  The large amplitude oscillatory shear (LAOS) has been extensively studied for
understanding the rheological responses of yield stress fluids. However, the
employed methodology for determining the yield stress remains uncertain albeit
the fact that many classical or plausible methods exist in the literature.
Along these lines, herein, based on Fourier transform (FT) rheology, stress
decomposition, and stress bifurcation, a new straightforward method termed as
algebraic stress bifurcation was developed. More specifically, the main goal
was to determine the yield stress and investigate the solid-liquid transition
of fluids in LAOS. A simple and efficient mathematical framework was
established and verified by the KVHB, Saramito, Giesekus models, and FT
rheology. The main strength of this approach is that only the data from the
stress/strain sweep are required instead of Lissajous curves. Alternative
curves based on the first harmonic were constructed to demonstrate the
non-critical role of both higher harmonics and phenomenological Lissajous
curves in determining yield stress. The determined start and end yield points
in the solid-liquid transition were compared with the already existing methods.
Furthermore, the resulting solid-liquid transition region was analyzed by FT
rheology, stress decomposition, and sequence of the physical process to obtain
information on nonlinearity and intracycle/intercycle yielding. Our work
provides fruitful insights for explaining and reducing the complexities of the
stress bifurcation technique by using an easy-to-understand and implement
format. Therefore, a concise theoretical framework was introduced for
understanding the concept of yield stress, the intercycle yielding process, and
the rational choice of yield stress measurement techniques.


  Cells in multicellular organisms adhere to the extracellular matrix through
two-dimensional clusters spanning a size range from very few to thousands of
adhesion bonds. For many common receptor-ligand systems, the ligands are
tethered to a surface via polymeric spacers with finite binding range, thus
adhesion cluster stability crucially depends on receptor-ligand distance. We
introduce a one-step master equation which incorporates the effect of
cooperative binding through a finite number of polymeric ligand tethers. We
also derive Fokker-Planck and mean field equations as continuum limits of the
master equation. Polymers are modeled either as harmonic springs or as
worm-like chains. In both cases, we find bistability between bound and unbound
states for intermediate values of receptor-ligand distance and calculate the
corresponding switching times. For small cluster sizes, stochastic effects
destabilize the clusters at large separation, as shown by a detailed analysis
of the stochastic potential resulting from the Fokker-Planck equation.


  We calculate the dimensions of operators in three and six dimensional
superconformal field theories by using the duality between these theories at
large N and D=11 supergravity on $AdS_{4/7} \times S^{7/4}$. We find that for
the duality relations to work the Kaluza--Klein masses given in the
supergravity literature must be rescaled and/or shifted.


  Imitation can be viewed as a means of enhancing learning in multiagent
environments. It augments an agent's ability to learn useful behaviors by
making intelligent use of the knowledge implicit in behaviors demonstrated by
cooperative teachers or other more experienced agents. We propose and study a
formal model of implicit imitation that can accelerate reinforcement learning
dramatically in certain cases. Roughly, by observing a mentor, a
reinforcement-learning agent can extract information about its own capabilities
in, and the relative value of, unvisited parts of the state space. We study two
specific instantiations of this model, one in which the learning agent and the
mentor have identical abilities, and one designed to deal with agents and
mentors with different action sets. We illustrate the benefits of implicit
imitation by integrating it with prioritized sweeping, and demonstrating
improved performance and convergence through observation of single and multiple
mentors. Though we make some stringent assumptions regarding observability and
possible interactions, we briefly comment on extensions of the model that relax
these restricitions.


  This paper is devoted to give a simplified proof of the trace theorem for
functions of bounded deformation defined on bounded Lipschitz domains of
$\mathbb{R}^n$. As a consequence, the existence of one-sided Lebesgue limits on
countably $\mathcal{H}^{n-1}$-rectifiable sets is also established.


  We study the cost of parallelizing weak-to-strong boosting algorithms for
learning, following the recent work of Karbasi and Larsen. Our main results are
two-fold:
  - First, we prove a tight lower bound, showing that even "slight"
parallelization of boosting requires an exponential blow-up in the complexity
of training.
  Specifically, let $\gamma$ be the weak learner's advantage over random
guessing. The famous \textsc{AdaBoost} algorithm produces an accurate
hypothesis by interacting with the weak learner for $\tilde{O}(1 / \gamma^2)$
rounds where each round runs in polynomial time.
  Karbasi and Larsen showed that "significant" parallelization must incur
exponential blow-up: Any boosting algorithm either interacts with the weak
learner for $\Omega(1 / \gamma)$ rounds or incurs an $\exp(d / \gamma)$ blow-up
in the complexity of training, where $d$ is the VC dimension of the hypothesis
class. We close the gap by showing that any boosting algorithm either has
$\Omega(1 / \gamma^2)$ rounds of interaction or incurs a smaller exponential
blow-up of $\exp(d)$.
  -Complementing our lower bound, we show that there exists a boosting
algorithm using $\tilde{O}(1/(t \gamma^2))$ rounds, and only suffer a blow-up
of $\exp(d \cdot t^2)$.
  Plugging in $t = \omega(1)$, this shows that the smaller blow-up in our lower
bound is tight. More interestingly, this provides the first trade-off between
the parallelism and the total work required for boosting.


  In this paper, we present a novel framework for studying the syntactic
completeness of computational effects and we apply it to the exception effect.
When applied to the states effect, our framework can be seen as a
generalization of Pretnar's work on this subject. We first introduce a relative
notion of Hilbert-Post completeness, well-suited to the composition of effects.
Then we prove that the exception effect is relatively Hilbert-Post complete, as
well as the "core" language which may be used for implementing it; these proofs
have been formalized and checked with the proof assistant Coq.


  We review the effect of scale evolution on a number of different correlations
in double parton scattering (DPS). The strength of the correlations generally
decreases with the scale but at a rate which greatly varies between different
types. Through studies of the evolution, an understanding of which correlations
can be of experimental relevance in different processes and kinematical regions
is obtained.


  The elastic response is studied of a single flexible chain grafted on a rigid
plane and an ensemble of non-interacting tethered chains. It is demonstrated
that the entropic theory of rubber elasticity leads to conclusions that
disagree with experimental data. A modification of the conventional approach is
proposed, where the end-to-end distribution function (treated as the governing
parameter) is replaced by the average energy of a chain. It is revealed that
this refinement ensures an adequate description of the mechanical behavior of
flexible chains. Results of numerical simulation are compared with observations
on uniaxial compression of a layer of grafted chains, and an acceptable
agreement is shown between the model predictions and the experimental data.
Based on the analysis of combined compression and shear, a novel
micro-mechanism is proposed for the reduction of friction of polymer melts at
rigid walls.


  An effective simulation of quantum entanglement is presented using classical
fields modulated with n pseudorandom phase sequences (PPSs) that constitute a
n2^n-dimensional Hilbert space with a tensor product structure. Applications to
classical fields are examplied by effective simulation of both Bell and GHZ
states, and a correlation analysis was performed to characterize the
simulation. Results that strictly comply with criteria of quantum entanglement
were obtained and the approach was also shown to be applicable to a system
consisting of n quantum particles.


  We study the design of learning architectures for behavioural planning in a
dense traffic setting. Such architectures should deal with a varying number of
nearby vehicles, be invariant to the ordering chosen to describe them, while
staying accurate and compact. We observe that the two most popular
representations in the literature do not fit these criteria, and perform badly
on an complex negotiation task. We propose an attention-based architecture that
satisfies all these properties and explicitly accounts for the existing
interactions between the traffic participants. We show that this architecture
leads to significant performance gains, and is able to capture interactions
patterns that can be visualised and qualitatively interpreted. Videos and code
are available at https://eleurent.github.io/social-attention/.


  The design spectrum of a simple graph $G$ is the set of positive integers $n$
such that there exists an edgewise decomposition of the complete graph $K_n$
into $n(n - 1)/(2 |E(G)|)$ copies of $G$. We compute the design spectra for
7788 6-regular graphs with 12 vertices.


  In the present work, we study meson systems consisting of quark-antiquark. We
solve lippman-Schwinger equation numerically for heavy meson systems. We
attempt to find a non-relativistic potential model through which we can solve
the quark-antiquark bound state problem. The coefficients so obtained are in
agreement with Martin potential coefficients. Via this method we also determine
the strong coupling constant for the mesons tt, tc, and tb, which is a
coefficient of Cornell potential.


  Integer factorization is one of the vital algorithms discussed as a part of
analysis of any black-box cipher suites where the cipher algorithm is based on
number theory. The origin of the problem is from Discrete Logarithmic Problem
which appears under the analysis of the crypto-graphic algorithms as seen by a
crypt-analyst. The integer factorization algorithm poses a potential in
computational science too, obtaining the factors of a very large number is
challenging with a limited computing infrastructure. This paper analyses the
Pollards Rho heuristic with a varying input size to evaluate the performance
under a multi-core environment and also to estimate the threshold for each
computing infrastructure.


  In this work, we propose the design and analysis of a novel continuous robust
controller for a class of multi--input multi--output (MIMO) nonlinear uncertain
systems. The systems under consideration contains unstructured uncertainties in
their drift and input matrices. The proposed controller compensates the overall
system uncertainties and achieves asymptotic tracking where only the sign of
the leading minors of the input gain matrix is assumed to be known. A Lyapunov
based argument backed up with an integral inequality is applied to prove
stability of the proposed controller and asymptotic convergence of the error
signals. Simulation results are presented in order to illustrate the viability
of the proposed method.


  It is proved that the distributions of scaling limits of Continuous Time
Random Walks (CTRWs) solve integro-differential equations akin to Fokker-Planck
Equations for diffusion processes. In contrast to previous such results, it is
not assumed that the underlying process has absolutely continuous laws.
Moreover, governing equations in the backward variables are derived. Three
examples of anomalous diffusion processes illustrate the theory.


  Understanding the emergence and evolution of multicellularity and cellular
differentiation is a core problem in biology. We develop a quantitative model
that shows that a multicellular form emerges from genetically identical
unicellular ancestors when the compartmentalization of poorly compatible
physiological processes into component cells of an aggregate produces a fitness
advantage. This division of labour between the cells in the aggregate occurs
spontaneously at the regulatory level due to mechanisms present in unicellular
ancestors and does not require any genetic pre-disposition for a particular
role in the aggregate or any orchestrated cooperative behaviour of aggregate
cells. Mathematically, aggregation implies an increase in the dimensionality of
phenotype space that generates a fitness landscape with new fitness maxima, and
in which the unicellular states of optimized metabolism become fitness saddle
points. Evolution of multicellularity is modeled as evolution of a hereditary
parameter, the propensity of cells to stick together, which determines the
fraction of time a cell spends in the aggregate form. Stickiness can increase
evolutionarily due to the fitness advantage generated by the division of labour
between cells in an aggregate.


  We perform a NNLO (and a LO) global parton analysis in which we include the
new precise data for deep inelastic scattering from HERA and for inclusive jet
production at the Tevatron, together with the improved knowledge of the
three-loop splitting functions. The results are compared with our recent NLO
analyses. The LO fit produces significantly worse results in general, but gives
a surprisingly good fit to the Tevatron high-E_T jet data. For the approximate
NNLO analysis we notice a slight improvement in the quality of the global fit,
and find that the partons are changed by up to 10% at Q^2=10 GeV^2$, in
particular in the x<0.01 regime.


  We present a study of the superconducting properties of the candidate
topological superconductor Ti_(3)Sb. Electrical transport measurements show
zero resistance with a T_(c,onset) of ~ 5.9 K with a transition width
{\Delta}T_c~ 0.6 K. The superconducting phase boundaries as derived from
magneto-transport and magnetic susceptibility measurements agree well. We
estimate an upper critical field Bc2(0)~4.5 T. A Ginzburg-Landau (GL) analysis
yields values of the coherence length and penetration depth of {\zeta} = 6.2 nm
and {\lambda} = 340 nm, respectively, and a GL parameter ~ 55, indicating
extreme type-II behavior. Furthermore, we observed a step height in the
specific heat ({\Delta}C_e)/({\gamma}T_c )~1.61, a value larger than the
Bardeen-Cooper-Schrieffer (BCS) value of 1.43, suggesting modest coupling.
Measurements of the temperature dependence of the London penetration depth via
the tunnel-diode oscillator (TDO) technique down to ~ 450 mK show a full
superconducting gap, consistent with a conventional s-wave gap structure.


  We consider the use of polarization properties as a means to discriminate
between Synchrotron Self-Absorption (SSA) and Free--Free Absorption (FFA) in
GHz-Peaked Spectrum (GPS) sources. The polarization position angle (PA) of
synchrotron radiation at high frequencies for the optically thin regime is
perpendicular to the magnetic field, whereas it is parallel to the magnetic
field at low frequencies for the optically thick regime. Therefore, SSA
produces a change in PA of $90^{\circ}$ across the spectral peak, while FFA
does not result in such a change. We analyzed polarization data from VLA
observations for six GPS sources to see if such a change in PA was present. Our
results indicate that there is no significant evidence for $90^{\circ}$ change
in PA across the spectral peak, suggesting that FFA is more likely than SSA for
low-frequency cutoffs in these sources.


  The IDIA Visualisation Laboratory based at the University of Cape Town is
exploring the use of virtual reality technology to visualise and analyse
astronomical data. The iDaVIE software suite currently under development reads
from both volumetric data cubes and sparse multi-dimensional catalogs,
rendering them in a room-scale immersive environment that allows the user to
intuitively view, navigate around and interact with features in three
dimensions. This paper will highlight how the software imports from common
astronomy data formats and processes the information for loading into the Unity
game engine. It will also describe what tools are currently available to the
user and the various performance optimisations made for seamless use.
Applications by astronomers will be reviewed in addition to the features we
plan to include in future releases.


  Migraine is a common disabling headache disorder characterized by recurrent
episodes sometimes preceded or accompanied by focal neurological symptoms
called aura. The relation between two subtypes, migraine without aura (MWoA)
and migraine with aura (MWA), is explored with the aim to identify targets for
neuromodulation techniques. To this end, a dynamically regulated control system
is schematically reduced to a network of the trigeminal nerve, which innervates
the cranial circulation, an associated descending modulatory network of
brainstem nuclei, and parasympathetic vasomotor efferents. This extends the
idea of a migraine generator region in the brainstem to a larger network and is
still simple and explicit enough to open up possibilities for mathematical
modeling in the future. In this study, it is suggested that the migraine
generator network (MGN) is driven and may therefore respond differently to
different spatio-temporal noxious input in the migraine subtypes MWA and MWoA.
The noxious input is caused by a cortical perturbation of homeostasis, known as
spreading depression (SD). The MGN might even trigger SD in the first place by
a failure in vasomotor control. As a consequence, migraine is considered as an
inherently dynamical disease to which a linear course from upstream to
downstream events would not do justice. Minimally invasive and noninvasive
neuromodulation techniques are briefly reviewed and their rational is discussed
in the context of the proposed mechanism.


  With the advancement of robotics and AI technologies in the past decade, we
have now entered the age of autonomous machines. In this new age of information
technology, autonomous machines, such as service robots, autonomous drones,
delivery robots, and autonomous vehicles, rather than humans, will provide
services. In this article, through examining the technical challenges and
economic impact of the digital economy, we argue that scalability is both
highly necessary from a technical perspective and significantly advantageous
from an economic perspective, thus is the key for the autonomy industry to
achieve its full potential. Nonetheless, the current development paradigm,
dubbed Autonomy 1.0, scales with the number of engineers, instead of with the
amount of data or compute resources, hence preventing the autonomy industry to
fully benefit from the economies of scale, especially the exponentially
cheapening compute cost and the explosion of available data. We further analyze
the key scalability blockers and explain how a new development paradigm, dubbed
Autonomy 2.0, can address these problems to greatly boost the autonomy
industry.


  The presence of defects in material continua is known to produce internal
permanent strained states. Extending the theory of defects to four dimensions
and allowing for the appropriate signature, it is possible to apply these
concepts to space-time. In this case a defect would induce a non-trivial metric
tensor, which can be interpreted as a gravitational field. The image of a
defect in space-time can be applied to the description of the Big Bang. A
review of the four-dimensional generalisation of defects and an application to
the expansion of the universe will be presented.


  We consider physics beyond the Standard Model in which a long-lived
electromagnetically charged massive particle species (CHAMP) appears. We
discuss the unique sensitivity the early Universe exhibits on the mere presence
and on the decay of such a particle. A CHAMP can be realized in supersymmetric
extensions of the Standard Model. We carry out a detailed study of gravitino
dark matter scenarios in which the lighter stau is the lightest Standard Model
superpartner and thus the CHAMP. Particularly stringent constraints on the
gravitino-stau scenario arise from the thermal catalysis of primordial
nucleosynthesis reactions. This motivates a thorough investigation of the
thermal freeze-out process of the long-lived stau. There, we show that even the
most stringent cosmological constraints can potentially be evaded.


  The separated radial part of a massive complex scalar wave equation in the
Kerr-Sen geometry is shown to satisfy the generalized spheroidal wave equation
which is, in fact, a confluent Heun equation up to a multiplier. The Hawking
evaporation of scalar particles in the Kerr-Sen black hole background is
investigated by the Damour-Ruffini-Sannan's method. It is shown that quantum
thermal effect of the Kerr-Sen black hole has the same characteras that of the
Kerr-Newman black hole.


  We discuss supersymmetry breaking via 3-form fluxes in chiral supersymmetric
type IIB orientifold vacua with D3- and D7-branes. After a general discussion
of possible choices of fluxes allowing for stabilizing of a part of the moduli,
we determine the resulting effective action including all soft supersymmetry
breaking terms. We also extend the computation of our previous work concerning
the matter field metrics arising from various open string sectors, in
particular focusing on the 1/2 BPS D3/D7-brane configuration. Afterwards, the
F-theory lift of our constructions is investigated.


  We theoretically investigate the dependence of the enhancement of optical
near-fields at nanometric tips on the shape, size, and material of the tip. We
confirm a strong dependence of the field enhancement factor on the radius of
curvature. In addition, we find a surprisingly strong increase of field
enhancement with increasing opening angle of the nanotips. For gold and
tungsten nanotips in the experimentally relevant parameter range (radius of
curvature $\geq 5\,$nm at $800\,$nm laser wavelength), we obtain field
enhancement factors of up to ${\sim}35$ for Au and ${\sim}12$ for W for large
opening angles. We confirm this strong dependence on the opening angle for many
other materials featuring a wide variety in their dielectric response. For
dielectrics, the opening angle dependence is traced back to the electrostatic
force of the induced surface charge at the tip shank. For metals, the plasmonic
response strongly increases the field enhancement and shifts the maximum field
enhancement to smaller opening angles.


  Our interest in this paper is a generalization of the additive
Deligne-Simpson problem which is originally defined for Fuchsian differential
equations on the Riemann sphere. We shall extend this problem to differential
equations having an arbitrary number of unramified irregular singular points
and determine the existence of solutions of the generalized additive
Deligne-Simpson problems. Moreover we apply this result to the geometry of the
moduli spaces of stable meromorphic connections of trivial bundles on the
Riemann sphere. Namely, open embedding of the moduli spaces into quiver
varieties is given and the non-emptiness condition of the moduli spaces is
determined. Furthermore the connectedness of the moduli spaces is shown.


  We study the adaptation dynamics of an initially maladapted population
evolving via the elementary processes of mutation and selection. The evolution
occurs on rugged fitness landscapes which are defined on the multi-dimensional
genotypic space and have many local peaks separated by low fitness valleys. We
mainly focus on the Eigen's model that describes the deterministic dynamics of
an infinite number of self-replicating molecules. In the stationary state, for
small mutation rates such a population forms a {\it quasispecies} which
consists of the fittest genotype and its closely related mutants. The
quasispecies dynamics on rugged fitness landscape follow a punctuated (or
step-like) pattern in which a population jumps from a low fitness peak to a
higher one, stays there for a considerable time before shifting the peak again
and eventually reaches the global maximum of the fitness landscape. We
calculate exactly several properties of this dynamical process within a
simplified version of the quasispecies model.


  We introduce a method of analyzing entanglement enhanced quantum games on
regular lattices of agents. Our method is valid for setups with periodic and
non-periodic boundary conditions. To demonstrate our approach we study two
different types games, namely the prisoner's dilemma game and a cooperative
Parrondo's game. In both cases we obtain results showing, that entanglement is
a crucial resource necessary for the agents to achieve positive capital gain.


  We analyze the latest published solar neutrino data assuming an arbitrary
neutrino oscillation/conversion mechanism suppresses the electron neutrino flux
from the Sun independent of energy. For oscillations/transitions into active
(sterile) neutrinos such mechanisms are ruled out at 99.96 (99.9997) % C.L.
assuming the standard solar model by Bahcall and Pinnsoneault '95 correctly
predicts all solar neutrino fluxes within their estimated uncertainties. Even
if one allows for $^8{\rm B}$ and $^7{\rm Be}$ solar neutrino fluxes that are
vastly different from the ones in contemporary standard solar models these
mechanisms are strongly disfavored by the data.


  We discuss methods for {\em a priori} selection of parameters to be estimated
in inverse problem formulations (such as Maximum Likelihood, Ordinary and
Generalized Least Squares) for dynamical systems with numerous state variables
and an even larger number of parameters. We illustrate the ideas with an
in-host model for HIV dynamics which has been successfully validated with
clinical data and used for prediction.


  Charge noise is a major obstacle to improved gate fidelities in silicon spin
qubits. Numerous methods exist to mitigate charge noise, including improving
device fabrication, dynamical decoupling, and real-time parameter estimation.
In this work, we demonstrate a new class of techniques to mitigate charge noise
in semiconductor quantum dots by controlling the noise sources themselves.
Using two different classical feedback methods, we stabilize an individual
charged two-level fluctuator in a Si/SiGe quantum dot. These control methods
reduce the low-frequency component of the noise power spectrum by an order of
magnitude. These techniques also enable stabilizing the fluctuator in either of
its states. In the future, such techniques may enable improved coherence times
in quantum-dot spin qubits.


  Treatment effect heterogeneity (TEH), or variability in treatment effect for
different subgroups within a population, is of significant interest in clinical
trial analysis. Causal forests (Wager and Athey, 2018) is a highly popular
method for this problem, but like many other methods for detecting TEH, its
criterion for separating subgroups focuses on differences in absolute risk.
This can dilute statistical power by masking nuance in the relative risk, which
is often a more appropriate quantity of clinical interest. In this work, we
propose and implement a methodology for modifying causal forests to target
relative risk using a novel node-splitting procedure based on generalized
linear model (GLM) comparison. We present results on simulated and real-world
data that suggest relative risk causal forests can capture otherwise unobserved
sources of heterogeneity.


  Io, the most volcanically active body in the solar system, loses heat through
eruptions of hot lava. Heat is supplied by tidal heating and is thought to be
transferred through the mantle by magmatic segregation, a mode of transport
that sets it apart from convecting terrestrial planets. We present a model that
couples magmatic transport of tidal heat to the volcanic system in the crust,
in order to determine the controls on crustal thickness, magmatic intrusions,
and eruption rates. We demonstrate that magmatic intrusions are a key component
of Io's crustal heat balance; around 80% of the magma delivered to the base of
the crust must be emplaced and frozen as plutons to match rough estimates of
crustal thickness. As magma ascends from a partially molten mantle into the
crust, a decompacting boundary layer forms, which can explain inferred
observations of a high-melt-fraction region.


  This paper presents a novel WiFi-Visual data fusion method for indoor robot
(TIAGO++) localization. This method can use 10 WiFi samples and 4
low-resolution images ($58 \times 58$ in pixels) to localize a indoor robot
with an average error distance about 1.32 meters. The experiment test is 3
months after the data collection in a general teaching building, whose WiFi and
visual environments are partially changed. This indirectly shows the robustness
of the proposed method.
  Instead of neural network design, this paper focuses on the soft data fusion
to prevent unbounded errors in visual localization. A double-layer soft data
fusion is proposed. The proposed soft data fusion includes the first-layer
WiFi-Visual feature fusion and the second-layer decision vector fusion.
Firstly, motivated by the excellent capability of neural network in image
processing and recognition, the temporal-spatial features are extracted from
WiFi data, these features are represented in image form. Secondly, the WiFi
temporal-spatial features in image form and the visual features taken by the
robot camera are combined together, and are jointly exploited by a
classification neural network to produce a likelihood vector for WiFi-Visual
localization. This is called first-layer WiFi-Visual fusion. Similarly, these
two types of features can exploited separately by neural networks to produce
another two independent likelihood vectors. Thirdly, the three likelihood
vectors are fused by Hadamard product and median filtering to produce the final
likelihood vector for localization. This called the second-layer decision
vector fusion. The proposed soft data fusion does not apply any threshold or
prioritize any data source over the other in the fusion process. It never
excludes the positions of low probabilities, which can avoid the information
loss due to a hard decision. The demo video is provided. The code will be open.


  It has been established that endowing classical phase space with a Riemannian
metric is sufficient for describing quantum mechanics. In this letter we argue
that, while sufficient, the above condition is certainly not necessary in
passing from classical to quantum mechanics. Instead, our approach to quantum
mechanics is modelled on a statement that closely resembles Darboux's theorem
for symplectic manifolds.


  This is a semi-expository paper on the easier aspects of the Explicit Formula
for the Riemann Zeta Function. The topics reviewed here include: Weil's
criterion for the Riemann Hypothesis and its probabilistic interpretation,
various formulations of the contribution corresponding to the real place,
Haran's version of the Explicit Formula, and the author's own derivation which
puts all places on the same footing. This derivation, an addendum to Tate's
Thesis, is in the spirit of Weil's insights towards an adelic understanding of
the Explicit Formula. Whereas the analyst would likely formulate the Explicit
Formula as a multiplicative convolution, Haran's theorem shows it is also an
additive convolution. An intriguing conductor operator is considered whose
spectral analysis is equivalent to the Explicit Formula. At a finite place it
has a positive cuspidal spectrum. I also comment on the flexibility still left
in the Explicit Formula, which shows that it has a symmetry group containing
the non-zero rational numbers.


  It was shown that pre-trained models with self-supervised learning (SSL)
techniques are effective in various downstream speech tasks. However, most such
models are trained on single-speaker speech data, limiting their effectiveness
in mixture speech. This motivates us to explore pre-training on mixture speech.
This work presents SA-WavLM, a novel pre-trained model for mixture speech.
Specifically, SA-WavLM follows an "extract-merge-predict" pipeline in which the
representations of each speaker in the input mixture are first extracted
individually and then merged before the final prediction. In this pipeline,
SA-WavLM performs speaker-informed extractions with the consideration of the
interactions between different speakers. Furthermore, a speaker shuffling
strategy is proposed to enhance the robustness towards the speaker absence.
Experiments show that SA-WavLM either matches or improves upon the
state-of-the-art pre-trained models.


  We provide an explicit construction that allows one to easily decompose a
graph braid group as a graph of groups. This allows us to compute the braid
groups of a wide range of graphs, as well as providing two general criteria for
a graph braid group to split as a non-trivial free product, answering two
questions of Genevois. We also use this to distinguish certain right-angled
Artin groups and graph braid groups. Additionally, we provide an explicit
example of a graph braid group that is relatively hyperbolic, but is not
hyperbolic relative to braid groups of proper subgraphs. This answers another
question of Genevois in the negative.


  We prove that the entropy compression method systematized by L. Esperet and
A. Parreau [11] can be applied to any problem formulated in the variable
version of the Lov\'asz Local Lemma. As an application, we prove the existence
of legitimate colorings for projective planes with small orders, which extends
results of N. Alon and Z. F\"uredi [2]. In fact, we allow different numbers of
colors, proving that projective planes of any order can be legitimate colored
with 42 colors.


  Good many-body methods for medium and heavy nuclei are important. Here we
combine ideas from standard generator-coordinate methods (GCM) and the
so-called Monte Carlo shell model, and set forth a novel approach: starting
from a mean-field solution (Hartree-Fock-Bogoliubov), we create a set of
non-orthogonal basis states, by using low-lying vibrational
quasiparticleTamm-Dancoff modes, and then project onto states of good angular
momentum and particle number. The results we benchmark against full shell model
calculations. Even with just a few such modes we find improvement over standard
GCM calculations in excitation spectra. We also find significant improvement in
$0\nu\beta\beta$ nuclear matrix elements.


  This paper focuses on indefinite stochastic mean-field linear-quadratic
(MF-LQ, for short) optimal control problems, which allow the weighting matrices
for state and control in the cost functional to be indefinite. The solvability
of stochastic Hamiltonian system and Riccati equations is presented under both
positive definite case and indefinite case. The optimal controls in open-loop
form and closed-loop form are obtained, respectively. Moreover, the dynamic
mean-variance problem can be solved within the framework of the indefinite
MF-LQ problem. Other two examples shed light on the theoretical results
established.


  This paper presents a new algorithm for online estimation of a sequence of
homographies applicable to image sequences obtained from robotic vehicles
equipped with vision sensors. The approach taken exploits the underlying
Special Linear group structure of the set of homographies along with gyroscope
measurements and direct point-feature correspondences between images to develop
temporal filter for the homography estimate. Theoretical analysis and
experimental results are provided to demonstrate the robustness of the proposed
algorithm. The experimental results show excellent performance even in the case
of very fast camera motion (relative to frame rate), severe occlusion, and in
the presence of specular reflections.


  We study the price of anarchy of mechanisms in the presence of risk-averse
agents. Previous work has focused on agents with quasilinear utilities,
possibly with a budget. Our model subsumes this as a special case but also
captures that agents might be less sensitive to payments than in the
risk-neutral model. We show that many positive price-of-anarchy results proved
in the smoothness framework continue to hold in the more general risk-averse
setting. A sufficient condition is that agents can never end up with negative
quasilinear utility after playing an undominated strategy. This is true, e.g.,
for first-price and second-price auctions. For all-pay auctions, similar
results do not hold: We show that there are Bayes-Nash equilibria with
arbitrarily bad social welfare compared to the optimum.


  This paper was withdrawn by arXiv administrators upon request of the
Chairperson and Spokesperson of the L3 Collaboration.


  We show that the set of transfer matrices of an arbitrary fusion type for an
integrable quantum model obey these bilinear functional relations, which are
identified with an integrable dynamical system on a Grassmann manifold (higher
Hirota equation). The bilinear relations were previously known for a particular
class of transfer matrices corresponding to rectangular Young diagrams. We
extend this result for general Young diagrams. A general solution of the
bilinear equations is presented.


  We identify the Grothendieck group of the tangle Floer dg algebra with a
tensor product of certain $U_q(gl(1|1))$ representations. Under this
identification, up to a scalar factor, the map on the Grothendieck group
induced by the tangle Floer dg bimodule associated to a tangle agrees with the
Reshetikhin-Turaev homomorphism for that tangle. We also introduce dg bimodules
which act on the Grothendieck group as the generators $E$ and $F$ of
$U_q(gl(1|1))$.


  A correlated material in the vicinity of an insulator-metal transition (IMT)
exhibits rich phenomenology and variety of interesting phases. A common avenue
to induce IMTs in Mott insulators is doping, which inevitably leads to
disorder. While disorder is well known to create electronic inhomogeneity,
recent theoretical studies have indicated that it may play an unexpected and
much more profound role in controlling the properties of Mott systems. Theory
predicts that disorder might play a role in driving a Mott insulator across an
IMT, with the emergent metallic state hosting a power law suppression of the
density of states (with exponent close to 1; V-shaped gap) centered at the
Fermi energy. Such V-shaped gaps have been observed in Mott systems but their
origins are as yet unknown. To investigate this, we use scanning tunneling
microscopy and spectroscopy to study isovalent Ru substitutions in
Sr$_3$(Ir$_{1-x}$Ru$_x$)$_2$O$_7$ which drives the system into an
antiferromagnetic, metallic state. Our experiments reveal that many core
features of the IMT such as power law density of states, pinning of the Fermi
energy with increasing disorder, and persistence of antiferromagnetism can be
understood as universal features of a disordered Mott system near an IMT and
suggest that V-shaped gaps may be an inevitable consequence of disorder in
doped Mott insulators.


  We consider a renewal process that is conditioned on the number of events in
a fixed time horizon. We prove that a centered and scaled version of this
process converges to a Brownian bridge, as the number of events grows large,
which relies on first establishing a functional strong law of large numbers
result to determine the centering. These results are consistent with the
asymptotic behavior of a conditioned Poisson process. We prove the limit
theorems over triangular arrays of exchangeable random variables, obtained by
conditionning a sequence of independent and identically distributed renewal
processes. We construct martingale difference sequences with respect to these
triangular arrays, and use martingale convergence results in our proofs. To
illustrate how these results apply to performance analysis in queueing, we
prove that the workload process of a single server queue with conditioned
renewal arrival process can be approximated by a reflected diffusion having the
sum of a Brownian Bridge and Brownian motion as input to its regulator mapping.


  The rapid increase in the number of space debris represents a substantial
threat to the sustained viability of space operations. Monitoring these debris
is critical for space situational awareness. Therefore, it has become of
immense importance to understand the impact of solar activity on the space
debris orbit. This study examines the effect of solar cycles, specifically
Solar Cycles 22, 23, and 24, on the orbital decay of space debris. Utilizing
TLE data for 95 objects in LEO and MEO dating back to the 1960s, we examined
the orbital decay rates of these objects across the three solar cycles. Our
analysis reveals a significant correlation between orbital decay and various
indices serving as proxies for solar and geomagnetic activity. Notably, Solar
Cycle 22 exhibited the highest decay rates, while Solar Cycle 24 showed the
lowest. Moreover, we observed a similar impact at altitudes exceeding 2000 km,
albeit with a time lag of over 14 months compared to the shorter lag observed
at LEO orbits during peak solar activity. These findings underscore the crucial
relationship between solar activity and its enduring influence on space debris.


  The operation of gas detectors is often limited by secondary effects,
originating from avalanche-induced photons and ions. Ion backflow is one of the
effects limiting the operation of a gas detector at high flux, by giving rise
to space charge which disturbs the electric field locally. For the Micromegas
detector, a large fraction of the secondary positive ions created in the
avalanche can be stopped at the micro-mesh. The present work involves
measurements of the ion backflow fraction (using an experimental setup
comprising of two drift planes) in bulk Micromegas detectors as a function of
detector design parameters. These measured characteristics have also been
compared in detail to numerical simulations using the Garfield framework that
combines packages such as neBEM, Magboltz and Heed. Further, the effect of
using a second micro-mesh on ion backflow and other parameters has been studied
numerically.


  For more than 300 different patterns of the 3Q systems, the ground-state 3Q
potential $V_{\rm 3Q}^{\rm g.s.}$ is investigated using SU(3) lattice QCD with
$12^3\times 24$ at $\beta=5.7$ and $16^3\times 32$ at $\beta=5.8, 6.0$ at the
quenched level. As a result of the detailed analyses, we find that the
ground-state potential $V_{\rm 3Q}^{\rm g.s.}$ is well described with so-called
Y-ansatz as $V_{\rm 3Q}=-A_{\rm 3Q}\sum_{i<j}\frac1{|{\bf r}_i-{\bf r}_j|}
+\sigma_{\rm 3Q} L_{\rm min}+C_{\rm 3Q}$, with the accuracy better than 1%.
Here, $L_{\rm min}$ denotes the minimal value of total flux-tube length. We
also studythe excited-state potential $V_{\rm 3Q}^{\rm e.s.}$ using lattice QCD
with $16^3\times 32$ at $\beta=5.8, 6.0$ for more than 100 patterns of the 3Q
systems. The energy gap between $V_{\rm 3Q}^{\rm g.s.}$ and $V_{\rm 3Q}^{\rm
e.s.}$, which physically means the gluonic excitation energy, is found to be
about 1 GeV in the typical hadronic scale. Finally, we suggest a possible
scenario which connects the success of the quark model to QCD.


  Existing point-cloud based 3D object detectors use convolution-like operators
to process information in a local neighbourhood with fixed-weight kernels and
aggregate global context hierarchically. However, non-local neural networks and
self-attention for 2D vision have shown that explicitly modeling long-range
interactions can lead to more robust and competitive models. In this paper, we
propose two variants of self-attention for contextual modeling in 3D object
detection by augmenting convolutional features with self-attention features. We
first incorporate the pairwise self-attention mechanism into the current
state-of-the-art BEV, voxel and point-based detectors and show consistent
improvement over strong baseline models of up to 1.5 3D AP while simultaneously
reducing their parameter footprint and computational cost by 15-80% and 30-50%,
respectively, on the KITTI validation set. We next propose a self-attention
variant that samples a subset of the most representative features by learning
deformations over randomly sampled locations. This not only allows us to scale
explicit global contextual modeling to larger point-clouds, but also leads to
more discriminative and informative feature descriptors. Our method can be
flexibly applied to most state-of-the-art detectors with increased accuracy and
parameter and compute efficiency. We show our proposed method improves 3D
object detection performance on KITTI, nuScenes and Waymo Open datasets. Code
is available at https://github.com/AutoVision-cloud/SA-Det3D.


  Optimally encoding classical information in a quantum system is one of the
oldest and most fundamental challenges of quantum information theory. Holevo's
bound places a hard upper limit on such encodings, while the
Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many
classical messages can be "packed" into a given quantum system. In this
article, we use Sen's recent quantum joint typicality results to prove a
one-shot multiparty quantum packing lemma generalizing the HSW theorem. The
lemma is designed to be easily applicable in many network communication
scenarios. As an illustration, we use it to straightforwardly obtain quantum
generalizations of well-known classical coding schemes for the relay channel:
multihop, coherent multihop, decode-forward, and partial decode-forward. We
provide both finite blocklength and asymptotic results, the latter matching
existing classical formulas. Given the key role of the classical packing lemma
in network information theory, our packing lemma should help open the field to
direct quantum generalization.


  This article is concerned with data-driven analysis of discrete-time systems
under aperiodic sampling, and in particular with a data-driven estimation of
the maximum sampling interval (MSI). The MSI is relevant for analysis of and
controller design for cyber-physical, embedded and networked systems, since it
gives a limit on the time span between sampling instants such that stability is
guaranteed. We propose tools to compute the MSI for a given controller and to
design a controller with a preferably large MSI, both directly from a
finite-length, noise-corrupted state-input trajectory of the system. We follow
two distinct approaches for stability analysis, one taking a robust control
perspective and the other a switched systems perspective on the aperiodically
sampled system. In a numerical example and a subsequent discussion, we
demonstrate the efficacy of our developed tools and compare the two approaches.


  This precis is aimed as a practical field-guide to situations in which shear
banding might be expected in complex fluids subject to an applied shear flow.
Separately for several of the most common flow protocols, it summarises the
characteristic signatures in the measured bulk rheological signals that suggest
the presence of banding in the underlying flow field. It does so both for a
steady applied shear flow, and for the time-dependent protocols of shear
startup, step stress, finite strain ramp, and large amplitude oscillatory
shear. An important message is that banding might arise rather widely in flows
with a strong enough time-dependence, even in fluids that do not support
banding in a steadily applied shear flow. This suggests caution in comparing
experimental data with theoretical calculations that assume a homogeneous shear
flow. In a brief postlude, we also summarise criteria in similar spirit for the
onset of necking in extensional filament stretching.


  In "Universal rigidity on the line, point orde" it is shown, answering a
question of Jord\'an and Nguyen, that universal rigidity of a generic bar-joint
framework in R^1 depends on more than the ordering of the vertices. The graph G
that was used in that paper is a ladder with three rungs. Here we provide a
general answer when that ladder with three rungs in the line is universally
rigid and when it is not.


  This paper introduces a computational method for generating metric Travelling
Salesman Problem (TSP) instances having a large integrality gap. The method is
based on the solution of an integer programming problem, called IH-OPT, that
takes as input a fractional solution of the Subtour Elimination Problem (SEP)
on a TSP instance and computes a TSP instance having an integrality gap larger
than or equal to the integrality gap of the first instance. The decision
variables of IH-OPT are the entries of the TSP cost matrix, and the constraints
are defined by the intersection of the metric cone with an exponential number
of inequalities, one for each possible TSP tour. Given the very large number of
constraints, we have implemented a branch-and-cut algorithm for solving IH-OPT.
Then, by sampling cost vectors over the metric polytope and by solving the
corresponding SEP, we can generate random fractional vertices of the SEP
polytope. If we solve the IH-OPT problem for every sampled vertex using our
branch-and-cut algorithm, we can select the generated TSP instance (i.e., cost
vector), yielding the longest runtime for Concorde, the state-of-the-art TSP
solver. Our computational results show that our method is very effective in
producing challenging instances. As a by-product, we release the Hard-TSPLIB, a
library of 41 small metric TSP instances which have a large integrality gap and
are challenging in terms of runtime for Concorde.


  We exhibit exact conformal field theory descriptions of SO(N) and Sp(N) pairs
of Seiberg-dual gauge theories within string theory. The N=1 gauge theories
with flavour are realized as low energy limits of the worldvolume theories on
D-branes in unoriented non-critical superstring backgrounds. These unoriented
backgrounds are obtained by constructing exact crosscap states in the
SL(2,R)/U(1) coset conformal field theory using the modular bootstrap method.
Seiberg duality is understood by studying the behaviour of the boundary and
crosscap states under monodromy in the closed string parameter space.


  With the increasing precision requirements and growing spectrum of
applications of Monte Carlo simulations the evaluation of different components
of such simulations and their systematic ambiguities become of utmost interest.
In the following, we will address the question of systematic errors for Photos
Monte Carlo for simulation of bremsstrahlung corrections in final states, which
can not, in principle, be identified as a decay of resonances. It is possible,
because the program features explicit and exact parametrization of phase space
for multi-body plus multi-photon final states. The Photos emission kernel for
some processes consist of complete matrix element, in the remaining cases
appropriate approximation is used. Comparisons with results of simulations,
from generators based on exact phase space and exact fixed order matrix
elements, can be used. For the purpose of such validations Photos provides an
option to restrict emissions to single photon only. In the current work we
concentrate on final state bremsstrahlung in $q \bar{q}(e^+e^-) \to l^+l^-
l^+l^- \gamma$ and $\gamma\gamma \to l^+l^- \gamma$ processes. The reference
distributions used as a cross-check are obtained from the fixed-order MadGraph
Monte Carlo simulations. For the purpose of validation we concentrate on those
phase space regions where Photos is not expected to work on the basis of its
design alone. These phase space regions of hard, non-collinear photons, do not
contribute to large logarithmic terms. We find that in these phase space
regions the differences between Photos and MadGraph results do not surpass a
few percent and these regions, in turn, contribute about 10% to the observed
process rates. This is encouraging in view of the possible ambiguities for
precise calculation of realistic observables.


  The existence of a crumpled phase for self-avoiding elastic surfaces was
postulated more than three decades ago using simple Flory-like scaling
arguments. Despite much effort, its stability in a microscopic environment has
been the subject of much debate. In this paper we show how a crumpled phase
develops reliably and consistently upon subjecting a thin spherical shell to
active fluctuations. We find a master curve describing how the relative volume
of a shell changes with the strength of the active forces, that applies for
every shell independent of size and elastic constants. Furthermore, we extract
a general expression for the onset active force beyond which a shell begins to
crumple. Finally, we calculate how the size exponent varies along the crumpling
curve.


  The recently proposed eight-component relativistic wave equation is applied
to the scattering of a photon from a free electron (Compton scattering). It is
found that in spite of the considerable difference in the structure of this
equation and that of Dirac the cross section is given by the Klein-Nishina
formula.


  In this paper, we study the number of equilibria of the replicator-mutator
dynamics for both deterministic and random multi-player two-strategy
evolutionary games. For deterministic games, using Decartes' rule of signs, we
provide a formula to compute the number of equilibria in multi-player games via
the number of change of signs in the coefficients of a polynomial. For
two-player social dilemmas (namely, the Prisoner's Dilemma, Snowdrift, Stag
Hunt, and Harmony), we characterize (stable) equilibrium points and
analytically calculate the probability of having a certain number of equilibria
when the payoff entries are uniformly distributed. For multi-player random
games whose payoffs are independently distributed according to a normal
distribution, by employing techniques from random polynomial theory, we compute
the expected or average number of internal equilibria. In addition, we perform
extensive simulations by sampling and averaging over a large number of possible
payoff matrices to compare with and illustrate analytical results. Numerical
simulations also suggest several interesting behaviour of the average number of
equilibria when the number of players is sufficiently large or when the
mutation is sufficiently small. In general, we observe that introducing
mutation results in a larger average number of internal equilibria than when
mutation is absent, implying that mutation leads to larger behavioural
diversity in dynamical systems. Interestingly, this number is largest when
mutation is rare rather than when it is frequent.


  The QCD phase diagram lies at the heart of what the RHIC Physics Program is
all about. While RHIC has been operating very successfully at or close to its
maximum energy for almost a decade, it has become clear that this collider can
also be operated at lower energies down to 5 GeV without extensive upgrades. An
exploration of the full region of beam energies available at the RHIC facility
is imperative. The STAR detector, due to its large uniform acceptance and
excellent particle identification capabilities, is uniquely positioned to carry
out this program in depth and detail. The first exploratory beam energy scan
(BES) run at RHIC took place in 2010 (Run 10), since several STAR upgrades,
most importantly a full barrel Time of Flight detector, are now completed which
add new capabilities important for the interesting physics at BES energies. In
this document we discuss current proposed measurements, with estimations of the
accuracy of the measurements given an assumed event count at each beam energy.


  Large language models (LLMs) can solve complex multi-step problems, but
little is known about how these computations are implemented internally.
Motivated by this, we study how LLMs answer multi-hop queries such as "The
spouse of the performer of Imagine is". These queries require two information
extraction steps: a latent one for resolving the first hop ("the performer of
Imagine") into the bridge entity (John Lennon), and one for resolving the
second hop ("the spouse of John Lennon") into the target entity (Yoko Ono).
Understanding how the latent step is computed internally is key to
understanding the overall computation. By carefully analyzing the internal
computations of transformer-based LLMs, we discover that the bridge entity is
resolved in the early layers of the model. Then, only after this resolution,
the two-hop query is solved in the later layers. Because the second hop
commences in later layers, there could be cases where these layers no longer
encode the necessary knowledge for correctly predicting the answer. Motivated
by this, we propose a novel "back-patching" analysis method whereby a hidden
representation from a later layer is patched back to an earlier layer. We find
that in up to 57% of previously incorrect cases there exists a back-patch that
results in the correct generation of the answer, showing that the later layers
indeed sometimes lack the needed functionality. Overall our methods and
findings open further opportunities for understanding and improving latent
reasoning in transformer-based LLMs.


  We introduce some invariants of Fano varieties and propose a Mukai-type
conjecture which characterizes the product of projective spaces. Moreover, we
prove that the Ambro--Kawamata effective non-vanishing conjecture implies the
Mukai-type conjecture.


  In the last decade, exponential data growth supplied machine learning-based
algorithms' capacity and enabled their usage in daily-life activities.
Additionally, such an improvement is partially explained due to the advent of
deep learning techniques, i.e., stacks of simple architectures that end up in
more complex models. Although both factors produce outstanding results, they
also pose drawbacks regarding the learning process as training complex models
over large datasets are expensive and time-consuming. Such a problem is even
more evident when dealing with video analysis. Some works have considered
transfer learning or domain adaptation, i.e., approaches that map the knowledge
from one domain to another, to ease the training burden, yet most of them
operate over individual or small blocks of frames. This paper proposes a novel
approach to map the knowledge from action recognition to event recognition
using an energy-based model, denoted as Spectral Deep Belief Network. Such a
model can process all frames simultaneously, carrying spatial and temporal
information through the learning process. The experimental results conducted
over two public video dataset, the HMDB-51 and the UCF-101, depict the
effectiveness of the proposed model and its reduced computational burden when
compared to traditional energy-based models, such as Restricted Boltzmann
Machines and Deep Belief Networks.


  Contextual bandits algorithms aim to choose the optimal arm with the highest
reward out of a set of candidates based on the contextual information. Various
bandit algorithms have been applied to real-world applications due to their
ability of tackling the exploitation-exploration dilemma. Motivated by online
recommendation scenarios, in this paper, we propose a framework named Graph
Neural Bandits (GNB) to leverage the collaborative nature among users empowered
by graph neural networks (GNNs). Instead of estimating rigid user clusters as
in existing works, we model the "fine-grained" collaborative effects through
estimated user graphs in terms of exploitation and exploration respectively.
Then, to refine the recommendation strategy, we utilize separate GNN-based
models on estimated user graphs for exploitation and adaptive exploration.
Theoretical analysis and experimental results on multiple real data sets in
comparison with state-of-the-art baselines are provided to demonstrate the
effectiveness of our proposed framework.


  Deploying, configuring, and managing large clusters is very a demanding and
cumbersome task due to the complexity of such systems and the variety of skills
needed. One needs to perform low-level configuration of the cluster nodes to
ensure their interoperability and connectivity, as well as install, configure
and provision the needed services.
  In this paper we address this problem and demonstrate how to build a Big Data
analytic platform on Amazon EC2 in a matter of minutes. Moreover, to use our
tool, embedded into a public Amazon Machine Image, the user does not need to be
an expert in system administration or Big Data service configuration. Our tool
dramatically reduces the time needed to provision clusters, as well as the cost
of the infrastructure. Researchers enjoy an additional benefit of having a
simple way to specify the experimental environments they use, so that their
experiments can be easily reproduced by anyone using our tool.


  Along with the improvement of radar technologies, Automatic Target
Recognition (ATR) using Synthetic Aperture Radar (SAR) and Inverse SAR (ISAR)
has come to be an active research area. SAR/ISAR are radar techniques to
generate a two-dimensional high-resolution image of a target. Unlike other
similar experiments using Convolutional Neural Networks (CNN) to solve this
problem, we utilize an unusual approach that leads to better performance and
faster training times. Our CNN uses complex values generated by a simulation to
train the network; additionally, we utilize a multi-radar approach to increase
the accuracy of the training and testing processes, thus resulting in higher
accuracies than the other papers working on SAR/ISAR ATR. We generated our
dataset with 7 different aircraft models with a radar simulator we developed
called RadarPixel; it is a Windows GUI program implemented using Matlab and
Java programming, the simulator is capable of accurately replicating a real
SAR/ISAR configurations. Our objective is to utilize our multi-radar technique
and determine the optimal number of radars needed to detect and classify
targets.


  The paper studies an oligopolistic equilibrium model of financial agents who
aim to share their random endowments. The risk-sharing securities and their
prices are endogenously determined as the outcome of a strategic game played
among all the participating agents. In the complete-market setting, each
agent's set of strategic choices consists of the security payoffs and the
pricing kernel that are consistent with the optimal-sharing rules; while in the
incomplete setting, agents respond via demand functions on a vector of given
tradeable securities. It is shown that at the (Nash) risk-sharing equilibrium,
the sharing securities are suboptimal, since agents submit for sharing
different risk exposures than their true endowments. On the other hand, the
Nash equilibrium prices stay unaffected by the game only in the special case of
agents with the same risk aversion. In addition, agents with sufficiently lower
risk aversion act as predatory traders, since they absorb utility surplus from
the high risk averse agents and reduce the efficiency of sharing. The main
results of the paper also hold under the generalized models that allow the
presence of noise traders and heterogeneity in agents' beliefs.


  We have synthesized magnesium cage compounds $R$Ni$_{2}$Mg$_{20}$ ($R$ = Pr
and Nd). We report the measurements of electrical resistivity $\rho$, magnetic
susceptibility $\chi$, isothermal magnetization $M$, and specific heat $C$.
Polycrystalline samples with $R$ = Pr and Nd were obtained by annealing, while
the counterparts for $R$ = La, Ce, and Y were found to be absent. The
${\rho}(T)$ data for $R$ = Pr and Nd monotonically decrease on cooling from 300
K to 40 K and exhibit shoulders at around 13 K and 15 K, respectively. The
Curie-Weiss behaviors of the ${\chi}(T)$ data indicate the trivalent states of
both the Pr and Nd ions. For $R$ = Pr, the maximum in $C(T)$ at around 7 K is
reproduced by a doublet-triplet two-level model with an energy gap of 14 K. The
peak in $C(T)$ at 0.7 K is attributed to a short-range order of quadrupolar
degrees of freedom in the non-Kramers ground doublet. On the other hand, for
$R$ = Nd, a maximum in $C(T)$ at around 9 K is explained by thermal excitation
from a ground state doublet to an excited quartet separated by 23 K. Upon
further cooling, $C(T)$ shows a lambda-shaped peak at 1.5 K. By applying
magnetic fields up to 2 T, the peak becomes broad and shifts to higher
temperatures, which is a characteristic of a ferromagnetic order.


  Distributed acoustic sensing technology is increasingly being used to support
production and well management within the oil and gas sector, for example to
improve flow monitoring and production profiling. This sensing technology is
capable of recording substantial data volumes at multiple depths within an oil
well, giving unprecedented insights into production behaviour. However the
technology is also prone to recording periods of anomalous behaviour, where the
same physical features are concurrently observed at multiple depths. Such
features are called `stripes' and are undesirable, detrimentally affecting well
performance modelling. This paper focuses on the important challenge of
developing a principled approach to identifying such anomalous periods within
distributed acoustic signals. We extend recent work on classifying locally
stationary wavelet time series to an online setting and, in so doing, introduce
a computationally-efficient online procedure capable of accurately identifying
anomalous regions within multivariate time series.


  We present a complete quantum mechanical description of a flat FRW universe
with equation of state p=\rho. We find a detailed correspondence with our
heuristic picture of such a universe as a dense black hole fluid. Features of
the geometry are derived from purely quantum input.


  We present a modified version of the nudged elastic band (NEB) algorithm to
find minimum energy paths con-necting two known configurations. We show that
replacing the harmonic band-energy term with a discretized version of the
Onsager-Machlup action leads to a NEB algorithm with adaptive spring lengths
that automatically increase the resolution of the minimum energy path around
the saddle point of the potential energy surface. The method has the same
computational cost per optimization step of the standard NEB algorithm and does
not introduce additional parameters. We present applications to the
isomerization of alanine dipeptide, the elimination of hydrogen from ethane and
the healing of a 5-77-5 defect in graphene.


  Citations are widely considered in scientists' evaluation. As such,
scientists may be incentivized to inflate their citation counts. While previous
literature has examined self-citations and citation cartels, it remains unclear
whether scientists can purchase citations. Here, we compile a dataset of ~1.6
million profiles on Google Scholar to examine instances of citation fraud on
the platform. We survey faculty at highly-ranked universities, and confirm that
Google Scholar is widely used when evaluating scientists. Intrigued by a
citation-boosting service that we unravelled during our investigation, we
contacted the service while undercover as a fictional author, and managed to
purchase 50 citations. These findings provide conclusive evidence that
citations can be bought in bulk, and highlight the need to look beyond citation
counts.


  We give a statement on extension with estimates of convex functions defined
on a linear subspace, inspired by similar extension results concerning metrics
on positive line bundles


  Among numerical libraries capable of computing gradient descent optimization,
JAX stands out by offering more features, accelerated by an intermediate
representation known as Jaxpr language. However, editing the Jaxpr code is not
directly possible. This article introduces JaxDecompiler, a tool that
transforms any JAX function into an editable Python code, especially useful for
editing the JAX function generated by the gradient function. JaxDecompiler
simplifies the processes of reverse engineering, understanding, customizing,
and interoperability of software developed by JAX. We highlight its
capabilities, emphasize its practical applications especially in deep learning
and more generally gradient-informed software, and demonstrate that the
decompiled code speed performance is similar to the original.


  In this article, we consider two dynamical systems: the McMillan sextupole
and octupole integrable mappings, originally proposed by Edwin McMillan. Both
represent the simplest symmetric McMillan maps, characterized by a single
intrinsic parameter. While these systems find numerous applications across
various domains of mathematics and physics, some of their dynamical properties
remain unexplored. We aim to bridge this gap by providing a comprehensive
description of all stable trajectories, including the parametrization of
invariant curves, Poincar\'e rotation numbers, and canonical action-angle
variables.
  In the second part, we establish connections between these maps and general
chaotic maps in standard form. Our investigation reveals that the McMillan
sextupole and octupole serve as first-order approximations of the dynamics
around the fixed point, akin to the linear map and quadratic invariant (known
as the Courant-Snyder invariant in accelerator physics), which represents
zeroth-order approximations (referred to as linearization). Furthermore, we
propose a novel formalism for nonlinear Twiss parameters, which accounts for
the dependence of rotation number on amplitude. This stands in contrast to
conventional betatron phase advance used in accelerator physics, which remains
independent of amplitude. Notably, in the context of accelerator physics, this
new formalism demonstrates its capability in predicting dynamical aperture
around low-order resonances for flat beams, a critical aspect in beam
injection/extraction scenarios.


  Given a finite group $\Gamma$, a regular $t$-balanced Cayley map (RBCM$_{t}$
for short) is a regular Cayley map $\mathcal{CM}(G,\Omega,\rho)$ such that
$\rho(\omega)^{-1}=\rho^{t}(\omega)$ for all $\omega\in\Omega$.
  In this paper, we clarify a connection between quotients of polynomial rings
and RBCM$_{t}$'s on abelian groups, so as to propose a new approach for
classifying RBCM$_{t}$'s. We obtain many new results, in particular, a complete
classification for RBCM$_{t}$'s on abelian 2-groups.


  The abundance of oxygen was determined for selected very metal-poor G-K stars
(six giants and one turn-off star) based on the high S/N and high-resolution
spectra observed with Keck HIRES in the red through near-IR region comprising
the permitted O I lines (7771-5, 8446) along with the [O I] forbidden line at
6363 A. It turned out that both the abundances from the permitted line
features, O I 7771-5 and O I 8446, agree quite well with each other, while the
forbidden line yields somewhat discrepant and divergent abundances with a
tendency of being underestimated on the average. The former (7773/8446)
solution, which we believe to be more reliable, gives a fairly tight [O/Fe] vs.
[Fe/H] relation such that increasing steadily from [O/Fe] = 0.6 (at [Fe/H] =
-1.5) to [O/Fe] = 1.0 (at [Fe/H] = -3.0), in reasonable consistency with the
trend recently reported based on the analysis of the UV OH lines. We would
suspect that some kind of weakening mechanism may occasionally act on the
formation of [O I] forbidden lines in metal-poor stars. Therefore, [O I] lines
may not be so a reliable abundance indicator as has been generally believed.


  Inhomogeneities in the wave field due to wave groups, currents, and shoaling
among other ocean processes can affect the mean water level. In this work, the
classical and unsolved problem of continuously computing the set-down and the
following set-up induced by wave breaking on a shoal of constant finite slope
is tackled. This is possible by using available theoretical knowledge on how to
approximate the distribution of wave random phases in finite depth. Then, the
non-homogeneous spectral analysis of the wave field allows the computation of
the ensemble average by means of the phase distribution and the inversion of
the integral of the second moment for the special case of a shoaling process
with uniform phase distribution. In doing so, I am able to obtain a direct
effect of the slope magnitude on the phases distribution. Therefore, an
analytical and slope-dependent mean water level with continuity over the entire
range of water depth is provided.


  Suppose $X$ is a finite discrete space with at least two elements, $\Gamma$
is a nonempty countable set, and consider self--map $\varphi:\Gamma\to\Gamma$.
We prove that the generalized shift $\sigma_\varphi:X^\Gamma\to X^\Gamma$ with
$\sigma_\varphi((x_\alpha)_{\alpha\in\Gamma})=(x_{\varphi(\alpha)})_{\alpha\in\Gamma}$
(for $(x_\alpha)_{\alpha\in\Gamma}\in X^\Gamma$) is:
  $\bullet$ distributional chaotic (uniform, type 1, type 2) if and only if
$\varphi:\Gamma\to\Gamma$ has at least a non-quasi-periodic point,
  $\bullet$ dense distributional chaotic if and only if
$\varphi:\Gamma\to\Gamma$ does not have any periodic point,
  $\bullet$ transitive distributional chaotic if and only if
$\varphi:\Gamma\to\Gamma$ is one--to--one without any periodic point.
  We complete the text by counterexamples.


  We propose a new class of estimators of the multivariate response linear
regression coefficient matrix that exploits the assumption that the response
and predictors have a joint multivariate Normal distribution. This allows us to
indirectly estimate the regression coefficient matrix through shrinkage
estimation of the parameters of the inverse regression, or the conditional
distribution of the predictors given the responses. We establish a convergence
rate bound for estimators in our class and we study two examples. The first
example estimator exploits an assumption that the inverse regression's
coefficient matrix is sparse. The second example estimator exploits an
assumption that the inverse regression's coefficient matrix is rank deficient.
These estimators do not require the popular assumption that the forward
regression coefficient matrix is sparse or has small Frobenius norm. Using
simulation studies, we show that our example estimators outperform relevant
competitors for some data generating models.


  We calculate the tree and penguin amplitudes in the $B^0\to\pi^+\pi^-$ decay
channel employing the perturbative QCD factorization approach. Using the
amplitudes as input with the theoretical uncertainties sufficiently considered,
we constrain the UT angle $\gamma$ to $53^\circ\leq\gamma\leq70^\circ$, from
the measurements of the CP violation parameters $C_{\pi^+\pi^-}$ and
$S_{\pi^+\pi^-}$ in $B^0\to\pi^+\pi^-$. The U-spin breaking effect between
$B^0\to\pi^+\pi^-$ and $B_s^0\to K^+K^-$ is estimated to be around 30\%.


  Levy flights and fractional Brownian motion (fBm) have become exemplars of
the heavy tailed jumps and long-ranged memory widely seen in physics. Natural
time series frequently combine both effects, and linear fractional stable
motion (lfsm) is a model process of this type, combining alpha-stable jumps
with a memory kernel. In contrast complex physical spatiotemporal diffusion
processes where both the above effects compete have for many years been
modelled using the fully fractional (FF) kinetic equation for the continuous
time random walk (CTRW), with power laws in the pdfs of both jump size and
waiting time. We derive the analogous kinetic equation for lfsm and show that
it has a diffusion coefficient with a power law in time rather than having a
fractional time derivative like the CTRW. We discuss some preliminary results
on the scaling of burst "sizes" and "durations" in lfsm time series, with
applications to modelling existing observations in space physics and elsewhere.


  Cloud radio access networks (C-RAN) and Mobile Cloud Computing (MCC) have
emerged as promising candidates for the next generation access network
techniques. MCC enables resource limited mobile devices to offload
computationally intensive tasks to the cloud, while C-RAN offers a technology
that addresses the increasing mobile traffic. In this paper, we propose a
protocol for task offloading and for managing resources in both C-RAN and
mobile cloud together using a centralised controller. Experiments on resource
management using cloud auto-scaling shows that resource (CPU, RAM, Storage)
scaling times vary.


  Research over the past decade has shown diminishing empirical evidence for
major galaxy mergers being a dominating or even important mechanism for the
growth of supermassive black holes in galaxies and the triggering of optically
or X-ray selected active galactic nuclei (AGN). We here for the first time test
whether such a connection exists at least in the most plausible part of
parameter space for this mechanism: the highest specific accretion rate
broad-line AGNs at the peak epoch of black hole activity around z = 2. To that
end we examine 21 galaxies hosting a high accreting black hole (L/Ledd > 0.7)
observed with HST/WFC3 and 92 stellar mass- and redshift- matched inactive
galaxies taken from the CANDELS survey. We removed the AGN point sources from
their host galaxies and avoided bias in visual classification by adding and
then subtracting mock point sources to and from the comparison galaxies,
producing matched residual structures for both sets. The resulting samples were
joined, randomized, and subsequently visually ranked with respect to perceived
strength of structural distortions by 10 experts. The ensuing individual
rankings were combined into a consensus sequence and from this we derived
merger fractions for both samples. With the merger fractions f$_{m,agn}$ = 0.24
$\pm$ 0.09 for the AGN host galaxy sample and f$_{m,ina}$ = 0.19 $\pm$ 0.04 for
the inactive galaxies, we find no significant difference between the AGN host
galaxies and inactive galaxies. Also, both samples display comparable fractions
of disk-dominated galaxies. These findings are consistent with previous studies
for different AGN populations, and we conclude that even black hole growth at
the highest specific accretion rates and at the peak of cosmic AGN activity is
not predominantly caused by major mergers. (abriged)


  A search for the rare decays $B^0_s\to\mu^+\mu^-$ and $B^0\to\mu^+\mu^-$ is
performed at the LHCb experiment using data collected in $pp$ collisions
corresponding to a total integrated luminosity of 4.4 fb$^{-1}$. An excess of
$B^0_s\to\mu^+\mu^-$ decays is observed with a significance of 7.8 standard
deviations, representing the first observation of this decay in a single
experiment. The branching fraction is measured to be ${\cal
B}(B^0_s\to\mu^+\mu^-)=\left(3.0\pm 0.6^{+0.3}_{-0.2}\right)\times 10^{-9}$,
where the first uncertainty is statistical and the second systematic. The first
measurement of the $B^0_s\to\mu^+\mu^-$ effective lifetime,
$\tau(B^0_s\to\mu^+\mu^-)=2.04\pm 0.44\pm 0.05$ ps, is reported. No significant
excess of $B^0\to\mu^+\mu^-$ decays is found and a 95 % confidence level upper
limit, ${\cal B}(B^0\to\mu^+\mu^-)<3.4\times 10^{-10}$, is determined. All
results are in agreement with the Standard Model expectations.


  We present science highlights and performance from the Swift X-ray Telescope
(XRT), which was launched on November 20, 2004. The XRT covers the 0.2-10 keV
band, and spends most of its time observing gamma-ray burst (GRB)afterglows,
though it has also performed observations of many other objects. By mid-August
2007, the XRT had observed over 220 GRB afterglows, detecting about 96% of
them. The XRT positions enable followup ground-based optical observations, with
roughly 60% of the afterglows detected at optical or near IR wavelengths.
Redshifts are measured for 33% of X-ray afterglows. Science highlights include
the discovery of flaring behavior at quite late times, with implications for
GRB central engines; localization of short GRBs, leading to observational
support for compact merger progenitors for this class of bursts; a mysterious
plateau phase to GRB afterglows; as well as many other interesting observations
such as X-ray emission from comets, novae, galactic transients, and other
objects.


  The low-temperature magnetoresistance of parabolic quantum wells displays
pronounced minima between integer filling factors. Concomitantly the Hall
effect exhibits overshoots and plateau-like features next to well-defined
ordinary quantum Hall plateaus. These effects set in with the occupation of the
second subband. We discuss our observations in the context of single-particle
Landau fan charts of a two-subband system empirically extended by a density
dependent subband separation and an enhanced spin-splitting g*.


  Stochastic gradient descent (SGD) is a promising method for solving
large-scale inverse problems, due to its excellent scalability with respect to
data size. The current mathematical theory in the lens of regularization theory
predicts that SGD with a polynomially decaying stepsize schedule may suffer
from an undesirable saturation phenomenon, i.e., the convergence rate does not
further improve with the solution regularity index when it is beyond a certain
range. In this work, we present a refined convergence rate analysis of SGD, and
prove that saturation actually does not occur if the initial stepsize of the
schedule is sufficiently small. Several numerical experiments are provided to
complement the analysis.


  In this paper we show that the problem of identifying an edge $(i,j)$ in a
graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing
exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak
edge. We then develop a polynomial time approximation algorithm for the vertex
cover problem with performance guarantee $2-\frac{1}{1+\sigma}$, where $\sigma$
is an upper bound on a measure related to a weak edge of a graph. Further, we
discuss a new relaxation of the vertex cover problem which is used in our
approximation algorithm to obtain smaller values of $\sigma$. We also obtain
linear programming representations of the vertex cover problem for special
graphs. Our results provide new insights into the approximability of the vertex
cover problem - a long standing open problem.


  Creating large LiDAR datasets with pixel-level labeling poses significant
challenges. While numerous data augmentation methods have been developed to
reduce the reliance on manual labeling, these methods predominantly focus on
static scenes and they overlook the importance of data augmentation for dynamic
scenes, which is critical for autonomous driving. To address this issue, we
propose D-Aug, a LiDAR data augmentation method tailored for augmenting dynamic
scenes. D-Aug extracts objects and inserts them into dynamic scenes,
considering the continuity of these objects across consecutive frames. For
seamless insertion into dynamic scenes, we propose a reference-guided method
that involves dynamic collision detection and rotation alignment. Additionally,
we present a pixel-level road identification strategy to efficiently determine
suitable insertion positions. We validated our method using the nuScenes
dataset with various 3D detection and tracking methods. Comparative experiments
demonstrate the superiority of D-Aug.


  Certification of quantum nonlocality plays a central role in practical
applications like device-independent quantum cryptography and random number
generation protocols. These applications entail the challenging problem of
certifying quantum nonlocality, something that is hard to achieve when the
target quantum state is weakly entangled, or when the source of errors is high,
e.g. when photons propagate through the atmosphere or a long optical fiber.
Here, we introduce a technique to find a Bell inequality with the largest
possible gap between the quantum prediction and the classical local hidden
variable limit for a given set of measurement frequencies. Our method
represents an efficient strategy to certify quantum nonlocal correlations from
experimental data without requiring extra measurements, in the sense that there
is no Bell inequality with a larger gap than the one provided. Furthermore, we
also reduce the photodetector efficiency required to close the detection
loophole. We illustrate our technique by improving the detection of quantum
nonlocality from experimental data obtained with weakly entangled photons.


  We show that all $n$-qubit entangled states, with the exception of tensor
products of single-qubit and bipartite maximally-entangled states, admit
Hardy-type proofs of non-locality without inequalities or probabilities. More
precisely, we show that for all such states, there are local, one-qubit
observables such that the resulting probability tables are logically contextual
in the sense of Abramsky and Brandenburger, this being the general form of the
Hardy-type property. Moreover, our proof is constructive: given a state, we
show how to produce the witnessing local observables. In fact, we give an
algorithm to do this. Although the algorithm is reasonably straightforward, its
proof of correctness is non-trivial. A further striking feature is that we show
that $n+2$ local observables suffice to witness the logical contextuality of
any $n$-qubit state: two each for two for the parties, and one each for the
remaining $n-2$ parties.


  Global well-posedness of strong solutions and existence of the global
attractor to the initial and boundary value problem of 2D Boussinesq system in
a periodic channel with non-homogeneous boundary conditions for the temperature
and viscosity and thermal diffusivity depending on the temperature are proved.


  We use a suite of simulated images based on Year 1 of the Dark Energy Survey
to explore the impact of galaxy neighbours on shape measurement and shear
cosmology. The hoopoe image simulations include realistic blending, galaxy
positions, and spatial variations in depth and PSF properties. Using the
im3shape maximum-likelihood shape measurement code, we identify four mechanisms
by which neighbours can have a non-negligible influence on shear estimation.
These effects, if ignored, would contribute a net multiplicative bias of $m
\sim 0.03 - 0.09$ in the DES Y1 im3shape catalogue, though the precise impact
will be dependent on both the measurement code and the selection cuts applied.
This can be reduced to percentage level or less by removing objects with close
neighbours, at a cost to the effective number density of galaxies
$n_\mathrm{eff}$ of 30%. We use the cosmological inference pipeline of DES Y1
to explore the cosmological implications of neighbour bias and show that
omitting blending from the calibration simulation for DES Y1 would bias the
inferred clustering amplitude $S_8\equiv \sigma_8 (\Omega _\mathrm{m}
/0.3)^{0.5}$ by $2 \sigma$ towards low values. Finally, we use the hoopoe
simulations to test the effect of neighbour-induced spatial correlations in the
multiplicative bias. We find the impact on the recovered $S_8$ of ignoring such
correlations to be subdominant to statistical error at the current level of
precision.


  Low phase noise MEMS oscillators necessitate resonators with high f-Q.
Resonators achieving high f-Q (mechanical frequency-quality factor product)
close to the thermo-elastic damping (TED) limit have been demonstrated at
expense of feed-through. Here we present a study comparing frequency scaling of
quality factors of wineglass and radial modes in a ring resonator using an
opto-mechanical two port transmission measurement. Higher harmonics of the
wineglass mode show an increasing trend in the f-Q product, as compared to a
saturation of f-Q for radial modes. The measured f-Q of 5.11e13Hz at 9.82GHz in
air at room temperature for a wineglass mode is close to the highest measured
values in silicon resonators.


  In this article, applying the quasi-Gorenstein analogous of the Ulrich's
deformation of certain Gorenstein rings we show that some homological
conjectures, including the Monomial Conjecture, Big Cohen-Macaulay Algebra
Conjecture as well as the Small Cohen-Macaulay Conjecture reduce to the
excellent unique factorization domains. Some other reductions of the Monomial
Conjecture are also proved. We, moreover, show that certain almost complete
intersections adhere the Monomial Conjecture.


  The social connections people form online affect the quality of information
they receive and their online experience. Although a host of socioeconomic and
cognitive factors were implicated in the formation of offline social ties, few
of them have been empirically validated, particularly in an online setting. In
this study, we analyze a large corpus of geo-referenced messages, or tweets,
posted by social media users from a major US metropolitan area. We linked these
tweets to US Census data through their locations. This allowed us to measure
emotions expressed in the tweets posted from an area, the structure of social
connections, and also use that area's socioeconomic characteristics in
analysis. %We extracted the structure of online social interactions from the
people mentioned in tweets from that area. We find that at an aggregate level,
places where social media users engage more deeply with less diverse social
contacts are those where they express more negative emotions, like sadness and
anger. Demographics also has an impact: these places have residents with lower
household income and education levels. Conversely, places where people engage
less frequently but with diverse contacts have happier, more positive messages
posted from them and also have better educated, younger, more affluent
residents. Results suggest that cognitive factors and offline characteristics
affect the quality of online interactions. Our work highlights the value of
linking social media data to traditional data sources, such as US Census, to
drive novel analysis of online behavior.


  We investigate a generalized empirical likelihood approach in a two-group
setting where the constraints on parameters have a form of U-statistics. In
this situation, the summands that consist of the constraints for the empirical
likelihood are not independent, and a weight of each summand may not have a
direct interpretation as a probability point mass, dissimilar to the common
empirical likelihood constraints based on independent summands. We show that
the resulting empirical likelihood ratio statistic has a weighted chi-squared
distribution in the univariate case and a combination of weighted chi-squared
distributions in the multivariate case. Through an extensive Monte-Carlo study,
we show that the proposed methods applied for some well-known U-statistics have
robust Type I error control under various underlying distributions including
cases with a violation of exchangeability under null hypotheses. For the
application, we employ the proposed methods to test hypotheses in crossover
designs demonstrating an adaptability of the proposed methods in various
hypothesis tests.


  This is a revised version of a part of the author's preprint "On p-adic
uniformization of fake projective planes" (preprint, Max-Planck-Institut fuer
Mathematik, 1998 (121)).
  In this paper we construct explicitly a Shimura surface of PEL-type,
associated to a certain unitary group, whose connected components are
isomorphic to Mumford's fake projective plane. We also give the canonical
model, Shimura field and number of connected components of this Shimura
surface. As a consequence of the construction we prove that the Mumford's fake
projective plane is an arithmetic complex unit-ball quotient, and has the 7-th
cyclotomic field as a field of definition.
  In Tohoku Math. J. 50 (1998), 537-555, Masanori Ishida and the author
discussed two other possible fake projective planes. The author has also
obtained the corresponding results as above for these fake projective planes
and has written them in the above preprint, which is available in the web page:
http://www.mpim-bonn.mpg.de/html/preprints/preprints.html


  The Burau representation enables to define many other representations of the
braid group $B_n$ by the topological operation of ``cabling braids''. We show
here that these representations split into copies of the Burau representation
itself and of a representation of $B_n/(P_n,P_n)$. In particular, we show that
there is no gain in terms of faithfulness by cabling the Burau representation.


  The star HD 147379 was recently announced as a host of a low-mass exoplanet
by Reiners et al. (2017). That announcement included a discussion of the
possible detection of a periodic signal in the radial velocity observations
around 21.1 days, which was interpreted as rotational variability of the star.
We have examined the light curve of this star as observed by the KELT transit
survey, and we find a significant periodic signal in the light curve of 22.0064
days, supporting the interpretation of Reiners et al. (2017) of the rotational
variation of the star.


  Although semantic communication (SC) has shown its potential in efficiently
transmitting multi-modal data such as text, speeches and images, SC for videos
has focused primarily on pixel-level reconstruction. However, these SC systems
may be suboptimal for downstream intelligent tasks. Moreover, SC systems
without pixel-level video reconstruction present advantages by achieving higher
bandwidth efficiency and real-time performance of various intelligent tasks.
The difficulty in such system design lies in the extraction of task-related
compact semantic representations and their accurate delivery over noisy
channels. In this paper, we propose an end-to-end SC system for video question
answering (VideoQA) tasks called VideoQA-SC. Our goal is to accomplish VideoQA
tasks directly based on video semantics over noisy or fading wireless channels,
bypassing the need for video reconstruction at the receiver. To this end, we
develop a spatiotemporal semantic encoder for effective video semantic
extraction, and a learning-based bandwidth-adaptive deep joint source-channel
coding (DJSCC) scheme for efficient and robust video semantic transmission.
Experiments demonstrate that VideoQA-SC outperforms traditional and advanced
DJSCC-based SC systems that rely on video reconstruction at the receiver under
a wide range of channel conditions and bandwidth constraints. In particular,
when the signal-to-noise ratio is low, VideoQA-SC can improve the answer
accuracy by 5.17% while saving almost 99.5% of the bandwidth at the same time,
compared with the advanced DJSCC-based SC system. Our results show the great
potential of task-oriented SC system design for video applications.


  Gene regulatory networks typically have low in-degrees, whereby any given
gene is regulated by few of the genes in the network. They also tend to have
broad distributions for the out-degree. What mechanisms might be responsible
for these degree distributions? Starting with an accepted framework of the
binding of transcription factors to DNA, we consider a simple model of gene
regulatory dynamics. There, we show that selection for a target expression
pattern leads to the emergence of minimum connectivities compatible with the
selective constraint. As a consequence, these gene networks have low in-degree,
and "functionality" is parsimonious, i.e. is concentrated on a sparse number of
interactions as measured for instance by their essentiality. Furthermore, we
find that mutations of the transcription factors drive the networks to have
broad out-degrees. Finally, these classes of models are evolvable, i.e.
significantly different genotypes can emerge gradually under mutation-selection
balance.


  We present a new quantitative technique that determines the times and
durations of substorm expansion and recovery phases and possible growth phases
based on percentiles of the rate of change of auroral electrojet indices. By
being able to prescribe different percentile values, we can determine the onset
and duration of substorm phases for smaller or larger variations of the auroral
index or indeed any auroral zone ground-based magnetometer data. We apply this
technique to the SuperMAG AL (SML) index and compare our expansion phase onset
times with previous lists of substorm onsets. We find that more than 50% of
events in previous lists occur within 20 min of our identified onsets. We also
present a comparison of superposed epoch analyses of SML based on our onsets
identified by our technique and existing onset lists and find that the general
characteristics of the substorm bay are comparable. By prescribing user-defined
thresholds, this automated, quantitative technique represents an improvement
over any visual identification of substorm onsets or indeed any fixed threshold
method.


  In this paper we consider the problem of unambiguous discrimination between a
set of linearly independent pure quantum states. We show that the design of the
optimal measurement that minimizes the probability of an inconclusive result
can be formulated as a semidefinite programming problem. Based on this
formulation, we develop a set of necessary and sufficient conditions for an
optimal quantum measurement. We show that the optimal measurement can be
computed very efficiently in polynomial time by exploiting the many well-known
algorithms for solving semidefinite programs, which are guaranteed to converge
to the global optimum.
  Using the general conditions for optimality, we derive necessary and
sufficient conditions so that the measurement that results in an equal
probability of an inconclusive result for each one of the quantum states is
optimal. We refer to this measurement as the equal-probability measurement
(EPM). We then show that for any state set, the prior probabilities of the
states can be chosen such that the EPM is optimal.
  Finally, we consider state sets with strong symmetry properties and equal
prior probabilities for which the EPM is optimal. We first consider
geometrically uniform state sets that are defined over a group of unitary
matrices and are generated by a single generating vector. We then consider
compound geometrically uniform state sets which are generated by a group of
unitary matrices using multiple generating vectors, where the generating
vectors satisfy a certain (weighted) norm constraint.


  We prove an instance of the cyclic sieving phenomenon in non-crossing
connected graphs, as conjectured by S.-P. Eu.