  We consider the production and two-photon decay of the $CP$-even Higgs bosons
($h^0$ and $H^0$) of the Minimal Supersymmetric Standard Model (MSSM) at the
Large Hadron Collider. We study in detail the dependence of the cross section
on various parameters of the MSSM, especially the dependence on the mixing
effects in the squark sector due to the Higgs bilinear parameter $\mu$ and the
soft supersymmetry breaking parameter $A$. We find that the cross section for
the production of these Higgs bosons has a significant dependence on the
parameters which determine the chiral mixing in the squark sector. The cross
section times the two-photon branching ratio of $h^0$ is of the order of
15--25~fb in much of the parameter space that remains after imposing the
present experimental constraints. For the $H^0$ the two-photon branching ratio
is only significant if the $H^0$ is light, but then the cross section times the
branching ratio may exceed 200~fb. The QCD corrections due to quark loop
contributions are known to increase the cross section by 50\%. We find the
dependence of the cross section on the gluon distribution function used to be
rather insignificant.


  A generalization of the classical Kapitza pendulum is considered: an inverted
planar mathematical pendulum with a vertically vibrating pivot point in a
time-periodic horizontal force field. We study the existence of forced
oscillations in the system. It is shown that there always exists a periodic
solution along which the rod of the pendulum never becomes horizontal, i.e. the
pendulum never falls, provided the period of vibration and the period of
horizontal force are commensurable. We also present a sufficient condition for
the existence of at least two different periodic solutions without falling. We
show numerically that there exist stable periodic solutions without falling.


  We develop a new class of genetic algorithm that computationally determines
efficient pulse sequences to implement a quantum gate U in a three-qubit
system. The method is shown to be quite general, and the same algorithm can be
used to derive efficient sequences for a variety of target matrices. We
demonstrate this by implementing the inversion-on-equality gate efficiently
when the spin-spin coupling constants $J_{12}=J_{23}=J$ and $J_{13}=0$. We also
propose new pulse sequences to implement the Parity gate and Fanout gate, which
are about 50% more efficient than the previous best efforts. Moreover, these
sequences are shown to require significantly less RF power for their
implementation. The proposed algorithm introduces several new features in the
conventional genetic algorithm framework. We use matrices instead of linear
chains, and the columns of these matrices have a well defined hierarchy. The
algorithm is a genetic algorithm coupled to a fast local optimizer, and is
hence a hybrid GA. It shows fast convergence, and running on a MATLAB platform
takes about 20 minutes on a standard personal computer to derive efficient
pulse sequences for any target 8X8 matrix $U$.


  The framework of Integral Quadratic Constraints of Lessard et al. (2014)
reduces the computation of upper bounds on the convergence rate of several
optimization algorithms to semi-definite programming (SDP). Followup work by
Nishihara et al. (2015) applies this technique to the entire family of
over-relaxed Alternating Direction Method of Multipliers (ADMM). Unfortunately,
they only provide an explicit error bound for sufficiently large values of some
of the parameters of the problem, leaving the computation for the general case
as a numerical optimization problem. In this paper we provide an exact
analytical solution to this SDP and obtain a general and explicit upper bound
on the convergence rate of the entire family of over-relaxed ADMM. Furthermore,
we demonstrate that it is not possible to extract from this SDP a general bound
better than ours. We end with a few numerical illustrations of our result and a
comparison between the convergence rate we obtain for the ADMM with known
convergence rates for the Gradient Descent.


  Although the two-body charmed decays $B_{(s)} \to \bar D_{(s)}^{(*)}P$ and
$\bar D_{(s)}^{(*)}V$, where $P$($V$) denotes a light pseudoscalar(vector)
meson, are CKM suppressed comparing with the $B_{(s)} \to D_{(s)}^{(*)}P$ and $
D_{(s)}^{(*)}V$ decays, they are important in the CKM angle $\gamma=\phi_3$
extraction method. We investigated these decays in the perturbative QCD
approach to the leading order of $m_D/m_B$ and $\Lambda_{\rm{QCD}}/m_D$
expansion. We find that the nonfactorizable emission diagrams and the
annihilation diagrams are not negligible in many of these channels. The
numerical results show that most channels have branching ratios with an order
of $10^{-6}$ or $10^{-7}$. The ratio needed for the CKM angle $\gamma$
extraction is estimated as $r = \frac{|A(B^- \to \bar{D}^0 K^-)|}{|A(B^- \to
D^0 K^-)|} = 0.092_{-0.003-0.003}^{+0.012+0.003},$ which is too small for the
experiments. Some of the $ B_{(s)}\to \bar D_{(s)}^*V$ decays have a very large
transversely polarized contribution that can reach 80%.


  Let Delta be a random spherical triangle (meaning that vertices are
independent and uniform on the unit sphere). A closed-form expression for the
area density of Delta has been known since 1867; a complicated integral
expression for the perimeter density was found in 1994. Does there exist a
closed-form expression for the latter? We attempt to answer this question from
several directions. An outcome of our work is the exact value of the perimeter
density at the point pi.


  Recent advances in robot-assisted surgery have resulted in progressively more
precise, efficient, and minimally invasive procedures, sparking a new era of
robotic surgical intervention. This enables doctors, in collaborative
interaction with robots, to perform traditional or minimally invasive surgeries
with improved outcomes through smaller incisions. Recent efforts are working
toward making robotic surgery more autonomous which has the potential to reduce
variability of surgical outcomes and reduce complication rates. Deep
reinforcement learning methodologies offer scalable solutions for surgical
automation, but their effectiveness relies on extensive data acquisition due to
the absence of prior knowledge in successfully accomplishing tasks. Due to the
intensive nature of simulated data collection, previous works have focused on
making existing algorithms more efficient. In this work, we focus on making the
simulator more efficient, making training data much more accessible than
previously possible. We introduce Surgical Gym, an open-source high performance
platform for surgical robot learning where both the physics simulation and
reinforcement learning occur directly on the GPU. We demonstrate between
100-5000x faster training times compared with previous surgical learning
platforms. The code is available at:
https://github.com/SamuelSchmidgall/SurgicalGym.


  In this paper, a linearized semi-implicit finite difference scheme is
proposed for solving the two-dimensional (2D) space fractional nonlinear
Schr\"{o}dinger equation (SFNSE).The scheme has the property of mass and energy
conservation on the discrete level, with an unconditional stability and a
second order accuracy for both time and spatial variables. The main
contribution of this paper is an optimal pointwise error estimate for the 2D
SFNSE, which is rigorously established and proved for the first time. Moreover,
a novel technique is proposed for dealing with the nonlinear term in the
equation, which plays an essential role in the error estimation. Finally, the
numerical results confirm well with the theoretical findings.


  Various recent results of new particle searches at the Fermilab Tevatron are
presented. No evidence is found for supersymmetric particles (chargino,
gluino), leptoquark bosons and heavy gauge bosons in p-pbar collisions at
sqrt{s} = 1.8 TeV. Excluded mass regions for each particle are determined.


  Ab initio calculations indicate that the ground state for Ga adsorption on Al
(100) is on-surface with local unit coverage. On Ga-coated Al (100), the bridge
diffusion barrier for Al is large, but the Al$\rightarrow$Ga {\it exchange
barrier is zero}: the ensuing incorporation of randomly deposited Al's into the
Ga overlayer realizes a percolation network, efficiently recoated by Ga atoms.
Based on calculated energetics, we predict rough surface growth at all
temperatures; modeling the growth by a random deposition model with partial
relaxation, we find a power-law divergent roughness $w\sim t^{\,0.07\pm0.02}$.


  In this work, we investigate the possibility of enhancing the thermoelectric
power (Seebeck coefficient) in graphene devices by strain and doping
engineering. While a local strain can result in the misalignment of Dirac cones
of different graphene sections in the k-space, doping engineering leads to
their displacement in energy. By combining these two effects, we demonstrate
that a conduction gap as large as a few hundreds meV can be achieved and hence
the enhanced Seebeck coefficient can reach a value higher than 1.4 mV/K in
graphene doped heterojunctions with a locally strained area. Such
hetero-channels appear to be very promising for enlarging the applications of
graphene devices as in strain and thermal sensors.


  We introduce the notion of resultant of two planar curves in the tropical
geometry framework. We prove that the tropicalization of the algebraic
resultant can be used to compute the stable intersection of two tropical plane
curves. It is shown that, for two generic preimages of the curves to an
algebraic framework, their intersection projects exactly onto the stable
intersection of the curves. It is also given sufficient conditions for such a
generality in terms of the residual coefficients of the algebraic coefficients
of defining equations of the curves.


  We compare the eigenvalues of the Dirac and Laplace operator on a
two-dimensional torus with respect to the trivial spin structure. In
particular, we compute their variation up to order 4 upon deformation of the
flat metric, study the corresponding Hamiltonian and discuss several families
of examples.


  The interconnection between quantum mechanics and probabilistic classical
mechanics for a free relativistic particle is derived in terms of Wigner
functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of
WF is achieved by first defining a bilocal 4-current and then taking its
Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases
also lend themselves to a closely parallel treatment provided the Kemmer-
Duffin beta-matrix formalism is employed for the former. Calculation of WF is
carried out in a Lorentz-covariant fashion by standard `trace' techniques. The
results are compared with a recent derivation due to Bosanac.


  We update our numerical investigation of topological structures around static
quarks in pure gauge QCD by results of the first runs including dynamical
quarks. Simulations were performed on an $8^3\times4$ lattice, with $SU(3)$
Wilson action, with 3 flavours of quarks of equal mass, both in the confinement
and deconfinement phase. In the confinement phase we observe indications for
the existence of a flux tube between a static quark and antiquark, flux-tube
breaking for large separations, and local correlation between the topological
charge density and chiral condensate. In the deconfinement phase almost all
configurations turn out to be topologically trivial.


  Following ideas of Bondarko, we construct a DG category whose homotopy
category is equivalent to the full subcategory of motives over a base-scheme
$S$ generated by the motives of smooth projective $S$-schemes, assuming that
$S$ is itself smooth over a perfect field.


  We study a non-supersymmetric $E_8\times\bar E_8$ compactification of
M-theory on $S^1/Z_2$, related to the supersymmetric $E_8\times E_8$ theory by
a chirality flip at one of the boundaries. This system represents an M-theory
analog of the D-brane anti-D-brane systems of string theory. Alternatively,
this compactification can be viewed as a model of supersymmetry breaking in the
``brane-world'' approach to phenomenology. We calculate the Casimir energy of
the system at large separations, and show that there is an attractive Casimir
force between the $E_8$ and $\bar E_8$ boundary. We predict that a tachyonic
instability develops at separations of order the Planck scale, and discuss the
possibility that the M-theory fivebrane might appear as a topological defect
supported by the $E_8\times\bar E_8$ system. Finally, we analyze the eventual
fate of the configuration, in the semiclassical approximation at large
separations: the two ends of the world annihilate by nucleating wormholes
between the two boundaries.


  For a convex body $K\subset\mathbb{R}^d$ the mean distance
$\Delta(K)=\mathbb{E}|X_1-X_2|$ is the expected Euclidean distance of two
independent and uniformly distributed random points $X_1,X_2\in K$. Optimal
lower and upper bounds for ratio between $\Delta(K)$ and the first intrinsic
volume $V_1(K)$ of $K$ (normalized mean width) are derived and degenerate
extremal cases are discussed. The argument relies on Riesz's rearrangement
inequality and the solution of an optimization problem for powers of concave
functions. The relation with results known from the existing literature is
reviewed in detail.


  We use a ten dimensional dual string background to aspects of the physics
large N four dimensional SU(N) gauge theory, where its fundamental quarks are
charged under a background electric field. The theory is N=2 supersymmetric for
vanishing temperature and electric field. At zero temperature, we observe that
the electric field induces a phase transition associated with the dissociation
of the mesons into their constituent quarks. This is an analogue of an
insulator-metal transition, since the system goes from being an insulator with
zero current (in the applied field) to a conductor with free charge carriers
(the quarks). At finite temperature this phenomenon persists, with the
dissociation transition become subsumed into the more familiar meson melting
transition. Here, the dissociation phenomenon reduces the critical melting
temperature.


  In spin transport experiments with spin currents propagating through
antiferromagnetic (AFM) material, the antiferromagnet is treated as a mainly
passive spin conductor not generating nor adding any spin current to the
system. The spin current transmissivity of the AFM NiO is affected by magnetic
fluctuations, peaking at the N\'eel temperature and decreasing by lowering the
temperature. In order to study the role of the AFM in local and nonlocal spin
transport experiments, we send spin currents through NiO of various thickness
placed on Y$_3$Fe$_5$O$_{12}$. The spin currents are injected either
electrically or by thermal gradients and measured at a wide range of
temperatures and magnetic field strengths. The transmissive role is reflected
in the sign change of the local electrically injected signals and the decrease
in signal strength of all other signals by lowering the temperature. The
thermally generated signals, however, show an additional upturn below 100$\,$K
which are unaffected by an increased NiO thickness. A change in the thermal
conductivity could affect these signals. The temperature and magnetic field
dependence is similar as for bulk NiO, indicating that NiO itself contributes
to thermally induced spin currents.


  Writing and argumentation are critical to both professional physics and
physics education. However, the skill of making an extended argument in writing
is often overlooked in physics classrooms, apart from certain practices like
lab notebooks or mathematical proofs. Computation is also critical to both
professional physics and, increasingly, physics education. In recent years we
have begun to develop a class of assignment, known as a computational essay, to
both leverage the creative affordances of computation and help students build
their argumentative writing skills. Computational essays are a type of essay or
report that combine text and code to express an idea or make an argument,
usually written in notebook software. In this article, we describe the
motivation and philosophy behind computational essays, as well as initial
results from a pilot implementation in an introductory undergraduate
electricity and magnetism course.


  It is shown that the action for Hamiltonian equations of motion can be
brought into invariant symplectic form. In other words, it can be formulated
directly in terms of the symplectic structure $\omega$ without any need to
choose some 1-form $\gamma$, such that $\omega= d \gamma$, which is not unique
and does not even generally exist in a global sense.


  The Theorems of Pappus and Desargues are generalized by two special formulas
that hold in the three-dimensional vector space over a field.


  Sustainable aviation fuels have the potential for reducing emissions and
environmental impact. To help identify viable sustainable aviation fuels and
accelerate research, several machine learning models have been developed to
predict relevant physiochemical properties. However, many of the models have
limited applicability, leverage data from complex analytical techniques with
confined spectral ranges, or use feature decomposition methods that have
limited interpretability. Using liquid-phase Fourier Transform Infrared (FTIR)
spectra, this study presents a structured method for creating accurate and
interpretable property prediction models for neat molecules, aviation fuels,
and blends. Liquid-phase FTIR spectra measurements can be collected quickly and
consistently, offering high reliability, sensitivity, and component specificity
using less than 2 mL of sample. The method first decomposes FTIR spectra into
fundamental building blocks using Non-negative Matrix Factorization (NMF) to
enable scientific analysis of FTIR spectra attributes and fuel properties. The
NMF features are then used to create five ensemble models for predicting final
boiling point, flash point, freezing point, density at 15C, and kinematic
viscosity at -20C. All models were trained using experimental property data
from neat molecules, aviation fuels, and blends. The models accurately predict
properties while enabling interpretation of relationships between compositional
elements of a fuel, such as functional groups or chemical classes, and its
properties. To support sustainable aviation fuel research and development, the
models and data are available on an interactive web tool.


  Contact $P$-wave interactions connected to the Larmor interaction of a
magnetic dipole and Thomas spin precession in the filed of an electric
quadrupole are described and their implications for spectroscopy of exotic
$\Omega^{-}$-atoms are studied. In order to evaluate the magnitude of the
contact $P$-wave interactions as compared to the conventional long-range
interactions and the sensitivity of spectroscopic data to the
$\Omega^{-}$-hyperon quadrupole moment, we consider $2P$ states of $\Omega
^{-}$ atoms formed with light stable nuclei with spins $I \geq 1/2$ and atomic
numbers $Z \leq 10$. The energy level splitting caused by the contact
interactions is 2-5 orders of magnitude smaller than the conventional
long-range interactions. Strong decay widths of $p\Omega ^{-}$ atoms due to
reactions $p\Omega^{-} \to \Lambda \Xi^{0}$ and $p\Omega^{-} \to \Sigma \Xi$,
induced by $t$-channel kaon exchanges, are calculated. $\Omega ^{-}$ atoms
formed with the light nuclei have strong widths 5-6 orders of magnitude higher
than splitting caused by the contact interactions. The low-$L$ pattern in the
energy spectra of intermediate- and high-$Z$ $\Omega ^{-}$ atoms thus cannot be
observed. The $\Omega ^{-}$ quadrupole moment can be measured by observing
$X$-rays from circular transitions between high-$L$ levels in $\Omega^{-}$
exotic atoms. The effect of strong interactions in $^{208}$Pb$\Omega ^{-}$
atoms is negligible starting from $L \sim 10$. The contact $P$-wave
interactions exist in ordinary atoms and $\mu$-meson atoms.


  We introduce two new no-regret algorithms for the stochastic shortest path
(SSP) problem with a linear MDP that significantly improve over the only
existing results of (Vial et al., 2021). Our first algorithm is computationally
efficient and achieves a regret bound
$\widetilde{O}\left(\sqrt{d^3B_{\star}^2T_{\star} K}\right)$, where $d$ is the
dimension of the feature space, $B_{\star}$ and $T_{\star}$ are upper bounds of
the expected costs and hitting time of the optimal policy respectively, and $K$
is the number of episodes. The same algorithm with a slight modification also
achieves logarithmic regret of order
$O\left(\frac{d^3B_{\star}^4}{c_{\min}^2\text{gap}_{\min}}\ln^5\frac{dB_{\star}
K}{c_{\min}} \right)$, where $\text{gap}_{\min}$ is the minimum sub-optimality
gap and $c_{\min}$ is the minimum cost over all state-action pairs. Our result
is obtained by developing a simpler and improved analysis for the
finite-horizon approximation of (Cohen et al., 2021) with a smaller
approximation error, which might be of independent interest. On the other hand,
using variance-aware confidence sets in a global optimization problem, our
second algorithm is computationally inefficient but achieves the first
"horizon-free" regret bound $\widetilde{O}(d^{3.5}B_{\star}\sqrt{K})$ with no
polynomial dependency on $T_{\star}$ or $1/c_{\min}$, almost matching the
$\Omega(dB_{\star}\sqrt{K})$ lower bound from (Min et al., 2021).


  We develop two generalizations of contraction theory, namely,
semi-contraction and weak-contraction theory. First, using the notion of
semi-norm, we propose a geometric framework for semi-contraction theory. We
introduce matrix semi-measures and characterize their properties. We show that
the spectral abscissa of a matrix is the infimum over weighted semi-measures.
For dynamical systems, we use the semi-measure of their Jacobian to
characterize the contractivity properties of their trajectories. Second, for
weakly contracting systems, we prove a dichotomy for the asymptotic behavior of
their trajectories and novel sufficient conditions for convergence to an
equilibrium. Third, we show that every trajectory of a doubly-contracting
system, i.e., a system that is both weakly and semi-contracting, converges to
an equilibrium point. Finally, we apply our results to various important
network systems including affine averaging and affine flow systems,
continuous-time distributed primal-dual algorithms, and networks of
diffusively-coupled dynamical systems. For diffusively-coupled systems, the
semi-contraction theory leads to a sufficient condition for synchronization
that is sharper, in general, than previously-known tests.


  The commuting variety of a reductive Lie algebra $\mathfrak{g}$ is the
underlying variety of a well defined subscheme of
$\mathfrak{g}\times\mathfrak{g}$. In this note, it is proved that this scheme
is normal and Cohen-Macaulay. In particular, its ideal of definition is a prime
ideal. As a matter of fact, this theorem results from a so called Property (P)
for a simple Lie algebra. This property says that some cohomology complexes are
exact.


  We propose a finite automaton-style solution concept for supergames. In our
model, we define an equilibrium to be a cycle of state switches and a supergame
to be an infinite walk on states of a finite stage game. We show that if the
stage game is locally non-cooperative, and the utility function is monotonously
decreasing as the number of defective agents increases, the symmetric
multiagent prisoners' dilemma supergame must contain one symmetric equilibrium
and can contain asymmetric equilibria.


  In this paper, iterative multi-user detection techniques for multi-beam
communications are presented. The solutions are based on a successive
interference cancellation architecture and a channel decoding to treat the
co-channel interference. Beams forming and channels coefficients are estimated
and updated iteratively. A developed technique of signals combining allows
power improvement of the useful received signal; and then reduction of the bit
error rates with low signal to noise ratios. The approach is applied to a
synchronous multi-beam satellite link under an additive white Gaussian channel.
Evaluation of the techniques is done with computer simulations, where a noised
and multi-access environment is considered. The simulations results show the
good performance of the proposed solutions.


  We develop algebraic geometry for general Segal's Gamma-rings and show that
this new theory unifies two approaches we had considered earlier on (for a
geometry under Spec Z). The starting observation is that the category obtained
by gluing together the category of commutative rings and that of pointed
commutative monoids, that we used in our previous work to define F1-schemes, is
naturally a full subcategory of the category of Segal's Gamma-rings. In this
paper we develop the affine case of this general algebraic geometry: one
distinctive feature is that the spectrum Spec(A) of a Gamma-ring is in general
a Grothendieck site rather than a point set endowed with a topology. Two
striking features of this new geometry are that it is the natural domain for
cyclic homology and for homological algebra, and that new operations, which do
not make sense in ordinary algebraic geometry, are here available. For
instance, in this new context, the quotient of a ring by a multiplicative
subgroup is still a Gamma-ring to which our general theory applies. Thus the
adele class space gives rise naturally to a Gamma-ring. Finally, we show that
our theory is not a special case of the T\"oen-Vaqui\' e general theory of
algebraic geometry under Spec Z.


  It is pointed out that the meson mixing matrix elements usually considered
responsible for the bulk of the observed few-body charge symmetry breaking are
naturally $q^2$-dependent in QCD. For $\pi^o-\eta$ mixing, using the usual
representation of the pseudoscalar fields, the leading $q^2$ dependence can be
explicitly calculated using chiral perturbation theory to one loop, the result
being a significant decrease in the magnitude of the matrix element in going
from timelike to spacelike values of $q^2$. Since it is the latter range of
$q^2$ which is relevant to NN scattering and the few-body bound state, this
result calls into serious question the standard treatment of few-body charge
symmetry breaking contributions associated with $\pi^o-\eta$ and $\rho -\omega$
mixing.


  We give a construction of Gorenstein projective $\tau$-tilting modules in
terms of tensor products of modules. As a consequence, we give a class of
non-self-injective algebras admitting non-trivial Gorenstein projective
$\tau$-tilting modules. Moreover, we show that a finite dimensional algebra
$\Lambda$ over an algebraically closed field is $CM$-$\tau$-tilting finite if
$T_n(\Lambda)$ is $CM$-$\tau$-tilting finite which gives a partial answer to a
question on $CM$-$\tau$-tilting finite algebras posed by Xie and Zhang.


  We present both an overview and a perspective of recent experimental advances
and proposed new approaches to performing computation using memristors. A
memristor is a 2-terminal passive component with a dynamic resistance depending
on an internal parameter. We provide an brief historical introduction, as well
as an overview over the physical mechanism that lead to memristive behavior.
This review is meant to guide nonpractitioners in the field of memristive
circuits and their connection to machine learning and neural computation.


  The intellectual property protection of deep learning (DL) models has
attracted increasing serious concerns. Many works on intellectual property
protection for Deep Neural Networks (DNN) models have been proposed. The vast
majority of existing work uses DNN watermarking to verify the ownership of the
model after piracy occurs, which is referred to as passive verification. On the
contrary, we focus on a new type of intellectual property protection method
named active copyright protection, which refers to active authorization control
and user identity management of the DNN model. As of now, there is relatively
limited research in the field of active DNN copyright protection. In this
review, we attempt to clearly elaborate on the connotation, attributes, and
requirements of active DNN copyright protection, provide evaluation methods and
metrics for active copyright protection, review and analyze existing work on
active DL model intellectual property protection, discuss potential attacks
that active DL model copyright protection techniques may face, and provide
challenges and future directions for active DL model intellectual property
protection. This review is helpful to systematically introduce the new field of
active DNN copyright protection and provide reference and foundation for
subsequent work.


  We show that the two-dimensional (2D) local Hamiltonian problem with the
constraint that the ground state obeys area laws is QMA-complete. We also prove
similar results in 2D translation-invariant systems and for the 3D Heisenberg
and Hubbard models with local magnetic fields. Consequently, unless MA = QMA,
not all ground states of 2D local Hamiltonians with area laws have efficient
classical representations that support efficient computation of local
expectation values. In the future, even if area laws are proved for ground
states of 2D gapped systems, the computational complexity of these systems
remains unclear.


  Contemporary deep learning multi-scale deblurring models suffer from many
issues: 1) They perform poorly on non-uniformly blurred images/videos; 2)
Simply increasing the model depth with finer-scale levels cannot improve
deblurring; 3) Individual RGB frames contain a limited motion information for
deblurring; 4) Previous models have a limited robustness to spatial
transformations and noise. Below, we extend the DMPHN model by several
mechanisms to address the above issues: I) We present a novel self-supervised
event-guided deep hierarchical Multi-patch Network (MPN) to deal with blurry
images and videos via fine-to-coarse hierarchical localized representations;
II) We propose a novel stacked pipeline, StackMPN, to improve the deblurring
performance under the increased network depth; III) We propose an event-guided
architecture to exploit motion cues contained in videos to tackle complex blur
in videos; IV) We propose a novel self-supervised step to expose the model to
random transformations (rotations, scale changes), and make it robust to
Gaussian noises. Our MPN achieves the state of the art on the GoPro and
VideoDeblur datasets with a 40x faster runtime compared to current multi-scale
methods. With 30ms to process an image at 1280x720 resolution, it is the first
real-time deep motion deblurring model for 720p images at 30fps. For StackMPN,
we obtain significant improvements over 1.2dB on the GoPro dataset by
increasing the network depth. Utilizing the event information and
self-supervision further boost results to 33.83dB.


  With the wide application of machine translation, the testing of Machine
Translation Systems (MTSs) has attracted much attention. Recent works apply
Metamorphic Testing (MT) to address the oracle problem in MTS testing. Existing
MT methods for MTS generally follow the workflow of input transformation and
output relation comparison, which generates a follow-up input sentence by
mutating the source input and compares the source and follow-up output
translations to detect translation errors, respectively. These methods use
various input transformations to generate test case pairs and have successfully
triggered numerous translation errors. However, they have limitations in
performing fine-grained and rigorous output relation comparison and thus may
report many false alarms and miss many true errors. In this paper, we propose a
word closure-based output comparison method to address the limitations of the
existing MTS MT methods. We first propose word closure as a new comparison
unit, where each closure includes a group of correlated input and output words
in the test case pair. Word closures suggest the linkages between the
appropriate fragment in the source output translation and its counterpart in
the follow-up output for comparison. Next, we compare the semantics on the
level of word closure to identify the translation errors. In this way, we
perform a fine-grained and rigorous semantic comparison for the outputs and
thus realize more effective violation identification. We evaluate our method
with the test cases generated by five existing input transformations and the
translation outputs from three popular MTSs. Results show that our method
significantly outperforms the existing works in violation identification by
improving the precision and recall and achieving an average increase of 29.9%
in F1 score. It also helps to increase the F1 score of translation error
localization by 35.9%.


  For any accessible partially hyperbolic homogeneous flow, we show that all
smooth time changes are K and hence mixing of all orders. We also establish
stable ergodicity for time-one map of these time changes.


  Using data from the Near-Infrared S0 Survey (NIRS0S) of nearby, early-type
galaxies, we examine the distribution of bar strengths in S0 galaxies as
compared to S0/a and Sa galaxies, and as compared to previously published bar
strength data for Ohio State University Bright Spiral Galaxy Survey (OSUBSGS)
spiral galaxies. Bar strengths based on the gravitational torque method are
derived from 2.2 micron Ks-band images for a statistical sample of 138 (98 S0,
40 S0/a,Sa) galaxies having a mean total blue magnitude <B_T> <= 12.5 and
generally inclined less than 65 degrees. We find that S0 galaxies have weaker
bars on average than spiral galaxies in general, even compared to their closest
spiral counterparts, S0/a and Sa galaxies. The differences are significant and
cannot be due entirely to uncertainties in the assumed vertical scale-heights
or in the assumption of constant mass-to-light ratios. Part of the difference
is likely due simply to the dilution of the bar torques by the higher mass
bulges seen in S0s. If spiral galaxies accrete external gas, as advocated by
Bournaud & Combes, then the fewer strong bars found among S0s imply a lack of
gas accretion according to this theory. If S0s are stripped former spirals, or
else are evolved from former spirals due to internal secular dynamical
processes which deplete the gas as well as grow the bulges, then the weaker
bars and the prevalence of lenses in S0 galaxies could further indicate that
bar evolution continues to proceed during and even after gas depletion


  Precomputed Radiance Transfer (PRT) remains an attractive solution for
real-time rendering of complex light transport effects such as glossy global
illumination. After precomputation, we can relight the scene with new
environment maps while changing viewpoint in real-time. However, practical PRT
methods are usually limited to low-frequency spherical harmonic lighting.
All-frequency techniques using wavelets are promising but have so far had
little practical impact. The curse of dimensionality and much higher data
requirements have typically limited them to relighting with fixed view or only
direct lighting with triple product integrals. In this paper, we demonstrate a
hybrid neural-wavelet PRT solution to high-frequency indirect illumination,
including glossy reflection, for relighting with changing view. Specifically,
we seek to represent the light transport function in the Haar wavelet basis.
For global illumination, we learn the wavelet transport using a small
multi-layer perceptron (MLP) applied to a feature field as a function of
spatial location and wavelet index, with reflected direction and material
parameters being other MLP inputs. We optimize/learn the feature field
(compactly represented by a tensor decomposition) and MLP parameters from
multiple images of the scene under different lighting and viewing conditions.
We demonstrate real-time (512 x 512 at 24 FPS, 800 x 600 at 13 FPS) precomputed
rendering of challenging scenes involving view-dependent reflections and even
caustics.


  We introduce a new approach for the synthesis of Mealy machines from
specifications in linear-time temporal logic (LTL), where the number of cycles
in the state graph of the implementation is limited by a given bound. Bounding
the number of cycles leads to implementations that are structurally simpler and
easier to understand. We solve the synthesis problem via an extension of
SAT-based bounded synthesis, where we additionally construct a witness
structure that limits the number of cycles. We also establish a
triple-exponential upper and lower bound for the potential blow-up between the
length of the LTL formula and the number of cycles in the state graph.


  For a comprehensive understanding of planetary formation and evolution, we
need to investigate the environment in which planets form: circumstellar disks.
Here we present high-contrast imaging observations of V4046 Sagittarii, a
20-Myr-old close binary known to host a circumbinary disk. We have discovered
the presence of rotating shadows in the disk, caused by mutual occultations of
the central binary. Shadow-like features are often observed in
disks\cite{garufi,marino15}, but those found thus far have not been due to
eclipsing phenomena. We have used the phase difference due to light travel time
to measure the flaring of the disk and the geometrical distance of the system.
We calculate a distance that is in very good agreement with the value obtained
from the Gaia mission's Data Release 2 (DR2), and flaring angles of $\alpha =
6.2 \pm 0.6 $ deg and $\alpha = 8.5 \pm 1.0 $ deg for the inner and outer disk
rings, respectively. Our technique opens up a path to explore other binary
systems, providing an independent estimate of distance and the flaring angle, a
crucial parameter for disk modelling.


  Data-Free Knowledge Distillation (DFKD) has made significant recent strides
by transferring knowledge from a teacher neural network to a student neural
network without accessing the original data. Nonetheless, existing approaches
encounter a significant challenge when attempting to generate samples from
random noise inputs, which inherently lack meaningful information.
Consequently, these models struggle to effectively map this noise to the
ground-truth sample distribution, resulting in prolonging training times and
low-quality outputs. In this paper, we propose a novel Noisy Layer Generation
method (NAYER) which relocates the random source from the input to a noisy
layer and utilizes the meaningful constant label-text embedding (LTE) as the
input. LTE is generated by using the language model once, and then it is stored
in memory for all subsequent training processes. The significance of LTE lies
in its ability to contain substantial meaningful inter-class information,
enabling the generation of high-quality samples with only a few training steps.
Simultaneously, the noisy layer plays a key role in addressing the issue of
diversity in sample generation by preventing the model from overemphasizing the
constrained label information. By reinitializing the noisy layer in each
iteration, we aim to facilitate the generation of diverse samples while still
retaining the method's efficiency, thanks to the ease of learning provided by
LTE. Experiments carried out on multiple datasets demonstrate that our NAYER
not only outperforms the state-of-the-art methods but also achieves speeds 5 to
15 times faster than previous approaches. The code is available at
https://github.com/tmtuan1307/nayer.


  We present a method for the calculation of the effects of external
irradiation on the geometrical shape of the secondary in a close binary
containing a compact star, the source of the radiation, and a normal companion
star, where we include the possibility of shadowing by an accretion disc. The
model is based on a simple modification of the standard Roche binary potential
in which the radiation-pressure force is parameterised using the ratio of the
radiation to the gravitational force. We have constructed numerical solutions
of approximate 3-dimensional irradiated equipotential surfaces to demonstrate
the main geometrical effects of external radiation pressure. For systems in
which the inner Lagrangian point is irradiated directly and for sufficiently
high irradiation fluxes, the critical condition for which the secondary fills
its tidal lobe changes from an inner to an outer critical configuration, where
the critical equipotential surface connects to one of the outer rather than the
inner Lagrangian point. Such a situation may apply to evaporating binary pulsar
systems (e.g. PSR 1957+20), stars orbiting supermassive black holes in AGN and
some high-mass X-ray binaries (including Centaurus X-3). For systems containing
an accretion disc, which shadows the inner Lagrangian point from the external
irradiation, the presence of significant radiation pressure causes a
non-axisymmetric deformation of the stellar surface. We have calculated
modified Roche potentials to determine the main effects on the optical
lightcurves and radial velocity curves for typical binary parameters. Compared
to previous studies, the inclusion of irradiation-pressure effects results in
changes in the derived system parameters (e.g. component masses, radial
velocities) that may be as high as 30 per cent.


  Recently, the Visual Question Answering (VQA) task has gained increasing
attention in artificial intelligence. Existing VQA methods mainly adopt the
visual attention mechanism to associate the input question with corresponding
image regions for effective question answering. The free-form region based and
the detection-based visual attention mechanisms are mostly investigated, with
the former ones attending free-form image regions and the latter ones attending
pre-specified detection-box regions. We argue that the two attention mechanisms
are able to provide complementary information and should be effectively
integrated to better solve the VQA problem. In this paper, we propose a novel
deep neural network for VQA that integrates both attention mechanisms. Our
proposed framework effectively fuses features from free-form image regions,
detection boxes, and question representations via a multi-modal multiplicative
feature embedding scheme to jointly attend question-related free-form image
regions and detection boxes for more accurate question answering. The proposed
method is extensively evaluated on two publicly available datasets, COCO-QA and
VQA, and outperforms state-of-the-art approaches. Source code is available at
https://github.com/lupantech/dual-mfa-vqa.


  Change of the energy characteristics of muon bundles with an increase of the
primary cosmic ray particles energy can be a key to solving the problem of muon
excess in the extensive air showers (EAS) observed in a number of experiments.
In this work the data on the energy deposit of multi-muon events in a wide
range of zenith angles (and as a consequence in a wide range of primary
particles energies) obtained with NEVOD-DECOR setup over a long time period are
presented. The experimental data are compared with the results of simulations
of EAS muon component performed using CORSIKA code.


  We prove the long standing conjecture in the theory of two-point boundary
value problems that completeness and Dunford's spectrality imply Birkhoff
regularity. In addition we establish the even order part of S.G.Krein's
conjecture that dissipative differential operators are Birkhoff-regular and
give sharp estimate of the norms of spectral projectors in the odd case.
  Considerations are based on a new direct method, exploiting \textit{almost
orthogonality} of Birkhoff's solutions of the equation $l(y)=\lambda y$, which
was discovered earlier by the author.


  Recent deep learning based approaches have outperformed classical stereo
matching methods. However, current deep learning based end-to-end stereo
matching methods adopt a generic encoder-decoder style network with skip
connections. To limit computational requirement, many networks perform
excessive down sampling, which results in significant loss of useful low-level
information. Additionally, many network designs do not exploit the rich
multi-scale contextual information. In this work, we address these
aforementioned problems by carefully designing the network architecture to
preserve required spatial information throughout the network, while at the same
time achieve large effective receptive field to extract multiscale contextual
information. For the first time, we create a synthetic disparity dataset
reflecting real life images captured using a smartphone; this enables us to
obtain state-of-the-art results on common real life images. The proposed model
DISCO is pre-trained on the synthetic Scene Flow dataset and evaluated on
popular benchmarks and our in-house dataset of challenging real life images.
The proposed model outperforms existing state-of-the-art methods in terms of
quality as well as quantitative metrics.


  We revisit the Jaynes-Cummings and anti-Jaynes-Cummings model through the
lens of Lie theory, aiming to highlight the efficacy of an operator-based
approach for diagonalization. We focus on explicitly delineating the steps from
an underlying abstract supersymmetry, provided by the $u(1 \vert 1)$
superalgebra, into concrete proper states and energies in the laboratory frame.
Additionally, we explore the anisotropic Rabi model possessing an underlying
supersymmetry, provided by the $osp(2 \vert 2)$ superalgebra, in a squeezed
reference frame, where it is possible to approximate its spectral
characteristics by an effective Jaynes--Cummings model. Finally, we identify a
regime for a factorizable anisotropic Rabi model, exhibiting an equally spaced,
double degenerate energy spectrum with a unique ground state energy. Our work
aims to merge mathematical physics with practical quantum optics, underscoring
the critical role of Lie theory.


  The maximal Orlicz spaces such that the mixed logarithmic means of multiple
Walsh-Fourier series for the functions from these spaces converge in measure
and in norm are found.


  We consider an active scalar equation that is motivated by a model for
magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive
equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast,
the critically diffusive equation is well-posed. In this case we give an
example of a steady state that is nonlinearly unstable, and hence produces a
dynamo effect in the sense of an exponentially growing magnetic field.


  In spite of the close connection between the evaluation of quantified Boolean
formulas (QBF) and propositional satisfiability (SAT), tools and techniques
which exploit structural properties of SAT instances are known to fail for QBF.
This is especially true for the structural parameter treewidth, which has
allowed the design of successful algorithms for SAT but cannot be
straightforwardly applied to QBF since it does not take into account the
interdependencies between quantified variables.
  In this work we introduce and develop dependency treewidth, a new structural
parameter based on treewidth which allows the efficient solution of QBF
instances. Dependency treewidth pushes the frontiers of tractability for QBF by
overcoming the limitations of previously introduced variants of treewidth for
QBF. We augment our results by developing algorithms for computing the
decompositions that are required to use the parameter.


  The advent of the Internet of Things (IoT) has brought forth an era of
unprecedented connectivity, with an estimated 80 billion smart devices expected
to be in operation by the end of 2025. These devices facilitate a multitude of
smart applications, enhancing the quality of life and efficiency across various
domains. Machine Learning (ML) serves as a crucial technology, not only for
analyzing IoT-generated data but also for diverse applications within the IoT
ecosystem. For instance, ML finds utility in IoT device recognition, anomaly
detection, and even in uncovering malicious activities. This paper embarks on a
comprehensive exploration of the security threats arising from ML's integration
into various facets of IoT, spanning various attack types including membership
inference, adversarial evasion, reconstruction, property inference, model
extraction, and poisoning attacks. Unlike previous studies, our work offers a
holistic perspective, categorizing threats based on criteria such as adversary
models, attack targets, and key security attributes (confidentiality,
availability, and integrity). We delve into the underlying techniques of ML
attacks in IoT environment, providing a critical evaluation of their mechanisms
and impacts. Furthermore, our research thoroughly assesses 65 libraries, both
author-contributed and third-party, evaluating their role in safeguarding model
and data privacy. We emphasize the availability and usability of these
libraries, aiming to arm the community with the necessary tools to bolster
their defenses against the evolving threat landscape. Through our comprehensive
review and analysis, this paper seeks to contribute to the ongoing discourse on
ML-based IoT security, offering valuable insights and practical solutions to
secure ML models and data in the rapidly expanding field of artificial
intelligence in IoT.


  The hybrid halide perovskite CH$_3$NH$_3$PbI$_3$ is easy to manufacture and
inexpensive. Despite these, its efficiency as a solar cell is comparable to
today's efficient solar cells. For these reasons, it is attracting a lot of
attention today. However, the effects of the CH$_3$NH$_3^+$ (MA) molecule in
the perovskite structure on the electronic and structural properties are still
a matter of debate. Previous studies have generally focused on the rotation of
the MA molecule. In this study, from a different perspective, the effects of
the movement of the MA molecule along the C-N axis are investigated. With this
method, the effects of the MA molecule were examined in a more controlled way.
In this study, density functional theory (DFT) that accounts for van der Waals
(vdW) interactions was used in the calculations for the cases. According to the
data obtained, H-I ionic bonds are formed between the MA molecule and the
inorganic framework. Within the structure, the H-I bond length tends to be
preserved, although the position of the MA changes. In this mechanism, the I
ion plays an important role by moving away from its place in the Pb-I-Pb
alignment. The position of the I ion determines the nature of the band gap
transition. Another effect is on the value of the band gap. Depending on the
position of the I ion, the band gap may narrow by about 0.26 eV. The separation
of the I ion from the Pb-I-Pb alignment by the effect of the MA molecule breaks
the inverse symmetry. According to the data obtained from this study, this
mechanism in the band gap is due to the breaking of the inverse symmetry in the
crystal structure.


  We study the interplay between disorder, interactions and decoherence induced
by spontaneous emission process. Interactions are included in the Anderson
model via a mean-field approximation, and a simple model for spontaneous
emission is introduced. Numerical simulations allow us to study the effects of
decoherence on different dynamical regimes. Physical pictures for the
mechanisms at play are discussed and provide simple interpretations. Finally,
we discuss the validity of scaling laws on the initial state width.


  We present a parallel data-driven strategy to identify finite-dimensional
functional spaces invariant under the Koopman operator associated to an unknown
dynamical system. We build on the Symmetric Subspace Decomposition (SSD)
algorithm, a centralized method that under mild conditions on data sampling
provably finds the maximal Koopman-invariant subspace and all Koopman
eigenfunctions in an arbitrary finite-dimensional functional space. A network
of processors, each aware of a common dictionary of functions and equipped with
a local set of data snapshots, repeatedly interact over a directed
communication graph. Each processor receives its neighbors' estimates of the
invariant dictionary and refines its estimate by applying SSD with its local
data on the intersection of the subspaces spanned by its own dictionary and the
neighbors' dictionaries. We identify conditions on the network topology to
ensure the algorithm identifies the maximal Koopman-invariant subspace in the
span of the original dictionary, characterize its time, computational, and
communication complexity, and establish its robustness against communication
failures.


  We apply the bar construction to the nerve of a double Lie groupoid to obtain
a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental
groupoid from the fundamental double groupoid of a Lie groupoid. In the case of
a symplectic double groupoid, we study the induced closed 2-form on the
associated local Lie 2-groupoid, which leads us to propose a definition of a
symplectic 2-groupoid.


  A topology optimization formulation including a model of the layer-by-layer
additive manufacturing (AM) process is considered. Defined as a multi-objective
minimization problem, the formulation accounts for the performance and cost of
both the final and partially manufactured designs and allows for considering
AM-related issues such as overhang and residual stresses in the optimization.
The formulation is exemplified by stiffness optimization in which the overhang
is limited by adding mechanical or thermal compliance as a measure of the cost
of partially manufactured designs. Convergence of the model as the approximate
layer-by-layer model is refined is shown theoretically, and an extensive
numerical study indicates that this convergence can be fast, thus making it a
computationally viable approach useful for including AM-related issues into
topology optimization. The examples also show that drips and sharp corners
associated with some geometry-based formulations for overhang limitation can be
avoided. The codes used in this article are written in Python using only open
sources libraries and are available for reference.


  Context. The diffuse gamma-ray emission of $^{26}{\rm Al}$ at 1.8 MeV
reflects ongoing nucleosynthesis in the Milky Way, and traces massive-star
feedback in the interstellar medium due to its 1 Myr radioactive lifetime.
Interstellar-medium morphology and dynamics are investigated in astrophysics
through 3D hydrodynamic simulations in fine detail, as only few suitable
astronomical probes are available. Aims. We compare a galactic-scale
hydrodynamic simulation of the Galaxy's interstellar medium, including feedback
and nucleosynthesis, with gamma-ray data on $^{26}{\rm Al}$ emission in the
Milky Way extracting constraints that are only weakly dependent on the
particular realisation of the simulation or Galaxy structure. Methods. Due to
constraints and biases in both the simulations and the gamma-ray observations,
such comparisons are not straightforward. For a direct comparison, we perform
maximum likelihood fits of simulated sky maps as well as observation-based
maximum entropy maps to measurements with INTEGRAL/SPI. To study general
morphological properties, we compare the scale heights of $^{26}{\rm Al}$
emission produced by the simulation to INTEGRAL/SPI measurements.} Results. The
direct comparison shows that the simulation describes the observed inner Galaxy
well, but differs significantly from the observed full-sky emission morphology.
Comparing the scale height distribution, we see similarities for small scale
height features and a mismatch at larger scale heights. We attribute this to
the prominent foreground emission sites that are not captured by the
simulation.


  We study the dynamics of the quintom dark energy model using state-of-the-art
cosmological observations. The set of equations has been converted into an
autonomous system using suitable transformations of the variables. We have
discussed the fixed points of the model and the general phase-space behavior,
in particular, in finding the existence of the tracker solutions for this
model. The observations suggest that at late times the phantom field should
dominate the dark energy sector with an approximately 15% share to the
quintessence counterpart, and with both fields tracking the background at early
times. A Bayesian model comparison with LambdaCDM has also been done by
computing the Bayes factor and a positive preference has been obtained for the
quintom model. Although not fully resolved, the Hubble tension can be reduced
to 2.6{\sigma} when compared with the value of H0 reported in [1] and to
1.6{\sigma} when compared with that of [2].


  In this paper, we consider the problem of minimizing the sum of nonconvex and
possibly nonsmooth functions over a connected multi-agent network, where the
agents have partial knowledge about the global cost function and can only
access the zeroth-order information (i.e., the functional values) of their
local cost functions. We propose and analyze a distributed primal-dual
gradient-free algorithm for this challenging problem. We show that by
appropriately choosing the parameters, the proposed algorithm converges to the
set of first order stationary solutions with a provable global sublinear
convergence rate. Numerical experiments demonstrate the effectiveness of our
proposed method for optimizing nonconvex and nonsmooth problems over a network.


  The purpose of this note is to describe a framework which unifies radial,
chordal and dipolar SLE. When the definition of SLE(kappa;rho) is extended to
the setting where the force points can be in the interior of the domain, radial
SLE(kappa) becomes chordal SLE(kappa;rho), with rho=kappa-6, and vice versa. We
also write down the martingales describing the Radon-Nykodim derivative of
SLE(kappa;rho_1,...,rho_n) with respect to SLE(kappa).


  Testing the implementation of deep learning systems and their training
routines is crucial to maintain a reliable code base. Modern software
development employs processes, such as Continuous Integration, in which changes
to the software are frequently integrated and tested. However, testing the
training routines requires running them and fully training a deep learning
model can be resource-intensive, when using the full data set. Using only a
subset of the training data can improve test run time, but can also reduce its
effectiveness. We evaluate different ways for training set reduction and their
ability to mimic the characteristics of model training with the original full
data set. Our results underline the usefulness of training set reduction,
especially in resource-constrained environments.


  We define a certain Hecke theoretic notion of family of smooth admissible
representations of $GL_n(F)$, or of products of such groups, where $F$ is a
nonarchimedean local field of characteristic zero. While this notion of family
is rather weak a priori, we show that it implies strong rigidity properties for
the Bernstein-Zelevinsky presentations of the members of such families, as well
as for the variation of their epsilon factors (attached to arbitrary functorial
lifts). Examples of such families come often from the theory of eigenvarieties,
and in this case our results imply analyticity properties for the epsilon
factors of the members of these families.


  Millimeter wave (mmWave) is an attractive candidate for high-speed mobile
communications in the future. However, due to the propagation characteristics
of mmWave, beam and and and and alignment becomes a key challenge for serving
users with fast moving speeds. In this paper, we develop a joint beam and
channel tracking algorithm that can track beams from the horizontal and
vertical directions by using two-dimensional (2D) phased antenna arrays. A
general sequence of optimal trial beamforming parameters is obtained to achieve
the minimum Cramer-Rao lower bound (CRLB) of joint beam and channel tracking
asymptotically as antenna number grows to infinity. This sequence is proved to
be asymptotically optimal in different conditions, e.g., channel coefficients,
path directions, and antenna array sizes. We prove that the proposed algorithm
converges to the minimum CRLB in static scenarios. Simulation results show that
our algorithm outperforms several existing algorithms in tracking accuracy and
speed band.


  Based on a general theory of descendant trees of finite p-groups and the
virtual periodicity isomorphisms between the branches of a coclass subtree, the
behavior of algebraic invariants of the tree vertices and their automorphism
groups under these isomorphisms is described with simple transformation laws.
For the tree of finite 3-groups with elementary bicyclic commutator quotient,
the information content of each coclass subtree with metabelian mainline is
shown to be finite. As a striking novelty in this paper, evidence is provided
of co-periodicity isomorphisms between coclass forests which reduce the
information content of the entire metabelian skeleton and a significant part of
non-metabelian vertices to a finite amount of data.


  Theoretical treatments of tunneling in electronic devices are often based on
one-dimensional (1D) approximations. Here we show that for many nanoscale
devices, such as widely studied semiconductor gate-defined quantum dots, 1D
approximations yield an incorrect functional dependence on the tunneling
parameters (e.g., lead width and barrier length) and an incorrect magnitude for
the transport conductance. Remarkably, the physics of tunneling in 2D or 3D
also yields transport behavior that appears classical (like Ohm's law), even
deep in the quantum regime.


  In contrast to radial velocity surveys, results from microlensing surveys
indicate that giant planets with masses greater than the critical mass for core
accretion ($\sim 0.1~M_{\rm Jup}$) are relatively common around low-mass stars.
Using the methodology developed in the first paper, we predict the sensitivity
of M-dwarf radial velocity (RV) surveys to analogs of the population of planets
inferred by microlensing. We find that RV surveys should detect a handful of
super-Jovian ($>M_{\rm Jup}$) planets at the longest periods being probed.
These planets are indeed found by RV surveys, implying that the demographic
constraints inferred from these two methods are consistent. We combine the
results from both methods to estimate planet frequencies spanning wide regions
of parameter space. We find that the frequency of Jupiters and super-Jupiters
($1\lesssim m_p\sin{i}/M_{\rm Jup}\lesssim 13$) with periods $1\leq P/{\rm
days}\leq 10^4$ is $f_{\rm J}=0.029^{+0.013}_{-0.015}$, a median factor of 4.3
($1.5-14$ at 95% confidence) smaller than the inferred frequency of such
planets around FGK stars of $0.11\pm 0.02$. However, we find the frequency of
all giant planets with $30\lesssim m_p\sin{i}/M_{\oplus}\lesssim 10^4$ and
$1\leq P/{\rm days}\leq 10^4$ to be $f_{\rm G}=0.15^{+0.06}_{-0.07}$, only a
median factor of 2.2 ($0.73-5.9$ at 95% confidence) smaller than the inferred
frequency of such planets orbiting FGK stars of $0.31\pm 0.07$. For a more
conservative definition of giant planets ($50\lesssim
m_p\sin{i}/M_{\oplus}\lesssim 10^4$), we find $f_{\rm G'}=0.11\pm 0.05$, a
median factor of 2.2 ($0.73-6.7$ at 95% confidence) smaller than that inferred
for FGK stars of $0.25\pm 0.05$. Finally, we find the frequency of all planets
with $1\leq m_p\sin{i}/M_{\oplus}\leq 10^4$ and $1\leq P/{\rm days}\leq10^4$ to
be $f_p=1.9\pm 0.5$.


  Using the effective rotational Hamiltonian method, we have conducted an
analysis of the D218O ground and the first excited vibration state rotational
energy levels. The analysis was based on the effective Hamiltonians represented
in several forms: the Watson Hamiltonian, the Hamiltonian expressed in terms of
Pad\'e-Borel approximants, and the Hamiltonian in terms of generating function
expansions. The rotational and centrifugal constants have been determined from
the fitting, which describe the rotational energy levels with an accuracy close
to that of the experimental data. The predictive performance of the model with
respect to highly excited rotational states has been evaluated against the
global variation calculations. The radii of convergence of the effective
rotation Hamiltonian series have been determined.


  We study those Artin groups which, modulo their centers, are finite index
subgroups of the mapping class group of a sphere with at least 5 punctures. In
particular, we show that any injective homomorphism between these groups is
parameterized by a homeomorphism of a punctured sphere together with a map to
the integers. We also give a generating set for the automorphism group of the
pure braid group on at least 4 strands. The technique, following Ivanov, is to
prove that every superinjective map of the complex of curves of a sphere with
at least 5 punctures is induced by a homeomorphism.


  Multiple hypothesis testing, a situation when we wish to consider many
hypotheses, is a core problem in statistical inference that arises in almost
every scientific field. In this setting, controlling the false discovery rate
(FDR), which is the expected proportion of type I error, is an important
challenge for making meaningful inferences. In this paper, we consider the
problem of controlling FDR in an online manner. Concretely, we consider an
ordered, possibly infinite, sequence of hypotheses, arriving one at each
timestep, and for each hypothesis we observe a p-value along with a set of
features specific to that hypothesis. The decision whether or not to reject the
current hypothesis must be made immediately at each timestep, before the next
hypothesis is observed. The model of multi-dimensional feature set provides a
very general way of leveraging the auxiliary information in the data which
helps in maximizing the number of discoveries.
  We propose a new class of powerful online testing procedures, where the
rejections thresholds (significance levels) are learnt sequentially by
incorporating contextual information and previous results. We prove that any
rule in this class controls online FDR under some standard assumptions. We then
focus on a subclass of these procedures, based on weighting significance
levels, to derive a practical algorithm that learns a parametric weight
function in an online fashion to gain more discoveries. We also theoretically
prove, in a stylized setting, that our proposed procedures would lead to an
increase in the achieved statistical power over a popular online testing
procedure proposed by Javanmard & Montanari (2018). Finally, we demonstrate the
favorable performance of our procedure, by comparing it to state-of-the-art
online multiple testing procedures, on both synthetic data and real data
generated from different applications.


  Non-classical probability (along with its underlying logic) is a defining
feature of quantum mechanics. A formulation that incorporates them, inherently
and directly, would promise a unified description of seemingly different
prescriptions of non-classicality of states that have been proposed so far.
This paper sets up such a formalism. It is based on elementary considerations,
free of ad-hoc definitions, and is completely operational. It permits a
systematic construction of non-classicality conditions on states and also to
quantify the non-classicality, at the same time. This quantification, as shown
for the example of two level systems, can serve as a measure of coherence and
can be furthermore, harnessed to obtain a measure for pure state entanglement
for coupled two level systems.


  Smart meters (SMs) measure and report users' energy consumption to the
utility provider (UP) in almost real-time, providing a much more detailed
depiction of the consumer's energy consumption compared to their analog
counterparts. This increased rate of information flow to the UP, together with
its many potential benefits, raise important concerns regarding user privacy.
This work investigates, from an information theoretic perspective, the privacy
that can be achieved in a multi-user SM system in the presence of an
alternative energy source (AES). To measure privacy, we use the mutual
information rate between the users' real energy consumption profile and the SM
readings that are available to the UP. The objective is to characterize the
\textit{privacy-power function}, defined as the minimal information leakage
rate that can be obtained with an average power limited AES. We characterize
the privacy-power function in a single-letter form when the users' energy
demands are assumed to be independent and identically distributed over time.
Moreover, for binary and exponentially distributed energy demands, we provide
an explicit characterization of the privacy-power function. For any discrete
energy demands, we demonstrate that the privacy-power function can always be
efficiently evaluated numerically. Finally, for continuous energy demands, we
derive an explicit lower-bound on the privacy-power function, which is tight
for exponentially distributed loads.


  To date, high-resolution electron microscopy has largely relied on using the
phase of the exit wave function at the exit surface to form a high-resolution
electron microscopic image. We have for the first time used chromatic
aberration correction to implement a new imaging mode to achieve amplitude
contrast imaging in high-resolution electron microscopy, allowing us to obtain
directly interpretable high-resolution electron microscopic images with
discrimination between light and heavy atomic columns. Using this imaging
approach, we have successfully visualized the atomic structure in a
BaTiO3/CaTiO3 superlattice with high spatial accuracy and discrimination
between Ba and Ca columns, providing direct visualization of the Ca and Ba
associated oxygen octahedral tilt that controls ferroelectric behavior in these
superlattice structures. Furthermore, this approach offers new opportunities to
unravel the structure in a wide range of materials, especially complex oxides
with exotic behaviors based on specific structural arrangements.


  This PhD thesis develops an integrated mathematical model for autonomic
nervous system control on cardiovascular activity. The model extensively covers
cardiovascular neural pathways including a wide range of afferent sensory
neurons, central processing by autonomic premotor neurons, efferent outputs via
preganglionic and postganglionic autonomic neurons and dynamics of
neurotransmitters at cardiovascular effectors organs. We performed over 500
cardiovascular experiments using clinical autonomic tests on 72 subjects
ranging from 11 to 82 years old and collected typical cardiovascular signals
such as electrocardiogram, arterial pulse, arterial blood pressure, respiration
pattern, galvanic skin response and skin temperature. After statistical
evaluation in the time and frequency domains, the data were especially used to
resolving a constrained optimization task. Results bring evidences supporting
the hypothesis that Mayer waves result from a rhythmic sympathetic discharge of
pacemaker-like sympathetic premotor neurons. Simulation also shows that
vagally-mediated tachycardia, observed during vagal maneuvers on some subjects
could be related to the secretion of vasoactive neurotransmitters by the vagal
nerve. We additionally identified model parameters for estimating the resting
sympathetic and parasympathetic tone which are believed to be linked to some
pathological states. Results show higher vagal tone on young subjects with a
decreasing trend with aging, what agrees with the data from heart rate
variability studies. Tonic sympathetic activity was found to possibly emerge
from pacemaker premotor neurons, but also from activation of chemoreceptors to
a lesser extent. The thesis opens perspectives for future work including
validating the markers of autonomic tone provided by our model against data
from experiments with pharmacological blockers and invasive neural activity
recordings.


  For some class of geometric flows, we obtain the (logarithmic) Sobolev
inequalities and their equivalence up to different factors directly and also
obtain the long time non-collapsing and non-inflated properties, which
generalize the results in the case of Ricci flow or List-Ricci flow or
harmonic-Ricci flow. As applications, for mean curvature flow in Lorentzian
space with nonnegative sectional curvature and twisted K\"ahler-Ricci flow on
Fano manifolds, we get the results above.


  A general conformal mapping is proposed to design omnidirectional broadband
wave absorbers by transformation method. When applied to electromagnetic (EM)
and acoustic waves, the existing material parameters of the EM and acoustic
omnidirectional absorbers, which are previously obtained by Hamiltonian optics
and geometry acoustics, can be recovered. In addition, magnetic and
mass-density-controlled omnidirectional absorbers for EM and acoustic waves can
also be designed, respectively. We then apply the conformal mapping to design
an omnidirectional elastic wave absorber, the corresponding material
realization of such elastic absorber is also proposed and validated by
numerical simulation.


  This paper is about the efficient generation of dense, colored models of
city-scale environments from range data and in particular, stereo cameras.
Better maps make for better understanding; better understanding leads to better
robots, but this comes at a cost. The computational and memory requirements of
large dense models can be prohibitive. We provide the theory and the system
needed to create city-scale dense reconstructions. To do so, we apply a
regularizer over a compressed 3D data structure while dealing with the complex
boundary conditions this induces during the data-fusion stage. We show that
only with these considerations can we swiftly create neat, large, "well
behaved" reconstructions. We evaluate our system using the KITTI dataset and
provide statistics for the metric errors in all surfaces created compared to
those measured with 3D laser. Our regularizer reduces the median error by 40%
in 3.4 km of dense reconstructions with a median accuracy of 6 cm. For
subjective analysis, we provide a qualitative review of 6.1 km of our dense
reconstructions in an attached video. These are the largest dense
reconstructions from a single passive camera we are aware of in the literature.


  Given the impending timeline of developing good-quality quantum processing
units, it is time to rethink the approach to advance quantum computing
research. Rather than waiting for quantum hardware technologies to mature, we
need to start assessing in tandem the impact of the occurrence of quantum
computing, or rather Quantum Computing Logic (QC-Logic), on various scientific
fields. This is where the subtitle comes from. A new scientific revolution is
unfolding. In making real scientific progress, we need to use an additional and
complementary approach, which the NISQ program or any follow-up approach does
not propose. We must be aware that defining, implementing, and testing quantum
concepts in any field is tremendous work. The main reason is that QC initiates
an overall revolution in all scientific fields, and how those machines will be
used in daily life is a very big challenge. That is why we propose a complete
update of the first PISQ paper. We still advocate the additional PISQ approach:
Perfect Intermediate-Scale Quantum computing based on a well-established
concept of perfect qubits. We expand the quantum road map with (N)FTQC, which
stands for (Non) Fault-Tolerant Quantum Computing. This will allow researchers
to focus exclusively on developing new applications by defining the algorithms
in terms of perfect qubits and evaluating them in two ways. Either executed on
quantum computing simulators executed on supercomputers or hardware-based qubit
chips. This approach will be explained in this paper. Our planet needs a
long-term vision and solution. It will enable universities and companies alike
to accelerate the development of new quantum algorithms, build the necessary
know-how, and thus address one of the key bottlenecks within the quantum
industry: the lack of talent to develop well-tested quantum applications.


  The initial growth of MnBi on MnAs terminated (GaMn)As is studied by means of
synchrotron based photoelectron spectroscopy. From analysis of surface core
level shifts we conclude that a continued epitaxial MnBi layer is formed, in
which the MnAs/MnBi interface occurs between As and Bi atomic planes. The well
defined 1x2 surface reconstruction of the MnAs surface in preserved for up to 2
ML of MnBi before clear surface degradation occurs.


  Let $B(n,p)$ denote a binomial random variable with parameters $n$ and $p$.
Chv\'{a}tal's theorem says that for any fixed $n\geq 2$, as $m$ ranges over
$\{0,\ldots,n\}$, the probability $q_m:=P(B(n,m/n)\leq m)$ is the smallest when
$m$ is closest to $\frac{2n}{3}$. Motivated by this theorem, in this note we
consider the infimum value of the probability $P(X\leq E[X])$, where $X$ is a
negative binomial random variable. As a consequence, we give an affirmative
answer to the conjecture posed in [Statistics and Probability Letters, 200
(2023) 109871].


  Global Navigation Satellite Systems (GNSS) provide global positioning and
timing. Multiple receivers with known reference positions (stations) can assist
mobile receivers (rovers) in obtaining GNSS corrections and achieve
centimeter-level accuracy on consumer devices. However, GNSS spoofing and
jamming, nowadays achievable with off-the-shelf devices, are serious threats to
the integrity and robustness of public correction networks. In this demo, we
show how manipulation of the Position Navigation and Timing (PNT) solution at
the reference station is reflected in the loss of baseline fix or degraded
accuracy at the rover. Real Time Kinematics (RTK) corrections are valuable but
fundamentally vulnerable: attacking the reference stations can harm all
receivers (rovers) that rely on the targeted reference station.


  We analyze Keck Hires observations of rotation in F, G, and K dwarf members
of the open cluster M34 (NGC 1039), which is 250 Myr old, and we compare them
to the Pleiades, Hyades, and NGC 6475. The upper bound to rotation seen in M34
is about a factor of two lower than for the 100 Myr-old Pleiades, but most M34
stars are well below this upper bound, and it is the overall convergence in
rotation rates that is most striking. A few K dwarfs in M34 are still rapid
rotators, suggesting that they have undergone core-envelope decoupling,
followed by replenishment of surface angular momentum from an internal
reservoir. Our comparison of rotation in these clusters indicates that the time
scale for the coupling of the envelope to the core must be close to 100 Myr if
decoupling does, in fact, occur.


  We propose a new numerical algorithm for computing the tensor rank
decomposition or canonical polyadic decomposition of higher-order tensors
subject to a rank and genericity constraint. Reformulating this computational
problem as a system of polynomial equations allows us to leverage recent
numerical linear algebra tools from computational algebraic geometry. We
characterize the complexity of our algorithm in terms of an algebraic property
of this polynomial system -- the multigraded regularity. We prove effective
bounds for many tensor formats and ranks, which are of independent interest for
overconstrained polynomial system solving. Moreover, we conjecture a general
formula for the multigraded regularity, yielding a (parameterized) polynomial
time complexity for the tensor rank decomposition problem in the considered
setting. Our numerical experiments show that our algorithm can outperform
state-of-the-art numerical algorithms by an order of magnitude in terms of
accuracy, computation time, and memory consumption.


  For the two dimensional Schr\"odinger equation in a bounded domain, we prove
uniqueness of determination of potentials in $W^1_p(\Omega),\,\, p>2$ in the
case where we apply all possible Neumann data supported on an arbitrarily
non-empty open set $\widetilde\Gamma$ of the boundary and observe the
corresponding Dirichlet data on $\widetilde{\Gamma}$. An immediate consequence
is that one can uniquely determine a conductivity in $W^3_p(\Omega)$ with $p>2$
by measuring the voltage on an open subset of the boundary corresponding to
current supported in the same set.


  We show that the proportion of polynomials of degree $n$ over the finite
field with $q$ elements, which have a divisor of every degree below $n$, is
given by $c_q n^{-1} + O(n^{-2})$. More generally, we give an asymptotic
formula for the proportion of polynomials, whose set of degrees of divisors has
no gaps of size greater than $m$. To that end, we first derive an improved
estimate for the proportion of polynomials of degree $n$, all of whose
non-constant divisors have degree greater than $m$. In the limit as $q \to
\infty$, these results coincide with corresponding estimates related to the
cycle structure of permutations.


  We study Zariski-like topologies on a proper class $X\varsubsetneqq L$ of a
complete lattice $\mathcal{L}=(L,\wedge ,\vee ,0,1)$. We consider $X$ with the
so called classical Zariski topology $(X,\tau ^{cl})$ and study its topological
properties (e.g. the separation axioms, the connectedness, the compactness) and
provide sufficient conditions for it to be $\textit{spectral}$. We say that
$\mathcal{L}$ is $X$\emph{-top} iff% \begin{equation*} \tau :=\{X\backslash
V(a)\mid a\in L\},\text{ where }V(a)=\{x\in L\mid a\leq x\} \end{equation*}% is
a topology. We study the interplay between the \textit{algebraic properties} of
an $X$-top complete lattice $\mathcal{L}$ and the $\textit{% topological
properties}$ of $(X,\tau ^{cl})=(X,\tau ).$ Our results are applied to several
spectra which are proper classes of $\mathcal{L}% :=LAT(_{R}M)$ where $M$ is a
left module over an arbitrary associative ring $% R$ (e.g. the spectra of
prime, coprime, fully prime submodules) of $M$ as well as to several spectra of
the dual complete lattice $\mathcal{L}^{0}$ (e.g. the spectra of first, second
and fully coprime submodules of $M$).


  Model-based recursive partitioning (MOB) and its extension, metaMOB, are
potent tools for identifying subgroups with differential treatment effects. In
the metaMOB approach random effects are used to model heterogeneity of the
treatment effects when pooling data from various trials. In situations where
interventions offer only small overall benefits and require extensive, costly
trials with a large participant enrollment, leveraging individual-participant
data (IPD) from multiple trials can help identify individuals who are most
likely to benefit from the intervention. We explore the application of MOB and
metaMOB in the context of non specific low back pain treatment, using
synthesized data based on a subset of the individual participant data
meta-analysis by Patel et al. Our study underscores the need to explore
heterogeneity in intercepts and treatment effects to identify subgroups with
differential treatment effects in IPD meta-analyses.


  We investigate experimentally the statistical properties of active and
passive scalar fields in turbulent Rayleigh-B\'{e}nard convection in water, at
$Ra\sim10^{10}$. Both the local concentration of fluorescence dye and the local
temperature are measured near the sidewall of a rectangular cell. It is found
that, although they are advected by the same turbulent flow, the two scalars
distribute differently. This difference is twofold, i.e. both the quantities
themselves and their small-scale increments have different distributions. Our
results show that there is a certain buoyant scale based on time domain, i.e.
the Bolgiano time scale $t_B$, above which buoyancy effects are significant.
Above $t_B$, temperature is active and is found to be more intermittent than
concentration, which is passive. This suggests that the active scalar possesses
a higher level of intermittency in turbulent thermal convection. It is further
found that the mixing of both scalar fields are isotropic for scales larger
than $t_B$ even though buoyancy acts on the fluid in the vertical direction.
Below $t_B$, temperature is passive and is found to be more anisotropic than
concentration. But this higher degree of anisotropy is attributed to the higher
diffusivity of temperature over that of concentration. From the simultaneous
measurements of temperature and concentration, it is shown that two scalars
have similar autocorrelation functions and there is a strong and positive
correlation between them.


  We present a novel multimodal dataset developed by expert astronomers to
automate the detection and localisation of multi-component extended radio
galaxies and their corresponding infrared hosts. The dataset comprises 4,155
instances of galaxies in 2,800 images with both radio and infrared modalities.
Each instance contains information on the extended radio galaxy class, its
corresponding bounding box that encompasses all of its components, pixel-level
segmentation mask, and the position of its corresponding infrared host galaxy.
Our dataset is the first publicly accessible dataset that includes images from
a highly sensitive radio telescope, infrared satellite, and instance-level
annotations for their identification. We benchmark several object detection
algorithms on the dataset and propose a novel multimodal approach to identify
radio galaxies and the positions of infrared hosts simultaneously.


  We explore the problem of scattering in a medium modulated by a superluminal
rectangular pulse, with the pulse modulation realized through transverse
excitations. We solve this problem in the moving frame where the modulation
appears purely temporal, since the solution to a purely temporal modulation is
known. Upon this basis, we use a graphical approach to find the angle and
frequency of the wave scattered by the modulation under oblique incidence. This
study reveals that superluminal modulations deflect plane waves
retro-directively, and refocus cylindrical waves to a shifted point of space
with respect to the original source.


  Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic
subgroup of the finite general linear group GL(n,q). We show that the number of
P(q)-conjugacy classes in GL(n,q) is, as a function of q, a polynomial in q
with integer coefficients. This answers a question of J. Alperin.


  Language identification is the task of automatically determining the identity
of a language conveyed by a spoken segment. It has a profound impact on the
multilingual interoperability of an intelligent speech system. Despite language
identification attaining high accuracy on medium or long utterances(>3s), the
performance on short utterances (<=1s) is still far from satisfactory. We
propose a BERT-based language identification system (BERT-LID) to improve
language identification performance, especially on short-duration speech
segments. We extend the original BERT model by taking the phonetic
posteriorgrams (PPG) derived from the front-end phone recognizer as input. Then
we deployed the optimal deep classifier followed by it for language
identification. Our BERT-LID model can improve the baseline accuracy by about
6.5% on long-segment identification and 19.9% on short-segment identification,
demonstrating our BERT-LID's effectiveness to language identification.


  Excitons in atomically-thin semiconductors necessarily lie close to a
surface, and therefore their properties are expected to be strongly influenced
by the surrounding dielectric environment. However, systematic studies
exploring this role are challenging, in part because the most readily
accessible exciton parameter -- the exciton's optical transition energy -- is
largely \textit{un}affected by the surrounding medium. Here we show that the
role of the dielectric environment is revealed through its systematic influence
on the \textit{size} of the exciton, which can be directly measured via the
diamagnetic shift of the exciton transition in high magnetic fields. Using
exfoliated WSe$_2$ monolayers affixed to single-mode optical fibers, we tune
the surrounding dielectric environment by encapsulating the flakes with
different materials, and perform polarized low-temperature magneto-absorption
studies to 65~T. The systematic increase of the exciton's size with dielectric
screening, and concurrent reduction in binding energy (also inferred from these
measurements), is quantitatively compared with leading theoretical models.
These results demonstrate how exciton properties can be tuned in future 2D
optoelectronic devices.


  This paper presents a simultaneous localization and map-assisted environment
recognition (SLAMER) method. Mobile robots usually have an environment map and
environment information can be assigned to the map. Important information for
mobile robots such as no entry zone can be predicted if localization has
succeeded since relative pose of them can be known. However, this prediction is
failed when localization does not work. Uncertainty of pose estimate must be
considered for robustly using the map information. In addition, robots have
external sensors and environment information can be recognized using the
sensors. This on-line recognition of course contains uncertainty; however, it
has to be fused with the map information for robust environment recognition
since the map also contains uncertainty owing to over time. SLAMER can
simultaneously cope with these uncertainties and achieves accurate localization
and environment recognition. In this paper, we demonstrate LiDAR-based
implementation of SLAMER in two cases. In the first case, we use the
SemanticKITTI dataset and show that SLAMER achieves accurate estimate more than
traditional methods. In the second case, we use an indoor mobile robot and show
that unmeasurable environmental objects such as open doors and no entry lines
can be recognized.


  The paper develops a method for discrete computational Fourier analysis of
functions defined on quasicrystals and other almost periodic sets. A key point
is to build the analysis around the emerging theory of quasicrystals and
diffraction in the setting on local hulls and dynamical systems. Numerically
computed approximations arising in this way are built out of the Fourier module
of the quasicrystal in question, and approximate their target functions
uniformly on the entire infinite space.
  The methods are entirely group theoretical, being based on finite groups and
their duals, and they are practical and computable. Examples of functions based
on the standard Fibonacci quasicrystal serve to illustrate the method (which is
applicable to all quasicrystals modeled on the cut and project formalism).


  We demonstrate a quantum key distribution with a secure bit rate exceeding 1
Mbit/s over 50 km fiber averaged over a continuous 36-hours period. Continuous
operation of high bit rates is achieved using feedback systems to control path
length difference and polarization in the interferometer and the timing of the
detection windows. High bit rates and continuous operation allows finite key
size effects to be strongly reduced, achieving a key extraction efficiency of
96% compared to keys of infinite lengths.


  Nearly 50 years ago, the first radio signals from cosmic ray air showers were
detected. After many successful studies, however, research ceased not even 10
years later. Only a decade ago, the field was revived with the application of
powerful digital signal processing techniques. Since then, the detection
technique has matured, and we are now in a phase of transition from small-scale
experiments accessing energies below 1018 eV to experiments with a reach for
energies beyond 1019 eV. We have demonstrated that air shower radio signals
carry information on both the energy and the mass of the primary particle, and
current experiments are in the process of quantifying the precision with which
this information can be accessed. All of this rests on a solid understanding of
the radio emission processes which can be interpreted as a coherent
superposition of geomagnetic emission, Askaryan charge-excess radiation, and
Cherenkov-like coherence effects arising in the density gradient of the
atmosphere. In this article, I highlight the "state of the art" of radio
detection of cosmic rays and briefly discuss its perspectives for the next few
years.


  Statistical dynamics of financial systems is investigated, based on a model
of a randomly coupled equation system driven by a stochastic Langevin force.
Anticorrelations of price returns, and subdiffusion of prices is found from the
model, and and compared with those calculated from historical $/EURO exchange
rates.


  Effective collaboration in multi-robot systems requires accurate and robust
estimation of relative localization: from cooperative manipulation to
collaborative sensing, and including cooperative exploration or cooperative
transportation. This paper introduces a novel approach to collaborative
localization for dense scene reconstruction in heterogeneous multi-robot
systems comprising ground robots and micro-aerial vehicles (MAVs). We solve the
problem of full relative pose estimation without sliding time windows by
relying on UWB-based ranging and Visual Inertial Odometry (VIO)-based egomotion
estimation for localization, while exploiting lidars onboard the ground robots
for full relative pose estimation in a single reference frame. During
operation, the rigidity eigenvalue provides feedback to the system. To tackle
the challenge of path planning and obstacle avoidance of MAVs in GNSS-denied
environments, we maintain line-of-sight between ground robots and MAVs. Because
lidars capable of dense reconstruction have limited FoV, this introduces new
constraints to the system. Therefore, we propose a novel formulation with a
variant of the Dubins multiple traveling salesman problem with neighborhoods
(DMTSPN) where we include constraints related to the limited FoV of the ground
robots. Our approach is validated with simulations and experiments with real
robots for the different parts of the system.


  In the rendezvous problem, two parties with different labelings of the
vertices of a complete graph are trying to meet at some vertex at the same
time. It is well-known that if the parties have predetermined roles, then the
strategy where one of them waits at one vertex, while the other visits all $n$
vertices in random order is optimal, taking at most $n$ steps and averaging
about $n/2$. Anderson and Weber considered the symmetric rendezvous problem,
where both parties must use the same randomized strategy. They analyzed
strategies where the parties repeatedly play the optimal asymmetric strategy,
determining their role independently each time by a biased coin-flip. By tuning
the bias, Anderson and Weber achieved an expected meeting time of about $0.829
n$, which they conjectured to be asymptotically optimal.
  We change perspective slightly: instead of minimizing the expected meeting
time, we seek to maximize the probability of meeting within a specified time
$T$. The Anderson-Weber strategy, which fails with constant probability when
$T= \Theta(n)$, is not asymptotically optimal for large $T$ in this setting.
Specifically, we exhibit a symmetric strategy that succeeds with probability
$1-o(1)$ in $T=4n$ steps. This is tight: for any $\alpha < 4$, any symmetric
strategy with $T = \alpha n$ fails with constant probability. Our strategy uses
a new combinatorial object that we dub a "rendezvous code," which may be of
independent interest.
  When $T \le n$, we show that the probability of meeting within $T$ steps is
indeed asymptotically maximized by the Anderson-Weber strategy. Our results
imply new lower bounds, showing that the best symmetric strategy takes at least
$0.638 n$ steps in expectation. We also present some partial results for the
symmetric rendezvous problem on other vertex-transitive graphs.


  We construct a new Quillen model, based on the notions of Drinfeld's DG
quotient and localization pair, for the Morita homotopy theory of DG
categories. This new Quillen model carries a natural closed symmetric monoidal
structure and allows us to re-interpret Toen's construction of the internal
Hom-functor for the homotopy category of DG categories as a total right derived
internal Hom-functor.


  We present a framework for the simulation of rigid and deformable bodies in
the presence of contact and friction. Our method is based on a non-smooth
Newton iteration that solves the underlying nonlinear complementarity problems
(NCPs) directly. This approach allows us to support nonlinear dynamics models,
including hyperelastic deformable bodies and articulated rigid mechanisms,
coupled through a smooth isotropic friction model. The fixed-point nature of
our method means it requires only the solution of a symmetric linear system as
a building block. We propose a new complementarity preconditioner for NCP
functions that improves convergence, and we develop an efficient GPU-based
solver based on the conjugate residual (CR) method that is suitable for
interactive simulations. We show how to improve robustness using a new
geometric stiffness approximation and evaluate our method's performance on a
number of robotics simulation scenarios, including dexterous manipulation and
training using reinforcement learning.


  This study develops an asymptotic theory for estimating the time-varying
characteristics of locally stationary functional time series (LSFTS). We
investigate a kernel-based method to estimate the time-varying covariance
operator and the time-varying mean function of an LSFTS. In particular, we
derive the convergence rate of the kernel estimator of the covariance operator
and associated eigenvalue and eigenfunctions and establish a central limit
theorem for the kernel-based locally weighted sample mean. As applications of
our results, we discuss methods for testing the equality of time-varying mean
functions in two functional samples.


  We present a summary of spectra of Seyfert galaxies observed by the OSSE
detector aboard Compton Gamma Ray Observatory. We obtain average spectra of
Seyferts of type 1 and 2, and find they are well fitted by thermal
Comptonization. We present detailed parameter ranges for the plasma temperature
and the Compton parameter in the case of spherical and slab geometries. We find
both the average and individual OSSE spectra of Seyfert 2s are significantly
harder than those of Seyfert 1s, which difference can be due to anisotropy of
Compton reflection and/or Thomson-thick absorption.