  We investigate the effect of non-linear dispersion relations on the
bispectrum. In particular, we study the case were the modified relations do not
violate the WKB condition at early times, focusing on a particular example
which is exactly solvable: the Jacobson-Corley dispersion relation with quartic
correction with positive coefficient to the squared linear relation. We find
that the corrections to the standard result for the bispectrum are suppressed
by a factor $\frac{H^2}{p_c^2}$ where $p_c$ is the scale where the modification
to the dispersion relation becomes relevant. The modification is {\it mildly}
configuration-dependent and equilateral configurations are more suppressed with
respect to the local ones, by a factor of one percent. There is no
configuration leading to enhancements. We then analyze the results in the
framework of particle creation using the approximate gluing method of
Brandenberger and Martin, which relates more directly to the modeling of the
trans-Planckian physics via modifications of the vacuum at a certain cutoff
scale. We show that the gluing method overestimates the leading order
correction to the spectrum and bispectrum by one and two orders, respectively,
in $\frac{H}{p_c}$. We discuss the various approximation and conclude that for
dispersion relations not violating WKB at early times the particle creation is
small and does not lead to enhanced contributions to the bispectrum. We also
show that in many cases enhancements do not occur when modeling the
trans-Planckian physics via modifications of the vacuum at a certain cutoff
scale. Most notably they are only of order O(1) when the Bogolyubov
coefficients accounting for particle creation are determined by the Wronskian
condition and the minimization of the uncertainty between the field and its
conjugate momentum.


  The recent LHC data have once more brought the issue of the formation of
thermalized state of matter in hadron-hadron collisions into the forefront. In
this letter, we have shown that the scaling of the information entropy of the
chaotically produced particles is valid up to recently available data from p+p
collisions at $\sqrt{s}$ = 2.36 TeV obtained by ALICE experiment. We predict
that at the highest energies projected for LHC, almost all the particles will
be produced chaotically, indicating that a collective behavior should be
observed in hadronic collisions, as indicated by one of present authors quite
some time ago.


  We study the impact of a modified expansion rate on the dark matter relic
abundance in a class of scalar-tensor theories. The scalar-tensor theories we
consider are motivated from string theory constructions, which have conformal
as well as disformally coupled matter to the scalar. We investigate the effects
of such a conformal coupling to the dark matter relic abundance for a wide
range of initial conditions, masses and cross-sections. We find that exploiting
all possible initial conditions, the annihilation cross-section required to
satisfy the dark matter content can differ from the thermal average
cross-section in the standard case. We also study the expansion rate in the
disformal case and find that physically relevant solutions require a nontrivial
relation between the conformal and disformal functions. We study the effects of
the disformal coupling in an explicit example where the disformal function is
quadratic.


  Let $\Sigma = X\cup X^{-1} = \{ x_1 ,x_2 ,..., x_m ,x_1^{-1} ,x_2^{-1} ,...,
x_m^{-1} \}$ and let $G$ be a group with set of generators $\Sigma$. Let
$\mathfrak{L} (G) =\left\{ \left. \omega \in \Sigma^* \; \right\vert \;\omega
\equiv e \; (\textrm{mod} \; G) \right\} \subseteq \Sigma^*$ be the group
language representing $G$, where $\Sigma^*$ is a free monoid over $\Sigma$ and
$e$ is the identity in $G$. The problem of determining whether a context-free
language is subset of a group language is discussed. Polynomial algorithms are
presented for testing whether a regular language, or a linear language is
included in a group language. A few finite sets are built, such that each of
them is included in the group language $\mathfrak{L} (G)$ if and only if the
respective context-free language is included in $\mathfrak{L} (G)$.


  The COVID-19 epidemic that emerged in Wuhan China at the end of 2019 hit
Italy particularly hard, yielding the implementation of strict national
lockdown rules (Phase 1). There is now a hot ongoing debate in Italy and abroad
on what the best strategy is to restart a country to exit a national lockdown
(Phase 2). Previous studies have focused on modelling possible restarting
scenarios at the national level, overlooking the fact that Italy, as other
nations around the world, is divided in administrative regions who can
independently oversee their own share of the Italian National Health Service.
In this study, we show that regionalism, and heterogeneity between regions, is
essential to understand the spread of the epidemic and, more importantly, to
design effective post Lock-Down strategies to control the disease. To achieve
this, we model Italy as a network of regions and parameterize the model of each
region on real data spanning almost two months from the initial outbreak. Using
the model, we confirm the effectiveness at the regional level of the national
lockdown strategy implemented so far by the Italian government to mitigate the
spread of the disease and show its efficacy at the regional level. We also
propose that differentiated, albeit coordinated, regional interventions can be
effective in Phase 2 to restart the country and avoid future recurrence of the
epidemic, while avoiding saturation of the regional health systems and
mitigating impact on costs. Our study and methodology can be easily extended to
other levels of granularity (provinces or counties in the same region or states
in other federal countries, etc.) to support policy- and decision-makers.


  To efficiently establish training databases for machine learning methods,
collaborative and crowdsourcing platforms have been investigated to
collectively tackle the annotation effort. However, when this concept is ported
to the medical imaging domain, reading expertise will have a direct impact on
the annotation accuracy. In this study, we examine the impact of expertise and
the amount of available annotations on the accuracy outcome of a liver
segmentation problem in an abdominal computed tomography (CT) image database.
In controlled experiments, we study this impact for different types of weak
annotations. To address the decrease in accuracy associated with lower
expertise, we propose a method for outlier correction making use of a weakly
labelled atlas. Using this approach, we demonstrate that weak annotations
subject to high error rates can achieve a similarly high accuracy as
state-of-the-art multi-atlas segmentation approaches relying on a large amount
of expert manual segmentations. Annotations of this nature can realistically be
obtained from a non-expert crowd and can potentially enable crowdsourcing of
weak annotation tasks for medical image analysis.


  Conformal Prediction (CP) is a popular uncertainty quantification method that
provides distribution-free, statistically valid prediction sets, assuming that
training and test data are exchangeable. In such a case, CP's prediction sets
are guaranteed to cover the (unknown) true test output with a user-specified
probability. Nevertheless, this guarantee is violated when the data is
subjected to adversarial attacks, which often result in a significant loss of
coverage. Recently, several approaches have been put forward to recover CP
guarantees in this setting. These approaches leverage variations of randomised
smoothing to produce conservative sets which account for the effect of the
adversarial perturbations. They are, however, limited in that they only support
$\ell^2$-bounded perturbations and classification tasks. This paper introduces
VRCP (Verifiably Robust Conformal Prediction), a new framework that leverages
recent neural network verification methods to recover coverage guarantees under
adversarial attacks. Our VRCP method is the first to support perturbations
bounded by arbitrary norms including $\ell^1$, $\ell^2$, and $\ell^\infty$, as
well as regression tasks. We evaluate and compare our approach on image
classification tasks (CIFAR10, CIFAR100, and TinyImageNet) and regression tasks
for deep reinforcement learning environments. In every case, VRCP achieves
above nominal coverage and yields significantly more efficient and informative
prediction regions than the SotA.


  We design a consistent Galerkin scheme for the approximation of the vectorial
modified Korteweg-de Vries equation. We demonstrate that the scheme conserves
energy up to machine precision. In this sense the method is consistent with the
energy balance of the continuous system. This energy balance ensures there is
no numerical dissipation allowing for extremely accurate long time simulations
free from numerical artifacts. Various numerical experiments are shown
demonstrating the asymptotic convergence of the method with respect to the
discretisation parameters. Some simulations are also presented that correctly
capture the unusual interactions between solitons in the vectorial setting.


  The variety DQD of semi-Heyting algebras with a weak negation, called dually
quasi-De Morgan operation, and several of its subvarieties were investigated in
a series of four papers. In this paper we define and investigate a new
subvariety JID of DQD, called JI-distributive, dually quasi-De Morgan
semi-Heyting algebras, as well as the variety DSt of dually Stone semi-Heyting
algebras. We first prove that DSt and JID are discriminator varieties of level
1 and level 2, respectively. Secondly, we give a characterization of
subdirectly irreducible algebras of the subvariety JID1 of level 1 of JID. As a
first application of it, we derive that the variety JID1 is the join of the
variety DSt and the variety of De Morgan Boolean semi-Heyting algebras. As a
second application, we give a concrete description of the subdirectly
irreducible algebras in the subvariety JIDL1 of JID1 defined by the linear
identity, and deduce that the variety JIDL1 is the join of the variety DStHC
generated by the dually Stone Heyting chains and the variety generated by the
4-element De Morgan Boolean Heyting algebra. Several applications of this
result are also given, including a description of the lattice of subvarieties
of JIDL1, equational bases of all subvarieties of JIDL1, and the amalgamation
property of all subvarieties of DStHC.


  We say that a subgraph $F$ of a graph $G$ is singular if the degrees $d_G(v)$
are all equal or all distinct for the vertices $v\in V(F)$. The singular Ramsey
number Rs$(F)$ is the smallest positive integer $n$ such that, for every $m\geq
n$, in every edge 2-coloring of $K_m$, at least one of the color classes
contains $F$ as a singular subgraph. In a similar flavor, the singular Tur\'an
number Ts$(n,F)$ is defined as the maximum number of edges in a graph of order
$n$, which does not contain $F$ as a singular subgraph. In this paper we
initiate the study of these extremal problems. We develop methods to estimate
Rs$(F)$ and Ts$(n,F)$, present tight asymptotic bounds and exact results.


  Autonomous surface vehicles (ASV) allow the investigation of coastal areas,
ports and harbors as well as harsh and dangerous environments such as the
arctic regions. Despite receiving increasing attention, the hydrodynamic
analysis of ASV performance subject to variable operational parameters is
little investigated. In this context, this paper presents a multi-fidelity (MF)
hydrodynamic analysis of an ASV, namely the Shallow Water Autonomous
Multipurpose Platform (SWAMP), at surveying speed in calm water and subject to
variable payload and location of the center of mass, accounting for the variety
of equipment that the vehicle can carry. The analysis is conducted in deep
water, which is the condition mostly encountered by the ASV during surveys of
coastal and harbors areas. Quantities of interest are the resistance, the
vehicle attitude, and the wave generated in the region between the catamaran
hulls. These are assessed using a Reynolds Averaged Navier Stokes Equation
(RANSE) code and a linear potential flow (PF) solver. The objective is to
accurately assess the quantities of interest, along with identifying the
limitation of PF analysis in the current context. Finally, a multi-fidelity
Gaussian Process (MF-GP) model is obtained combining RANSE and PF solutions.
The latter also include variable grid refinement and coupling between
hydrodynamic loads and rigid body equations of motion. The surrogate model is
iteratively refined using an active learning approach. Numerical results show
that the MF-GP is effective in producing response surfaces of the SWAMP
performance with a limited computational cost. It is highlighted how the SWAMP
performance is significantly affected not only by the payload, but also by the
location of the center of mass. The latter can be therefore properly calibrated
to minimize the resistance and allow for longer-range operations.


  For finitely generated nilpotent groups, we employ Mal'cev coordinates to
solve several classical algorithmic problems efficiently. Computation of normal
forms, the membership problem, the conjugacy problem, and computation of
presentations for subgroups are solved using only logarithmic space and
quasilinear time. Logarithmic space presentation-uniform versions of these
algorithms are provided. Compressed-word versions of the same problems, in
which each input word is provided as a straight-line program, are solved in
polynomial time.


  In the Pacific Coast of Colombia there is a type of marimba called marimba de
chonta, which provides the melodic and harmonic contour for traditional music
with characteristic chants and dances. The tunings of this marimba are based on
the voice of female singers and allows musical practices, as a transposition
that preserves relative distances between bars. Here we show that traditional
tunings are consistent with isotonic scales, and that they have changed in the
last three decades due to the influence of Western music. Specifically, low
octaves have changed into just octaves. Additionally, consonance properties of
this instrument include the occurrence of a broad minimum of dissonance that is
used in the musical practices, while the narrow local peaks of dissonance are
avoided. We found that the main reason for this is the occurrence of
uncertainties in the tunings with respect to the mathematical successions of
isotonic scales. We conclude that in this music the emergence of tunings and
musical practices cannot be considered as separate issues. Consonance, timbre,
and musical practices are entangled.


  Scattering phase shifts of a meson-meson system in staggered 3-dimensional
lattice QED are computed. The main task of the simulation is to obtain a
discrete set of two-body energy levels. These are extracted from a 4-point time
correlation matrix and then used to obtain scattering phase shifts. The results
for the l=0 and l=2 partial waves are consistent with short- range repulsion
and intermediate-range attraction of the residual meson- meson interaction.


  The main aim of this article is to characterize inner Poisson structure on a
quantum cluster algebra without coefficients. Mainly, we prove that inner
Poisson structure on a quantum cluster algebra without coefficients is always a
standard Poisson structure. In order to relate with compatible Poisson
structure, we introduce the concept of so-called locally inner Poisson
structure on a quantum cluster algebra and then show it is equivalent to
locally standard Poisson structure in the case without coefficients. Based on
the result from \cite{LP} we obtain finally the equivalence between locally
inner Poisson structure and compatible Poisson structure in this case.


  Understanding egocentric human-object interaction (HOI) is a fundamental
aspect of human-centric perception, facilitating applications like AR/VR and
embodied AI. For the egocentric HOI, in addition to perceiving semantics e.g.,
''what'' interaction is occurring, capturing ''where'' the interaction
specifically manifests in 3D space is also crucial, which links the perception
and operation. Existing methods primarily leverage observations of HOI to
capture interaction regions from an exocentric view. However, incomplete
observations of interacting parties in the egocentric view introduce ambiguity
between visual observations and interaction contents, impairing their efficacy.
From the egocentric view, humans integrate the visual cortex, cerebellum, and
brain to internalize their intentions and interaction concepts of objects,
allowing for the pre-formulation of interactions and making behaviors even when
interaction regions are out of sight. In light of this, we propose harmonizing
the visual appearance, head motion, and 3D object to excavate the object
interaction concept and subject intention, jointly inferring 3D human contact
and object affordance from egocentric videos. To achieve this, we present
EgoChoir, which links object structures with interaction contexts inherent in
appearance and head motion to reveal object affordance, further utilizing it to
model human contact. Additionally, a gradient modulation is employed to adopt
appropriate clues for capturing interaction regions across various egocentric
scenarios. Moreover, 3D contact and affordance are annotated for egocentric
videos collected from Ego-Exo4D and GIMO to support the task. Extensive
experiments on them demonstrate the effectiveness and superiority of EgoChoir.
Code and data will be open.


  Using molecular dynamics we investigate the thermodynamics, dynamics and
structure of 250 diatomic molecules interacting by a core-softened potential.
This system exhibits thermodynamics, dynamics and structural anomalies: a
maximum in density-temperature plane at constante pressure and maximum and
minimum points in the diffusivity and translational order parameter against
density at constant temperature. Starting with very dense systems and
decreasing density the mobility at low temperatures first increases, reach a
maximum, then decreases, reach a minimum and finally increases. In the
pressure-temperature phase diagram the line of maximum translational order
parameter is located outside the line of diffusivity extrema that is enclosing
the temperature of maximum density line. We compare our results with the
monomeric system showing that the anisotropy due to the dumbbell leads to a
much larger solid phase and to the appearance of a liquid crystal phase. the
double ranged thermodynamic and dynamic anomalies.


  We evaluate the potential of the ESA Cornerstone Mission GAIA in helping
populate the database of nearby stars ($d < 25$ pc) for subsequent target
selection for DARWIN/TPF. The GAIA high-precision astrometric measurements will
make it an ideal tool for a complete screening of the expected several
thousands stars within 25 pc in order to identify and characterize (or rule out
the presence of) Jupiter signposts. GAIA astrometry will be instrumental in
complementing radial velocity surveys of F-G-K stars, and will more effectively
search for massive planets the large database of nearby M dwarfs, which are
less easily accessible with precision spectroscopy. The ability to determine
the actual planet masses and inclination angles for detected systems,
especially those with low-mass primaries (M $< 0.6$ M$_\odot$), stems as a
fundamental contribution GAIA will make toward the final target selection for
DARWIN/TPF, thus complementing exo-zodiacal dust emission observations from
ground-based observatories such as Keck, LBTI, and VLTI.


  We prove an entanglement area law for a class of 1D quantum systems involving
infinite-dimensional local Hilbert spaces. This class of quantum systems
include bosonic models such as the Hubbard-Holstein model, and both U(1) and
SU(2) lattice gauge theories in one spatial dimension. Our proof relies on new
results concerning the robustness of the ground state and spectral gap to the
truncation of Hilbert space, applied within the approximate ground state
projector (AGSP) framework from previous work. In establishing this area law,
we develop a system-size independent bound on the expectation value of local
observables for Hamiltonians without translation symmetry, which may be of
separate interest. Our result provides theoretical justification for using
tensor network methods to study the ground state properties of quantum systems
with infinite local degrees of freedom.


  Various nonlinear characteristics of solid states, such as the circular
photogalvanic effect of time-reversal symmetric insulators, the quantized
photogalvanic effect of Weyl semimetals, and the nonlinear Hall effect of
time-reversal symmetric metals, have been associated with the Berry curvature
dipole (BCD). Here, we explore the question of whether the Berry curvature
dipole and multipoles of time-reversal symmetric insulators can be traced in
the nonlinear optical responses. We performed real-time time-dependent density
functional theory calculations and examined the second harmonic generation
susceptibility tensors. The two-band term of the susceptibility tensor is
sharply proportional to the interband BCD, dominating over the Hall response
once the cancellation effect of the multiple reflection symmetries is lifted.
We suggest that the nonlinear Hall component of the second-harmonic spectra of
insulators can also be utilized as an effective tool to extract the band
structure geometry through Berry curvature dipole and possibly multipoles.


  The anisotropic fluid equations governing a frictionless obliquely-flowing
plasma around an essentially arbitrarily shaped three-dimensional ion-absorbing
object in a strong magnetic field are solved analytically in the quasi-neutral
drift-approximation, neglecting parallel temperature gradients. The effects of
transverse displacements traversing the magnetic presheath are also quantified.
It is shown that the parallel collection flux density dependence upon external
Mach-number is $n_\infty c_s \exp[-1 -(M_{\parallel\infty}-
M_\perp\cot\theta)]$ where $\theta$ is the angle (in the plane of field and
drift velocity) of the object-surface to the magnetic-field and
$M_{\parallel\infty}$ is the external parallel flow. The perpendicular drift,
$\M_\perp$, appearing here consists of the external $\E\wedge\B$ drift plus a
weighted sum of the ion and electron electron diamagnetic drifts that depends
upon the total angle of the surface to the magnetic field. It is that somewhat
counter-intuitive combination that an oblique (transverse) Mach probe
experiment measures.


  In this work we shall review the (phased) inverse scattering problem and then
pursue the phaseless reconstruction from far-field data with the help of the
concept of scattering coefficients. We perform sensitivity, resolution and
stability analysis of both phased and phaseless problems and compare the degree
of ill-posedness of the phased and phaseless reconstructions. The phaseless
reconstruction is highly nonlinear and much more severely ill-posed. Algorithms
are provided to solve both the phased and phaseless reconstructions in the
linearized case. Stability is studied by estimating the condition number of the
inversion process for both the phased and phaseless cases. An optimal strategy
is suggested to attain the infimum of the condition numbers of the phaseless
reconstruction, which may provide an important guidance for efficient phaseless
measurements in practical applications. To the best of our knowledge, the
stability analysis in terms of condition numbers are new for the phased and
phaseless inverse scattering problems, and are very important to help us
understand the degree of ill-posedness of these inverse problems. Numerical
experiments are provided to illustrate the theoretical asymptotic behavior, as
well as the effectiveness and robustness of the phaseless reconstruction
algorithm.


  Action selection policies (ASPs), used to compose low-level robot skills into
complex high-level tasks are commonly represented as neural networks (NNs) in
the state of the art. Such a paradigm, while very effective, suffers from a few
key problems: 1) NNs are opaque to the user and hence not amenable to
verification, 2) they require significant amounts of training data, and 3) they
are hard to repair when the domain changes. We present two key insights about
ASPs for robotics. First, ASPs need to reason about physically meaningful
quantities derived from the state of the world, and second, there exists a
layered structure for composing these policies. Leveraging these insights, we
introduce layered dimension-informed program synthesis (LDIPS) - by reasoning
about the physical dimensions of state variables, and dimensional constraints
on operators, LDIPS directly synthesizes ASPs in a human-interpretable
domain-specific language that is amenable to program repair. We present
empirical results to demonstrate that LDIPS 1) can synthesize effective ASPs
for robot soccer and autonomous driving domains, 2) requires two orders of
magnitude fewer training examples than a comparable NN representation, and 3)
can repair the synthesized ASPs with only a small number of corrections when
transferring from simulation to real robots.


  The aim of this paper is to construct a Riemann-Lagrange geometry on 1-jet
spaces, in the sense of d-connections, d-torsions, d-curvatures,
electromagnetic d-field and geometric electromagnetic Yang-Mills energy,
starting from a given linear ODEs system or a given superior order ODE. The
case of a non-homogenous linear ODE of superior order is disscused.


  We describe the geometry of the leading singularity locus of the traintrack
integral family directly in momentum twistor space. For the two-loop case,
known as the elliptic double box, the leading singularity locus is a genus one
curve, which we obtain as an intersection of two quadrics in $\mathbb{P}^{3}$.
At three loops, we obtain a K3 surface which arises as a branched surface over
two genus-one curves in $\mathbb{P}^{1} \times \mathbb{P}^{1}$. We present an
analysis of its properties. We also discuss the geometry at higher loops and
the supersymmetrization of the construction.


  We compute the Euler characteristics of the moduli spaces of abelian vortices
on curves with nodal and cuspidal singularities. This generalizes our previous
work where only nodes were taken into account. The result we obtain is again
consistent with the expected reconciliation between the vortex picture of D2-D0
branes and the proposal by Gopakumar and Vafa.


  The detection of a branched alkyl molecule in the high-mass star forming
protocluster Sgr B2(N) permitted by the advent of ALMA revealed a new dimension
of interstellar chemistry. Astrochemical simulations subsequently predicted
that beyond a certain degree of molecular complexity, branched molecules could
even dominate over their straight-chain isomers. More generally, we aim at
probing further the presence in the ISM of complex organic molecules with the
capacity to exhibit both a normal and iso form, via the attachment of a
functional group to either a primary or secondary carbon atom. We used the
imaging spectral line survey survey ReMoCA performed with ALMA and the results
of a recent spectroscopic study of propanol to search for the iso and normal
isomers of this molecule in the hot molecular core Sgr B2(N2). We expanded the
network of the astrochemical model MAGICKAL to explore the formation routes of
propanol. We report the first interstellar detection of iso-propanol toward a
position of Sgr B2(N2) that shows narrow linewidths. We also report the first
secure detection of normal-propanol in a hot core. i-Propanol is found to be
nearly as abundant as n-propanol, with an abundance ratio of 0.6 similar to the
ratio of 0.4 that we obtained previously for i- and n-propyl cyanide in Sgr
B2(N2). The results are in good agreement with the outcomes of our
astrochemical models, which indicate that OH-radical addition to propylene in
dust-grain ice mantles, driven by water photodissociation, can produce
appropriate quantities of n- and i-propanol. The n-to-i ratio in Sgr B2(N2) may
be a direct inheritance of the branching ratio of this reaction process. The
detection of n- and i-propanol and their ratio indicate that the modest
preference toward the normal form of propyl cyanide determined previously may
be a more general feature among similarly sized interstellar molecules.
[abridged]


  The use of classical multiple-pass approach for phase estimation which mimics
the behavior of the N00N states, is compared with quantum techniques. It is
shown that in the presence of losses its performance is significantly worse
than the one of the optimal quantum strategy.


  In recent works by Yang et al. (2017a,b), and Yagli et al. (2019),
geographical, temporal, and sequential deterministic reconciliation of
hierarchical photovoltaic (PV) power generation have been considered for a
simulated PV dataset in California. In the first two cases, the reconciliations
are carried out in spatial and temporal domains separately. To further improve
forecasting accuracy, in the third case these two reconciliation approaches are
sequentially applied. During the replication of the forecasting experiment,
some issues emerged about non-negativity and coherence (in space and/or in
time) of the sequentially reconciled forecasts. Furthermore, while the accuracy
improvement of the considered approaches over the benchmark persistence
forecasts is clearly visible at any data granularity, we argue that an even
better performance may be obtained by a thorough exploitation of cross-temporal
hierarchies. In this paper the cross-temporal point forecast reconciliation
approach is applied to generate non-negative, fully coherent (both in space and
time) forecasts. In particular, some relationships between two-step, iterative
and simultaneous cross-temporal reconciliation procedures are for the first
time established, non-negativity issues of the final reconciled forecasts are
correctly dealt with in a simple way, and the most recent cross-temporal
reconciliation approaches are adopted. The normalised Root Mean Square Error is
used to measure forecasting accuracy, and a statistical multiple comparison
procedure is performed to rank the approaches. Besides assuring full coherence,
and non-negativity of the reconciled forecasts, the results show that for the
considered dataset, cross-temporal forecast reconciliation significantly
improves on the sequential procedures proposed by Yagli et al. (2019), at any
cross-sectional level of the hierarchy and for any temporal granularity.


  General relativity does not allow one to specify the topology of space,
leaving the possibility that space is multiply rather than simply connected. We
review the main mathematical properties of multiply connected spaces, and the
different tools to classify them and to analyse their properties. Following
their mathematical classification, we describe the different possible
muticonnected spaces which may be used to construct Friedmann-Lemaitre universe
models. Observational tests concern the distribution of images of discrete
cosmic objects or more global effects, mainly those concerning the Cosmic
Microwave Background. According to the 2003-2006 WMAP data releases, various
deviations from the flat infinite universe model predictions hint at a possible
non-trivial topology for the shape of space. In particular, a finite universe
with the topology of the Poincar\'e dodecahedral spherical space fits
remarkably well the data and is a good candidate for explaining both the local
curvature of space and the large angle anomalies in the temperature power
spectrum. Such a model of a small universe, whose volume would represent only
about 80% the volume of the observable universe, offers an observational
signature in the form of a predictable topological lens effect on one hand, and
rises new issues on the physics of the early universe on the other hand.


  This paper proposes a pipeline to automatically track and measure
displacement and vibration of structural specimens during laboratory
experiments. The latest Mask Regional Convolutional Neural Network (Mask R-CNN)
can locate the targets and monitor their movement from videos recorded by a
stationary camera. To improve precision and remove the noise, techniques such
as Scale-invariant Feature Transform (SIFT) and various filters for signal
processing are included. Experiments on three small-scale reinforced concrete
beams and a shaking table test are utilized to verify the proposed method.
Results show that the proposed deep learning method can achieve the goal to
automatically and precisely measure the motion of tested structural members
during laboratory experiments.


  The multi-armed bandit (MAB) problem is a classic example of the
exploration-exploitation dilemma. It is concerned with maximising the total
rewards for a gambler by sequentially pulling an arm from a multi-armed slot
machine where each arm is associated with a reward distribution. In static
MABs, the reward distributions do not change over time, while in dynamic MABs,
each arm's reward distribution can change, and the optimal arm can switch over
time. Motivated by many real applications where rewards are binary, we focus on
dynamic Bernoulli bandits. Standard methods like $\epsilon$-Greedy and Upper
Confidence Bound (UCB), which rely on the sample mean estimator, often fail to
track changes in the underlying reward for dynamic problems. In this paper, we
overcome the shortcoming of slow response to change by deploying adaptive
estimation in the standard methods and propose a new family of algorithms,
which are adaptive versions of $\epsilon$-Greedy, UCB, and Thompson sampling.
These new methods are simple and easy to implement. Moreover, they do not
require any prior knowledge about the dynamic reward process, which is
important for real applications. We examine the new algorithms numerically in
different scenarios and the results show solid improvements of our algorithms
in dynamic environments.


  We find a phenomenon in a non-gravitational gauge theory analogous to the
replica wormhole in a quantum gravity theory. We consider a reservoir of a
scalar field coupled with a gauge theory contained in a region with a boundary
by an axion-like coupling. When the replica trick is used to compute the
entanglement entropy for a subregion in the reservoir, a tuple of instantons
distributed across the replica sheets gives a non-perturbative contribution. As
an explicit and solvable example, we consider a discrete scalar field coupled
to a 2d pure gauge theory and observe how the replica instantons reproduce the
entropy directly calculated from the reduced density matrix. In addition, we
notice that the entanglement entropy can detect the confinement of a 2d gauge
theory.


  In this work, we introduce a novel method for entity resolution author
disambiguation in bibliographic networks. Such a method is based on a 2-steps
network traversal using topological similarity measures for rating candidate
nodes. Topological similarity is widely used in the Link Prediction application
domain to assess the likelihood of an unknown link. A similarity function can
be a good approximation for equality, therefore can be used to disambiguate,
basing on the hypothesis that authors with many common co-authors are similar.
Our method has experimented on a graph-based representation of the public DBLP
Computer Science database. The results obtained are extremely encouraging
regarding Precision, Accuracy, and Specificity. Further good aspects are the
locality of the method for disambiguation assessment which avoids the need to
know the global network, and the exploitation of only a few data, e.g. author
name and paper title (i.e., co-authorship data).


  We introduce semi-invariant Riemannian submersions from almost Hermitian
manifolds onto Riemannian manifolds. We give examples, investigate the geometry
of foliations which are arisen from the definition of a Riemannian submersion
and find necessary-sufficient conditions for total manifold to be locally
product Riemannian manifold. We also find necessary and sufficient conditions
for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a
classification for semi-invariant submersions with totally umbilical fibers and
show that such submersions put some restrictions on total manifolds.


  We discuss three topics related to the neutron star (NS) mass spectrum. At
first we discuss the possibility to form low-mass ($ M \stackrel{<}{\sim} 1
M_{\odot}$) and suggest this is possible only due to fragmentation of rapidly
rotating proto-NSs. Such low-mass NSs should have very high spatial velocities
which could allow identification. A critical assessment of this scenario is
given. Secondly, we discuss mass growth due to accretion for NSs in close
binary systems. With the help of numerical population synthesis calculations we
derive the mass spectrum of massive ($M > 1.8 M_{\odot}$) NSs. Finally, we
discuss the role of the mass spectrum in population studies of young cooling
NSs. We formulate a kind of {\it mass constraint} which can be helpful, in our
opinion, in discussing different competive models of the thermal evolution of
NSs.


  We show that (equivariant) K-theoretic 3-point Gromov-Witten invariants of
genus zero on a Grassmann variety are equal to triple intersections computed in
the ordinary (equivariant) K-theory of a two-step flag manifold, thus
generalizing an earlier result of Buch, Kresch, and Tamvakis. In the process we
show that the Gromov-Witten variety of curves passing through 3 general points
is irreducible and rational. Our applications include Pieri and Giambelli
formulas for the quantum K-theory ring of a Grassmannian, which determine the
multiplication in this ring. Our formula for Gromov-Witten invariants can be
partially generalized to cominuscule homogeneous spaces by using a construction
of Chaput, Manivel, and Perrin.


  In this paper we give some generalizations and improvements of the Pavlovi\'c
result on the Holland-Walsh type characterization of the Bloch space of
continuously differentiable (smooth) functions in the unit ball in
$\mathbf{R}^m$.


  We show how the snowflake phononic crystal structure, which has been realized
experimentally recently, can be turned into a topological insulator for sound
waves. This idea, based purely on simple geometrical modifications, could be
readily implemented on the nanoscale.


  In this paper the multicasting of independent parallel Gaussian sources over
a binary erasure broadcasted channel is considered. Multiresolution embedded
quantizer and layered joint source-channel coding schemes are used in order to
serve simultaneously several users at different channel capacities. The convex
nature of the rate-distortion function, computed by means of reverse
water-filling, allows us to solve relevant convex optimization problems
corresponding to different performance criteria. Then, layered joint
source-channel codes are constructed based on the concatenation of embedded
scalar quantizers with binary rateless encoders.


  In this review I discuss the characteristics and the formation of all classes
of millisecond pulsars (MSPs). The main focus is on the stellar astrophysics of
X-ray binaries leading to the production of fully recycled MSPs with white
dwarf (WD) or substellar semi-degenerate companions. Depending on the nature of
the companion star MSPs are believed to form from either low-mass X-ray
binaries (LMXBs) or intermediate-mass X-ray binaries (IMXBs). For each of these
two classes of X-ray binaries the evolutionary status of the donor star -- or
equivalently, the orbital period -- at the onset of the Roche-lobe overflow
(RLO) is the determining factor for the outcome of the mass-transfer phase and
thus the nature of the MSP formed. Furthermore, the formation of binary MSPs is
discussed in context of the (P,P_dot)-diagram, as well as new interpretations
of the Corbet diagram. Finally, I present new models of Case A RLO of IMXBs in
order to reproduce the two solar mass pulsar PSR J1614-2230.


  We report on the unexpected uniform spin chain physics in CuNCN, the
insulating nitride analog of copper oxides. Based on full-potential band
structure calculations, we derive the relevant microscopic parameters, estimate
individual exchange couplings, and establish a realistic spin model of this
compound. The structure of CuNCN contains chains of edge-sharing CuN(4)
squares. As a surprise, in contrast to analogous [CuO(2)] chains in
"edge-sharing" cuprates, the leading magnetic interactions J ~ 2500 K run
perpendicular to the structural [CuN(2)] chains via bridging NCN groups. The
resulting spin model of a uniform chain is in agreement with the experimentally
observed temperature-independent magnetic susceptibility below 300 K. The
nearest-neighbor and next-nearest-neighbor interactions along the structural
[CuN(2)] chains are J(1) ~ -500 K and J(2) ~ 100 K, respectively. Despite the
frustrating nature of J(1) and J(2), we assign the anomaly at 70 K to
long-range magnetic ordering, which is likely collinear with antiparallel and
parallel arrangement of spins along the 'c' and 'a' directions, respectively.
The pronounced one-dimensionality of the spin system should lead to a reduction
in the ordered moment and to a suppression of the transition anomaly in the
specific heat, thus impeding the experimental observation of the long-range
ordering. Our results suggest CuNCN as a promising material for ballistic heat
transport within spin chains, while the sizable bandwidth W ~ 3 eV may lead to
a metal-insulator transition and other exotic properties under high pressure.


  We present the theory for Multiple Energy X-ray Holography (MEXH), using a
multipole expansion for the scattered field. We find that light polarization
plays a crucial role in the reconstruction of the image, and we suggest how to
use it in order to eliminate aberration effects. The method we propose is
alternative to the SWIFT method (scattered-wave--included Fourier transform),
but has the advantage that no theoretical calculations are required to redefine
the hologram.


  A method is presented which restricts the space of paths entering the path
integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing
paths which possess at least $\alpha$ derivatives. The method introduces two
external parameters, and induces the appearance of a particular time scale
$\epsilon_D$ such that for time intervals longer than $\epsilon_D$ the model
behaves as usual quantum mechanics. However, for time scales smaller than
$\epsilon_D$, modifications to standard formulation of quantum theory occur.
This restriction renders convergent some quantities which are usually divergent
in the time-continuum limit $\epsilon\rightarrow 0$. We illustrate the model by
computing several meaningful physical quantities such as the mean square
velocity $\langle v^2 \rangle $, the canonical commutator, the Schrodinger
equation and the energy levels of the harmonic oscillator. It is shown that an
adequate choice of the parameters introduced makes the evolution unitary.


  Quantum Key Distribution (QKD) offers unconditional security in principle.
Many QKD protocols have been proposed and demonstrated to ensure secure
communication between two authenticated users. Continuous variable (CV) QKD
offers many advantages over discrete variable (DV) QKD since it is
cost-effective, compatible with current classical communication technologies,
efficient even in daylight, and gives a higher secure key rate. Keeping this in
view, we demonstrate a discrete modulated CVQKD protocol in the free space
which is robust against polarization drift. We also present the simulation
results with a noise model to account for the channel noise and the effects of
various parameter changes on the secure key rate. These simulation results help
us to verify the experimental values obtained for the implemented CVQKD.


  In this note we point out that primordial black holes could be much shorter
lived than usually assumed if there is a large hidden sector of particles that
only interacts gravitationally with the particles of the standard model. The
observation of the explosion of one of these black holes would severely
constrain the energy scale at which gravity becomes strong.


  The spread of inaccurate and misleading information may alter behaviours and
complicate crisis management, especially during an emergency like the COVID-19
pandemic. This paper aims to investigate information diffusion during the
COVID-19 pandemic by evaluating news consumption on YouTube. First, we analyse
more than 2 million users' engagement with 13,000 videos released by 68 YouTube
channels, labelled with a political bias and fact-checking index. Then, we
study the relationship between each user\~Os political preference and their
consumption of questionable (i.e., poorly fact-checked) and reliable
information. Our results, quantified using measures from information theory,
provide evidence for the existence of echo chambers across two dimensions
represented by political bias and the trustworthiness of information channels.
We observe that the echo chamber structure cannot be reproduced after properly
randomising the users' interaction patterns. Moreover, we observe a relation
between the political bias of users and their tendency to consume highly
questionable news.


  Suppose that Alice plans to buy a physical good from Bob over a programmable
Blockchain. Alice does not trust Bob, so she is not willing to pay before the
good is delivered off-chain. Similarly, Bob does not trust Alice, so he is not
willing to deliver the good before getting paid on-chain. Moreover, they are
not inclined to use the services of a trusted third-party. Traditionally, such
scenarios are handled by game-theoretic escrow smart contracts, such as
BitHalo. In this work, we first show that the common method for this problem
suffers from a major flaw which can be exploited by Bob in order to extort
Alice. We also show that, unlike the case of auctions, this flaw cannot be
addressed by a commitment-scheme-based approach. We then provide a much more
general result: assuming that the two sides are rational actors and the smart
contract language is Turing-complete, there is no escrow smart contract that
can facilitate this exchange without either relying on third parties or
enabling at least one side to extort the other.


  In this paper we intend to extend some ideas of a recently proposed
Lorentz-invariant Bohmian model, obeying Klein-Gordon equations, but
considering particles with a spin different than zero. First we build a Bohmian
model for a single particle, closely related to the Bohm-Dirac model, but using
Nikolic's ideas on a space-time probability density and the introduction of a
synchronization parameter \sigma for the particle trajectory. We prove that, in
the case of a spinor whose component phases become equal when \plank \to 0, it
is possible to use the usual Bohmian Mechanics procedures to obtain the
classical limit. We extend these ideas for a two-particle system, based on two
non-local but covariant Dirac-like equations.


  We compute the number density of nonlinear seed fluctuations which have the
right number density to be able to explain the presence of one supermassive
black hole per galaxy, as a function of redshift. We find that there is an
interesting range of symmetry breaking scales for which the density of seeds is
larger that what is predicted in the standard cosmological model with Gaussian
primordial fluctuations. Hence, global defects may help in light of the
mounting tension between the standard cosmological model and observations of
supermassive black hole candidates at high redshifts.


  One of the main challenges online social systems face is the prevalence of
antisocial behavior, such as harassment and personal attacks. In this work, we
introduce the task of predicting from the very start of a conversation whether
it will get out of hand. As opposed to detecting undesirable behavior after the
fact, this task aims to enable early, actionable prediction at a time when the
conversation might still be salvaged.
  To this end, we develop a framework for capturing pragmatic devices---such as
politeness strategies and rhetorical prompts---used to start a conversation,
and analyze their relation to its future trajectory. Applying this framework in
a controlled setting, we demonstrate the feasibility of detecting early warning
signs of antisocial behavior in online discussions.


  In this short survey we want to present some of the impact of Minkowski's
successive minima within Convex and Discrete Geometry. Originally related to
the volume of an $o$-symmetric convex body, we point out relations of the
successive minima to other functionals, as e.g., the lattice point enumerator
or the intrinsic volumes and we present some old and new conjectures about
them. Additionally, we discuss an application of successive minima to a version
of Siegel's lemma.


  We discuss an astrometric timing effect on data analysis of continuous
gravitational waves from rapidly rotating isolated neutron stars. Special
attention is directed to the possibility of determining their distances by
measuring the curvature of the wave fronts. We predict that if continuous
gravitational waves from an unknown neutron star with a stable rotation are
detected around 1kHz within 1/3yr by initial LIGO detectors and the ellipticity
parameter epsilon is smaller than 10^{-6}, the distance r to the source can be
estimated with relative error \Delta r/r of \sim 10% by using the broad band
configuration of advanced LIGO detectors over 3 years. By combining the
observed amplitude of the waves with the estimated distance, information on the
parameter $\epsilon$ can be obtained purely through gravitational wave
measurements.


  The parity violating model based on teleparallel gravity is a competitive
scheme for parity violating gravity, which has been preliminary studied in the
literature. To further investigate the parity violating model in teleparallel
gravity, in this paper, we construct all independent parity-odd terms that are
quadratic in torsion tensor and coupled to a scalar field in a way without
higher-order derivatives. Using these parity-odd terms, we formulate a general
parity violating scalar-tensor model in teleparallel gravity and obtain its
equations of motion. To explore potentially viable models within the general
model, we investigate the cosmological application of a submodel of the general
model in which terms above the second power of torsion are eliminated. We focus
on analyzing cosmological perturbations and identify the conditions that
preserve the parity violating signal of gravitational waves at linear order
while avoiding the ghost instability.


  Speeding up adiabatic method has attracted much attention with the wide
applications in quantum information processing. In this paper, two kinds of
methods, Lewis-Riesenfeld invariant-based inverse engineering and
transitionless quantum driving are applied to implement speeding up adiabatic
state conversion in optomechanical system. The perfect population transfer can
be achieved within a short time. At last, the energetic cost is analysed for
the transitionless quantum driving.


  In this article, we explore the dynamical decoherence of the chromophores
within a green fluorescent protein when coupled to a finite-temperature
dielectric environment. Such systems are of significant interest due to their
anomalously long coherence lifetimes compared to other biomolecules. We work
within the spin-boson model and employ the Hierarchical Equations of Motion
formalism which allows for the accounting of the full non-perturbative and
non-Markovian characteristics of the system dynamics. We analyse the level
coherence of independent green fluorescent protein chromophores and the energy
transfer dynamics in homo-dimer green fluorescent proteins, focusing on the
effect of dielectric relaxation on the timescales of these systems. Using the
Fluctuation-Dissipation theorem, we generate spectral densities from local
electric susceptibility generated from Poisson's equation and employ a Debye
dielectric model for the solvent environment. For different system
architectures, we identify a number of very striking features in the dynamics
of the chromophore induced by the dielectric relaxation of the environment,
resulting in strong memory effects that extend the coherence lifetime of the
system. Remarkably, the complex architecture of the green fluorescent protein,
which includes a cavity-like structure around the atomic system, is well suited
to preserving the coherences in the homo-dimer system. The system dynamics
generate a dynamical correlation between the coherent energy transfer between
its sub-systems and the entropy production, which can lead to transient
reductions in entropy, a unique feature of the non-Markovian nature of the
system-environment interaction.


  This paper establishs the large deviation principle (LDP) for multiple
averages on $\mathbb{N}^d$. We extend the previous work of [Carinci et al.,
Indag. Math. 2012] to multidimensional lattice $\mathbb{N}^d$ for $d\geq 2$.
The same technique is also applicable to the weighted multiple average launched
by Fan [Fan, Adv. Math. 2021]. Finally, the boundary conditions are imposed to
the multiple sum and explicit formulae of the energy functions with respect to
the boundary conditions are obtained.


  We propose the reliability constrained k-rooted minimum spanning forest, a
relevant optimization problem whose aim is to find a k-rooted minimum cost
forest that connects given customers to a number of supply vertices, in such a
way that a minimum required reliability on each path between a customer and a
supply vertex is satisfied and the cost is a minimum. The reliability of an
edge is the probability that no failure occurs on that edge, whereas the
reliability of a path is the product of the reliabilities of the edges in such
path. The problem has relevant applications in the design of networks, in
fields such as telecommunications, electricity and transports. For its
solution, we propose a mixed integer linear programming model, and an adaptive
large neighborhood search metaheuristic which invokes several shaking and local
search operators. Extensive computational tests prove that the metaheuristic
can provide good quality solutions in very short computing times.


  We consider the space of complete and separable metric spaces which are
equipped with a probability measure. A notion of convergence is given based on
the philosophy that a sequence of metric measure spaces converges if and only
if all finite subspaces sampled from these spaces converge. This topology is
metrized following Gromov's idea of embedding two metric spaces isometrically
into a common metric space combined with the Prohorov metric between
probability measures on a fixed metric space. We show that for this topology
convergence in distribution follows - provided the sequence is tight - from
convergence of all randomly sampled finite subspaces. We give a
characterization of tightness based on quantities which are reasonably easy to
calculate. Subspaces of particular interest are the space of real trees and of
ultra-metric spaces equipped with a probability measure. As an example we
characterize convergence in distribution for the (ultra-)metric measure spaces
given by the random genealogies of the Lambda-coalescents. We show that the
Lambda-coalescent defines an infinite (random) metric measure space if and only
if the so-called "dust-free"-property holds.


  Let $X$ be a simplicial set. We construct a novel adjunction between the
categories of retractive spaces over $X$ and of $X_{+}$-comodules, then apply
recent work on left-induced model category structures (arXiv:1401.3651v2
[math.AT],arXiv:1509.08154 [math.AT]) to establish the existence of a left
proper, simplicial model category structure on the category of $X_+$-comodules,
with respect to which the adjunction is a Quillen equivalence after
localization with respect to some generalized homology theory. We show moreover
that this model category structure stabilizes, giving rise to a model category
structure on the category of $\Sigma^\infty X_{+}$-comodule spectra.
  The Waldhausen $K$-theory of $X$, $A(X)$, is thus naturally weakly equivalent
to the Waldhausen $K$-theory of the category of homotopically finite
$\Sigma^\infty X_{+}$-comodule spectra, with weak equivalences given by twisted
homology. For $X$ simply connected, we exhibit explicit, natural weak
equivalences between the $K$-theory of this category and that of the category
of homotopically finite $\Sigma^{\infty}(\Omega X)_+$-modules, a more familiar
model for $A(X)$. For $X$ not necessarily simply connected, we have localized
versions of these results.
  For $H$ a simplicial monoid, the category of $\Sigma^{\infty}H_{+}$-comodule
algebras admits an induced model structure, providing a setting for defining
homotopy coinvariants of the coaction of $\Sigma^{\infty}H_{+}$ on a
$\Sigma^{\infty}H_{+}$-comodule algebra, which is essential for homotopic
Hopf-Galois extensions of ring spectra as originally defined by Rognes in
arXiv:math/0502183v2} and generalized in arXiv:0902.3393v2 [math.AT]. An
algebraic analogue of this was only recently developed, and then only over a
field (arXiv:1401.3651v2 [math.AT]).


  We consider SU($3$) fermions on the triangular lattice in the presence of a
gauge potential which stabilizes a quantum Hall insulator (QHI) at the density
of one particle per lattice site. We investigate the effect of the Hubbard
interaction, favoring magnetic long-range order, and a three-sublattice
potential (TSP), favoring a normal insulator (NI), on the system. For weak TSP
we find that the Hubbard interaction drives the QHI into a three-sublattice
magnetic Mott insulator (MMI). For intermediate values of TSP we identify two
transition points upon increasing the Hubbard interaction. The first transition
is from the NI to the QHI and the second transition is from the QHI to the MMI.
For large values of the TSP a charge-ordered magnetic insulator (COMI) emerges
between the NI and the QHI, leading to an interaction-driven COMI-to-QHI
transition.


  The recently discovered 125 GeV boson appears very similar to a Standard
Model Higgs, but with data favoring an enhanced h to gamma gamma rate. A number
of groups have found that fits would allow (or, less so after the latest
updates, prefer) that the h-t-tbar coupling have the opposite sign. This can be
given meaning in the context of an electroweak chiral Lagrangian, but it might
also be interpreted to mean that a new colored and charged particle runs in
loops and produces the opposite-sign hGG amplitude to that generated by
integrating out the top, as well as a contribution reinforcing the W-loop
contribution to hFF. In order to not suppress the rate of h to WW and h to ZZ,
which appear to be approximately Standard Model-like, one would need the loop
to "overshoot," not only canceling the top contribution but producing an
opposite-sign hGG vertex of about the same magnitude as that in the SM. We
argue that most such explanations have severe problems with fine-tuning and,
more importantly, vacuum stability. In particular, the case of stop loops
producing an opposite-sign hGG vertex of the same size as the Standard Model
one is ruled out by a combination of vacuum decay bounds and LEP constraints.
We also show that scenarios with a sign flip from loops of color octet charged
scalars or new fermionic states are highly constrained.


  In the standard cascade picture of 3D turbulent fluid flows, energy is input
at a constant rate at large scales. Energy is then transferred to smaller
scales by an intermittent process that has been the focus of a vast literature.
However, the energy input at large scales is not constant in most real
turbulent flows. We explore the signatures of these fluctuations of large scale
energy input on small scale turbulence statistics. Measurements were made in a
flow between oscillating grids, with Re up to 271, in which temporal variations
in the large scale energy input can be introduced by modulating the oscillating
grid frequency. We find that the Kolmogorov constant for second order
longitudinal structure functions depends on the magnitude of the fluctuations
in the large scale energy input. We can quantitatively predict the measured
change with a model based on Kolmogorov's refined similarity theory. The
effects of fluctuations of the energy input can also be observed using
structure functions conditioned on the instantaneous large scale velocity. A
linear parameterization using the curvature of the iconditional structure
functions provides a fairly good match with the measured changes in the
Kolmogorov constant. Conditional structure functions are found to provide a
more sensitive measure of the presence of fluctuations in the large scale
energy input than inertial range scaling coefficients.


  We consider the degree to which "21 cm tomography" of the high-redshift
Universe can distinguish different ionization histories. Using a new analytic
model for the size distribution of HII regions that associates these ionized
bubbles with large-scale galaxy overdensities, we compute the angular power
spectrum and other statistical properties of the 21 cm brightness temperature
during reionization. We show that the HII regions imprint features on the power
spectrum that allow us to separate histories with discrete bubbles from those
with partial uniform ionization (by, for example, X-rays). We also show that
"double reionization" scenarios will modify the morphology of the bubbles in
ways that depend on the mechanism through which the first generation of sources
shuts off. If, for example, the transition occurs globally at a fixed redshift,
the first generation imprints a persistent feature on the 21 cm power spectrum.
Finally, we compare our model to one in which voids are ionized first. While
the power spectra of these two models are qualitatively similar, we show that
the underlying distributions of neutral hydrogen differ dramatically and
suggest that other statistical tests can distinguish them. The next generation
of low-frequency radio telescopes will have the sensitivity to distinguish all
of these models and strongly constrain the history and morphology of
reionization.


  Two accretion columns have been argued to form over the surface of a newborn
millisecond magnetar for an extremely high accretion rate
$\gtrsim1.8\times10^{-2}M_\odot\ {\rm s^{-1}}$ that may occur in the
core-collapse of a massive star. In this paper, we investigate the
characteristics of these accretion columns and their gravitational wave (GW)
radiation. For a typical millisecond magnetar (surface magnetic field strength
$B\sim10^{15}$ G and initial spin period $P\sim1$ ms), we find (1) its
accretion columns are cooled via neutrinos and can reach a height $\sim1$ km
over the stellar surface; (2) its column-induced characteristic GW strain is
comparable to the sensitivities of the next generation ground-based GW
detectors within a horizon $\sim1$ Mpc; (3) the magnetar can survive only a few
tens of seconds; (4) during the survival timescale, the height of the accretion
columns increases rapidly to the peak and subsequently decreases slowly; (5)
the column mass, characteristic GW strain, and maximum GW luminosity have
simultaneous peaks in a similar rise-fall evolution. In addition, we find that
the magnetar's spin evolution is dominated by the column accretion torque. A
possible association with failed supernova is also discussed.


  We collected a large dataset consisting of nearly 900 unique participants.
For every participant we recorded two 30 second uncompressed videos,
synchronized PPG waveforms and a single blood pressure measurement. Gender, age
and skin color were also registered for every participant. The dataset includes
roughly equal numbers of males and females, as well as participants of all
ages. While the skin color distribution could have been more balanced, the
dataset contains individuals from every skin color. The data was collected in a
diverse set of locations to ensure a wide variety of backgrounds and lighting
conditions. In an effort to assist in the research and development of remote
vital sign measurement we are now opening up access to this dataset.


  Quantum-mechanical fluctuations between competing phases at $T=0$ induce
exotic finite-temperature collective excitations that are not described by the
standard Landau Fermi liquid framework. These excitations exhibit anomalous
temperature dependences, or non-Fermi liquid behavior, in the transport and
thermodynamic properties in the vicinity of a quantum critical point, and are
often intimately linked to the appearance of unconventional Cooper pairing as
observed in strongly correlated systems including the high-$T_c$ cuprate and
iron pnictide superconductors. The presence of superconductivity, however,
precludes direct access to the quantum critical point, and makes it difficult
to assess the role of quantum-critical fluctuations in shaping anomalous
finite-temperature physical properties. Here we report temperature-field scale
invariance of non-Fermi liquid thermodynamic, transport, and Hall quantities in
a non-superconducting iron-pnictide,
Ba(Fe$_{1/3}$Co$_{1/3}$Ni$_{1/3}$)$_{2}$As$_{2}$, indicative of quantum
criticality at zero temperature and zero applied magnetic field. Beyond a
linear in temperature resistivity, the hallmark signature of strong
quasiparticle scattering, we find the scattering rate that obeys a universal
scaling relation between temperature and applied magnetic fields down to the
lowest energy scales. Together with the dominance of hole-like carriers close
to the zero-temperature and zero-field limits, the scale invariance, isotropic
field response, and lack of applied pressure sensitivity suggests a unique
quantum critical system that does not drive a pairing instability.


  We report on a strain-induced and temperature dependent uniaxial anisotropy
in V$_{2}$O$_{3}$/Ni hybrid thin films, manifested through the interfacial
strain and sample microstructure, and its consequences on the angular dependent
magnetization reversal. X-ray diffraction and reciprocal space maps identify
the in-plane crystalline axes of the V$_{2}$O$_{3}$; atomic force and scanning
electron microscopy reveal oriented rips in the film microstructure.
Quasi-static magnetometry and dynamic ferromagnetic resonance measurements
identify a uniaxial magnetic easy axis along the rips. Comparison with films
grown on sapphire without rips shows a combined contribution from strain and
microstructure in the V$_{2}$O$_{3}$/Ni films. Magnetization reversal
characteristics captured by angular-dependent first order reversal curve
measurements indicate a strong domain wall pinning along the direction
orthogonal to the rips, inducing an angular-dependent change in the reversal
mechanism. The resultant anisotropy is tunable with temperature and is most
pronounced at room temperature, which is beneficial for potential device
applications.


  In Linear Hashing ($\mathsf{LH}$) with $\beta$ bins on a size $u$ universe
${\mathcal{U}=\{0,1,\ldots, u-1\}}$, items $\{x_1,x_2,\ldots, x_n\}\subset
\mathcal{U}$ are placed in bins by the hash function $$x_i\mapsto (ax_i+b)\mod
p \mod \beta$$ for some prime $p\in [u,2u]$ and randomly chosen integers $a,b
\in [1,p]$. The "maxload" of $\mathsf{LH}$ is the number of items assigned to
the fullest bin. Expected maxload for a worst-case set of items is a natural
measure of how well $\mathsf{LH}$ distributes items amongst the bins.
  Fix $\beta=n$. Despite $\mathsf{LH}$'s simplicity, bounding $\mathsf{LH}$'s
worst-case maxload is extremely challenging. It is well-known that on random
inputs $\mathsf{LH}$ achieves maxload $\Omega\left(\frac{\log n}{\log\log
n}\right)$; this is currently the best lower bound for $\mathsf{LH}$'s expected
maxload. Recently Knudsen established an upper bound of $\widetilde{O}(n^{1 /
3})$. The question "Is the worst-case expected maxload of $\mathsf{LH}$
$n^{o(1)}$?" is one of the most basic open problems in discrete math.
  In this paper we propose a set of intermediate open questions to help
researchers make progress on this problem. We establish the relationship
between these intermediate open questions and make some partial progress on
them.


  We construct an abelian category A(G) of sheaves over a category of closed
subgroups of the r-torus G and show it is of finite injective dimension. It can
be used as a model for rational $G$-spectra in the sense that there is a
homology theory
  \piA_*: G-spectra/Q --> A(G) on rational G-spectra with values in A(G), and
the associated Adams spectral sequence converges for all rational $G$-spectra
and collapses at a finite stage.


  We prove that the class of finitely presented inverse monoids whose
Sch\"utzenberger graphs are quasi-isometric to trees has a uniformly solvable
word problem, furthermore, the languages of their Sch\"utzenberger automata are
context-free. On the other hand, we show that there is a finitely presented
inverse monoid with hyperbolic Sch\"utzenberger graphs and an unsolvable word
problem.


  COVID-19 had an unprecedented impact on scientific collaboration. The
pandemic and its broad response from the scientific community has forged new
relationships among domain experts, mathematical modelers, and scientific
computing specialists. Computationally, however, it also revealed critical gaps
in the ability of researchers to exploit advanced computing systems. These
challenging areas include gaining access to scalable computing systems, porting
models and workflows to new systems, sharing data of varying sizes, and
producing results that can be reproduced and validated by others. Informed by
our team's work in supporting public health decision makers during the COVID-19
pandemic and by the identified capability gaps in applying high-performance
computing (HPC) to the modeling of complex social systems, we present the
goals, requirements, and initial implementation of OSPREY, an open science
platform for robust epidemic analysis. The prototype implementation
demonstrates an integrated, algorithm-driven HPC workflow architecture,
coordinating tasks across federated HPC resources, with robust, secure and
automated access to each of the resources. We demonstrate scalable and
fault-tolerant task execution, an asynchronous API to support fast
time-to-solution algorithms, an inclusive, multi-language approach, and
efficient wide-area data management. The example OSPREY code is made available
on a public repository.


  We give detailed descriptions of gluing pseudoholomorphic maps in symplectic
geometry, especially in the presence of an obstruction bundle. The main
motivation is to try to compare the symplectic and enumerative invariants of
algebraic manifolds. These descriptions can also be used to enumerate rational
curves with high-order degeneracies of local nature in projective spaces.


  The directionality of optical signals provides an opportunity for efficient
space reuse of optical links in visible light communication (VLC). Space reuse
in VLC can enable multiple access communication from multiple light emitting
transmitters. However, traditional VLC system design using photo-receptors
requires at least one receiving photodetector element for each light emitter,
thus constraining VLC to always require a light emitter-to-light receiving
element pair. In this paper, we propose, design and evaluate a novel
architecture for VLC that can enable multiple-access reception using a
photoreceptor receiver that uses only a single photodiode. The novel design
includes a liquid-crystal-display (LCD) based shutter system that can be
automated to control and enable selective reception of light beams from
multiple transmitters. We evaluate the feasibility of multiple access on a
single photodiode from two light emitting diode (LED) transmitters and the
performance of the communication link using bit-error-rate (BER) and
packet-error-rate (PER) metrics. Our experiment and trace based evaluation
reveals the feasibility of multiple LED reception on a single photodiode and
estimated throughput of the order of Mbps.


  We present a texture network called Deep Encoding Pooling Network (DEP) for
the task of ground terrain recognition. Recognition of ground terrain is an
important task in establishing robot or vehicular control parameters, as well
as for localization within an outdoor environment. The architecture of DEP
integrates orderless texture details and local spatial information and the
performance of DEP surpasses state-of-the-art methods for this task. The GTOS
database (comprised of over 30,000 images of 40 classes of ground terrain in
outdoor scenes) enables supervised recognition. For evaluation under realistic
conditions, we use test images that are not from the existing GTOS dataset, but
are instead from hand-held mobile phone videos of similar terrain. This new
evaluation dataset, GTOS-mobile, consists of 81 videos of 31 classes of ground
terrain such as grass, gravel, asphalt and sand. The resultant network shows
excellent performance not only for GTOS-mobile, but also for more general
databases (MINC and DTD). Leveraging the discriminant features learned from
this network, we build a new texture manifold called DEP-manifold. We learn a
parametric distribution in feature space in a fully supervised manner, which
gives the distance relationship among classes and provides a means to
implicitly represent ambiguous class boundaries. The source code and database
are publicly available.


  Let G be a simple graph of order $n$ and $\mu_1,\mu_2,\ldots,\mu_n$ the roots
of its matching polynomial. The matching energy of $G$ is defined as the sum
$\sum_{i=1}^n|\mu_i|$. Let $K_{n-1,1}^k$ be the graph obtained from $K_1\cup
K_{n-1}$ by adding $k$ edges between $V(K_1)$ and $V(K_{n-1})$. In this paper,
we show that $K_{n-1,1}^k$ has maximum matching energy among all connected
graph with order $n$ and edge connectivity $k$.


  We construct a gauge theory model on the 4-dimensional $\rho$-Minkowski
space-time, a particular deformation of the Minkowski space-time recently
considered. The corresponding star product results from a combination of Weyl
quantization map and properties of the convolution algebra of the special
Euclidean group. We use noncommutative differential calculi based on twisted
derivations together with a twisted notion of noncommutative connection. The
twisted derivations pertain to the Hopf algebra of $\rho$-deformed
translations, a Hopf subalgebra of the $\rho$-deformed Poincar\'e algebra which
can be viewed as defining the quantum symmetries of the $\rho$-Minkowski
space-time. The gauge theory model is left invariant under the action of the
$\rho$-deformed Poincar\'e algebra. The kinetic part of the action is found to
coincide with the one of the usual (commutative) electrodynamics.


  We here investigate the entanglement structure of the ground state of a
(3+1)-dimensional U(1) quantum spin liquid, which is described by the
deconfined phase of a compact U(1) gauge theory. A gapless photon is the only
low-energy excitation, with matter existing as deconfined but gapped
excitations of the system. It is found that, for a given bipartition of the
system, the elements of the entanglement spectrum can be grouped according to
the electric flux between the two regions, leading to a useful interpretation
of the entanglement spectrum in terms of electric charges living on the
boundary. The entanglement spectrum is also given additional structure due to
the presence of the gapless photon. Making use of the Bisognano-Wichmann
theorem and a local thermal approximation, these two contributions to the
entanglement (particle and photon) are recast in terms of boundary and bulk
contributions, respectively. Both pieces of the entanglement structure give
rise to universal subleading terms (relative to the area law) in the
entanglement entropy, which are logarithmic in the system size (log L), as
opposed to the subleading constant term in gapped topologically ordered
systems. The photon subleading logarithm arises from the low-energy conformal
field theory and is essentially local in character. The particle subleading
logarithm arises due to the constraint of closed electric loops in the
wavefunction and is shown to be the natural generalization of topological
entanglement entropy to the U(1) spin liquid. This contribution to the
entanglement entropy can be isolated by means of the Grover-Turner-Vishwanath
construction (which generalizes the Kitaev-Preskill scheme to three
dimensions).


  We study Josephson junctions between a multi-band iron-pnictide
Ba1-xNaxFe2As2 and conventional s-wave superconductors Nb and Cu/Nb bilayer. We
observe that junctions with a Cu interlayer exhibit much larger IcRn, despite a
weaker proximity-induced superconductivity. This counterintuitive result is
attributed to the difference in Fermi surface geometries of Nb and Cu, which
leads to a selective one-band tunneling from Cu and a non-selective multi-band
tunnelng from Nb. The latter leads to a mutual cancellation of supercurrents
due to the sign-reversal s+- symmetry of the order parameter in the pnictide.
Our results indicate that Fermi surface geometries play a crucial role for
pnictide-based junctions. This provides a new tool for phase sensitive studies
and paves a way to a conscious engineering of such junctions.


  Online communities are not safe spaces for user privacy. Even though existing
research focuses on creating and improving various content moderation
strategies and privacy preserving technologies, platforms hosting online
communities support features allowing users to surveil one another--leading to
harassment, personal data breaches, and offline harm. To tackle this problem,
we introduce a new, work-in-progress framework for analyzing data privacy
within vulnerable, identity-based online communities. Where current SOUPS
papers study surveillance and longitudinal user data as two distinct challenges
to user privacy, more work needs to be done in exploring the sites where
surveillance and historical user data assemble. By synthesizing over 40 years
of developments in the analysis of surveillance, we derive properties of online
communities that enable the abuse of user data by fellow community members and
suggest key steps to improving security for vulnerable users. Deploying this
new framework on new and existing platforms will ensure that online communities
are privacy-conscious and designed more inclusively.


  Ciliated microorganisms near the base of the aquatic food chain either swim
to encounter prey or attach at a substrate and generate feeding currents to
capture passing particles. Here, we represent attached and swimming ciliates
using a popular spherical model in viscous fluid with slip surface velocity
that afford analytical expressions of ciliary flows. We solve an
advection-diffusion equation for the concentration of dissolved nutrients,
where the P'eclet number (Pe) reflects the ratio of diffusive to advective time
scales. For a fixed hydrodynamic power expenditure, we ask what ciliary surface
velocities maximize nutrient flux at the microorganism's surface. We find that
surface motions that optimize feeding depend on Pe. For freely swimming
microorganisms at finite Pe, it is optimal to swim by employing a "treadmill"
surface motion, but in the limit of large Pe, there is no difference between
this treadmill solution and a symmetric dipolar surface velocity that keeps the
organism stationary. For attached microorganisms, the treadmill solution is
optimal for feeding at Pe below a critical value, but at larger Pe values, the
dipolar surface motion is optimal. We verified these results in open-loop
numerical simulations, asymptotic analysis, and using an adjoint-based
optimization method. Our findings challenge existing claims that optimal
feeding is optimal swimming across all P'eclet numbers, and provide new
insights into the prevalence of both attached and swimming solutions in oceanic
microorganisms.


  We identify a sample of 22 host galaxies of Type Ia Supernovae (SNe Ia) at
redshifts 0.95<z<1.8 discovered in the Hubble Space Telescope (HST)
observations of the Great Observatories Origins Deep Survey (GOODS) fields. We
measure the photometry of the hosts in Spitzer Space Telescope and ground-based
imaging of the GOODS fields to provide flux densities from the U-band to 24
microns. We fit the broad-band photometry of each host with Simple Stellar
Population (SSP) models to estimate the age of the stellar population giving
rise to the SN Ia explosions. We break the well-known age-extinction degeneracy
in such analyses using the Spitzer 24 micron data to place upper limits on the
thermally reprocessed, far-infrared emission from dust. The ages of these
stellar populations give us an estimate of the delay times between the first
epoch of star-formation in the galaxies and the explosion of the SNe Ia. We
find a bi-modal distribution of delay times ranging from 0.06 - 4.75 Gyrs. We
also constrain the first-epoch of low mass star formation using these results,
showing that stars of mass <8 Msun were formed within 3 Gyrs after the Big Bang
and possibly by z~6. This argues against a truncated stellar initial mass
function in high redshift galaxies.


  Quantum information can be encoded in the set of steady-states (SSS) of a
driven-dissipative system. Non steady-states are separated by a large
dissipative gap that adiabatically decouples them way while the dynamics inside
the SSS is governed by an effective, dissipation-projected, Hamiltonian. The
latter results from a highly non-trivial interplay between a weak driving with
the fast relaxation process that continuously projects the system back to the
SSS. This amounts to a novel type of environment-induced quantum Zeno effect.
We prove that the dissipation-projected dynamics is of geometric nature and
that it is robust against different types of hamiltonian and dissipative
perturbations. Remarkably, in some cases an effective unitary dynamics can
emerge out of purely dissipative interactions.


  The accurate modeling of the dielectric properties of water is crucial for
many applications in physics, computational chemistry and molecular biology.
This becomes possible in the framework of nonlocal electrostatics, for which we
propose a novel formulation allowing for numerical solutions for the nontrivial
molecular geometries arising in the applications mentioned before. Our approach
is based on the introduction of a secondary field, $\psi$, which acts as the
potential for the rotation free part of the dielectric displacement field ${\bf
D}$. For many relevant models, the dielectric function of the medium can be
expressed as the Green's function of a local differential operator. In this
case, the resulting coupled Poisson (-Boltzmann) equations for $\psi$ and the
electrostatic potential $\phi$ reduce to a system of coupled PDEs. The approach
is illustrated by its application to simple geometries.


  This paper presents a multi-agent reinforcement learning (MARL) scheme for
proactive Multi-Camera Collaboration in 3D Human Pose Estimation in dynamic
human crowds. Traditional fixed-viewpoint multi-camera solutions for human
motion capture (MoCap) are limited in capture space and susceptible to dynamic
occlusions. Active camera approaches proactively control camera poses to find
optimal viewpoints for 3D reconstruction. However, current methods still face
challenges with credit assignment and environment dynamics. To address these
issues, our proposed method introduces a novel Collaborative Triangulation
Contribution Reward (CTCR) that improves convergence and alleviates multi-agent
credit assignment issues resulting from using 3D reconstruction accuracy as the
shared reward. Additionally, we jointly train our model with multiple world
dynamics learning tasks to better capture environment dynamics and encourage
anticipatory behaviors for occlusion avoidance. We evaluate our proposed method
in four photo-realistic UE4 environments to ensure validity and
generalizability. Empirical results show that our method outperforms fixed and
active baselines in various scenarios with different numbers of cameras and
humans.


  Bloch oscillations (BOs) refer to a periodically oscillatory motion of
particle in lattice systems driven by a constant force. By temporally
modulating acoustic waveguides, BOs can be generalized from spatial to
frequency domain, opening new possibilities for spectrum manipulations. The
modulation can induce mode transitions in the waveguide band and form an
artificial frequency lattice, with the mismatched wave vector during
transitions acting as a constant force that drives frequency Bloch oscillations
(FBOs). Furthermore, the modulation phase accompanying transitions serves as a
gauge potential that controls the initial oscillation phase, providing an
additional degree of freedom to tailor FBOs. We report that multiple FBOs with
judiciously designed oscillation phases can be further cascaded to realize
acoustic spectrum self-imaging, unidirectional transduction and bandwidth
engineering. The study proposes the concept of FBOs in acoustic systems and
functionalizes its cascade configurations for advanced control of sound
spectrum. This paradigm may find versatile applications in underwater secure
communication, voice encryption and signal processing.


  The three-dimensional (3D) coordinates of stereoscopically triangulated loops
provide strong constraints for magnetic field models of active regions in the
solar corona. Here we use STEREO/A and B data from some 500 stereoscopically
triangulated loops observed in four active regions (2007 Apr 30, May 9, May 19,
Dec 11), together with SOHO/MDI line-of-sight magnetograms. We measure the
average misalignment angle between the stereoscopic loops and theoretical
magnetic field models, finding a mismatch of $\mu=19^\circ-46^\circ$ for a
potential field model, which is reduced to $\mu=14^\circ-19^\circ$ for a
non-potential field model parameterized by twist parameters. The residual error
is commensurable with stereoscopic measurement errors ($\mu_{SE} \approx
8^\circ-12^\circ$). We developed a potential field code that deconvolves a
line-of-sight magnetogram into three magnetic field components $(B_x, B_y,
B_z)$, as well as a non-potential field forward-fitting code that determines
the full length of twisted loops ($L \approx 50-300$ Mm), the number of twist
turns (median $N_{twist}=0.06$), the nonlinear force-free $\alpha$-parameter
(median $\alpha \approx 4 \times 10^{-11}$ cm$^{-1}$), and the current density
(median $j_z \approx 1500$ Mx cm$^{-2}$ s$^{-1}$). All twisted loops are found
to be far below the critical value for kink instability, and Joule dissipation
of their currents is found be be far below the coronal heating requirement. The
algorithm developed here, based on an analytical solution of nonlinear
force-free fields that is accurate to second order (in the force-free parameter
$\alpha$), represents the first code that enables fast forward-fitting to
photospheric magnetograms and stereoscopically triangulated loops in the solar
corona.


  Extending the idea formulated in Makino {\it{et al}}[Phys.Rev.E
{\bf{67}},066205], that is based on the Berry--Robnik approach [M.V. Berry and
M. Robnik, J. Phys. A {\bf{17}}, 2413], we investigate the statistical
properties of a two-point spectral correlation for a classically integrable
quantum system. The eigenenergy sequence of this system is regarded as a
superposition of infinitely many independent components in the semiclassical
limit. We derive the level number variance (LNV) in the limit of infinitely
many components and discuss its deviations from Poisson statistics. The slope
of the limiting LNV is found to be larger than that of Poisson statistics when
the individual components have a certain accumulation. This property agrees
with the result from the semiclassical periodic-orbit theory that is applied to
a system with degenerate torus actions[D. Biswas, M.Azam,and S.V.Lawande, Phys.
Rev. A {\bf 43}, 5694].


  Biomolecular binding kinetics including the association (kon) and
dissociation (koff) rates are critical parameters for therapeutic design of
small-molecule drugs, peptides and antibodies. Notably, drug molecule residence
time or dissociation rate has been shown to correlate with their efficacies
better than binding affinities. A wide range of modeling approaches including
quantitative structure-kinetic relationship models, Molecular Dynamics
simulations, enhanced sampling and Machine Learning have been developed to
explore biomolecular binding and dissociation mechanisms and predict binding
kinetic rates. Here, we review recent advances in computational modeling of
biomolecular binding kinetics, with an outlook for future improvements.


  We investigate the Lagrangian mechanism of the kinematic ``fluctuation''
magnetic dynamo in turbulent plasma flow at small magnetic Prandtl numbers. The
combined effect of turbulent advection and plasma resistivity is to carry
infinitely many field lines to each space point, with the resultant magnetic
field at that point given by the average over all the individual line vectors.
As a consequence of the roughness of the advecting velocity, this remains true
even in the limit of zero resistivity. We show that the presence of dynamo
effect requires sufficient angular correlation of the passive line-vectors that
arrive simultaneously at the SAME space point. We demonstrate this in detail
for the Kazantsev-Kraichnan model of kinematic dynamo with a Gaussian advecting
velocity that is spatially rough and white-noise in time. In the regime where
dynamo action fails, we also obtain the precise rate of decay of the magnetic
energy. These exact results for the model are obtained by a generalization of
the ``slow-mode expansion'' of Bernard, Gawedzki and Kupiainen to non-Hermitian
evolution. Much of our analysis applies also to magnetohydrodynamic turbulence.


  The spontaneous spin polarization of strongly interacting matter due to
axial-vector and tensor type interactions is studied at zero temperature and
high baryon-number densities. We start with the mean-field Lagrangian for the
axial-vector and tensor interaction channels, and find in the chiral limit that
the spin polarization due to the tensor mean field ($U$) takes place first as
the density increases for sufficiently strong coupling constants, and then that
due to the axial-vector mean field ($A$) emerges in the region of finite tensor
mean field. This can be understood that making the axial-vector mean field
finite requires a broken chiral symmetry somehow, which is achieved by the
finite tensor mean field in the present case. It is also found from symmetry
argument that there appear the type I (II) Nambu-Goldstone modes with a linear
(quadratic) dispersion in the spin polarized phase with $U\neq0$ and $A=0$
($U\neq0$ and $A\neq0$), although these two phases exhibit the same symmetry
breaking pattern.


  Causal asymmetry is one of the great surprises in predictive modelling: the
memory required to predict the future differs from the memory required to
retrodict the past. There is a privileged temporal direction for modelling a
stochastic process where memory costs are minimal. Models operating in the
other direction incur an unavoidable memory overhead. Here we show that this
overhead can vanish when quantum models are allowed. Quantum models forced to
run in the less natural temporal direction not only surpass their optimal
classical counterparts, but also any classical model running in reverse time.
This holds even when the memory overhead is unbounded, resulting in quantum
models with unbounded memory advantage.


  The recent excess over the Standard Model prediction in the \mu \gamma
missing-E_T channel reported by CDF can be well-explained by resonant smuon
production with a single dominant R-parity violating coupling \lambda'_{211},
in the context of models where the gravitino is the lightest supersymmetric
particle. The slepton decays to the lightest neutralino and a muon followed by
neutralino decaying to a gravitino and photon. The kinematical distributions
are fitted well by our hypothesis and we use them to constrain the available
parameter space. The model also provides an explanation for the ee\gamma\gamma
missing-E_T event observed in Run I of the Tevatron by the CDF experiment. Our
model predicts an excess of between 5 and 35 events in a \gamma missing-E_T
channel at Run I. We provide predictions for signatures expected by the model
at Run II.


  I review models trying to explain dwarf-nova outbursts and soft X-ray
transients. The disc-instability model for dwarf-novae is still in its
preliminary state of development: its predictions depend very strongly on the
unknown viscosity mechanism. It is also doubtful that a {\sl pure}
disc-instability phenomenon will be able to describe {\sl all} types of
dwarf-nova outbursts, in particular superoutbursts. The disc-instability model
for SXTs suffers from the same difficulties but in addition its predictions are
contradicted by observations of transient sources in quiescence. The
illuminated mass-transfer model cannot describe correctly the time-scales of
SXT events for main-sequence secondaries with masses less than 1$M_{\odot}$.
The existence of at least three systems with $P_{\rm orb} < 10$ hr seems to
rule it out as an explanation of the SXT phenomenon.


  High surface density, rapidly star-forming galaxies are observed to have
$\approx 50-100\,{\rm km\,s^{-1}}$ line-of-sight velocity dispersions, which
are much higher than expected from supernova driving alone, but may arise from
large-scale gravitational instabilities. Using three-dimensional simulations of
local regions of the interstellar medium, we explore the impact of high
velocity dispersions that arise from these disk instabilities. Parametrizing
disks by their surface densities and epicyclic frequencies, we conduct a series
of simulations that probe a broad range of conditions. Turbulence is driven
purely horizontally and on large scales, neglecting any energy input from
supernovae. We find that such motions lead to strong global outflows in the
highly-compact disks that were common at high redshifts, but weak or negligible
mass loss in the more diffuse disks that are prevalent today. Substantial
outflows are generated if the one-dimensional horizontal velocity dispersion
exceeds $\approx 35\,{\rm km\,s^{-1}},$ as occurs in the dense disks that have
star formation rate densities above $\approx 0.1\,{\rm M}_\odot\,{\rm
yr}^{-1}\,{\rm kpc}^{-2}.$ These outflows are triggered by a thermal runaway,
arising from the inefficient cooling of hot material coupled with successive
heating from turbulent driving. Thus, even in the absence of stellar feedback,
a critical value of the star-formation rate density for outflow generation can
arise due to a turbulent heating instability. This suggests that in strongly
self-gravitating disks, outflows may be enhanced by, but need not caused by,
energy input from supernovae.


  The free rider problem is one of the most well-studied problems in economics.
The solution proposed mainly is punitive in order to deter people from free
riding. In this work, we introduce quantum strategies and study the problem in
the thermodynamic limit by drawing analogies with the 1D Ising model. We
observe that for maximum entanglement, irrespective of the payoffs, quantum
strategy is the equilibrium solution, solving the free rider problem.


  Urban density, in the form of residents' and visitors' concentration, is long
considered to foster diverse exchanges of interpersonal knowledge and skills,
which are intrinsic to sustainable human settlements. However, with current
urban studies primarily devoted to city and district-level analysis, we cannot
unveil the elemental connection between urban density and diversity. Here we
use an anonymized and privacy-enhanced mobile data set of 0.5 million opted-in
users from three metropolitan areas in the U.S to show that at the scale of
urban streets, density is not the only path to diversity. We represent the
diversity of each street with the Experienced Social Mixing (ESM), which
describes the chances of people meeting diverse income groups throughout their
daily experience. We conduct multiple experiments and show that the
concentration of visitors only explains 26% of street-level ESM. However,
adjacent amenities, residential diversity, and income level account for 44% of
the ESM. Moreover, using longitudinal business data, we show that streets with
an increased number of food businesses have seen an increased ESM from 2016 to
2018. Lastly, although streets with more visitors are more likely to have
crime, diverse streets tend to have fewer crimes. These findings suggest that
cities can leverage many tools beyond density to curate a diverse and safe
street experience for people.


  Future HEP experiments present stringent challenges to calorimeter materials
in radiation tolerance, time response and project cost. The 2019 report of the
DOE Basic Research Needs Study on High Energy Physics Detector Research and
Development points out three priority research directions for future
calorimetry. Following these research directions letters of interest were
submitted to the Snowmass organized by the Division of Particles and Fields of
the American Physics Society. This report summarizes materials to be developed
in the form of inorganic, liquid (oil- and water-based), and plastic
scintillators and wavelength shifters to advance HEP calorimetry to face the
challenges in radiation hardness, fast timing, and cost-effectiveness. Some of
these materials may also find applications for future HEP time-of-flight
system, and beyond HEP in nuclear physics, hard X-ray imaging and medical
instruments.