  This paper presents a critical analysis of the literature and perspective
research ideas for modeling the epidemics caused by the SARS-CoV-2 virus. It
goes beyond deterministic population dynamics to consider several key
complexity features of the system under consideration. In particular, the
multiscale features of the dynamics from contagion to the subsequent dynamics
of competition between the immune system and the proliferating virus. Other
topics addressed in this work include the propagation of epidemics in a
territory, taking into account local transportation networks, the heterogeneity
of the population, and the study of social and economic problems in populations
involved in the spread of epidemics. The overall content aims to show how new
mathematical tools can be developed to address the above topics and how
mathematical models and simulations can contribute to the decision making of
crisis managers.


  In vitro neuronal culture is an important research platform in cellular and
network neuroscience. However, neurons cultured on a homogeneous scaffold form
dense, randomly connected networks and display excessively synchronized
activity; this phenomenon has limited their applications in network-level
studies, such as studies of neuronal ensembles, or coordinated activity by a
group of neurons. Herein, we develop polydimethylsiloxane-based microfluidic
devices to create small neuronal networks exhibiting a hierarchically modular
structure resembling the connectivity observed in the mammalian cortex. The
strength of intermodular coupling was manipulated by varying the width and
height of the microchannels that connect the modules. Using fluorescent calcium
imaging, we observe that the spontaneous activity in networks with smaller
microchannels (2.2$-$5.5 $\mu$m$^2$) had lower synchrony and exhibit a
threefold variety of neuronal ensembles. Optogenetic stimulation demonstrates
that a reduction in intermodular coupling enriches evoked neuronal activity
patterns and that repeated stimulation induces plasticity in neuronal ensembles
in these networks. These findings suggest that cell engineering technologies
based on microfluidic devices enable in vitro reconstruction of the intricate
dynamics of neuronal ensembles, thus providing a robust platform for studying
neuronal ensembles in a well-defined physicochemical environment.


  Radical membership testing, and the special case of Hilbert's Nullstellensatz
(HN), is a fundamental computational algebra problem. It is NP-hard; and has a
famous PSPACE algorithm due to effective Nullstellensatz bounds. We identify a
useful case of these problems where practical algorithms, and improved bounds,
could be given, when the transcendence degree $r$ of the input polynomials is
smaller than the number of variables $n$. If $d$ is the degree bound on the
input polynomials, then we solve radical membership (even if input polynomials
are blackboxes) in around $d^r$ time. The prior best was $> d^n$ time (always,
$d^n\ge d^r$). Also, we significantly improve effective Nullstellensatz
degree-bound, when $r\ll n$. Structurally, our proof shows that these problems
reduce to the case of $r+1$ polynomials of transcendence degree $\ge r$. This
input instance (corresponding to none or a unique annihilator) is at the core
of HN's hardness. Our proof methods invoke basic algebraic-geometry.


  We present the mean spectral energy distribution (SED) of a sample of
optically selected quasars (QSOs) at redshifts of $1 \le z \le 5$. To derive
it, we exploit photometric information from SDSS, UKIDSS, and WISE surveys in
combination with a stacking analysis of \textit{Herschel}, \textit{AKARI}, and
\textit{Planck} maps at the location of the QSOs. The near-UV and optical parts
of the reconstructed mean rest-frame SED are similar to those found in other
studies. However, the SED shows an excess at 1-2 $\mu$m (when compared to the
aforementioned SEDs normalized in the near-UV) and a prominent bump around 4-6
$\mu$m, followed by a decrease out to $\sim 20 \,\mu$m and a subsequent far-IR
bump. From the fitted SEDs we estimate the average active galactic nuclei (AGN)
luminosity $L_{\rm AGN}$ and star formation rate (SFR) as function of cosmic
time, finding typical $L_{\rm AGN} \sim 10^{46} - 10^{47}$ erg/s and SFR $\sim
50 - 1000\, M_{\odot}/$yr. We develop mid-IR based criteria to split the QSO
sample, finding that these allow us to move along the average relationship in
the SFR vs. $L_{\rm AGN}$ diagram toward increasing AGN luminosities. When
interpreted in the context of the in-situ coevolution scenario presented by
Lapi et al. 2014, our results suggest that the detection in the far-IR band is
an effective criterion to select objects where the star formation is on the
verge of being affected by energy/momentum feedback from the central AGN.


  The special fiber of the local model of a PEL Shimura variety with
Iwahori-type level structure admits a cellular decomposition. The set of strata
is in a natural way a finite subset of the affine Weyl group determined by the
Shimura data. In this paper, we generalize and give a new proof of a theorem of
Kottwitz and Rapoport concerning the description of this set for the case of
linear and symplectic groups. For higher rank groups not of type A_n, we
produce counterexamples showing the situation is not as nice in general. Also,
we recover a theorem of Deodhar characterizing the Bruhat order on S_n.


  In the present paper we completely classify locally free sheaves of rank $2$
with vanishing intermediate cohomology modules on the image of the Segre
embedding $\mathbb{P}^2\times\mathbb{P}^2\subseteq\mathbb{P}^8$ and its general
hyperplane sections.
  Such a classification extends similar already known results regarding del
Pezzo varieties with Picard numbers $1$ and $3$ and dimension at least $3$.


  The first year of observations by the Planck satellite mission shows that the
cosmic microwave background (CMB) fluctuations are consistent with gaussian
statistics in the primordial perturbations, a key prediction of the simplest
models of inflation. However, there are hints of anomalies in the CMB power
spectrum and bispectrum. We check for the possibility that some of these
anomalous features have a common physical origin in a transient reduction of
the inflaton speed of sound. We do this by exploiting predicted correlations
between the power spectrum and bispectrum. Our results suggest that current
data might already be sensitive enough to detect transient reductions in the
speed of sound as mild as a few percent. Since this is a signature of
interactions, it opens a new window for the detection of extra degrees of
freedom during inflation.


  We explore applications of the maximum entropy method (MEM) to determine
properties of unstable particles using the four-dimensional O(4) $\phi^4$
theory as a laboratory. The spectral function of the correlation function of
the unstable $\sigma$ particle is calculated with MEM, and shown to yield
reliable results for both the mass of $\sigma$ and the energy of the two-pion
state. Calculations are also made for the case in which $\sigma$ is stable.
Distinctive differences in the volume dependence of the $\sigma$ mass and
two-pion energy for the stable and unstable cases are analyzed in terms of
perturbation theory.


  Dear Visitor and Charleston Reconstructed were location-based augmented
reality (AR) experiences created between 2018 and 2020 dealing with two
controversial monument sites in the US. The projects were motivated by the
ability of AR to 1) link layers of context to physical sites in ways that are
otherwise difficult or impossible and 2) to visualize changes to physical
spaces, potentially inspiring changes to the spaces themselves. We discuss the
projects' motivations, designs, and deployments. We reflect on how physical
changes to the projects' respective sites radically altered their outcomes, and
we describe lessons for future work in location-based AR, particularly for
projects in contested spaces.


  A representation formula for the solution of the $\infty$-Laplace equation is
constructed in a punctured square, the prescribed boundary values being $u=0$
on the sides and $u=1$ at the centre. This so-called $\infty$-potential is
obtained with a hodograph method. The heat equation is used and one of Jacobi's
Theta functions appears. The formula disproves a conjecture.


  We consider the actions for ten--dimensional $p$--branes and $D$--branes in
an arbitrary curved background and discuss some of their properties. We comment
on how the $SL(2,R)$ duality symmetry acts on the five--brane actions.


  We study adiabatic charge transfer in a superconducting Cooper pair pump,
focusing on the influence of current measurement on coherence. We investigate
the limit where the Josephson coupling energy $E_J$ between the various parts
of the system is small compared to the Coulomb charging energy $E_C$. In this
case the charge transferred in a pumping cycle $Q_P \sim 2e$, the charge of one
Cooper pair: the main contribution is due to incoherent Cooper pair tunneling.
We are particularly interested in the quantum correction to $Q_P$, which is due
to coherent tunneling of pairs across the pump and which depends on the
superconducting phase difference $\phi_0$ between the electrodes: $1-Q_P/(2e)
\sim (E_J/E_C) \cos \phi_0$. A measurement of $Q_P$ tends to destroy the phase
coherence. We first study an arbitrary measuring circuit and then specific
examples and show that coherent Cooper pair transfer can in principle be
detected using an inductively shunted ammeter.


  A nonlinear parabolic differential equation is presented which has at least
one equilibrium. This equilibrium is shown to have a negative definite
linearization, but a spectrum which includes zero. An elementary construction
shows that the equilibrium is not stable.


  The most general large ${\cal N}=4$ superconformal ${\cal W}_{\infty}$
algebra, containing in addition to the superconformal algebra one
supermultiplet for each integer spin, is analysed in detail. It is found that
the ${\cal W}_{\infty}$ algebra is uniquely determined by the levels of the two
$\mathfrak{su}(2)$ algebras, a conclusion that holds both for the linear and
the non-linear case. We also perform various cross-checks of our analysis, and
exhibit two different types of truncations in some detail.


  We classify up to equivalence the gradings on Hurwitz superalgebras and on
symmetric composition superalgebras, over any field. Also, classifications up
to isomorphism are given in case the field is algebraically closed. By grading,
here we mean group grading.


  In the context of networked control systems, event-triggered control (ETC)
has emerged as a major topic due to its alleged resource usage reduction
capabilities. However, this is mainly supported by numerical simulations, and
very little is formally known about the traffic generated by ETC. This work
devises a method to estimate, and in some cases to determine exactly, the
minimum average inter-sample time (MAIST) generated by periodic event-triggered
control (PETC) of linear systems. The method involves abstracting the traffic
model using a bisimulation refinement algorithm and finding the cycle of
minimum average length in the graph associated to it. This always gives a lower
bound to the actual MAIST. Moreover, if this cycle turns out to be related to a
periodic solution of the closed-loop PETC system, the performance metric is
exact.


  Directed acyclic graphs or Bayesian networks that are popular in many AI
related sectors for probabilistic inference and causal reasoning can be mapped
to probabilistic circuits built out of probabilistic bits (p-bits), analogous
to binary stochastic neurons of stochastic artificial neural networks. In order
to satisfy standard statistical results, individual p-bits not only need to be
updated sequentially, but also in order from the parent to the child nodes,
necessitating the use of sequencers in software implementations. In this
article, we first use SPICE simulations to show that an autonomous hardware
Bayesian network can operate correctly without any clocks or sequencers, but
only if the individual p-bits are appropriately designed. We then present a
simple behavioral model of the autonomous hardware illustrating the essential
characteristics needed for correct sequencer-free operation. This model is also
benchmarked against SPICE simulations and can be used to simulate large scale
networks. Our results could be useful in the design of hardware accelerators
that use energy efficient building blocks suited for low-level implementations
of Bayesian networks. The autonomous massively parallel operation of our
proposed stochastic hardware has biological relevance since neural dynamics in
brain is also stochastic and autonomous by nature.


  We use precision microwave spectroscopy of magnetically trapped, ultra-cold
87Rb to characterize intra- and inter-state density correlations. The cold
collision shifts for both normal and condensed clouds are measured. The results
verify the presence of the sometimes controversial "factors of two", in
normal-cloud mean-field energies, both within a particular state and between
two distinct spin species. One might expect that as two spin species decohere,
the inter-state factor of two would revert to unity, but the associated
frequency chirp one naively expects from such a trend is not observed in our
data.


  This paper shows how to manage null entries in pairwise comparisons matrices.
Although assessments can be imprecise, since subjective criteria are involved,
the classical pairwise comparisons theory expects all of them to be available.
In practice, some experts may not be able (or available) to provide all
assessments. Therefore managing null entries is a necessary extension of the
pairwise comparisons method. It is shown that certain null entries can be
recovered on the basis of the transitivity property which each pairwise
comparisons matrix is expected to satisfy.


  We consider the curve shortening flow applied to a class of figure-eight
curves: those with dihedral symmetry, convex lobes, and a monotonicity
assumption on the curvature. We prove that when (non-conformal) linear
transformations are applied to the solution so as to keep the bounding box the
unit square, the renormalized limit converges to a quadrilateral which we call
a bowtie. Along the way we prove that suitably chosen arcs of our evolving
curves, when suitably rescaled, converge to the Grim Reaper Soliton under the
flow. Our Grim Reaper Theorem is an analogue of a theorem of S. Angenent, which
is proven in the locally convex case.


  The effects of complex, mixed-ion radiation fields on neuronal function
remain largely unexplored. Here, we present a complete analysis of the
nano-scale physics associated with broad-spectrum galactic cosmic ray (GCR)
irradiation in a realistic cornu ammonis 1 (CA1) pyramidal neuron geometry.
  We simulate the entire 33 ion-energy beam fluence distribution currently in
use at the NASA Space Radiation Laboratory galactic cosmic ray simulator
(GCRSim). We use the TOol for PArticle Simulation (TOPAS) and TOPAS-nBio Monte
Carlo-based track structure simulation toolkits to assess the dosimetry,
physics processes, and fluence statistics of different neuronal compartments at
the nanometer scale. We also make comparisons between the full GCRSim
distribution and a simplified 6 ion-energy spectrum (SimGCRSim).
  We show that across all physics processes, ionizations mediate the majority
of the energy deposition $(68 \pm 1\%)$, though vibrational excitations are the
most abundant ($70 \pm 2\%$ of all energy deposition events). We report that
neuronal energy deposition by proton and $\alpha$-particle tracks declines
approximately hyperbolically with increasing primary particle energy at
mission-relevant energies. We also demonstrate an inverted exponential
relationship between dendritic segment irradiation probability and neuronal
absorbed dose. Finally, we find that there are no significant differences in
the average physical responses between the GCRSim and SimGCRSim fluence
distributions.
  To our knowledge, this is the first nano-scale simulation study of a
realistic neuron geometry using the GCRSim and SimGCRSim fluence distributions.
The results presented here are expected to aid in the interpretation of future
experimental results and help guide future study designs.


  We address the problem of robust state reconstruction for discrete-time
nonlinear systems when the actuators and sensors are injected with (potentially
unbounded) attack signals. Exploiting redundancy in sensors and actuators and
using a bank of unknown input observers (UIOs), we propose an observer-based
estimator capable of providing asymptotic estimates of the system state and
attack signals under the condition that the numbers of sensors and actuators
under attack are sufficiently small. Using the proposed estimator, we provide
methods for isolating the compromised actuators and sensors. Numerical examples
are provided to demonstrate the effectiveness of our methods.


  We explore an elementary construction that produces finitely presented groups
with diverse homological finiteness properties -- the {\em binary subgroups},
$B(\Sigma,\mu)<G_1\times\dots\times G_m$. These full subdirect products require
strikingly few generators. If each $G_i$ is finitely presented, $B(\Sigma,\mu)$
is finitely presented. When the $G_i$ are non-abelian limit groups (e.g. free
or surface groups), the $B(\Sigma,\mu)$ provide new examples of finitely
presented, residually-free groups that do not have finite classifying spaces
and are not of Stallings-Bieri type. These examples settle a question of
Minasyan relating different notions of rank for residually-free groups. Using
binary subgroups, we prove that if $G_1,\dots,G_m$ are perfect groups, each
requiring at most $r$ generators, then $G_1\times\dots\times G_m$ requires at
most $r \lfloor \log_2 m+1 \rfloor$ generators.


  Glickenstein \cite{Glickenstein} and Glickenstein-Thomas \cite{GT} introduced
the discrete conformal structures on surfaces in an axiomatic approach and
studied its classification. In this paper, we give a full classification of the
discrete conformal structures on surfaces, which completes Glickenstein-Thomas'
classification. As a result, we find some new classes of discrete conformal
structures on surfaces, including some of the generalized circle packing
metrics introduced by Guo-Luo \cite{GL2}. The relationships between the
discrete conformal structures on surfaces and the 3-dimensional hyperbolic
geometry are also discussed.


  We propose a method for unsupervised abstractive opinion summarization, that
combines the attributability and scalability of extractive approaches with the
coherence and fluency of Large Language Models (LLMs). Our method, HIRO, learns
an index structure that maps sentences to a path through a semantically
organized discrete hierarchy. At inference time, we populate the index and use
it to identify and retrieve clusters of sentences containing popular opinions
from input reviews. Then, we use a pretrained LLM to generate a readable
summary that is grounded in these extracted evidential clusters. The modularity
of our approach allows us to evaluate its efficacy at each stage. We show that
HIRO learns an encoding space that is more semantically structured than prior
work, and generates summaries that are more representative of the opinions in
the input reviews. Human evaluation confirms that HIRO generates significantly
more coherent, detailed and accurate summaries.


  Transformer-based pretrained language models (PLMs) offer unmatched
performance across the majority of natural language understanding (NLU) tasks,
including a body of question answering (QA) tasks. We hypothesize that
improvements in QA methodology can also be directly exploited in dialog NLU;
however, dialog tasks must be \textit{reformatted} into QA tasks. In
particular, we focus on modeling and studying \textit{slot labeling} (SL), a
crucial component of NLU for dialog, through the QA optics, aiming to improve
both its performance and efficiency, and make it more effective and resilient
to working with limited task data. To this end, we make a series of
contributions: 1) We demonstrate how QA-tuned PLMs can be applied to the SL
task, reaching new state-of-the-art performance, with large gains especially
pronounced in such low-data regimes. 2) We propose to leverage contextual
information, required to tackle ambiguous values, simply through natural
language. 3) Efficiency and compactness of QA-oriented fine-tuning are boosted
through the use of lightweight yet effective adapter modules. 4) Trading-off
some of the quality of QA datasets for their size, we experiment with larger
automatically generated QA datasets for QA-tuning, arriving at even higher
performance. Finally, our analysis suggests that our novel QA-based slot
labeling models, supported by the PLMs, reach a performance ceiling in
high-data regimes, calling for more challenging and more nuanced benchmarks in
future work.


  2D LiDAR SLAM (Simultaneous Localization and Mapping) is widely used in
indoor environments due to its stability and flexibility. However, its mapping
procedure is usually operated by a joystick in static environments, while
indoor environments often are dynamic with moving objects such as people. The
generated map with noisy points due to the dynamic objects is usually
incomplete and distorted. To address this problem, we propose a framework of
2D-LiDAR-based SLAM without manual control that effectively excludes dynamic
objects (people) and simplify the process for a robot to map an environment.
The framework, which includes three parts: people tracking, filtering and
following. We verify our proposed framework in experiments with two classic
2D-LiDAR-based SLAM algorithms in indoor environments. The results show that
this framework is effective in handling dynamic objects and reducing the
mapping error.


  In collaboration with the Observatories of Palermo and Rome and the SAX-SDC
we are constructing a multi-site interactive archive system featuring specific
analysis tools. In this context we developed a detection algorithm based on the
Wavelet Transform (WT) and performed a systematic analysis of all ROSAT-HRI
public data (~3100 observations +1000 to come). The WT is specifically suitable
to detect and characterize extended sources while properly detecting point
sources in very crowded fields. Moreover, the good angular resolution of HRI
images allows the source extension and position to be accurately determined.
This effort has produced the BMW (Brera Multiscale Wavelet) catalogue, with
more than 19,000 sources detected at the 4.2 sigma level. For each source
detection we have information on the X-ray flux and extension, allowing for
instance to select complete samples of extended X-ray sources such as candidate
clusters of galaxies or SNR's. Here we present an overview of first results
from several undergoing projects which make use of the BMW catalogue.


  The effectiveness of projection methods for solving systems of linear
inequalities is investigated. It is shown that they have a computational
advantage over some alternatives and that this makes them successful in
real-world applications. This is supported by experimental evidence provided in
this paper on problems of various sizes (up to tens of thousands of unknowns
satisfying up to hundreds of thousands of constraints) and by a discussion of
the demonstrated efficacy of projection methods in numerous scientific
publications and commercial patents (dealing with problems that can have over a
billion unknowns and a similar number of constraints).


  The past decade has witnessed a booming development of topological photonics,
which revolutionizes the methodology for controlling the behavior of light. A
gigantic achievement is to engineer robust confined modes localized at
interfaces between topologically distinct regions, where the optical context
can trigger exotic topological phenomena exclusive to photons. Here, we provide
an experimentally flexible approach to engineering topologically induced
interface states in the visible regime via a unique design of complex
superlattice formed by connecting two component superlattices of distinguished
topological phases. Assisted by the intrinsic pseudospin degree due to the
splitting between TM and TE polarized modes, we attain a precise manipulation
of the spin-dependent topological interface states that can manifest themselves
straightforwardly through transmission spectra. More specifically, since these
topological localized modes stem from the hybridization of artificial photonic
orbitals that are of topological origin as well, they are deemed as a novel
topological effect and thus named as the secondary topological interface
states. Our work develops an innovative and productive strategy to tune
topologically protected localized modes, based on which various applications
such as selective local enhancement can be exploited.


  Neutrino mass patterns and mixing have been studied in the context of
next-to-minimal supersymmetric standard model (NMSSM) with three gauge singlet
neutrino superfields. We consider the case with the assumption of R-parity
conservation. The vacuum expectation value of the singlet scalar field $S$ of
NMSSM induces the Majorana masses for the right-handed neutrinos as well as the
usual $\mu$-term. The contributions to the light neutrino mass matrix at the
tree level as well as one-loop level are considered, consistent with the
tri-bimaximal pattern of neutrino mixing. Light neutrino masses arise at the
tree level through a TeV scale seesaw mechanism involving the right-handed
neutrinos. Although all the three light neutrinos acquire non-zero masses at
the tree-level, we show that the one-loop contributions can be comparable in
size under certain conditions.


  The effects of any quantum measurement can be described by a collection of
measurement operators {M_m} acting on the quantum state of the measured system.
However, the Hilbert space formalism tends to obscure the relationship between
the measurement results and the physical properties of the measured system. In
this paper, a characterization of measurement operators in terms of measurement
resolution and disturbance is developed. It is then possible to formulate
uncertainty relations for the measurement process that are valid for arbitrary
input states. The motivation of these concepts is explained from a quantum
communication viewpoint. It is shown that the intuitive interpretation of
uncertainty as a relation between measurement resolution and disturbance
provides a valid description of measurement back action. Possible applications
to quantum cryptography, quantum cloning, and teleportation are discussed.


  We present the results of calculations defining global, three-dimensional
representations of the complex-valued potential-energy surfaces of the doublet
B1, doublet A1, and doublet B2 metastable states of the water anion that
underlie the physical process of dissociative electron attachment to water. The
real part of the resonance energies is obtained from configuration-interaction
calculations performed in a restricted Hilbert space, while the imaginary part
of the energies (the widths) is derived from complex Kohn scattering
calculations. A diabatization is performed on the 2A1 and 2B2 surfaces, due to
the presence of a conical intersection between them. We discuss the
implications that the shapes of the constructed potential-energy surfaces will
have upon the nuclear dynamics of dissociative electron attachment to H2O.
  This work originally appeared as Phys Rev A 75, 012710 (2007). Typesetting
errors in the published version have been corrected here.


  Cross-view video geo-localization (CVGL) aims to derive GPS trajectories from
street-view videos by aligning them with aerial-view images. Despite their
promising performance, current CVGL methods face significant challenges. These
methods use camera and odometry data, typically absent in real-world scenarios.
They utilize multiple adjacent frames and various encoders for feature
extraction, resulting in high computational costs. Moreover, these approaches
independently predict each street-view frame's location, resulting in
temporally inconsistent GPS trajectories. To address these challenges, in this
work, we propose GAReT, a fully transformer-based method for CVGL that does not
require camera and odometry data. We introduce GeoAdapter, a
transformer-adapter module designed to efficiently aggregate image-level
representations and adapt them for video inputs. Specifically, we train a
transformer encoder on video frames and aerial images, then freeze the encoder
to optimize the GeoAdapter module to obtain video-level representation. To
address temporally inconsistent trajectories, we introduce TransRetriever, an
encoder-decoder transformer model that predicts GPS locations of street-view
frames by encoding top-k nearest neighbor predictions per frame and
auto-regressively decoding the best neighbor based on the previous frame's
predictions. Our method's effectiveness is validated through extensive
experiments, demonstrating state-of-the-art performance on benchmark datasets.
Our code is available at https://github.com/manupillai308/GAReT.


  We calculate low scale gravity effects on the cross section for
neutrino-nucleon scattering at center of mass energies up to the
Greisen-Zatsepin-Kuzmin (GZK) scale, in the eikonal approximation. We compare
the cases of an infinitely thin brane embedded in n=5 compactified
extra-dimensions, and of a brane with a physical tension M_{S}=1 TeV and
M_{S}=10 TeV. The extra dimensional Planck scale M_{D} is set at 10^{3} GeV and
2\times10^{3} GeV. We also compare our calculations with neutral current
standard model calculations in the same energy range, and compare the thin
brane eikonal cross section to its saddle point approximation. New physics
effects enhance the cross section by orders of magnitude on average. They are
quite sensitive to M_{S} and M_{D} choices, though much less sensitive to n.


  Face forgery has attracted increasing attention in recent applications of
computer vision. Existing detection techniques using the two-branch framework
benefit a lot from a frequency perspective, yet are restricted by their fixed
frequency decomposition and transform. In this paper, we propose to Adaptively
learn Frequency information in the two-branch Detection framework, dubbed AFD.
To be specific, we automatically learn decomposition in the frequency domain by
introducing heterogeneity constraints, and propose an attention-based module to
adaptively incorporate frequency features into spatial clues. Then we liberate
our network from the fixed frequency transforms, and achieve better performance
with our data- and task-dependent transform layers. Extensive experiments show
that AFD generally outperforms.


  In certain unconventional superconductors with sizable electronic
correlations, the availability of closely competing pairing channels leads to
characteristic soft collective fluctuations of the order parameters, which
leave fingerprints in many observables and allow to scrutinize the phase
competition. Superconducting layered materials, where electron-electron
interactions are enhanced with decreasing thickness, are promising candidates
to display these correlation effects. In this work, we report the existence of
a soft collective mode in single-layer NbSe$_2$, observed as a characteristic
resonance excitation in high resolution tunneling spectra. This resonance is
observed along with higher harmonics, its frequency $\Omega/2\Delta$ is
anticorrelated with the local superconducting gap $\Delta$, and its amplitude
gradually vanishes by increasing the temperature and upon applying a magnetic
field up to the critical values (T$_C$ and H$_{C2}$), which sets an unambiguous
link to the superconducting state. Aided by a microscopic model that captures
the main experimental observations, we interpret this resonance as a collective
Leggett mode that represents the fluctuation towards a proximate f-wave triplet
state, due to subleading attraction in the triplet channel. Our findings
demonstrate the fundamental role of correlations in superconducting 2D
transition metal dichalcogenides, opening a path towards unconventional
superconductivity in simple, scalable and transferable 2D superconductors.


  Legged robots are physically capable of navigating a diverse variety of
environments and overcoming a wide range of obstructions. For example, in a
search and rescue mission, a legged robot could climb over debris, crawl
through gaps, and navigate out of dead ends. However, the robot's controller
needs to respond intelligently to such varied obstacles, and this requires
handling unexpected and unusual scenarios successfully. This presents an open
challenge to current learning methods, which often struggle with generalization
to the long tail of unexpected situations without heavy human supervision. To
address this issue, we investigate how to leverage the broad knowledge about
the structure of the world and commonsense reasoning capabilities of
vision-language models (VLMs) to aid legged robots in handling difficult,
ambiguous situations. We propose a system, VLM-Predictive Control (VLM-PC),
combining two key components that we find to be crucial for eliciting
on-the-fly, adaptive behavior selection with VLMs: (1) in-context adaptation
over previous robot interactions and (2) planning multiple skills into the
future and replanning. We evaluate VLM-PC on several challenging real-world
obstacle courses, involving dead ends and climbing and crawling, on a Go1
quadruped robot. Our experiments show that by reasoning over the history of
interactions and future plans, VLMs enable the robot to autonomously perceive,
navigate, and act in a wide range of complex scenarios that would otherwise
require environment-specific engineering or human guidance.


  Common asset holding by financial institutions, namely portfolio overlap, is
nowadays regarded as an important channel for financial contagion with the
potential to trigger fire sales and thus severe losses at the systemic level.
In this paper we propose a method to assess the statistical significance of the
overlap between pairs of heterogeneously diversified portfolios, which then
allows us to build a validated network of financial institutions where links
indicate potential contagion channels due to realized portfolio overlaps. The
method is implemented on a historical database of institutional holdings
ranging from 1999 to the end of 2013, but can be in general applied to any
bipartite network where the presence of similar sets of neighbors is of
interest. We find that the proportion of validated network links (i.e., of
statistically significant overlaps) increased steadily before the 2007-2008
global financial crisis and reached a maximum when the crisis occurred. We
argue that the nature of this measure implies that systemic risk from fire
sales liquidation was maximal at that time. After a sharp drop in 2008,
systemic risk resumed its growth in 2009, with a notable acceleration in 2013,
reaching levels not seen since 2007. We finally show that market trends tend to
be amplified in the portfolios identified by the algorithm, such that it is
possible to have an informative signal about financial institutions that are
about to suffer (enjoy) the most significant losses (gains).


  Tanglegrams are drawings of two rooted binary phylogenetic trees and a
matching between their leaf sets. The trees are drawn crossing-free on opposite
sides with their leaf sets facing each other on two vertical lines. Instead of
minimizing the number of pairwise edge crossings, we consider the problem of
minimizing the number of block crossings, that is, two bundles of lines
crossing each other locally. With one tree fixed, the leaves of the second tree
can be permuted according to its tree structure. We give a complete picture of
the algorithmic complexity of minimizing block crossings in one-sided
tanglegrams by showing NP-completeness, constant-factor approximations, and a
fixed-parameter algorithm. We also state first results for non-binary trees.


  One of the core challenges in open-plan workspaces is to ensure a good level
of concentration for the workers while performing their tasks. Hence, being
able to infer concentration levels of workers will allow building designers,
managers, and workers to estimate what effect different open-plan layouts will
have and to find an optimal one. In this research, we present an
ambient-physical system to investigate the concentration inference problem.
Specifically, we deploy a series of pervasive sensors to capture various
ambient and physical signals related to perceived concentration at work. The
practicality of our system has been tested on two large open-plan workplaces
with different designs and layouts. The empirical results highlight promising
applications of pervasive sensing in occupational concentration inference,
which can be adopted to enhance the capabilities of modern workplaces.


  In this letter, we fabricated and characterized chalcogenide glass resonators
monolithically integrated on mid-infrared transparent CaF2 substrates. The
devices feature an intrinsic Q-factor of 4E5 at 5.2 micron wavelength, which
represents the highest Q-factor reported in planar mid-infrared resonators. It
is found that moisture can significantly impact the device performance when the
device was exposed to an ambient environment, although the high-Q
characteristics can be restored after undergoing an annealing treatment. Using
these devices, we further demonstrated on-chip cavity-enhanced spectroscopy to
quantify mid-IR absorption of ethanol solutions around 5.2 micron wavelength.


  Generalizing the algebraic formulation of the First Fundamental Theorem of
Calculus (FFTC), a class of constraints involving a pair of operators was
considered in \cite{ZGK2}. For a given constraint, the existences of extensions
of differential and Rota-Baxter operators, of liftings of monads and comonads,
and of mixed distributive laws are shown to be equivalent. In this paper, we
give a classification of the constraints satisfying these equivalent
conditions.


  The ability to describe strongly interacting matter at finite temperature and
baryon density provides the means to determine, for instance, the equation of
state of QCD at non-zero baryon chemical potential. From a theoretical point of
view, direct lattice simulations are hindered by the numerical sign problem,
which prevents the use of traditional methods based on importance sampling.
Despite recent successes, simulations using the complex Langevin method have
been shown to exhibit instabilities, which cause convergence to wrong results.
We introduce and discuss the method of Dynamic Stabilisation (DS), a
modification of the complex Langevin process aimed at solving these
instabilities. We present results of DS being applied to the heavy-dense
approximation of QCD, as well as QCD with staggered fermions at zero chemical
potential and finite chemical potential at high temperature. Our findings show
that DS can successfully deal with the aforementioned instabilities, opening
the way for further progress.


  We have performed our spectroscopic and multi-color photometric observations
of the recurrent nova U Scorpii at the earliest stage of the 2010 outburst.
0.37 days after the discovery of the outburst, we can see broad and prominent
emission lines of Balmer series, He I, N II, N III, O I and Mg II on the
spectra. The FWHM of H$\alpha$ line yields an expansion velocity of
approximately 6200 km/s. This line also accompanies a blue shifted absorption
line (so called P Cygni profile). 1.37 days after the discovery, H$\alpha$ line
shows a nearly flat-topped profile in contrast to the previous day. From our
multi-color photometry, we can see its rapid decline (one magnitude per day) of
the brightness in each color band.


  The collision-free velocity model is a microscopic pedestrian model, which
despite its simplicity, reproduces fairly well several self-organization
phenomena in pedestrian dynamics. The model consists of two components: a
direction sub-model that combines individual desired moving direction and
neighbor's influence to imitate the process of navigating in a two-dimensional
space, and an intrinsically collision-free speed sub-model which controls the
speed of the agents with respect to the distance to their neighbors.
  In this paper we generalize the collision-free velocity model by introducing
the influence of walls and extending the distance calculations to
velocity-based ellipses. Besides, we introduce enhancements to the direction
sub-module that smooth the direction changes of pedestrians in the simulation;
a shortcoming that was not visible in the original model due to the symmetry of
the circular shapes. Moreover, the introduced improvements mitigate backward
movements, leading to a more realistic distribution of pedestrians especially
in bottleneck scenarios.
  We study by simulation the effects of the pedestrian's shape by comparing the
fundamental diagram in narrow and wide corridors. Furthermore, we validate our
generalized approach by investigating the flow through bottlenecks with varying
exit's widths.


  By using the density functional theory (DFT) combined with the molecular
dynamics (MD) simulations, structural and electronic properties of mono-vacancy
(MV) defect in M\"obius strip formed from graphene are investigated. Two kinds
of MV are observed depending on the local structures around defects. At static
condition, in the curved areas of M\"obius strip, MV has the configuration of
one pentagon and one nonagon ring (59-type), which is similar to that of carbon
nanotubes and graphene. the most stable MV appear in the twisted areas and has
a profile of two pentagon and two hexagon rings (5566-type) with one sp3
hybridized carbon at the central site. While DFT-MD simulations prove that the
5566-type MV is an unstable configuration at room temperature and will
transform into a 59-type MV. Additionally, the melting behavior of graphene
based M\"obius strips are investigated through empirical potential MD
simulations, and we find that their melting temperature is about 2750 K, which
is lower than that of carbon nanotubes and graphene.


  In view of the presence of a superpotential, the dual of a gauge theory like
SQCD contains two coupling parameters. The method of the Reduction of Couplings
is used in order to express the parameter of the superpotential in terms of the
dual gauge coupling. In the conformal window and above it, a unique, isolated
solution is obtained. The coupling parameter of the superpotential is given
simply by f times the square of the gauge coupling. Here f is a function of the
the number of colors and the number of flavors, and it is known explicitly. The
solution is valid to all orders in the asymptotic expansion, and it is the
appropriate choice for the dual theory. The same solution exists in the free
magnetic interval. A `general' solution with non-integer powers is discussed,
as are some exceptional cases.


  The coherent charge transport through an illuminated graphene ribbon is
studied as function of electronic doping, frequency and strength of the
electromagnetic driving, for monochromatic circularly polarized light. We focus
on the DC current carried by 2D bulk carriers which is dominant (over edge
transport) for short and wide enough samples. Broad dips in conductance are
predicted for one-photon and multi-photon resonances between the valence and
conductance bands. The residual conductance can be associated with evanescent
states and related to dynamical gaps in the Floquet quasi-energy spectrum.


  Gaia's Radial Velocity Spectrometer (RVS) has been operating in routine phase
for over one year since initial commissioning. RVS continues to work well but
the higher than expected levels of straylight reduce the limiting magnitude.
The end-of-mission radial-velocity (RV) performance requirement for G2V stars
was 15 km/s at V = 16.5 mag. Instead, 15 km/s precision is achieved at 15 < V <
16 mag, consistent with simulations that predict a loss of 1.4 mag. Simulations
also suggest that changes to Gaia's onboard software could recover ~0.14 mag of
this loss. Consequently Gaia's onboard software was upgraded in April 2015. The
status of this new commissioning period is presented, as well as the latest
scientific performance of the on-ground processing of RVS spectra. We
illustrate the implications of the RVS limiting magnitude on Gaia's view of the
Milky Way's halo in 6D using the Gaia Universe Model Snapshot (GUMS).


  We study the Euler characteristic of the Milnor fibre of a hypersurface
singularity. This invariant is given in terms of the Euler characteristic of a
fibre in between the original singularity and its Milnor fibre and in terms of
the Euler characteristics associated to strata of the in-between fibre.
  From this we can deduce a result of Massey and Siersma regarding
singularities with a one-dimensional critical locus. The result is also applied
to the study of equisingularity. The famous Brian\c{c}on-Speder-Teissier result
states that a family of isolated hypersurface singularities is equisingular if
and only if its $\mu ^*$-sequence is constant. We show that if a similar
sequence for a family of corank 1 complex analytic mappings from n-space to
(n+1)-space is constant, then the image of the family of mappings is
equisingular. For families of corank 1 maps from 3-space to 4-space we show
that the converse is true also.


  Many real-world complex networks simultaneously exhibit topological features
of scale-free behaviour and hierarchical organization. In this regard,
deterministic scale-free [A.-L. Barab\'asi \etal, Physica A, 299, 3 (2001)] and
pseudofractal scale-free [S. N. Dorogovtsev \etal, Phy. Rev. E, 65, 6 (2002)]
networks constitute notable models which simultaneously incorporate the
aforementioned properties. The rules governing the formation of such networks
are completely deterministic. However, real-world networks are presumably
neither completely deterministic, nor perfectly hierarchical. Therefore, we
suggest here perfectly hierarchical scale-free networks with randomly rewired
edges as better representatives of practical networked systems. In particular,
we preserve the scale-free degree distribution of the various deterministic
networks but successively relax the hierarchical structure while rewiring them.
We utilize the framework of master stability function in investigating the
synchronizability of dynamical systems coupled on such rewired networks.
Interestingly, this reveals that the process of rewiring is capable of
significantly enhancing, as well as, deteriorating the synchronizability of the
resulting networks. We investigate the influence of rewiring edges on the
topological properties of the rewired networks and, in turn, their relation to
the synchronizability of the respective topologies. Finally, we compare the
synchronizability of deterministic scale-free and pseudofractcal scale-free
networks with that of random scale-free networks (generated using the classical
Barab\'asi-Albert model of growth and preferential attachment) and find that
the latter ones promote synchronizability better than their deterministic
counterparts.


  Given a level set $E$ of an arbitrary multiplicative function $f$, we
establish, by building on the fundamental work of Frantzikinakis and Host
[13,14], a structure theorem which gives a decomposition of $\mathbb{1}_E$ into
an almost periodic and a pseudo-random parts. Using this structure theorem
together with the technique developed by the authors in [3], we obtain the
following result pertaining to polynomial multiple recurrence.
  Let $E=\{n_1<n_2<\ldots\}$ be a level set of an arbitrary multiplicative
function with positive density. Then the following are equivalent:
  - $E$ is divisible, i.e. the upper density of the set $E\cap u\mathbb{N}$ is
positive for all $u\in\mathbb{N}$;
  - $E$ is an averaging set of polynomial multiple recurrence, i.e. for all
measure preserving systems $(X,\mathcal{B},\mu,T)$, all $A\in\mathcal{B}$ with
$\mu(A)>0$, all $\ell\geq 1$ and all polynomials $p_i\in\mathbb{Z}[x]$,
$i=1,\ldots,\ell$, with $p_i(0)=0$ we have $$
\lim_{N\to\infty}\frac{1}{N}\sum_{j=1}^N \mu\big(A\cap
T^{-p_1(n_j)}A\cap\ldots\cap T^{-p_\ell(n_j)}A\big)>0. $$
  We also show that if a level set $E$ of a multiplicative function has
positive upper density, then any self-shift $E-r$, $r\in E$, is a set of
averaging polynomial multiple recurrence. This in turn leads to the following
refinement of the polynomial Szemer\'edi theorem (cf. [4]).
  Let $E$ be a level set of an arbitrary multiplicative function, suppose $E$
has positive upper density and let $r\in E$. Then for any set $D\subset
\mathbb{N}$ with positive upper density and any polynomials
$p_i\in\mathbb{Q}[t]$, $i=1,\ldots,\ell$, which satisfy
$p_i(\mathbb{Z})\subset\mathbb{Z}$ and $p_i(0)=0$ for all
$i\in\{1,\ldots,\ell\}$, there exists $\beta>0$ such that the set $$
\left\{\,n\in E-r:\overline{d}\Big(D\cap (D-p_1(n))\cap \ldots\cap(D-p_\ell(n))
\Big)>\beta \,\right\} $$ has positive lower density.


  We extend the Malitsky-Tam forward-reflected-backward (FRB) splitting method
for inclusion problems of monotone operators to nonconvex minimization
problems. By assuming the generalized concave Kurdyka-{\L}ojasiewicz (KL)
property of a quadratic regularization of the objective, we show that the FRB
method converges globally to a stationary point of the objective and enjoys
finite length property. The sharpness of our approach is guaranteed by virtue
of the exact modulus associated with the generalized concave KL property.
Numerical experiments suggest that FRB is competitive compared to the
Douglas-Rachford method and the Bo\c{t}-Csetnek inertial Tseng's method.


  We consider apictorial edge-matching puzzles, in which the goal is to arrange
a collection of puzzle pieces with colored edges so that the colors match along
the edges of adjacent pieces. We devise an algebraic representation for this
problem and provide conditions under which it exactly characterizes a puzzle.
Using the new representation, we recast the combinatorial, discrete problem of
solving puzzles as a global, polynomial system of equations with continuous
variables. We further propose new algorithms for generating approximate
solutions to the continuous problem by solving a sequence of convex
relaxations.


  Dimension reduction is a technique used to transform data from a
high-dimensional space into a lower-dimensional space, aiming to retain as much
of the original information as possible. This approach is crucial in many
disciplines like engineering, biology, astronomy, and economics. In this paper,
we consider the following dimensionality reduction instance: Given an
n-dimensional probability distribution p and an integer m<n, we aim to find the
m-dimensional probability distribution q that is the closest to p, using the
Kullback-Leibler divergence as the measure of closeness. We prove that the
problem is strongly NP-hard, and we present an approximation algorithm for it.


  This theoretical paper is devoted to developing a rigorous theory for
demystifying the global convergence phenomenon in a challenging scenario:
learning over-parameterized Rectified Linear Unit (ReLU) nets for very high
dimensional dataset under very mild assumptions. A major ingredient of our
analysis is a fine-grained analysis of random activation matrices. The
essential virtue of dissecting activation matrices is that it bridges the
dynamics of optimization and angular distribution in high-dimensional data
space. This angle-based detailed analysis leads to asymptotic characterizations
of gradient norm and directional curvature of objective function at each
gradient descent iteration, revealing that the empirical loss function enjoys
nice geometrical properties in the overparameterized setting. Along the way, we
significantly improve existing theoretical bounds on both over-parameterization
condition and learning rate with very mild assumptions for learning very high
dimensional data. Moreover, we uncover the role of the geometrical and spectral
properties of the input data in determining desired over-parameterization size
and global convergence rate. All these clues allow us to discover a novel
geometric picture of nonconvex optimization in deep learning: angular
distribution in high-dimensional data space $\mapsto$ spectrums of
overparameterized activation matrices $\mapsto$ favorable geometrical
properties of empirical loss landscape $\mapsto$ global convergence phenomenon.
Furthremore, our theoretical results imply that gradient-based nonconvex
optimization algorithms have much stronger statistical guarantees with much
milder over-parameterization condition than exisiting theory states for
learning very high dimensional data, which is rarely explored so far.


  The recently discovered layered BiS2-based superconductors have attracted a
great deal of interest due to their structural similarity to cuprate and
iron-pnictide superconductors. We have performed Raman scattering measurements
on two superconducting crystals NdO0.5F0.5BiS2 (Tc = 4.5 K) and NdO0.7F0.3BiS2
(Tc = 4.8 K). The observed Raman phonon modes are assigned with the aid of
first-principles calculations. The asymmetrical phonon mode around 118 cm-1
reveals a small electron-phonon (e-ph) coupling constant 0.16, which is
insufficient to generate superconductivity at ~ 4.5 K. In the Raman spectra
there exists a clear temperature-dependent hump around 100 cm-1, which can be
well understood in term of inter-band vertical transitions around Fermi
surface. The transitions get boosted when the particular rectangular-like Fermi
surface meets band splitting caused by spin-orbit coupling. It enables a unique
and quantitative insight into the band splitting.


  Researchers often treat data-driven and theory-driven models as two disparate
or even conflicting methods in travel behavior analysis. However, the two
methods are highly complementary because data-driven methods are more
predictive but less interpretable and robust, while theory-driven methods are
more interpretable and robust but less predictive. Using their complementary
nature, this study designs a theory-based residual neural network (TB-ResNet)
framework, which synergizes discrete choice models (DCMs) and deep neural
networks (DNNs) based on their shared utility interpretation. The TB-ResNet
framework is simple, as it uses a ($\delta$, 1-$\delta$) weighting to take
advantage of DCMs' simplicity and DNNs' richness, and to prevent underfitting
from the DCMs and overfitting from the DNNs. This framework is also flexible:
three instances of TB-ResNets are designed based on multinomial logit model
(MNL-ResNets), prospect theory (PT-ResNets), and hyperbolic discounting
(HD-ResNets), which are tested on three data sets. Compared to pure DCMs, the
TB-ResNets provide greater prediction accuracy and reveal a richer set of
behavioral mechanisms owing to the utility function augmented by the DNN
component in the TB-ResNets. Compared to pure DNNs, the TB-ResNets can modestly
improve prediction and significantly improve interpretation and robustness,
because the DCM component in the TB-ResNets stabilizes the utility functions
and input gradients. Overall, this study demonstrates that it is both feasible
and desirable to synergize DCMs and DNNs by combining their utility
specifications under a TB-ResNet framework. Although some limitations remain,
this TB-ResNet framework is an important first step to create mutual benefits
between DCMs and DNNs for travel behavior modeling, with joint improvement in
prediction, interpretation, and robustness.


  Vision in adverse weather conditions, whether it be snow, rain, or fog is
challenging. In these scenarios, scattering and attenuation severly degrades
image quality. Handling such inclement weather conditions, however, is
essential to operate autonomous vehicles, drones and robotic applications where
human performance is impeded the most. A large body of work explores removing
weather-induced image degradations with dehazing methods. Most methods rely on
single images as input and struggle to generalize from synthetic
fully-supervised training approaches or to generate high fidelity results from
unpaired real-world datasets. With data as bottleneck and most of today's
training data relying on good weather conditions with inclement weather as
outlier, we rely on an inverse rendering approach to reconstruct the scene
content. We introduce ScatterNeRF, a neural rendering method which adequately
renders foggy scenes and decomposes the fog-free background from the
participating media-exploiting the multiple views from a short automotive
sequence without the need for a large training data corpus. Instead, the
rendering approach is optimized on the multi-view scene itself, which can be
typically captured by an autonomous vehicle, robot or drone during operation.
Specifically, we propose a disentangled representation for the scattering
volume and the scene objects, and learn the scene reconstruction with
physics-inspired losses. We validate our method by capturing multi-view
In-the-Wild data and controlled captures in a large-scale fog chamber.


  The availability of data sets with large numbers of variables is rapidly
increasing. The effective application of Bayesian variable selection methods
for regression with these data sets has proved difficult since available Markov
chain Monte Carlo methods do not perform well in typical problem sizes of
interest. The current paper proposes new adaptive Markov chain Monte Carlo
algorithms to address this shortcoming. The adaptive design of these algorithms
exploits the observation that in large $p$ small $n$ settings, the majority of
the $p$ variables will be approximately uncorrelated a posteriori. The
algorithms adaptively build suitable non-local proposals that result in moves
with squared jumping distance significantly larger than standard methods. Their
performance is studied empirically in high-dimensional problems (with both
simulated and actual data) and speedups of up to 4 orders of magnitude are
observed. The proposed algorithms are easily implementable on multi-core
architectures and are well suited for parallel tempering or sequential Monte
Carlo implementations.


  In this paper, we considered new solutions for four-dimensional
asymptotically AdS black holes with scalar hair and discuss about Hawking
temperature in the context of dark energy by using the tunneling method. We
obtain modification of the Hawking temperature due to presence of the dark
energy.


  Connections of the living human brain, on a macroscopic scale, can be mapped
by a diffusion MR imaging based workflow. Since the same anatomic regions can
be corresponded between distinct brains, one can compare the presence or the
absence of the edges, connecting the very same two anatomic regions, among
multiple cortices. Previously, we have constructed the consensus braingraphs on
1015 vertices first in five, then in 96 subjects in the Budapest Reference
Connectome Server v1.0 and v2.0, respectively. Here we report the construction
of the version 3.0 of the server, generating the common edges of the
connectomes of variously parameterizable subsets of the 1015-vertex connectomes
of 477 subjects of the Human Connectome Project's 500-subject release. The
consensus connectomes are downloadable in csv and GraphML formats, and they are
also visualized on the server's page. The consensus connectomes of the server
can be considered as the "average, healthy" human connectome since all of their
connections are present in at least $k$ subjects, where the default value of
$k=209$, but it can also be modified freely at the web server. The webserver is
available at \url{http://connectome.pitgroup.org}.


  A nonparametric approach for policy learning for POMDPs is proposed. The
approach represents distributions over the states, observations, and actions as
embeddings in feature spaces, which are reproducing kernel Hilbert spaces.
Distributions over states given the observations are obtained by applying the
kernel Bayes' rule to these distribution embeddings. Policies and value
functions are defined on the feature space over states, which leads to a
feature space expression for the Bellman equation. Value iteration may then be
used to estimate the optimal value function and associated policy. Experimental
results confirm that the correct policy is learned using the feature space
representation.


  Origami-based design holds promise for developing materials whose mechanical
properties are tuned by crease patterns introduced to thin sheets. Although
there has been heuristic developments in constructing patterns with desirable
qualities, the bridge between origami and physics has yet to be fully
developed. To truly consider origami structures as a class of materials,
methods akin to solid mechanics need to be developed to understand their
long-wavelength behavior. We introduce here a lattice theory for examining the
mechanics of origami tessellations in terms of the topology of their crease
pattern and the relationship between the folds at each vertex. This formulation
provides a general method for associating mechanical properties with periodic
folded structures, and allows for a concrete connection between more
conventional materials and the mechanical metamaterials constructed using
origami-based design.


  (Abridged) X-ray observations of synchrotron rims in supernova remnant (SNR)
shocks show evidence of strong magnetic field amplification (a factor of ~100
between the upstream and downstream medium). This amplification may be due to
plasma instabilities driven by shock-accelerated cosmic rays (CRs). One
candidate is the cosmic ray current-driven (CRCD) instability (Bell 2004),
caused by the electric current of large Larmor radii CRs propagating parallel
to the upstream magnetic field. Particle-in-cell (PIC) simulations have shown
that the back-reaction of the amplified field on CRs would limit the
amplification factor of this instability to less than ~10 in galactic SNRs. In
this paper, we study the possibility of further amplification driven near
shocks by "magnetized" CRs, whose Larmor radii are smaller than the length
scale of the field that was previously amplified by the CRCD instability. We
find that additional amplification can occur due to a new instability, driven
by the CR current perpendicular to the field, which we term the "perpendicular
current-driven instability" (PCDI). We derive the growth rate of this
instability, and, using PIC simulations, study its non-linear evolution and
saturation. We find that PCDI increases the amplification of the field
(amplification factor up to ~45, not including the shock compression) and
discuss its observational signatures. Our results strengthen the idea of CRs
driving a significant part of the magnetic field amplification observed in SNR
shocks.


  \begin{abstract} In this manuscript, we answer a list of longstanding open
problems on weak phase retrieval including: (1) A complete classification of
the vectors $\{x_i\}_{i=1}^2$ in $\RR^3$ that do weak phase retrieval; (2) We
show that frames doing weak phase retrieval in $\RR^n$ must span $\RR^n$; (3)
We give an example of a set of vectors doing phase retrieval but their
orthogonal complement hyperplanes fail weak phase retrieval; (4) We give a
classification of weak phase retrievable frames - which makes clear the
difference between phase retrieval and weak phase retrieval; (5) We classify
when weak phase retrievable frames also do norm retrieval. We then introduce
the notion of weak phase retrieval by projections and develop their basic
properties. We then look at phase (norm) retrieval by projections. We end with
some open problems.
  We provide numerous examples to show that our results are best possible.
\end{abstract}


  In low temperature scanning tunneling microscopy (STM) experiments a cerium
adatom on Ag(100) possesses two discrete states with significantly different
apparent heights. These atomic switches also exhibit a Kondo-like feature in
spectroscopy experiments. By extensive theoretical simulations we find that
this behavior is due to diffusion of hydrogen from the surface onto the Ce
adatom in the presence of the STM tip field. The cerium adatom possesses
vibrational modes of very low energy (3-4meV) and very high efficiency (> 20%),
which are due to the large changes of Ce-states in the presence of hydrogen.
The atomic vibrations lead to a Kondo-like feature at very low bias voltages.
We predict that the same low-frequency/high-efficiency modes can also be
observed at lanthanum adatoms.


  Attack graphs are commonly used to analyse the security of medium-sized to
large networks. Based on a scan of the network and likelihood information of
vulnerabilities, attack graphs can be transformed into Bayesian Attack Graphs
(BAGs). These BAGs are used to evaluate how security controls affect a network
and how changes in topology affect security. A challenge with these
automatically generated BAGs is that cycles arise naturally, which make it
impossible to use Bayesian network theory to calculate state probabilities. In
this paper we provide a systematic approach to analyse and perform computations
over cyclic Bayesian attack graphs. %thus providing a generic approach to
handle cycles as well as unifying the theory of Bayesian attack graphs. Our
approach first formally introduces two commonly used versions of Bayesian
attack graphs and compares their expressiveness. We then present an
interpretation of Bayesian attack graphs based on combinational logic circuits,
which facilitates an intuitively attractive systematic treatment of cycles. We
prove properties of the associated logic circuit and present an algorithm that
computes state probabilities without altering the attack graphs (e.g., remove
an arc to remove a cycle). Moreover, our algorithm deals seamlessly with all
cycles without the need to identify their types. A set of experiments using
synthetically created networks demonstrates the scalability of the algorithm on
computer networks with hundreds of machines, each with multiple
vulnerabilities.


  An experimental comparison of the conversion gain and harmonic distortion
performance between Switching and Modulation architectures of an all-optical
photonic sampler mixer up-converter using a Semiconductor Optical
Amplifier-based Mach-Zehnder Interferometer (SOA-MZI) is presented. The process
of frequency up-conversion from 1 GHz to 9 GHz is evaluated. Because of their
different principle of operation, the Switching architecture demonstrates
higher positive conversion gain by approximately 6 dB and 8 dB for standard and
differential configuration, respectively, while the Modulation architecture
achieves lower harmonic distortion up to 8 dB, depending on the modulation
index of the 1 GHz signal.


  We prove a dynamical version of the Mordell-Lang conjecture for etale
endomorphisms of quasiprojective varieties. We use p-adic methods inspired by
the work of Skolem, Mahler, and Lech, combined with methods from algebraic
geometry. As special cases of our result we obtain a new proof of the classical
Mordell-Lang conjecture for cyclic subgroups of a semiabelian variety, and we
also answer positively a question of Keeler/Rogalski/Stafford for critically
dense sequences of closed points of a Noetherian integral scheme.


  Mountain-generated inertia-gravity waves (IGWs) affect the dynamics of both
the atmosphere and the ocean through the mean force they exert as they interact
with the flow. A key to this interaction is the presence of critical-level
singularities or, when planetary rotation is taken into account, inertial-level
singularities, where the Doppler-shifted wave frequency matches the local
Coriolis frequency. We examine the role of the latter singularities by studying
the steady wavepacket generated by a multiscale mountain in a rotating linear
shear flow at low Rossby number. Using a combination of WKB and saddle-point
approximations, we provide an explicit description of the form of the
wavepacket, of the mean forcing it induces, and of the mean-flow response.
  We identify two distinguished regimes of wave propagation: Regime I applies
far enough from a dominant inertial level for the standard ray-tracing
approximation to be valid; Regime II applies to a thin region where the
wavepacket structure is controlled by the inertial-level singularities. The
wave--mean-flow interaction is governed by the change in Eliassen--Palm (or
pseudomomentum) flux. This change is localised in a thin inertial layer where
the wavepacket takes a limiting form of that found in Regime II. We solve a
quasi-geostrophic potential-vorticity equation forced by the divergence of the
Eliassen--Palm flux to compute the wave-induced mean flow. Our results,
obtained in an inviscid limit, show that the wavepacket reaches a
large-but-finite distance downstream of the mountain (specifically, a distance
of order $k_*^{1/2} \Delta^{3/2}$, where $k_*^{-1}$ and $\Delta$ measure the
wave and envelope scales of the mountain) and extends horizontally over a
similar scale.


  The relativistic generalization of the Brownian motion is discussed. We show
that the transformation property of the noise term is determined by requiring
for the equilibrium distribution function to be Lorentz invariant, such as the
J\"uttner distribution function. It is shown that this requirement generates an
entanglement between the force term and the noise so that the noise itself
should not be a covariant quantity.


  A spin-orbit coupled quantum wire, with one end proximate to an s-wave
superconductor, can become a topological superconductor, with a Majorana mode
localized at each end of the superconducting region. It was recently shown that
coupling one end of such a topological superconductor to $two$ normal channels
of interacting electrons leads to a novel type of frustration and a quantum
critical point when both channels couple with equal strength. We propose an
experimental method to access this critical point in a $single$ quantum wire
and show its resilience to disorder.


  We present constraints on the stellar-mass distribution of distant galaxies.
These stellar-mass estimates derive from fitting population-synthesis models to
the galaxies' observed multi-band spectrophotometry. We discuss the complex
uncertainties (both statistical and systematic) that are inherent to this
method, and offer future prospects to improve the constraints. Typical
uncertainties for galaxies at z ~ 2.5 are ~ 0.3 dex (statistical), and factors
of ~ 3 (systematic). By applying this method to a catalog of NICMOS-selected
galaxies in the Hubble Deep Field North, we generally find a lack of
high-redshift galaxies (z > 2) with masses comparable to those of present-day
``L*'' galaxies. At z < 1.8, galaxies with L*-sized masses do emerge, but with
a number density below that at the present epoch. Thus, it seems massive,
present-day galaxies were not fully assembled by z ~ 2.5, and that further star
formation and/or merging are required to assemble them from these high-redshift
progenitors. Future progress on this subject will greatly benefit from upcoming
surveys such as those planned with HST/ACS and SIRTF.


  We study $B \to K^* \rho$ modes that are analogues of the much studied $B\to
K \pi$ modes with B decaying to two vector mesons instead of pseudoscalar
mesons, using topological amplitudes in the quark diagram approach. We show how
$B \to K^*\rho$ modes can be used to obtain many more observables than those
for $B \to K \pi$ modes, even though the quark level subprocesses of both modes
are exactly the same. All the theoretical parameters (except for the weak phase
$\gamma$), such as the magnitudes of the topological amplitudes and their
strong phases, can be determined in terms of the observables without any
model-dependent assumption. We demonstrate how $B\to K^*\rho$ can also be used
to verify if there exist any relations between theoretical parameters, such as
the hierarchy relations between the topological amplitudes and possible
relations between the strong phases. Conversely, if there exist reliable
theoretical estimates of amplitudes and strong phases, the presence of New
physics could be probed. We show that if the tree and color-supressed tree are
related to the electroweak penguins and color-supressed electroweak penguins,
it is not only possible to verify the validity of such relations but also to
have a clean measurement of New Physics parameters. We also present a numerical
study to examine which of the observables are more sensitive to New Physics.


  As is well-known, spontaneous CP-violation in the strong interaction is
possible at theta = pi, which is commonly referred to as Dashen's phenomenon.
This phenomenon has been studied extensively using chiral Lagrangians. Here the
two-flavor NJL model at theta = pi is discussed. It turns out that the
occurrence of spontaneous CP-violation depends on the strength of the 't Hooft
determinant interaction, which describes the effect of instanton interactions.
The dependence of the phase structure, and in particular of the CP-violating
phase, on the quark masses, temperature, baryon and isospin chemical potential
is examined in detail. The latter dependence shows a modification of the
charged pion condensed phase first discussed by Son and Stephanov.


  Compressed sensing of sparse sources can be improved by incorporating prior
knowledge of the source. In this paper we demonstrate a method for optimal
selection of weights in weighted $L_1$ norm minimization for a noiseless
reconstruction model, and show the improvements in compression that can be
achieved.


  Planetary obliquity and eccentricity influence climate by shaping the spatial
and temporal patterns of stellar energy incident at a planet's surface,
affecting both the annual mean climate and magnitude of seasonal variability.
Previous work has demonstrated the importance of both planetary obliquity and
eccentricity for climate and habitability, but most studies have not explicitly
modeled the response of life to these parameters. While exaggerated seasons may
be stressful to some types of life, a recent study found an increase in marine
biological activity for moderately high obliquities <45$^{\circ}$ assuming an
Earth-like eccentricity. However, it is unclear how life might respond to
obliquities >45$^{\circ}$, eccentricities much larger than Earth's, or the
combination of both. To address this gap, we use cGENIE-PlaSim, a 3-D marine
biogeochemical model coupled to an atmospheric general circulation model, to
investigate the response of Earth-like marine life to a large range of
obliquities (0-90$^{\circ}$) and eccentricities (0-0.4). We find that marine
biological activity increases with both increasing obliquity and eccentricity
across the parameter space we considered, including the combination of high
obliquity and high eccentricity. We discuss these results in the context of
remote biosignatures, and we argue that planets with high obliquity and/or
eccentricity may be superhabitable worlds that are particularly favorable for
exoplanet life detection.


  Combining large segmented space telescopes, coronagraphy and wavefront
control methods is a promising solution to produce a dark hole (DH) region in
the coronagraphic image of an observed star and study planetary companions. The
thermal and mechanical evolution of such a high-contrast facility leads to
wavefront drifts that degrade the DH contrast during the observing time, thus
limiting the ability to retrieve planetary signals. Lyot-style coronagraphs are
starlight suppression systems that remove the central part of the image for an
unresolved observed star, the point spread function, with an opaque focal plane
mask (FPM). When implemented with a flat mirror containing an etched pinhole,
the mask rejects part of the starlight through the pinhole which can be used to
retrieve information about low-order aberrations. We propose an active control
scheme using a Zernike wavefront sensor (ZWFS) to analyze the light rejected by
the FPM, control low-order aberrations, and stabilize the DH contrast. The
concept formalism is first presented before characterizing the sensor behavior
in simulations and in laboratory. We then perform experimental tests to
validate a wavefront control loop using a ZWFS on the HiCAT testbed. By
controlling the first 11 Zernike modes, we show a decrease in wavefront error
standard deviation by a factor of up to 9 between open- and closed-loop
operations using the ZWFS. In the presence of wavefront perturbations, we show
the ability of this control loop to stabilize a DH contrast around 7x10^-8 with
a standard deviation of 7x10^-9. Active control with a ZWFS proves a promising
solution in Lyot coronagraphs with an FPM-filtered beam to control and
stabilize low-order wavefront aberrations and DH contrast for exoplanet imaging
with future space missions.


  We generalize Kuznetsov's theory of homological projective duality to the
setting of noncommutative algebraic geometry. Simultaneously, we develop the
theory over general base schemes, and remove the usual smoothness, properness,
and transversality hypotheses.


  Attenuation and scatter correction (AC) is crucial for quantitative Positron
Emission Tomography (PET) imaging. Recently, direct application of AC in the
image domain using deep learning approaches has been proposed for the hybrid
PET/MR and dedicated PET systems that lack accompanying transmission or
anatomical imaging. This study set out to investigate deep learning-based AC in
the image domain using different input settings.


  Identification and verification of molecular properties such as side effects
is one of the most important and time-consuming steps in the process of
molecule synthesis. For example, failure to identify side effects before
submission to regulatory groups can cost millions of dollars and months of
additional research to the companies. Failure to identify side effects during
the regulatory review can also cost lives. The complexity and expense of this
task have made it a candidate for a machine learning-based solution. Prior
approaches rely on complex model designs and excessive parameter counts for
side effect predictions. We believe reliance on complex models only shifts the
difficulty away from chemists rather than alleviating the issue. Implementing
large models is also expensive without prior access to high-performance
computers. We propose a heuristic approach that allows for the utilization of
simple neural networks, specifically the recurrent neural network, with a 98+%
reduction in the number of required parameters compared to available large
language models while still obtaining near identical results as top-performing
models.


  This paper is about the rate of convergence of the Markov chain
$X_{n+1}=AX_{n}+B_{n}$ (mod $p$), where $A$ is an integer matrix with nonzero
eigenvalues and ${B_{n}}_{n}$ is a sequence of independent and identically
distributed integer vectors, with support not parallel to a proper subspace of
$Q^{k}$ invariant under $A$. If $|\lambda_{i}|\not=1$ for all eigenvalues
$\lambda_{i}$ of $A$, then $n=O((\ln p)^{2}) $ steps are sufficient and
$n=O(\ln p)$ steps are necessary to have $X_{n}$ sampling from a nearly uniform
distribution. Conversely, if $A$ has the eigenvalues $\lambda_{i}$ that are
roots of positive integer numbers, $|\lambda_{1}|=1$ and $|\lambda_{i}|>1$ for
all $i\not=1$, then $O(p^{2}) $ steps are necessary and sufficient.


  The structure of a magnetized quark-hybrid stars (QHS) is modeled using a
standard relativistic mean-field equation of state (EoS) for the description of
hadronic matter. For quark matter we consider a bag model EoS which is modified
perturbatively to account for the presence of a uniform magnetic field. The
mass-radius (M-R) relationship, gravitational redshift and rotational Kepler
periods of such stars are compared with those of standard neutron stars (NS).


  We present a new iterative method to reduce eccentricity in black-hole-binary
simulations. Given a good first estimate of low-eccentricity starting momenta,
we evolve puncture initial data for ~4 orbits and construct improved initial
parameters by comparing the inspiral with post-Newtonian calculations. Our
method is the first to be applied directly to the gravitational-wave (GW)
signal, rather than the orbital motion. The GW signal is in general less
contaminated by gauge effects, which, in moving-puncture simulations, limit
orbital-motion-based measurements of the eccentricity to an uncertainty of
$\Delta e \sim 0.002$, making it difficult to reduce the eccentricity below
this value. Our new method can reach eccentricities below $10^{-3}$ in one or
two iteration steps; we find that this is well below the requirements for GW
astronomy in the advanced detector era. Our method can be readily adapted to
any compact-binary simulation with GW emission, including black-hole-binary
simulations that use alternative approaches, and neutron-star-binary
simulations. We also comment on the differences in eccentricity estimates based
on the strain $h$, and the Newman-Penrose scalar $\Psi_4$.


  The rapid spread of the novel coronavirus (COVID-19) has severely impacted
almost all countries around the world. It not only has caused a tremendous
burden on health-care providers to bear, but it has also brought severe impacts
on the economy and social life. The presence of reliable data and the results
of in-depth statistical analyses provide researchers and policymakers with
invaluable information to understand this pandemic and its growth pattern more
clearly. This paper combines and processes an extensive collection of publicly
available datasets to provide a unified information source for representing
geographical regions with regards to their pandemic-related behavior. The
features are grouped into various categories to account for their impact based
on the higher-level concepts associated with them. This work uses several
correlation analysis techniques to observe value and order relationships
between features, feature groups, and COVID-19 occurrences. Dimensionality
reduction techniques and projection methodologies are used to elaborate on
individual and group importance of these representative features. A specific
RNN-based inference pipeline called DoubleWindowLSTM-CP is proposed in this
work for predictive event modeling. It utilizes sequential patterns and enables
concise record representation while using but a minimal amount of historical
data. The quantitative results of our statistical analytics indicated critical
patterns reflecting on many of the expected collective behavior and their
associated outcomes. Predictive modeling with DoubleWindowLSTM-CP instance
exhibits efficient performance in quantitative and qualitative assessments
while reducing the need for extended and reliable historical information on the
pandemic.


  Most of our understanding of bacterial chemotaxis comes from studies of
Escherichia coli. However, recent evidence suggests significant departures from
the E. coli paradigm in other bacterial species. This variation may stem from
different species inhabiting distinct environments and thus adapting to
specific environmental pressures. In particular, these complex and dynamic
environments may be poorly represented by standard experimental and theoretical
models. In this work, we study the performance of various chemotactic
strategies under a range of stochastic time- and space-varying attractant
distributions in silico. We describe a novel type of response in which the
bacterium tumbles more when attractant concentration is increasing, in contrast
to the response of E. coli, and demonstrate how this response explains the
behavior of aerobically-grown Rhodobacter sphaeroides. In this "speculator"
response, bacteria compare the current attractant concentration to the
long-term average. By tumbling persistently when the current concentration is
higher than the average, bacteria maintain their position in regions of high
attractant concentration. If the current concentration is lower than the
average, or is declining, bacteria swim away in search of more favorable
conditions. When the attractant distribution is spatially complex but
slowly-changing, this response is as effective as that of E. coli.


  We study the Abelian Thirring Model when the fermionic fields have
non-conserved chiral charge: $\Delta {\cal Q}_5 =N$. One of the main features
we find for this model is the dependence of the Virasoro central charge on both
the Thirring coupling constant and $N$. We show how to evaluate correlation
functions and in particular we compute the conformal dimensions for fermions
and fermionic bilinears, which depend on the fermionic chiral charge. Finally
we build primary fields with arbitrary conformal weight.


  There is a significant need for principled uncertainty reasoning in machine
learning systems as they are increasingly deployed in safety-critical domains.
A new approach with uncertainty-aware regression-based neural networks (NNs),
based on learning evidential distributions for aleatoric and epistemic
uncertainties, shows promise over traditional deterministic methods and typical
Bayesian NNs, notably with the capabilities to disentangle aleatoric and
epistemic uncertainties. Despite some empirical success of Deep Evidential
Regression (DER), there are important gaps in the mathematical foundation that
raise the question of why the proposed technique seemingly works. We detail the
theoretical shortcomings and analyze the performance on synthetic and
real-world data sets, showing that Deep Evidential Regression is a heuristic
rather than an exact uncertainty quantification. We go on to discuss
corrections and redefinitions of how aleatoric and epistemic uncertainties
should be extracted from NNs.


  UniFrac is a commonly used metric in microbiome research for comparing
microbiome profiles to one another ("beta diversity"). The recently implemented
Striped UniFrac added the capability to split the problem into many independent
subproblems and exhibits near linear scaling. In this paper we describe steps
undertaken in porting and optimizing Striped Unifrac to GPUs. We reduced the
run time of computing UniFrac on the published Earth Microbiome Project dataset
from 13 hours on an Intel Xeon E5-2680 v4 CPU to 12 minutes on an NVIDIA Tesla
V100 GPU, and to about one hour on a laptop with NVIDIA GTX 1050 (with minor
loss in precision). Computing UniFrac on a larger dataset containing 113k
samples reduced the run time from over one month on the CPU to less than 2
hours on the V100 and 9 hours on an NVIDIA RTX 2080TI GPU (with minor loss in
precision). This was achieved by using OpenACC for generating the GPU offload
code and by improving the memory access patterns. A BSD-licensed implementation
is available, which produces a C shared library linkable by any programming
language.


  Several independent lines of evidence suggest that the stellar initial mass
function (IMF) in early-type galaxies becomes increasingly `bottom-heavy' with
increasing galaxy mass and/or velocity dispersion, sigma. Here we consider
evidence for IMF variation in a sample of relatively compact early-type
galaxies drawn from the Sloan Digital Sky Survey. These galaxies are of
sufficiently high stellar density that a dark halo likely makes a minor
contribution to the total dynamical mass, Mdyn, within one effective radius. We
fit our detailed stellar population synthesis models to the stacked absorption
line spectra of these galaxies in bins of sigma and find evidence from
IMF-sensitive spectral features for a bottom-heavy IMF at high sigma. We also
apply simple `mass-follows-light' dynamical models to the same data and find
that Mdyn is significantly higher than what would be expected if these galaxies
were stellar dominated and had a universal Milky Way IMF. Adopting Mdyn M_*
therefore implies that the IMF is `heavier' at high sigma. Most importantly,
the quantitative amount of inferred IMF variation is very similar between the
two techniques, agreeing to within 0.1 dex in mass. The agreement between two
independent techniques, when applied to the same data, provides compelling
evidence for systematic variation in the IMF as a function of early-type galaxy
velocity dispersion. Any alternative explanations must reproduce both the
results from dynamical and stellar population-based techniques.


  The general analysis of the rare Bc->D^*_s l^+ l^- decay is presented by
using the most general, model independent effective Hamiltonian. The
dependencies of the branching ratios, longitudinal, normal and transversal
polarization asymmetries for l^- and the combined asymmetries for l^- and l^+
on the new Wilson coefficients are investigated. Our analysis shows that the
lepton polarization asymmetries are very sensitive to the scalar and tensor
type interactions, which will be very useful in looking for new physics beyond
the standard model.


  The definition of Linear Symmetry-Based Disentanglement (LSBD) formalizes the
notion of linearly disentangled representations, but there is currently no
metric to quantify LSBD. Such a metric is crucial to evaluate LSBD methods and
to compare to previous understandings of disentanglement. We propose
$\mathcal{D}_\mathrm{LSBD}$, a mathematically sound metric to quantify LSBD,
and provide a practical implementation for $\mathrm{SO}(2)$ groups.
Furthermore, from this metric we derive LSBD-VAE, a semi-supervised method to
learn LSBD representations. We demonstrate the utility of our metric by showing
that (1) common VAE-based disentanglement methods don't learn LSBD
representations, (2) LSBD-VAE as well as other recent methods can learn LSBD
representations, needing only limited supervision on transformations, and (3)
various desirable properties expressed by existing disentanglement metrics are
also achieved by LSBD representations.


  One of the major challenges for low-rank multi-fidelity (MF) approaches is
the assumption that low-fidelity (LF) and high-fidelity (HF) models admit
"similar" low-rank kernel representations. Low-rank MF methods have
traditionally attempted to exploit low-rank representations of linear kernels,
which are kernel functions of the form $K(u,v) = v^T u$ for vectors $u$ and
$v$. However, such linear kernels may not be able to capture low-rank behavior,
and they may admit LF and HF kernels that are not similar. Such a situation
renders a naive approach to low-rank MF procedures ineffective. In this paper,
we propose a novel approach for the selection of a near-optimal kernel function
for use in low-rank MF methods. The proposed framework is a two-step strategy
wherein: (1) hyperparameters of a library of kernel functions are optimized,
and (2) a particular combination of the optimized kernels is selected, through
either a convex mixture (Additive Kernels) or through a data-driven
optimization (Adaptive Kernels). The two resulting methods for this generalized
framework both utilize only the available inexpensive low-fidelity data and
thus no evaluation of high-fidelity simulation model is needed until a kernel
is chosen. These proposed approaches are tested on five non-trivial problems
including multi-fidelity surrogate modeling for one- and two-species molecular
systems, gravitational many-body problem, associating polymer networks,
plasmonic nano-particle arrays, and an incompressible flow in channels with
stenosis. The results for these numerical experiments demonstrate the numerical
stability efficiency of both proposed kernel function selection procedures, as
well as high accuracy of their resultant predictive models for estimation of
quantities of interest. Comparisons against standard linear kernel procedures
also demonstrate increased accuracy of the optimized kernel approaches.


  We address the challenge of quantifying Bayesian uncertainty and
incorporating it in offline use cases of finite-state Markov Decision Processes
(MDPs) with unknown dynamics. Our approach provides a principled method to
disentangle epistemic and aleatoric uncertainty, and a novel technique to find
policies that optimise Bayesian posterior expected value without relying on
strong assumptions about the MDP's posterior distribution. First, we utilise
standard Bayesian reinforcement learning methods to capture the posterior
uncertainty in MDP parameters based on available data. We then analytically
compute the first two moments of the return distribution across posterior
samples and apply the law of total variance to disentangle aleatoric and
epistemic uncertainties. To find policies that maximise posterior expected
value, we leverage the closed-form expression for value as a function of
policy. This allows us to propose a stochastic gradient-based approach for
solving the problem. We illustrate the uncertainty quantification and Bayesian
posterior value optimisation performance of our agent in simple, interpretable
gridworlds and validate it through ground-truth evaluations on synthetic MDPs.
Finally, we highlight the real-world impact and computational scalability of
our method by applying it to the AI Clinician problem, which recommends
treatment for patients in intensive care units and has emerged as a key use
case of finite-state MDPs with offline data. We discuss the challenges that
arise with Bayesian modelling of larger scale MDPs while demonstrating the
potential to apply our methods rooted in Bayesian decision theory into the real
world. We make our code available at
https://github.com/filippovaldettaro/finite-state-mdps .


  We show that the neutrino mixing pattern with the large mixing required for
the atmospheric neutrino problem and the small mixing angle MSW solution for
the solar neutrino problem can be naturally generated through radiative
magnification, even though all the mixing angles at the seesaw scale may be
small. This can account for the neutrino anomalies as well as the CHOOZ
constraints in the context of quark-lepton unified theories, where the quark
and lepton mixing angles are expected to be similar in magnitude at the high
scale. We also indicate the 4$\nu$ mixing scenarios for which this mechanism of
radiative magnification can provide a natural explanation.


  We construct a smooth area preserving flow on a genus 2 surface with exactly
one open uniquely ergodic component, that is asymmetrically bounded by
separatrices of non-degenerate saddles and that is nevertheless not mixing.


  Given a knowledge base KB containing first-order and statistical facts, we
consider a principled method, called the random-worlds method, for computing a
degree of belief that some formula Phi holds given KB. If we are reasoning
about a world or system consisting of N individuals, then we can consider all
possible worlds, or first-order models, with domain {1,...,N} that satisfy KB,
and compute the fraction of them in which Phi is true. We define the degree of
belief to be the asymptotic value of this fraction as N grows large. We show
that when the vocabulary underlying Phi and KB uses constants and unary
predicates only, we can naturally associate an entropy with each world. As N
grows larger, there are many more worlds with higher entropy. Therefore, we can
use a maximum-entropy computation to compute the degree of belief. This result
is in a similar spirit to previous work in physics and artificial intelligence,
but is far more general. Of equal interest to the result itself are the
limitations on its scope. Most importantly, the restriction to unary predicates
seems necessary. Although the random-worlds method makes sense in general, the
connection to maximum entropy seems to disappear in the non-unary case. These
observations suggest unexpected limitations to the applicability of
maximum-entropy methods.


  We study the evolution of cooperation in public goods games on the square
lattice, focusing on the effects that are brought about by different sizes of
groups where individuals collect their payoffs and search for potential
strategy donors. We find that increasing the group size does not necessarily
lead to mean-field behavior, as is traditionally observed for games governed by
pairwise interactions, but rather that public cooperation may be additionally
promoted by means of enhanced spatial reciprocity that sets in for very large
groups. Our results highlight that the promotion of cooperation due to spatial
interactions is not rooted solely in having restricted connections amongst
players, but also in individuals having the opportunity to collect payoffs
separately from their direct opponents. Moreover, in large groups the presence
of a small number of defectors is bearable, which makes the mixed phase region
expand with increasing group size. Having a chance of exploiting distant
players, however, offers defectors a new way to break the phalanx of
cooperators, and even to resurrect from small numbers to eventually completely
invade the population.


  Many systems, including polymers and molecular liquids, when adequately
cooled and/or compressed, solidify into a disordered solid, i.e., a glass.
The~transition is not abrupt, featuring progressive decrease of the microscopic
mobility and huge slowing down of the relaxation.} A~distinctive aspect of
glass-forming materials is the microscopic dynamical heterogeneity (DH), i.e.,
the presence of regions with almost immobile particles coexisting with others
where highly mobile ones are located. Following the first compelling evidence
of a strong correlation between vibrational dynamics and ultraslow relaxation,
we posed the question if the vibrational dynamics encodes predictive
information on DH. Here, we review our results, drawn from molecular-dynamics
numerical simulation of polymeric and molecular glass-formers, with a special
focus on both the breakdown of the Stokes--Einstein relation between diffusion
and viscosity, and the size of the regions with correlated displacements.