  In this paper, we address web-scale visual entity recognition, specifically
the task of mapping a given query image to one of the 6 million existing
entities in Wikipedia. One way of approaching a problem of such scale is using
dual-encoder models (eg CLIP), where all the entity names and query images are
embedded into a unified space, paving the way for an approximate k-NN search.
Alternatively, it is also possible to re-purpose a captioning model to directly
generate the entity names for a given image. In contrast, we introduce a novel
Generative Entity Recognition (GER) framework, which given an input image
learns to auto-regressively decode a semantic and discriminative ``code''
identifying the target entity. Our experiments demonstrate the efficacy of this
GER paradigm, showcasing state-of-the-art performance on the challenging OVEN
benchmark. GER surpasses strong captioning, dual-encoder, visual matching and
hierarchical classification baselines, affirming its advantage in tackling the
complexities of web-scale recognition.


  Let F be a field of characteristic two. We determine all non-hyperbolic
quadratic forms over F that are Witt equivalent to a second trace form.


  It has been shown observationally that star formation (SF) correlates tightly
with the presence of molecular hydrogen (H$_2$). Therefore it would be
important to investigate its implication on galaxy formation in a cosmological
context. In the present work, we track the H$_2$ mass fraction within our
cosmological smoothed particle hydrodynamics (SPH) code GADGET-3 using an
equilibrium analytic model by Krumholz et al. This model allows us to regulate
the star formation in our simulation by the local abundance of H$_2$ rather
than the total cold gas density, and naturally introduce the dependence of star
formation on metallicity. We investigate implications of the equilibrium
H$_2$-based SF model on galaxy population properties, such as the
stellar-to-halo mass ratio (SHMR), baryon fraction, cosmic star formation rate
density (SFRD), galaxy specific SFR, galaxy stellar mass functions (GSMF), and
Kennicutt-Schmidt (KS) relationship. The advantage of our work over the
previous ones is having a large sample of simulated galaxies in a cosmological
volume from high-redshift to $z=0$. We find that low-mass halos with
M$_{DM}<10^{10.5}$ M$_\odot$ are less efficient in producing stars in the
H$_2$-based SF model at $z\geq6$, which brings the simulations to a better
agreement with observational estimates of SHMR and GSMF at the low-mass end.
This is particularly evident by a reduction in the number of low-mass galaxies
at M$_\star\leq10^{8}$ M$_\odot$ in the GSMF. The overall SFRD is also reduced
at high-$z$ in the H$_2$ run, which results in slightly higher SFRD at
low-redshift due to more abundant gas available for star formation at later
times. This new H$_2$ model is able to reproduce the empirical KS relationship
at $z=0$ naturally without the need for setting its normalization by hand, and
overall it seems to have more advantages than the previous pressure-based SF
model.


  Let (X,d) be a finite metric space. This paper first discusses the spectrum
of the p-distance matrix of a finite metric space of p-negative type and then
gives upper and lower bounds for the so called gap of a finite metric space of
strict p-negative type. Furthermore estimations for the gap under a certain
glueing construction for finite metric spaces are given and finally be applied
to finite ultrametric spaces.


  We present deep, wide-field J, H and Ks images taken with IRIS2 on the Anglo
Australian Telescope, towards the massive star formation region G305.2+0.2.
Combined with 3.6, 4.5, 5.8 and 8.0 micron data from the GLIMPSE survey on the
Spitzer Space Telescope, we investigate the properties of the embedded stellar
populations. After removing contamination from foreground stars we separate the
sources based on their IR colour. Strong extended emission in the GLIMPSE
images hampers investigation of the most embedded sources towards the known
sites of massive star formation. However, we find a sizeable population of IR
excess sources in the surrounding region free from these completeness effects.
Investigation reveals the recent star formation activity in the region is more
widespread than previously known.
  Stellar density plots show the embedded cluster in the region, G305.24+0.204,
is offset from the dust emission. We discuss the effect of this cluster on the
surrounding area and argue it may have played a role in triggering sites of
star formation within the region. Finally, we investigate the distribution of
IR excess sources towards the cluster, in particular their apparent lack
towards the centre compared with its immediate environs.


  In this paper, we study the near horizon symmetry and gravitational charges
in the Newman-Penrose formalism. In particular we investigate the effect from
topological terms. We find that the Pontryagin term and Gauss-Bonnet term have
significant influence on the near horizon charges and bring interesting novel
features. We show that the gravitational charge derived from a general class of
topological terms including the Pontryagin term and Gauss-Bonnet term can be
obtained from the ambiguities of the symplectic potential.


  The mini-proceedings of the Workshop on Meson Transition Form Factors held in
Cracow from May 29th to 30th, 2012 introduce the meson transition form factor
project with special emphasis on the interrelations between the various form
factors (on-shell, single off-shell, double off-shell). Short summaries of the
talks presented at the workshop follow.


  This article presents a spiking neuroevolutionary system which implements
memristors as plastic connections, i.e. whose weights can vary during a trial.
The evolutionary design process exploits parameter self-adaptation and variable
topologies, allowing the number of neurons, connection weights, and
inter-neural connectivity pattern to emerge. By comparing two phenomenological
real-world memristor implementations with networks comprised of (i) linear
resistors (ii) constant-valued connections, we demonstrate that this approach
allows the evolution of networks of appropriate complexity to emerge whilst
exploiting the memristive properties of the connections to reduce learning
time. We extend this approach to allow for heterogeneous mixtures of memristors
within the networks; our approach provides an in-depth analysis of network
structure. Our networks are evaluated on simulated robotic navigation tasks;
results demonstrate that memristive plasticity enables higher performance than
constant-weighted connections in both static and dynamic reward scenarios, and
that mixtures of memristive elements provide performance advantages when
compared to homogeneous memristive networks.


  We demonstrate a method to obtain homogeneous atom-cavity coupling by
selecting and keeping $^{87}$Rb atoms that are near maximally coupled to the
cavity's standing-wave mode. We select atoms by imposing an AC Stark shift on
the ground state hyperfine microwave transition frequency with light injected
into the cavity. We then induce a spin flip with microwaves that are resonant
for atoms that are near maximally coupled to the cavity mode of interest, after
which, we use radiation pressure forces to remove from the cavity all the atoms
in the initial spin state. Achieving greater homogeneity in the atom-cavity
coupling will potentially enhance entanglement generation, intracavity driving
of atomic transitions, cavity-optomechanics, and quantum simulations. This
approach can easily be extended to other atomic species with microwave or
optical transitions.


  The effect of Cu-doping at Mn-site on structural, magnetic and transport
properties in electron-doped manganites La0.85Te0.15Mn1-xCuxO3 has been
investigated. Based on the analysis of structural parameter variations, the
valence state of the Cu ion in Cu-doped manganites is suggested to be +2. All
samples undergo the paramagnetic-ferromagnetic (PM-FM) phase transition. The
Curie temperature decreases and the transition becomes broader with increasing
Cu-doping level, in contrast, the magnetization magnitude of Cu-doping samples
at low temperatures increase as x \leq 0.15. The insulator-metal (I-M)
transition moves to lower temperatures with increasing Cu-doping content and
disappears as x > 0.1. In addition, the higher temperature resistivity r peak
in double-peak-like r(T) curves observed in no Cu-doping sample is completely
suppressed as Cu-doping level x = 0.1 and r(T) curve only shows single I-M
transition at the low temperature well below . The results are discussed
according to the change of magnetic exchange interaction caused by Cu-doping.


  In this paper we introduce the Wastewater Treatment Plant Problem, a
real-world scheduling problem, and compare the performance of several tools on
it. We show that, for a naive modeling, state-of-the-art SMT solvers outperform
other tools ranging from mathematical programming to constraint programming. We
use both real and randomly generated benchmarks.
  From this and similar results, we claim for the convenience of developing
compiler front-ends being able to translate from constraint programming
languages to the SMT-LIB standard language.


  This paper proposes a modification to the traditional multiline
thru-reflect-line (TRL) or line-reflect-line (LRL) calibration method used for
vector network analyzers (VNAs). Our proposed method eliminates the need for a
thru (or line) standard by using an arbitrary transmissive two-port device in
combination with an additional reflect standard. This combination of standards
allows us to arbitrarily set the location of the calibration plane using
physical artifacts. In contrast to the standard multiline TRL method, the
suggested approach avoids a post-processing step to shift the calibration plane
if a line standard is used. We demonstrate our proposed method with
measurements on a printed circuit board (PCB) and compare it to the multiline
TRL method with a perfectly defined thru.


  A combined approach that uses the vibrational self-consistent field (VSCF)
and vibrational configuration interaction (VCI) method together with the
semiclassical instanton theory was developed to study vibrational tunneling
spectra of molecules with multiple wells. The method can be applied to
calculate low-lying vibrational states in the systems with arbitrary number of
wells, which are not necessarily related by a symmetry operation. It is
particularly suited to systems in which the wells are separated by large
potential barriers and tunneling splittings are small, so that the exact
quantum-mechanical methods come at a prohibitive computational cost. The
accuracy of the method was tested on a two-dimensional double-well model system
and on malonaldehyde, and the results were compared with the exact
quantum-mechanical calculations. The method was subsequently applied to the
asymmetrically deuterated malonaldehyde, which has non-degenerate vibrational
frequencies in the two wells. The spectrum is obtained at a cost of single-well
VSFC/VCI calculations. The interactions between states of different wells are
computed semiclassically at a comparatively negligible computational cost. The
method is particularly suited to the computation and assignment of spectra in
the studies of water clusters.


  Hierarchical modeling of abundance in space or time using closed-population
mark-recapture under heterogeneity (model M$_{h}$) presents two challenges: (i)
finding a flexible likelihood in which abundance appears as an explicit
parameter and (ii) fitting the hierarchical model for abundance. The first
challenge arises because abundance not only indexes the population size, it
also determines the dimension of the capture probabilities in heterogeneity
models. A common approach is to use data augmentation to include these capture
probabilities directly into the likelihood and fit the model using Bayesian
inference via Markov chain Monte Carlo (MCMC). Two such examples of this
approach are (i) explicit trans-dimensional MCMC, and (ii) superpopulation data
augmentation. The superpopulation approach has the advantage of simple
specification that is easily implemented in BUGS and related software. However,
it reparameterizes the model so that abundance is no longer included, except as
a derived quantity. This is a drawback when hierarchical models for abundance,
or related parameters, are desired. Here, we analytically compare the two
approaches and show that they are more closely related than might appear
superficially. We exploit this relationship to specify the model in a way that
allows us to include abundance as a parameter and that facilitates hierarchical
modeling using readily available software such as BUGS. We use this approach to
model trends in grizzly bear abundance in Yellowstone National Park from
1986-1998.


  One of the nicest results in cosmological perturbation theory is the
analytical resummaton of the leading corrections at large momentum, which was
obtained by Crocce and Scoccimarro for the propagator. Using an exact evolution
equation, we generalize this result, by showing that a class of next-to-leading
corrections can also be resummed at all orders in perturbation theory. The new
corrections modify the propagator by a few percent in the Baryonic Acoustic
Oscillation range of scales, and therefore cannot be neglected in resummation
schemes aiming at an accuracy compatible with future generation galaxy surveys.
Similar tools can be employed to derive improved approximations for the Power
Spectrum.


  We claim to give the definitive theory of what we call the `knee-jerk
mapping', which is the basis for a class of optimization algorithms introduced
by Baum, and promoted by Dempster, Laird, and Rubin under the name `EM
algorithm'.


  The radio complex Sgr B region is observed with the X-Ray Imaging
Spectrometers (XIS) on board Suzaku. This region exhibits diffuse iron lines at
6.4, 6.7 and 6.9 keV, which are K$\alpha$ lines of Fe \emissiontype{I} (neutral
iron), Fe\emissiontype{XXV} (He-like iron) and Fe\emissiontype{XXVI} (H-like
iron), respectively. The high energy resolving power of the XIS provides the
separate maps of the K-shell transition lines from Fe\emissiontype{I} (6.4 keV)
and Fe\emissiontype{XXV} (6.7 keV). Although the 6.7 keV line is smoothly
distributed over the Sgr B region, a local excess is found near at $(l, b) =
(\timeform {0D.61}, \timeform{0D.01})$, possibly a new SNR. The plasma
temperature is \textit{kT} $\sim$3 keV and the age is estimated to be around
several$\times10^{3}$ years. The 6.4 keV image is clumpy with local excesses
nearby Sgr B2 and at $(l, b) = (\timeform{0D.74}, -\timeform{0D.09})$. Like Sgr
B2, this excess may be another candidate of an X-ray reflection nebula (XRN).


  Cybersickness is a serious usability problem in virtual reality. Postural (or
balance) instability theory has emerged as one of the major hypotheses for the
cause of cybersickness. In this paper, we conducted a two-week-long experiment
to observe the trends in user balance learning and sickness tolerance under
different experimental conditions to analyze the potential inter-relationship
between them. The experimental results have shown, aside from the obvious
improvement in balance performance itself, that accompanying balance training
had a stronger effect of increasing tolerance to cybersickness than mere
exposure to VR. In addition, training in immersive VR was found to be more
effective than using the 2D-based non-immersive medium, especially for the
transfer effect to other non-training VR content.


  A promising route to testing quantum gravity in the laboratory is to look for
gravitationally-induced entanglement (GIE) between two or more quantum matter
systems. Proposals for such tests have principally used microsolid systems,
with highly non-classical states, such as N00N states or highly-squeezed
states. Here, we consider, for the first time, GIE between two atomic gas
interferometers as a test of quantum gravity. We propose placing the two
interferometers next to each other in parallel and looking for correlations in
the number of atoms at the output ports as evidence of GIE and quantum gravity.
GIE is possible without challenging macroscopic superposition states, such as
N00N or Schr\"odinger cat states, and instead there can be just classical-like
'coherent' states of atoms. This requires the total mass of the atom
interferometers to be on the Planck mass scale, and long integration times.
However, with current state-of-the-art quantum squeezing in cold atoms, we
argue that the mass scale can be reduced to approachable levels and detail how
such a mass scale can be achieved in the near future.


  Spherical Harmonic Transforms (SHT) are at the heart of many scientific and
practical applications ranging from climate modelling to cosmological
observations. In many of these areas new, cutting-edge science goals have been
recently proposed requiring simulations and analyses of experimental or
observational data at very high resolutions and of unprecedented volumes. Both
these aspects pose formidable challenge for the currently existing
implementations of the transforms.
  This paper describes parallel algorithms for computing SHT with two variants
of intra-node parallelism appropriate for novel supercomputer architectures,
multi-core processors and Graphic Processing Units (GPU). It also discusses
their performance, alone and embedded within a top-level, MPI-based
parallelisation layer ported from the S2HAT library, in terms of their
accuracy, overall efficiency and scalability. We show that our inverse SHT run
on GeForce 400 Series GPUs equipped with latest CUDA architecture ("Fermi")
outperforms the state of the art implementation for a multi-core processor
executed on a current Intel Core i7-2600K. Furthermore, we show that an
MPI/CUDA version of the inverse transform run on a cluster of 128 Nvidia Tesla
S1070 is as much as 3 times faster than the hybrid MPI/OpenMP version executed
on the same number of quad-core processors Intel Nahalem for problem sizes
motivated by our target applications. Performance of the direct transforms is
however found to be at the best comparable in these cases. We discuss in detail
the algorithmic solutions devised for major steps involved in the transforms
calculation, emphasising those with a major impact on their overall
performance, and elucidates the sources of the dichotomy between the direct and
the inverse operations.


  Audio-Visual Source Localization (AVSL) aims to locate sounding objects
within video frames given the paired audio clips. Existing methods
predominantly rely on self-supervised contrastive learning of audio-visual
correspondence. Without any bounding-box annotations, they struggle to achieve
precise localization, especially for small objects, and suffer from blurry
boundaries and false positives. Moreover, the naive semi-supervised method is
poor in fully leveraging the information of abundant unlabeled data. In this
paper, we propose a novel semi-supervised learning framework for AVSL, namely
Dual Mean-Teacher (DMT), comprising two teacher-student structures to
circumvent the confirmation bias issue. Specifically, two teachers, pre-trained
on limited labeled data, are employed to filter out noisy samples via the
consensus between their predictions, and then generate high-quality
pseudo-labels by intersecting their confidence maps. The sufficient utilization
of both labeled and unlabeled data and the proposed unbiased framework enable
DMT to outperform current state-of-the-art methods by a large margin, with CIoU
of 90.4% and 48.8% on Flickr-SoundNet and VGG-Sound Source, obtaining 8.9%,
9.6% and 4.6%, 6.4% improvements over self- and semi-supervised methods
respectively, given only 3% positional-annotations. We also extend our
framework to some existing AVSL methods and consistently boost their
performance.


  Process development is typically associated with lengthy wet-lab experiments
for the identification of good candidate setups and operating conditions. In
this paper, we present the key features of a model-based approach for the
identification and assessment of process design space (DSp), integrating the
analysis of process performance and flexibility. The presented approach
comprises three main steps: (1) model development & problem formulation, (2)
DSp identification, and (3) DSp analysis. We demonstrate how such an approach
can be used for the identification of acceptable operating spaces that enable
the assessment of different operating points and quantification of process
flexibility. The above steps are demonstrated on Protein A chromatographic
purification of antibody-based therapeutics used in biopharmaceutical
manufacturing.


  Neural language models are often trained with maximum likelihood estimation
(MLE), where the next word is generated conditioned on the ground-truth word
tokens. During testing, however, the model is instead conditioned on previously
generated tokens, resulting in what is termed exposure bias. To reduce this gap
between training and testing, we propose using optimal transport (OT) to match
the sequences generated in these two modes. An extension is further proposed to
improve the OT learning, based on the structural and contextual information of
the text sequences. The effectiveness of the proposed method is validated on
machine translation, text summarization, and text generation tasks.


  In this paper we use the ``Millennium Simulation'' to re-examine the mass
assembly history of dark matter halos and the age dependence of halo
clustering. We use eight different definitions of halo formation times to
characterize the different aspects of the assembly history of a dark matter
halo. We find that these formation times have different dependence on halo
mass. While some formation times characterize well the hierarchical nature of
halo formation, in the sense that more massive halos have later formation, the
trend is reversed for other definitions of the formation time. In particular,
the formation times that are likely to be related to the formation of galaxies
in dark halos show strong trends of ``down-sizing'', in that lower-mass halos
form later. We also investigate how the correlation amplitude of dark matter
halos depends on the different formation times. We find that this dependence is
quite strong for some definitions of formation time but weak or absent for
other definitions. In particular, the correlation amplitude of halos of a given
mass is almost independent of their last major merger time. For the definitions
that are expected to be more related to the formation of galaxies in dark
halos, a significant assembly bias is found only for halos less massive than
M_*. We discuss our results in connection to the hierarchical assembly of dark
matter halos, the ``archaeological down-sizing'' observed in the galaxy
population, and the observed color-dependence of the clustering strength of
galaxy groups and clusters.


  In this paper, we introduce and examine a fractional linear birth--death
process $N_{\nu}(t)$, $t>0$, whose fractionality is obtained by replacing the
time derivative with a fractional derivative in the system of
difference-differential equations governing the state probabilities
$p_k^{\nu}(t)$, $t>0$, $k\geq0$. We present a subordination relationship
connecting $N_{\nu}(t)$, $t>0$, with the classical birth--death process $N(t)$,
$t>0$, by means of the time process $T_{2\nu}(t)$, $t>0$, whose distribution is
related to a time-fractional diffusion equation. We obtain explicit formulas
for the extinction probability $p_0^{\nu}(t)$ and the state probabilities
$p_k^{\nu}(t)$, $t>0$, $k\geq1$, in the three relevant cases $\lambda>\mu$,
$\lambda<\mu$, $\lambda=\mu$ (where $\lambda$ and $\mu$ are, respectively, the
birth and death rates) and discuss their behaviour in specific situations. We
highlight the connection of the fractional linear birth--death process with the
fractional pure birth process. Finally, the mean values $\mathbb{E}N_{\nu}(t)$
and $\operatorname {\mathbb{V}ar}N_{\nu}(t)$ are derived and analyzed.


  A novel approach to an old symmetry problem is developed. A new proof is
given for the following symmetry problem, studied earlier.


  We calculate the ground-state properties of unpolarized two-component Fermi
gas by the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation
to the zero effective range of the attractive two-particle interaction, we find
$E/E_{\rm free}$ to be 0.212(2), 0.407(2), 0.409(3) and 0.398(3) for 4, 14, 38
and 66 atoms, respectively. Our results indicate that the dependence of the
total energy on the effective range is sizable and the extrapolation is
therefore quite important. In order to test the quality of nodal surfaces and
to estimate the impact of the fixed-node approximation we perform released-node
DMC calculations for 4 and 14 atoms. Analysis of the released-node and the
fixed-node results suggests that the main sources of the fixed-node errors are
long-range correlations which are difficult to sample in the released-node
approaches due to the fast growth of the bosonic noise. Besides energies, we
evaluate the two-body density matrix and the condensate fraction. We find that
the condensate fraction for the 66 atom system converges to 0.56(1) after the
extrapolation to the zero interaction range.


  Thermophoresis is a transport phenomenon induced by a temperature gradient.
Very small objects dispersed in a fluid medium and in a temperature gradient
present a non homogeneous steady density. Analysing this phenomenon within the
theoretical scenario of non interacting Brownian motion one can assume that
those particles are driven by a spatially dependent mechanical force. This
implies the existence of a potential which was derived in a previous work. From
this potential the qualitative properties of the force and the Soret
coefficient were obtained. Nevertheless a quantitative correlation between the
theory and the experimental data were not consistently proved. Here it is
presented a methodology to match this theory with the experimental data, which
it is used to analyse the experimental information of sodium docecyl sulfate
(SDS) micelles.


  Tensor network methods are becoming increasingly important for high-energy
physics, condensed matter physics and quantum information science (QIS). We
discuss the impact of tensor network methods on lattice field theory, quantum
gravity and QIS in the context of High Energy Physics (HEP). These tools will
target calculations for strongly interacting systems that are made difficult by
sign problems when conventional Monte Carlo and other importance sampling
methods are used. Further development of methods and software will be needed to
make a significant impact in HEP. We discuss the roadmap to perform quantum
chromodynamics (QCD) related calculations in the coming years. The research is
labor intensive and requires state of the art computational science and
computer science input for its development and validation. We briefly discuss
the overlap with other science domains and industry.


  In this paper we consider reinforcement learning tasks with progressive
rewards; that is, tasks where the rewards tend to increase in magnitude over
time. We hypothesise that this property may be problematic for value-based deep
reinforcement learning agents, particularly if the agent must first succeed in
relatively unrewarding regions of the task in order to reach more rewarding
regions. To address this issue, we propose Spectral DQN, which decomposes the
reward into frequencies such that the high frequencies only activate when large
rewards are found. This allows the training loss to be balanced so that it
gives more even weighting across small and large reward regions. In two domains
with extreme reward progressivity, where standard value-based methods struggle
significantly, Spectral DQN is able to make much farther progress. Moreover,
when evaluated on a set of six standard Atari games that do not overtly favour
the approach, Spectral DQN remains more than competitive: While it
underperforms one of the benchmarks in a single game, it comfortably surpasses
the benchmarks in three games. These results demonstrate that the approach is
not overfit to its target problem, and suggest that Spectral DQN may have
advantages beyond addressing reward progressivity.


  We report a search for the decay ${\overline B}^{0}\rightarrow{\Lambda_{\rm
c}^{+}}{\overline p}{p}{\overline p}$. Using a data sample of $471 \times
10^6\: B{\overline B}$ pairs collected with the BABAR detector at the PEP-II
storage ring at SLAC, we find no events and set an upper limit on the branching
fraction ${\cal B}({\overline B}^{0}\rightarrow{\Lambda_{\rm c}^{+}}{\overline
p}{p}{\overline p}) \times\frac{{\cal B}(\Lambda_{\rm c}^{+}\rightarrow p K^{-}
\pi^{+})}{0.050} < 2.8\times10^{-6}$ at $90\,%$ C.L., where we have normalized
${\cal B}(\Lambda_{\rm c}^{+}\rightarrow p K^{-} \pi^{+})$ to the world average
value.


  We performed numerical simulations and experiments on Josephson vortex flow
transistors based on parallel arrays of YBa2Cu3O(7-x) grain boundary junctions
with a cross gate-line allowing to operate the same devices in two different
modes named Josephson fluxon transistor (JFT) and Josephson fluxon-antifluxon
transistor (JFAT). The simulations yield a general expression for the current
gain vs. number of junctions and normalized loop inductance and predict higher
current gain for the JFAT. The experiments are in good agreement with
simulations and show improved coupling between gate line and junctions for the
JFAT as compared to the JFT.


  A Generalized Morse Potential (GMP) is an extension of the Morse Potential
(MP) with an additional exponential term and an additional parameter that
compensate for MP's erroneous behavior in the long range part of the
interaction potential. Because of the additional term and parameter, the
vibrational levels of the GMP cannot be solved analytically, unlike the case
for the MP. We present several numerical approaches for solving the vibrational
problem of the GMP based on Galerkin methods, namely the Laguerre Polynomial
Method (LPM), the Symmetrized Laguerre Polynomial Method (SLPM) and the
Polynomial Expansion method (PEM) and apply them to the vibrational levels of
the homonuclear diatomic molecules B$_2$, O$_2$ and F$_2$, for which high level
theoretical Full CI potential energy surfaces and experimentally measured
vibrational levels have been reported. Overall the LPM produces vibrational
states for the GMP that are converged to within spectroscopic accuracy of 0.01
cm$^{-1}$ in between 1 and 2 orders of magnitude faster and with much fewer
basis functions / grid points than the Colbert-Miller Discrete Variable
Representation (CM-DVR) method for the three homonuclear diatomic molecules
examined in this study.


  Many real-world tasks require an agent to reason jointly over text and visual
objects, (e.g., navigating in public spaces), which we refer to as
context-sensitive text-rich visual reasoning. Specifically, these tasks require
an understanding of the context in which the text interacts with visual
elements within an image. However, there is a lack of existing datasets to
benchmark the state-of-the-art multimodal models' capability on
context-sensitive text-rich visual reasoning. In this paper, we introduce
ConTextual, a novel dataset featuring human-crafted instructions that require
context-sensitive reasoning for text-rich images. We conduct experiments to
assess the performance of 14 foundation models (GPT-4V, Gemini-Pro-Vision,
LLaVA-Next) and establish a human performance baseline. Further, we perform
human evaluations of the model responses and observe a significant performance
gap of 30.8% between GPT-4V (the current best-performing Large Multimodal
Model) and human performance. Our fine-grained analysis reveals that GPT-4V
encounters difficulties interpreting time-related data and infographics.
However, it demonstrates proficiency in comprehending abstract visual contexts
such as memes and quotes. Finally, our qualitative analysis uncovers various
factors contributing to poor performance including lack of precise visual
perception and hallucinations. Our dataset, code, and leaderboard can be found
on the project page https://con-textual.github.io/


  MINOS is a long baseline neutrino oscillation experiment designed to make
precision measurements of the neutrino mixing parameters associated with the
atmospheric neutrino mass splitting. Using a neutrino beam from the Main
Injector (NuMI) facility at Fermilab, it compares the neutrino energy spectrum
for neutrino interactions observed in two large detectors located at Fermilab
and in the Soudan mine in northern Minnesota at a distance of 735km. We
describe initial results for electron neutrino appearance in MINOS after two
years of data-taking. We observe 35 events in the Far Detector with a
background prediction of $27\pm 5 {\rm (stat.)} \pm 2 {\rm (syst.)$ based on
the measurement in the Near Detector. The 1.5$\sigma$ excess of events can be
interpreted in terms of $\nu_{\mu}$ to $\nu_{e}$ oscillations. At 90% CL we
obtain an upper limit range of $\sin^2(2\theta_{13})< 0.28-0.34$ for the normal
neutrino mass hierarchy and $\sin^2(2\theta_{13})< 0.36-0.42$ for the inverted
hierarchy depending upon $\delta_{CP}$.


  We present a string theory realization for the correspondence between quantum
integrable models and supersymmetric gauge theories. The quantization results
from summing the effects of fundamental strings winding around a compact
direction. We discuss the examples of the XXZ gauge/Bethe correspondence and
five-dimensional \Omega--deformed SYM on M x S^1.


  We study connections between the problem of the existence of positive
solutions for certain nonlinear equations and weighted norm inequalities. In
particular, we obtain explicit criteria for the solvability of the Dirichlet
problem $$\aligned -& \Delta u = v \, u^q + w, \quad u \ge 0 \quad \text {on}
\quad \Omega, \\ &u = 0 \quad \text {on} \quad \partial \Omega, \endaligned $$
on a regular domain $\Omega$ in $\bold R^n$ in the ``superlinear case'' $q >
1$. The coefficients $v, w$ are arbitrary positive measurable functions (or
measures) on $\Omega$. We also consider more general nonlinear differential and
integral equations, and study the spaces of coefficients and solutions
naturally associated with these problems, as well as the corresponding
capacities.
  Our characterizations of the existence of positive solutions take into
account the interplay between $v$, $w$, and the corresponding Green's kernel.
They are not only sufficient, but also necessary, and are established without
any a priori regularity assumptions on $v$ and $w$; we also obtain sharp
two-sided estimates of solutions up to the boundary. Some of our results are
new even if $v \equiv 1$ and $\Omega$ is a ball or half-space.
  The corresponding weighted norm inequalities are proved for integral
operators with kernels satisfying a refined version of the so-called $3
G$-inequality by an elementary ``integration by parts'' argument. This also
gives a new unified proof for some classical inequalities including the
Carleson measure theorem for Poisson integrals and trace inequalities for Riesz
potentials and Green potentials.


  Order statistics arising from $m$ independent but not identically distributed
random variables are typically constructed by arranging some $X_{1}, X_{2},
\ldots, X_{m}$, with $X_{i}$ having distribution function $F_{i}(x)$, in
increasing order denoted as $X_{(1)} \leq X_{(2)} \leq \ldots \leq X_{(m)}$. In
this case, $X_{(i)}$ is not necessarily associated with $F_{i}(x)$. Assuming
one can simulate values from each distribution, one can generate such "non-iid"
order statistics by simulating $X_{i}$ from $F_{i}$, for $i=1,2,\ldots, m$, and
arranging them in order. In this paper, we consider the problem of simulating
ordered values $X_{(1)}, X_{(2)}, \ldots, X_{(m)}$ such that the marginal
distribution of $X_{(i)}$ is $F_{i}(x)$. This problem arises in Bayesian
principal components analysis (BPCA) where the $X_{i}$ are ordered eigenvalues
that are a posteriori independent but not identically distributed. We propose a
novel coupling-from-the-past algorithm to "perfectly" (up to computable order
of accuracy) simulate such {\emph{order-constrained non-iid}} order statistics.
We demonstrate the effectiveness of our approach for several examples,
including the BPCA problem.


  The $Z_3$-invariant next-to-minimal supersymmetric standard model (NMSSM) can
provide a candidate for dark matter (DM). It can also be used to explain the
hypothesis that the Higgs signal observed on the Large Hadron Collider (LHC)
comes from the contribution of the two lightest CP-even Higgs bosons, whose
masses are near 125 GeV. At present, XENON1T, LUX, and PandaX experiments have
imposed very strict restrictions on direct collision cross sections of {dark
matter}. In this paper, we consider a scenario that the observed Higgs signal
is the superposition of two mass-degenerate Higgs in the $Z_3$-invariant NMSSM
and scan the seven-dimension parameter space composing of $\lambda, \kappa,
\tan\beta, \mu, A_k, A_t, M_1$ via the Markov chain Monte Carlo (MCMC) method.
We find that the DM relic density, as well as the LHC searches for sparticles,
especially the DM direct detections, has provided a strong limit on the
parameter space. %Please check intended meaning has been retained. The allowed
parameter space is featured by a relatively small $\mu \le 300$ GeV and about
$\tan\beta\in(10,20)$. In addition, the DM is Higgsino-dominated because of
$|\frac{2\kappa}{\lambda}|>1$. Moreover, the co-annihilation between
$\tilde{\chi}_1^0$ and $\tilde{\chi}_1^\pm$ must be taken into account to
obtain the reasonable DM relic density.


  We present exact quantum solutions for a noncommutative, multidimensional
cosmological model and show that stabilization of extra dimensions sets in with
the introduction of noncommutativity between the scale factors. An
interpretation is offered to accommodate the notion of time, rendering
comparison with the classical solutions possible.


  This document describes the theory used for the calculation of track
geometric irregularities on a Track Geometry Measuring System (TGMS) to be
installed in railway vehicles. The TGMS includes a computer for data
acquisition and process, a set of sensors including an inertial measuring unit
(IMU, 3D gyroscope and 3D accelerometer), two video cameras and an encoder. The
main features of the proposed system are: 1. It is capable to measure track
alignment, vertical profile, cross-level, gauge, twist and rail-head profile
using non-contact technology. 2. It can be installed in line railway vehicles.
It is compact and low cost. Provided that the equipment sees the rail heads
when the vehicle is moving, it can be installed in any body of the vehicle: at
the wheelsets level, above primary suspension (bogie frame) or above the
secondary suspension (car body).


  In recent years, there has been growing interest in utilizing modern machine
learning techniques to learn heuristic functions for forward search algorithms.
Despite this, there has been little theoretical understanding of what they
should learn, how to train them, and why we do so. This lack of understanding
has resulted in the adoption of diverse training targets (suboptimal vs optimal
costs vs admissible heuristics) and loss functions (e.g., square vs absolute
errors) in the literature. In this work, we focus on how to effectively utilize
the information provided by admissible heuristics in heuristic learning. We
argue that learning from poly-time admissible heuristics by minimizing mean
square errors (MSE) is not the correct approach, since its result is merely a
noisy, inadmissible copy of an efficiently computable heuristic. Instead, we
propose to model the learned heuristic as a truncated gaussian, where
admissible heuristics are used not as training targets but as lower bounds of
this distribution. This results in a different loss function from the MSE
commonly employed in the literature, which implicitly models the learned
heuristic as a gaussian distribution. We conduct experiments where both MSE and
our novel loss function are applied to learning a heuristic from optimal plan
costs. Results show that our proposed method converges faster during training
and yields better heuristics.


  In this present paper, we solve the $\partial\bar{\partial}$ for extendable
currents definite in a pseudoconvexe unbounded domain of $\mathbb{C}^n$ .


  Bacterial nanocellulose (BNC) was used to synthesize rigid polyurethane foams
(RPUFs) based on its reaction with the isocyanate precursor (ISO route) and
also by using the conventional procedure (POL route). The results indicated
that at only 0.1 wt. % of BNC, drastic improvements of specific elastic
compressive modulus (+244.2 %) and strength (+77.5 %) were found. The reaction
of BNC with the precursor was corroborated through the measurement of
isocyanate number and the BNC caused a significant nucleation effect,
decreasing the cell size up to 39.7%. DSC analysis revealed that the BNC had a
strong effect on post-cure enthalpy, decreasing its value when the ISO route
was implemented. DMA analysis revealed that the RPUFs developed using the ISO
route proved to have an improved damping factor, regardless of BNC
concentration. These results emphasize the importance of using the ISO route to
achieve foamed nanocomposites with improved specific mechanical properties.


  A multiphysics finite volume method (FVM) solver, coupling neutronics and
shock physics, is under development at Politecnico di Milano for the analysis
of shock imploding fissile materials [1]. The proposed solver can be a useful
tool to make preliminary safety assessment of subcritical plutonium experiments
[2] and, more in general, to perform criticality safety evaluations in case of
strongly energetic events (such as chemical explosions) involving fissile
materials [3]. To this aim, a multi-group SP3 neutron transport model is
coupled with a hydrodynamic shock physics model [4], suitable to describe the
propagation of strong shockwaves in solid materials. The shock physics module
implements a dynamic mesh to reproduce material deformations and its governing
equations are written in an Arbitrary Lagrangian Eulerian (ALE) formulation to
preserve the mesh quality in case of large distortions.


  The Zeeman effect offers unique opportunities for magnetic manipulation of
the spin degree of freedom (DOF). Recently, valley Zeeman splitting, referring
to the lifting of valley degeneracy, has been demonstrated in two-dimensional
transition metal dichalcogenides (TMDs) at liquid helium temperature. However,
to realize the practical applications of valley pseudospins, the valley DOF
must be controllable by a magnetic field at room temperature, which remains a
significant challenge. Magnetic doping in TMDs can enhance the Zeeman
splitting, however, to achieve this experimentally is not easy. Here, we report
unambiguous magnetic manipulation of valley Zeeman splitting at 300 K (g =
-6.4) and 10 K (g = -11) in a CVD-grown Fe-doped MoS2 monolayer; the effective
g factor can be tuned to -20.7 by increasing the Fe dopant concentration, which
represents an approximately fivefold enhancement as compared to undoped MoS2.
Our measurements and calculations reveal that the enhanced splitting and geff
factors are due to the Heisenberg exchange interaction of the localized
magnetic moments (Fe 3d electrons) with MoS2 through the d-orbital
hybridization.


  The emission rate of a point dipole can be strongly increased in presence of
a well-designed optical antenna. Yet, optical antenna design is largely based
on radio-frequency rules, ignoring e.g.~ohmic losses and non-negligible field
penetration in metals at optical frequencies. Here we combine reciprocity and
Poynting's theorem to derive a set of optical-frequency antenna design rules
for benchmarking and optimizing the performance of optical antennas driven by
single quantum emitters. Based on these findings a novel plasmonic cavity
antenna design is presented exhibiting a considerably improved performance
compared to a reference two-wire antenna. Our work will be useful for the
design of high-performance optical antennas and nanoresonators for diverse
applications ranging from quantum optics to antenna-enhanced single-emitter
spectroscopy and sensing.


  Intersection with the debris of a large (50-100 km) short-period comet during
the Upper Palaeolithic provides a satisfactory explanation for the catastrophe
of celestial origin which has been postulated to have occurred around 12900 BP,
and which presaged a return to ice age conditions of duration ~1300 years. The
Taurid Complex appears to be the debris of this erstwhile comet; it includes at
least 19 of the brightest near-Earth objects. Sub-kilometre bodies in meteor
streams may present the greatest regional impact hazard on timescales of human
concern.


  We study the three-dimensional two-band Anderson model of localization and
compare our results to experimental results for amorphous metallic alloys
(AMA). Using the transfer-matrix method, we identify and characterize the
metal-insulator transitions as functions of Fermi level position, band
broadening due to disorder and concentration of alloy composition. The
appropriate phase diagrams of regions of extended and localized electronic
states are studied and qualitative agreement with AMA such as Ti-Ni and Ti-Cu
metallic glasses is found. We estimate the critical exponents nu_W, nu_E and
nu_x when either disorder W, energy E or concentration x is varied,
respectively. All our results are compatible with the universal value nu ~ 1.6
obtained in the single-band Anderson model.


  To unravel the origin of the dielectric anomaly at the antiferromagnetic
ordering of magnetoelectric Bi$_2$Fe$_4$O$_9$ we performed neutron powder
diffraction measurements across the N$\acute{\rm e}$el temperature, $T_{\rm
N}$. Both local structures and long-range symmetry are studied using the
complementary analyses of atomic pair distribution function (PDF) and Rietveld
methods at temperatures 300~K, 250~K, and 200~K. We present that PDF peaks
which reflect local atomic arrangements exhibit a noticeable variation below
$T_{\rm N}$ without long-range symmetry change. The implication of the PDF
evolution is discussed in view of a local structural distortion at the onset of
the antiferromagnetic ordering.


  In this paper we consider online mirror descent (OMD) algorithms, a class of
scalable online learning algorithms exploiting data geometric structures
through mirror maps. Necessary and sufficient conditions are presented in terms
of the step size sequence $\{\eta_t\}_{t}$ for the convergence of an OMD
algorithm with respect to the expected Bregman distance induced by the mirror
map. The condition is $\lim_{t\to\infty}\eta_t=0,
\sum_{t=1}^{\infty}\eta_t=\infty$ in the case of positive variances. It is
reduced to $\sum_{t=1}^{\infty}\eta_t=\infty$ in the case of zero variances for
which the linear convergence may be achieved by taking a constant step size
sequence. A sufficient condition on the almost sure convergence is also given.
We establish tight error bounds under mild conditions on the mirror map, the
loss function, and the regularizer. Our results are achieved by some novel
analysis on the one-step progress of the OMD algorithm using smoothness and
strong convexity of the mirror map and the loss function.


  We present a \asnmr Nuclear Magnetic Resonance (NMR) and resistivity study of
the effect of 5.5 MeV proton irradiation on the optimal electron doped ($x=$
0.068) and overdoped ($x=$ 0.107) Ba(Fe$_{1-x}$Rh$_x$)$_2$As$_2$ iron based
superconductors. While the proton induced defects only mildly suppress the
critical temperature and increase residual resistivity in both compositions,
sizable broadening of the NMR spectra was observed in all the irradiated
samples at low temperature. The effect is significantly stronger in the
optimally doped sample where the Curie Weiss temperature dependence of the line
width suggests the onset of ferromagnetic correlations coexisting with
superconductivity at the nanoscale. 1/T$_2$ measurements revealed that the
energy barrier characterizing the low energy spin fluctuations of these
compounds is enhanced upon proton irradiation, suggesting that the defects are
likely slowing down the fluctuations between ($0,\pi)$ and ($\pi$,0) nematic
ground states.


  The main results from a deep X-ray observation of M82 are summarised:
spatially-dependent chemical abundances, temperature structure of the gas,
charge-exchange emission lines in the spectrum. We also present an update of
the chemical bundances, based on a more refined extraction of spectra.


  We consider corrections to nucleon correlation functions arising from times
that are far from the asymptotic limit. For such times, the single nucleon
state is contaminated by the pion-nucleon and pion-delta continuum. We use
heavy baryon chiral perturbation theory to derive the spectral representation
of the nucleon two-point function. Finite time corrections to the axial current
correlation function are also derived. Pion-nucleon excited state contributions
drive the axial correlator upward, while contributions from the interference of
pion-delta and pion-nucleon states drive the axial correlator downward. Our
results can be compared qualitatively to optimized nucleon correlators
calculated in lattice QCD, because the chiral corrections characterize only
low-energy excitations above the ground state. We show that improved nucleon
operators can lead to an underestimation of the nucleon axial charge.


  Unmanned Aerial Vehicle (UAV) path planning algorithms often assume a
knowledge reward function or priority map, indicating the most important areas
to visit. In this paper we propose a method to create priority maps for
monitoring or intervention of dynamic spreading processes such as wildfires.
The presented optimization framework utilizes the properties of positive
systems, in particular the separable structure of value (cost-to-go) functions,
to provide scalable algorithms for surveillance and intervention. We present
results obtained for a 16 and 1000 node example and convey how the priority map
responds to changes in the dynamics of the system. The larger example of 1000
nodes, representing a fictional landscape, shows how the method can integrate
bushfire spreading dynamics, landscape and wind conditions. Finally, we give an
example of combining the proposed method with a travelling salesman problem for
UAV path planning for wildfire intervention.


  We use geometric ideas coming from certain classic algebraic constructions to
associate, to every classical field theory, a symmetric monoidal double functor
from the double category of cobordisms with corners to a certain symmetric
monoidal double category. We call symmetric monoidal double functors so
constructed cylinder topological quantum field theories. Our initial
formulation of cylinder topological quantum field theory is presented in a
purely topological context. We present appropriate refinements in order to
accommodate information relevant to classical field theory.


  The 325MHz, {\beta}=0.40 superconducting single spoke cavity (Spoke040) was
one of the most challenges for the China-ADS (Accelerator Driven System)
project. The design was finished, and the fabrication was in progressing. In
this paper, we studied the main radio frequency (RF) and mechanical parameters,
and compared the arc-shaped and plate-shaped end group structures.


  Using a support vector machine requires to set two types of hyperparameters:
the soft margin parameter C and the parameters of the kernel. To perform this
model selection task, the method of choice is cross-validation. Its
leave-one-out variant is known to produce an estimator of the generalization
error which is almost unbiased. Its major drawback rests in its time
requirement. To overcome this difficulty, several upper bounds on the
leave-one-out error of the pattern recognition SVM have been derived. Among
those bounds, the most popular one is probably the radius-margin bound. It
applies to the hard margin pattern recognition SVM, and by extension to the
2-norm SVM. In this report, we introduce a quadratic loss M-SVM, the M-SVM^2,
as a direct extension of the 2-norm SVM to the multi-class case. For this
machine, a generalized radius-margin bound is then established.


  We describe an invariant of links in the three-sphere which is closely
related to Khovanov's Jones polynomial homology. Our construction replaces the
symmetric algebra appearing in Khovanov's definition with an exterior algebra.
The two invariants have the same reduction modulo 2, but differ over the
rationals. There is a reduced version which is a link invariant whose graded
Euler characteristic is the normalized Jones polynomial.


  It is argued that in the case of a smooth transition across a
(dilaton-driven) curvature bounce the growing mode of the vector fluctuations
matches continuously with a decaying mode at later times. Analytical examples
of this observation are given both in the presence and in the absence of fluid
sources. In the case of multidimensional bouncing models the situation is
different, since the system of differential equations describing the vector
modes of the geometry has a richer structure. The amplification of the vector
modes of the geometry is specifically investigated in a regular
five-dimensional bouncing curvature model where scale factors of the external
and internal manifolds evolve at a dual rate. Vector fluctuations, in this
case, can be copiously produced and are continuous across the bounce. The
relevance of these results is critically illustrated.


  A systematic construction of the energy-density functional within the local
density approximation is presented. The Hartree-Fock equations corresponding to
such a functional are solved in case of rotating superdeformed nuclei. The
identical bands in $^{152}$Dy, $^{151}$Tb, and $^{150}$Gd are investigated and
the time-odd components in the rotating mean field are analyzed.


  The classical procedures which define the relativistic notion of space-time
can be implemented in the framework of Quantum Field Theory. Only relying on
the conformal symmetries of field propagation, time-frequency transfer and
localization lead to the definition of time-frequency references and positions
in space-time as quantum observables. Quantum positions have a non vanishing
commutator identifying with spin, both observables characterizing quantum
localization in space-time. Frame transformations to accelerated frames differ
from their classical counterparts. Conformal symmetry nevertheless allows to
extend the covariance rules underlying the formalism of general relativity
under an algebraic form suiting the quantum framework.


  The two most commonly used hypergeometric functions are the confluent
hypergeometric function and the Gauss hypergeometric function. We review the
available techniques for accurate, fast, and reliable computation of these two
hypergeometric functions in different parameter and variable regimes. The
methods that we investigate include Taylor and asymptotic series computations,
Gauss-Jacobi quadrature, numerical solution of differential equations,
recurrence relations, and others. We discuss the results of numerical
experiments used to determine the best methods, in practice, for each parameter
and variable regime considered. We provide 'roadmaps' with our recommendation
for which methods should be used in each situation.


  In the Shortest Superstring problem, we are given a set of strings and we are
asking for a common superstring, which has the minimum number of characters.
The Shortest Superstring problem is NP-hard and several constant-factor
approximation algorithms are known for it. Of particular interest is the GREEDY
algorithm, which repeatedly merges two strings of maximum overlap until a
single string remains. The GREEDY algorithm, being simpler than other
well-performing approximation algorithms for this problem, has attracted
attention since the 1980s and is commonly used in practical applications.
  Tarhio and Ukkonen (TCS 1988) conjectured that GREEDY gives a
2-approximation. In a seminal work, Blum, Jiang, Li, Tromp, and Yannakakis
(STOC 1991) proved that the superstring computed by GREEDY is a
4-approximation, and this upper bound was improved to 3.5 by Kaplan and Shafrir
(IPL 2005).
  We show that the approximation guarantee of GREEDY is at most
$(13+\sqrt{57})/6 \approx 3.425$, making the first progress on this question
since 2005. Furthermore, we prove that the Shortest Superstring can be
approximated within a factor of $(37+\sqrt{57})/18\approx 2.475$, improving
slightly upon the currently best $2\frac{11}{23}$-approximation algorithm by
Mucha (SODA 2013).


  We explore the conceptual usefulness of Riemannian geometric tools induced by
the statistical concept of distinguishability in quantifying the effect of a
depolarizing channel on quantum states. Specifically, we compare the geometries
of the interior of undeformed and deformed Bloch spheres related to density
operators on a two-dimensional Hilbert space. We show that randomization
emerges geometrically through a smaller infinitesimal quantum line element on
the deformed Bloch sphere while the uniform contraction manifests itself via a
deformed set of geodesics where the spacial components of the deformed
four-Bloch vector are simply the contracted versions of the undeformed Bloch
vector components.


  Intersecting D-brane models seem to be one of the most promising avenues to
embed the Standard Model physics within the string context. We review here
different aspects of these models. Topics include the question of SUSY and
quasi-SUSY in intersecting brane models, model-building, the brane
recombination interpretation of the SM Higgs mechanism, Yukawa couplings, the
lowering of the string scale and possible new Z's accessible to accelerators.


  The value of the tensor-to-scalar ratio $r$ in the region allowed by the
latest $Planck$ 2015 measurements can be associated to a large variety of
inflationary models. We discuss here the potential of future Cosmic Microwave
Background cosmological observations in disentangling among the possible
theoretical scenarios allowed by our analyses of current $Planck$ temperature
and polarization data. Rather than focusing only on $r$, we focus as well on
the running of the primordial power spectrum, $\alpha_s$ and the running of
thereof, $\beta_s$. Our Fisher matrix method benefits from a detailed and
realistic appraisal of the expected foregrounds. Future cosmological probes, as
the COrE mission, may be able to reach an unprecedented accuracy in the
extraction of $\beta_s$ and rule out the most favoured inflationary models.


  A quasispecies evolving on a fitness landscape with a single peak of
fluctuating height is studied. In the approximation that back mutations can be
ignored, the rate equations can be solved analytically. It is shown that the
error threshold on this class of dynamic landscapes is defined by the time
average of the selection pressure. In the case of a periodically fluctuating
fitness peak we also study the phase-shift and response amplitude of the
previously documented low-pass filter effect. The special case of a small
harmonic fluctuation is treated analytically.


  In this paper we investigate realization theory of a class of non-linear
systems, called Nash systems. Nash systems are non-linear systems whose vector
fields and readout maps are analytic semi-algebraic functions. In this paper we
will present a characterization of minimality in terms of observability and
reachability and show that minimal Nash systems are isomorphic. The results are
local in nature, i.e. they hold only for small time intervals. The hope is that
the presented results can be extended to hold globally.


  A direct WIMP (Weakly Interacting Massive Particle) detector with a neutron
veto system is designed to better reject neutrons. Two experimental
configurations are studied in the present paper: one is for an Xe detector
enclosed in a Gd-loaded scintillator and the other one is for an Xe detector
placed inside a reactor neutrino detector. The Gd-doped liquid scintillator (or
the neutrino detector) is used as a neutron veto device. The neutron
backgrounds for the two experimental designs have been estimated using Geant4
simulations. The results show that the neutron backgrounds can decrease to
O(0.1) events per year per tonne of liquid Xenon. We calculate the
sensitivities to spin-independent WIMP-nucleon elastic scattering. An exposure
of one tonne $\times$ year could reach a cross-section of about
6$\times$$10^{-11}$ pb.


  For a finite field of odd cardinality $q$, we show that the sequence of
iterates of $aX^2+c$, starting at $0$, always recurs after $O(q/\log\log q)$
steps. For $X^2+1$ the same is true for any starting value. We suggest that the
traditional "Birthday Paradox" model is inappropriate for iterates of $X^3+c$,
when $q$ is 2 mod 3.


  For the entangled neutral kaon system we formulate a Bell inequality
sensitive to CP violation in mixing. Via this Bell inequality we obtain a bound
on the leptonic CP asymmetry which is violated by experimental data.
Furthermore, we connect the Bell inequality with a decoherence approach and
find a lower bound on the decoherence parameter which practically corresponds
to Furry's hypothesis.


  We describe the spaces of the positive and tropical points of the moduli
space $\mathcal{P}_{PGL_2,\Sigma}$ introduced by Goncharov--Shen [GS19] as
certain Teichm\"uller and lamination spaces, respectively, with additional data
of pinnings. In the case where the surface $\Sigma$ has no punctures, we obtain
the formulae relating various functions on the Teichm\"uller space with
pinnings: $\lambda$-lengths, cross ratio coordinates, and Wilson lines. A
topological description of the tropicalized amalgamation map is given in terms
of $\mathcal{P}$-laminations.
  Based on our topological study of these "$\mathcal{P}$-type" spaces, we
investigate the compatibility of the Fock--Goncharov duality maps
$\mathbb{I}_\mathcal{A}$, $\mathbb{I}_\mathcal{X}$ constructed by
[FG06,FG07,MSW13,GS15] under the extended ensemble map. We also discuss the
amalgamation of bracelet bases.


  Although a fair amount of work has been devoted to growing Monte-Carlo merger
trees which resemble those built from an N-body simulation, comparatively
little effort has been invested in quantifying the caveats one necessarily
encounters when one extracts trees directly from such a simulation. To somewhat
revert the tide, this paper seeks to provide its reader with a comprehensive
study of the problems one faces when following this route. The first step to
building merger histories of dark matter haloes and their subhaloes is to
identify these structures in each of the time outputs (snapshots) produced by
the simulation. Even though we discuss a particular implementation of such an
algorithm (called AdaptaHOP) in this paper, we believe that our results do not
depend on the exact details of the implementation but extend to most if not all
(sub)structure finders. We then highlight different ways to build merger
histories from AdaptaHOP haloes and subhaloes, contrasting their various
advantages and drawbacks. We find that the best approach to (sub)halo merging
histories is through an analysis that goes back and forth between
identification and tree building rather than one which conducts a
straightforward sequential treatment of these two steps. This is rooted in the
complexity of the merging trees which have to depict an inherently dynamical
process from the partial temporal information contained in the collection of
instantaneous snapshots available from the N-body simulation.


  The automation of factories and manufacturing processes has been accelerating
over the past few years, boosted by the Industry 4.0 paradigm, including
diverse scenarios with mobile, flexible agents. Efficient coordination between
mobile robots requires reliable wireless transmission in highly dynamic
environments, often with strict timing requirements. Goal-oriented
communication is a possible solution for this problem: communication decisions
should be optimized for the target control task, providing the information that
is most relevant to decide which action to take. From the control perspective,
networked control design takes the communication impairments into account in
its optmization of physical actions. In this work, we propose a joint design
that combines goal-oriented communication and networked control into a single
optimization model, an extension of a multiagent POMDP which we call
Cyber-Physical POMDP (CP-POMDP). The model is flexible enough to represent
several swarm and cooperative scenarios, and we illustrate its potential with
two simple reference scenarios with a single agent and a set of supporting
sensors. Joint training of the communication and control systems can
significantly improve the overall performance, particularly if communication is
severely constrained, and can even lead to implicit coordination of
communication actions.


  In this paper we explore the existing tensions in the local cosmological
expansion rate, $H_0$, and amplitude of the clustering of large-scale structure
at $8\, h^{-1}\mathrm{Mpc}$, $\sigma_8$, as well as models that claim to
alleviate these tensions. We consider seven models: evolving dark energy
($w$CDM), extra radiation ($N_\mathrm{eff}$), massive neutrinos, curvature,
primordial magnetic fields (PMF), self-interacting neutrino models, and early
dark energy (EDE). We test these models against three data sets that span the
full range of measurable cosmological epochs, have significant precision, and
are well-tested against systematic effects: the Planck 2018 cosmic microwave
background data, the Sloan Digital Sky Survey baryon acoustic oscillation scale
measurements, and the Pantheon catalog of Type Ia supernovae. We use the recent
SH0ES $H_0$ measurement and several measures of $\sigma_8$ (and its related
parameter $S_8=\sigma_8\sqrt{\Omega_\mathrm{m}/0.3}$). We find that four models
are above the "strong" threshold in Bayesian model selection, $w$CDM,
$N_\mathrm{eff}$, PMF, and EDE. However, only EDE also relieves the $H_0$
tension in the full data sets to below 2$\sigma$. Contrarily, no model
alleviates the $S_8/\sigma_8$ tension in the full data set, nor does better
than $\Lambda$CDM in the combined case of both $H_0$ and $S_8/\sigma_8$
tensions.


  During the growth of a cold dark matter halo, the direction of its spin can
undergo rapid changes. These could disrupt or even destroy a stellar disc
forming in the halo, possibly resulting in the generation of a bulge or
spheroid. We investigate the frequency of significant changes in the
orientation of the angular momentum vector of dark matter haloes ("spin
flips"), and their degree of correlation with mergers. We focus on haloes of
mass similar to that of the Milky Way (MW) halo at redshift z=0 (log M/(Msol/h)
= 12.0 to 12.5) and consider flips in the spin of the whole halo or just its
inner parts. We find that a greater fraction of major mergers are associated
with large spin flips than minor mergers. However, since major mergers are
rare, the vast majority (93%) of large whole-halo spin flips (angle change >=
45 degrees) coincide with small mass changes, not major mergers. The spin
vector of the inner halo experiences much more frequent flips than the halo as
a whole. Over their entire lifetimes (i.e. after a halo acquires half of its
final mass), over 10% of halos experience a flip of at least 45 degrees in the
spin of the entire halo and nearly 60 percent experience a flip this large in
the inner halo. These numbers are reduced to 9 percent for the whole halo and
47 percent for the inner halo when we consider only haloes with no major
mergers after formation. Our analysis suggests that spin flips (whose effects
are not currently included in galaxy formation models) could be an important
factor in the morphological transformation of disc galaxies.


  Given positive coprime integers $a$ and $b$ and a natural number $h$, we
obtain reciprocity relations which can be used to quickly evaluate summations
like $\sum_{i=1}^{h} \{\frac{ib}{a}\}^2$ and $\sum_{i=1}^{h} \lfloor
\frac{ib}{a} \rfloor^2$, where $\lfloor x \rfloor$ and $\{x\}$ denote the floor
function and the fractional part of $x$, respectively.


  The burgeoning fields of quantum computing and quantum key distribution have
created a demand for a quantum memory. The gradient echo memory scheme is a
quantum memory candidate for light storage that can boast efficiencies
approaching unity, as well as the flexibility to work with either two or three
level atoms. The key to this scheme is the frequency gradient that is placed
across the memory. Currently the three level implementation uses a Zeeman
gradient and warm atoms. In this paper we model a new gradient creation
mechanism - the ac Stark effect - to provide an improvement in the flexibility
of gradient creation and field switching times. We propose this scheme in
concert with a move to cold atoms (~1 mK). These temperatures would increase
the storage times possible, and the small ensemble volumes would enable large
ac Stark shifts with reasonable laser power. We find that memory bandwidths on
the order of MHz can be produced with experimentally achievable laser powers
and trapping volumes, with high precision in gradient creation and switching
times on the order of nanoseconds possible. By looking at the different
decoherence mechanisms present in this system we determine that coherence times
on the order of 10s of milliseconds are possible, as are delay-bandwidth
products of approximately 50 and efficiencies over 90%.


  In 1996, Huisen-Yau proved that every three-dimensional, asymptotically
Schwarzschilden manifold with positive mass is uniquely foliated by stable
spheres of constant mean curvature and they defined the center of mass using
this CMC-foliation. Rigger and Neves-Tian showed in 2004 and 2009/10 analogous
existence and uniqueness theorems for three-dimensional, asymptotically Anti-de
Sitter and asymptotically hyperbolic manifolds with positive mass aspect
function, respectively. Last year, Cederbaum-Cortier-Sakovich proved that the
CMC-foliation characterizes the center of mass in the hyperbolic setting, too.
In this article, the existence and the uniqueness of the CMC-foliation are
further generalized to the wider class of asymptotically hyperbolic manifolds
which do not necessarily have a well-defined mass aspect function, but only a
timelike mass vector. Furthermore, we prove that the CMC-foliation also
characterizes the center of mass in this more general setting.


  Pulsar electrodynamics has been built up by taking ingredients from two
models, the vacuum-dipole model, which ignores the magnetosphere but includes
the inductive electric field due to the obliquely rotating magnetic dipole, and
the corotating-magnetosphere model, which neglects the vacuum inductive
electric field and assumes a corotating magnetosphere. We argue that the
inductive field can be neglected only if it is screened by a current, ${\bi
J}_{\rm sc}$, which we calculate for a rigidly rotating magnetosphere.
Screening of the parallel component of the inductive field can be effective,
but the perpendicular component cannot be screened in a pulsar magnetosphere.
The incompletely screened inductive electric field has not been included in any
model for a pulsar magnetosphere, and taking it into account has important
implications. One effect is that it implies that the magnetosphere cannot be
corotating, and we suggest that drift relative to corotation offers a natural
explanation for the drifting of subpulses. A second effect is that this
screening of the parallel inductive electric field must break down in the outer
magnetosphere, and this offers a natural explanation for the acceleration of
the electrons that produce pulsed gamma-ray emission.


  We describe a simple and efficient scheme for the readout of a tunable flux
qubit, and present preliminary experimental tests for the preparation,
manipulation and final readout of the qubit state, performed in incoherent
regime at liquid Helium temperature. The tunable flux qubit is realized by a
double SQUID with an extra Josephson junction inserted in the large
superconducting loop, and the readout is performed by applying a current ramp
to the junction and recording the value for which there is a voltage response,
depending on the qubit state. This preliminary work indicates the feasibility
and efficiency of the scheme.


  Real-world datasets inevitably contain biases that arise from different
sources or conditions during data collection. Consequently, such inconsistency
itself acts as a confounding factor that disturbs the cluster analysis.
Existing methods eliminate the biases by projecting data onto the orthogonal
complement of the subspace expanded by the confounding factor before
clustering. Therein, the interested clustering factor and the confounding
factor are coarsely considered in the raw feature space, where the correlation
between the data and the confounding factor is ideally assumed to be linear for
convenient solutions. These approaches are thus limited in scope as the data in
real applications is usually complex and non-linearly correlated with the
confounding factor. This paper presents a new clustering framework named
Sanitized Clustering Against confounding Bias (SCAB), which removes the
confounding factor in the semantic latent space of complex data through a
non-linear dependence measure. To be specific, we eliminate the bias
information in the latent space by minimizing the mutual information between
the confounding factor and the latent representation delivered by Variational
Auto-Encoder (VAE). Meanwhile, a clustering module is introduced to cluster
over the purified latent representations. Extensive experiments on complex
datasets demonstrate that our SCAB achieves a significant gain in clustering
performance by removing the confounding bias. The code is available at
\url{https://github.com/EvaFlower/SCAB}.


  The Lee-Wick Standard Model at temperatures near electroweak scale is
considered, with the aim of studying the electroweak phase transition. While
Lee-Wick theories possess states of negative norm, they are not pathological
but instead are treated by imposing particular boundary conditions and using
particular integration contours in the calculation of S-matrix elements. It is
not immediately clear how to extend this prescription to formulate the theory
at finite temperature; we explore two different pictures of finite-temperature
LW theories, and calculate the thermodynamic variables and the (one-loop)
thermal effective potential. We apply these results to study the Lee-Wick
Standard Model and find that the electroweak phase transition is a continuous
crossover, much like in the Standard Model. However, the high-temperature
behavior is modified due to cancellations between thermal corrections arising
from the negative- and positive-norm states.


  Artificial intelligence (AI)-based decision support systems have demonstrated
value in predicting post-hepatectomy liver failure (PHLF) in hepatocellular
carcinoma (HCC). However, they often lack transparency, and the impact of model
explanations on clinicians' decisions has not been thoroughly evaluated.
Building on prior research, we developed a variational autoencoder-multilayer
perceptron (VAE-MLP) model for preoperative PHLF prediction. This model
integrated counterfactuals and layerwise relevance propagation (LRP) to provide
insights into its decision-making mechanism. Additionally, we proposed a
methodological framework for evaluating the explainability of AI systems. This
framework includes qualitative and quantitative assessments of explanations
against recognized biomarkers, usability evaluations, and an in silico clinical
trial. Our evaluations demonstrated that the model's explanation correlated
with established biomarkers and exhibited high usability at both the case and
system levels. Furthermore, results from the three-track in silico clinical
trial showed that clinicians' prediction accuracy and confidence increased when
AI explanations were provided.


  An efficient way for the control of spin wave propagation in a magnetic
medium is the use of periodic patterns known as magnonic crystals (MCs).
However, the fabrication of MCs especially bi-components, with periodicity on
nanoscale, is a challenging task due to the requirement for sharp interfaces.
An alternative method to circumvent this problem is to use homogeneous
ferromagnetic film with modified periodically surrounding. The structure is
also suitable for exploiting nonreciprocal properties of the surface spin
waves. In this work, we demonstrate that the magnonic band structure forms in
thin permalloy film due to dynamical magnetostatic coupling with Ni stripes
near its surface. We show, that the band gap width can be systematically tuned
by the changing interlayer thickness between film and stripes. We show also the
effect of nonreciprocity, which is seen at the band gap edge shifted from the
Brillouin zone boundary and also in nonreciprocal interaction of propagating
spin waves in Py film with the standing spin waves in Ni stripes. Our findings
open possibility for further investigation and exploitation of the
nonreciprocity and band structure in magnonic devices.


  Measurements of single top and rare top quark production may be sensitive to
theories of physics beyond the standard model (SM), including those in which
the energy scale of new physics is beyond the energies directly accessible at
the Large Hadron Collider. Such models may be observable through signatures
like forbidden SM interactions or deviations of the top quark's couplings from
the SM predictions. An overview of recent searches from the ATLAS and CMS
Collaborations is presented, with a focus on flavor-changing neutral currents.


  We extend low-temperature series for the second moment of the correlation
function in $d=3$ simple-cubic Ising model from $u^{15}$ to $u^{26}$ using
finite-lattice method, and combining with the series for the susceptibility we
obtain the low-temperature series for the second-moment correlation length to
$u^{23}$. An analysis of the obtained series by inhomogeneous differential
approximants gives critical exponents $ 2\nu^{\prime} + \gamma^{\prime} \approx
2.55 $ and $ 2\nu^{\prime} \approx 1.27 $.


  A new approach is proposed, namely CSSF MIMO radar, which applies the
technique of step frequency (SF) to compressive sensing (CS) based multi-input
multi-output (MIMO) radar. The proposed approach enables high resolution range,
angle and Doppler estimation, while transmitting narrowband pulses. The problem
of joint angle-Doppler-range estimation is first formulated to fit the CS
framework, i.e., as an L1 optimization problem. Direct solution of this problem
entails high complexity as it employs a basis matrix whose construction
requires discretization of the angle-Doppler-range space. Since high resolution
requires fine space discretization, the complexity of joint range, angle and
Doppler estimation can be prohibitively high. For the case of slowly moving
targets, a technique is proposed that achieves significant complexity reduction
by successively estimating angle-range and Doppler in a decoupled fashion and
by employing initial estimates obtained via matched filtering to further reduce
the space that needs to be digitized. Numerical results show that the
combination of CS and SF results in a MIMO radar system that has superior
resolution and requires far less data as compared to a system that uses a
matched filter with SF.


  Event-based cameras are bio-inspired vision sensors whose pixels work
independently from each other and respond asynchronously to brightness changes,
with microsecond resolution. Their advantages make it possible to tackle
challenging scenarios in robotics, such as high-speed and high dynamic range
scenes. We present a solution to the problem of visual odometry from the data
acquired by a stereo event-based camera rig. Our system follows a parallel
tracking-and-mapping approach, where novel solutions to each subproblem (3D
reconstruction and camera pose estimation) are developed with two objectives in
mind: being principled and efficient, for real-time operation with commodity
hardware. To this end, we seek to maximize the spatio-temporal consistency of
stereo event-based data while using a simple and efficient representation.
Specifically, the mapping module builds a semi-dense 3D map of the scene by
fusing depth estimates from multiple local viewpoints (obtained by
spatio-temporal consistency) in a probabilistic fashion. The tracking module
recovers the pose of the stereo rig by solving a registration problem that
naturally arises due to the chosen map and event data representation.
Experiments on publicly available datasets and on our own recordings
demonstrate the versatility of the proposed method in natural scenes with
general 6-DoF motion. The system successfully leverages the advantages of
event-based cameras to perform visual odometry in challenging illumination
conditions, such as low-light and high dynamic range, while running in
real-time on a standard CPU. We release the software and dataset under an open
source licence to foster research in the emerging topic of event-based SLAM.


  We consider the effect of network structure on the evolution of a population.
Models of this kind typically consider a population of fixed size and
distribution. Here we consider eco-evolutionary dynamics where population size
and distribution can change through birth, death and migration, all of which
are separate processes. This allows complex interaction and migration
behaviours that are dependent on competition. For migration, we assume that the
response of individuals to competition is governed by tolerance to their group
members, such that less tolerant individuals are more likely to move away due
to competition. We looked at the success of a mutant in the rare mutation limit
for the complete, cycle and star networks. Unlike models with fixed population
size and distribution, the distribution of the individuals per site is
explicitly modelled by considering the dynamics of the population. This in turn
determines the mutant appearance distribution for each network. Where a mutant
appears impacts its success as it determines the competition it faces. For low
and high migration rates the complete and cycle networks have similar mutant
appearance distributions resulting in similar success levels for an invading
mutant. A higher migration rate in the star network is detrimental for mutant
success because migration results in a crowded central site where a mutant is
more likely to appear.


  Transitive closure logic is a known extension of first-order logic obtained
by introducing a transitive closure operator. While other extensions of
first-order logic with inductive definitions are a priori parametrized by a set
of inductive definitions, the addition of the transitive closure operator
uniformly captures all finitary inductive definitions. In this paper we present
an infinitary proof system for transitive closure logic which is an infinite
descent-style counterpart to the existing (explicit induction) proof system for
the logic. We show that, as for similar systems for first-order logic with
inductive definitions, our infinitary system is complete for the standard
semantics and subsumes the explicit system. Moreover, the uniformity of the
transitive closure operator allows semantically meaningful complete
restrictions to be defined using simple syntactic criteria. Consequently, the
restriction to regular infinitary (i.e. cyclic) proofs provides the basis for
an effective system for automating inductive reasoning.


  An isotropic expansion for the QGP is proposed in curved Kasner spacetime for
an experimental configuration with three dimensional set of beams. The fluid of
relativistic particles has no shear viscosity but the nonzero bulk viscosity
$\zeta$ is time dependent and its value could explain the enormous entropy per
baryon of our Universe. In addition, $\zeta$ equals the bulk viscosity of the
anisotropic compressible fluid conjectured for the interior of a black hole.


  The radiative decay $\BSgamma$ and the mixing $\BsBs$ are discussed in the
vector-like quark model which contains extra SU(2)-singlet quarks with the same
electric charges as the up-type and down-type quarks. Constraints on the
extended Cabibbo-Kobayashi-Maskawa matrix are obtained from the experimental
results for the branching ratio of $\BSgamma$ . Within these experimental
bounds, any value of the branching ratio can be accounted for by the
contributions from the vector-like quarks. In sizable ranges of the model
parameters, the mixing parameter for $\BsBs$ is much different from the
prediction of the standard model.


  In this work, we study optimization problems of the form $\min_x \max_y f(x,
y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\mathcal{M}
\times \mathcal{N}$ and is $\mu_x$-strongly geodesically convex (g-convex) in
$x$ and $\mu_y$-strongly g-concave in $y$, for $\mu_x, \mu_y \geq 0$. We design
accelerated methods when $f$ is $(L_x, L_y, L_{xy})$-smooth and $\mathcal{M}$,
$\mathcal{N}$ are Hadamard. To that aim we introduce new g-convex optimization
results, of independent interest: we show global linear convergence for
metric-projected Riemannian gradient descent and improve existing accelerated
methods by reducing geometric constants. Additionally, we complete the analysis
of two previous works applying to the Riemannian min-max case by removing an
assumption about iterates staying in a pre-specified compact set.


  Motivated by the need for a theoretical study in a planar geometry that can
easily be implemented experimentally, we study the pressure driven Poiseuille
flow of a shear banding fluid. After discussing the "basic states" predicted by
a one dimensional calculation that assumes a flat interface between the bands,
we proceed to demonstrate such an interface to be unstable with respect to the
growth of undulations along it. We give results for the growth rate and
wavevector of the most unstable mode that grows initially, as well as for the
ultimate flow patterns to which the instability leads. We discuss the relevance
of our predictions to the present state of the experimental literature
concerning interfacial instabilities of shear banded flows, in both
conventional rheometers and microfluidic channels.


  We consider a fractal Wilson loop $<F_{P}>$ and present physical arguments
why this should be a relevant observable in nature. We show for non-compact
SU(2) lattice gauge theory in the next to leading order of strong coupling
expansion that $<F_{P}>$ obeys an area law behavior and is gauge invariant.


  Knowledge Graphs (KG) constitute a flexible representation of complex
relationships between entities particularly useful for biomedical data. These
KG, however, are very sparse with many missing edges (facts) and the
visualisation of the mesh of interactions nontrivial. Here we apply a
compositional model to embed nodes and relationships into a vectorised semantic
space to perform graph completion. A visualisation tool based on Convolutional
Neural Networks and Self-Organised Maps (SOM) is proposed to extract high-level
insights from the KG. We apply this technique to a subset of CTD, containing
interactions of compounds with human genes / proteins and show that the
performance is comparable to the one obtained by structural models.


  This pedagogical document explains three variational representations that are
useful when comparing the efficiencies of reversible Markov chains: (i) the
Dirichlet form and the associated variational representations of the spectral
gaps; (ii) a variational representation of the asymptotic variance of an
ergodic average; and (iii) the conductance, and the equivalence of a non-zero
conductance to a non-zero right spectral gap.


  In spectroscopy of charged particles, narrow peaks may appear in initially
smooth continuous spectra if magnetic transport of the particles is involved.
As such unexpected peaks may be misinterpreted as new physics, their generation
is investigated for various experimental configurations.


  In this paper, we introduce two symmetric directed graphs depending on
supports of signals and windows, and we show that the connectivity of those
graphs provides either necessary and sufficient conditions to phase retrieval
of a signal from magnitude measurements of its multiple-window short-time
Fourier transform. Also we propose an algebraic reconstruction algorithm, and
provide an error estimate to our algorithm when magnitude measurements are
corrupted by deterministic/random noises.


  The ability of a honeybee swarm to select the best nest site plays a
fundamental role in determining the future colony's fitness. To date, the
nest-site selection process has mostly been modelled and theoretically analysed
for the case of binary decisions. However, when the number of alternative nests
is larger than two, the decision process dynamics qualitatively change. In this
work, we extend previous analyses of a value-sensitive decision-making
mechanism to a decision process among N nests. First, we present the
decision-making dynamics in the symmetric case of N equal-quality nests. Then,
we generalise our findings to a best-of-N decision scenario with one superior
nest and N-1 inferior nests, previously studied empirically in bees and ants.
Whereas previous binary models highlighted the crucial role of inhibitory
stop-signalling, the key parameter in our new analysis is the relative time
invested by swarm members in individual discovery and in signalling behaviours.
Our new analysis reveals conflicting pressures on this ratio in symmetric and
best-of-N decisions, which could be solved through a time-dependent signalling
strategy. Additionally, our analysis suggests how ecological factors
determining the density of suitable nest sites may have led to selective
pressures for an optimal stable signalling ratio.


  I present here the most recent experimental results in the search for Lepton
Flavor and Lepton Number Violating decays of charged leptons, and the
perspectives in this field for the next future.


  Quantum Machine Learning (QML) models are aimed at learning from data encoded
in quantum states. Recently, it has been shown that models with little to no
inductive biases (i.e., with no assumptions about the problem embedded in the
model) are likely to have trainability and generalization issues, especially
for large problem sizes. As such, it is fundamental to develop schemes that
encode as much information as available about the problem at hand. In this work
we present a simple, yet powerful, framework where the underlying invariances
in the data are used to build QML models that, by construction, respect those
symmetries. These so-called group-invariant models produce outputs that remain
invariant under the action of any element of the symmetry group $\mathfrak{G}$
associated to the dataset. We present theoretical results underpinning the
design of $\mathfrak{G}$-invariant models, and exemplify their application
through several paradigmatic QML classification tasks including cases when
$\mathfrak{G}$ is a continuous Lie group and also when it is a discrete
symmetry group. Notably, our framework allows us to recover, in an elegant way,
several well known algorithms for the literature, as well as to discover new
ones. Taken together, we expect that our results will help pave the way towards
a more geometric and group-theoretic approach to QML model design.


  The Engineering Development Array (EDA) is a single test station for Square
Kilometre Array (SKA) precursor technology. We have used the EDA to detect
low-frequency radio recombination lines (RRLs) from the Galactic Centre region.
Low-frequency RRLs are an area of interest for future low-frequency SKA work as
these lines provide important information on the physical properties of the
cold neutral medium. In this project we investigate the EDA, its bandpass and
the radio frequency interference environment for low-frequency spectroscopy. We
present line spectra from 30 to 325 MHz for the Galactic Centre region. The
decrease in sensitivity for the EDA at the low end of the receiver prevents
carbon and hydrogen RRLs to be detected below 40 and 60 MHz respectively. RFI
strongly affects frequencies in the range 276-292, 234-270, 131-138, 95-102 and
below 33 MHz. Cn$\alpha$ RRLs were detected in absorption for quantum levels n
= 378 to 550 (39-121 MHz) and in emission for n = 272 to 306 (228-325 MHz).
Cn$\beta$ lines were detected in absorption for n = 387 to 696 (39-225 MHz).
Hn$\alpha$ RRLs were detected in emission for n = 272 to 480 (59-325 MHz).
Hn$\beta$ lines were detected for n = 387 to 453 (141-225 MHz). The stacked
Hn$\alpha$ detection at 63 MHz is the lowest frequency detection made for
hydrogen RRLs and shows that a cold (partially) ionized medium exists along the
line of sight to the Galactic Centre region. The size and velocity of this cold
H$^{+}$ gas indicates that it is likely associated with the nearby
Riegel-Crutcher cloud.


  Estimating a covariance matrix and its associated principal components is a
fundamental problem in contemporary statistics. While optimal estimation
procedures have been developed with well-understood properties, the increasing
demand for privacy preservation introduces new complexities to this classical
problem. In this paper, we study optimal differentially private Principal
Component Analysis (PCA) and covariance estimation within the spiked covariance
model.
  We precisely characterize the sensitivity of eigenvalues and eigenvectors
under this model and establish the minimax rates of convergence for estimating
both the principal components and covariance matrix. These rates hold up to
logarithmic factors and encompass general Schatten norms, including spectral
norm, Frobenius norm, and nuclear norm as special cases.
  We introduce computationally efficient differentially private estimators and
prove their minimax optimality, up to logarithmic factors. Additionally,
matching minimax lower bounds are established. Notably, in comparison with
existing literature, our results accommodate a diverging rank, necessitate no
eigengap condition between distinct principal components, and remain valid even
if the sample size is much smaller than the dimension.


  We consider the following question: Given $n$ lines and $n$ circles in
$\mathbb{R}^3$, what is the maximum number of intersection points lying on at
least one line and on at least one circle of these families. We prove that if
there are no $n^{1/2}$ curves (lines or circles) lying on an algebraic surface
of degree at most two, then the number of these intersection points is
$O(n^{3/2})$.


  The properties of static spherically symmetric black holes, which carry
electric and magnetic charges, and which are coupled to the dilaton in the
presence of a cosmological term (Liouville-type potential, or cosmological
constant) are reviewed.


  In 1975, Koornwinder gave a method to construct orthogonal polynomials in two
variables using the classical Jacobi polynomials. In [5], the authors
introduced some new examples of Koornwinder polynomials obtained from the
Koornwinder construction (see also [10]). The aim of this paper is to give the
parameter derivative representations in the form of \begin{equation*}
\frac{\partial P_{n,k}(\lambda;x,y)}{\partial\lambda} = \sum_{m=0}^{n-1}
\sum_{j=0}^{m}d_{n,j,m}P_{m,j}(\lambda;x,y) +
\sum_{j=0}^{k}e_{n,j,k}P_{n,j}(\lambda;x,y) \end{equation*} for some
Koornwinder polynomials where $\lambda$ is a parameter and $0\leq k\leq n$;
$n,k=0,1,2,...$ and to present orthogonality properties of the parametric
derivatives of these polynomials.


  The main focus of this paper is a pair of new approximation algorithms for
certain integer programs. First, for covering integer programs {min cx: Ax >=
b, 0 <= x <= d} where A has at most k nonzeroes per row, we give a
k-approximation algorithm. (We assume A, b, c, d are nonnegative.) For any k >=
2 and eps>0, if P != NP this ratio cannot be improved to k-1-eps, and under the
unique games conjecture this ratio cannot be improved to k-eps. One key idea is
to replace individual constraints by others that have better rounding
properties but the same nonnegative integral solutions; another critical
ingredient is knapsack-cover inequalities. Second, for packing integer programs
{max cx: Ax <= b, 0 <= x <= d} where A has at most k nonzeroes per column, we
give a (2k^2+2)-approximation algorithm. Our approach builds on the iterated LP
relaxation framework. In addition, we obtain improved approximations for the
second problem when k=2, and for both problems when every A_{ij} is small
compared to b_i. Finally, we demonstrate a 17/16-inapproximability for covering
integer programs with at most two nonzeroes per column.


  Motivated by the recent extraction of the helicity amplitudes for the D+ ->
K*0bar mu+ nu decay, done by the FOCUS collaboration, we determine helicity
amplitudes for the D+ -> K*0bar l nu, D+ -> rho0 l nu and Ds -> phi l nu
semileptonic decays using the knowledge of the relevant form factors. The
vector and axial form factors for D -> V l nu decays are parameterized by
including contributions of charm meson resonances and using the HQET and SCET
limits. In the case that the vector form factor receives contributions from two
poles while axial form factors are dominated by a single pole for D+ -> K*0bar
l nu, we obtain better agreement with the experimental result then when all of
them are dominated by single poles.


  We compare the semiclassical Hartree-Fock approximation for a trapped Bose
gas to a direct Path Integral Quantum Monte Carlo simulation. The chosen
parameters correspond to current Rb experiments. We observe corrections to the
mean-field density profile. The Path Integral calculation reveals an increase
of the number of condensed particles, which is of the same order as a
previously computed result for a homogeneous system. We discuss the
experimental observability of the effect and propose a method to analyze data
of in-situ experiments.