
$O((1/\varepsilon)^2 n)$ space. More specifically, we show that if the 2D
offline insertion-only weighted nearest-neighbor problem with $k_1$ operations
in which at most $k_2$ operations are insertions can be solved in $f(k_1,k_2)$
time, then the $(1+\varepsilon)$-approximate SSSP problem in weighted unit-disk
graphs can be solved in $O(n \log n+f(n,O(\varepsilon^{-2})))$ time. Because of
the $\Omega(n \log n)$-time lower bound of the problem (even when approximation
is allowed), both of our algorithms are almost optimal.


  We study the design of Bayesian incentive compatible mechanisms in single
parameter domains, for the objective of optimizing social efficiency as
measured by social cost. In the problems we consider, a group of participants
compete to receive service from a mechanism that can provide such services at a
cost. The mechanism wishes to choose which agents to serve in order to maximize
social efficiency, but is not willing to suffer an expected loss: the agents'
payments should cover the cost of service in expectation.
  We develop a general method for converting arbitrary approximation algorithms
for the underlying optimization problem into Bayesian incentive compatible
mechanisms that are cost-recovering in expectation. In particular, we give
polynomial time black-box reductions from the mechanism design problem to the
problem of designing a social cost minimization algorithm without incentive
constraints. Our reduction increases the expected social cost of the given
algorithm by a factor of O(log(min{n, h})), where n is the number of agents and
h is the ratio between the highest and lowest nonzero valuations in the
support. We also provide a lower bound illustrating that this inflation of the
social cost is essential: no BIC cost-recovering mechanism can achieve an
approximation factor better than \Omega(log(n)) or \Omega(log(h)) in general.
  Our techniques extend to show that a certain class of truthful algorithms can
be made cost-recovering in the non-Bayesian setting, in such a way that the
approximation factor degrades by at most O(log(min{n, h})). This is an
improvement over previously-known constructions with inflation factor O(log n).


  We study the effects of $\delta$-function periodic kicks on the Floquet
energy-momentum dispersion in graphene. We find that a rich variety of
dispersions can appear depending on the parameters of the kicking: at certain
points in the Brillouin zone, the dispersion can become linear but anisotropic,
linear in one direction and quadratic in the perpendicular direction, gapped
with a quadratic dispersion, or completely flat (called dynamical
localization). We show all these results analytically and demonstrate them
numerically through the dynamics of wave packets propagating in graphene. We
propose experimental methods for producing these effects.


  Adversarial training (AT) with samples generated by Fast Gradient Sign Method
(FGSM), also known as FGSM-AT, is a computationally simple method to train
robust networks. However, during its training procedure, an unstable mode of
"catastrophic overfitting" has been identified in arXiv:2001.03994 [cs.LG],
where the robust accuracy abruptly drops to zero within a single training step.
Existing methods use gradient regularizers or random initialization tricks to
attenuate this issue, whereas they either take high computational cost or lead
to lower robust accuracy. In this work, we provide the first study, which
thoroughly examines a collection of tricks from three perspectives: Data
Initialization, Network Structure, and Optimization, to overcome the
catastrophic overfitting in FGSM-AT.
  Surprisingly, we find that simple tricks, i.e., a) masking partial pixels
(even without randomness), b) setting a large convolution stride and smooth
activation functions, or c) regularizing the weights of the first convolutional
layer, can effectively tackle the overfitting issue. Extensive results on a
range of network architectures validate the effectiveness of each proposed
trick, and the combinations of tricks are also investigated. For example,
trained with PreActResNet-18 on CIFAR-10, our method attains 49.8% accuracy
against PGD-50 attacker and 46.4% accuracy against AutoAttack, demonstrating
that pure FGSM-AT is capable of enabling robust learners. The code and models
are publicly available at
https://github.com/UCSC-VLAA/Bag-of-Tricks-for-FGSM-AT.


  Helton and Nie conjectured that every convex semialgebraic set over the field
of real numbers can be written as the projection of a spectrahedron. Recently,
Scheiderer disproved this conjecture. We show, however, that the following
result, which may be thought of as a tropical analogue of this conjecture, is
true: over a real closed nonarchimedean field of Puiseux series, the convex
semialgebraic sets and the projections of spectrahedra have precisely the same
images by the nonarchimedean valuation. The proof relies on game theory
methods.


  We classify irreducible unitary representations of the group of all infinite
matrices over a $p$-adic field ($p\ne 2$) with integer elements
  equipped with a natural topology. Any irreducible representation passes
through a group $GL$ of infinite matrices over a residue ring modulo $p^k$.
Irreducible representations of the latter group are induced from
finite-dimensional representations of certain open subgroups.


  Manual annotation of large-scale point cloud dataset for varying tasks such
as 3D object classification, segmentation and detection is often laborious
owing to the irregular structure of point clouds. Self-supervised learning,
which operates without any human labeling, is a promising approach to address
this issue. We observe in the real world that humans are capable of mapping the
visual concepts learnt from 2D images to understand the 3D world. Encouraged by
this insight, we propose CrossPoint, a simple cross-modal contrastive learning
approach to learn transferable 3D point cloud representations. It enables a
3D-2D correspondence of objects by maximizing agreement between point clouds
and the corresponding rendered 2D image in the invariant space, while
encouraging invariance to transformations in the point cloud modality. Our
joint training objective combines the feature correspondences within and across
modalities, thus ensembles a rich learning signal from both 3D point cloud and
2D image modalities in a self-supervised fashion. Experimental results show
that our approach outperforms the previous unsupervised learning methods on a
diverse range of downstream tasks including 3D object classification and
segmentation. Further, the ablation studies validate the potency of our
approach for a better point cloud understanding. Code and pretrained models are
available at http://github.com/MohamedAfham/CrossPoint.


  In this paper we consider Artin local K-algebras with maximal length in the
class of Artin algebras with given embedding dimension and socle type. They
have been widely studied by several authors, among others by Iarrobino,
Fr\"oberg and Laksov. If the local K-algebra is Gorenstein of socle degree 3,
then the authors proved that it is canonically graded, i.e. analytically
isomorphic to its associated graded ring. This unexpected result has been
extended to compressed level K-algebras of socle degree 3 by A. De Stefani. In
this paper we end the investigation proving that extremal Artin Gorenstein
local K-algebras of socle degree s \le 4 are canonically graded, but the result
does not extend to extremal Artin Gorenstein local rings of socle degree 5 or
to compressed level local rings of socle degree 4 and type >1. As a consequence
we present results on Artin compressed local K-algebras having a specified
socle type.


  Nanoscale forces play an important role in different scanning probe
microscopies, most notably atomic force microscopy (AFM). In contrast, in
scanning near-field optical microscopy (SNOM) a light-induced coupled local
optical polarization between tip and sample is typically detected by scattering
to the far field. Measurements of the optical gradient force associated with
that optical near-field excitation would offer a novel optical scanning probe
modality. Here we provide a generalized theory of optical gradient force
nano-imaging and -spectroscopy. We quantify magnitude and distance dependence
of the optical gradient force and its spectral response. We show that the
optical gradient force is dispersive for single particle electronic and
vibrational resonances, distinct from recent claims of its experimental
observation. In contrast, the force can be absorptive for collective
resonances. We provide a guidance for its measurements and distinction from
competing processes such as thermal expansion.


  We have measured the low-temperature transport properties of an open quantum
dot formed in a clean one-dimensional channel. For the first time, at zero
magnetic field, continuous and periodic oscillations superimposed upon
ballistic conductance steps are observed when the conductance through the dot
$G$ exceeds $2e^2/h$. We ascribe the observed conductance oscillations to
evidence for Coulomb charging effects in an open dot. This is supported by the
evolution of the oscillating features for $G>2e^2/h$ as a function of both
temperature and barrier transparency. Our results strongly suggest that at zero
magnetic field, current theoretical and experimental understanding of Coulomb
charging effects overlooks charging in the presence of fully transmitted 1D
channels.


  For the Gauss sums which are defined by S_n(a,q) := \sum_{x (mod q)}
e(ax^n/q), Stechkin (1975) conjectured that the quantity A := \sup_{n,q\ge 2}
\max_{\gcd(a,q)=1} |S_n(a,q)|/q^(1-1/n) is finite. Shparlinski (1991) proved
that A is finite, but in the absence of effective bounds on the sums S_n(a,q)
the precise determination of A has remained intractable for many years. Using
recent work of Cochrane and Pinner (2011) on Gauss sums with prime moduli, in
this paper we show that with the constant given by A =
|S_6(4787,4606056)|/4606056^(5/6) = 4.709236... one has the sharp inequality
|S_n(a,q)| \le Aq^(1-1/n) for all n,q \ge 2 and all integers a with gcd(a,q)=1.
One interesting aspect of our method is that we apply effective lower bounds
for the center density in the sphere packing problem due to Cohn and Elkies
(2003) to optimize the running time of our primary computational algorithm.


  We report the first study of electrical resistivity, magnetization, and
specific heat on YbCo$_2$. The measurements on a single-phased sample of
YbCo$_2$ bring no evidence of magnetic ordering down to 0.3 K in a zero
magnetic field. The manifestations of low Kondo temperature are observed. The
specific heat value divided by temperature, C/T, keeps increasing
logarithmically beyond 7 J/mol.K2 with decreasing temperature down to 0.3 K
without no sign of magnetic ordering, suggesting a very large electronic
specific heat. Analysis of the magnetic specific heat indicates that the large
portion of the low-temperature specific heat is not explained simply by the low
Kondo temperature but is due to the strong intersite magnetic correlation in
both the 3d and 4f electrons. Temperature-dependent measurements under static
magnetic fields up to 7 T are carried out, which show the evolution of
field-induced transition above 2 T. The transition temperature increases with
increasing field, pointing to a ferromagnetic character. The extrapolation of
the transition temperature to zero field suggests that YbCo$_2$ is in the very
proximity of the quantum critical point. These results indicate that in the
unique case of YbCo$_2$, the itinerant electron magnetism of Co 3d-electrons
and the Kondo effect within the vicinity of quantum criticality of Yb 4f-local
moments can both play a role.


  Maximally supersymmetric Yang--Mills theory in four dimensions can be
formulated on a space-time lattice while exactly preserving a single
supersymmetry. Here we explore in detail this lattice theory, paying particular
attention to its strongly coupled regime. Targeting a theory with gauge group
SU(N), the lattice formulation is naturally described in terms of gauge group
U(N). Although the U(1) degrees of freedom decouple in the continuum limit we
show that these degrees of freedom lead to unwanted lattice artifacts at strong
coupling. We demonstrate that these lattice artifacts can be removed, leaving
behind a lattice formulation based on the SU(N) gauge group with the expected
apparently conformal behavior at both weak and strong coupling.


  Over ten years ago, Fermi observed an excess of GeV gamma rays from the
Galactic Center whose origin is still under debate. One explanation for this
excess involves annihilating dark matter; another requires an unresolved
population of millisecond pulsars concentrated at the Galactic Center. In this
work, we use the results from LIGO/Virgo's most recent all-sky search for
quasi-monochromatic, persistent gravitational-wave signals from isolated
neutron stars, which is estimated to be about 20-50\% of the population, to
determine whether unresolved millisecond pulsars could actually explain this
excess. First, we choose a luminosity function that determines the number of
millisecond pulsars required to explain the observed excess. Then, we consider
two models for deformations on millisecond pulsars to determine their
ellipticity distributions, which are directly related to their
gravitational-wave radiation. Lastly, based on null results from the O3
Frequency-Hough all-sky search for continuous gravitational waves, we find that
a large set of the parameter space in the pulsar luminosity function can be
excluded. We also evaluate how these exclusion regions may change with respect
to various model choices. Our results are the first of their kind and represent
a bridge between gamma-ray astrophysics, gravitational-wave astronomy, and
dark-matter physics.


  We study the dynamics and velocity-force curves of a skyrmion moving over a
two-dimensional periodic substrate using simulations of a particle-based
skyrmion model, focusing on the role of the non-dissipative Magnus term. In the
overdamped limit, the skyrmion depins into a sliding state with a Hall angle of
zero. When a Magnus term is included, the Hall angle is nonzero in the absence
of a substrate. On a periodic substrate, the Hall angle varies with the drive
amplitude. Due to the substrate symmetry the Hall angle does not change
continuously with drive, but forms a series of discrete steps at rational
ratios of the skyrmion velocity components perpendicular and parallel to the
drive direction, when the skyrmion motion locks to symmetry directions of the
substrate for fixed intervals of the drive amplitude. On each step, the Hall
angle is constant and the skyrmion motion is orderly. Transitions between
locked phases generate pronounced cusps in the velocity-force curves, as well
as regions of negative differential mobility. The number of observable locking
steps increases when the relative strength of the Magnus term increases. We
find an overshoot phenomena where the Hall angle exceeds the clean limit value,
as well as an acceleration effect where the skyrmion moves faster over a
substrate than through a clean sample. These effects are robust for different
types of periodic substrates. With a simple model for a skyrmion interacting
with a single pin, we can capture the behavior of the Hall angle. The Magnus
term induces a curvature in the skrymion orbit as it moves through the pin,
resulting in a side step phenomenon that decreases with increasing drive. When
the Magnus term is large, the range of impact parameters that permit the
skyrmion to be trapped by the pin is small, which is a reasons that strong
Magnus force effects reduce the pinning in skyrmion systems.


  The number of events observed in neutrino telescopes depends on the neutrino
fluxes in the Earth, their absorption while crossing the Earth and their
interaction in the detector. In this paper, we investigate the impact of the
QCD dynamics at high energies on the energy dependence of the average
inelasticity and angular dependence of the absorption probability during the
neutrino propagation through the Earth, as well in the determination of the
properties of the incident astrophysical neutrino flux. Moreover, the number of
events at the IceCube and IceCube - Gen2 are estimated considering different
scenarios for the QCD dynamics and assuming the presence of a hypothetical
Super - Glashow flux, which peaks for energies above the Glashow resonance.


  In order to decrease the measuring cycle time on the coordinate measuring
machine (CMM) a robot workstation for the positioning of measuring objects was
created. The application of a simple 5-axis industrial robot enables the
positioning of the objects within the working space of CMM and measuring of
different surfaces on the same object without human intervention. In this
article an upgrade of an existing robot workstation through different design
measures is shown. The main goal of this upgrade is to improve the measuring
accuracy of the complex robot-CMM system.


  Combination and aggregation techniques can significantly improve forecast
accuracy. This also holds for probabilistic forecasting methods where
predictive distributions are combined. There are several time-varying and
adaptive weighting schemes such as Bayesian model averaging (BMA). However, the
quality of different forecasts may vary not only over time but also within the
distribution. For example, some distribution forecasts may be more accurate in
the center of the distributions, while others are better at predicting the
tails. Therefore, we introduce a new weighting method that considers the
differences in performance over time and within the distribution. We discuss
pointwise combination algorithms based on aggregation across quantiles that
optimize with respect to the continuous ranked probability score (CRPS). After
analyzing the theoretical properties of pointwise CRPS learning, we discuss B-
and P-Spline-based estimation techniques for batch and online learning, based
on quantile regression and prediction with expert advice. We prove that the
proposed fully adaptive Bernstein online aggregation (BOA) method for pointwise
CRPS online learning has optimal convergence properties. They are confirmed in
simulations and a probabilistic forecasting study for European emission
allowance (EUA) prices.


  In this work we consider the electroweak interaction between two massive
neutrinos in the non-relativistic limit. We find that in this limit the
interaction can be null.


  We analyze the morphological stability against azimuthal, axial, and general
helical perturbations for epitaxial core-shell nanowires in the growth regimes
limited by either surface diffusion or evaporation-condensation surface
kinetics. For both regimes, we find that geometric parameters (i.e., core
radius and shell thickness) play a central role in determining whether the
nanowire remains cylindrical or its shell breaks up into epitaxial islands
similar to those observed during Stranski-Krastanow growth in thin epilayers.
The combination of small cores and rapid growth of the shell emerge as key
ingredients for stable shell growth. Our results provide an explanation for the
different core-shell morphologies reported in the Si-Ge system experimentally,
and also identify a growth-induced intrinsic mechanism for the formation of
helical nanowires.


  Dust emission is an important tool in studies of star-forming clouds, as a
tracer of column density and indirectly via the dust evolution that is
connected to the history and physical conditions of the clouds. We examine
radiative transfer (RT) modelling of dust emission over an extended cloud
region, using a filament in the Taurus molecular cloud as an example. We
examine how well far-infrared observations can be used to determine both the
cloud and the dust properties. Using different assumptions of the cloud shape,
radiation field, and dust properties, we fit RT models to Herschel observations
of the Taurus filament. Further comparisons are made with measurements of the
near-infrared extinction. The models are used to examine the degeneracies
between the different cloud parameters and the dust properties. The results
show significant dependence on the assumed cloud structure and the spectral
shape of the external radiation field. If these are constrained to the most
likely values, the observations can be explained only if the dust far-infrared
(FIR) opacity has increased by a factor of 2-3 relative to the values in
diffuse medium. However, a narrow range of FIR wavelengths provides only weak
evidence of the spatial variations in dust, even in the models covering several
square degrees of a molecular cloud. The analysis of FIR dust emission is
affected by several sources of uncertainty. Further constraints are therefore
needed from observations at shorter wavelengths, especially regarding the
trends in dust evolution.


  Although their existence is not yet confirmed observationally, intermediate
mass black holes (IMBHs) may play a key role in the dynamics of galactic
nuclei. In this paper, we neglect the effect of the nuclear star cluster itself
and investigate only how a small reservoir of IMBHs influences the secular
dynamics of stellar-mass black hole binaries, using N-body simulations. We show
that our simplifications are valid and that the IMBHs significantly enhance
binary evaporation by pushing the binaries into the Hill-unstable region of
parameter space, where they are separated by the SMBH's tidal field. For
binaries in the S-cluster region of the Milky Way, IMBHs drive the binaries to
merge in up to 1-6% of cases, assuming five IMBHs within 5 pc of mass 10,000
solar masses each. Observations of binaries in the Galactic center may strongly
constrain the population of IMBHs therein.


  We study anomalous $W^-W^+Z/\gamma$ couplings due to dimension-$6$ operators
in the production process $e^-e^+ \to W^-W^+$ followed by semi-leptonic decay
using polarizations and spin-spin correlations of $W$ bosons. The construction
of some of the polarization and spin-spin correlation asymmetries required one
to distinguish between two decay quarks coming from $W^+$ decay. We developed
an artificial neural network (ANN) and a boosted decision tree (BDT) to
distinguish down-type jets from up-type jets and used them to put constraint on
anomalous couplings at International Linear Collider (ILC) running at $\sqrt{s}
= 250$ GeV with integrated luminosities of $\mathcal{L} \in \{100 \
\text{fb}^{-1}, \ 250 \ \text{fb}^{-1}, \ 1000 \ \text{fb}^{-1}, \ 3000 \
\text{fb}^{-1}\}$. We find that the use of polarization and spin correlation
observables, on top of the cross-sections, significantly improves the limits on
anomalous coupling compared to the earlier studies.


  Despite the fact that pulsars have been observed for almost half a century,
many questions have remained unanswered. We use the analysis of X-ray
observations in order to study the polar cap region of radio pulsars. The size
of the hot spots implies that the magnetic field configuration just above the
stellar surface differs significantly from a purely dipole one. We can estimate
the surface magnetic field as of the order of $10^{14}\,{\rm G}$. On the other
hand, the temperature of the hot spots is about a few million Kelvins. Based on
these two facts the Partially Screened Gap (PSG) model was proposed to describe
the Inner Acceleration Region (IAR). The PSG model assumes that the temperature
of the actual polar cap is equal to the so-called critical value, i.e. the
temperature at which the outflow of thermal ions from the surface screens the
gap completely.
  We have found that, depending on the conditions above the polar cap, the
generation of high energetic photons in IAR can be caused either by Curvature
Radiation (CR) or by Inverse Compton Scattering (ICS). This results in two
different scenarios of breaking the acceleration gap: the so-called PSG-off
mode for CR-dominated gaps and the PSG-on mode ICS-dominated gaps. The
existence of two different mechanisms of gap breakdown naturally explains the
mode-changing and the pulse nulling. Furthermore, the mode changes of the IAR
may explain the anti-correlation of radio and X-ray emission in very recent
observations of PSR B0943+10 (Hermsen et al., 2013).
  Simultaneous analysis of X-ray and radio properties have allowed to develop a
model which explains the drifting subpulse phenomenon. According to this model
the drift takes place when the charge density in IAR differs from the
Goldreich-Julian co-rotational density. The proposed model allows to verify
both the radio drift parameters and X-ray efficiency of the observed pulsars.


  The aforementioned celebrated model, though a breakthrough in Stochastic
processes and a great step toward the construction of the Brownian motion leads
to a paradox: infinite propagation speed and violation of the 2nd law of
thermodynamics. We adapt the model by assuming the diffusion matrix dependent
of the concentration of particles, rather than constant it was up to Einstein,
and prove a finite propagation speed under the assumption of a qualified
decrease of the diffusion for small concentration. The method involves a
nonlinear degenerated parabolic PDE in divergent form, a parabolic Sobolev-type
inequality and the Ladyzhenskaya-Uraltseva iteration lemma.


  Knowledge-based potentials were developed to investigate the differentiation
of native structures from their decoy sets. This work presents the construction
of two different distance-dependent potential energy functions based on two
fundamental assumptions using mathematical modeling. Here, a model was
developed using basic mathematical methods, and the carbon-alpha form is the
simplest form of protein representation. We aimed to reduce computational
volume and distinguish the native structure from the decoy structures. For this
purpose, according to Anfinsens dogma, we assumed that the energy of each model
structure should be more favorable than the corresponding native type. In the
second one, we thought that the energy difference between the native and decoy
structures changes linearly with the root-mean-square deviation of structures.
These knowledge-based potentials are expressed by the B-spline basis functions
of the pairwise distances between Ca-Ca of inter-residues. The potential
function parameters in the above two approaches were optimized using the linear
programming algorithm on a massive collection of Titan-HRD and tested on the
remainder. We found that the potential functions produced by Anfinsens dogma
detect native structures more accurately than those developed by the
root-mean-square deviation. Both linear programming knowledge-based potentials
(LPKP) successfully detect the native structures from an ensemble of decoys.
However, the LPKP of the first approach can correctly identify 130 native
structures out of 150 tested cases with an average rank of 1.67. While the
second approach LPKP detects 124 native structures from their decoys. We
concluded that linear programming is promising for generating knowledge-based
potential functions. All the training and testing sets used for this work are
available online and downloaded from http://titan.princeton.edu/HRDecoys.


  The fundamental BCJ-relation is a linear relation between primitive tree
amplitudes with different cyclic orderings. The cyclic orderings differ by the
insertion place of one gluon. The coefficients of the fundamental BCJ-relation
are linear in the Lorentz invariants $2 p_i p_j$. The BCJ-relations are well
established for pure gluonic amplitudes as well as for amplitudes in ${\mathcal
N}=4$ super-Yang-Mills theory. Recently, it has been conjectured that the
BCJ-relations hold also for QCD amplitudes. In this paper we give a proof of
this conjecture. The proof is valid for massless and massive quarks.


  The paper focuses on the accuracy improvement of stiffness models for
parallel manipulators, which are employed in high-speed precision machining. It
is based on the integrated methodology that combines analytical and numerical
techniques and deals with multidimensional lumped-parameter models of the
links. The latter replace the link flexibility by localized 6-dof virtual
springs describing both translational/rotational compliance and the coupling
between them. There is presented detailed accuracy analysis of the stiffness
identification procedures employed in the commercial CAD systems (including
statistical analysis of round-off errors, evaluating the confidence intervals
for stiffness matrices). The efficiency of the developed technique is confirmed
by application examples, which deal with stiffness analysis of translational
parallel manipulators.


  We report on X-ray emission from members of the recently discovered Tucanae
association, a group of stars with youth signatures and similar space motion.
The Tucanae association is the nearest known region of recent star formation
(at 45 pc) far from molecular clouds. We have made use of the ROSAT Data
Archive, and searched for X-rays from Tucanae stars in both ROSAT All-Sky
Survey (RASS) and pointed observations. The RASS detection rate for the Tucanae
members is 59%. We compare the X-ray luminosity function of the Tucanae
association to that of other star forming regions and young star clusters. Both
the X-ray luminosity function and the strong variability observed in the X-ray
lightcurves suggest that the examined stars are young, on the order of 10-30
Myrs.


  We examine the extent to which primordial black holes (PBHs) can constitute
the observed dark matter while also giving rise to the measured
matter-antimatter asymmetry and account for the observed baryon abundance
through asymmetric Hawking radiation generated by a derivative coupling of
curvature to the baryon-lepton current. We consider both broad and
monochromatic mass spectra for this purpose. For the monochromatic spectrum we
find that the correct dark matter and baryon energy densities are recovered for
peak masses of the spectrum of $M_{\rm pk} \geq 10^{12}$ kg whereas for the
broad case the observed energy densities can be reproduced regardless of peak
mass. Adopting some simplifications for the early-time expansion history as a
first approximation, we also find that the measured baryon asymmetry can be
recovered within an order of magnitude. We argue furthermore that the correct
value of the baryon-lepton yield can in principle be retrieved for scenarios
where a significant amount of the radiation is produced by PBH decay during or
after reheating, as is expected when the decaying PBHs also cause reheating, or
when an early matter-dominated phase is considered. We conclude from this first
analysis that the model merits further investigation.


  We show the existence of $n$-complements for generalized pairs with
additional Diophantine approximation properties when the coefficients of
boundaries belong to a DCC set.


  The low lying excitations of coreless vortex states in F = 1 spinor
Bose-Einstein condensates (BECs) are theoretically investigated using the
Gross-Pitaevskii and Bogoliubov-de Gennes equations. The spectra of the
elementary excitations are calculated for different spin-spin interaction
parameters and ratios of the number of particles in each sublevel. There exist
dynamical instabilities of the vortex state which are suppressed by
ferromagnetic interactions, and conversely, enhanced by antiferromagnetic
interactions. In both of the spin-spin interaction regimes, we find vortex
splitting instabilities in analogy with scalar BECs. In addition, a phase
separating instability is found in the antiferromagnetic regime.


  Improving employees' understanding of digital forensic technical terms and
concepts within an organisation is likely to increase the potential of
successful collaboration during a cyber security incident (e.g. data breach)
investigation within that organisation. In this paper, we seek to determine
whether multimedia presentations, in this case videos, are an effective tool in
improving a learner's technical understanding of digital forensic terms and
concepts. Using the cognitive theory of multimedia learning as the underlying
theoretical lens, we surveyed nine participants from the financial sector who
have cyber security-related responsibilities. With the exception of one
participant, the study found that the use of multimedia presentations can
improve participants' understanding of technical digital forensic terms and
concepts. Potential future research questions are also identified.


  We investigate attention as the active pursuit of useful information. This
contrasts with attention as a mechanism for the attenuation of irrelevant
information. We also consider the role of short-term memory, whose use is
critical to any model incapable of simultaneously perceiving all information on
which its output depends. We present several simple synthetic tasks, which
become considerably more interesting when we impose strong constraints on how a
model can interact with its input, and on how long it can take to produce its
output. We develop a model with a different structure from those seen in
previous work, and we train it using stochastic variational inference with a
learned proposal distribution.


  The layered perovskite Sr$_2$RuO$_4$ serves as a model material of the
two-dimensional (2D) Fermi liquid but also exhibits various emergent phenomena
including the non-Fermi-liquid (NFL) behavior under external perturbations such
as uniaxial pressure and chemical substitutions. Here we present the
thermoelectric transport of electron-doped system Sr$_{2-y}$La$_{y}$RuO$_4$, in
which a filling-induced Lifshitz transition occurs at the Van Hove singularity
(VHS) point of $y\approx 0.2$. We find that the sign of the low-temperature
thermopower becomes negative only near the VHS point, where the NFL behavior
has been observed in the earlier work. This observation is incompatible with
either a numerical calculation within a constant relaxation-time approximation
or a toy-model calculation for the 2D Lifshitz transition adopting an elastic
carrier scattering. As a promising origin of the observed negatively enhanced
thermopower, we propose a skewed NFL state, in which an inelastic scattering
with a considerable odd-frequency term plays a crucial role to negatively
enhance the thermopower.


  Cubic vertices for symmetric higher-spin gauge fields of integer spins in
$(A)dS_d$ are analyzed. $(A)dS_d$ generalization of the previously known action
in $AdS_4$, that describes cubic interactions of symmetric massless fields of
all integer spins $s\geq 2$, is found. A new cohomological formalism for the
analysis of vertices of higher-spin fields of any symmetry and/or order of
nonlinearity is proposed within the frame-like approach. Using examples of
spins two and three it is demonstrated how nontrivial vertices in $(A)dS_d$,
including Einstein cubic vertex, can result from the $AdS$ deformation of
trivial Minkowski vertices. A set of higher-derivative cubic vertices for any
three bosonic fields of spins $s\geq 2$ is proposed, which is conjectured to
describe all vertices in $AdS_d$ that can be constructed in terms of connection
one-forms and curvature two-forms of symmetric higher-spin fields. A problem of
reconstruction of a full nonlinear action starting from known unfolded
equations is discussed. It is shown that the normalization of free higher-spin
gauge fields compatible with the flat limit relates the noncommutativity
parameter $\hbar$ of the higher-spin algebra to the $(A)dS$ radius.


  A system of dispersive representations of the
Omn\`es-Khuri-Treiman-Sawyer-Wali type for the final-state interactions in the
amplitudes of the $K\to\pi\pi\pi$ weak transitions is constructed, under the
assumptions that CP and isospin symmetries are conserved. Both the $\Delta I =
1/2$ and $\Delta I = 3/2$ transition channels are considered. The set of
single-variable functions involved in these representations is identified, and
the polynomial ambiguities in their definitions are discussed. Numerical
solutions for the system of coupled integral relations satisfied by these
functions are provided, and the determination of the subtraction constants in
terms of the experimental information on the amplitudes in the decay region is
addressed.


  Time-of-Flight (ToF) cameras require active illumination to obtain depth
information thus the power of illumination directly affects the performance of
ToF cameras. Traditional ToF imaging algorithms is very sensitive to
illumination and the depth accuracy degenerates rapidly with the power of it.
Therefore, the design of a power efficient ToF camera always creates a painful
dilemma for the illumination and the performance trade-off. In this paper, we
show that despite the weak signals in many areas under extreme short exposure
setting, these signals as a whole can be well utilized through a learning
process which directly translates the weak and noisy ToF camera raw to depth
map. This creates an opportunity to tackle the aforementioned dilemma and make
a very power efficient ToF camera possible. To enable the learning, we collect
a comprehensive dataset under a variety of scenes and photographic conditions
by a specialized ToF camera. Experiments show that our method is able to
robustly process ToF camera raw with the exposure time of one order of
magnitude shorter than that used in conventional ToF cameras. In addition to
evaluating our approach both quantitatively and qualitatively, we also discuss
its implication to designing the next generation power efficient ToF cameras.
We will make our dataset and code publicly available.


  Covariate shift relaxes the widely-employed independent and identically
distributed (IID) assumption by allowing different training and testing input
distributions. Unfortunately, common methods for addressing covariate shift by
trying to remove the bias between training and testing distributions using
importance weighting often provide poor performance guarantees in theory and
unreliable predictions with high variance in practice. Recently developed
methods that construct a predictor that is inherently robust to the
difficulties of learning under covariate shift are restricted to minimizing
logloss and can be too conservative when faced with high-dimensional learning
tasks. We address these limitations in two ways: by robustly minimizing various
loss functions, including non-convex ones, under the testing distribution; and
by separately shaping the influence of covariate shift according to different
feature-based views of the relationship between input variables and example
labels. These generalizations make robust covariate shift prediction applicable
to more task scenarios. We demonstrate the benefits on classification under
covariate shift tasks.


  We map certain highly correlated electron systems on lattices with
geometrical frustration in the motion of added particles or holes to the
spatial defect-defect correlations of dimer models in different geometries.
These models are studied analytically and numerically. We consider different
coverings for four different lattices: square, honeycomb, triangular, and
diamond. In the case of hard-core dimer covering, we verify the existed results
for the square and triangular lattice and obtain new ones for the honeycomb and
the diamond lattices while in the case of loop covering we obtain new numerical
results for all the lattices and use the existing analytical Liouville field
theory for the case of square lattice.The results show power-law correlations
for the square and honeycomb lattice, while exponential decay with distance is
found for the triangular and exponential decay with the inverse distance on the
diamond lattice. We relate this fact with the lack of bipartiteness of the
triangular lattice and in the latter case with the three-dimensionality of the
diamond. The connection of our findings to the problem of fractionalized charge
in such lattices is pointed out.


  We consider quark-hadron duality relations and QCD sum rules for correlators
involving exotic tetraquark currents, here specializing to the case of
quark-exchange processes. We point out the differences they exhibit with
respect to the cases involving ordinary bilinear quark currents. Based on the
observation that only diagrams possessing at least four-quark singularities can
contribute to the formation of tetraquark states, we show that the quark-hadron
duality relations and the corresponding sum rules split into two
non-overlapping relations. The ultimate tetraquark-adequate QCD sum rule is
concerned only with one of these relations, in which the operator product
expansion starts with diagrams of order $O(\alpha_s^2)$.


  Capabilities of long-range flight and vertical take-off and landing (VTOL)
are essential for Urban Air Mobility (UAM). Tiltrotor VTOLs have the advantage
of balancing control simplicity and system complexity due to their redundant
control authority. Prior work on controlling these aircraft either requires
separate controllers and switching modes for different vehicle configurations
or performs the control allocation on separate actuator sets, which cannot
fully use the potential of the redundancy of tiltrotor. This paper introduces a
unified MPC-based control strategy for a customized tiltrotor VTOL Unmanned
Aerial Vehicle (UAV), which does not require mode-switching and can perform the
control allocation in a consistent way. The incorporation of four independently
controllable rotors in VTOL design offers an extra level of redundancy,
allowing the VTOL to accommodate actuator failures. The result shows that our
approach outperforms PID controllers while maintaining unified control. It
allows the VTOL to perform smooth acceleration/deceleration, and precise
coordinated turns. In addition, the independently controlled tilts enable the
vehicle to handle actuator failures, ensuring that the aircraft remains
operational even in the event of a servo or motor malfunction.


  We analyze Susskind's proposal of applying the non-commutative Chern-Simons
theory to the quantum Hall effect. We study the corresponding regularized
matrix Chern-Simons theory introduced by Polychronakos. We use holomorphic
quantization and perform a change of matrix variables that solves the Gauss law
constraint. The remaining physical degrees of freedom are the complex
eigenvalues that can be interpreted as the coordinates of electrons in the
lowest Landau level with Laughlin's wave function. At the same time, a
statistical interaction is generated among the electrons that is necessary to
stabilize the ground state. The stability conditions can be expressed as the
highest-weight conditions for the representations of the W-infinity algebra in
the matrix theory. This symmetry provides a coordinate-independent
characterization of the incompressible quantum Hall states.


  This paper presents an opinion on the potential of using large language
models to query on both unstructured and structured data. It also outlines some
research challenges related to the topic of building question-answering systems
for both types of data.


  In this paper we discuss a minor modification of a previous SU(5) x A5
flavour model which exhibits at leading order golden ratio mixing and sum rules
for the heavy and the light neutrino masses. Although this model could predict
all mixing angles well it fails in generating a sufficient large baryon
asymmetry via the leptogenesis mechanism. We repair this deficit here, discuss
model building aspects and give analytical estimates for the generated baryon
asymmetry before we perform a numerical parameter scan. Our setup has only a
few parameters in the lepton sector. This leads to specific constraints and
correlations between the neutrino observables. For instance, we find that in
the model considered only the neutrino mass spectrum with normal mass ordering
and values of the lightest neutrino mass in the interval 10-18 meV are
compatible with the current data on the neutrino oscillation parameters. With
the introduction of only one NLO operator, the model can accommodate
successfully simultaneously even at 1$\sigma$ level the current data on
neutrino masses, on neutrino mixing and the observed value of the baryon
asymmetry.


  Motivated by superstring theories on $AdS_3$, we construct spacetime
superconformal algebras (SCAs) living on the $AdS_3$ boundary in terms of the
transversal physical degrees of freedom. The SCAs constructed are N=4 large,
middle algebras, and N=3 algebra, corresponding to superstring theories on
$AdS_3 \times S ^3 \times S^3 \times S ^1$, $AdS_3 \times S ^3 \times T ^4 $
and $AdS_3 \times (S^3\times S^3\times S^1)/Z_2$ backgrounds respectively.


  Deep neural networks have shown great potential in image reconstruction
problems in Euclidean space. However, many reconstruction problems involve
imaging physics that are dependent on the underlying non-Euclidean geometry. In
this paper, we present a new approach to learn inverse imaging that exploit the
underlying geometry and physics. We first introduce a non-Euclidean
encoding-decoding network that allows us to describe the unknown and
measurement variables over their respective geometrical domains. We then learn
the geometry-dependent physics in between the two domains by explicitly
modeling it via a bipartite graph over the graphical embedding of the two
geometry. We applied the presented network to reconstructing electrical
activity on the heart surface from body-surface potential. In a series of
generalization tasks with increasing difficulty, we demonstrated the improved
ability of the presented network to generalize across geometrical changes
underlying the data in comparison to its Euclidean alternatives.


  The two-particle angular correlation functions, $R_2$, of pions, kaons, and
protons in Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 14.5, 19.6, 27, 39,
62.4, and 200 GeV were measured by the STAR experiment at RHIC. These
correlations were measured for both like-sign and unlike-sign charge
combinations and versus the centrality. The correlations of pions and kaons
show the expected near-side ({\it i.e.}, at small relative angles) peak
resulting from short-range mechanisms. The amplitudes of these short-range
correlations decrease with increasing beam energy. However, the proton
correlation functions exhibit strong anticorrelations in the near-side region.
This behavior is observed for the first time in an A+A collision system. The
observed anticorrelation is $p_{T}$-independent and decreases with increasing
beam energy and centrality. The experimental results are also compared to the
Monte Carlo models UrQMD, Hijing, and AMPT.


  We present an elementary way of computing the Donaldson-Futaki invariant
associated to a test-configuration of an anti-canonically polarized Fano
reductive group compactification. In addition, we explain how to obtain
examples of real Einstein manifolds from K-stable Fano manifolds.


  Consider CLE$_4$ in the unit disk and let $\ell$ be the loop of the CLE$_4$
surrounding the origin. Schramm, Sheffield and Wilson determined the law of the
conformal radius seen from the origin of the domain surrounded by $\ell$. We
complement their result by determining the law of the extremal distance between
$\ell$ and the boundary of the unit disk. More surprisingly, we also compute
the joint law of these conformal radius and extremal distance. This law
involves first and last hitting times of a one-dimensional Brownian motion.
Similar techniques also allow us to determine joint laws of some extremal
distances in a critical Brownian loop-soup cluster.


  A non-Abelian version of the Hirota-Miwa equation is considered. In an
earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it
was shown how solutions expressed as quasideterminants could be constructed for
this system by means of Darboux transformations. In this paper we discuss these
solutions from a different perspective and show that the solutions are
quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may
be written as a quasi-Pl\"{u}cker relation. The special case of the matrix
Hirota-Miwa equation is also considered using a more traditional, bilinear
approach and the techniques are compared.


  The evolution equations for a plasma comprising multiple species of charged
fluids with relativistic bulk and thermal motion are derived. It is shown that
a minimal fluid coupling model allows a natural casting of the evolution
equations in terms of generalized vorticity which treats the fluid motion and
electromagnetic fields equally. Equilibria can be found using a variational
principle based on minimizing the total enstrophy subject to energy and
helicity constraints. A subset of these equilibria correspond to minimum
energy. The equations for these states are presented with example solutions
showing the structure of the relaxed states.