  The existence of a minimal measurable length is a common feature of various
approaches to quantum gravity such as string theory, loop quantum gravity and
black-hole physics. In this scenario, all commutation relations are modified
and the Heisenberg uncertainty principle is changed to the so-called
Generalized (Gravitational) Uncertainty Principle (GUP). Here, we present a
one-dimensional nonperturbative approach to quantum mechanics with minimal
length uncertainty relation which implies X=x to all orders and P=p+(1/3)\beta
p^3 to first order of GUP parameter \beta, where X and P are the generalized
position and momentum operators and [x,p]=i\hbar. We show that this formalism
is an equivalent representation of the seminal proposal by Kempf, Mangano, and
Mann and predicts the same physics. However, this proposal reveals many
significant aspects of the generalized uncertainty principle in a simple and
comprehensive form and the existence of a maximal canonical momentum is
manifest through this representation. The problems of the free particle and the
harmonic oscillator are exactly solved in this GUP framework and the effects of
GUP on the thermodynamics of these systems are also presented. Although X, P,
and the Hamiltonian of the harmonic oscillator all are formally self-adjoint,
the careful study of the domains of these operators shows that only the
momentum operator remains self-adjoint in the presence of the minimal length
uncertainty. We finally discuss the difficulties with the definition of
potentials with infinitely sharp boundaries.


  This paper presents a theoretical, idealized model of the thinking process
with the following characteristics: 1) the model can produce complex thought
sequences and can be generalized to new inputs, 2) it can receive and maintain
input information indefinitely for the generation of thoughts and later use,
and 3) it supports learning while executing. The crux of the model lies within
the concept of internal consistency, or the generated thoughts should always be
consistent with the inputs from which they are created. Its merit, apart from
the capability to generate new creative thoughts from an internal mechanism,
depends on the potential to help training to generalize better. This is
consequently enabled by separating input information into several parts to be
handled by different processing components with a focus mechanism to fetch
information for each. This modularized view with the focus binds the model with
the computationally capable Turing machines. And as a final remark, this paper
constructively shows that the computational complexity of the model is at
least, if not surpass, that of a universal Turing machine.


  A category which generalises to higher dimensions many of the features of the
Temperley-Lieb category is introduced.


  This paper gives a complete analysis of worst-case equilibria for various
versions of weighted congestion games with two players and affine cost
functions. The results are exact price of anarchy bounds which are parametric
in the weights of the two players, and establish exactly how the primitives of
the game enter into the quality of equilibria. Interestingly, some of the
worst-cases are attained when the players' weights only differ slightly. Our
findings also show that sequential play improves the price of anarchy in all
cases, however, this effect vanishes with an increasing difference in the
players' weights. Methodologically, we obtain exact price of anarchy bounds by
a duality based proof mechanism, based on a compact linear programming
formulation that computes worst-case instances. This mechanism yields
duality-based optimality certificates which can eventually be turned into
purely algebraic proofs.


  Inclusive beauty-quark production in two-photon collisions has been measured
at LEP using an integrated luminosity of 698 pb-1 collected by the ALEPH
detector with sqrt(s) between 130 and 209 GeV. The b quarks were identified
using lifetime information. The cross section is found to be sigma(e+ e- --> e+
e- b \bar{b} X) = (5.4 +/- 0.8 (stat) +/- 0.8 (syst)) pb which is consistent
with Next-to-Leading Order QCD.


  Wireless access technologies have been extensively developed aiming to give
users the ability to connect to their expected networks anytime, anywhere. This
leads to an increment of the number of wireless interfaces integrated into a
single mobile device, hence, it allows the device to be able to connect to
multiple access networks. However, in some specific cases such as natural
disasters, having an uncorrupted and timely information exchanging means is
critical for affected victims to survive or to connect to the outside world.
This is because the essential network infrastructures in these cases could be
destroyed causing a large number of systems to stop working. In that cases, the
victims need a heterogeneous communications network in which they can
communicate, without a doubt, by using different wireless access technologies,
i.e., Bluetooth or Wi-Fi. The network must also be able to smoothly change the
access technologies, or called a vertical handover, to ensure QoS for ongoing
applications. In addition, the network must have a mechanism to save energy.
For hese reasons, an SDN approach, which has been proposed in a previous work,
is considered. The performance of the system has been validated by a set of
experiments in a real testbed. The obtained results show that the proposed
vertical handover can save at least 24.42 per cent of the energy consumed by
the wireless communication. The handover delay with different UDP traffic is
less than 150ms. Moreover, the network allows a device using Bluetooth to talk
with another one using Wi-Fi over a heterogeneous connection where the
end-to-end jitter is mainly below 20ms and the packet loss rate is as small as
0.2 per cent.


  We investigate the phase space of parameters in the Pati-Salam model derived
in the context of D-branes scenarios, requiring low energy string scale. We
find that a non-supersymmetric version complies with a string scale as low as
10 TeV, while in the supersymmetric version the string scale raises up to ~2 x
10^7 TeV. The limited energy region for RGE running demands a large tan(beta)
in order to have experimentally acceptable masses for the top and bottom
quarks.


  We consider the action of symplectic monodromy on chain-level enhancements of
quantum cohomology. First, we construct a family version of
$A_\infty$-structure on quantum cohomology (this should morally correspond to
Hochschild cohomology of a "family of Fukaya categories over the circle").
Following Kaledin, we look at the obstruction class of this structure, and
argue that it can be related to a quantum version of Massey products on the one
hand (which, in nice cases, can be related to actual counts of rational curves)
and to the classical Andreadakis-Johnson theory of the Torelli group on the
other hand.
  In the second part of the paper, we go hunting for exotic symplectomorphism:
these are elements of infinite order in the kernel $$\mathcal{K}(M,\omega) :=
\pi_0 \mathrm{Symp}(M,\omega) \to \pi_0 \mathrm{Diff}^+(M,\omega)$$ of the
forgetful map from the symplectic mapping class group to the ordinary MCG. We
demonstrate how we can apply the theory above to prove the existence of such
elements $\psi_Y$ for certain a Fano 3-fold obtained by blowing-up
$\mathbb{P}^3$ at a genus 4 curve. Unlike the four-dimensional case, no power
of a Dehn twist around Lagrangian 3-spheres can be exotic (because they have
infinite order in smooth MCG).
  In the final part of the paper, the classical connection between our Fano
varieties and cubic 3-folds allows us to prove the existence of a new
phenomena: "exotic relations" in the subgroup generated by all Dehn twists.
Namely, it turns out we can factor some power of $[\psi_Y]$ in $\pi_0
\mathrm{Symp}(Y,\omega)$ into 3-dimensional Dehn twists. So the isotopy class
of the product in the ordinary MCG is torsion, but of infinite order in the
symplectic MCG.


  I propose a discrete model for the Gell-Mann matrices, which allows them to
participate in discrete symmetries of three generations of four types of
elementary fermions, in addition to their usual role in describing a continuous
group $SU(3)$ of colour symmetries. This model sheds new light on the
mathematical (rather than physical) necessity for `mixing' between the various
gauge groups $SU(3)$, $SU(2)$ and $U(1)$ of the Standard Model. In particular
it shows how the anti-Hermitian version of Pauli matrices can act non-trivially
on a unitary version of the Gell-Mann matrices, which leads to a non-trivial
mixing between the weak and strong nuclear forces.
  The unitary version of the Gell-Mann matrices can in turn act non-trivially
on a quaternionic version of Dirac matrices, which leads to a non-trivial
mixing between the strong force and the shape of spacetime defined by the Dirac
matrices. Hence this model implies a mixing between the electro-weak-strong
forces on the one hand and gravity, as described by General Relativity, on the
other. This mixing in turn implies the necessity for both general relativistic
corrections to the Standard Model of Particle Physics, and quantum corrections
to General Relativity. Contrary to general expectation, both types of
corrections seem to be large enough to be tested experimentally.


  We introduce probability-graphons which are probability kernels that
generalize graphons to the case of weighted graphs. Probability-graphons appear
as the limit objects to study sequences of large weighted graphs whose
distribution of subgraph sampling converge. The edge-weights are taken from a
general Polish space, which also covers the case of decorated graphs. Here,
graphs can be either directed or undirected. Starting from a distance $d_m$
inducing the weak topology on measures, we define a cut distance on
probability-graphons, making it a Polish space, and study the properties of
this cut distance. In particular, we exhibit a tightness criterion for
probability-graphons related to relative compactness in the cut distance. We
also prove that under some conditions on the distance $d_m$, which are
satisfied for some well-know distances like the Prohorov distance, and the
Fortet-Mourier and Kantorovitch-Rubinstein norms, the topology induced by the
cut distance on the spaceof probability-graphons is independent from the choice
of $d_m$. Eventually, we prove that this topology coincides with the topology
induced by the convergence in distribution of the sampled subgraphs.


  In this paper, we develop a computational approach for computing most likely
trajectories describing rare events that correspond to the emergence of
non-dominant genotypes. This work is based on the large deviations approach for
discrete Markov chains describing the genetic evolution of large bacterial
populations. We demonstrate that a gradient descent algorithm developed in this
paper results in the fast and accurate computation of most-likely trajectories
for a large number of bacterial genotypes. We supplement our analysis with
extensive numerical simulations demonstrating the computational advantage of
the designed gradient descent algorithm over other, more simplified,
approaches.


  Modern language models mostly take sub-words as input, a design that balances
the trade-off between vocabulary size, number of parameters, and performance.
However, sub-word tokenization still has disadvantages like not being robust to
noise and difficult to generalize to new languages. Also, the current trend of
scaling up models reveals that larger models require larger embeddings but that
makes parallelization hard. Previous work on image classification proves
splitting raw input into a sequence of chucks is a strong, model-agnostic
inductive bias. Based on this observation, we rethink the existing
character-aware method that takes character-level inputs but makes word-level
sequence modeling and prediction. We overhaul this method by introducing a
cross-attention network that builds word-level representation directly from
bytes, and a sub-word level prediction based on word-level hidden states to
avoid the time and space requirement of word-level prediction. With these two
improvements combined, we have a token free model with slim input embeddings
for downstream tasks. We name our method Byte2Word and perform evaluations on
language modeling and text classification. Experiments show that Byte2Word is
on par with the strong sub-word baseline BERT but only takes up 10\% of
embedding size. We further test our method on synthetic noise and cross-lingual
transfer and find it competitive to baseline methods on both settings.


  We propose a deep neural network framework for computing prices and deltas of
American options in high dimensions. The architecture of the framework is a
sequence of neural networks, where each network learns the difference of the
price functions between adjacent timesteps. We introduce the least squares
residual of the associated backward stochastic differential equation as the
loss function. Our proposed framework yields prices and deltas on the entire
spacetime, not only at a given point. The computational cost of the proposed
approach is quadratic in dimension, which addresses the curse of dimensionality
issue that state-of-the-art approaches suffer. Our numerical simulations
demonstrate these contributions, and show that the proposed neural network
framework outperforms state-of-the-art approaches in high dimensions.


  Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry
that are asymptotic to Minkowski light cones at infinity. We develop the
equations of these surfaces and examine their properties. In particular, we
show that they are free of caustics for all positive values of the Kerr radial
coordinate r. Useful applications include the propagation of high-frequency
waves, the definition of Kruskal-like coordinates for a spinning black hole and
the characteristic initial-value problem.


  We analyze transverse momentum ($Q_T$) resummation of a colorless final
state, e.g. Higgs production in gluon fusion or the production of a lepton pair
via the Drell-Yan mechanism, in the limit where the invariant mass of the final
state is much less then the center-of-mass energy, i.e. $Q^2\ll s$. We show how
the traditional resummation of logarithms of $Q_T/Q$ can be supplemented with
the resummation of the leading logarithmic contributions at small $x=Q^2/s$ and
we compute the necessary ingredients to perform such joint resummation.


  The objective of the present article is to construct the first examples of
(non-trivial) non-commutative projective Calabi-Yau schemes in the sense of
Artin and Zhang.


  The Sachdev-Ye-Kitaev (SYK) model can be used to describe black holes (BHs)
in two-dimensional nearly-anti-de-Sitter gravity. We show that when such BHs
are perturbed by a time-dependent negative-energy perturbation, their interior
can be partially revealed. In the SYK model, a partial measurement of the state
of the Majorana fermion pairs allows one to construct a matching time-dependent
negative-energy perturbation of the BH geometry that shifts the state of the BH
away from its equilibrium state. Kourkoulou and Maldacena showed that, if the
perturbation is strong enough, the interior can be fully exposed and the BH
disappears. Here, we show that when the perturbation is weaker than the
threshold for full exposure, it effectively moves the horizon of the BH
inwards, thus partially exposing the interior of the BH and leaving behind a
smaller BH. The exposure is in proportion to the number of measured Majorana
pairs and so also in proportion to the magnitude of the energy of the
perturbation. From the boundary, the partial measurement is perceived as a
burst of radiation whose strength and duration are proportional to the number
of measured Majorana pairs.


  Let $M^n$ be either a simply connected space form or a rank-one symmetric
space of noncompact type. We consider Weingarten hypersurfaces of
$M\times\mathbb R$, which are those whose principal curvatures $k_1,\dots ,k_n$
and angle function $\theta$ satisfy a relation $W(k_1,\dots,k_n,\theta^2)=0,$
being $W$ a differentiable function which is symmetric with respect to
$k_1,\dots, k_n.$ When $\partial W/\partial k_i>0$ on the positive cone of
$\mathbb R^n,$ a strictly convex Weingarten hypersurface determined by $W$ is
said to be elliptic. We show that, for a certain class of Weingarten functions
$W,$ there exist rotational strictly convex Weingarten hypersurfaces of
$M\times\mathbb R$ which are either topological spheres or entire graphs over
$M.$ We establish a Jellett-Liebmann-type theorem by showing that a compact,
connected and elliptic Weingarten hypersurface of either $\mathbb
S^n\times\mathbb R$ or $\mathbb H^n\times\mathbb R$ is a rotational embedded
sphere. Other uniqueness results for complete elliptic Weingarten hypersurfaces
of these ambient spaces are obtained. We also obtain existence results for
constant scalar curvature hypersurfaces of $\mathbb S^n\times\mathbb R$ and
$\mathbb H^n\times\mathbb R$ which are either rotational or invariant by
translations (parabolic or hyperbolic). We apply our methods to give new proofs
of the main results by Manfio and Tojeiro on the classification of constant
sectional curvature hypersurfaces of $\mathbb S^n\times\mathbb R$ and $\mathbb
H^n\times\mathbb R.$


  In this paper, we study the algorithmic complexity of the Mastermind game,
where results are single-color black pegs. This differs from the usual
dual-color version of the game, but better corresponds to applications in
genetics. We show that it is NP-complete to determine if a sequence of
single-color Mastermind results have a satisfying vector. We also show how to
devise efficient algorithms for discovering a hidden vector through
single-color queries. Indeed, our algorithm improves a previous method of
Chvatal by almost a factor of 2.


  The attribution method provides a direction for interpreting opaque neural
networks in a visual way by identifying and visualizing the input
regions/pixels that dominate the output of a network. Regarding the attribution
method for visually explaining video understanding networks, it is challenging
because of the unique spatiotemporal dependencies existing in video inputs and
the special 3D convolutional or recurrent structures of video understanding
networks. However, most existing attribution methods focus on explaining
networks taking a single image as input and a few works specifically devised
for video attribution come short of dealing with diversified structures of
video understanding networks. In this paper, we investigate a generic
perturbation-based attribution method that is compatible with diversified video
understanding networks. Besides, we propose a novel regularization term to
enhance the method by constraining the smoothness of its attribution results in
both spatial and temporal dimensions. In order to assess the effectiveness of
different video attribution methods without relying on manual judgement, we
introduce reliable objective metrics which are checked by a newly proposed
reliability measurement. We verified the effectiveness of our method by both
subjective and objective evaluation and comparison with multiple significant
attribution methods.


  Under limited available resources, strategies for mitigating the propagation
of an epidemic such as random testing and contact tracing become inefficient.
Here, we propose to accurately allocate the resources by computing over time an
individual risk of infection based on the partial observation of the epidemic
spreading on a contact network; this risk is defined as the probability of
getting infected from any possible transmission chain up to length two,
originating from recently detected individuals. To evaluate the performance of
our method and the effects of some key parameters, we perform comparative
simulated experiments using data generated by an agent-based model.


  In this paper, we propose a relay selection amplify-and-forward (RS-AF)
protocol in general bi-directional relay networks with two sources and $N$
relays. In the proposed scheme, the two sources first transmit to all the
relays simultaneously, and then a single relay with a minimum sum symbol error
rate (SER) will be selected to broadcast the received signals back to both
sources. To facilitate the selection process, we propose a simple sub-optimal
Min-Max criterion for relay selection, where a single relay which minimizes the
maximum SER of two source nodes will be selected. Simulation results show that
the proposed Min-Max selection has almost the same performance as the optimal
selection with lower complexity. We also present a simple asymptotic SER
expression and make comparison with the conventional all-participate
amplify-and-forward (AP-AF) relaying scheme. The analytical results are
verified through simulations. To improve the system performance, optimum power
allocation (OPA) between the sources and the relay is determined based on the
asymptotic SER. Simulation results indicate that the proposed RS-AF scheme with
OPA yields considerable performance improvement over an equal power allocation
(EPA) scheme, specially with large number of relay nodes.


  Counter-rotating vortices in miscible two-component Bose-Einstein
condensates, in which superflows counter-rotate between the two components
around the overlapped vortex cores, are studied theoretically in a
pancake-shaped potential. In a linear stability analysis with the Bogoliubov-de
Gennes model, we show that counter-rotating vortices are dynamically unstable
against splitting into multiple vortices. The instability shows characteristic
behaviors as a result of countersuperflow instability, which causes relaxation
of relative flows between the two components in binary condensates. The
characteristic behaviors are completely different from those of multiquantum
vortices in single-component Bose-Einstein condensates; the number of vortices
generated by the instability can become larger than the initial winding number
of the counter-rotating vortex. We also investigate the nonlinear dynamics of
the instability by numerically solving the Gross-Pitaevskii equations. The
nonlinear dynamics drastically changes when the winding number of
counter-rotating vortices becomes larger, which lead to nucleation of vortex
pairs outside of the vortex core. The instability eventually develops into
turbulence after the relaxation of the relative rotation between the two
components.


  We study the equivalence/duality between various non-commutative gauge models
at the classical and quantum level. The duality is realised by a linear
Seiberg-Witten-like map. The infinitesimal form of this map is analysed in more
details.


  Recommendation algorithms are known to suffer from popularity bias; a few
popular items are recommended frequently while the majority of other items are
ignored. These recommendations are then consumed by the users, their reaction
will be logged and added to the system: what is generally known as a feedback
loop. In this paper, we propose a method for simulating the users interaction
with the recommenders in an offline setting and study the impact of feedback
loop on the popularity bias amplification of several recommendation algorithms.
We then show how this bias amplification leads to several other problems such
as declining the aggregate diversity, shifting the representation of users'
taste over time and also homogenization of the users experience. In particular,
we show that the impact of feedback loop is generally stronger for the users
who belong to the minority group.


  Here we demonstrate nanometer thick iron garnet films suitable for the
magneto-optical applica-tions. Bismuth-substituted iron garnet films of
compositions Bi{_1}Y{_2}Fe{_5}O{_{12}} and Bi{_1}Tm{_2}Fe{_5}O{_{12}} deposited
on gadolinium gallium garnet substrate are fabricated and characterized. Their
thicknesses range from 2 to 10 nm, which corresponds to just a few crystal
lattice constants. Faraday rotation of the nanofilms reaches 29.7 deg/{\mu}m at
420 nm which is comparable and even a bit better than single crystal micrometer
thick films of similar composition. The film surface morphology by atomic force
microscopy gives root mean square (RMS) roughness of the nanofilms as small as
0.13 nm that is also similar to the RMS of single crystal micrometer thick
films. The Bi{_1}Tm{_2}Fe{_5}O{_{12}} films demonstrate effective uniaxial
anisotropy. These all make the fabricated nanofilms very promising for their
po-tential applications in magneto-optical devices and quantum technologies.


  We introduce a stochastic spin-wave theory tailored to describe quantum
trajectories in continuously monitored long-range interacting spin systems. Our
method, based on the bosonization of spin-wave excitations on top of a strong
collective polarization, enables the efficient simulation of large-scale
interacting spins, offering insights into nonlinear features of the dynamics
such as entanglement and trajectory correlations. We showcase the versatility
of our framework by exploring an entanglement phase transition in a monitored
spin system with power-law interactions and dwelling on how our method
mitigates the experimental challenges of post-selection in detecting monitored
quantum phases.


  The TRAPPIST-1 system is the first transiting planet system found orbiting an
ultra-cool dwarf star. At least seven planets similar to Earth in radius and in
mass were previously found to transit this host star. Subsequently, TRAPPIST-1
was observed as part of the K2 mission and, with these new data, we report the
measurement of an 18.77 d orbital period for the outermost planet, TRAPPIST-1h,
which was unconstrained until now. This value matches our theoretical
expectations based on Laplace relations and places TRAPPIST-1h as the seventh
member of a complex chain, with three-body resonances linking every member. We
find that TRAPPIST-1h has a radius of 0.727 Earth radii and an equilibrium
temperature of 173 K. We have also measured the rotational period of the star
at 3.3 d and detected a number of flares consistent with a low-activity,
middle-aged, late M dwarf.


  We briefly discuss the status of the NNLL QCD calculations in the inclusive
rare B decay $B \to X_s \ell^+ \ell^-$. Two important ingredients, the two-loop
matrix elements of the four quark operator ${\cal O}_2$ and the bremsstrahlung
contributions, were quite recently finalised. The new contributions
significantly improve the sensitivity of the inclusive decay $B \to X_s l^+
l^-$ decay in testing extensions of the standard model in the sector of flavour
dynamics; for instance the two-loop calculation cuts the low- scale uncertainty
in half and the bremsstrahlung calculation leads to a 10% shift of the position
of the zero of the forward- backward asymmetry.


  To each of the symmetry groups of the Platonic solids we adjoin a carefully
designed involution yielding topological generators of PU(2) which have optimal
covering properties as well as efficient navigation. These are a consequence of
optimal strong approximation for integral quadratic forms associated with
certain special quaternion algebras and their arithmetic groups. The generators
give super efficient 1-qubit quantum gates and are natural building blocks for
the design of universal quantum gates.


  We address the problem of model-free distributed stabilization of
heterogeneous multi-agent systems using reinforcement learning (RL). Two
algorithms are developed. The first algorithm solves a centralized linear
quadratic regulator (LQR) problem without knowing any initial stabilizing gain
in advance. The second algorithm builds upon the results of the first
algorithm, and extends it to distributed stabilization of multi-agent systems
with predefined interaction graphs. Rigorous proofs are provided to show that
the proposed algorithms achieve guaranteed convergence if specific conditions
hold. A simulation example is presented to demonstrate the theoretical results.


  This paper has been withdrawn by the author due to the presented idea is
wrong.


  A disturbance decoupling problem for a $n$-link chain pendulum on a cart is
considered. A model of the cart developed in a coordinate-free framework and
the linearized equations of this system are considered from [1]. It is shown
that it is possible to design a suitable state feedback such that the angular
position or velocity of the $n^{th}$-link can always be decoupled from the
disturbance coming at the cart.


  In this paper, we propose an enhanced Huffman coded orthogonal
frequency-division multiplexing with index modulation (EHC-OFDM-IM) scheme. The
proposed scheme is capable of utilizing all legitimate subcarrier activation
patterns (SAPs) and adapting the bijective mapping relation between SAPs and
leaves on a given Huffman tree according to channel state information (CSI). As
a result, a dynamic codebook update mechanism is obtained, which can provide
more reliable transmissions. We take the average block error rate (BLER) as the
performance evaluation metric and approximate it in closed form when the
transmit power allocated to each subcarrier is independent of channel states.
Also, we propose two CSI-based power allocation schemes with different
requirements for computational complexity to further improve the error
performance. Subsequently, we carry out numerical simulations to corroborate
the error performance analysis and the proposed dynamic power allocation
schemes. By studying the numerical results, we find that the depth of the
Huffman tree has a significant impact on the error performance when the
SAP-to-leaf mapping relation is optimized based on CSI. Meanwhile, through
numerical results, we also discuss the trade-off between error performance and
data transmission rate and investigate the impacts of imperfect CSI on the
error performance of EHC-OFDM-IM.


  Space-time (ST) wave packets are pulsed optical beams endowed with precise
spatio-temporal structure by virtue of which they exhibit unique and useful
characteristics, such as propagation invariance and tunable group velocity. We
study in detail here, and in two accompanying papers, the refraction of ST wave
packets at planar interfaces between non-dispersive, homogeneous, isotropic
dielectrics. We formulate a law of refraction that determines the change in the
ST wave-packet group velocity across such an interface as a consequence of a
newly identified optical refractive invariant that we call 'the spectral
curvature'. Because the spectral curvature vanishes in conventional optical
fields where the spatial and temporal degrees of freedom are separable, these
phenomena have not been observed to date. We derive the laws of refraction for
baseband, X-wave, and sideband ST wave packets that reveal fascinating
refractive phenomena, especially for the former class of wave packets. We
predict theoretically, and confirm experimentally in the accompanying papers,
refractive phenomena such as group-velocity invariance (ST wave packets whose
group velocity does not change across the interface), anomalous refraction
(group-velocity increase in higher-index media), group-velocity inversion
(change in the sign of the group velocity upon refraction but not its
magnitude), and the dependence of the group velocity of the refracted ST wave
packet on the angle of incidence.


  Anomalous inter-layer atomic transport of deposited impurity atoms on Al(111)
has been found by constant temperature molecular dynamics simulations. The
low-energy deposition of Pt on Al(111) leads to oscillatory adsorbate-substrate
interaction and to a low-temperature ballistic injection of the deposited
particles to below the topmost layer. The ultrafast injection of a Pt atom
coincides with the ejection of a substrate atom to the surface (ballistic
replacement or exchange mechanism). This is in agreement with the experimental
findings in which thin film rich in Al has been found on the surface after
deposition of few MLs of Pt. We attribute the anomalous inter-layer transport
to the size-mismatched impurity/host interaction and we point out the role of
atomic size mismatch in biasing towards intermixing. The deposition induced
low-temperature disordering of surface Al atoms with few transient Al adatoms
has also been observed. The ultrafast injection of the impurity particles to
the substrate is assisted by the transient out-of-plane and lateral circulating
motion of few surface atoms arranged nearly in a hexagonal symmetry. The atomic
injection of Pt can be regarded as a superexchange process driven by the
transient and collective motion of few surface atoms. A chaotic surface state
assisted mechanism could also be a possible explanation of the unexpected
phenomenon.


  The existence of a natural and projectively equivariant quantization in the
sense of Lecomte [20] was proved recently by M. Bordemann [4], using the
framework of Thomas-Whitehead connections. We give a new proof of existence
using the notion of Cartan projective connections and we obtain an explicit
formula in terms of these connections. Our method yields the existence of a
projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant
quantization exists in the flat situation in the sense of [18], thus solving
one of the problems left open by M. Bordemann.


  We use the continuation and bifurcation package pde2path to numerically
analyze infinite time horizon optimal control problems for parabolic systems of
PDEs. The basic idea is a two step approach to the canonical systems, derived
from Pontryagin's maximum principle. First we find branches of steady or
time-periodic states of the canonical systems, i.e., canonical steady states
(CSS) respectively canonical periodic states (CPS), and then use these results
to compute time-dependent canonical paths connecting to a CSS or a CPS with the
so called saddle point property. This is a (high dimensional) boundary value
problem in time, which we solve by a continuation algorithm in the initial
states. We first explain the algorithms and then the implementation via some
example problems and associated pde2path demo directories. The first two
examples deal with the optimal management of a distributed shallow lake, and of
a vegetation system, both with (spatially, and temporally) distributed
controls. These examples show interesting bifurcations of so called patterned
CSS, including patterned optimal steady states. As a third example we discuss
optimal boundary control of a fishing problem with boundary catch. For the case
of CPS-targets we first focus on an ODE toy model to explain and validate the
method, and then discuss an optimal pollution mitigation PDE model.


  We present the discovery of two extended $\sim$0.12 mag dimming events of the
weak-lined T-Tauri star V1334. The start of the first event was missed but came
to an end in late 2003, and the second began in February 2009, and continues as
of November 2016. Since the egress of the current event has not yet been
observed, it suggests a period of $>$13 years if this event is periodic.
Spectroscopic observations suggest the presence of a small inner disk, although
the spectral energy distribution shows no infrared excess. We explore the
possibility that the dimming events are caused by an orbiting body (e.g. a disk
warp or dust trap), enhanced disk winds, hydrodynamical fluctuations of the
inner disk, or a significant increase in the magnetic field flux at the surface
of the star. We also find a $\sim$0.32 day periodic photometric signal that
persists throughout the 2009 dimming which appears to not be due to ellipsoidal
variations from a close stellar companion. High precision photometric
observations of V1334 Tau during K2 campaign 13, combined with simultaneous
photometric and spectroscopic observations from the ground, will provide
crucial information about the photometric variability and its origin.


  (abridged) MR2251-178 was the first quasar initially discovered in X-rays,
and the first one found to host a warm absorber. The quasar turned out to be an
outstanding object in many respects. It has a high ratio of X-ray/optical
luminosity, is surrounded by the largest quasar emission-line nebula known, and
is located in the outskirts of a cluster of galaxies. Here, we present results
from an analysis of the X-ray spectral, temporal, and spatial properties of
this source and its environment based on deep ROSAT observations.
  Remarkably, we do not detect any excess X-ray cold absorption expected to
originate from the giant gas nebula surrounding MR2251-178. This excludes the
presence of a huge HI envelope around the quasar. The X-ray spectrum of
MR2251-178 is best fit by a warm-absorbed powerlaw with an ionization parameter
log U = 0.5 and a column density log N_w = 22.6 which, however, cannot be the
same material as the giant optical emission line nebula. The mean (0.1--2.4)keV
X-ray luminosity amounts to 10^{45} erg/s.
  A spatial analysis shows that the bulk of the X-ray emission from the quasar
is consistent with a point source, as expected in view of the powerlaw-shaped
X-ray spectrum and the rapid X-ray variability we detect. In addition, extended
emission appears at weak emission levels, including a bridge between the quasar
and the cD galaxy of the cluster.
  The X-ray emission from the intra-cluster medium is weak or absent. None of
the other member galaxies of the cluster to which MR 2251-178 belongs, are
detected in X-rays. However, east of the quasar there is a significant excess
of X-ray sources, several of them without optical counterparts on the UK
Schmidt plates.


  A survey of red giants in the globular cluster M3 with the Hydra multi-object
spectrograph on the WIYN 3.5-m telescope indicated a prominent Li I 6707 $\AA$
feature in the red giant vZ 1050. Follow-up spectroscopy with the ARC 3.5-m
telescope confirmed this observation and yielded a derived abundance of
A(Li)$_{NLTE}$ = 1.6 $\pm$ 0.05. In addition, the high oxygen and low sodium
abundances measured from the same spectrum suggest that vZ 1050 is a first
generation cluster star. The location vZ 1050 above the horizontal branch and
blueward of the red giant branch in the cluster's color-magnitude diagram
places vZ 1050 on M3's asymptotic giant branch. The likely source for the
enhanced lithium abundance is the Cameron-Fowler mechanism operating in vZ 1050
itself.


  The single nucleotide polymorphism (SNP) is the most widely studied type of
genetic variation. A haplotype is defined as the sequence of alleles at SNP
sites on each haploid chromosome. Haplotype information is essential in
unravelling the genome-phenotype association. Haplotype assembly is a
well-known approach for reconstructing haplotypes, exploiting reads generated
by DNA sequencing devices. The Minimum Error Correction (MEC) metric is often
used for reconstruction of haplotypes from reads. However, problems with the
MEC metric have been reported. Here, we investigate the MEC approach to
demonstrate that it may result in incorrectly reconstructed haplotypes for
devices that produce error-prone long reads. Specifically, we evaluate this
approach for devices developed by Illumina, Pacific BioSciences and Oxford
Nanopore Technologies. We show that imprecise haplotypes may be reconstructed
with a lower MEC than that of the exact haplotype. The performance of MEC is
explored for different coverage levels and error rates of data. Our simulation
results reveal that in order to avoid incorrect MEC-based haplotypes, a
coverage of 25 is needed for reads generated by Pacific BioSciences RS systems.


  Random walks and polygons are used to model polymers. In this paper we
consider the extension of writhe, self-linking number and linking number to
open chains. We then study the average writhe, self-linking and linking number
of random walks and polygons over the space of configurations as a function of
their length. We show that the mean squared linking number, the mean squared
writhe and the mean squared self-linking number of oriented uniform random
walks or polygons of length $n$, in a convex confined space, are of the form
$O(n^2)$. Moreover, for a fixed simple closed curve in a convex confined space,
we prove that the mean absolute value of the linking number between this curve
and a uniform random walk or polygon of $n$ edges is of the form $O(\sqrt{n})$.
Our numerical studies confirm those results. They also indicate that the mean
absolute linking number between any two oriented uniform random walks or
polygons, of $n$ edges each, is of the form O(n). Equilateral random walks and
polygons are used to model polymers in $\theta$-conditions. We use numerical
simulations to investigate how the self-linking and linking number of
equilateral random walks scale with their length.


  We consider the problem of private information retrieval (PIR) where a single
user with private side information aims to retrieve multiple files from a
library stored (uncoded) at a number of servers. We assume the side information
at the user includes a subset of files stored privately (i.e., the server does
not know the indices of these files). In addition, we require that the identity
of the requests and side information at the user are not revealed to any of the
servers. The problem involves finding the minimum load to be transmitted from
the servers to the user such that the requested files can be decoded with the
help of received and side information. By providing matching lower and upper
bounds, for certain regimes, we characterize the minimum load imposed to all
the servers (i.e., the capacity of this PIR problem). Our result shows that the
capacity is the same as the capacity of a multi-message PIR problem without
private side information, but with a library of reduced size. The effective
size of the library is equal to the original library size minus the size of
side information.


  Researchers and practitioners have recently reframed powerful Large Language
Models (LLMs) as agents, enabling them to automate complex tasks largely via
the use of specialized functions. To facilitate the development of LLM agents,
we present a novel paradigm of training LLM agents without modifying the LLM
weights, which is particularly useful when the LLMs are difficult or
inaccessible for modifications. Inspired by how humans continuously forge tools
to adapt to real-world tasks, rather than change our biological structure to
fit a static set of tools, we propose to progressively forge agent's functions
to better solve the downstream tasks instead of modifying the LLM weights. By
treating the functions as learnable `agent parameters' and leveraging the
fundamental idea of model training in artificial intelligence, we develop
AgentOptimizer that employs the LLM to update agents' functions and devise an
agent training algorithm with two strategies, roll-back, and early-stop, to
streamline the training process. With extensive experiments, we showcase that
the agent training paradigm could significantly improve the performance of
representative LLM agents in various downstream tasks. We also study the
behavior of the agent training regarding aspects like the learning curve and
domain transferability.


  Two-color finite density QCD is free from the sign problem, and it is thus
regarded as a good model to check the validity of the analytic continuation
method. We study the method in terms of the corresponding chiral random matrix
model. It is found that at temperatures slightly higher than the pseudo
critical temperature, the ratio type of extrapolated function works well in
accordance with the results of the Monte Carlo simulations.


  We investigate the dynamics of DNA translocation through a nanopore driven by
an external force using Langevin dynamics simulations in two dimensions (2D) to
study how the translocation dynamics depend on the details of the DNA
sequences. We consider a coarse-grained model of DNA built from two bases $A$
and $C$, having different base-pore interactions, {\textit e.g.}, a strong
(weak) attractive force between the pore and the base $A$ ($C$) inside the
pore. From a series of studies on hetero-DNAs with repeat units $A_mC_n$, we
find that the translocation time decreases exponentially as a function of the
volume fraction $f_C$ of the base $C$. %($\epsilon_{pC} < \epsilon_{pA}$). For
longer $A$ sequences with $f_C \le 0.5$, the translocation time strongly
depends on the orientation of DNA, namely which base enters the pore first. Our
studies clearly demonstrate that for a DNA of certain length $N$ with repeat
units $A_mC_n$, the pattern exhibited by the waiting times of the individual
bases and their periodicity can unambiguously determine the values of $m$, $n$
and $N$ respectively. Therefore, a prospective experimental realization of this
phenomenon may lead to fast and efficient sequence detection technic.


  We demonstrate the feasibility of a nonperturbative analysis of quantum field
theory in the worldline formalism with the help of an efficient numerical
algorithm. In particular, we compute the effective action for a
super-renormalizable field theory with cubic scalar interaction in four
dimensions in quenched approximation (small-$N_f$ expansion) to all orders in
the coupling. We observe that nonperturbative effects exert a strong influence
on the infrared behavior, rendering the massless limit well defined in contrast
to the perturbative expectation. Our numerical method is based on a direct use
of probability distributions for worldline ensembles, preserves all Euclidean
spacetime symmetries, and thus represents a new nonperturbative tool for an
investigation of continuum quantum field theory.


  Visual place recognition is a challenging task in the field of computer
vision, and autonomous robotics and vehicles, which aims to identify a location
or a place from visual inputs. Contemporary methods in visual place recognition
employ convolutional neural networks and utilize every region within the image
for the place recognition task. However, the presence of dynamic and
distracting elements in the image may impact the effectiveness of the place
recognition process. Therefore, it is meaningful to focus on task-relevant
regions of the image for improved recognition. In this paper, we present
PlaceFormer, a novel transformer-based approach for visual place recognition.
PlaceFormer employs patch tokens from the transformer to create global image
descriptors, which are then used for image retrieval. To re-rank the retrieved
images, PlaceFormer merges the patch tokens from the transformer to form
multi-scale patches. Utilizing the transformer's self-attention mechanism, it
selects patches that correspond to task-relevant areas in an image. These
selected patches undergo geometric verification, generating similarity scores
across different patch sizes. Subsequently, spatial scores from each patch size
are fused to produce a final similarity score. This score is then used to
re-rank the images initially retrieved using global image descriptors.
Extensive experiments on benchmark datasets demonstrate that PlaceFormer
outperforms several state-of-the-art methods in terms of accuracy and
computational efficiency, requiring less time and memory.


  Improved knowledge of diffuse Galactic emission is important to maximize the
scientific return from scheduled CMB anisotropy missions. Cross-correlation of
microwave maps with maps of the far-IR dust continuum show a ubiquitous
microwave emission component whose spatial distribution is traced by far-IR
dust emission. The spectral index of this emission, beta_{radio} = -2.2 (+0.5
-0.7) is suggestive of free-free emission but does not preclude other
candidates. Comparison of H-alpha and microwave results show that both data
sets have positive correlations with the far-IR dust emission. Microwave data,
however, are consistently brighter than can be explained solely from free-free
emission traced by H-alpha. This ``anomalous'' microwave emission can be
explained as electric dipole radiation from small spinning dust grains. The
anomalous component at 53 GHz is 2.5 times as bright as the free-free emission
traced by H-alpha, providing an approximate normalization for models with
significant spinning dust emission.


  It is a classical fact that for any $\varepsilon > 0$, a random permutation
of length $n = (1 + \varepsilon) k^2 / 4$ typically contains a monotone
subsequence of length $k$. As a far-reaching generalization, Alon conjectured
that a random permutation of this same length $n$ is typically $k$-universal,
meaning that it simultaneously contains every pattern of length $k$. He also
made the simple observation that for $n = O(k^2 \log k)$, a random length-$n$
permutation is typically $k$-universal. We make the first significant progress
towards Alon's conjecture by showing that $n = 2000 k^2 \log \log k$ suffices.


  In this paper, we consider the non-singular extension problem of
circle-valued Morse functions on closed orientable surfaces. The problem is
when can a submersion from a collaring of a closed orientable surface to a
circle, which is a circle-valued Morse function on the boundary, be extended to
a submersion from a 3-dimensional manifold to a circle. We provide necessary
and sufficient conditions for the existence of a non-singular extension of a
circle-valued Morse function as the main theorem. After that, we consider a
special case that the surface is a torus as one application of the theorem.


  We investigate the robustness of the many-body localized (MBL) phase to the
quantum-avalanche instability by studying the dynamics of a localized spin
chain coupled to a $T=\infty$ thermal bath through its leftmost site. By
analyzing local magnetizations, we estimate the size of the thermalized sector
of the chain and find that it increases logarithmically slowly in time. This
logarithmically slow propagation of the thermalization front allows us to lower
bound the slowest thermalization time, and find a broad parameter range where
it scales fast enough with the system size that MBL is robust against
thermalization induced by avalanches. The further finding that the imbalance --
a global quantity measuring localization -- thermalizes over a time scale
exponential both in disorder strength and system size is in agreement with
these results.


  We develop an efficient algorithm for a spatially inhomogeneous matrix-valued
quantum Boltzmann equation derived from the Hubbard model. The distribution
functions are $2 \times 2$ matrix-valued to accommodate the spin degree of
freedom, and the scalar quantum Boltzmann equation is recovered as special case
when all matrices are proportional to the identity. We use Fourier
discretization and fast Fourier transform to efficiently evaluate the collision
kernel with spectral accuracy, and numerically investigate periodic, Dirichlet
and Maxwell boundary conditions. Model simulations quantify the convergence to
local and global thermal equilibrium.


  We present SherLIiC, a testbed for lexical inference in context (LIiC),
consisting of 3985 manually annotated inference rule candidates (InfCands),
accompanied by (i) ~960k unlabeled InfCands, and (ii) ~190k typed textual
relations between Freebase entities extracted from the large entity-linked
corpus ClueWeb09. Each InfCand consists of one of these relations, expressed as
a lemmatized dependency path, and two argument placeholders, each linked to one
or more Freebase types. Due to our candidate selection process based on strong
distributional evidence, SherLIiC is much harder than existing testbeds because
distributional evidence is of little utility in the classification of InfCands.
We also show that, due to its construction, many of SherLIiC's correct InfCands
are novel and missing from existing rule bases. We evaluate a number of strong
baselines on SherLIiC, ranging from semantic vector space models to state of
the art neural models of natural language inference (NLI). We show that
SherLIiC poses a tough challenge to existing NLI systems.


  We study an electron that interacts with phonons or other linear or nonlinear
excitations as it resonantly tunnels. The method we use is based on mapping a
many-body problem in a large variational space exactly onto a one-body problem.
The method is conceptually simpler than previous Green's function approaches,
and allows the essentially exact numerical solution of much more general
problems. We solve tunneling problems with transverse channels, multiple sites
coupled to phonons, and multiple phonon degrees of freedom and excitations.


  A method to find relations between the operators in the mesonic Lagrangian of
Chiral Perturbation Theory at order p^6 is presented. The procedure can be used
to establish if the basis of operators in the Lagrangian is minimal. As an
example, we apply the method to the two-flavour case in the absence of scalar
and pseudo-scalar sources (s=p=0), and conclude that the minimal Lagrangian
contains 27 independent operators.


  Two different methods are used to study the existence and stability of the
(1+1)-dimensional $\Phi^4$ oscillon. The variational technique approximates it
by a periodic function with a set of adiabatically changing parameters. An
alternative approach treats oscillons as standing waves in a finite-size box;
these are sought as solutions of a boundary-value problem on a two-dimensional
domain. The numerical analysis reveals that the standing wave's
energy-frequency diagram is fragmented into disjoint segments with
$\omega_{n-1} < \omega < \omega_{n-2}$, where $\omega_n=\frac{2}{n+1}$. In the
interval $(\omega_{n-1}, \omega_{n-2})$, the structure's small-amplitude wings
are formed by the $n$-th harmonic radiation ($n=2,3, ...$). All standing waves
are practically stable: perturbations may result in the deformation of the
wave's radiation wings but do not affect its core. The variational
approximation involving the first, zeroth and second harmonic components
provides an accurate description of the oscillon with the frequency in
$(\omega_1, \omega_0)$, but breaks down as $\omega$ falls out of that interval.


  The main aim of this study is to report basic knowledge on how a protein
corona (PC) could affect or modify the way in which multifunctionalized
nanoparticles interact with cells. With this purpose, we have firstly optimized
the development of a target-specific nanocarrier by coupling a specific
fluorescent antibody on the surface of functionalized lipid liquid nanocapsules
(LLNCs). Thus, an anti-HER2-FITC antibody ({\alpha}HER2) has been used, HER2
being a surface receptor that is overexpressed in several tumor cells.
Subsequently, the in vitro formation of a PC has been developed using fetal
bovine serum supplemented with human fibrinogen. Dynamic Light Scattering
(DLS), Nanoparticle Tracking Analysis (NTA), Laser Doppler Electrophoresis
(LDE), and Gel Chromatography techniques have been used to assure a complete
physico-chemical characterization of the nano-complexes with
(LLNCs-{\alpha}HER2-PC) and without (LLNCs-{\alpha}HER2) the surrounding PC. In
addition, cellular assays were performed to study the cellular uptake and the
specific cellular-nanocarrier interactions using the SKBR3 (high expression of
HER2) breast cancer cell line and human dermal fibroblasts (HDFa) (healthy cell
line without expression of HER2 receptors as control), showing that the SKBR3
cell line had a higher transport rate (50-fold) than HDFa at 60 min with
LLNCs-{\alpha}HER2. Moreover, the SKBR3 cell line incubated with
LLNCs-{\alpha}HER2-PC suffered a significant reduction (40%) in the uptake.
These results suggest that the formation of a PC onto LLNCs does not prevent
specific cell targeting, although it does have an important influence on cell
uptake.


  This paper is a first step in the study of the recurrence behavior in random
dynamical systems and randomly perturbed dynamical systems. In particular we
define a concept of quenched and annealed return times for systems generated by
the composition of random maps. We moreover prove that for super-polynomially
mixing systems, the random recurrence rate is equal to the local dimension of
the stationary measure.


  We investigate the impact of photochemistry and X-ray ionization on the
molecular composition of, and ionization fraction in, a protoplanetary disk
surrounding a typical T Tauri star. We use a sophisticated physical model,
which includes a robust treatment of the radiative transfer of UV and X-ray
radiation, and calculate the time-dependent chemical structure using a
comprehensive chemical network. In previous work, we approximated the
photochemistry and X-ray ionization, here, we recalculate the photoreaction
rates using the explicit UV wavelength spectrum and wavelength-dependent
reaction cross sections. We recalculate the X-ray ionization rate using our
explicit elemental composition and X-ray energy spectrum. We find
photochemistry has a larger influence on the molecular composition than X-ray
ionization. Observable molecules sensitive to the photorates include OH, HCO+,
N2H+, H2O, CO2 and CH3OH. The only molecule significantly affected by the X-ray
ionization is N2H+ indicating it is safe to adopt existing approximations of
the X-ray ionization rate in typical T Tauri star-disk systems. The
recalculation of the photorates increases the abundances of neutral molecules
in the outer disk, highlighting the importance of taking into account the shape
of the UV spectrum in protoplanetary disks. A recalculation of the
photoreaction rates also affects the gas-phase chemistry due to the adjustment
of the H/H2 and C+/C ratios. The disk ionization fraction is not significantly
affected by the methods adopted to calculate the photochemistry and X-ray
ionization. We determine there is a probable 'dead zone' where accretion is
suppressed, present in a layer, Z/R <~ 0.1 - 0.2, in the disk midplane, within
R \approx 200 AU.


  The increasing importance of well-controlled ordered nanostructures on
surfaces represents a challenge for existing metrology techniques. To develop
such nanostructures and monitor complex processing constraints fabrication,
both a dimensional reconstruction of nanostructures and a characterization
(ideally a quantitative characterization) of their composition is required. In
this work, we present a soft X-ray fluorescence-based methodology that allows
both of these requirements to be addressed at the same time. By applying the
grazing-incidence X-ray fluorescence technique and thus utilizing the X-ray
standing wave field effect, nanostructures can be investigated with a high
sensitivity with respect to their dimensional and compositional
characteristics. By varying the incident angles of the exciting radiation,
element-sensitive fluorescence radiation is emitted from different regions
inside the nanoobjects. By applying an adequate modeling scheme, these datasets
can be used to determine the nanostructure characteristics. We demonstrate
these capabilities by performing an element-sensitive reconstruction of a
lamellar grating made of Si$_3$N$_4$, where GIXRF data for the O-K$\alpha$ and
N-K$\alpha$ fluorescence emission allows a thin oxide layer to be reconstructed
on the surface of the grating structure. In addition, we employ the technique
also to three dimensional nanostructures and derive both dimensional and
compositional parameters in a quantitative manner.


  Fingering instabilities akin to the Rayleigh-Taylor (RT) instability in
fluids have been observed in a binary granular system consisting of dense and
small particles layered on top of lighter and larger particles, when the system
is subjected to vertical vibration and fluidizing gas flow. Using observations
from experiments and numerical modelling we explore whether the theory
developed to describe the Rayleigh-Taylor (RT) instability in fluids is also
applicable to binary granular systems. Our results confirm the applicability of
the classic RT instability theory for binary granular systems demonstrating
that several key features are observed in both types of systems, viz: (i) The
characteristic wavenumber of the instability is constant with time, (ii) the
amplitude of the characteristic wavenumber initially grows exponentially and
(iii) the dispersion relation between the wavenumbers k of the interface
instability and the growth rates n(k) of their amplitudes holds in both
fluid-fluid and binary granular systems. Our results also demonstrate that
inter-particle friction is essential for the RT instability to occur in
granular media. For zero particle friction the interface instability bears a
greater resembles to the Richtmyer-Meshkov instability. We further define a
yield criterion Y for the interface by treating the granular medium as a
viscoplastic material; only for Y > 15 fingering occurs. Interestingly,
previous work has shown that instabilities in the Earth's lower mantle, another
viscoplastic material, also occur for similar values of Y.


  EROS (Exp\'erience de Recherche d'Objets Sombres) has been monitoring the
luminosity of 4 million stars in the Large Magellanic Cloud in order to search
for gravitational microlensing by unseen objects in the galactic halo. We
present here the results from 3 years of EROS Schmidt plates data. Two stars
exhibit light curves that are consistent with a sizeable microlensing effect.
CCD data obtained later on revealed that one of these stars is an eclipsing
binary system. Combining Schmidt plates data and the published results from our
16 CCD camera, we set upper limits on the number of unseen objects in the halo
in the mass range $[10^{-7},1]\Msol$. (Submitted for publication in Astronomy
and Astrophysics)


  The recent observation of a transmitted Thz pulse oscillating at three times
the frequency of the incident light paves the way to a new protocol to access
resonant excitations in a superconductor. Here we show that this non-linear
optical process is dominated by light-induced excitation of Cooper pairs, in
analogy with a standard Raman experiment. The collective amplitude (Higgs)
fluctuations of the superconducting order parameter give in general a smaller
contribution, unless one designs the experiment by combining properly the light
polarization with the lattice symmetry.


  Energy-function-based safety certificates can provide provable safety
guarantees for the safe control tasks of complex robotic systems. However, all
recent studies about learning-based energy function synthesis only consider the
feasibility, which might cause over-conservativeness and result in less
efficient controllers. In this work, we proposed the magnitude regularization
technique to improve the efficiency of safe controllers by reducing the
conservativeness inside the energy function while keeping the promising
provable safety guarantees. Specifically, we quantify the conservativeness by
the magnitude of the energy function, and we reduce the conservativeness by
adding a magnitude regularization term to the synthesis loss. We propose the
SafeMR algorithm that uses reinforcement learning (RL) for the synthesis to
unify the learning processes of safe controllers and energy functions.
Experimental results show that the proposed method does reduce the
conservativeness of the energy functions and outperforms the baselines in terms
of the controller efficiency while guaranteeing safety.


  We study the impact of dimension-six operators of the standard model
effective field theory relevant for vector-boson fusion and associated Higgs
boson production at the LHC. We present predictions at the next-to-leading
order accuracy in QCD that include matching to parton showers and that rely on
fully automated simulations. We show the importance of the subsequent reduction
of the theoretical uncertainties in improving the possible discrimination
between effective field theory and standard model results, and we demonstrate
that the range of the Wilson coefficient values allowed by a global fit to LEP
and LHC Run~I data can be further constrained by LHC Run~II future results.


  There has been an explosion of multimodal content generated on social media
networks in the last few years, which has necessitated a deeper understanding
of social media content and user behavior. We present a novel
content-independent content-user-reaction model for social multimedia content
analysis. Compared to prior works that generally tackle semantic content
understanding and user behavior modeling in isolation, we propose a generalized
solution to these problems within a unified framework. We embed users, images
and text drawn from open social media in a common multimodal geometric space,
using a novel loss function designed to cope with distant and disparate
modalities, and thereby enable seamless three-way retrieval. Our model not only
outperforms unimodal embedding based methods on cross-modal retrieval tasks but
also shows improvements stemming from jointly solving the two tasks on Twitter
data. We also show that the user embeddings learned within our joint multimodal
embedding model are better at predicting user interests compared to those
learned with unimodal content on Instagram data. Our framework thus goes beyond
the prior practice of using explicit leader-follower link information to
establish affiliations by extracting implicit content-centric affiliations from
isolated users. We provide qualitative results to show that the user clusters
emerging from learned embeddings have consistent semantics and the ability of
our model to discover fine-grained semantics from noisy and unstructured data.
Our work reveals that social multimodal content is inherently multimodal and
possesses a consistent structure because in social networks meaning is created
through interactions between users and content.


  We investigate the ground state properties of an equal mixture of two species
of bosons in its Mott-insulator phase at a filling factor two per site. We
identify one type of spin triplet-singlet transition through the competition of
ground state. When the on-site interaction is weak ($U<U_c$) the two particles
prefer to stay in the lowest band and with weak tunnelling between neighboring
sites the system is mapped into an effective spin-1 ferromagnetic exchange
Hamiltonian. When the interaction is tuned by a Feshbach resonance to be large
enough ($U>U_c$), higher band will be populated. Due to the orbital coupling
term $S^+S^-$ in the Hamiltonian, the two atoms in different orbits on a site
would form an on-site singlet. For a non-SU(2)-symmetric model, easy-axis or
easy-plane ferromagnetic spin exchange models may be realized corresponding to
phase separation or counter-flow superfluidity, respectively.


  The interlock drive system generates traction by penetrating narrow
articulated spikes into the ground and by using the strength of the deeper soil
layers to resist horizontal draft forces. The system promises good tractive
performance in low gravity environments where tires generate little traction
due to low vehicle weight. Possible applications include heavy-duty vehicles
for civil engineering tasks like earthmoving or mining excavation. Safe vehicle
operation in complex terrain geometry requires lateral vehicle stability to
prevent vehicle rollover. Good lateral stability is a particular requirement
for excavation and piling operations where the margins of safety define the
terrain geometry that can be worked in, and it is a major constraint in
operational planning. An earthmoving vehicle that can operate at a high roll
angle reduces the need to maintain ramps in pits and on piles and can shorten
and simplify the paths for individual maneuvers. Here we report on several
field trials on the lateral stability of an earthmoving vehicle that uses the
interlock drive systems. We find that the vehicle can work well at roll angles
of up to 20{\deg}, but that it needs further improvement if work at roll angles
of 30{\deg} or more is required.


  This paper draws a proposal of a set of parameters and methods for accuracy
evaluation of visual inspection systems. The case of a monochrome board is
treated, but practically all conclusions and methods may be extended for colour
acquisition. Basically, the proposed parameters are grouped in five sets as
follows:Internal noise;Video ADC cuantisation parameters;Analogue processing
section parameters;Dominant frequencies;Synchronisation (lock-in) accuracy. On
basis of this set of parameters was developed a software environment, in
conjunction with a test signal generator that allows the "test" images. The
paper also presents conclusions of evaluation for two types of video
acquisition boards


  We establish a version of von Staudt's theorem on mappings which preserve
harmonic quadruples for projective lines over (not necessarily commutative)
rings with "sufficiently many" units, in particular 2 has to be a unit.


  In this work, we utilized the methodology outlined in the IEEE Standard
2846-2022 for "Assumptions in Safety-Related Models for Automated Driving
Systems" to extract information on the behavior of other road users in driving
scenarios. This method includes defining high-level scenarios, determining
kinematic characteristics, evaluating safety relevance, and making assumptions
on reasonably predictable behaviors. The assumptions were expressed as
kinematic bounds. The numerical values for these bounds were extracted using
Python scripts to process realistic data from the UniD dataset. The resulting
information enables Automated Driving Systems designers to specify the
parameters and limits of a road user's state in a specific scenario. This
information can be utilized to establish starting conditions for testing a
vehicle that is equipped with an Automated Driving System in simulations or on
actual roads.


  We consider node-weighted survivable network design (SNDP) in planar graphs
and minor-closed families of graphs. The input consists of a node-weighted
undirected graph $G=(V,E)$ and integer connectivity requirements $r(uv)$ for
each unordered pair of nodes $uv$. The goal is to find a minimum weighted
subgraph $H$ of $G$ such that $H$ contains $r(uv)$ disjoint paths between $u$
and $v$ for each node pair $uv$. Three versions of the problem are
edge-connectivity SNDP (EC-SNDP), element-connectivity SNDP (Elem-SNDP) and
vertex-connectivity SNDP (VC-SNDP) depending on whether the paths are required
to be edge, element or vertex disjoint respectively. Our main result is an
$O(k)$-approximation algorithm for EC-SNDP and Elem-SNDP when the input graph
is planar or more generally if it belongs to a proper minor-closed family of
graphs; here $k=\max_{uv} r(uv)$ is the maximum connectivity requirement. This
improves upon the $O(k \log n)$-approximation known for node-weighted EC-SNDP
and Elem-SNDP in general graphs [Nutov, TALG'12]. We also obtain an $O(1)$
approximation for node-weighted VC-SNDP when the connectivity requirements are
in $\{0,1,2\}$; for higher connectivity our result for Elem-SNDP can be used in
a black-box fashion to obtain a logarithmic factor improvement over currently
known general graph results. Our results are inspired by, and generalize, the
work of [Demaine, Hajiaghayi and Klein, TALG'14] who obtained constant factor
approximations for node-weighted Steiner tree and Steiner forest problems in
planar graphs and proper minor-closed families of graphs via a primal-dual
algorithm.


  The study of non-line-of-sight (NLOS) imaging is growing due to its many
potential applications, including rescue operations and pedestrian detection by
self-driving cars. However, implementing NLOS imaging on a moving camera
remains an open area of research. Existing NLOS imaging methods rely on
time-resolved detectors and laser configurations that require precise optical
alignment, making it difficult to deploy them in dynamic environments. This
work proposes a data-driven approach to NLOS imaging, PathFinder, that can be
used with a standard RGB camera mounted on a small, power-constrained mobile
robot, such as an aerial drone. Our experimental pipeline is designed to
accurately estimate the 2D trajectory of a person who moves in a
Manhattan-world environment while remaining hidden from the camera's
field-of-view. We introduce a novel approach to process a sequence of dynamic
successive frames in a line-of-sight (LOS) video using an attention-based
neural network that performs inference in real-time. The method also includes a
preprocessing selection metric that analyzes images from a moving camera which
contain multiple vertical planar surfaces, such as walls and building facades,
and extracts planes that return maximum NLOS information. We validate the
approach on in-the-wild scenes using a drone for video capture, thus
demonstrating low-cost NLOS imaging in dynamic capture environments.


  This manuscript describes the elements of a theory of information tailored to
control and decision tasks and specifically to visual data. The concept of
Actionable Information is described, that relates to a notion of information
championed by J. Gibson, and a notion of "complete information" that relates to
the minimal sufficient statistics of a complete representation. It is shown
that the "actionable information gap" between the two can be reduced by
exercising control on the sensing process. Thus, senging, control and
information are inextricably tied. This has consequences in the so-called
"signal-to-symbol barrier" problem, as well as in the analysis and design of
active sensing systems. It has ramifications in vision-based control,
navigation, 3-D reconstruction and rendering, as well as detection,
localization, recognition and categorization of objects and scenes in live
video.
  This manuscript has been developed from a set of lecture notes for a summer
course at the First International Computer Vision Summer School (ICVSS) in
Scicli, Italy, in July of 2008. They were later expanded and amended for
subsequent lectures in the same School in July 2009. Starting on November 1,
2009, they were further expanded for a special topics course, CS269, taught at
UCLA in the Spring term of 2010.


  The Holographic Wess--Zumino (HWZ) consistency conditions are shown through a
step by step mapping of renormalization group flows to Hamiltonian systems, to
lead to the Holographic anomaly. These conditions codify how the energy scale,
when treated as the emergent bulk direction in Holographic theories, is put on
equal footing as the other directions of the space the field theory inhabits.
So, this is a defining feature of theories possessing local Holographic bulk
duals. In four dimensional Holographic conformal field theories, the $a$ and
$c$ anomaly coefficients are equated, and this is seen as a defining property
of theories which possess General Relativity coupled to matter as a dual.
Hence, showing how the former consistency conditions leads to the latter
relation between anomaly coefficients adds evidence to the claim that the HWZ
conditions are a defining feature of theories possessing local gravity duals.


  The stable torsion length in a group is the stable word length with respect
to the set of all torsion elements. We show that the stable torsion length
vanishes in crystallographic groups. We then give a linear programming
algorithm to compute a lower bound for stable torsion length in free products
of groups. Moreover, we obtain an algorithm that exactly computes stable
torsion length in free products of finite groups. The nature of the algorithm
shows that stable torsion length is rational in this case. As applications, we
give the first exact computations of stable torsion length for nontrivial
examples.


  Estimates of the deuterium abundance in quasar absorbers are reviewed,
including a brief account of incorrect claims published by the author and a
brief review of the problem of hydrogen contamination. It is concluded that the
primordial abundance may be universal with a value $(D/H)_P\approx 10^{-4}$,
within about a factor of two, corresponding to $\Omega_B h_{0.7}^2\approx 0.02$
or $\eta_{10}\approx 2.7$ in the Standard Big Bang. This agrees with current
limits on primordial helium, $Y_P\le 0.243$, which are shown to be surprisingly
insensitive to models of stellar enrichment. It also agrees with a tabulated
sum of the total density of baryons in observed components. Much lower
primordial deuterium ($\approx 2\times 10^{-5}$) is also possible but disagrees
with currently estimated helium abundances; the larger baryon density in this
case fits better with current models of the Lyman-$\alpha$ forest but requires
the bulk of the baryons to be in some currently uncounted form.


  To investigate the properties of iron-based superconductors, we examined
different kinds of Josephson junctions using Co-doped Ba-122 thin films. Based
on bicrystalline SrTiO3 substrates we prepared grain boundary (GB) junctions,
which showed clear Josephson effects. We present electrical measurements at
varying temperatures and magnetic fields. Furthermore, we prepared hybrid
junctions using thin film technique. Confined by a Ba-122 base electrode (S)
and a PbIn counter electrode (S') two different geometries of hybrid junctions
are formed: a planar SNS' junction with a gold barrier (N) in between and an
edge-type junction with an interface-engineered barrier. All three kinds of
junctions showed asymmetric resistively shunted junction-like (RSJ) behavior
with ICRN products of 20.2 /mu V (GB junctions), 18.4 /mu V (planar SNS'
junctions) and 12.3 /mu V (edge-type junctions), respectively. An excess
current could be observed at all junctions.


  We study the one-dimensional t-J-J'-model in the limit of small hole doping
$x$ and small $J/t$, $J'/t$. Special emphasis is put on the regime $J'/J
\approx .5$ where a spin gap is present at small doping and the undoped spin
chain is strongly dimerized. Using a perturbative approach and Luttinger liquid
arguments, we demonstrate for this non-integrable class of models that the
charge degrees of freedom behave as non-interacting spinless solitons in the
dilute hole limit. Our approach is also used to evaluate the energy and mass
renormalization of a single hole. Interestingly, the corrections of these
quantities are in powers of $\sqrt{J/t}$. At $J'/J=.5$ we construct a
variational spin-polaron wave function for the hole and find good agreement
with our perturbative results.


  A theoretical particle-number conserving quantum field theory based on the
concept of imaginary time is presented and applied to the scenario of a
coherent atomic laser field at ultra-cold temperatures. The proposed
theoretical model describes the analytical derivation of the frequency comb
spectrum for an atomic laser realized from modeling a coherent atomic beam of
condensate and non-condensate quantum field components released from a trapped
Bose-Einstein condensate at a given repetition phase and frequency. The
condensate part of the atomic vapor is assumed to be subjected to thermal noise
induced by the temperature of the surrounding thermal atomic cloud. This new
quantum approach uses time periodicity and an orthogonal decomposition of the
quantum field in a complex-valued quantum field representation to derive and
model the quantum field's forward- and backward-propagating components as a
standing wave field in the same unique time and temperature domain without
quantitative singularities at finite temperatures. The complex-valued atom
laser field, the resulting frequency comb, and the repetition frequency
distribution with the varying shape of envelopes are numerically monitored
within a Monte-Carlo sampling method, as a function of temperature and trap
frequency of the external confinement.


  This article develops the numerical and theoretical study of a reconstruction
algorithm of a potential in a wave equation from boundary measurements, using a
cost functional built on weighted energy terms coming from a Carleman estimate.
More precisely, this inverse problem for the wave equation consists in the
determination of an unknown time-independent potential from a single
measurement of the Neumann derivative of the solution on a part of the
boundary. While its uniqueness and stability properties are already well known
and studied, a constructive and globally convergent algorithm based on Carleman
estimates for the wave operator was recently proposed in [L. Baudouin, M. de
Buhan and S. Ervedoza, Global carleman estimates for waves and applications,
Comm. Partial Differential Equations 38 (2013), no. 5]. However, the numerical
implementation of this strategy still presents several challenges, that we
propose to address here.


  On the twisted Fock spaces $ \mathcal{F}^\lambda(\C^{2n}) $ we consider a
family of unitary operators $\rho_\lambda(a,b) $ indexed by $ (a,b) \in \C^n
\times \C^n.$ The composition formula for $ \rho_\lambda(a,b) \circ
\rho_\lambda(a^\prime,b^\prime) $ leads us to a group $ \He^n_\lambda(\C) $
which contains two copies of the Heisenberg group $ \He^n.$ The operators $
\rho_\lambda(a,b) $ lift to $ \He_\lambda^n(\C) $ providing an irreducible
unitary representation. However, its restriction to $ \He^n_\lambda(\R) $ is
not irreducible.


  The Spiking Neural Network (SNN) is a biologically inspired neural network
infrastructure that has recently garnered significant attention. It utilizes
binary spike activations to transmit information, thereby replacing
multiplications with additions and resulting in high energy efficiency.
However, training an SNN directly poses a challenge due to the undefined
gradient of the firing spike process. Although prior works have employed
various surrogate gradient training methods that use an alternative function to
replace the firing process during back-propagation, these approaches ignore an
intrinsic problem: gradient vanishing. To address this issue, we propose a
shortcut back-propagation method in our paper, which advocates for transmitting
the gradient directly from the loss to the shallow layers. This enables us to
present the gradient to the shallow layers directly, thereby significantly
mitigating the gradient vanishing problem. Additionally, this method does not
introduce any burden during the inference phase. To strike a balance between
final accuracy and ease of training, we also propose an evolutionary training
framework and implement it by inducing a balance coefficient that dynamically
changes with the training epoch, which further improves the network's
performance. Extensive experiments conducted over static and dynamic datasets
using several popular network structures reveal that our method consistently
outperforms state-of-the-art methods.


  This paper considers a Gaussian multiple-access channel with random user
activity where the total number of users $\ell_n$ and the average number of
active users $k_n$ may grow with the blocklength $n$. For this channel, it
studies the maximum number of bits that can be transmitted reliably per
unit-energy as a function of $\ell_n$ and $k_n$. When all users are active with
probability one, i.e., $\ell_n = k_n$, it is demonstrated that if $k_n$ is of
an order strictly below $n/\log n$, then each user can achieve the single-user
capacity per unit-energy $(\log e)/N_0$ (where $N_0/ 2$ is the noise power) by
using an orthogonal-access scheme. In contrast, if $k_n$ is of an order
strictly above $n/\log n$, then the capacity per unit-energy is zero.
Consequently, there is a sharp transition between orders of growth where
interference-free communication is feasible and orders of growth where reliable
communication at a positive rate per unit-energy is infeasible. It is further
demonstrated that orthogonal-access schemes in combination with orthogonal
codebooks, which achieve the capacity per unit-energy when the number of users
is bounded, can be strictly suboptimal.
  When the user activity is random, i.e., when $\ell_n$ and $k_n$ are
different, it is demonstrated that if $k_n\log \ell_n$ is sublinear in $n$,
then each user can achieve the single-user capacity per unit-energy $(\log
e)/N_0$. Conversely, if $k_n\log \ell_n$ is superlinear in $n$, then the
capacity per unit-energy is zero. Consequently, there is again a sharp
transition between orders of growth where interference-free communication is
feasible and orders of growth where reliable communication at a positive rate
is infeasible that depends on the asymptotic behaviours of both $\ell_n$ and
$k_n$. It is further demonstrated that orthogonal-access schemes, which are
optimal when $\ell_n = k_n$, can be strictly suboptimal.


  We characterise the elements of the (maximum) idempotent generated
subsemigroup of the Kauffman monoid in terms of combinatorial data associated
to certain normal forms. We also calculate the smallest size of a generating
set and idempotent generating set.


  The annual temperature cycle of the earth closely follows the annual cycle of
solar flux. At temperate latitudes, both driving and response cycles are well
described by a strong annual sinusoidal component and a non-vanishing
semiannual component. A new analysis of historical weather station records in
the United States determines persistent annual and semiannual variation with
high precision. Historical annual temperature ranges are consistent with prior
studies. Semiannual temperature cycles were much stronger than expected based
on the semiannual solar driving. Instead, these cycles were consistent with
multiplicative effects of two annual cycles. Our methods provide a quantitative
window into the climate's nonlinear response to solar driving, which is of
potential value in testing climate models.


  Wordnets are rich lexico-semantic resources. Linked wordnets are extensions
of wordnets, which link similar concepts in wordnets of different languages.
Such resources are extremely useful in many Natural Language Processing (NLP)
applications, primarily those based on knowledge-based approaches. In such
approaches, these resources are considered as gold standard/oracle. Thus, it is
crucial that these resources hold correct information. Thereby, they are
created by human experts. However, human experts in multiple languages are hard
to come by. Thus, the community would benefit from sharing of such manually
created resources. In this paper, we release mappings of 18 Indian language
wordnets linked with Princeton WordNet. We believe that availability of such
resources will have a direct impact on the progress in NLP for these languages.


  A method is given for calculating the strict minimum message length (SMML)
estimator for 1-dimensional exponential families with continuous sufficient
statistics. A set of $n$ equations are found that the $n$ cut-points of the
SMML estimator must satisfy. These equations can be solved using Newton's
method and this approach is used to produce new results and to replicate
results that C. S. Wallace obtained using his boundary rules for the SMML
estimator. A rigorous proof is also given that, despite being composed of step
functions, the posterior probability corresponding to the SMML estimator is a
continuous function of the data.


  RIn-Close_CVC is an efficient (take polynomial time per bicluster), complete
(find all maximal biclusters), correct (all biclusters attend the user-defined
level of consistency) and non-redundant (all the obtained biclusters are
maximal and the same bicluster is not enumerated more than once) enumerative
algorithm for mining maximal biclusters with constant values on columns in
numerical datasets. Despite RIn-Close_CVC has all these outstanding properties,
it has a high computational cost in terms of memory usage because it must keep
a symbol table in memory to prevent a maximal bicluster to be found more than
once. In this paper, we propose a new version of RIn-Close_CVC, named
RIn-Close_CVC2, that does not use a symbol table to prevent redundant
biclusters, and keeps all these four properties. We also prove that these
algorithms actually possess these properties. Experiments are carried out with
synthetic and real-world datasets to compare RIn-Close_CVC and RIn-Close_CVC2
in terms of memory usage and runtime. The experimental results show that
RIn-Close_CVC2 brings a large reduction in memory usage and, in average,
significant runtime gain when compared to its predecessor.


  The activity of at least one repeating Fast Radio Burst (FRB) source is
periodically modulated. If this modulation is the result of precession of the
rotation axis and throat of an accretion disc around a black hole, driven by a
companion that is also the source of accreted mass, then it may be possible to
constrain the mass of the black hole. The dynamics is analogous to that of
superorbital periods in ordinary mass-transfer binaries in which the accreting
object may be a stellar-mass black hole, a neutron star or a white dwarf, but
in the FRB source it may be an intermediate mass black hole. In a semi-detached
(mass-transferring) binary the orbital period is related to the mean density of
the mass-losing star. Assuming a value for its density and identifying the
observed modulation period as a disc precession period would determine the mass
ratio and the mass of the black hole. This model and magnetar-SNR models make
distinguishable predictions of the evolution of the FRB rotation measure that
may soon be tested in FRB 121102.


  Hitherto, six P-type planets are found around five binary systems, i.e.
Kepler-16 b, 34 b, 35 b, 38 b, 47 b, c, which are all Neptune or Jupiter-like
planets. The stability of planets and the habitable zones are influenced by the
gravitational and radiative perturbations of binary companions. In this Letter,
we check the stability of an additional habitable Earth-mass planet in each
system. Based on our simulations in 10 Myr, a habitable "Earth" is hardly
stable in Kepler-16 while a stable "Earth" in Kepler-47 close to the boundaries
of the habitable zone is possible. In contrast, Kepler-34, 35 and 38 seem to
have high probabilities of being able to tolerate a stable "Earth" in their
habitable zones. The affects of transit time variations are quite small due to
the small mass of an undetected "Earth", except that of Kepler-16 b. With a
time precision of 0.001 day(~ 88 s), an "Earth" in the corotational resonance
with Kepler-16 b can be detected in 3 years, while habitable "Earths" in
Kepler-34 and 38 systems can be detected in 10 years. Habitable "Earths" in
Kepler-35 and 47 are not likely to be detected in 10 years under this
precision.


  It is well-known that gravitationally induced vacuum polarization often
violates the point-wise energy conditions and sometimes violates the averaged
energy conditions. In this paper I begin a systematic attack on the question of
where and by how much the various energy conditions are violated. I work in the
test-field limit, and focus on conformally coupled massless scalar fields in
Schwarzschild spacetime, using the Hartle--Hawking vacuum. I invoke a mixture
of analytical and numerical techniques, and critically compare the qualitative
behaviour to be expected from the Page approximation with that adduced from the
numerical calculations of Anderson, Hiscock, and Samuel. I show that the
various point-wise energy conditions are violated in a series of onion-like
layers located between the unstable photon orbit and the event horizon, the
sequence of violations being DEC, WEC, and (NEC+SEC). Furthermore the ANEC is
violated for *some* of the null geodesics trapped in this region. Having
established the basic machinery in this paper, the Boulware vacuum will be
treated in a companion paper, while other exensions should be straightforward.


  The energy spectrum, composition and arrival directions of ultrahigh energy
cosmic rays (UHECRs) with energy above the cosmic ray ankle, measured by the
Pierre Auger Observatory, are inconsistent if their origin is assumed to be
extragalactic. Their observed properties, however, are those expected from
UHECRs accelerated by the highly relativistic jets emitted in Galactic gamma
ray bursts, most of which are beamed away from Earth. If this alternative
interpretation is correct, the observed break in the energy spectrum of UHECRs
around 50 EeV is not the Greisen-Zatsepin-Kuzmin cutoff but the energy
threshold for free escape of ultrahigh energy iron cosmic rays from the Galaxy
and above their respective free-escape threshold-energies, UHECR nuclei should
point back to their Galactic sources or their remnants rather than to active
galactic nuclei (AGN) within the GZK horizon.


  We propose the use of a tunneling electromechanical transducer to dynamically
detect Casimir forces between two conducting surfaces. The maximum distance for
which Casimir forces should be detectable with our method is around $1 \mu$m,
while the lower limit is given by the ability to approach the surfaces. This
technique should permit to study gravitational forces on the same range of
distances, as well as the vacuum friction provided that very low dissipation
mechanical resonators are used.


  We study a gas of point particles with hard-core repulsion in one dimension
where the particles move freely in-between elastic collisions. We prepare the
system with a uniform density on the infinite line. The velocities $\{v_i; i
\in \mathbb{Z} \}$ of the particles are chosen independently from a thermal
distribution. Using a mapping to the non-interacting gas, we analytically
compute the equilibrium spatio-temporal correlations $\langle v_i^m(t)
v_j^n(0)\rangle$ for arbitrary integers $m,n$. The analytical results are
verified with microscopic simulations of the Hamiltonian dynamics. The
correlation functions have ballistic scaling, as expected in an integrable
model.


  In this paper, we use the analytic method of Odlyzko and Richmond to study
the log-concavity of power series. If $f(z) = \sum_n a_nz^n$ is an infinite
series with $a_n \geq 1$ and $a_0 + \cdots + a_n = O(n + 1)$ for all $n$, we
prove that a super-polynomially long initial segment of $f^k(z)$ is
log-concave. Furthermore, if there exists constants $C > 1$ and $\alpha < 1$
such that $a_0 + \cdots + a_n = C(n + 1) - R_n$ where $0 \leq R_n \leq O((n +
1)^{\alpha})$, we show that an exponentially long initial segment of $f^k(z)$
is log-concave. This resolves a conjecture proposed by Letong Hong and the
author, which implies another conjecture of Heim and Neuhauser that the
Nekrasov-Okounkov polynomials $Q_n(z)$ are unimodal for sufficiently large $n$.


  Self-attention mechanisms have made striking state-of-the-art (SOTA) progress
in various sequence learning tasks, standing on the multi-headed dot product
attention by attending to all the global contexts at different locations.
Through a pseudo information highway, we introduce a gated component
self-dependency units (SDU) that incorporates LSTM-styled gating units to
replenish internal semantic importance within the multi-dimensional latent
space of individual representations. The subsidiary content-based SDU gates
allow for the information flow of modulated latent embeddings through skipped
connections, leading to a clear margin of convergence speed with gradient
descent algorithms. We may unveil the role of gating mechanism to aid in the
context-based Transformer modules, with hypothesizing that SDU gates,
especially on shallow layers, could push it faster to step towards suboptimal
points during the optimization process.


  Yor\`ub\'a is a widely spoken West African language with a writing system
rich in tonal and orthographic diacritics. With very few exceptions, diacritics
are omitted from electronic texts, due to limited device and application
support. Diacritics provide morphological information, are crucial for lexical
disambiguation, pronunciation and are vital for any Yor\`ub\'a text-to-speech
(TTS), automatic speech recognition (ASR) and natural language processing (NLP)
tasks. Reframing Automatic Diacritic Restoration (ADR) as a machine translation
task, we experiment with two different attentive Sequence-to-Sequence neural
models to process undiacritized text. On our evaluation dataset, this approach
produces diacritization error rates of less than 5%. We have released
pre-trained models, datasets and source-code as an open-source project to
advance efforts on Yor\`ub\'a language technology.


  We present an unstable periodic orbit in large eddy simulation of an
incompressible fluid in a periodic box subject to a constant body force. The
width of the inertial range of spatial scales, on which this simulation models
high-Reynolds-number turbulence, is about three quarters of a decade, and a
significant $-5/3$ scaling range is observed. We identify events of intense
energy transfer across spatial scales and relate them to vortical dynamics.


  A hadron resonance gas model including all known particles and resonances
with masses $m<2$ GeV and an exponentially rising density of Hagedorn states
for $m>2$ GeV is used to obtain an upper bound on the shear viscosity to
entropy density ratio, $\eta/s\approx1/(4\pi)$, of hadronic matter near $T_c$.
We found a large trace anomaly and small speed of sound near $T_c$, which agree
well with recent lattice calculations. We comment on the bulk viscosity to
entropy density ratio close to $T_c$.


  We show that complex representations of Clifford algebra can always be
reduced either to a real or to a quaternionic algebra depending on signature of
complex space thus showing that complex spinors are unavoidably either real
Majorana spinors or quaternionic spinors. We use this result to support (1,3)
signature for Minkowski space.


  This paper investigates a cross-modal retrieval problem in which a user would
like to retrieve a passage of music from a MIDI file by taking a cell phone
picture of a physical page of sheet music. While audio-sheet music retrieval
has been explored by a number of works, this scenario is novel in that the
query is a cell phone picture rather than a digital scan. To solve this
problem, we introduce a mid-level feature representation called a bootleg score
which explicitly encodes the rules of Western musical notation. We convert both
the MIDI and the sheet music into bootleg scores using deterministic rules of
music and classical computer vision techniques for detecting simple geometric
shapes. Once the MIDI and cell phone image have been converted into bootleg
scores, we estimate the alignment using dynamic programming. The most notable
characteristic of our system is that it does test-time adaptation and has no
trainable weights at all -- only a set of about 30 hyperparameters. On a
dataset containing 1000 cell phone pictures taken of 100 scores of classical
piano music, our system achieves an F measure score of .869 and outperforms
baseline systems based on commercial optical music recognition software.