  Spin glasses are paradigmatic models that deliver concepts relevant for a
variety of systems. However, rigorous analytical results are difficult to
obtain for spin-glass models, in particular for realistic short-range models.
Therefore large-scale numerical simulations are the tool of choice. Concepts
and algorithms derived from the study of spin glasses have been applied to
diverse fields in computer science and physics. In this work a one-dimensional
long-range spin-glass model with power-law interactions is discussed. The model
has the advantage over conventional systems in that by tuning the power-law
exponent of the interactions the effective space dimension can be changed thus
effectively allowing the study of large high-dimensional spin-glass systems to
address questions as diverse as the existence of an Almeida-Thouless line,
ultrametricity and chaos in short range spin glasses. Furthermore, because the
range of interactions can be changed, the model is a formidable test-bed for
optimization algorithms.


  The present study examines the linear instability characteristics of
double-diffusive mixed convective flow in a vertical channel with viscosity
stratification. The viscosity of the fluid is modelled as an exponential
function of temperature and concentration, with an activation energy parameter
determining its sensitivity to temperature variation. Three scenarios are
considered: buoyancy force due to thermal diffusion only, buoyancy force due to
temperature and solute acting in the same direction, and buoyancy force due to
temperature and solute acting in opposite directions. A generalized eigenvalue
problem is derived and solved numerically for linear stability analysis via the
Chebyshev spectral collocation method. Results indicate that higher values of
the activation energy parameter lead to increased flow stability. Additionally,
when both buoyant forces act in opposite directions, the Schmidt number has
both stabilizing and destabilizing effects across the range of activation
energy parameters, similar to the case of pure thermal diffusion. Furthermore,
the solutal-buoyancy-opposed base flow is found to be the most stable, while
the solutal-buoyancy-assisted base flow is the least stable. As expected, an
increase in Reynolds number is shown to decrease the critical Rayleigh number.


  Rigid body with rotors is a widespread mechanical system modeled after the
direct product $SO(3)\times S^1\times S^1\times S^1$, which under mild
assumptions is the symmetry group of the system. In this paper, the authors
present and compare different Lagrangian reduction procedures: Euler-Poincar\'e
reduction by the whole group and reduction by stages in different orders or
using different connections. The exposition keeps track of the equivalence of
equations as well as corresponding conservation laws.


  SXP 1062 is a Be X-ray binary located in the Small Magellanic Cloud. It hosts
a long-period X-ray pulsar and is likely associated with the supernova remnant
MCSNR J0127-7332. In this work we present a multi-wavelength view on SXP 1062
in different luminosity regimes. We consider monitoring campaigns in optical
(OGLE survey) and X-ray (SWIFT telescope). During these campaigns a tight
coincidence of X-ray and optical outbursts is observed. We interpret this as
typical Type I outbursts as often detected in Be X-ray binaries at periastron
passage of the neutron star. To study different X-ray luminosity regimes in
depth, during the source quiescence we observed it with XMM-Newton while
Chandra observations followed an X-ray outburst. Nearly simultaneously with
Chandra observations in X-rays, in optical the RSS/SALT telescope obtained
spectra of SXP 1062. On the basis of our multi-wavelength campaign we propose a
simple scenario where the disc of the Be star is observed face-on, while the
orbit of the neutron star is inclined with respect to the disc. According to
the model of quasi-spherical settling accretion our estimation of the magnetic
field of the pulsar in SXP 1062 does not require an extremely strong magnetic
field at the present time.


  We prove that arbitrary correlation functions of the H(3)+ model on a sphere
have a simple expression in terms of Liouville theory correlation functions.
This is based on the correspondence between the KZ and BPZ equations, and on
relations between the structure constants of Liouville theory and the H(3)+
model. In the critical level limit, these results imply a direct link between
eigenvectors of the Gaudin Hamiltonians and the problem of uniformization of
Riemann surfaces. We also present an expression for correlation functions of
the SL(2)/U(1) coset model in terms of correlation functions in Liouville
theory.


  We report on two optical realizations of the $1 \to 2$ asymmetric
phase-covariant cloning machines for polarization states of single photons. The
experimental setups combine two-photon interference and tunable polarization
filtering that enables us to control the asymmetry of the cloners. The first
scheme involves a special unbalanced bulk beam splitter exhibiting different
splitting ratios for vertical and horizontal polarizations, respectively. The
second implemented scheme consists of a balanced fiber coupler where photon
bunching occurs, followed by a free-space part with polarization filters. With
this later approach we were able to demonstrate very high cloning fidelities
which are above the universal cloning limit.


  Aims: In this work, we discuss a way to combine High Dispersion Spectroscopy
and High Contrast Imaging (HDS+HCI). For a planet located at a resolvable
angular distance from its host star, the starlight can be reduced up to several
orders of magnitude using adaptive optics and/or coronography. In addition, the
remaining starlight can be filtered out using high-dispersion spectroscopy,
utilizing the significantly different (or Doppler shifted) high-dispersion
spectra of the planet and star. In this way, HDS+HCI can in principle reach
contrast limits of ~1e-5 x 1e-5, although in practice this will be limited by
photon noise and/or sky-background.
  Methods: We present simulations of HDS+HCI observations with the E-ELT, both
probing thermal emission from a planet at infrared wavelengths, and starlight
reflected off a planet atmosphere at optical wavelengths. For the infrared
simulations we use the baseline parameters of the E-ELT and METIS instrument,
with the latter combining extreme adaptive optics with an R=100,000 IFS. We
include realistic models of the adaptive optics performance and atmospheric
transmission and emission. For the optical simulation we also assume R=100,000
IFS with adaptive optics capabilities at the E-ELT.
  Results: One night of HDS+HCI observations with the E-ELT at 4.8 um (d_lambda
= 0.07 um) can detect a planet orbiting alpha Cen A with a radius of R=1.5
R_earth and a twin-Earth thermal spectrum of T_eq=300 K at a signal-to-noise
(S/N) of 5. In the optical, with a Strehl ratio performance of 0.3, reflected
light from an Earth-size planet in the habitable zone of Proxima Centauri can
be detected at a S/N of 10 in the same time frame. Recently, first HDS+HCI
observations have shown the potential of this technique by determining the
spin-rotation of the young massive exoplanet beta Pictoris b. [abridged]


  This paper describes a study based on computational fluid dynamics (CFD) and
deep neural networks that focusing on predicting the flow field in differently
distorted U-shaped pipes. The main motivation of this work was to get an
insight about the justification of the deep learning paradigm in hydrodynamic
hull optimisation processes that heavily depend on computing turbulent flow
fields and that could be accelerated with models like the one presented. The
speed-up can be even several orders of magnitude by surrogating the CFD model
with a deep convolutional neural network. An automated geometry creation and
evaluation process was set up to generate differently shaped two-dimensional
U-bends and to carry out CFD simulation on them. This process resulted in a
database with different geometries and the corresponding flow fields
(2-dimensional velocity distribution), both represented on 128x128 equidistant
grids. This database was used to train an encoder-decoder style deep
convolutional neural network to predict the velocity distribution from the
geometry. The effect of two different representations of the geometry (binary
image and signed distance function) on the predictions was examined, both
models gave acceptable predictions with a speed-up of two orders of magnitude.


  Aims: I test the ejection scenario of formation of brown dwarfs and very
low-mass stars through the detection of a very wide ultracool binary.
  Methods: LEHPM 494 (M6.0 +/- 1.0 V) and DENIS-P J0021.0-4244 (M9.5 +/- 0.5 V)
are separated by 1.3 arcmin and are high proper motion co-moving ultracool
stars. I have used six astrometric epochs spaced 22 years to confirm their
common tangential velocity.
  Results: The angular separation between both low-mass stars keeps constant
with an uncertainty less than 0.1 %. I have also derived their most probable
heliocentric distance (23 +/- 2 pc), age interval (2-10 Ga) and masses (0.103
+/- 0.006 and 0.079 +/- 0.004 Msol). The pair, with a projected physical
separation of 1800 +/- 170 AU, is by far the widest ultracool binary ever found
in the field.
  Conclusions: This serendipitous and simple detection is inconsistent with
ultra low-mass formation ejection scenarios and complements current searches of
low-mass tight binaries.


  Density of states, dynamic (optical) conductivity and phase diagram of
strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model
are analyzed within the generalized dynamical mean field theory (DMFT+\Sigma
approximation). Strong correlations are accounted by DMFT, while disorder is
taken into account via the appropriate generalization of self-consistent theory
of localization. The DMFT effective single impurity problem is solved by
numerical renormalization group (NRG) and we consider the three-dimensional
system with semi-elliptic density of states. Correlated metal, Mott insulator
and correlated Anderson insulator phases are identified via the evolution of
density of states and dynamic conductivity, demonstrating both Mott-Hubbard and
Anderson metal-insulator transition and allowing the construction of complete
zero-temperature phase diagram of Anderson-Hubbard model. Rather unusual is the
possibility of disorder induced Mott insulator to metal transition.


  With the rapid development of large language models (LLMs) and ever-evolving
practical requirements, finding an efficient and effective alignment method has
never been more critical. However, the tension between the complexity of
current alignment methods and the need for rapid iteration in deployment
scenarios necessitates the development of a model-agnostic alignment approach
that can operate under these constraints. In this paper, we introduce Aligner,
a novel and simple alignment paradigm that learns the correctional residuals
between preferred and dispreferred answers using a small model. Designed as a
model-agnostic, plug-and-play module, Aligner can be directly applied to
various open-source and API-based models with only one-off training, making it
suitable for rapid iteration. Notably, Aligner can be applied to any powerful,
large-scale upstream models. Moreover, it can even iteratively bootstrap the
upstream models using corrected responses as synthetic human preference data,
breaking through the model's performance ceiling. Our experiments demonstrate
performance improvements by deploying the same Aligner model across 11
different LLMs, evaluated on the 3H dimensions (helpfulness, harmlessness, and
honesty). Specifically, Aligner-7B has achieved an average improvement of 68.9%
in helpfulness and 23.8% in harmlessness across the tested LLMs while also
effectively reducing hallucination. In the Alpaca-Eval leaderboard, stacking
Aligner-2B on GPT-4 Turbo improved its LC Win Rate from 55.0% to 58.3%,
surpassing GPT-4 Omni's 57.5% Win Rate (community report).


  We determine the power spectrum for inflation models covering all regimes
from cold (isentropic) to warm (nonisentropic) inflation. We work in the
context of the stochastic inflation approach, which can nicely describe both
types of inflationary regimes concomitantly. A throughout analysis is carried
out to determine the allowed parameter space for simple single field polynomial
chaotic inflation models that is consistent with the most recent cosmological
data from the nine-year Wilkinson Microwave Anisotropy Probe (WMAP) and in
conjunction with other observational cosmological sources. We present the
results for both the amplitude of the power spectrum, the spectral index and
for the tensor to scalar curvature perturbation amplitude ratio. We briefly
discuss cases when running is present. Despite single field polynomial-type
inflaton potential models be strongly disfavored, or even be already ruled out
in their simplest versions in the case of cold inflation, this is not the case
for nonisentropic inflation models in general (warm inflation in particular),
though higher order polynomial potentials (higher than quartic order) tend to
become less favorable also in this case, presenting a much smaller region of
parameter space compatible with the recent observational cosmological data. Our
findings also remain valid in face of the recently released Planck results.


  Let $G$ be a graph of maximum degree $\Delta$ and $k$ be an integer. The
$k$-recolouring graph of $G$ is the graph whose vertices are $k$-colourings of
$G$ and where two $k$-colourings are adjacent if they differ at exactly one
vertex. It is well-known that the $k$-recolouring graph is connected for $k\geq
\Delta+2$. Feghali, Johnson and Paulusma [Journal of Graph Theory,
83(4):340--358] showed that the $(\Delta+1)$-recolouring graph is composed by a
unique connected component of size at least $2$ and (possibly many) isolated
vertices.
  In this paper, we study the proportion of isolated vertices (also called
frozen colourings) in the $(\Delta+1)$-recolouring graph. Our main contribution
is to show that, if $G$ is connected, the proportion of frozen colourings of
$G$ is exponentially smaller than the total number of colourings. This
motivates the study of the Glauber dynamics on $(\Delta+1)$-colourings. In
contrast to the conjectured mixing time for $k\geq \Delta+2$ colours, we show
that the mixing time of the Glauber dynamics for $(\Delta+1)$-colourings can be
of quadratic order. Finally, we prove some results about the existence of
graphs with large girth and frozen colourings, and study frozen colourings in
random regular graphs.


  We investigate in detail the critical $N{=}2$ fermionic string with and
without a global ${\bf Z}_2$ twist. An analysis of BRST cohomology shows that
twisted sectors contain massless `spacetime' fermions which are {\it
non-local\/} with respect to the standard massless boson. However, two distinct
GSO projections exist, one (untwisted) retaining merely the usual boson and its
spectral-flow partner, the other (twisted) yielding two fermions and one boson,
on the massless level. The corresponding chiral BRST-invariant vertex operators
are constructed in certain pictures, and their fusion and picture-changing are
investigated, including the construction of inverse picture-changing operators.
The $N{=}2$ `spacetime supersymmetry' generators are {\it null\/} operators,
since the twisted massless states fail to interact. The untwisted three- and
four-point functions are recalculated at tree-level.


  The potential during inflation must be very flat in, at least, the direction
of the inflaton. In renormalizable global supersymmetry, flat directions are
ubiquitous, but they are not preserved in a generic supergravity theory. It is
known that at least some of them are preserved in no-scale supergravity, and
simple generalizations of it. We here study a more realistic generalization,
based on string-derived supergravity, using the linear supermultiplet formalism
for the dilaton. We consider a general class of hybrid inflation models, where
a Fayet-Illiopoulos $D$ term drives some fields to large values. The potential
is dominated by the $F$ term, but flatness is preserved in some directions.
This allows inflation, with the dilaton stabilized in its domain of attraction,
and some moduli stabilized at their vacuum values. Another modulus may be the
inflaton.


  A deep survey of the Large Magellanic Cloud at ~0.1-100TeV photon energies
with the Cherenkov Telescope Array is planned. We assess the detection
prospects based on a model for the emission of the galaxy, comprising the four
known TeV emitters, mock populations of sources, and interstellar emission on
galactic scales. We also assess the detectability of 30 Doradus and SN 1987A,
and the constraints that can be derived on the nature of dark matter. The
survey will allow for fine spectral studies of N157B, N132D, LMC P3, and 30
Doradus C, and half a dozen other sources should be revealed, mainly
pulsar-powered objects. The remnant from SN 1987A could be detected if it
produces cosmic-ray nuclei with a flat power-law spectrum at high energies, or
with a steeper index 2.3-2.4 pending a flux increase by a factor >3-4 over
~2015-2035. Large-scale interstellar emission remains mostly out of reach of
the survey if its >10GeV spectrum has a soft photon index ~2.7, but
degree-scale 0.1-10TeV pion-decay emission could be detected if the cosmic-ray
spectrum hardens above >100GeV. The 30 Doradus star-forming region is
detectable if acceleration efficiency is on the order of 1-10% of the
mechanical luminosity and diffusion is suppressed by two orders of magnitude
within <100pc. Finally, the survey could probe the canonical velocity-averaged
cross section for self-annihilation of weakly interacting massive particles for
cuspy Navarro-Frenk-White profiles.


  In this thesis, we study the three-loop QCD form factors. After an
introduction and a discussion of the physics motivation, we generate the quark
form factor using Qgraf. We then show how to bring the Feynman integrals into a
unique form by using various trivial symmetries such as shifts in loop momenta.
We then try (and fail) to reduce it to master integrals using the Laporta
algorithm. After a discussion of our implementation of the Laporta algorithm
(called "Solve") we perform an extensive classification of all the integrals
into irreducible, reducible and loop-by-loop integrable topologies. We devise
methods to deal with each of these cases. We show that our reduction code fails
to reduce only a small set of 11 topologies. We finally give some partial
results, and in the appendix we collect some already known master integrals.


  Presently clearing electrodes are being considered as a possible cure of
e-cloud driven problems in existing and future colliders. 'Invisible'
electrodes, made of a thin highly resistive layer pasted on a dielectric plate,
have been proposed as one of design solutions for the e-cloud clearing. For the
first time such electrodes were successfully used in the electron-positron
accumulator (EPA) of LEP. Similar electrodes had been using for a long time for
ion clearing purposes in the DAFNE electron ring. Theoretical considerations
and experimental measurements at DAFNE have revealed a substantial contribution
of the ion clearing electrodes (ICE) to the machine broad-band impedance giving
rise to several harmful effects degrading the collider performance. In this
paper we discuss the impact of the electrodes on DAFNE beam dynamics, show the
results of ICE wake field and impedance calculations and compare them with
available experimental data. We also describe the procedure of ICE removal from
the wiggler sections of the electron ring that has resulted in remarkable
improvements in terms of beam dynamics and geometric luminosity.


  We prove function field versions of the Zilber-Pink conjectures for varieties
supporting a variation of Hodge structures. A form of these results for Shimura
varieties in the context of unlikely intersections is the following. Let $S$ be
a connected pure Shimura variety with a fixed quasiprojective embedding. We
show that there is an explicitly computable function $B$ of two natural number
arguments so that for any field extension $K$ of the complex numbers and Hodge
generic irreducible proper subvariety $X \subsetneq S_K$, the set of
nonconstant points in the intersection of $X$ with the union of all special
subvarieties of $X$ of dimension less than the codimension of $X$ in $S$ is
contained in a proper subvariety of $X$ of degree bounded by
$B(\operatorname{deg}(X),\dim(X))$. Our techniques are differential algebraic
and rely on Ax-Schanuel functional transcendence theorems. We use these results
to show that the differential equations associated with Shimura varieties give
new examples of minimal, and sometimes, strongly minimal, types with trivial
forking geometry but non-$\aleph_0$-categorical induced structure.


  We report the observation in the direct space of the transport of a few
thousand charges submitted to a tunable electric field along the surface of a
silicon oxide layer. Charges are both deposited and observed using the same
Electrostatic Force Microscope. During the time range accessible to our
measurements (i.e. $t=1\sim1000\un{s}$), the transport of electrons is mediated
by traps in the oxide. We measure the mobility of electrons in the "surface"
states of the silicon oxide layer and show the dispersive nature of their
motion. It is also demonstrated that the saturation of deep oxide traps
strongly enhance the transport of electrons under lateral electric field.


  Answer Set Programming (ASP) emerged in the late 1990ies as a paradigm for
Knowledge Representation and Reasoning. The attractiveness of ASP builds on an
expressive high-level modeling language along with the availability of powerful
off-the-shelf solving systems. While the utility of incorporating aggregate
expressions in the modeling language has been realized almost simultaneously
with the inception of the first ASP solving systems, a general semantics of
aggregates and its efficient implementation have been long-standing challenges.
Aggregates have been proposed and widely used in database systems, and also in
the deductive database language Datalog, which is one of the main precursors of
ASP. The use of aggregates was, however, still restricted in Datalog (by either
disallowing recursion or only allowing monotone aggregates), while several ways
to integrate unrestricted aggregates evolved in the context of ASP. In this
survey, we pick up at this point of development by presenting and comparing the
main aggregate semantics that have been proposed for propositional ASP
programs. We highlight crucial properties such as computational complexity and
expressive power, and outline the capabilities and limitations of different
approaches by illustrative examples.


  We investigate the in-medium modification of the charmonium breakup processes
due to the Mott effect for light (pi, rho) and open-charm (D, D*)
quark-antiquark bound states at the chiral/deconfinement phase transition. The
Mott effect for the D-mesons effectively reduces the threshold for charmonium
breakup cross sections, which is suggested as an explanation of the anomalous
J/psi suppression phenomenon in the NA50 experiment. Further implications of
finite-temperature mesonic correlations for the hadronization of heavy flavors
in heavy-ion collisions are discussed.


  When studying the geometry of quantum states, it is acknowledged that mixed
states can be distinguished by infinitely many metrics. Unfortunately, this
freedom causes metric-dependent interpretations of physically significant
geometric quantities such as complexity and volume of quantum states. In this
paper, we present an insightful discussion on the differences between the Bures
and the Sj\"oqvist metrics inside a Bloch sphere. First, we begin with a formal
comparative analysis between the two metrics by critically discussing three
alternative interpretations for each metric. Second, we illustrate explicitly
the distinct behaviors of the geodesic paths on each one of the two metric
manifolds. Third, we compare the finite distances between an initial and final
mixed state when calculated with the two metrics. Interestingly, in analogy to
what happens when studying topological aspects of real Euclidean spaces
equipped with distinct metric functions (for instance, the usual Euclidean
metric and the taxicab metric), we observe that the relative ranking based on
the concept of finite distance among mixed quantum states is not preserved when
comparing distances determined with the Bures and the Sj\"oqvist metrics.
Finally, we conclude with a brief discussion on the consequences of this
violation of a metric-based relative ranking on the concept of complexity and
volume of mixed quantum states.


  Previous multilingual text-to-speech (TTS) approaches have considered
leveraging monolingual speaker data to enable cross-lingual speech synthesis.
However, such data-efficient approaches have ignored synthesizing emotional
aspects of speech due to the challenges of cross-speaker cross-lingual emotion
transfer - the heavy entanglement of speaker timbre, emotion, and language
factors in the speech signal will make a system produce cross-lingual synthetic
speech with an undesired foreign accent and weak emotion expressiveness. This
paper proposes the Multilingual Emotional TTS (METTS) model to mitigate these
problems, realizing both cross-speaker and cross-lingual emotion transfer.
Specifically, METTS takes DelightfulTTS as the backbone model and proposes the
following designs. First, to alleviate the foreign accent problem, METTS
introduces multi-scale emotion modeling to disentangle speech prosody into
coarse-grained and fine-grained scales, producing language-agnostic and
language-specific emotion representations, respectively. Second, as a
pre-processing step, formant shift-based information perturbation is applied to
the reference signal for better disentanglement of speaker timbre in the
speech. Third, a vector quantization-based emotion matcher is designed for
reference selection, leading to decent naturalness and emotion diversity in
cross-lingual synthetic speech. Experiments demonstrate the good design of
METTS.


  We review how the various large-scale data constrain cosmological parameters
and, consequently, theories for the origin of large-scale structure in the
Universe. We discuss the form of the power spectrum implied by the correlation
data of galaxies and argue by comparing the velocity field implied by the
distribution of light with the observed velocity flows that the bias parameter,
$b$, is likely to be constant in the linear regime. This then allows one to
estimate the density parameter, $\Omega$, and $b$ directly from the
\underline{data} on $\xi(r)$ and the velocity fields. We show that it is
consistent with low values of $\Omega^{0.6}/b$. We discuss the ways to
normalise the optical data at $z\sim0$ directly to the COBE (or other microwave
background) data. The data on high-$z$ \underline{galaxies} allows one to
further constrain the shape of the \underline{primordial} power spectrum at
scales which are non-linear today ($< 8h^{-1}$Mpc) and we discuss the
consistency of the data with inflationary models normalised to the large-scale
structure observations.


  A common task in empirical economics is to estimate \emph{interaction
effects} that measure how the effect of one variable $X$ on another variable
$Y$ depends on a third variable $H$. This paper considers the estimation of
interaction effects in linear panel models with a fixed number of time periods.
There are at least two ways to estimate interaction effects in this setting,
both common in applied work. Our theoretical results show that these two
approaches are distinct, and only coincide under strong conditions on
unobserved effect heterogeneity. Our empirical results show that the difference
between the two approaches is large, leading to conflicting conclusions about
the sign of the interaction effect. Taken together, our findings may guide the
choice between the two approaches in empirical work.


  Magnetic 3d-ions doped into wide-gap oxides show signatures of room
temperature ferromagnetism, although their concentration is two orders of
magnitude smaller than that in conventional magnets. The prototype of these
exceptional materials is Co-doped ZnO, for which an explanation of the room
temperature ferromagnetism is still elusive. Here we demonstrate that magnetism
originates from Co2+ oxygen-vacancy pairs with a partially filled level close
to the ZnO conduction band minimum. The magnetic interaction between these
pairs is sufficiently long-ranged to cause percolation at moderate
concentrations. However, magnetically correlated clusters large enough to show
hysteresis at room temperature already form below the percolation threshold and
explain the current experimental findings. Our work demonstrates that the
magnetism in ZnO:Co is entirely governed by intrinsic defects and a phase
diagram is presented. This suggests a recipe for tailoring the magnetic
properties of spintronics materials by controlling their intrinsic defects.


  Magnetotransport properties of ferromagnetic semiconductor (Ga,Mn)As have
been investigated. Measurements at low temperature (50 mK) and high magnetic
field (<= 27 T) have been employed in order to determine the hole concentration
p = 3.5x10^20 cm ^-3 of a metallic (Ga0.947Mn0.053)As layer. The analysis of
the temperature and magnetic field dependencies of the resistivity in the
paramagnetic region was performed with the use of the above value of p, which
gave the magnitude of p-d exchange energy |N0beta | ~ 1.5 eV.


  We present and discuss new visual wavelength-range observations of the inner
regions of the supernova remnant SNR 0540-69.3 that is located in the Large
Magellanic Cloud (LMC). These observations provide us with more spatial and
spectral information than were previously available for this object. We use
these data to create a detailed three-dimensional model of the remnant,
assuming linear expansion of the ejecta. With the observations and the model we
study the general three-dimensional structure of the remnant, and the influence
of an active region in the remnant - a "blob" - that we address in previous
papers. We used the fibre-fed integral-field spectrograph VIMOS at the Very
Large Telescope of the European Southern Observatory. The observations provide
us with three-dimensional data in [OIII]5007 and [SII]6717,6731 at an 0.33x0.33
spatial sampling and a velocity resolution of about 35 km/s. We decomposed the
two, partially overlapping, sulphur lines and used them to calculate electron
densities across the remnant at high signal-to-noise ratio. Our analysis
reveals a structure that stretches from the position of the "blob", and into
the plane of the sky at a position angle of about 60 degrees. We speculate that
the pulsar is positioned along this activity axis, where it has a velocity
along the line of sight of a few hundred km/s. The "blob" is most likely a
region of shock activity, as it is mainly bright in [SII]; future observations
of [OII]3729 would be useful to test whether the S/O abundance ratio is higher
than average for that location in the remnant. The striking resemblance in
X-rays between the pulsar wind nebula (PWN) of SNR 0540-69.3 and the Crab, in
combination with our findings in this paper, suggests that the symmetry axis is
part of a torus in the PWN. (abridged)


  For quantum systems with competing potentials, the conventional perturbation
theory often yields an asymptotic series and the subsequent numerical outcome
becomes uncertain. To tackle such kind of problems, we develop a general
solution scheme based on a new energy dissection idea. Instead of dividing the
potential energy into "unperturbed" and "perturbed" terms, a partition of the
kinetic energy is performed. By distributing the kinetic energy term in part
into each individual potential, the Hamiltonian can be expressed as the sum of
the subsystem Hamiltonians with respective competing potentials. The total
wavefunction is expanded by using a linear combination of the basis sets of
respective subsystem Hamiltonians. We first illustrate the solution procedure
using a simple system consisting of a particle under the action of double
delta-function potentials. Next, this method is applied to the prototype
systems of a charged harmonic oscillator in strong magnetic field and the
hydrogen molecule ion. Compared with the usual perturbation approach, this new
scheme converges much faster to the exact solutions for both eigenvalues and
eigenfunctions. When properly extended, this new solution scheme can be very
useful for dealing with strongly coupling quantum systems.


  We develop the convergence theory for a well-known method for the
interpolation of functions on the real axis with rational functions. Precise
new error estimates for the interpolant are de- rived using existing theory for
trigonometric interpolants. Estimates on the Dirichlet kernel are used to
derive new bounds on the associated interpolation projection operator. Error
estimates are desired partially due to a recent formula of the author for the
Cauchy integral of a specific class of so-called oscillatory rational
functions. Thus, error bounds for the approximation of the Fourier transform
and Cauchy integral of oscillatory smooth functions are determined. Finally,
the behavior of the differentiation operator is discussed. The analysis here
can be seen as an extension of that of Weber (1980) and Weideman (1995) in a
modified basis used by Olver (2009) that behaves well with respect to function
multiplication and differentiation.


  Naturalistic fMRI has been suggested to be a powerful alternative for
investigations of human brain function. Stimulus-induced activation has been
playing an essential role in fMRI-based brain function analyses. Due to the
complexity of the stimuli, however, detection of activations induced by
naturalistic stimuli (AINSs) has been a tricky problem, as AINS cannot be
detected simply in a model-driven way. In this study, we proposed a method to
detect AINS in a pseudo model-driven way. Inspired by the strategy of utilizing
the commonalities among the brains exposed to the same stimuli for
inter-subject correlation analysis, we established response models for one
subject by averaging the fMRI signals across several other subjects, and then
detected AINSs of the subject using general linear model. We evaluated the
effectiveness of AINS with both statistical and predictive analyses on
individual differences in sex and intelligence quotient (IQ), based on the four
movie fMRI runs included in the Human Connectome Project dataset. The results
indicate that AINS is not only sensitive to sex- and IQ-related differences,
but also specific enough to decode individuals' sex and IQ. Specifically,
activations in brain regions associated with visual-spatial processing were
observed to be consistently stronger in the males, and individuals with higher
IQ exhibited consistently stronger activations in regions within the visual and
the default mode networks. Predictions of individuals' sex and IQ were
significantly better than those based on random labels (P < 0.005). Taken
together, AINS advanced in this study can be an effective evaluation of human
brain function. The conceptual simplicity and easy application of its detection
may make AINS a favorable choice for future brain function analyses and
personalized medicine based on naturalistic fMRI.


  Using a minimal algebraic model for the thermodynamics of binary rod--polymer
mixtures, we provide evidence for a quintuple phase equilibrium; an observation
that seems to be at odds with the Gibbs phase rule for two-component systems.
Our model is based on equations of state for the relevant liquid crystal phases
that are in quantitative agreement with computer simulations. We argue that the
appearance of a quintuple equilibrium, involving an isotropic fluid, a nematic
and smectic liquid crystal, and two solid phases can be reconciled with a
generalized Gibbs phase rule in which the two intrinsic length scales of the
athermal colloid--polymer mixture act as additional field variables.


  We consider a parameter dependent periodic-logistic problem with a logistic
term involving a degeneracy that replicates time dependent refuges in the
habitat of a population. Working under no or very minimal assumptions on the
boundary regularity of the domain we show the existence of a time-periodic
solution which bifurcates with respect to the parameter and show their
stability. We show that under suitable assumptions that the periodic solution
blows up on part of the domain and remains finite on other parts when the
parameter approaches a critical value.


  We study the statistical mechanics of a $D$-dimensional array of Josephson
junctions in presence of a magnetic field on a lattice of side $2$. In the high
temperature region the thermodynamical properties can be computed in the limit
$D \to \infty$. A conjectural form of the thermodynamic properties in the low
temperature phase is obtained by assuming that they are the same of an
appropriate spin glass system, based on quenched disordered couplings.
Numerical simulations show that this conjecture is very accurate in one regime
of the magnetic field, while it is probably slightly inaccurate in a second
regime.


  Let F(z) be a newform of weight 2k and level one with a trivial character,
and assume that F(z) is a non-zero eigenform of all Hecke operators. In this
paper, we study nonvanishing for central values of twisted modular L-function
of F.


  We demonstrate that the general second-order scalar-tensor theories, which
have attracted attention as possible modified gravity models to explain the
late time cosmic acceleration, could be strongly constrained from the argument
of the gravitational Cherenkov radiation. To this end, we consider the purely
kinetic coupled gravity and the extended galileon model. In these models, the
propagation speed of tensor mode could be less than the speed of light, which
puts very strong constraints from the gravitational Cherenkov radiation.


  We give a new order-theoretic characterization of a complete Heyting and
co-Heyting algebra $C$. This result provides an unexpected relationship with
the field of Nash equilibria, being based on the so-called Veinott ordering
relation on subcomplete sublattices of $C$, which is crucially used in Topkis'
theorem for studying the order-theoretic stucture of Nash equilibria of
supermodular games.


  A new approach to the model-independent description of quantum field theories
will be introduced in the present work. The main feature of this new approach
is to incorporate in a local sense the principle of general covariance of
general relativity, thus giving rise to the concept of a "locally covariant
quantum field theory". Such locally covariant quantum field theories will be
described mathematically in terms of covariant functors between the categories,
on one side, of globally hyperbolic spacetimes with isometric embeddings as
morphisms and, on the other side, of *-algebras with unital injective
*-endomorphisms as morphisms. Moreover, locally covariant quantum fields can be
described in this framework as natural transformations between certain
functors. The usual Haag-Kastler framework of nets of operator-algebras over a
fixed spacetime background-manifold, together with covariant automorphic
actions of the isometry-group of the background spacetime, can be re-gained
from this new approach as a special case. Examples of this new approach are
also outlined. In case that a locally covariant quantum field theory obeys the
time-slice axiom, one can naturally associate to it certain automorphic
actions, called ``relative Cauchy-evolutions'', which describe the dynamical
reaction of the quantum field theory to a local change of spacetime background
metrics. The functional derivative of a relative Cauchy-evolution with respect
to the spacetime metric is found to be a divergence-free quantity which has, as
will be demonstrated in an example, the significance of an energy-momentum
tensor for the locally covariant quantum field theory. Furthermore, we discuss
the functorial properties of state spaces of locally covariant quantum field
theories that entail the validity of the principle of local definiteness.


  Assuming the existence of a field theory in D dimensions dual to
(D+1)-dimensional flat space, governed by the asymptotic symmetries of flat
space, we make some preliminary remarks about the properties of this field
theory. We review briefly some successes of the 3d bulk - 2d boundary case and
then focus on the 4d bulk - 3d boundary example, where the symmetry in question
is the infinite dimensional BMS4 algebra. We look at the constraints imposed by
this symmetry on a 3d field theory by constructing highest weight
representations of this algebra. We construct two and three point functions of
BMS primary fields and surprisingly find that symmetries constrain these
correlators to be identical to those of a 2d relativistic conformal field
theory. We then go one dimension higher and construct prototypical examples of
4d field theories which are putative duals of 5d Minkowski spacetimes. These
field theories are ultra-relativistic limits of electrodynamics and Yang-Mills
theories which exhibit invariance under the conformal Carroll group in D=4. We
explore the different sectors within these Carrollian gauge theories and
investigate the symmetries of the equations of motion to find that an infinite
ultra-relativistic conformal structure arises in each case.


  Large scale molecular dynamics and grand canonical Monte Carlo simulation
techniques are used to study the behavior of the interdiffusion of a solvent
into an entangled polymer matrix as the state of the polymer changes from a
melt to a glass. The weight gain by the polymer increases with time $t$ as
$t^{1/2}$ in agreement with Fickian diffusion for all cases studied, although
the diffusivity is found to be strongly concentration dependent especially as
one approaches the glass transition temperature of the polymer. The diffusivity
as a function of solvent concentration determined using the one-dimensional
Fick's model of the diffusion equation is compared to the diffusivity
calculated using the Darken equation from simulations of equilibrated
solvent-polymer solutions. The diffusivity calculated using these two different
approaches are in good agreement. The behavior of the diffusivity strongly
depends on the state of the polymer and is related to the shape of the solvent
concentration profile.


  We show that particle transport in a uniform, quantum multi-baker map, is
generically ballistic in the long time limit, for any fixed value of Planck's
constant. However, for fixed times, the semi-classical limit leads to
diffusion. Random matrix theory provides explicit analytical predictions for
the mean square displacement of a particle in the system. These results exhibit
a crossover from diffusive to ballistic motion, with crossover time from
diffusive to ballistic motion on the order of the inverse of Planck's constant.
We can argue, that for a large class of 1D quantum random walks, similar to the
quantum multi-baker, a sufficient condition for diffusion in the semi-classical
limit is classically chaotic dynamics in each cell. Using an initial
equilibrium density matrix, we find that diffusive behavior is recovered in the
semi-classical limit for such systems, without further interactions with the
environment.


  We study the phenomenon of \textit{in-context learning} (ICL) exhibited by
large language models, where they can adapt to a new learning task, given a
handful of labeled examples, without any explicit parameter optimization. Our
goal is to explain how a pre-trained transformer model is able to perform ICL
under reasonable assumptions on the pre-training process and the downstream
tasks. We posit a mechanism whereby a transformer can achieve the following:
(a) receive an i.i.d. sequence of examples which have been converted into a
prompt using potentially-ambiguous delimiters, (b) correctly segment the prompt
into examples and labels, (c) infer from the data a \textit{sparse linear
regressor} hypothesis, and finally (d) apply this hypothesis on the given test
example and return a predicted label. We establish that this entire procedure
is implementable using the transformer mechanism, and we give sample complexity
guarantees for this learning framework. Our empirical findings validate the
challenge of segmentation, and we show a correspondence between our posited
mechanisms and observed attention maps for step (c).


  With the development of large language models (LLMs) like the GPT series,
their widespread use across various application scenarios presents a myriad of
challenges. This review initially explores the issue of domain specificity,
where LLMs may struggle to provide precise answers to specialized questions
within niche fields. The problem of knowledge forgetting arises as these LLMs
might find it hard to balance old and new information. The knowledge repetition
phenomenon reveals that sometimes LLMs might deliver overly mechanized
responses, lacking depth and originality. Furthermore, knowledge illusion
describes situations where LLMs might provide answers that seem insightful but
are actually superficial, while knowledge toxicity focuses on harmful or biased
information outputs. These challenges underscore problems in the training data
and algorithmic design of LLMs. To address these issues, it's suggested to
diversify training data, fine-tune models, enhance transparency and
interpretability, and incorporate ethics and fairness training. Future
technological trends might lean towards iterative methodologies, multimodal
learning, model personalization and customization, and real-time learning and
feedback mechanisms. In conclusion, future LLMs should prioritize fairness,
transparency, and ethics, ensuring they uphold high moral and ethical standards
when serving humanity.


  We publicly release ATM, a Python package designed to model asteroid flux
measurements to estimate an asteroid's size, surface temperature distribution,
and emissivity. The full multi-dimensional posterior pdf is found using Markov
Chain Monte Carlo. Data files with $\sim$ 2.5 million WISE flux measurements
for $\sim$ 150,000 asteroids and additional MPC data are also included with the
package, as well as Python Jupyter Notebooks with examples of analysis. The
entirety of the analysis presented here, including all the figures, tables, and
catalogs, can be easily reproduced with these publicly released Notebooks. We
show that ATM can match the best-fit size estimates for well-observed asteroids
published in 2016 by the NEOWISE team (Mainzer et al. 2016) with a sub-percent
bias and a scatter of only 6%. We estimate that the accuracy of WISE-based
asteroid size estimates is approximately in the range of 15-20% for most
objects. We also study optical data collected by the Sloan Digital Sky Survey
(SDSS) and show that correlations of optical colors and WISE-based best-fit
model parameters indicate robustness of the latter. Our analysis also gives
support to the claim by Harris & Drube (2014) that candidate metallic asteroids
can be selected using the best-fit temperature parameter and infrared albedo.
We investigate a correlation between SDSS colors and optical albedo derived
using WISE-based size estimates and show that this correlation can be used to
estimate asteroid sizes with optical data alone, with a precision of about 21%
relative to WISE-based size estimates. After accounting for systematic errors,
the difference in accuracy between infrared and optical color-based size
estimates becomes less than a factor of two. (abridged)


  We attempt to characterize the geometry of Broad Absorption Line (BAL) QSOs
by studying a low redshift sample of 12 sources. We find that the majority of
these sources are Population A quasars as defined in (broad H-beta FWHM > 4000
kms/s; Sulenticet al 2000). A possible correlation between terminal velocity
and absolute V magnitude suggests that the bolometric luminosity to black hole
mass ratio \lm is a governing factor with classical BAL sources showing the
highest values. CIV 1549 emission in classical BAL sources shows a profile
blueshift that supports a disk wind/outflow scenario with a half opening angle
of < 50 deg. Observation of ``secondary'' mini-BAL features in the CIV 1549
emission profile motivates us to model BALs with an additional component that
may be involved with the BLR outflow and co-axial with the accretion disk.


  In this paper we investigate critical Gagliardo-Nirenberg, Trudinger-type and
Brezis-Gallouet-Wainger inequalities associated with the positive Rockland
operators on graded Lie groups, which includes the cases of $\mathbb R^n$,
Heisenberg, and general stratified Lie groups. As an application, using the
critical Gagliardo-Nirenberg inequality, the existence of least energy
solutions of nonlinear Schr\"{o}dinger type equations is obtained. We also
express the best constant in the critical Gagliardo-Nirenberg and Trudinger
inequalities in the variational form as well as in terms of the ground state
solutions of the corresponding nonlinear subelliptic equations. The obtained
results are already new in the setting of general stratified Lie groups
(homogeneous Carnot groups). Among new technical methods, we also extend
Folland's analysis of H\"older spaces from stratified Lie groups to general
homogeneous Lie groups.


  The MAGIC collaboration reports the detection of the blazar S5 0716+714
z=0.31+-0.08 in very high energy gamma-rays. The observations were performed in
November 2007 and in April 2008, and were triggered by the KVA telescope due to
the high optical state of the object. An overall significance of the signal
accounts to S =5.8sigma for 13.1 hours of data. Most of the signal S = 6.9sigma
comes from the April 2008 data sample during a higher optical state of the
object suggesting a possible correlation between the VHE gamma-ray and optical
emissions. The differential energy spectrum of the 2008 data sample follows a
power law with a photon index of Gamma = 3.45+-0.54_(stat)+-0.2_(syst), and the
integral flux above 400GeV is at the level of
7.5+-2.2_(stat)+-2.3_(syst)*10^-12 cm^-2 s^-1 corresponding to a 9% Crab Nebula
flux. Modeling of the broad band spectral energy distribution indicates that a
structured jet model appears to be more promising in describing the available
data than a simple one zone synchrotron self-Compton model.


  We investigate theoretically the behavior of proteins as well as other large
macromolecules which are incorporated into amphiphilic monolayers at the
air-water interface. We assume the monolayer to be in the coexistence region of
the ``main'' transition, where domains of the liquid condensed phase coexist
with the liquid expanded background. Using a simple mean-field free energy
accounting for the interactions between proteins and amphiphilic molecules, we
obtain the spatial protein distribution with the following characteristics.
When the proteins preferentially interact with either the liquid condensed or
liquid expanded domains, they will be dissolved in the respective phase. When
the proteins are energetically rather indifferent to the density of the
amphiphiles, they will be localized at the line boundary between the
(two-dimensional) liquid expanded and condensed phases. In between these two
limiting cases, a delocalization transition of the proteins takes place. This
transition is accessible by changing the temperature or the amount of
incorporated protein. These findings are in agreement with recent fluorescence
microscopy experiments. Our results also apply to lipid multicomponent
membranes showing coexistence of distinct fluid phases.


  Energy spectra of disordered systems share a common feature: if the entropy
of the quenched disorder is larger than the entropy of the dynamical variables,
the spectrum is locally that of a random energy model and the correlation
between energy and configuration is lost. We demonstrate this effect for the
Edwards-Anderson model, but we also discuss its universality.


  In model-based reinforcement learning for safety-critical control systems, it
is important to formally certify system properties (e.g., safety, stability)
under the learned controller. However, as existing methods typically apply
formal verification \emph{after} the controller has been learned, it is
sometimes difficult to obtain any certificate, even after many iterations
between learning and verification. To address this challenge, we propose a
framework that jointly conducts reinforcement learning and formal verification
by formulating and solving a novel bilevel optimization problem, which is
differentiable by the gradients from the value function and certificates.
Experiments on a variety of examples demonstrate the significant advantages of
our framework over the model-based stochastic value gradient (SVG) method and
the model-free proximal policy optimization (PPO) method in finding feasible
controllers with barrier functions and Lyapunov functions that ensure system
safety and stability.


  We prove that the category of vector bundles over a fixed smooth manifold and
its corresponding category of convenient modules are models for intuitionistic
differential linear logic. The exponential modality is modelled by composing
the jet comonad, whose Kleisli category has linear differential operators as
morphisms, with the more familiar distributional comonad, whose Kleisli
category has smooth maps as morphisms. Combining the two comonads gives a new
interpretation of the semantics of differential linear logic where the Kleisli
morphisms are smooth local functionals, or equivalently, smooth partial
differential operators, and the codereliction map induces the functional
derivative. This points towards a logic and hence computational theory of
non-linear partial differential equations and their solutions based on
variational calculus.


  Thanks to its high spectral resolution (~5 eV at 6 keV), the Soft X-ray
Spectrometer (SXS) on board Hitomi enables us to measure the detailed structure
of spatially resolved emission lines from highly ionized ions in galaxy
clusters for the first time. In this series of papers, using the SXS we have
measured the velocities of gas motions, metallicities and the multi-temperature
structure of the gas in the core of the Perseus cluster. Here, we show that
when inferring physical properties from line emissivities in systems like
Perseus, the resonant scattering (RS) effect should be taken into account. In
the Hitomi waveband, RS mostly affects the FeXXV He$\alpha$ line ($w$) - the
strongest line in the spectrum. The flux measured by Hitomi in this line is
suppressed by a factor ~1.3 in the inner ~30 kpc, compared to predictions for
an optically thin plasma; the suppression decreases with the distance from the
center. The $w$ line also appears slightly broader than other lines from the
same ion. The observed distortions of the $w$ line flux, shape and distance
dependence are all consistent with the expected effect of the resonant
scattering in the Perseus core. By measuring the ratio of fluxes in optically
thick ($w$) and thin (FeXXV forbidden, He$\beta$, Ly$\alpha$) lines, and
comparing these ratios with predictions from Monte Carlo radiative transfer
simulations, the velocities of gas motions have been obtained. The results are
consistent with the direct measurements of gas velocities from line broadening
described elsewhere in this series, although the systematic and statistical
uncertainties remain significant. Further improvements in the predictions of
line emissivities in plasma models, and deeper observations with future X-ray
missions will enable RS measurements to provide powerful constraints on the
amplitude and anisotropy of clusters gas motions.


  We propose a learning-based method that solves monocular stereo and can be
extended to fuse depth information from multiple target frames. Given two
unconstrained images from a monocular camera with known intrinsic calibration,
our network estimates relative camera poses and the depth map of the source
image. The core contribution of the proposed method is threefold. First, a
network is tailored for static scenes that jointly estimates the optical flow
and camera motion. By the joint estimation, the optical flow search space is
gradually reduced resulting in an efficient and accurate flow estimation.
Second, a novel triangulation layer is proposed to encode the estimated optical
flow and camera motion while avoiding common numerical issues caused by
epipolar. Third, beyond two-view depth estimation, we further extend the above
networks to fuse depth information from multiple target images and estimate the
depth map of the source image. To further benefit the research community, we
introduce tools to generate photorealistic structure-from-motion datasets such
that deep networks can be well trained and evaluated. The proposed method is
compared with previous methods and achieves state-of-the-art results within
less time. Images from real-world applications and Google Earth are used to
demonstrate the generalization ability of the method.


  An analytical perturbation theory of short-pulse, matter-wave superradiant
scatterings is presented. We show that Bragg resonant enhancement is
incapacitated and both positive and negative order scatterings contribute
equally. We further show that propagation gain is small and scattering events
primarily occur at the end of the condensate where the generated field has
maximum strength, thereby explaining the apparent ``asymmetry" in the scattered
components with respect to the condensate center. In addition, the generated
field travels near the speed of light in a vacuum, resulting in significant
spontaneous emission when the one-photon detuning is not sufficiently large.
Finally, we show that when the excitation rate increases, the generated-field
front-edge-steepening and peak forward-shifting effects are due to depletion of
the ground state matter wave.


  In this paper we give a self contained introduction to the conceptional and
mathematical foundations of quantum information theory. In the first part we
introduce the basic notions like entanglement, channels, teleportation etc. and
their mathematical description. The second part is focused on a presentation of
the quantitative aspects of the theory. Topics discussed in this context
include: entanglement measures, channel capacities, relations between both,
additivity and continuity properties and asymptotic rates of quantum
operations. Finally we give an overview on some recent developments and open
questions.


  We continue our earlier investigations of radial subspaces of Besov and
Lizorkin-Triebel spaces on $\R^d$. This time we study characterizations of
these subspaces by differences.


  Although magnetic reconnection takes place in three-dimensional space,
reconnection theory has focused on two-dimensional models for more than sixty
years. Well-posed three-dimensional mathematics associated with the theory of
fluid mixing provides a predictive and compelling explanation for why fast
magnetic reconnection is prevalent---exponentially large variations in the
separations between magnetic field lines. The proofs have been simplified to
remove any rational reason to maintain a focus on two dimensional models, which
fail to represent the mathematical properties of three-dimensional space.


  A thorough understanding of the mean-free-path (MFP) distribution of the
energy carriers is crucial to engineer and tune the transport properties of
materials. In this context, a significant body of work has investigated the
phonon and electron MFP distribution, however, similar studies of the magnon
MFP distribution have not been carried out so far. In this work, we used
thickness-dependence measurements of the longitudinal spin Seebeck (LSSE)
effect of yttrium iron garnet films to reconstruct the cumulative distribution
of a SSE related effective magnon MFP. By using the experimental data reported
by Guo et al. [Phys. Rev. X 6, 031012 (2016)], we adapted the phonon MFP
reconstruction algorithm proposed by A.J. Minnich, [Phys. Rev. Lett. 109,
205901 (2012)] and apply it to magnons. The reconstruction showed that magnons
with different MFP contribute in different manner to the total LSSE and the
effective magnon MFP distribution spreads far beyond their typical averaged
values.


  We investigate the following question: if a polynomial can be evaluated at
rational points by a polynomial-time boolean algorithm, does it have a
polynomial-size arithmetic circuit? We argue that this question is certainly
difficult. Answering it negatively would indeed imply that the constant-free
versions of the algebraic complexity classes VP and VNP defined by Valiant are
different. Answering this question positively would imply a transfer theorem
from boolean to algebraic complexity. Our proof method relies on Lagrange
interpolation and on recent results connecting the (boolean) counting hierarchy
to algebraic complexity classes. As a byproduct we obtain two additional
results: (i) The constant-free, degree-unbounded version of Valiant's
hypothesis that VP and VNP differ implies the degree-bounded version. This
result was previously known to hold for fields of positive characteristic only.
(ii) If exponential sums of easy to compute polynomials can be computed
efficiently, then the same is true of exponential products. We point out an
application of this result to the P=NP problem in the Blum-Shub-Smale model of
computation over the field of complex numbers.


  As one knows, for every Poisson manifold $M$ there exists a formal
noncommutative deformation of the algebra of functions on it; it is determined
in a unique way (up to an equivalence relation) by the given Poisson bivector.
Let a Lie algebra $\mathfrak g$ act by derivations on the functions on $M$. The
main question, which we shall address in this paper is whether it is possible
to lift this action to the derivations on the deformed algebra. It is easy to
see, that when dimension of $\mathfrak g$ is $1$, the only necessary and
sufficient condition for this is that the given action is by Poisson vector
fields. However, when dimension of $\mathfrak g$ is greater than $1$, the
previous methods do not work. In this paper we show how one can obtain a series
of homological obstructions for this problem, which vanish if there exists the
necessary extension.


  We present evidence that band gap narrowing at the heterointerface may be a
major cause of the large open circuit voltage deficit of Cu$_2$ZnSnS$_4$/CdS
solar cells. Band gap narrowing is caused by surface states that extend the
Cu$_2$ZnSnS$_4$ valence band into the forbidden gap. Those surface states are
consistently found in Cu$_2$ZnSnS$_4$, but not in Cu$_2$ZnSnSe$_4$, by
first-principles calculations. They do not simply arise from defects at
surfaces but are an intrinsic feature of Cu$_2$ZnSnS$_4$ surfaces. By including
those states in a device model, the outcome of previously published
temperature-dependent open circuit voltage measurements on Cu$_2$ZnSnS$_4$
solar cells can be reproduced quantitatively without necessarily assuming a
cliff-like conduction band offset with the CdS buffer layer. Our
first-principles calculations indicate that Zn-based alternative buffer layers
are advantageous due to the ability of Zn to passivate those surface states.
Focusing future research on Zn-based buffers is expected to significantly
improve the open circuit voltage and efficiency of pure-sulfide Cu$_2$ZnSnS$_4$
solar cells.


  Experimental results of inclusive hard-process cross sections in heavy-ion
collisions conventionally lean on a normalization computed from Glauber models
where the inelastic nucleon-nucleon cross section $\sigma_{\rm nn}^{\rm inel}$
-- a crucial input parameter -- is simply taken from proton-proton
measurements. In this letter, using the computed electro-weak boson production
cross sections in lead-lead collisions as a benchmark, we determine
$\sigma_{\rm nn}^{\rm inel}$ from the recent ATLAS data. We find a
significantly suppressed $\sigma_{\rm nn}^{\rm inel}$ relative to what is
usually assumed, show the consequences for the centrality dependence of the
cross sections, and address the phenomenon in an eikonal minijet model with
nuclear shadowing.


  We present HyperSum, an extractive summarization framework that captures both
the efficiency of traditional lexical summarization and the accuracy of
contemporary neural approaches. HyperSum exploits the pseudo-orthogonality that
emerges when randomly initializing vectors at extremely high dimensions
("blessing of dimensionality") to construct representative and efficient
sentence embeddings. Simply clustering the obtained embeddings and extracting
their medoids yields competitive summaries. HyperSum often outperforms
state-of-the-art summarizers -- in terms of both summary accuracy and
faithfulness -- while being 10 to 100 times faster. We open-source HyperSum as
a strong baseline for unsupervised extractive summarization.


  The foundation of two pioneering Usenet newsgroups in astrophysics - still
existent today - and some of the main milestones in their history have been
tracked from the origins at Princeton University in 1983 to 1994. To this aim,
in line with authoritative recommendations from the discipline of web history,
different kinds of sources have been retrieved and combined: mainly, online
archives of Usenet newsgroups and human sources. The latter have included on
one side the kind contribution provided by four astrophysicists, two of which
had a role in the maintaining of these newsgroups, through individual
interviews; on the other side that from the sixty-seven researchers who
answered a purpose-built questionnaire submitted within the Italian National
Institute for Astrophysics in May 2023.


  Tungsten carbide cobalt hardmetals are commonly used as cutting tools subject
to high operation temperature and pressures, where the mechanical performance
of the tungsten carbide phase affects the wear and lifetime of the material. In
this study, the mechanical behaviour of the isolated tungsten carbide (WC)
phase was investigated using single crystal micropillar compression.
Micropillars in two crystal orientations, 1-5 ${\mu}$m in diameter, were
fabricated using focused ion beam (FIB) machining and subsequently compressed
between room temperature and 600 {\deg}C. The activated plastic deformation
mechanisms were strongly anisotropic and weakly temperature dependent. The flow
stresses of basal-oriented pillars were about three times higher than the
prismatic pillars, and pillars of both orientations soften slightly with
increasing temperature. The basal pillars tended to deform by either unstable
cracking or unstable yield, whereas the prismatic pillars deformed by
slip-mediated cracking. However, the active deformation mechanisms were also
sensitive to pillar size and shape. Slip trace analysis of the deformed pillars
showed that {10-10} prismatic planes were the dominant slip plane in WC. Basal
slip was also activated as a secondary slip system at high temperatures.


  Data assimilation (DA) plays a pivotal role in diverse applications, ranging
from climate predictions and weather forecasts to trajectory planning for
autonomous vehicles. A prime example is the widely used ensemble Kalman filter
(EnKF), which relies on linear updates to minimize variance among the ensemble
of forecast states. Recent advancements have seen the emergence of deep
learning approaches in this domain, primarily within a supervised learning
framework. However, the adaptability of such models to untrained scenarios
remains a challenge. In this study, we introduce a novel DA strategy that
utilizes reinforcement learning (RL) to apply state corrections using full or
partial observations of the state variables. Our investigation focuses on
demonstrating this approach to the chaotic Lorenz '63 system, where the agent's
objective is to minimize the root-mean-squared error between the observations
and corresponding forecast states. Consequently, the agent develops a
correction strategy, enhancing model forecasts based on available system state
observations. Our strategy employs a stochastic action policy, enabling a Monte
Carlo-based DA framework that relies on randomly sampling the policy to
generate an ensemble of assimilated realizations. Results demonstrate that the
developed RL algorithm performs favorably when compared to the EnKF.
Additionally, we illustrate the agent's capability to assimilate non-Gaussian
data, addressing a significant limitation of the EnKF.


  Entity Linking is one of the most common Natural Language Processing tasks in
practical applications, but so far efficient end-to-end solutions with
multilingual coverage have been lacking, leading to complex model stacks. To
fill this gap, we release and open source BELA, the first fully end-to-end
multilingual entity linking model that efficiently detects and links entities
in texts in any of 97 languages. We provide here a detailed description of the
model and report BELA's performance on four entity linking datasets covering
high- and low-resource languages.


  In this paper we consider tensor perturbations produced at a bounce phase in
presence of the holonomy corrections. Here bounce phase and holonomy
corrections originate from Loop Quantum Cosmology. We re-derive formulas for
the corrections for the model with a scalar field content. Background dynamics
with a free scalar field and multi-fluid potential are considered. Since the
considerations are semi-classical effects of quantum fluctuations of the
background dynamics are not taken into account. Quantum and classical
back-reaction effects are also neglected. To find spectrum of the gravitational
waves both analytical approximations as well as numerical investigations were
performed. We have found analytical solutions on super-horizontal and
sub-horizontal regimes and derived corresponding tensor power spectra. Also
occupation number $n_{\bf k}$ and parameter $\Omega_{\text{gw}}$ were derived
in sub-horizontal limit, leading to its extremely low present value. Final
results are numerical power spectra of the gravitational waves produced in
presence of quantum holonomy corrections. The obtained spectrum has two UV and
IR branches where $\mathcal{P}_T \propto k^2$, however with the different
prefactors. Spectrum connecting these regions is in the form of oscillations.
We have found good agreement between numerical spectrum and this obtained from
the analytical model. Obtained spectrum can be directly applied as initial
conditions for the inflationary modes. We mention possible resulting
observational features of the CMB in particular B-type polarization.


  Let $s(n)$ denote the sum of proper divisors of an integer $n$. In 1992,
Erd\H{o}s, Granville, Pomerance, and Spiro (EGPS) conjectured that if
$\mathcal{A}$ is a set of integers with asymptotic density zero then
$s^{-1}(\mathcal{A})$ also has asymptotic density zero. In this paper we show
that the EGPS conjecture holds when $\mathcal{A}$ is taken to be a set of
integers with missing digits. In particular, we give a sharp upper bound for
the size of this preimage set. We also provide an overview of progress towards
the EGPS conjecture and survey recent work on sets of integers with missing
digits.


  An ultrasound measurement system was employed as a non-destructive method to
evaluate its reliability in predicting the tensile strength of tablets and
investigate the benefits of incorporating it in a continuous line,
manufacturing solid dosage forms. Tablets containing lactose, acetaminophen,
and magnesium stearate were manufactured continuously and in batches. The
effect of two processing parameters, compaction force and level of shear strain
were examined. Young's modulus and tensile strength of tablets were obtained by
ultrasound and diametrical mechanical testing, respectively. It was found that
as the blend was exposed to increasing levels of shear strain, the speed of
sound in the tablets decreased and the tablets became both softer and
mechanically weaker. Moreover, the results indicate that two separate tablet
material properties (e.g., relative density and Young's modulus) are necessary
in order to predict tensile strength. A strategy for hardness prediction is
proposed that uses the existing models for Young's modulus and tensile strength
of porous materials. Ultrasound testing was found to be very sensitive in
differentiating tablets with similar formulation but produced under different
processing conditions (e.g., different level of shear strain), thus, providing
a fast, and non-destructive method for hardness prediction that could be
incorporated to a continuous manufacturing process.


  This letter presents a 360{\deg} phase detector cell for performing
phase-shift measurements on multiple output systems. An analog phase detector,
capable of detecting a maximum range of {\pm}90{\deg}, has been used to perform
a double multiplication of two signals, both in-phase and phase-shifted. The
proposed solution broadens the frequency range beyond other solutions that
require to fulfill the quadrature condition. Subsequently, the possibility of
reaching the theoretical limit of phase shift within a hybrid coupler ({\Phi} <
90{\deg} {\pm} 90{\deg}) is discussed by using four straight-line equations to
characterize the phase detector response. The proposed solution allows to
extend up to 360{\deg} the phase detection range and provide an increased
immunity with respect to both impedance mismatching and phase deviations within
the hybrid coupler. To demonstrate the feasibility of the proposed design, a
phase detector cell prototype has been implemented using a commercial hybrid
coupler with a phase shift of 92.5{\deg} {\pm} 0.5{\deg} at 3.1-5.9 GHz, an
external switch and a microcontroller with 2 kB of memory. Measurements show a
range of detection of 360{\deg} ({\pm}180{\deg}) across the tested frequency
band of 2.7-6 GHz.


  We study the oblique corrections to the electroweak interaction in the
holographic model of technicolor theories. The oblique S parameter is expressed
in terms of a solution to the equations of motion for the AdS bulk gauge
fields. By analyzing the solution, we establish a rigorous proof that the S
parameter is positive and is reduced by walking. We also present the precise
numerical values for the S parameter of various technicolor models by solving
the equations numerically.


  We have found that the geometrically frustrated spin chain compound Ca3Co2O6
belonging to Ising like universality class with uniaxial anisotropy shows
kinetic arrest of first order intermediate phase (IP) to ferrimagnetic (FIM)
transition. In this system, dc magnetization measurements followed by different
protocols suggest the coexistence of high temperature IP with equilibrium FIM
phase in low temperature. Formation of metastable state due to hindered first
order transition has also been probed through cooling and heating in unequal
field (CHUF) protocol. Kinetically arrested high temperature IP appears to
persist down to almost the spin freezing temperature in this system.


  In this work we consider a quantum analog of Newton's bucket experiment in a
flat spacetime: we take an Unruh-DeWitt detector in interaction with a real
massless scalar field. We calculate the detector's excitation rate when it is
uniformly rotating around some fixed point and the field is prepared in the
Minkowski vacuum and also when the detector is inertial and the field is in the
Trocheries-Takeno vacuum state. These results are compared and the relations
with a quantum analog of Mach's principle are discussed.


  Light beams offer many degrees of freedom to be explored in discrete and
continuous domains. In addition to the possibility of entangling photons in
these many degrees of freedom, it makes light a very useful and versatile tool
for quantum information and quantum foundation purposes. In this thesis, we
endorse its importance and versatility by presenting novel contributions that
further explore both discrete and continuous degrees of freedom. It begins with
two experiments that use classical light and explore its analogous behavior to
quantum systems. The first one is a classical optics simulation of the dynamics
of a relativistic quantum particle. The second work is related to the theory of
mutually unbiased measurements that are effectively discrete but constructed
from continuous variables systems. In the second part of the thesis, three
works are presented that use the polarization and path discrete degrees of
freedom. The first one is a redefinition of the quantum nonlocal correlation
called steering in the multipartite scenario, based on an inconsistency in the
previous definition, namely the creation of this correlation from scratch using
operations that supposedly would not be able to do so. We call this exposure of
quantum steering. Steering exposure is observed with entangled photons. The
other two works are related to the experimental implementation of quantum
channels of qubits, one of them is a particular channel for which we test for
non-Markovianity using a operational measure called conditional past-future
(CPF) correlation. The thesis finishes with a proposal for an experimental
realization of any quantum channel of a single qubit, where the qubit is
realized by the polarization of single photons. The functioning of all optical
devices used is didactically explained.


  Color centers in hexagonal boron nitride (hBN) have attracted considerable
attention due to their remarkable optical properties enabling robust room
temperature photonics and quantum optics applications in the visible spectral
range. On the other hand, identification of the microscopic origin of color
centers in hBN has turned out to be a great challenge that hinders in-depth
theoretical characterization, on-demand fabrication, and development of
integrated photonic devices. This is also true for the blue emitter, which is
an irradiation damage in hBN emitting at 436 nm wavelengths with desirable
properties. Here, we propose the negatively charged nitrogen split interstitial
defect in hBN as a plausible microscopic model for the blue emitter. To this
end, we carry out a comprehensive first principles theoretical study of the
nitrogen interstitial. We carefully analyze the accuracy of first principles
methods and show that the commonly used HSE hybrid exchange-correlation
functional fails to describe the electronic structure of this defect. Using the
generalized Koopman's theorem, we fine tune the functional and obtain a
zero-phonon photoluminescence (ZPL) energy in the blue spectral range. We show
that the defect exhibits high emission rate in the ZPL line and features a
characteristic phonon side band that resembles the blue emitter's spectrum.
Furthermore, we study the electric field dependence of the ZPL and numerically
show that the defect exhibits a quadratic Stark shift for perpendicular to
plane electric fields, making the emitter insensitive to electric field
fluctuations in first order. Our work emphasize the need for assessing the
accuracy of common first principles methods in hBN and exemplifies a workaround
methodology. Furthermore, our work is a step towards understanding the
structure of the blue emitter and utilizing it in photonics applications.


  As main-sequence stars with C$>$O, dwarf carbon (dC) stars are never born
alone but inherit carbon-enriched material from a former asymptotic giant
branch (AGB) companion. In contrast to M dwarfs in post-mass transfer binaries,
C$_2$ and/or CN molecular bands allow dCs to be identified with
modest-resolution optical spectroscopy, even after the AGB remnant has cooled
beyond detectability. Accretion of substantial material from the AGB stars
should spin up the dCs, potentially causing a rejuvenation of activity
detectable in X-rays. Indeed, a few dozen dCs have recently been found to have
photometric variability with periods under a day. However, most of those are
likely post-common-envelope binaries (PCEBs), spin-orbit locked by tidal
forces, rather than solely spun-up by accretion. Here, we study the X-ray
properties of a sample of the five nearest known dCs with $Chandra$. Two are
detected in X-rays, the only two for which we also detected short-period
photometric variability. We suggest that the coronal activity detected so far
in dCs is attributable to rapid rotation due to tidal locking in short binary
orbits after a common-envelope phase, late in the thermally pulsing (TP) phase
of the former C-AGB primary (TP-AGB).


  We study the problem of computing the capacity of a discrete memoryless
channel under uncertainty affecting the channel law matrix, and possibly with a
constraint on the average cost of the input distribution. The problem has been
formulated in the literature as a max-min problem. We use the robust
optimization methodology to convert the max-min problem to a standard convex
optimization problem. For small-sized problems, and for many types of
uncertainty, such a problem can be solved in principle using interior point
methods (IPM). However, for large-scale problems, IPM are not practical. Here,
we suggest an $\mathcal{O}(1/T)$ first-order algorithm based on Nemirovski
(2004) which is applied directly to the max-min problem.


  Let $X^1,\ldots, X^d$ be sigma-martingales on $(\Omega,{\cal F}, P)$. We show
that every bounded martingale (with respect to the underlying filtration)
admits an integral representation w.r.t. $X^1,\ldots, X^d$ if and only if there
is no equivalent probability measure (other than $P$) under which
$X^1,\ldots,X^d$ are sigma-martingales.
  From this we deduce the second fundamental theorem of asset pricing- that
completeness of a market is equivalent to uniqueness of Equivalent
Sigma-Martingale Measure (ESMM).


  Let G be a connected simple Lie group with finite centre, K be a maximal
compact subgroup of G, and rank(G)= rank(K). Let \frak{g}_0=Lie(G),
\frak{k}_0=Lie(K) \subset \frak{g}_0, \frak{t}_0 be a maximal abelian
subalgebra of \frak{k}_0, \frak{g}=\frak{g}_0^\mathbb{C},
\frak{k}=\frak{k}_0^\mathbb{C}, and \frak{h}=\frak{t}_0^\mathbb{C}. In this
article, we have determined all Borel-de Siebenthal positive root systems of
\Delta=\Delta(\frak{g}, \frak{h}), the number of unitary equivalence classes of
all discrete series representations of G with trivial infinitesimal character,
the number of unitary equivalence classes of all holomorphic discrete series
representations of G (if G/K is Hermitian symmetric) with trivial infinitesimal
character, and the number of unitary equivalence classes of all Borel-de
Siebenthal discrete series representations of G (if G/K is not Hermitian
symmetric) with trivial infinitesimal character.


  In a molecular cloud dust opacity typically dominates over gas opacity, yet
in the vicinities of forming stars dust is depleted, and gas is the sole
provider of opacity. In the optically thin circumstellar environments the
radiation temperature cannot be assumed to be equal to the gas temperature,
hence the two-temperature Planck means are necessary to calculate the radiative
equilibrium.
  By using the two-temperature mean opacity one does obtain the proper
equilibrium gas temperature in a circumstellar environment, which is in a
chemical equilibrium. A careful consideration of a radiative transfer problem
reveals that the equilibrium temperature solution can be degenerate in an
optically thin gaseous environment.
  We compute mean gas opacities based on the publicly available code DFSYNTHE
by Kurucz and Castelli. We performed the calculations assuming local
thermodynamic equilibrium and an ideal gas equation of state. The values were
derived by direct integration of the high-resolution opacity spectrum.
  We produced two sets of gas opacity tables: Rosseland means and
two-temperature Planck means (the tables available via
http://cdsweb.u-strasbg.fr/ as well as via
http://www.mpia-hd.mpg.de/homes/malygin). For three metallicities [Me/H] =
0.0,+/-0.3 we covered the parameter range 3.48 <= log T_rad[K] <= 4.48 in
radiation temperature, 2.8 <= log T_gas[K]} <= 6.0 in gas temperature, and -10
<= log P[dyn cm^-2] <= 6 in gas pressure. We show that in the optically thin
circumstellar environment for a given stellar radiation field and local gas
density there are several equilibrium gas temperatures possible.
  We conclude that, in general, equilibrium gas temperature cannot be
determined without treating the temperature evolution.


  Electrons subjected to a strong spin-orbit coupling in two spatial dimensions
could form fractional incompressible quantum liquids without violating the
time-reversal symmetry. Here we construct a Lagrangian description of such
fractional topological insulators by combining the available experimental
information on potential host materials and the fundamental principles of
quantum field theory. This Lagrangian is a Landau-Ginzburg theory of spinor
fields, enhanced by a topological term that implements a state-dependent
fractional statistics of excitations whenever both particles and vortices are
incompressible. The spin-orbit coupling is captured by an external static SU(2)
gauge field. The presence of spin conservation or emergent U(1) symmetries
would reduce the topological term to the Chern-Simons effective theory tailored
to the ensuing quantum Hall state. However, the Rashba spin-orbit coupling in
solid-state materials does not conserve spin. We predict that it can
nevertheless produce incompressible quantum liquids with topological order but
without a quantized Hall conductivity. We discuss two examples of such liquids
whose description requires a generalization of the Chern-Simons theory. One is
an Abelian Laughlin-like state, while the other has a new kind of non-Abelian
many-body entanglement. Their quasiparticles exhibit fractional spin-dependent
exchange statistics, and have fractional quantum numbers derived from the
electron's charge and spin according to their transformations under
time-reversal. In addition to conventional phases of matter, the proposed
topological Lagrangian can capture a broad class of hierarchical Abelian and
non-Abelian topological states, involving particles with arbitrary spin or
general emergent SU(N) charges.


  Online continual learning aims to get closer to a live learning experience by
learning directly on a stream of data with temporally shifting distribution and
by storing a minimum amount of data from that stream. In this empirical
evaluation, we evaluate various methods from the literature that tackle online
continual learning. More specifically, we focus on the class-incremental
setting in the context of image classification, where the learner must learn
new classes incrementally from a stream of data. We compare these methods on
the Split-CIFAR100 and Split-TinyImagenet benchmarks, and measure their average
accuracy, forgetting, stability, and quality of the representations, to
evaluate various aspects of the algorithm at the end but also during the whole
training period. We find that most methods suffer from stability and
underfitting issues. However, the learned representations are comparable to
i.i.d. training under the same computational budget. No clear winner emerges
from the results and basic experience replay, when properly tuned and
implemented, is a very strong baseline. We release our modular and extensible
codebase at https://github.com/AlbinSou/ocl_survey based on the avalanche
framework to reproduce our results and encourage future research.


  In this paper, we study the existence and uniqueness of spatially
quasi-periodic solutions to the generalized KdV equation (gKdV for short) on
the real line with quasi-periodic initial data whose Fourier coefficients are
exponentially decaying. In order to solve for the Fourier coefficients of the
solution, we first reduce the nonlinear dispersive partial differential
equation to a nonlinear infinite system of coupled ordinary differential
equations, and then construct the Picard sequence to approximate them. However,
we meet, and have to deal with, the difficulty of studying {\bf the higher
dimensional discrete convolution operation for several functions}:
\[\underbrace{c\times\cdots\times c}_{\mathfrak p~\text{times}}~(\text{total
distance}):=\sum_{\substack{\clubsuit_1,\cdots,\clubsuit_{\mathfrak
p}\in\mathbb Z^\nu\\ \clubsuit_1+\cdots+\clubsuit_{\mathfrak p}=~\text{total
distance}}}\prod_{j=1}^{\mathfrak p}c(\clubsuit_j).\] In order to overcome it,
we apply a combinatorial method to reformulate the Picard sequence as a tree.
Based on this form, we prove that the Picard sequence is exponentially decaying
and fundamental ({\color{red}i.e., a} Cauchy sequence). We first give a
detailed discussion of the proof of the existence and uniqueness result in the
case $\mathfrak p=3$. Next, we prove existence and uniqueness in the general
case $\mathfrak p\geq 2$, which then covers the remaining cases $\mathfrak
p\geq 4$. As a byproduct, we recover the local result from \cite{damanik16}. We
exhibit the most important combinatorial index $\sigma$ and obtain a
relationship with other indices, which is essential to our proofs in the case
of general $\mathfrak p$.


  The cross section for the production of W bosons with subsequent decay W to
tau nu is measured with the ATLAS detector at the LHC. The analysis is based on
a data sample that was recorded in 2010 at a proton-proton center-of-mass
energy of sqrt(s) = 7 TeV and corresponds to an integrated luminosity of 34
pb^-1. The cross section is measured in a region of high detector acceptance
and then extrapolated to the full phase space. The product of the total W
production cross section and the W to tau nu branching ratio is measured to be
11.1 +/- 0.3 (stat) +/- 1.7 (syst) +/- 0.4 (lumi) nb.


  Evolutionary optimization algorithms, including particle swarm optimization
(PSO), have been successfully applied in oil industry for production planning
and control. Such optimization studies are quite challenging due to large
number of decision variables, production scenarios, and subsurface
uncertainties. In this work, a multi-stage, multi-swarm PSO (MS2PSO) is
proposed to fix certain issues with canonical PSO algorithm such as premature
convergence, excessive influence of global best solution, and oscillation.
  Multiple experiments are conducted using Olympus benchmark to compare the
efficacy of algorithms. Canonical PSO hyperparameters are first tuned to
prioritize exploration in early phase and exploitation in late phase. Next, a
two-stage multi-swarm PSO (2SPSO) is used where multiple-swarms of the first
stage collapse into a single swarm in the second stage. Finally, MS2PSO with
multiple stages and multiple swarms is used in which swarms recursively
collapse after each stage. Multiple swarm strategy ensures that diversity is
retained within the population and multiple modes are explored. Staging ensures
that local optima found during initial stage does not lead to premature
convergence. Optimization test case comprises of 90 control variables and a
twenty year period of flow simulation. It is observed that different algorithm
designs have their own benefits and drawbacks. Multiple swarms and stages help
algorithm to move away from local optima, but at the same time they may also
necessitate larger number of iterations for convergence. Both 2SPSO and MS2PSO
are found to be helpful for problems with high dimensions and multiple modes
where greater degree of exploration is desired.


  This work introduces a new music generation system, called
AffectMachine-Classical, that is capable of generating affective Classic music
in real-time. AffectMachine was designed to be incorporated into biofeedback
systems (such as brain-computer-interfaces) to help users become aware of, and
ultimately mediate, their own dynamic affective states. That is, this system
was developed for music-based MedTech to support real-time emotion
self-regulation in users. We provide an overview of the rule-based,
probabilistic system architecture, describing the main aspects of the system
and how they are novel. We then present the results of a listener study that
was conducted to validate the ability of the system to reliably convey target
emotions to listeners. The findings indicate that AffectMachine-Classical is
very effective in communicating various levels of Arousal ($R^2 = .96$) to
listeners, and is also quite convincing in terms of Valence (R^2 = .90). Future
work will embed AffectMachine-Classical into biofeedback systems, to leverage
the efficacy of the affective music for emotional well-being in listeners.


  We present a 9'x9' fully-sampled map of the CO J=1-0 emission in the nearby
starburst galaxy Maffei 2 obtained at the Five College Radio Astronomy
Observatory. The map reveals previously known strong CO emission in the central
starburst region as well as an extended asymmetric distribution with bright CO
lines at the ends of the bar and in a feature at the north-east edge of the
molecular disk. This northern feature, proposed previously to be an interacting
companion galaxy, could be a dwarf irregular galaxy, although the CO data are
also consistent with the feature being simply an extension of one of the spiral
arms. We estimate the total molecular gas mass of Maffei 2 to be (1.4-1.7)x10^9
Mo or ~3-4% of its dynamical mass. Adopting the recently determined lower value
for the CO-to-H2 conversion factor in the central region, our data lead to the
surprising result that the largest concentrations of molecular gas in Maffei 2
lie at the bar ends and in the putative dwarf companion rather than in the
central starburst. A gravitational stability analysis reveals that the extended
disk of Maffei 2 lies above the critical density for star formation; however,
whether the central region is also gravitationally unstable depends both on the
details of the rotation curve and the precise value of the CO-to-H2 conversion
factor in this region.


  We address the problem of projecting a point onto a quadratic hypersurface,
more specifically a central quadric. We show how this problem reduces to
finding a given root of a scalar-valued nonlinear function. We completely
characterize one of the optimal solutions of the projection as either the
unique root of this nonlinear function on a given interval, or as a point that
belongs to a finite set of computable solutions. We then leverage this
projection and the recent advancements in splitting methods to compute the
projection onto the intersection of a box and a quadratic hypersurface with
alternating projections and Douglas-Rachford splitting methods. We test these
methods on a practical problem from the power systems literature, and show that
they outperform IPOPT and Gurobi in terms of objective, execution time and
feasibility of the solution.


  We consider a class of statistical estimation problems in which we are given
a random data matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ (and possibly
some labels ${\boldsymbol y}\in{\mathbb R}^n$) and would like to estimate a
coefficient vector ${\boldsymbol \theta}\in{\mathbb R}^d$ (or possibly a
constant number of such vectors). Special cases include low-rank matrix
estimation and regularized estimation in generalized linear models (e.g.,
sparse regression). First order methods proceed by iteratively multiplying
current estimates by ${\boldsymbol X}$ or its transpose. Examples include
gradient descent or its accelerated variants.
  Celentano, Montanari, Wu proved that for any constant number of iterations
(matrix vector multiplications), the optimal first order algorithm is a
specific approximate message passing algorithm (known as `Bayes AMP'). The
error of this estimator can be characterized in the high-dimensional
asymptotics $n,d\to\infty$, $n/d\to\delta$, and provides a lower bound to the
estimation error of any first order algorithm. Here we present a simpler proof
of the same result, and generalize it to broader classes of data distributions
and of first order algorithms, including algorithms with non-separable
nonlinearities. Most importantly, the new proof technique does not require to
construct an equivalent tree-structured estimation problem, and is therefore
susceptible of a broader range of applications.


  In this paper, we propose a method for coarse camera pose computation which
is robust to viewing conditions and does not require a detailed model of the
scene. This method meets the growing need of easy deployment of robotics or
augmented reality applications in any environments, especially those for which
no accurate 3D model nor huge amount of ground truth data are available. It
exploits the ability of deep learning techniques to reliably detect objects
regardless of viewing conditions. Previous works have also shown that
abstracting the geometry of a scene of objects by an ellipsoid cloud allows to
compute the camera pose accurately enough for various application needs. Though
promising, these approaches use the ellipses fitted to the detection bounding
boxes as an approximation of the imaged objects. In this paper, we go one step
further and propose a learning-based method which detects improved elliptic
approximations of objects which are coherent with the 3D ellipsoid in terms of
perspective projection. Experiments prove that the accuracy of the computed
pose significantly increases thanks to our method and is more robust to the
variability of the boundaries of the detection boxes. This is achieved with
very little effort in terms of training data acquisition -- a few hundred
calibrated images of which only three need manual object annotation. Code and
models are released at
https://github.com/zinsmatt/3D-Aware-Ellipses-for-Visual-Localization.


  We investigated domain growth in switching processes between the low-spin and
high-spin phases in thermally induced hysteresis loops of spin-crossover (SC)
solids. Elastic interactions among the molecules induce effective long-range
interactions, and thus the boundary condition plays a significant role in the
dynamics. In contrast to SC systems with periodic boundary conditions, where
uniform configurations are maintained during the switching process, we found
that domain structures appear with open boundary conditions. Unlike Ising-like
models with short-range interactions, domains always grow from the corners of
the system. The present clustering mechanism provides an insight into the
switching dynamics of SC solids, in particular, in nano-scale systems.