  Byzantine fault-tolerant (BFT) protocols allow a group of replicas to come to
a consensus even when some of the replicas are Byzantine faulty. There exist
multiple BFT protocols to securely tolerate an optimal number of faults $t$
under different network settings. However, if the number of faults $f$ exceeds
$t$ then security could be violated. In this paper we mathematically formalize
the study of forensic support of BFT protocols: we aim to identify (with
cryptographic integrity) as many of the malicious replicas as possible and in
as a distributed manner as possible. Our main result is that forensic support
of BFT protocols depends heavily on minor implementation details that do not
affect the protocol's security or complexity. Focusing on popular BFT protocols
(PBFT, HotStuff, Algorand) we exactly characterize their forensic support,
showing that there exist minor variants of each protocol for which the forensic
supports vary widely. We show strong forensic support capability of LibraBFT,
the consensus protocol of Diem cryptocurrency; our lightweight forensic module
implemented on a Diem client is open-sourced and is under active consideration
for deployment in Diem. Finally, we show that all secure BFT protocols designed
for $2t+1$ replicas communicating over a synchronous network forensic support
are inherently nonexistent; this impossibility result holds for all BFT
protocols and even if one has access to the states of all replicas (including
Byzantine ones).


  This is the first of three papers that refine and extend portions of our
earlier preprint, "Depth of a knot tunnel." Together, they rework the entire
preprint.
  H. Goda, M. Scharlemann, and A. Thompson described a general construction of
all tunnels of all tunnel number 1 knots using "tunnel moves". We apply the
theory that we introduced in "The tree of knot tunnels" to study this
construction. In particular, we use it to calculate the number of distinct
minimal sequences of tunnel moves that can produce a given tunnel. As a
consequence, we see that for a sparse infinite set of tunnels, the minimal
sequence is unique, but generically a tunnel will have many such constructions.


  I report a coronal wave observed in Fexii, soft X-ray, and Halpha on November
6, 2006, jointly with a CME and a flare to show the spatial and temporal
relation of the wave and the CME. I also take advantage of the spectral
resolution of the wave to obtain an approximation of its temperature. Finally,
I compare the magnetic field topology to the wave location. The observations in
two band passes show bright fronts that are co-spatial when observed at the
same time, therefore I believe that the same wave is observed in different band
passes. The wave front is not observable in Halpha, but just in Fexii and in
soft X-ray, indicating that the temperature of the wave front is slightly
higher than the chromospheric temperature. The ratio of emission through two
SXI filters gives a temperature of 7 10^6 K for the wave front. The
northern-most edge of the CME footprint related to this wave corresponds to the
last location of the wave on the limb. The image processing reveals stationary
brightenings produced on the passage of the wave front. The potential spherical
extrapolation of the sun shows that those stationary brightenings are lying in
jumps of magnetic field lines connectivity.


  We prove the algebraic density property for the Calogero--Moser spaces
$\mathcal{C}_{n}$, and give a description of the identity component of the
group of holomorphic automorphisms of $\mathcal{C}_{n}$.


  A sensorless speed, average temperature and resistance estimation technique
based on Neural Network (NN) for brushed DC machines is proposed in this paper.
The literature on parameters and state spaces estimations of the Brushed DC
machines, shows a variety of approaches. However, these observers are sensitive
to a noise, on the model accuracy also are difficult to stabilize and to
converge. Furthermore, the majority of earlier works, estimate either the speed
or the temperature or the winding resistance. According to the literatures, the
Resilient backpropagation (RBP) as is the known as the faster BP algorithm,
Cascade-Forward Neural Network (CFNN), is known as the among accelerated
learning backpropagation algorithms, that's why where it is found in several
researches, also in several applications in these few years. The main objective
of this paper is to introduce an intelligent sensor based on resilient BP to
estimate simultaneously the speed, armature temperature and resistance of
brushed DC machines only from the measured current and voltage. A comparison
between the obtained results and the results of traditional estimator has been
made to prove the ability of the proposed method. This method can be embedded
in thermal monitoring systems, in high performance motor drives.


  It has now been known for over a decade that low-mass stars located in
star-forming regions are very frequently members of binary and multiple
systems, even more so than main sequence stars in the solar neighborhood. This
high multiplicity rate has been interpreted as the consequence of the
fragmentation of small molecular cores into a few seed objects that accrete to
their final mass from the remaining material and dynamically evolve into stable
multiple systems, possibly producing a few ejecta in the process. Analyzing the
statistical properties of young multiple systems in a variety of environments
therefore represents a powerful approach to place stringent constraints on star
formation theories. In this contribution, we first review a number of recent
results related to the multiplicity of T Tauri stars. We then present a series
of studies focusing on the multiplicity and properties of optically-undetected,
heavily embedded protostars. These objects are much younger than the previously
studied pre-main sequence stars, and they therefore offer a closer look at the
primordial population of multiple systems. In addition to these observational
avenues, we present new results of a series of numerical simulations that
attempt to reproduce the fragmentation of small molecular cores into multiple
systems, and compare these results to the observations.


  In this paper, we are concerned with the asymptotic behavior of the
Neumann-Poincare operator for Helmholtz system. By analyzing the asymptotic
behavior of spherical Bessel function near the origin and/or approach higher
order, we prove the asymptotic behavior of spectral of Neumann-Poincare
operator when frequency is small enough and/or the order is large enough. The
results show that spectral of Neumann-Poincare operator is continuous at the
origin and converges to zero from the complex plane in general.


  Transformation optics offers an unconventional approach to the control of
electromagnetic fields. A transformation optical structure is designed by first
applying a form-invariant coordinate transform to Maxwell's equations, in which
part of free space is distorted in some desired manner. The coordinate
transformation is then applied to the permittivity and permeability tensors to
yield the specification for a complex medium with desired functionality. The
transformation optical structures proposed to date, such as electromagnetic
"invisibility" cloaks and concentrators, are inherently reflectionless and
leave the transmitted wave undisturbed. Here we expand the class of
transformation optical structures by introducing finite, embedded coordinate
transformations, which allow the electromagnetic waves to be steered or
focused. We apply the method to the design of several devices, including a
parallel beam shifter and a beam splitter, both of which exhibit unusual
electromagnetic behavior as confirmed by 2D full-wave simulations. The devices
are designed to be reflectionless, in accordance with a straightforward
topological criterion.


  We address the problem of baryon number violation in Randall-Sundrum
backgrounds and provide a solution leading to a stable light Kaluza--Klein
fermion in warped GUT. This adds to the list of dark matter candidates which
stability can follow from ensuring proton stability in weak scale extensions of
the Standard Model


  A tutorial introduction to projective geometric algebra (PGA), a modern,
coordinate-free framework for doing euclidean geometry. PGA features: uniform
representation of points, lines, and planes; robust, parallel-safe join and
meet operations; compact, polymorphic syntax for euclidean formulas and
constructions; a single intuitive sandwich form for isometries; native support
for automatic differentiation; and tight integration of kinematics and rigid
body mechanics. Inclusion of vector, quaternion, dual quaternion, and exterior
algebras as sub-algebras simplifies the learning curve and transition path for
experienced practitioners. On the practical side, it can be efficiently
implemented, while its rich syntax enhances programming productivity. The basic
ideas are introduced in the 2D context; the 3D treatment focus on selected
topics. Advantages to traditional approaches are collected in a table at the
end. The article aims to be a self-contained introduction for practitioners of
euclidean geometry and includes numerous examples, figures, and tables.


  I. Hambleton, A. Korzeniewski and A. Ranicki proved that the signature of a
fibre bundle of closed, connected, compatibly oriented PL manifolds is always
multiplicative modulo 4. In this paper, we consider the Hirzebruch
$\chi_y$-genera for odd integers $y$ for a smooth fiber bundle such that the
base, fibre, and total space are compact complex algebraic manifolds (in the
complex analytic topology, not in the Zariski topology). We show that the
Hirzebruch $\chi_y$-genera of such a fibre bundle are always multiplicative
modulo 4. We also investigate multiplicativity modulo 8 and show that if $y$ is
congruent to 3 modulo 4, then the $\chi_y$-genera are multiplicative modulo 8.
We also show that when $y$ is congruent to 1 modulo 4, the Hirzebruch
$\chi_y$-genera of such a fiber bundle are multiplicative modulo 8 if and only
if the signature is multiplicative modulo 8, and that the non-multiplicativity
modulo 8, in this case, is identified with an Arf-Kervaire invariant.


  We present part of our investigations related to p-branes and Dp-branes
dynamics, duality between string theories/M-theory and (conformal) field
theories, as well as some semiclassical results for three-point correlation
functions, including finite-size effects on them.


  Quadrotors are widely employed across various domains, yet the conventional
type faces limitations due to underactuation, where attitude control is closely
tied to positional adjustments. In contrast, quadrotors equipped with tiltable
rotors offer overactuation, empowering them to track both position and attitude
trajectories. However, the nonlinear dynamics of the drone body and the
sluggish response of tilting servos pose challenges for conventional cascade
controllers. In this study, we propose a control methodology for tilting-rotor
quadrotors based on nonlinear model predictive control (NMPC). Unlike
conventional approaches, our method preserves the full dynamics without
simplification and utilizes actuator commands directly as control inputs.
Notably, we incorporate a first-order servo model within the NMPC framework.
Through simulation, we observe that integrating the servo dynamics not only
enhances control performance but also accelerates convergence. To assess the
efficacy of our approach, we fabricate a tiltable-quadrotor and deploy the
algorithm onboard at a frequency of 100Hz. Extensive real-world experiments
demonstrate rapid, robust, and smooth pose tracking performance.


  The Riemann hypothesis, which states that the non-trivial zeros of the
Riemann zeta function all lie on a certain line in the complex plane, is one of
the most important unresolved problems in mathematics. Inspired by the
P\'olya-Hilbert conjecture, we propose a new approach to finding a physical
system to study the Riemann zeros, which in contrast to previous examples, is
based on applying a time-periodic driving field. This driving allows us to
mould the quasienergies of the system (the analogue of the eigenenergies in the
absence of driving), so that they are directly governed by the zeta function.
We further show by numerical simulations that this allows the Riemann zeros to
be measured in currently accessible cold atom experiments.


  As the importance of research data gradually grows in sciences, data sharing
has come to be encouraged and even mandated by journals and funders in recent
years. Following this trend, the data availability statement has been
increasingly embraced by academic communities as a means of sharing research
data as part of research articles. This paper presents a quantitative study of
which mechanisms and repositories are used to share research data in PLOS ONE
articles. We offer a dynamic examination of this topic from the disciplinary
and temporal perspectives based on all statements in English-language research
articles published between 2014 and 2020 in the journal. We find a slow yet
steady growth in the use of data repositories to share data over time, as
opposed to sharing data in the paper or supplementary materials; this indicates
improved compliance with the journal's data sharing policies. We also find that
multidisciplinary data repositories have been increasingly used over time,
whereas some disciplinary repositories show a decreasing trend. Our findings
can help academic publishers and funders to improve their data sharing policies
and serve as an important baseline dataset for future studies on data sharing
activities.


  We use holography to study finite-temperature deformations of RG flows that
have exotic properties from an RG viewpoint. The holographic model consists of
five-dimensional gravity coupled to a scalar field with a potential. Each
negative extrema of the potential defines a dual conformal field theory. We
find all the black brane solutions on the gravity side and use them to
construct the thermal phase diagrams of the dual theories. We find an intricate
phase structure that reflects and extends the exotic properties at zero
temperature.


  Four terminal switching network is an alternative structure to realize the
logic functions in electronic circuit modeling. This network can be used to
implement a Boolean function with less number of switches than the two terminal
based CMOS switch. Each switch of the network is driven by a Boolean literal.
Any switch is connected to its four neighbors if a literal takes the value 1 ,
else it is disconnected. In our work, we aimed to develop a technique by which
we can find out if any Boolean function can be implemented with a given
four-terminal network. It is done using the path of any given lattice network.
First, we developed a synthesis tool by which we can create a library of
Boolean functions with a given four-terminal switching network and random
Boolean literals. This tool can be used to check the output of any lattice
network which can also function as a lattice network solver. In the next step,
we used the library functions to develop and test our MAPPING tool where the
functions were given as input and from the output, we can get the implemented
function in four terminal lattice network. Finally, we have proposed a
systematic procedure to implement any Boolean function with a efficient way by
any given one type of lattice network.


  Towards the high galactic latitude sky, the far-infrared (FIR) intensity is
tightly correlated to the total hydrogen column density which is made up of
atomic (HI) and molecular hydrogen (H$_{2})$. Above a certain column density
threshold, atomic hydrogen turns molecular. We analyse gas and dust properties
of intermediate-velocity clouds (IVCs) in the lower galactic halo to explore
their transition from the atomic to the molecular phase. Driven by
observations, we investigate the physical processes that transform a purely
atomic IVC into a molecular one. Data from the Effelsberg-Bonn HI-Survey
(EBHIS) are correlated to FIR wavebands of the Planck satellite and IRIS.
Modified black-body emission spectra are fitted to deduce dust optical depths
and grain temperatures. We remove the contribution of atomic hydrogen to the
FIR intensity to estimate molecular hydrogen column densities. Two IVCs show
different FIR properties, despite their similarity in HI, such as narrow
spectral lines and large column densities. One FIR bright IVC is associated
with H$_{2}$, confirmed by $^{12}$CO $(1\rightarrow0)$ emission; the other IVC
is FIR dim and shows no FIR excess, which indicates the absence of molecular
hydrogen. We propose that the FIR dim and bright IVCs probe the transition
between the atomic and molecular gas phase. Triggered by dynamical processes,
this transition happens during the descent of IVCs onto the galactic disk. The
most natural driver is ram pressure exerted onto the cloud by the increasing
halo density. Because of the enhanced pressure, the formation timescale of
H$_{2}$ is reduced, allowing the formation of large amounts of H$_{2}$ within a
few Myr.


  We consider quantum N=2 string embedded into the N=4 topological framework
from the perspective of the old covariant quantisation. Making use of the
causality and cyclic symmetry of tree amplitudes we argue that no Lorentz
covariant boson emission vertex can be constructed within the N=4 topological
formalism.


  Several second moment and other integral evaluations for the Riemann zeta
function $\zeta(s)$, Hurwitz zeta function $\zeta(s,a)$, and Lerch zeta
function $\Phi(z,s,a)$ are presented. Additional corollaries that are obtained
include previously known special cases for the Riemann zeta function
$\zeta(s)=\zeta(s,1)=\Phi(1,s,1)$. An example special case is: $$\int_R
{{|\zeta(1/2+it)|^2} \over {t^2+1/4}}dt=2\pi[\ln(2\pi)-\gamma],$$ with $\gamma$
the Euler constant. The asymptotic forms of certain fractional part integrals,
with and without logarithmic factors in the integrand, are presented.
Extensions and other approaches are mentioned.


  We experimentally demonstrate the phenomenon of electroosmotic dipole flow
that occurs around a localized surface charge region under the application of
an external electric field in a Hele-Shaw cell. We use localized deposition of
polyelectrolytes to create well-controlled surface charge variations, and show
that for a disk-shaped spot, the internal pressure distribution that arises,
results in uniform flow within the spot and dipole flow around it. We further
demonstrate the superposition of surface charge spots to create complex flow
patterns, without the use of physical walls.


  We define Lie subalgebras of the group algebra of a finite pseudo-reflection
group that are involved in the definition of the Cherednik KZ-systems, and
determine their structure. We provide applications for computing the Zariski
closure of the image of generalized (pure) braid group B inside the
representations of the corresponding Hecke algebras. We also get
unitarizability results for the representations of B originating from Hecke
algebras for suitable parameters, and relate our Lie algebras with the
topological closure of B in these compact cases.


  Stability is arguably one of the core concepts upon which our understanding
of dynamical and control systems has been built. The related notion of
incremental stability, however, has received much less attention until
recently, when it was successfully used as a tool for the analysis and design
of intrinsic observers, output regulation of nonlinear systems, frequency
estimators, synchronization of coupled identical dynamical systems, symbolic
models for nonlinear control systems, and bio-molecular systems. However, most
of the existing controller design techniques provide controllers enforcing
stability rather than incremental stability. Hence, there is a growing need to
extend existing methods or develop new ones for the purpose of designing
incrementally stabilizing controllers. In this paper, we develop a backstepping
design approach for incremental stability. The effectiveness of the proposed
method is illustrated by synthesizing a controller rendering a synchronous
generator incrementally stable.


  Sequential estimation of the success probability $p$ in inverse binomial
sampling is considered in this paper. For any estimator $\hat p$, its quality
is measured by the risk associated with normalized loss functions of
linear-linear or inverse-linear form. These functions are possibly asymmetric,
with arbitrary slope parameters $a$ and $b$ for $\hat p<p$ and $\hat p>p$
respectively. Interest in these functions is motivated by their significance
and potential uses, which are briefly discussed. Estimators are given for which
the risk has an asymptotic value as $p$ tends to $0$, and which guarantee that,
for any $p$ in $(0,1)$, the risk is lower than its asymptotic value. This
allows selecting the required number of successes, $r$, to meet a prescribed
quality irrespective of the unknown $p$. In addition, the proposed estimators
are shown to be approximately minimax when $a/b$ does not deviate too much from
$1$, and asymptotically minimax as $r$ tends to infinity when $a=b$.


  By utilizing symmetry analysis and electronic structure calculations, we
investigated the low-temperature orthorhombic phase of Ag$_{2}$Se in ${\cal
SG}$~17. In addition to the discovery of a nodal plane at $k_{z}=\pi$ protected
by the joint operation of time-reversal (${\cal T}$) and the 2-fold screw
rotation $S_{2z}$, we found 24 Weyl points mainly residing at the $k_{y}=0$
plane with notable Fermi arc and large quasiparticle interference pattern
(QPI). Due to the absence of mirror symmetry, a pair of Weyl points with
opposite chirality reside at different binding energies, which makes this
system an excellent material candidate for realizing the novel chiral anomaly
related phenomenon, such as the quantized circular photogalvanic and the chiral
magnetic effects. Furthermore, we also reveal the striking spin textures at
$k_{z}=\pi$ plane which demonstrates, in a large region of the surface
Brillouin Zone, a direction-selective spin polarization, which has a strong
implication to spintronic applications.


  We report the discovery of a radio pulsar with a characteristic age of 7300
years, making it one of the 10 apparently youngest Galactic pulsars known. PSR
J1357-6429, with a spin period of P = 166 ms and spin-down luminosity of 3.1e36
ergs/s, was detected during the Parkes multibeam survey of the Galactic plane.
We have measured a large rotational glitch in this pulsar, with Delta P/P =
-2.4e-6, similar in magnitude to those experienced occasionally by the Vela
pulsar. At a nominal distance of only ~ 2.5 kpc, based on the measured free
electron column density of 127 pc/cc and the electron distribution model of
Cordes & Lazio, this may be, after the Crab, the nearest very young pulsar
known. The pulsar is located near the radio supernova remnant candidate
G309.8-2.6.


  Localised modelling error in the near-surface layers of evolutionary stellar
models causes the frequencies of their normal modes of oscillation to differ
from those of actual stars with matching interior structures. These frequency
differences are referred to as the asteroseismic surface term. Global stellar
properties estimated via detailed constraints on individual mode frequencies
have previously been shown to be robust with respect to different
parameterisations of this surface term. It has also been suggested that this
may be true of a broader class of nonparametric treatments. We examine
systematic differences in inferred stellar properties with respect to different
surface-term treatments, both for a statistically large sample of main-sequence
stars, as well as for a sample of red giants, for which no such
characterisation has previously been done. For main-sequence stars, we
demonstrate that while masses and radii, and hence ages, are indeed robust to
the choice of surface term, the inferred initial helium abundance $Y_0$ is
sensitive to the choice of surface correction. This implies that
helium-abundance estimates returned from detailed asteroseismology are
methodology-dependent. On the other hand, for our red giant sample,
nonparametric surface corrections return dramatically different inferred
stellar properties than parametric ones. The nature of these differences
suggests that such nonparametric methods should be preferred for evolved stars;
this should be verified on a larger sample.


  Photon-induced nuclear excitation (i.e. photo-excitation) can be used for
production of nuclear isomers, which have potential applications in
astrophysics, energy storing, and medical diagnosis and treatment. This paper
presents a feasibility study on production of four nuclear isomers ({99m}^Tc,
{103m}^Rh and {113m, 115m}^In) using high-intensity {\gamma}-ray source based
on laser-electron Compton scattering (LCS), for use in the medical diagnosis
and treatment. The decay properties and the medical applications of these
nuclear isomers were reviewed. The cross-section curves, simulated yields and
activity of product of each photo-excitation process were calculated. The
cutoff energy of LCS {\gamma}-ray beam is optimized by adjusting the electron
energy in order to maximize the yields as well as the activities of
photo-excitation products. It is found that the achievable activity of
above-mentioned isomers can exceed 10 mCi for 6-hour target irradiation at an
intensity of the order of 10^{13} {\gamma}/s. Such magnitude of activity
satisfies the dose requirement of medical diagnosis. Our simulation results
suggest the prospect of producing medically interesting isomers with
photo-excitation using the state-of-art LCS {\gamma}-ray beam facility.


  With the ever-increasing reliance on digital networks for various aspects of
modern life, ensuring their security has become a critical challenge. Intrusion
Detection Systems play a crucial role in ensuring network security, actively
identifying and mitigating malicious behaviours. However, the relentless
advancement of cyber-threats has rendered traditional/classical approaches
insufficient in addressing the sophistication and complexity of attacks. This
paper proposes a novel 3-stage intrusion detection system inspired by a
simplified version of the Lockheed Martin cyber kill chain to detect advanced
multi-step attacks. The proposed approach consists of three models, each
responsible for detecting a group of attacks with common characteristics. The
detection outcome of the first two stages is used to conduct a feasibility
study on the possibility of predicting attacks in the third stage. Using the
ToN IoT dataset, we achieved an average of 94% F1-Score among different stages,
outperforming the benchmark approaches based on Random-forest model. Finally,
we comment on the feasibility of this approach to be integrated in a real-world
system and propose various possible future work.


  Let $\mathcal{C}$ be a weakly idempotent complete extriangulated category. In
contrast with the Hovey correspondence of admissible model structures on weakly
idempotent complete exact categories from two complete cotorsion pairs, we give
a construction of model structures on $\mathcal{C}$ from only one complete
cotorsion pair. Our main result not only generalizes the work by
Beligiannis-Reiten and Cui-Lu-Zhang, but also provides methods to construct
model structures from silting objects of $\mathcal{C}$ and co-$t$-structures in
triangulated categories.


  In dimension greater than four, we prove that if a Hermitian non-Kaehler
manifold is of pointwise constant antiholomorphic sectional curvatures, then it
is of constant sectional curvatures.


  Investigating the behavior of noninteracting fermions subjected to local
dephasing, we reveal that quasi-particle dephasing can induce superdiffusive
transport. This superdiffusion arises from nodal points within the momentum
distribution of local dephasing quasi-particles, leading to asymptotic
long-lived modes. By studying the dynamics of the Wigner function, we
rigorously elucidate how the dynamics of these enduring modes give rise to
L\'evy walk processes, a renowned mechanism underlying superdiffusion
phenomena. Our research demonstrates the controllability of dynamical scaling
exponents by selecting quasi-particles and extends its applicability to higher
dimensions, underlining the pervasive nature of superdiffusion in dephasing
models.


  Massive ETGs are thought to form through a two-phase process. At early times,
an intense and fast starburst forms blue and disk-dominated galaxies. After
quenching, the remaining structures become red, compact and massive, i.e., 'red
nuggets'. Then, a time-extended second phase which is dominated by mergers,
causes structural evolution and size growth. Given the stochastic nature of
mergers, a small fraction of red nuggets survives, without any interaction,
massive and compact until today: relic galaxies. Since this fraction depends on
the processes dominating the size growth, counting relics at low-z is a
valuable way to disentangle between different galaxy evolution models. In this
paper, we introduce the INvestigating Stellar Population In RElics (INSPIRE)
Project, that aims at spectroscopically confirming and fully characterizing a
large number of relics at 0.1<z<0.5. We focus here on the first results based
on a pilot program targeting three systems, representative of the whole sample.
For these, we extract 1D optical spectra over an aperture comprising ~30 % of
the galaxies light, and obtain line-of-sight integrated stellar velocity and
velocity dispersion. We also infer the stellar [$\alpha$/Fe] abundance from
line-index measurements and mass-weighted age and metallicity from
full-spectral fitting with single stellar population models. Two galaxies have
large integrated stellar velocity dispersion values, confirming their massive
nature. They are populated by stars with super-solar metallicity and
[$\alpha$/Fe]. Both objects have formed >80 % of their stellar mass within a
short (0.5 - 1.0 Gyrs) initial star formation episode occurred only ~1 Gyr
after the Big Bang. The third galaxy has a more extended star formation history
and a lower velocity dispersion. Thus we confirm two out of three candidates as
relics.


  We present a new set of Cepheid, full amplitude, nonlinear, convective models
which are pulsationally unstable in the second overtone (SO). Hydrodynamical
models were constructed by adopting a chemical composition typical for Cepheids
in the Small Magellanic Cloud (SMC) and stellar masses ranging from 3.25 to 4
solar masses. Predicted phi{21} Fourier parameters agree, within current
uncertainties, with empirical data for pure first and second overtone variables
as well as for first/second overtone (FO/SO) double-mode Cepheids collected by
Udalski et al. (1999a,b) in the SMC. On the other hand, predicted I band
amplitudes are systematically larger than the observed ones in the short period
range. We also find, in agreement with empirical evidence, that the region
within which both second and first overtones attain a stable limit cycle widens
when moving toward lower luminosities. Moreover, predicted P{SO}/P{FO} and
P{FO}/P{F} period ratios agree quite well with empirical period ratios for
FO/SO and F/FO double-mode SMC Cepheids. Finnaly, current models support the
evidence that pure SO Cepheids and SO components in FO/SO Cepheids are good
distance indicators.


  We observed two nearby galaxies with potential or weak indications of nuclear
activity, M32 and M81, with the MIRLIN mid-IR camera at N band (10.79 microns).
M32 is not detected, but we give detailed measurements of the nucleus of M81.
Our observations of M81 show a bright nuclear point source at N, and comparison
to measurements made in the early 1970's gives an increase in nuclear flux of
nearly a factor of two. If the comparison is accurate, the nuclear mid-IR
emission must ultimately be powered by a variable, compact source, similar to
that in Seyferts and quasars. M81 has been classified in the literature as a
low-luminosity LINER, not a pure Seyfert galaxy. Further, it has been suggested
that this and other low-luminosity AGN may have intrinsically different spectra
than Seyferts and quasars. However, we find that the relative fluxes in the
X-ray, MIR, and radio bands, all essentially unaffected by extinction and
galaxy pollution, show a nuclear continuum remarkably like that of a bona fide
Seyfert or quasar.


  We prove the ordinary Hecke orbit conjecture for Shimura varieties of Hodge
type at primes of good reduction. We make use of the global Serre-Tate
coordinates of Chai as well as recent results of D'Addezio about the $p$-adic
monodromy of isocrystals. The new ingredients in this paper are a general
monodromy theorem for Hecke-stable subvarieties for Shimura varieties of Hodge
type, and a rigidity result for the formal completions of ordinary Hecke
orbits. Along the way we show that classical Serre--Tate coordinates can be
described using unipotent formal groups, generalising results of Howe.


  This article introduces and explains a computer algebra system (CAS) wxMaxima
for Calculus teaching and learning at the tertiary level. The didactic
reasoning behind this approach is the need to implement an element of
technology into classrooms to enhance students' understanding of Calculus
concepts. For many mathematics educators who have been using CAS, this material
is of great interest, particularly for secondary teachers and university
instructors who plan to introduce an alternative CAS into their classrooms. By
highlighting both the strengths and limitations of the software, we hope that
it will stimulate further debate not only among mathematics educators and
software users but also also among symbolic computation and software
developers.


  We show how to implement quantum transport, generate entangled state and
achieve spatial entanglement distribution via topological Thouless pumping in
one-dimensional disordered lattices. We introduce the on-site disorders to
suppress the high-order resonant tunneling (which cause wavepacket dispersion)
and realize dispersionless Thouless pumping. The interplay between the on-site
disorders and the band topology enables robust unidirectional transport. We
also demonstrate how to prepare spatially entangled two-particle NOON state via
Hong-Ou-Mandel interference assisted by the Thouless pumping. The quantum
entanglement can be well preserved during the distribution between spatially
separated sites. Our system paves a way to wide applications of topology in
quantum information process.


  The Ramsey number $r_k(p, q)$ is the smallest integer $N$ that satisfies for
every red-blue coloring on $k$-subsets of $[N]$, there exist $p$ integers such
that any $k$-subset of them is red, or $q$ integers such that any $k$-subset of
them is blue. In this paper, we study the lower bounds for small Ramsey numbers
on hypergraphs by constructing counter-examples and recurrence relations. We
present a new algorithm to prove lower bounds for $r_k(k+1, k+1)$. In
particular, our algorithm is able to prove $r_5(6,6) \ge 72$, where there is
only trivial lower bound on $5$-hypergraphs before this work. We also provide
several recurrence relations to calculate lower bounds based on lower bound
values on smaller $p$ and $q$. Combining both of them, we achieve new lower
bounds for $r_k(p, q)$ on arbitrary $p$, $q$, and $k \ge 4$.


  We present the Lagrangian whose corresponding action is the trace K action
for General Relativity. Although this Lagrangian is second order in the
derivatives, it has no second order time derivatives and its behaviour at space
infinity in the asymptotically flat case is identical to other alternative
Lagrangians for General Relativity, like the gamma-gamma Lagrangian used by
Einstein. We develop some elements of the variational principle for field
theories with boundaries, and apply them to second order Lagrangians, where we
stablish the conditions -- proposition 1 -- for the conservation of the Noether
charges. From this general approach a pre-symplectic form is naturally obtained
that features two terms, one from the bulk and another from the boundary. When
applied to the trace K Lagrangian, we recover a pre-symplectic form first
introduced using a different approach. We prove that all diffeomorphisms
satisfying certain restrictions at the boundary -- that keep room for a
realization of the Poincar\'e group -- will yield Noether conserved charges. In
particular, the computation of the total energy gives, in the asymptotically
flat case, the ADM result.


  We consider the $(1+\epsilon)$-approximate nearest neighbor search problem:
given a set $X$ of $n$ points in a $d$-dimensional space, build a data
structure that, given any query point $y$, finds a point $x \in X$ whose
distance to $y$ is at most $(1+\epsilon) \min_{x \in X} \|x-y\|$ for an
accuracy parameter $\epsilon \in (0,1)$. Our main result is a data structure
that occupies only $O(\epsilon^{-2} n \log(n) \log(1/\epsilon))$ bits of space,
assuming all point coordinates are integers in the range $\{-n^{O(1)} \ldots
n^{O(1)}\}$, i.e., the coordinates have $O(\log n)$ bits of precision. This
improves over the best previously known space bound of $O(\epsilon^{-2} n
\log(n)^2)$, obtained via the randomized dimensionality reduction method of
Johnson and Lindenstrauss (1984). We also consider the more general problem of
estimating all distances from a collection of query points to all data points
$X$, and provide almost tight upper and lower bounds for the space complexity
of this problem.


  The Langevin equation is a common tool to model diffusion at a
single-particle level. In non-homogeneous environments, such as aqueous
two-phase systems or biological condensates with different diffusion
coefficients in different phases, the solution to a Langevin equation is not
unique unless the interpretation of stochastic integrals involved is selected.
We analyze the diffusion of particles in such systems and evaluate the mean,
the mean square displacement, and the distribution of particles, as well as the
variance of the time-averaged mean-squared displacements. Our analytical
results provide a method to choose the interpretation parameter from single
particle tracking experiments.


  We present Open Images V4, a dataset of 9.2M images with unified annotations
for image classification, object detection and visual relationship detection.
The images have a Creative Commons Attribution license that allows to share and
adapt the material, and they have been collected from Flickr without a
predefined list of class names or tags, leading to natural class statistics and
avoiding an initial design bias. Open Images V4 offers large scale across
several dimensions: 30.1M image-level labels for 19.8k concepts, 15.4M bounding
boxes for 600 object classes, and 375k visual relationship annotations
involving 57 classes. For object detection in particular, we provide 15x more
bounding boxes than the next largest datasets (15.4M boxes on 1.9M images). The
images often show complex scenes with several objects (8 annotated objects per
image on average). We annotated visual relationships between them, which
support visual relationship detection, an emerging task that requires
structured reasoning. We provide in-depth comprehensive statistics about the
dataset, we validate the quality of the annotations, we study how the
performance of several modern models evolves with increasing amounts of
training data, and we demonstrate two applications made possible by having
unified annotations of multiple types coexisting in the same images. We hope
that the scale, quality, and variety of Open Images V4 will foster further
research and innovation even beyond the areas of image classification, object
detection, and visual relationship detection.


  This paper deals with Mellin transforms of rational functions $g/f$ in
several variables. We prove that the polar set of such a Mellin transform
consists of finitely many families of parallel hyperplanes, with all planes in
each such family being integral translates of a specific facial hyperplane of
the Newton polytope of the denominator $f$. The Mellin transform is naturally
related to the so called coamoeba $\mathcal{A}'_f:=\text{Arg}\,(Z_f)$, where
$Z_f$ is the zero locus of $f$ and $\text{Arg}$ denotes the mapping that takes
each coordinate to its argument. In fact, each connected component of the
complement of the coamoeba $\mathcal{A}'_f$ gives rise to a different Mellin
transform. The dependence of the Mellin transform on the coefficients of $f$,
and the relation to the theory of $A$-hypergeometric functions is also
discussed in the paper.


  Observable thermodynamical properties of the intracluster medium (ICM)
reflect the complex interplay between AGN feedback and the gravitational
collapse of haloes. Using the large volume TNG300 simulation of the
IllustrisTNG project we provide predictions for X-ray and Sunyaev-Zel'dovich
(SZ) scaling relations for a sample of over 30,000 haloes that cover a wide
mass range from galaxies to massive galaxy clusters ($M_{\rm 500crit}$ $\in
[10^{12}$ M$_{\odot} - 2\times 10^{15}$ M$_{\odot}$]). We produce mock X-ray
observations of simulated haloes using methods that are consistent with
observational techniques. Thus, we investigate the scaling relations between
the soft-band X-ray luminosity, spectroscopic temperature, gas mass fraction,
$Y_{\rm X}$ and $Y_{\rm SZ}$ as a function of halo mass, and we find broad
agreement between IllustrisTNG and the observed relations. Our results
highlight the scatter and bias introduced by estimated masses, and thus the
importance of converting simulated ICM properties to the observable space when
comparing simulations to current X-ray observations. The wide range of halo
masses in our sample provides new insights into the shape of the X-ray and SZ
scaling relations across three orders of magnitude in mass. Our findings show
strong evidence for a break in $z=0$ scaling relations. We introduce a smoothly
broken power law model which robustly captures the location of this break, the
width of the transition region around the break, as well as the slope
dependence on halo mass. Our results inform the next generation of subgrid
black hole feedback models and provide predictions for ongoing and future
observational surveys.


  It is well known that the low energy expansion of tree-level superstring
scattering amplitudes satisfies a suitably defined version of maximum
transcendentality. In this paper it is argued that there is a natural extension
of this definition that applies to the genus-one four-graviton Type II
superstring amplitude to all orders in the low-energy expansion. To obtain this
result, the integral over the genus-one moduli space is partitioned into a
region ${\cal M}_R$ surrounding the cusp and its complement ${\cal M}_L$, and
an exact expression is obtained for the contribution to the amplitude from
${\cal M}_R$. The low-energy expansion of the ${\cal M}_R$ contribution is
proven to be free of irreducible multiple zeta-values to all orders. The
contribution to the amplitude from ${\cal M}_L$ is computed in terms of modular
graph functions up to order $D^{12} {\cal R}^4$ in the low-energy expansion,
and general arguments are used beyond this order to conjecture the
transcendentality properties of the ${\cal M}_L$ contributions. Maximal
transcendentality of the full amplitude holds provided we assign a non-zero
weight to certain harmonic sums, an assumption which is familiar from
transcendentality assignments in quantum field theory amplitudes.


  Microscopic model of the interaction of spins with a microwave field in a
random-anisotropy magnet has been developed. Numerical results show that
microwave absorption occurs in a broad range of frequencies due to the
distribution of Imry-Ma domains on sizes and effective anisotropy. That
distribution is also responsible for the weak dependence of the absorption on
the damping. At a fixed frequency of the ac-field the spatial pattern of the
amplitude of spin oscillations exhibits maxima corresponding to the
oscillations of resonant magnetic domains. The dependence of the peak
absorption frequency on the ratio of the magnitude of per-spin random
anisotropy to the strength of the ferromagnetic exchange agrees with the
scaling derived from the Imry-Ma argument. The effect noticeably increases in
low-dimensional systems, suggesting that materials comprised of microscopic
amorphous leaves and wires can be promising candidates for enhanced microwave
absorption.


  Let f traverse a sequence of classical holomorphic newforms of fixed weight
and increasing squarefree level q tending to infinity. We prove that the
pushforward of the mass of f to the modular curve of level 1 equidistributes
with respect to the Poincar\'{e} measure.
  Our result answers affirmatively the squarefree level case of a conjecture
spelled out by Kowalski, Michel and Vanderkam (2002) in the spirit of a
conjecture of Rudnick and Sarnak (1994).
  Our proof follows the strategy of Holowinsky and Soundararajan (2008) who
show that newforms of level 1 and large weight have equidistributed mass. The
new ingredients required to treat forms of fixed weight and large level are an
adaptation of Holowinsky's reduction of the problem to one of bounding shifted
sums of Fourier coefficients (which on the surface makes sense only in the
large weight limit), an evaluation of the p-adic integral needed to extend
Watson's formula to the case of three newforms where the level of one divides
but need not equal the common squarefree level of the other two, and some
additional technical work in the problematic case that the level has many small
prime factors.


  We model the adiabatic inspiral of relativistic binary neutron stars in a
quasi-equilibrium (QE) approximation, and compute the gravitational wavetrain
from the late phase of the inspiral. We compare corotational and irrotational
sequences and find a significant difference in the inspiral rate, which is
almost entirely caused by differences in the binding energy. We also compare
our results with those of a point-mass post-Newtonian calculation. We
illustrate how the late inspiral wavetrain computed with our QE numerical
scheme can be matched to the subsequent plunge and merger waveform calculated
with a fully relativistic hydrodynamics code.


  The acute respiratory distress syndrome (ARDS) is a severe form of hypoxemic
respiratory failure with in-hospital mortality of 35-46%. High mortality is
thought to be related in part to challenges in making a prompt diagnosis, which
may in turn delay implementation of evidence-based therapies. A deep neural
network (DNN) algorithm utilizing unbiased ventilator waveform data (VWD) may
help to improve screening for ARDS. We first show that a convolutional neural
network-based ARDS detection model can outperform prior work with random forest
models in AUC (0.95+/-0.019 vs. 0.88+/-0.064), accuracy (0.84+/-0.026 vs
0.80+/-0.078), and specificity (0.81+/-0.06 vs 0.71+/-0.089). Frequency
ablation studies imply that our model can learn features from low frequency
domains typically used for expert feature engineering, and high-frequency
information that may be difficult to manually featurize. Further experiments
suggest that subtle, high-frequency components of physiologic signals may
explain the superior performance of DL models over traditional ML when using
physiologic waveform data. Our observations may enable improved
interpretability of DL-based physiologic models and may improve the
understanding of how high-frequency information in physiologic data impacts the
performance our DL model.


  Measurements of the spin-lattice relaxation rate 1/T_1 by nuclear magnetic
resonance for the one-dimensional Heisenberg antiferromagnet Sr_2CuO_3 have
provided evidence for a diffusion-like contribution at finite temperature and
small wave-vector. By analyzing real-time data for the auto- and
nearest-neighbor spin-spin correlation functions obtained by the density-matrix
renormalization group I show that such a contribution indeed exists for
temperatures T>J, where J is the coupling constant, but that it becomes
exponentially suppressed for T << J. I present evidence that the
frequency-dependence of 1/T_1 in the Heisenberg case is smoothly connected to
that in the free fermion case where the exponential suppression of the
diffusion-like contribution is easily understood.


  We study the distillability of a certain class of bipartite density operators
which can be obtained via depolarization starting from an arbitrary one. Our
results suggest that non-positivity of the partial transpose of a density
operator is not a sufficient condition for distillability, when the dimension
of both subsystems is higher than two.


  We show that non-abelian quantum statistics can be studied using certain
topological invariants which are the homology groups of configuration spaces.
In particular, we formulate a general framework for describing quantum
statistics of particles constrained to move in a topological space $X$. The
framework involves a study of isomorphism classes of flat complex vector
bundles over the configuration space of $X$ which can be achieved by
determining its homology groups. We apply this methodology for configuration
spaces of graphs. As a conclusion, we provide families of graphs which are good
candidates for studying simple effective models of anyon dynamics as well as
models of non-abelian anyons on networks that are used in quantum computing.
These conclusions are based on our solution of the so-called universal
presentation problem for homology groups of graph configuration spaces for
certain families of graphs.


  In a magnetic field, vortices significantly contribute to the dark counts of
single-photon detectors made of superconducting wires, and they are also
limiting the critical current of such devices. To address this issue, we
prepared superconducting microwires with a pinhole grid from WSi thin films and
report on corresponding critical-current and count-rate measurements in an
external magnetic field B. When compared to corresponding devices without
pinholes, the critical current only weakly depends on the magnetic field at B <
16 mT and it is even larger already at B > 10 mT. Moreover, dark counts are not
only suppressed in zero field, but particularly in magnetic fields B < 16 mT,
while photon counts are virtually field insensitive in the same range of the
magnetic field.


  In this paper, we aim to develop a unified view of causal and non-causal
feature selection methods. The unified view will fill in the gap in the
research of the relation between the two types of methods. Based on the
Bayesian network framework and information theory, we first show that causal
and non-causal feature selection methods share the same objective. That is to
find the Markov blanket of a class attribute, the theoretically optimal feature
set for classification. We then examine the assumptions made by causal and
non-causal feature selection methods when searching for the optimal feature
set, and unify the assumptions by mapping them to the restrictions on the
structure of the Bayesian network model of the studied problem. We further
analyze in detail how the structural assumptions lead to the different levels
of approximations employed by the methods in their search, which then result in
the approximations in the feature sets found by the methods with respect to the
optimal feature set. With the unified view, we are able to interpret the output
of non-causal methods from a causal perspective and derive the error bounds of
both types of methods. Finally, we present practical understanding of the
relation between causal and non-causal methods using extensive experiments with
synthetic data and various types of real-word data.


  High pressure electrical resistivity and x-ray diffraction experiments have
been performed on Fe single crystals. The crystallographic investigation
provides direct evidence that in the martensitic $bcc \rightarrow hcp$
transition at 14 GPa the $\lbrace 110\rbrace_{bcc}$ become the $\lbrace
002\rbrace_{hcp}$ directions. During a pressure cycle, resistivity shows a
broad hysteresis of 6.5 GPa, whereas superconductivity, observed between 13 and
31 GPa, remains unaffected. Upon increasing pressure an electronic instability,
probably a quantum critical point, is observed at around 19 GPa and, close to
this pressure, the superconducting $T_{c}$ and the isothermal resistivity
($0<T<300\,$K) attain maximum values. In the superconducting pressure domain,
the exponent $n = 5/3$ of the temperature power law of resistivity and its
prefactor, which mimics $T_{c}$, indicate that ferromagnetic fluctuations may
provide the glue for the Cooper pairs, yielding unconventional
superconductivity.


  When studying the dynamics of Vertical-Cavity Surface-Emitting Lasers, and
their polarization properties, the spin-flip model appears to be the simplest
model qualitatively reproducing all dynamical features that have been observed
experimentally. Nonetheless, because of the fast time-scale of the
spin-relaxation processes, the specific role and the importance of the
spin-population difference - which is one of the specific feature of the
spin-flip model - has been continuously questioned. In fact, the debate
regarding the possible adiabatic elimination of the spin-population remains
fully open.
  In this paper, our goal is to bring new light into this issue by
demonstrating that this variable is essential to preserve the most complex
dynamical features predicted by the spin-flip model, such as polarization
chaos, and, therefore, needs to be conserved. To do so, we first perform a
detailed analysis, focusing on the chaotic dynamics, to determine the minimal
embedding dimension for the spin-flip model. As the latter confirms that a
reduction of the model could be envisaged, we then consider the adiabatic
elimination of the spin-population difference to highlight and explain its
failure to reproduce essential dynamical features obtained in the original
model.


  Let $S=S_1S_2S_3\ldots S_n$ be a finite string. Write $S$ in the form
$XYY\ldots Y=XY^k$, consisting of a prefix $X$ (which may be empty), followed
by $k$ copies of a non-empty string $Y$. Then, the greatest value of this
integer $k$ is called the curling number of $S$ and is denoted by $cn(S)$. Let
the degree sequence of the graph $G$ be written as a string of identity curling
subsequences say, $X^{k_1}_1\circ X^{k_2}_2\circ X^{k_3}_3 \ldots \circ
X^{k_l}_l$. The compound curling number of $G$, denoted $cn^c(G)$ is defined to
be, $cn^n(G) = \prod\limits^{l}_{i=1}k_i$. In this paper, we discuss the
curling number and compound curling number of certain products of graphs.


  Dynamics of the Fermi-Pasta-Ulam (FPU) system on a two-dimensional square
lattice is considered in the limit of small-amplitude long-scale waves with
slow transverse modulations. In the absence of transverse modulations, dynamics
of such waves, even at an oblique angle with respect to the square lattice, is
known to be described by the Korteweg-de Vries (KdV) equation. For the three
basic directions (horizontal, vertical, and diagonal), we prove that the
modulated waves are well described by the Kadomtsev-Petviashvili (KP-II)
equation. The result was expected long ago but proving rigorous bounds on the
approximation error turns out to be complicated due to the nonlocal terms of
the KP-II equation and the vector structure of the FPU systems on
two-dimensional lattices. We have obtained these error bounds by extending the
local well-posedness result for the KP-II equation in Sobolev spaces and by
controlling the error terms with energy estimates. The bounds are useful in the
analysis of transverse stability of solitary and periodic waves in
two-dimensional FPU systems due to many results available for the KP-II
equation.


  We introduce and study in a general setting the concept of homogeneity of an
operator and, in particular, the notion of homogeneity of an integral operator.
In the latter case, homogeneous kernels of such operators are also studied. The
concept of homogeneity is associated with transformations of a measure -
measure dilations, which are most natural in the context of our general
research scheme. For the study of integral operators, the notions of weak and
strong homogeneity of the kernel are introduced. The weak case is proved to
generate a homogeneous operator in the sense of our definition, while the
stronger condition corresponds to the most relevant specific examples - classes
of homogeneous integral operators on various metric spaces, and allows us to
obtain an explicit general form for the kernels of such operators. The examples
given in the article - various specific cases - illustrate general statements
and results given in the paper and at the same time are of interest in their
own way.


  The influence of an underlying current on 3-wave interactions of capillary
water waves is studied. The fact that in irrotational flow resonant 3-wave
interactions are not possible can be invalidated by the presence of an
underlying current of constant non-zero vorticity. We show that: 1) wave trains
in flows with constant non-zero vorticity are possible only for two-dimensional
flows; 2) only positive constant vorticities can trigger the appearance of
three-wave resonances; 3) the number of positive constant vorticities which do
trigger a resonance is countable; 4) the magnitude of a positive constant
vorticity triggering a resonance can not be too small.


  We have developed capacitively-transduced nanomechanical resonators using
sp$^2$-rich diamond-like carbon (DLC) thin films as conducting membranes. The
electrically conducting DLC films were grown by physical vapor deposition at a
temperature of $500{\,\,}^\circ$C. Characterizing the resonant response, we
find a larger than expected frequency tuning that we attribute to the membrane
being buckled upwards, away from the bottom electrode. The possibility of using
buckled resonators to increase frequency tuning can be of advantage in rf
applications such as tunable GHz filters and voltage-controlled oscillators.


  In this paper, we consider improving the efficiency of information-based
autonomous robot exploration in unknown and complex environments. We first
utilize Gaussian process (GP) regression to learn a surrogate model to infer
the confidence-rich mutual information (CRMI) of querying control actions, then
adopt an objective function consisting of predicted CRMI values and prediction
uncertainties to conduct Bayesian optimization (BO), i.e., GP-based BO (GPBO).
The trade-off between the best action with the highest CRMI value
(exploitation) and the action with high prediction variance (exploration) can
be realized. To further improve the efficiency of GPBO, we propose a novel
lightweight information gain inference method based on Bayesian kernel
inference and optimization (BKIO), achieving an approximate logarithmic
complexity without the need for training. BKIO can also infer the CRMI and
generate the best action using BO with bounded cumulative regret, which ensures
its comparable accuracy to GPBO with much higher efficiency. Extensive
numerical and real-world experiments show the desired efficiency of our
proposed methods without losing exploration performance in different
unstructured, cluttered environments. We also provide our open-source
implementation code at https://github.com/Shepherd-Gregory/BKIO-Exploration.


  A wandering domain for a diffeomorphism is an open connected set whose
iterates are pairwise disjoint. We endow A^n = T^n x R^n with its usual exact
symplectic structure. An integrable diffeomorphism {\Phi}^h, i.e. the time-one
map of a Hamiltonian h which depends only on the action variables, has no
nonempty wandering domains. The aim of this paper is to estimate the size
(measure and Gromov capacity) of wandering domains in the case of an exact
symplectic perturbation of {\Phi}^h , in the analytic or Gevrey category. Upper
estimates are related to Nekhoroshev theory, lower estimates are related to
examples of Arnold diffusion. This is a contribution to the "quantitative
Hamiltonian perturbation theory" initiated in previous works on the optimality
of long term stability estimates and diffusion times; our emphasis here is on
discrete systems because this is the natural setting to study wandering
domains.


  The intracavity power, and hence sensitivity, of optomechanical sensors is
commonly limited by parametric instability. Here we characterize the parametric
instability induced sensitivity degradation in a micron scale cavity
optomechanical system. Feedback via optomechanical transduction and electrical
gradient force actuation is applied to suppress the parametric instability. As
a result a 5.4 fold increase in mechanical motion transduction sensitivity is
achieved to a final value of $1.9\times 10^{-18}\rm m Hz^{-1/2}$.


  In mixed strategy 2\times2 population games, the realization of maximum
entropy (Maxent) is of the theoretical expectation. We evaluate this
theoretical prediction in the experimental economics game data. The data
includes 12 treatments and 108 experimental sessions in which the random match
human subjects pairs make simultaneous strategy moves repeated 200 rounds. Main
results are (1) We confirm that experimental entropy value fit the prediction
from Maxent well; and (2) In small proportion samples, distributions are
deviated from Maxent expectations; interesting is that, the deviated patterns
are significant more concentrated. These experimental findings could enhance
the understanding of social game behavior with the natural science rule ---
Maxent.


  Preference-based Reinforcement Learning (PbRL) is a paradigm in which an RL
agent learns to optimize a task using pair-wise preference-based feedback over
trajectories, rather than explicit reward signals. While PbRL has demonstrated
practical success in fine-tuning language models, existing theoretical work
focuses on regret minimization and fails to capture most of the practical
frameworks. In this study, we fill in such a gap between theoretical PbRL and
practical algorithms by proposing a theoretical reward-agnostic PbRL framework
where exploratory trajectories that enable accurate learning of hidden reward
functions are acquired before collecting any human feedback. Theoretical
analysis demonstrates that our algorithm requires less human feedback for
learning the optimal policy under preference-based models with linear
parameterization and unknown transitions, compared to the existing theoretical
literature. Specifically, our framework can incorporate linear and low-rank
MDPs with efficient sample complexity. Additionally, we investigate
reward-agnostic RL with action-based comparison feedback and introduce an
efficient querying algorithm tailored to this scenario.


  We discuss the science motivations and prospects for a joint analysis of
gravitational-wave (GW) and low-energy neutrino data to search for prompt
signals from nearby supernovae (SNe). Both gravitational-wave and low-energy
neutrinos are expected to be produced in the innermost region of a
core-collapse supernova, and a search for coincident signals would probe the
processes which power a supernova explosion. It is estimated that the current
generation of neutrino and gravitational-wave detectors would be sensitive to
Galactic core-collapse supernovae, and would also be able to detect
electromagnetically dark SNe. A joint GW-neutrino search would enable
improvements to searches by way of lower detection thresholds, larger distance
range, better live-time coverage by a network of GW and neutrino detectors, and
increased significance of candidate detections. A close collaboration between
the GW and neutrino communities for such a search will thus go far toward
realizing a much sought-after astrophysics goal of detecting the next nearby
supernova.


  The conclusion that the diffuse galaxy NGC1052-DF2 is deficient in dark
matter depends critically on the distance, as noted in the original publication
and subsequent works. The results of our preliminary assessment of the SBF
distance have already been referenced on the web. Here we present the details
of a more careful analysis, supply some context, and comment on the remaining
uncertainty.


  We revisit a classical crossword filling puzzle which already appeared in
Garey\&Jonhson's book. We are given a grid with $n$ vertical and horizontal
slots and a dictionary with $m$ words and are asked to place words from the
dictionary in the slots so that shared cells are consistent. We attempt to
pinpoint the source of intractability of this problem by taking into account
the structure of the grid graph, which contains a vertex for each slot and an
edge if two slots intersect. Our main approach is to consider the case where
this graph has a tree-like structure. Unfortunately, if we impose the common
rule that words cannot be reused, we show that the problem remains NP-hard even
under very severe structural restrictions. The problem becomes slightly more
tractable if word reuse is allowed, as we obtain an $m^{tw}$ algorithm in this
case, where $tw$ is the treewidth of the grid graph. However, even in this
case, we show that our algorithm cannot be improved. More strongly, we show
that under the ETH the problem cannot be solved in time $m^{o(k)}$, where $k$
is the number of horizontal slots of the instance.
  Motivated by these mostly negative results, we consider the much more
restricted case where the problem is parameterized by the number of slots $n$.
Here, we show that the problem becomes FPT, but the parameter dependence is
exponential in $n^2$. We show that this dependence is also justified: the
existence of an algorithm with running time $2^{o(n^2)}$ would contradict the
randomized ETH. Finally, we consider an optimization version of the problem,
where we seek to place as many words on the grid as possible. Here it is easy
to obtain a $\frac{1}{2}$-approximation, even on weighted instances. We show
that this algorithm is also likely to be optimal, as obtaining a better
approximation ratio in polynomial time would contradict the Unique Games
Conjecture.


  In the context of linear inverse problems, we propose and study a general
iterative regularization method allowing to consider large classes of
regularizers and data-fit terms. The algorithm we propose is based on a
primal-dual diagonal {descent} method. Our analysis establishes convergence as
well as stability results. Theoretical findings are complemented with numerical
experiments showing state of the art performances.


  The manifold which admits a genus-$2$ reducible Heegaard splitting is one of
the $3$-sphere, $\mathbb{S}^2 \times \mathbb{S}^1$, lens spaces and their
connected sums. For each of those manifolds except most lens spaces, the
mapping class group of the genus-$2$ splitting was shown to be finitely
presented. In this work, we study the remaining generic lens spaces, and show
that the mapping class group of the genus-$2$ Heegaard splitting is finitely
presented for any lens space by giving its explicit presentation. As an
application, we show that the fundamental groups of the spaces of the genus-$2$
Heegaard splittings of lens spaces are all finitely presented.


  This paper presents an efficient algorithm for the least-squares problem
using the point-to-plane cost, which aims to jointly optimize depth sensor
poses and plane parameters for 3D reconstruction. We call this least-squares
problem \textbf{Planar Bundle Adjustment} (PBA), due to the similarity between
this problem and the original Bundle Adjustment (BA) in visual reconstruction.
As planes ubiquitously exist in the man-made environment, they are generally
used as landmarks in SLAM algorithms for various depth sensors. PBA is
important to reduce drift and improve the quality of the map. However, directly
adopting the well-established BA framework in visual reconstruction will result
in a very inefficient solution for PBA. This is because a 3D point only has one
observation at a camera pose. In contrast, a depth sensor can record hundreds
of points in a plane at a time, which results in a very large nonlinear
least-squares problem even for a small-scale space. Fortunately, we find that
there exist a special structure of the PBA problem. We introduce a reduced
Jacobian matrix and a reduced residual vector, and prove that they can replace
the original Jacobian matrix and residual vector in the generally adopted
Levenberg-Marquardt (LM) algorithm. This significantly reduces the
computational cost. Besides, when planes are combined with other features for
3D reconstruction, the reduced Jacobian matrix and residual vector can also
replace the corresponding parts derived from planes. Our experimental results
verify that our algorithm can significantly reduce the computational time
compared to the solution using the traditional BA framework. Besides, our
algorithm is faster, more accuracy, and more robust to initialization errors
compared to the start-of-the-art solution using the plane-to-plane cost


  The geodesics of the Ellis-Bronnikov wormhole with two parameters are
studied. The asymmetric wormhole has only one light ring and one innermost
stable circular orbit located on one side of the wormhole throat. Consequently,
certain light rays can be reflected back by the wormhole. Additionally, the
same wormhole can have different appearances on both sides of the throat. We
present novel images of the wormhole with a light ring behind the throat in a
scenario with an accretion disk as the light source and in a backlit wormhole
scenario, which are distinct from the images of other compact objects and have
the potential to be observed.


  Social movements rely in large measure on networked communication
technologies to organize and disseminate information relating to the movements'
objectives. In this work we seek to understand how the goals and needs of a
protest movement are reflected in the geographic patterns of its communication
network, and how these patterns differ from those of stable political
communication. To this end, we examine an online communication network
reconstructed from over 600,000 tweets from a thirty-six week period covering
the birth and maturation of the American anticapitalist movement, Occupy Wall
Street. We find that, compared to a network of stable domestic political
communication, the Occupy Wall Street network exhibits higher levels of
locality and a hub and spoke structure, in which the majority of non-local
attention is allocated to high-profile locations such as New York, California,
and Washington D.C. Moreover, we observe that information flows across state
boundaries are more likely to contain framing language and references to the
media, while communication among individuals in the same state is more likely
to reference protest action and specific places and and times. Tying these
results to social movement theory, we propose that these features reflect the
movement's efforts to mobilize resources at the local level and to develop
narrative frames that reinforce collective purpose at the national level.


  Researchers from a growing range of fields and industries rely on
public-access census data. These data are altered by census-taking agencies to
minimize the risk of identification; one such disclosure avoidance measure is
the data swapping procedure. I study the effects of data swapping on
contingency tables using a dummy dataset, public-use American Community Survey
(ACS) data, and restricted-use ACS data accessed within the U.S.\ Census
Bureau. These simulations demonstrate that as the rate of swapping is varied,
the effect on joint distributions of categorical variables is no longer
understandable when the data swapping procedure attempts to target at-risk
individuals for swapping using a simple targeting criterion.


  These notes contain the written version of lectures given at the 2009 Les
Houches Summer School "Modern perspectives in lattice QCD: Quantum field theory
and high performance computing." The goal is to provide a pedagogical
introduction to the subject, and not a comprehensive review. Topics covered
include a general introduction, the inclusion of scaling violations in chiral
perturbation theory, partial quenching and mixed actions, chiral perturbation
theory with heavy kaons, and the effects of finite volume, both in the p- and
epsilon-regimes.


  We discover an explicit expansion formula for the powers $s$ of the Euler
Product (or Dedekind $\eta$-function) in terms of hook lengths of partitions,
where the exponent $s$ is any complex number. Several classical formulas have
been derived for certain integers $s$ by Euler, Jacobi, Klein, Fricke, Atkin,
Winquist, Dyson and Macdonald. In particular, Macdonald obtained expansion
formulas for the integer exponents $s$ for which there exists a semi-simple Lie
algebra of dimension $s$. For the type $A_l^{(a)}$ he has expressed the
$(t^2-1)$-st power of the Euler Product as a sum of weighted integer vectors of
length $t$ for any integer $t$. Kostant has considered the general case for any
positive integer $s$ and obtained further properties.
  -----
  The present paper proposes a new approach. We convert the weighted vectors of
length $t$ used by Macdonald in his identity for type $A_l^{(a)}$ to weighted
partitions with free parameter $t$, so that a new identity on the latter
combinatorial structures can be derived without any restrictions on $t$. The
surprise is that the weighted partitions have a very simple form in terms of
hook lengths of partitions. As applications of our formula, we find some new
identities about hook lengths, including the "marked hook formula". We also
improve a result due to Kostant. The proof of the Main Theorem is based on
Macdonald's identity for $A_l^{(a)}$ and on the properties of a bijection
between $t$-cores and integer vectors constructed by Garvan, Kim and Stanton.


  We propose a procedure to identify and classify genuine tripartite
entanglement in pure 3-qubit states via the Activated Bipartite Entanglement
(ABE), which is defined here as the difference between the Entanglement of
Assistance and the Entanglement of Formation. We show that for pure states
belonging to one of the two inequivalent classes of genuine tripartite
entanglement, i.e., GHZ or W states, the ABE is always greater than zero. For
separable and biseparable states it is always null. In addition, our approach
is capable to distinguish between genuine tripartite entangled states, those
belonging to the GHZ class from those belonging to the W class. We also present
an experimental proposal, by using linear optical circuits and internal degrees
of freedom of a single photon, to measure the ABE and to verify the
characterization via activated entanglement. The circuit simulation shows an
excellent agreement with theoretical prediction for a wide class of GHZ and W
states.


  In this article, we first establish the theory of optimal scores for speaker
recognition. Our analysis shows that the minimum Bayes risk (MBR) decisions for
both the speaker identification and speaker verification tasks can be based on
a normalized likelihood (NL). When the underlying generative model is a linear
Gaussian, the NL score is mathematically equivalent to the PLDA likelihood
ratio, and the empirical scores based on cosine distance and Euclidean distance
can be seen as approximations of this linear Gaussian NL score under some
conditions. We discuss a number of properties of the NL score and perform a
simple simulation experiment to demonstrate the properties of the NL score.


  We study the LFV Higgs production processes
$e^-\gamma\to\ell^-\phi\;(\ell=\mu,\tau; \phi=H, A)$ as a probe of Higgs
mediated LFV couplings at an electron-photon collider, where $H$ and $A$ are
extra CP even and odd Higgs bosons, respectively, in the two Higgs doublet
model. Under the constraints from the current data of muon and tau rare decay,
the cross section can be significantly large. It would improve the experimental
upper bounds on the effective LFV coupling constants. In addition, the
chirality nature of the LFV Higgs coupling constants can be measured by
selecting electron beam polarizations.


  We study measurement of the CP property of the Higgs boson at a photon linear
collider. One method where we take advantage of interference between
Higgs-production and background amplitudes is proposed. A broad peak of the
photon energy spectrum is helpful in observing the energy dependence of the
interference effects. Numerical results for the process $\gamma \gamma \to t
\bar{t}$ are shown as an example.


  We present the effects of nonlinear corrections to the single differential
cross section d\sigma/dQ^2 and the reduced cross section \sigma_r (x,Q^2) for
the neutral current (NC) e-p scattering at the leading order (LO) and the
next-to-leading order (NLO) approximations in perturbative quantum chromo
dynamics (QCD). Technically, based on the double Laplace transform method, we
first derive the effects of the nonlinear corrections to the proton structure
functions F2(x,Q^2) and FL(x,Q^2) and consequently obtain the corresponding
single differential and reduced cross sections. Our results clearly indicate
the consistency of the nonlinear behavior of the quark and gluon distributions
at low x values. Our numerical results ( obtained in a range of the virtuality
8.5 < Q2 < 5000 GeV ^2 and the Bjorken scale 10^(-5)< x < 1) show that the
effects of these nonlinear corrections to the proton structure functions are
more noticeable at x < 0.001 and, to some extent, control the incremental trend
of these functions at low x values. Moreover, a comparison of our numerical
results of the single differential and reduced cross sections at the NLO
approximations with those of H1 collaboration data shows that the nonlinear
corrections increase the accuracy of calculations rather than the linear
calculations at low to moderate Q^2 values for low x values.


  We propose magnetic quivers for partial implosion spaces. Such partial
implosions involve a choice of parabolic subgroup, with the Borel subgroup
corresponding to the standard implosion. In the subregular case we test the
conjecture by verifying that reduction by the Levi group gives the appropriate
nilpotent orbit closure. In the case of a parabolic corresponding to a hook
diagram we are also able to carry out this verification provided we work at
nonzero Fayet-Iliopoulos parameters.


  We obtain new lower bounds of the minimal genus of a locally flat surface
representing a 2-dimensional homology class in a topological 4-manifold with
boundary, using the von Neumann-Cheeger-Gromov $\rho$-invariant. As an
application our results are employed to investigate the slice genus of knots.
We illustrate examples with arbitrarily large slice genus for which our lower
bound is optimal but all previously known invariants vanish.


  In these notes we study the duality between sigma-models and Toda QFT's. We
claim that $\mathfrak{gl}(n|n)$ affine Toda field theory behaves in the strong
coupling limit as $\eta-$deformed $\mathbb{CP}(n-1)$ sigma-model plus a free
field.


  We consider the problem of designing distribution rules to share "welfare"
(cost or revenue) among individually strategic agents. There are many known
distribution rules that guarantee the existence of a (pure) Nash equilibrium in
this setting, e.g., the Shapley value and its weighted variants; however, a
characterization of the space of distribution rules that guarantee the
existence of a Nash equilibrium is unknown. Our work provides an exact
characterization of this space for a specific class of scalable and separable
games, which includes a variety of applications such as facility location,
routing, network formation, and coverage games. Given arbitrary local welfare
functions W, we prove that a distribution rule guarantees equilibrium existence
for all games (i.e., all possible sets of resources, agent action sets, etc.)
if and only if it is equivalent to a generalized weighted Shapley value on some
"ground" welfare functions W', which can be distinct from W. However, if
budget-balance is required in addition to the existence of a Nash equilibrium,
then W' must be the same as W. We also provide an alternate characterization of
this space in terms of "generalized" marginal contributions, which is more
appealing from the point of view of computational tractability. A possibly
surprising consequence of our result is that, in order to guarantee equilibrium
existence in all games with any fixed local welfare functions, it is necessary
to work within the class of potential games.


  Deep neural networks can generate images that are astonishingly realistic, so
much so that it is often hard for humans to distinguish them from actual
photos. These achievements have been largely made possible by Generative
Adversarial Networks (GANs). While deep fake images have been thoroughly
investigated in the image domain - a classical approach from the area of image
forensics - an analysis in the frequency domain has been missing so far. In
this paper, we address this shortcoming and our results reveal that in
frequency space, GAN-generated images exhibit severe artifacts that can be
easily identified. We perform a comprehensive analysis, showing that these
artifacts are consistent across different neural network architectures, data
sets, and resolutions. In a further investigation, we demonstrate that these
artifacts are caused by upsampling operations found in all current GAN
architectures, indicating a structural and fundamental problem in the way
images are generated via GANs. Based on this analysis, we demonstrate how the
frequency representation can be used to identify deep fake images in an
automated way, surpassing state-of-the-art methods.


  A strongly coupled ultracold plasma can be used as an excellent test platform
for studying many-body interactions associated with various plasma phenomena.
In this paper we discuss an approach that makes possible creation of the
steady-state ultracold plasma having various densities and temperatures by
means of continuous two-step optical excitation of calcium atoms in the MOT.
The parameters of the plasma are studied using laser-induced fluorescence of
calcium ions. The experimental results are well described by a simple
theoretical model involving equilibration of the continuous source of charged
particles by the hydrodynamical ion outflux and three-body recombination. The
strongly coupled plasma with the peak ion density of $6\cdot10^5$ cm$^{-3}$ and
the minimum electron temperature near 2 K has been prepared. Our steady-state
approach in combination with the strong magnetic confinement of the plasma will
make it possible to reach extremely strong coupling in such system.


  The operation of water distribution networks is a complex procedure aimed at
efficiently delivering consumers with adequate water quantity while ensuring
its safe quality. An added challenge is the dependency of the water quality
dynamics on the system's hydraulics, which influences the performance of the
water quality controller. Prior research has addressed either solving the
optimum operational hydraulic setting problem or regulating the water quality
dynamics as separate problems. Additionally, there have been efforts to couple
these two problems and solve one compact problem resulting in trade-offs
between the contradictory objectives. In contrast, this paper takes a novel
approach by examining the water quality dependency on the hydraulics from a
control-theoretic standpoint. More specifically, we explore the influence of
accountability for water quality controllability improvement when addressing
the pump scheduling problem. We examine its effects on the cumulative cost of
the interconnected systems as well as the subsequent performance of the water
quality controller. To achieve this, we develop a framework that incorporates
different controllability metrics within the operational hydraulic optimization
problem; its aim is attaining an adequate level of water quality control across
the system. We assess the aforementioned aspects' performance on various scaled
networks with a wide range of numerical scenarios.


  We consider a novel class of $f(\R)$ gravity theories where the connection is
related to the conformally scaled metric $\hat g_{\mu\nu}=C(\R)g_{\mu\nu}$ with
a scaling that depends on the scalar curvature $\R$ only. We call them
C-theories and show that the Einstein and Palatini gravities can be obtained as
special limits. In addition, C-theories include completely new physically
distinct gravity theories even when $f(\R)=\R$. With nonlinear $f(\R)$,
C-theories interpolate and extrapolate the Einstein and Palatini cases and may
avoid some of their conceptual and observational problems. We further show that
C-theories have a scalar-tensor formulation, which in some special cases
reduces to simple Brans-Dicke-type gravity. If matter fields couple to the
connection, the conservation laws in C-theories are modified. The stability of
perturbations about flat space is determined by a simple condition on the
lagrangian.


  Process mining has become one of the best programs that can outline the event
logs of production processes in visualized detail. We have addressed the
important problem that easily occurs in the industrial process called
Bottleneck. The analysis process was focused on extracting the bottlenecks in
the production line to improve the flow of production. Given enough stored
history logs, the field of process mining can provide a suitable answer to
optimize production flow by mitigating bottlenecks in the production stream.
Process mining diagnoses the productivity processes by mining event logs, this
can help to expose the opportunities to optimize critical production processes.
We found that there is a considerable bottleneck in the process because of the
weaving activities. Through discussions with specialists, it was agreed that
the main problem in the weaving processes, especially machines that were
exhausted in overloading processes. The improvement in the system has measured
by teamwork; the cycle time for process has improved to 91%, the worker's
performance has improved to 96%,product quality has improved by 85%, and lead
time has optimized from days and weeks to hours.


  We consider the luminous blue variable (LBV) star V532 in M33, also known as
Romano's star, in two different spectral states: in the optical minimum of
2007/2008 and during a local brightening in 2005. Optical spectra of low and
moderate resolution are modelled using the non-LTE model atmosphere code
CMFGEN. All the observed properties of the object in the minimum are well
described by a late nitrogen-sequence Wolf-Rayet (WN) star model with
relatively high hydrogen abundance (H/He=1.9), while the spectrum during the
outburst corresponds to the spectral class WN11 and is similar to the spectrum
of P Cyg. The atmosphere is enriched in nitrogen by about a factor of 6 in both
states. Most of the heavy element abundances are consistent with the chemical
composition of M33. Bolometric luminosity is shown to vary between the two
states by a factor of ~1.5. This makes V532 another example of an LBV that
shows variations in its bolometric luminosity during an outburst.


  We consider decidability problems associated with Engel's identity
($[\cdots[[x,y],y],\dots,y]=1$ for a long enough commutator sequence) in groups
generated by an automaton. We give a partial algorithm that decides, given
$x,y$, whether an Engel identity is satisfied. It succeeds, importantly, in
proving that Grigorchuk's $2$-group is not Engel. We consider next the problem
of recognizing Engel elements, namely elements $y$ such that the map
$x\mapsto[x,y]$ attracts to $\{1\}$. Although this problem seems intractable in
general, we prove that it is decidable for Grigorchuk's group: Engel elements
are precisely those of order at most $2$. Our computations were implemented
using the package FR within the computer algebra system GAP.


  A general method using multipliers for finding the conserved integrals for
any system of partial differential equations (PDEs) is reviewed and further
developed in several ways. Multipliers are expressions whose (summed) product
with a PDE (system) yields a local divergence identity which has the physical
meaning of a continuity equation involving a conserved density and a spatial
flux for solutions of the PDE (system). On spatial domains, the integral form
of a continuity equation yields a conserved integral. When a PDE (system) is
variational, multipliers correspond to symmetries of the variational principle,
and the local divergence identity relating a multiplier to a conserved integral
is the same as the variational identity used in Noether's theorem for
connecting conserved integrals to invariance of a variational principle. From
this viewpoint, the multiplier method is shown to constitute a modern form of
Noether's theorem in which the variational principle is not used. When a PDE
(system) is non-variational, multipliers are shown to be an adjoint counterpart
to symmetries, and the local divergence identity relating a multiplier to a
conserved integral is shown to be an adjoint generalization of the variational
identity underling Noether's theorem. Two main results are established for PDE
systems having a solved-form for leading derivatives, which encompasses all
typical PDEs of physical interest. First, all non-trivial conserved integrals
are shown to arise from non-trivial multipliers in a one-to-one manner, taking
into account certain equivalence freedoms. Second, a scaling formula based on
dimensional analysis is derived to obtain the conserved density and spatial
flux in any conserved integral, just using the corresponding multiplier and the
given PDE system. The derivations use a few basic tools from variational
calculus, for which a self-contained formulation is provided.


  Self-supervised pre-training appears as an advantageous alternative to
supervised pre-trained for transfer learning. By synthesizing annotations on
pretext tasks, self-supervision allows to pre-train models on large amounts of
pseudo-labels before fine-tuning them on the target task. In this work, we
assess self-supervision for the diagnosis of skin lesions, comparing three
self-supervised pipelines to a challenging supervised baseline, on five test
datasets comprising in- and out-of-distribution samples. Our results show that
self-supervision is competitive both in improving accuracies and in reducing
the variability of outcomes. Self-supervision proves particularly useful for
low training data scenarios ($<1\,500$ and $<150$ samples), where its ability
to stabilize the outcomes is essential to provide sound results.


  Let H be a spherical subgroup of minimal rank of the semisimple simply
connected complex algebraic group G. We define some functions on the
homogeneous space G/H that we call generalised spherical minors. When G = H x
H, we recover Fomin-Zelevinsky generalised minors. We prove that generalised
spherical minors satisfy some integer coefficients polynomial relations, that
extend the identities of classical generalised minors due to Fomin and
Zelevinsky, and that have the shape of exchange relations of LP-algebras.


  For a proper local embedding between two Deligne--Mumford stacks Y and X, we
find, under certain mild conditions, a new (possibly non-separated)
Deligne--Mumford stack X', with an etale, surjective and universally closed map
to the target X, and whose fiber product with the image of the local embedding
is a finite union of stacks with corresponding etale, surjective and
universally closed maps to Y. Moreover, a natural set of weights on the
substacks of X' allows the construction of a universally closed push-forward,
and thus a comparison between the Chow groups of X' and X. We apply the
construction above to the computation of the Chern classes of a weighted
blow-up along a regular local embedding via deformation to a weighted normal
cone and localization. We describe the stack X' in the case when X is the
moduli space of stable maps with local embeddings at the boundary. We apply the
methods above to find the Chern classes of the stable map spaces.


  The objective of this paper is to obtain asymptotic results for shifted sums
of multiplicative functions of the form $g \ast 1$, where the function $g$
satisfies the Ramanujan conjecture and has conjectured upper bounds on square
moments of its L-function. We establish that for $H$ within the range
$X^{1-2\varepsilon} \leq H \leq X^{1-\varepsilon}$, there exist constants
$B_{f,h}$ such that $$ \sum_{X\leq n \leq 2X}
f(n)f(n+h)-B_{f,h}X=O_{f,\varepsilon}\big(X^{1-\varepsilon/2}\big)$$ for all
but $O_{f,\varepsilon}\big(HX^{-1/44+6\varepsilon+o(1)}\big)$ integers $h \in
[1,H].$ Additionally, we establish power-saving error terms for almost all
integers $h$ in $[1, H]$ when $X^{87/88+7\varepsilon} \leq H \leq
X^{1-\varepsilon}$ and apply them to deduce mean-value estimates of long
Dirichlet polynomials. Our method is based on the Hardy-Littlewood circle
method. In order to treat minor arcs, we use the convolution structure and a
cancellation of $g(n)$ that are additively twisted, applying some arguments
from a paper of Matom\"a{}ki, Radziwi\l{}\l{} and Tao.


  We present the photometry of 16 91T/99aa-like Type Ia Supernovae (SNe Ia)
observed by the Las Cumbres Observatory. We also use an additional set of 21
91T/99aa-like SNe Ia and 87 normal SNe Ia from the literature for an analysis
of the standardizability of the luminosity of 91T/99aa-like SNe. We find that
91T/99aa-like SNe are 0.2 mag brighter than normal SNe Ia, even when fully
corrected by the light curve shapes and colors. The weighted root-mean-square
of 91T/99aa-like SNe (with $z_{CMB}>0.01$) Hubble residuals is $0.25\pm0.03$
mag, suggesting that 91T/99aa-like SNe are also excellent relative distance
indicators to $\pm$12%. We compare the Hubble residuals with the
pseudo-equivalent width (pEW) of Si II $\lambda\lambda$6355 around the date of
maximum brightness. We find that there is a broken linear correlation in
between those two measurements for our sample including both 91T/99aa-like and
normal SNe Ia. As the $pEW_{max}$(Si II $\lambda\lambda$6355) increasing, the
Hubble residual increases when $pEW_{max}$(Si II $\lambda\lambda$6355)$<55.6$
\r{A}. However, the Hubble residual stays constant beyond this. Given that
91T/99aa-like SNe possess shallower Si II lines than normal SNe Ia, the linear
correlation at $pEW_{max}$(Si II $\lambda\lambda$6355)$<55.6$ \r{A} can account
for the overall discrepancy of Hubble residuals derived from the two subgroups.
Such a systematic effect needs to be taken into account when using SNe Ia to
measure luminosity distances.


  We discuss the problem of construction of inference procedures which can
manipulate with uncertainties measured in ordinal scales and fulfill to the
property of strict monotonicity of conclusion. The class of A-valuations of
plausibility is considered where operations based only on information about
linear ordering of plausibility values are used. In this class the modus ponens
generating function fulfiling to the property of strict monotonicity of
conclusions is introduced.


  DIAL will enable users to analyze very large, event-based datasets using an
application that is natural to the data format. Both the dataset and the
processing may be distributed over a farm, a site (collection of farms) or a
grid (collection of sites). Here we describe the goals of the project, the
current design and implementation, and plans for future development. DIAL is
being developed within PPDG to understand the requirements that interactive
analysis places on the grid and within ATLAS to enable distributed interactive
analysis of event data.


  The large localized CP asymmetries observed by LHCb in three-body charmless
decays of $B$ mesons brings new challenge for experimentalists and their
traditional models to fit data. With higher statistics, rescattering and
three-body effects, previously ignored on data analysis, become more visible.
The time is ripe to use better theoretical assumptions as an ingredient in
order to improve the analysis. In this paper we address the issue of
rescattering effects in the charmless three-body decays of $B$ mesons. In
particular, we study the case of the $B^+ \to \pi^-\pi^+\pi^+$ decay and show
that the presence of hadronic loops shifts the P-wave phase near threshold to
below zero, and modify the position of the $\rho$-meson peak and it width, in
the Dalitz plot.


  We introduce higher order mean curvatures of screen almost conformal (SAC)
half-lightlike submanifolds of indefinite contact manifolds, admitting a
semi-symmetric non-metric connection, and use them to generalize some known
results of [6]. Also, we derive a new set of integration formulae via the
divergence of some special vector fields tangent to this submanifold. Several
examples are also included to illustrate the main concepts.


  The problem of the spreading of a granular mass released at the top of a
rough inclined plane was investigated. We experimentally measure the evolution
of the avalanche from the initiation up to the deposit using a Moir\'e image
processing technique. The results are quantitatively compared with the
prediction of an hydrodynamic model based on depth averaged equations. In the
model, the interaction between the flowing layer and the rough bottom is
described by a non trivial friction force whose expression is derived from
measurements on steady uniform flows. We show that the spreading of the mass is
quantitatively predicted by the model when the mass is released on a plane free
of particles. When an avalanche is triggered on an initially static layer, the
model fails in quantitatively predicting the propagation but qualitatively
captures the evolution.