  We have measured K-band surface brightness fluctuations (SBFs) of 19
early-type galaxies in the Fornax cluster. Combining our results with published
data, we find the absolute SBF magnitude Mbar_K = (-5.84)+(3.6)*[(V-I)-1.15].
The intrinsic cosmic scatter of Mbar_K appears to be larger than that of I-band
SBFs. The discovery of a correlation between K-band SBFs and V-I color is a new
clue into the star formation histories of early-type galaxies. This relation
naturally accounts for galaxies previously claimed to have anomalously bright
K-band SBFs, namely M32 and NGC 4489. Models indicate that the stellar
populations dominating the SBF signal have a significant range in age; some
scatter in metallicity may also be present. The youngest ages imply some
galaxies have very luminous giant branches, akin to those in intermediate-age
(few Gyr) Magellanic Cloud clusters. A few Fornax galaxies have unusually
bright K-band SBFs, perhaps originating from a high metallicity burst of star
formation in the last few Gyr. The increased spread and brightening of the
K-band SBFs with bluer (V-I) colors suggest that the lower mass cluster
galaxies may have had more extended and more heterogeneous star formation
histories than those of the more massive galaxies. (Abridged)


  This paper introduces the Generalized Fractional Compound Poisson Process
(GFCPP), which claims to be a unified fractional version of the compound
Poisson process (CPP) that encompasses existing variations as special cases. We
derive its distributional properties, generalized fractional differential
equations, and martingale properties. Some results related to the governing
differential equation about the special cases of jump distributions, including
exponential, Mittag-Leffler, Bernst\'ein, discrete uniform, truncated
geometric, and discrete logarithm. Some of processes in the literature such as
the fractional Poisson process of order $k$, P\'olya-Aeppli process of order
$k$, and fractional negative binomial process becomes the special case of the
GFCPP. Classification based on arrivals by time-changing the compound Poisson
process by the inverse tempered and the inverse of inverse Gaussian
subordinators are studied. Finally, we present the simulation of the sample
paths of the above-mentioned processes.


  Using the natural duality between linear functionals on tensor products of
C*-algebras with the trace class operators on a Hilbert space H and linear maps
of the C*-algebra into B(H), we give two characterizations of separability, one
relating it to abelianness of the definite set of the map, and one on tensor
products of nuclear and UHF C*-algebras


  This paper explores the Invariant Subspace Problem in operator theory and
functional analysis, examining its applications in various branches of
mathematics and physics. The problem addresses the existence of invariant
subspaces for bounded linear operators on a Hilbert space. We extensively
explore the significance of understanding the behavior of linear operators and
the existence of invariant subspaces, as well as their profound connections to
spectral theory, operator algebras, quantum mechanics, dynamical systems and
accelerator physics . By thoroughly exploring these applications, we aim to
highlight the wide-ranging impact and relevance of the invariant subspace
problem in mathematics and physics.


  In effective quantum field theory, a spin-1 vector boson can have a
technically natural small mass that does not originate from the Higgs
mechanism. For such theories, which may be written in St\"uckelberg form, there
is no point in field space at which the mass is exactly zero. I argue that
quantum gravity differs from, and constrains, effective field theory:
arbitrarily small St\"uckelberg masses are forbidden. In particular, the limit
in which the mass goes to zero lies at infinite distance in field space, and
this distance is correlated with a tower of modes becoming light according to
the Swampland Distance Conjecture. Application of Tower or Sublattice variants
of the Weak Gravity Conjecture makes this statement more precise: for a spin-1
vector boson with coupling constant $e$ and St\"uckelberg mass $m$, local
quantum field theory breaks down at energies at or below $\Lambda_{\rm UV} =
\min((m M_{\rm Pl}/e)^{1/2}, e^{1/3} M_{\rm Pl})$. Combined with
phenomenological constraints, this argument implies that the Standard Model
photon must be exactly massless. It also implies that much of the parameter
space for light dark photons, which are the target of many experimental
searches, is compatible only with Higgs and not St\"uckelberg mass terms. This
significantly affects the experimental limits and cosmological histories of
such theories. I explain various caveats and weak points of the arguments,
including loopholes that could be targets for model-building.


  In this paper, we explore a detectable imprint of massive fields with integer
spins $s \geq 2$, which may be predicted from string theory. It was shown that
such a massive non-zero spin field can generate the squeezed primordial
bispectrum which depends on the angle between the two wavenumbers. We show that
considering the contribution from the massive spin-2 field, the angular
dependent primordial non-Gaussianity (PNG) yields a strong scale dependence in
the bias parameter for the galaxy alignment, which becomes prominent at small
scales. As another example of an angular dependent PNG, we also consider the
primordial bispectrum where the angular dependence was introduced by a vector
field, while breaking the global rotational symmetry. As a consequence, we find
that the B-mode cosmic shear and non-diagonal components do not vanish. These
aspects provide qualitative differences from the PNG sourced by massive
non-zero spin fields.


  Models trained with empirical risk minimization (ERM) are revealed to easily
rely on spurious correlations, resulting in poor generalization. Group
distributionally robust optimization (group DRO) can alleviate this problem by
minimizing the worst-case loss over pre-defined groups. While promising, in
practice factors like expensive annotations and privacy preclude the
availability of group labels. More crucially, when taking a closer look at the
failure modes of out-of-distribution generalization, the typical procedure of
reweighting in group DRO loses efficiency. Hinged on the limitations, in this
work, we reformulate the group DRO framework by proposing Q-Diversity.
Characterized by an interactive training mode, Q-Diversity relaxes the group
identification from annotation into direct parameterization. Furthermore, a
novel mixing strategy across groups is presented to diversify the
under-represented groups. In a series of experiments on both synthetic and
real-world text classification tasks, results demonstrate that Q-Diversity can
consistently improve worst-case accuracy under different distributional shifts,
outperforming state-of-the-art alternatives.


  Strongly anisotropic spin-orbit coupling (SOC) renormalization and strongly
enhanced orbital magnetic moments are obtained in the fully self consistent
approach including the orbital off-diagonal spin and charge condensates. For
moderate tetragonal distortion as in $\rm Ca_2 RuO_4$, dominantly planar
antiferromagnetic (AFM) order with small canting of moments in and about the
crystal $c$ axis are obtained. For reduced tetragonal distortion, we find a
tunable regime wherein the magnetic order can be tuned (AFM or FM) by the bare
SOC strength and octahedral tilting magnitude. In this regime, with decreasing
tetragonal distortion, AFM order is maintained by progressively decreasing
octahedral tilting, as observed in $\rm Ca_{2-x}Sr_x RuO_4$. For purely planar
order, the only self consistent solution is FM order along crystal $b$ axis,
which is relevant for the bilayer ruthenate compound $\rm Ca_3 Ru_2 O_7$.


  We show that, for any n > 0, the Heisenberg interaction among 2n qubits (as
spin-1/2 particles) can be used to exactly implement an n-qubit parity gate,
which is equivalent in constant depth to an n-qubit fanout gate. Either
isotropic or nonisotropic versions of the interaction can be used. We
generalize our basic results by showing that any Hamiltonian (acting on
suitably encoded logical qubits), whose eigenvalues depend quadratically on the
Hamming weight of the logical qubit values, can be used to implement
generalized Mod_q gates for any q > 1.
  This paper is a sequel to quant-ph/0309163, and resolves a question left open
in that paper.


  A one-parameter family of coupled flows depending on a parameter $\kappa>0$
is introduced which reduces when $\kappa=1$ to the coupled flow of a metric
$\omega$ with a $(1,1)$-form $\alpha$ due recently to Y. Li, Y. Yuan, and Y.
Zhang. It is shown in particular that, for $\kappa\not=1$, estimates for
derivatives of all orders would follow from $C^0$ estimates for $\omega$ and
$\alpha$. Together with the monotonicity of suitably adapted energy
functionals, this can be applied to establish the convergence of the flow in
some situations, including on Riemann surfaces. Very little is known as yet
about the monotonicity and convergence of flows in presence of couplings, and
conditions such as $\kappa\not=1$ seem new and may be useful in the future.


  Recent experiments reported the puzzling zero energy modes associated with
ferromagnetic impurities in some iron-based superconductors with topological
band structures. Here, we show that the sufficiently strong exchange coupling
between a ferromagnetic impurity and substrate can trigger a quantum phase
transition, beyond which, the phase of the topological surface superconducting
order parameter around the impurity acquires a sign-change. In such a case, we
prove that a Kramers degenerate pair of Majorana modes can be induced at the
boundary separating the two sign-change regimes and trapped around the impurity
in the topological surface superconducting state. Furthermore, we show that our
theory can explain the controversial observations and confusing features of the
zero energy modes from recent experiments in some iron-based superconductors.


  In this paper we study circles tangent to conics. We show there are
generically $184$ complex circles tangent to three conics in the plane and we
characterize the real discriminant of the corresponding polynomial system. We
give an explicit example of $3$ conics with $136$ real circles tangent to them.
We conjecture that 136 is the maximal number of real circles. Furthermore, we
implement a hill-climbing algorithm to find instances of conics with many real
circles, and we introduce a machine learning model that, given three real
conics, predicts the number of circles tangent to these three conics.


  Galaxies, as well as their satellites, are known to form within the cosmic
web: the large, multi-scale distribution of matter in the universe. It is known
that the surrounding large scale structure (LSS) can impact and influence the
formation of galaxies, e.g. the spin and shape of haloes or galaxies are
correlated with the LSS and the correlation depends on halo mass or galaxy
morphology. In this work, we use group and filament catalogues constructed from
the SDSS DR12 to investigate the correlation between satellite systems and the
large scale filaments they are located in. We find that the distribution of
satellites is significantly correlated with filaments, namely the major axis of
the satellite systems are preferentially aligned with the spine of the closest
filament. Stronger alignment signals are found for the cases where the system
away from the filament spine, while systems close to the filament spine show
significantly weaker alignment. Our results suggest that satellites are
accreted along filaments, which agrees with previous works. The case of which
away from the filament spine may help us to understand how the filament forms
as well as the peculiar satellite distribution in the Local Universe.


  This paper is the first part of the manuscript written in April 2012 for my
academic Accreditation to supervise research. It offers a review of the double
beta experimental techniques. My purpose is to detail, for each technique, the
different origins of background, how they can be identified, and how they can
be reduced. Advantages and limitations are discussed. This review is organized
as follows. First, the question of the possible Majorana nature for the
neutrino is presented and the physic of neutrinoless double beta decay is
summarized. Then I begin by presenting the tracko-calo NEMO-3 and SuperNEMO
experiments. I've worked on these two experiments since 15 years. So it was
natural to start with them with a relatively more exhaustive description. I
will then present the germanium technique. I will then review the bolometer
technique. I will describe in detail the recent progress in scintillating
bolometers because I think that it is one of the most promising techniques.
Finally I will review the large liquid scintillator detectors and Xenon TPC.
The last chapter offers a summary of the different techniques and projects.


  We establish, in a rather general setting, an analogue of DiPerna-Lions
theory on well-posedness of flows of ODE's associated to Sobolev vector fields.
Key results are a well-posedness result for the continuity equation associated
to suitably defined Sobolev vector fields, via a commutator estimate, and an
abstract superposition principle in (possibly extended) metric measure spaces,
via an embedding into $\mathbb{R}^\infty$.
  When specialized to the setting of Euclidean or infinite dimensional (e.g.
Gaussian) spaces, large parts of previously known results are recovered at
once. Moreover, the class of ${\sf RCD}(K,\infty)$ metric measure spaces object
of extensive recent research fits into our framework. Therefore we provide, for
the first time, well-posedness results for ODE's under low regularity
assumptions on the velocity and in a nonsmooth context.


  We consider a generalized version of the birth-death (BD) and death-birth
(DB) processes introduced by Kaveh et al (2015), in which two constant
fitnesses, one for birth and the other for death, describe the selection
mechanism of the population. Rather than constant fitnesses, in this paper we
consider more general frequency-dependent fitness functions (allowing any
smooth functions) under the weak-selection regime. For a large population
structured as a star graph, we provide approximations for the fixation
probability which are solutions of certain ODEs (or systems of ODEs). For the
DB case, we prove that our approximation has an error of order 1/N, where N is
the size of the population. These approximations are obtained in the same
spirit of Chalub and Souza (2016) albeit with quite different techniques. The
general BD and DB processes contain, as special cases, the BD-* and DB-* (where
* can be either B or D) processes described in Hadjichrysanthou et al (2011) --
this class includes many examples of update rules used in the literature.


  We show herein that the population of star forming galaxies in the Bremer
Deep Field (BDF) have enough ionising power to form two large ionised bubbles
which could be in the process of merging into a large one with a volume of
14000 cMpc3. The sources identified in the BDF have been completed with a set
of expected low luminosity sources at z $\approx$ 7. We have estimated the
number of ionising photons per second produced by the different star forming
galaxies in the BDF. This number has been compared with the number that would
be required to ionise the bubbles around the two overdense regions. We have
used, as reference, ionising emissivities derived from the AMIGA cosmological
evolutionary model. We find that even using the most conservative estimates,
with a Lyman continuum escape fraction of 10\% the two regions we have defined
within the BDF would be reionised. Assuming more realistic estimates of the
ionising photon production efficiency, both bubbles would be in the process of
merging into a large reionised bubble, such as those that through percolation
completed the reionisation of the universe by z = 6. The rather small values of
the escape fraction required to reionise the BDF are compatible with the low
fraction of faint Ly{\alpha} emitters identified in the BDF. Finally, we
confirm that the low luminosity sources represent indeed the main contributors
to the BDF ionising photon production.


  We show that the S-matrix ansatz implies a semi-classical metric such that a
freely falling test particle will not cross the horizon in its proper time.
Instead of reaching the singularity it will reach ${\cal I^{+}}$.


  In this paper we study the residual solvability of the generalized free
product of finitely generated nilpotent groups. We show that these kinds of
structures are often residually solvable.


  We do Monte Carlo simulations of four 3D structural transitions, with
vector-spin models of their martensitic strain domains under quenches to $T$,
to test a generic post-quench Partial Equilibration Scenario (PES) of Ritort.
We indeed confirm that energy-lowering passages between fixed-energy shells
induce a signature PES distribution of an exponential tail in heat releases,
scaled in an effective search temperature. A linear vanishing of this
$T_{eff}(T)\sim T_d -T$ at a temperature $T_d$ where PES passage-searches
freeze, explains the Vogel-Fulcher like divergence of equilibration times $
e^{1/ T_{eff} (T)}\sim e^{1/(T_d -T)}$, extracted from incubation-time delays
of simulations and martensitic alloys.


  Research software is increasingly recognized as a vital component of the
scholarly record. Journals offer authors the opportunity to publish research
software papers, but often have different requirements for how these
publications should be structured and how code should be verified. In this
short case study we gather data from 20 Physical Science journals to trace the
frequency, quality control, and publishing criteria for software papers. Our
goal with the case study is to provide a proof-of-concept for doing descriptive
empirical work with software publication policies across numerous domains of
science and engineering. In the narrative we therefore provide descriptive
statistics showing how these journals differ in criteria required for
archiving, linking, verifying, and documenting software as part of a formal
publication. The contribution of this preliminary work is twofold: 1. We
provide case study of Physical Science research software publications over
time; 2. We demonstrate the use of a new survey method for analyzing research
software publication policies. In our conclusion, we describe how comparative
research into software publication policies can provide better criteria and
requirements for an emerging software publication landscape.


  We propose a method of separating a desired sound source from a
single-channel mixture, based on either a textual description or a short audio
sample of the target source. This is achieved by combining two distinct models.
The first model, SoundWords, is trained to jointly embed both an audio clip and
its textual description to the same embedding in a shared representation. The
second model, SoundFilter, takes a mixed source audio clip as an input and
separates it based on a conditioning vector from the shared text-audio
representation defined by SoundWords, making the model agnostic to the
conditioning modality. Evaluating on multiple datasets, we show that our
approach can achieve an SI-SDR of 9.1 dB for mixtures of two arbitrary sounds
when conditioned on text and 10.1 dB when conditioned on audio. We also show
that SoundWords is effective at learning co-embeddings and that our multi-modal
training approach improves the performance of SoundFilter.


  Consider a general branching process, a.k.a. Crump-Mode-Jagers process,
generated by a perturbed random walk $\eta_1$, $\xi_1+\eta_2$,
$\xi_1+\xi_2+\eta_3,\ldots$. Here, $(\xi_1,\eta_1)$, $(\xi_2, \eta_2),\ldots$
are independent identically distributed random vectors with arbitrarily
dependent positive components. Denote by $N_j(t)$ the number of the $j$th
generation individuals with birth times $\leq t$. Assume that $j=j(t)\to\infty$
and $j(t)=o(t^a)$ as $t\to\infty$ for some explicitly given $a>0$ (to be
specified in the paper). The corresponding $j$th generation belongs to the set
of intermediate generations. We provide sufficient conditions under which
finite-dimensional distributions of the process $(N_{\lfloor
j(t)u\rfloor}(t))_{u>0}$, properly normalized and centered, converge weakly to
those of an integral functional of a stable L\'{e}vy process with finite mean.


  The existence of multiple anomalous U(1)s is demonstrated explicitly in a
blow-up version of a heterotic Z_3 orbifold. Another blow-up of the same
orbifold supports further evidence for the type-I/heterotic duality in four
dimensions. It has a single anomalous U(1) which does not factorize
universally. As multiple anomalous U(1)s as well as non-universal factorization
have never been established on heterotic orbifolds explicitely, these findings
might appear contradictory at first sight. Possible inconsistencies are avoided
by reinterpreting a charged twisted state as a second non-universal localized
axion. The mismatch between the charges of the orbifold and blow-up spectra is
resolved by suitable field redefinitions. The anomaly of the field
redefinitions corresponds to the difference of blow-up and heterotic orbifold
anomalies.


  We report an unusual evolution of superconductivity (SC) in the
three-dimensional Dirac semimetal PdTe with increasing pressure up to $\sim$50
GPa. The compressed PdTe exhibits a sudden reversal in the superconducting
transition temperature $T\mathrm{_c}$, from an initial decrease with pressure
to an increase above a critical pressure $P\mathrm{_c} \approx$ 15 GPa, showing
a V-shaped feature composed of SC-I and SC-II phases due to a structural phase
transition through $P\mathrm{_c}$. Subsequently, the $T\mathrm{_c}$ goes into a
plateau around 2.5 K when the pressure is higher than $\sim$32 GPa. In
addition, we find the variations of carrier concentrations and mobilities also
manifest a similar trend on the pressure response as the $T\mathrm{_c}$, and
the normal-state electronic properties change from the electron-dominated
single-band model to two-carrier model after the structural phase transition,
implying the close correlation between electronic properties and two SC phases.
Our findings establish the SC of PdTe is highly tunable under varying
pressures.


  While the use of energy storage combined with grid-scale photovoltaic power
plants continues to grow, given current lithium-ion battery prices, there
remains uncertainty about the profitability of these solar-plus-storage
projects. At the same time, the rapid proliferation of electric vehicles is
creating a fleet of millions of lithium-ion batteries that will be deemed
unsuitable for the transportation industry once they reach 80 percent of their
original capacity. The repurposing and deployment of these batteries as
stationary energy storage provides an opportunity to reduce the cost of
solar-plus-storage systems, if the economics can be proven. We present a
techno-economic model of a solar-plus-second-life energy storage project in
California, including a data-based model of lithium nickel manganese cobalt
oxide battery degradation, to predict its capacity fade over time, and compare
it to a project that uses a new lithium-ion battery. By setting certain control
policy limits, to minimize cycle aging, we show that a system with SOC limits
in a 65 to 15 percent range, extends the project life to over 16 years,
assuming a battery reaches its end-of-life at 60 percent of its original
capacity. Under these conditions, a second-life project is more economically
favorable than a project that uses a new battery and 85 to 20 percent SOC
limits, for second-life battery costs that are less than 80 percent of the new
battery. The same system reaches break-even and profitability for second-life
battery costs that are less than 60 percent of the new battery. Our model shows
that using current benchmarked data for the capital and O&M costs of
solar-plus-storage systems, and a semi-empirical data-based degradation model,
it is possible for EV manufacturers to sell second-life batteries for less than
60 percent of their original price to developers of profitable
solar-plus-storage projects.


  Fractal dimension curves of urban growth can be modeled with sigmoid
functions, including logistic function and quadratic logistic function.
Different types of logistic functions indicate different spatial dynamics. The
fractal dimension curves of urban growth in western countries follows the
common logistic function, while these curves of cities in northern China
follows quadratic logistic function. Now we want to know whether all Chinese
cities follow the same rules of urban evolution. This paper is devoted to
exploring the fractals and fractal dimension properties of the city of Shenzhen
in southern China. The urban region is divided into four subareas, ArcGIS
technology, box-counting method is adopted to extract spatial datasets, and the
least squares regression is employed to estimate fractal parameters. The
results show that: (1) The urban form of Shenzhen city has clear fractal
structure, but fractal dimension values of different subareas are different;
(2) The fractal dimension growth curves of all the four study areas can only be
modeled by the common logistic function, and the goodness of fit increases over
time; (3) The peak of urban growth in Shenzhen had passed before 1986, the
fractal dimension growth is approaching its maximum capacity. Conclusions can
be reached that the urban form of Shenzhen bears characteristics of
multifractals, the fractal structure has been becoming better gradually through
self-organization, but its land resources are reaching the limits of growth.
The fractal dimension curves of Shenzhen's urban growth are similar to those of
European and American cities, but differ from those of the cities in northern
China. This suggests that there is subtle different dynamic mechanisms of city
development between northern and southern China.


  We derive an intuitive and novel method to represent nodes in a graph with
special unitary operators, or quantum operators, which does not require
parameter training and is competitive with classical methods on scoring
similarity between nodes. This method opens up future possibilities to apply
quantum algorithms for NLP or other applications that need to detect anomalies
within a network structure. Specifically, this technique leverages the
advantage of quantum computation, representing nodes in higher dimensional
Hilbert spaces. To create the representations, the local topology around each
node with a predetermined number of hops is calculated and the respective
adjacency matrix is used to derive the Hamiltonian. While using the local
topology of a node to derive a Hamiltonian is a natural extension of a graph
into a quantum circuit, our method differs by not assuming the quantum
operators in the representation a priori, but letting the adjacency matrix
dictate the representation. As a consequence of this simplicity, the set of
adjacency matrices of size $2^n \times 2^n$ generates a sub-vector space of the
Lie algebra of the special unitary operators, $\mathfrak{su}(2^n)$. This
sub-vector space in turn generates a subgroup of the Lie group of special
unitary operators, $\mathrm{SU}(2^n)$. Applications of our quantum embedding
method, in comparison with the classical algorithms GloVe (a natural language
processing embedding method) and FastRP (a general graph embedding method,
display superior performance in measuring similarity between nodes in graph
structures.


  We present a detailed construction of a completely symmetric representation
of the monodromy matrix by the use of Drinfel'd twists for the rational $sl(3)$
Heisenberg model without refering to the special symmetry of the model. With
the help of this representation we are able to resolve the hierarchy of the
nested Bethe wavevectors for the $sl(3)$ invariant rational Heisenberg model.


  This survey reviews Kauffman's model of folded ribbon knots: knots made of a
thin strip of paper folded flat in the plane. The ribbonlength is the length to
width ratio of such a ribbon, and the ribbonlength problem asks to minimize the
ribbonlength for a given knot type. We give a summary of known results. For the
most part, these are upper bounds of ribbonlength of twist knots and certain
families of torus knots. We discuss result of G. Tian, which give upper bounds
of ribbonlength in terms of crossing number. In addition, it turns out the
choice of fold affects the ribbonlength. We end with a discussion of three
different types of folded ribbon equivalence and give examples illustrating
their relationship to ribbonlength.


  Starting from interaction rules based on two levels of stochasticity we study
the influence of the microscopic dynamics on the macroscopic properties of
vehicular flow. In particular, we study the qualitative structure of the
resulting flux-density and speed-density diagrams for different choices of the
desired speeds. We are able to recover multivalued diagrams as a result of the
existence of a one-parameter family of stationary distributions, whose
expression is analytically found by means of a Fokker-Planck approximation of
the initial Boltzmann-type model.


  Variational wave functions have enabled exceptional scientific breakthroughs
related to the understanding of novel phases of matter. Examples include the
Bardeen-Cooper-Schrieffer theory of superconductivity, the description of the
fractional quantum Hall effect through the Laughlin state, and Feynman's
variational understanding of large-scale quantum effects in liquid Helium. More
recently, Gutzwiller-projected wave functions, typically constructed from
fermionic degrees of freedom, have been employed to examine quantum spin models
in the presence of competing interactions, where exotic phases with no
spontaneous symmetry breaking and fractional excitations may exist. In this
work, we investigate the aforementioned fermionic wave functions supplemented
with neural networks, specifically with the so-called restricted Boltzmann
machine (RBM), to boost their accuracy and obtain reliable approximations to
the ground state of generic spin models. In particular, we apply our neural
augmented fermionic construction to the description of both magnetically
ordered and disordered phases of increasing complexity, including cases where
the ground state displays a non-trivial sign structure. Even though the RBM
state is by far more effective for N\'eel states endowed with a particularly
simple sign structure, it provides a significant improvement over the original
fermionic state in highly frustrated regimes where a complex sign structure is
anticipated, thus marking the path to an understanding of strongly-correlated
spin models on the lattice via neural Gutzwiller-projected variational wave
functions.


  For a simple finite graph G denote by {G \brace k} the number of ways of
partitioning the vertex set of G into k non-empty independent sets (that is,
into classes that span no edges of G). If E_n is the graph on n vertices with
no edges then {E_n \brace k} coincides with {n \brace k}, the ordinary Stirling
number of the second kind, and so we refer to {G \brace k} as a graph Stirling
number.
  Harper showed that the sequence of Stirling numbers of the second kind, and
thus the graph Stirling sequence of E_n, is asymptotically normal ---
essentially, as n grows, the histogram of ({E_n \brace k})_{k \geq 0}, suitably
normalized, approaches the density function of the standard normal
distribution.
  In light of Harper's result, it is natural to ask for which sequences
(G_n)_{n \geq 0} of graphs is there asymptotic normality of ({G_n \brace k})_{k
\geq 0}. Do and Galvin conjectured that if for each n, G_n is acylic and has n
vertices, then asymptotic normality occurs, and they gave a proof under the
added condition that G_n has no more than o(\sqrt{n/\log n}) components.
  Here we settle Do and Galvin's conjecture in the affirmative, and
significantly extend it, replacing "acyclic" in their conjecture with
"co-chromatic with a quasi-threshold graph, and with negligible chromatic
number". Our proof combines old work of Navon and recent work of Engbers,
Galvin and Hilyard on the normal order problem in a Weyl algebra, and work of
Kahn on the matching polynomial of a graph.


  We consider the class of quasiprojective varieties admitting a dominant
morphism onto a curve with negative Euler characteristic. The existence of such
a morphism is a property of the fundamental group. We show that for a variety
in this class the number of maps onto a hyperbolic curve or surfaces can be
estimated in terms of the numerical invariants of the fundamental group. We use
this estimates to find the number of biholomorphic automorphisms of complements
to some arrangements of lines.


  Anomalously strong finite-size effects have been observed for the mean square
radius of gyration $R^2_K$ of Gaussian random polygons with a fixed knot $K$ as
a function of the number $N$ of polygonal nodes. Through computer simulations
with $N < 2000$, we find for several knots that the gyration radius $R^2_K$ can
be approximated by a power law: $R^2_K \sim N^{2 \nu_{K}^{eff}}$, where the
effective exponents $\nu_{K}^{eff}$ for the knots are larger than 0.5 and less
than 0.6. A crossover occurs for the gyration radius of the trivial knot, when
$N$ is roughly equal to the characteristic length $N_c$ of random knotting. For
the asymptotic behavior of $R^2_K$, however, we find that it is consistent with
the standard one with the scaling exponent 0.5. Thus, although the strong
finite-size effects of $R^2_K$ remain effective for extremely large values of
$N$, they can be matched with the asymptotic behavior of random walks.


  Revealing the robustness issues of natural language processing models and
improving their robustness is important to their performance under difficult
situations. In this paper, we study the robustness of paraphrase identification
models from a new perspective -- via modification with shared words, and we
show that the models have significant robustness issues when facing such
modifications. To modify an example consisting of a sentence pair, we either
replace some words shared by both sentences or introduce new shared words. We
aim to construct a valid new example such that a target model makes a wrong
prediction. To find a modification solution, we use beam search constrained by
heuristic rules, and we leverage a BERT masked language model for generating
substitution words compatible with the context. Experiments show that the
performance of the target models has a dramatic drop on the modified examples,
thereby revealing the robustness issue. We also show that adversarial training
can mitigate this issue.


  Recent studies have revealed the vulnerability of face recognition models
against physical adversarial patches, which raises security concerns about the
deployed face recognition systems. However, it is still challenging to ensure
the reproducibility for most attack algorithms under complex physical
conditions, which leads to the lack of a systematic evaluation of the existing
methods. It is therefore imperative to develop a framework that can enable a
comprehensive evaluation of the vulnerability of face recognition in the
physical world. To this end, we propose to simulate the complex transformations
of faces in the physical world via 3D-face modeling, which serves as a digital
counterpart of physical faces. The generic framework allows us to control
different face variations and physical conditions to conduct reproducible
evaluations comprehensively. With this digital simulator, we further propose a
Face3DAdv method considering the 3D face transformations and realistic physical
variations. Extensive experiments validate that Face3DAdv can significantly
improve the effectiveness of diverse physically realizable adversarial patches
in both simulated and physical environments, against various white-box and
black-box face recognition models.


  We use the Gutzwiller method to investigate the importance of the on-site
Coulomb interaction in graphene. We apply it to Hubbard Hamiltonian to study
the renormalization of the kinetic energy in graphene due to the on-site
Coulomb interaction. We find that a reasonable strength of the interaction has
a very weak effect in reducing the kinetic energy. Hence we predict that the
Brinkmann-Rice metal-insulator transition in graphene is not possible. The
effect is understood in terms of the high kinetic energy in graphene.


  Several Wilson loops on several lattice sizes are computed in Perturbation
Theory via a stochastic method. Applications include: Renormalons, the Mass
Term in Heavy Quark Effective Theory and (possibly) the beta-function.


  The experimental evidence for the Hall-Petch dependence of strength on the
inverse square-root of grain size is reviewed critically. Both the classic data
and more recent results are considered. While the data can be fitted to the
inverse square-root dependence excellently (but using two free fitting
parameters for each dataset), it is also consistent with a dependence on the
simple inverse of grain size (with one free fitting parameter for each
dataset). There have been difficulties, recognised for half-a-century, in
explaining the inverse square-root expression. A Bayesian analysis shows that
the data strongly supports the simple inverse expression proposed. Since this
expression derives from underlying theory, it is also more readily explicable.
It is concluded that the Hall-Petch effect is not to be explained by the
variety of theories found in the literature, but is a manifestation of, or
underlain by, the general size effect observed throughout micromechanics, due
to the inverse relationship between the stress required and the space available
for dislocation sources to operate.


  Directed high-speed motion of nanoscale objects in fluids (nano swimmers) can
have a wide range of applications like molecular machinery, nano robotics, drug
delivery, and material assembly. Here, we report ballistic plasmonic Au
nanoparticle (NP) swimmers with unprecedented speeds realized by not only
optical pushing but also pulling forces from a single Gaussian laser beam. Both
the optical pulling and high swimmer speeds are made possible by a unique
NP-laser interaction. The Au NP excited by the laser at the surface plasmon
resonance peak can generate a nanoscale bubble, which can encapsulate the NP
(i.e., supercavitation) to create a virtually frictionless environment for it
to move, like the Leidenfrost effect. While optical forces are mostly positive,
certain NP-bubble configurations can lead to negative optical forces that pull
the NP to swims against the photon stream. The demonstrated ultra-fast,
light-driven NP movement may benefit a wide range of nano- and bio-applications
and provide new insights to the field of negative optical force.


  This paper is devoted to the study of metric subregularity and strong
subregularity of any positive order $q$ for set-valued mappings in finite and
infinite dimensions. While these notions have been studied and applied earlier
for $q=1$ and---to a much lesser extent---for $q\in(0,1)$, no results are
available for the case $q>1$. We derive characterizations of these notions for
subgradient mappings, develop their sensitivity analysis under small
perturbations, and provide applications to the convergence rate of Newton-type
methods for solving generalized equations.


  Semidefinite programs (SDPs) can be solved in polynomial time by interior
point methods, but scalability can be an issue. To address this shortcoming,
over a decade ago, Burer and Monteiro proposed to solve SDPs with few equality
constraints via rank-restricted, non-convex surrogates. Remarkably, for some
applications, local optimization methods seem to converge to global optima of
these non-convex surrogates reliably. Although some theory supports this
empirical success, a complete explanation of it remains an open question. In
this paper, we consider a class of SDPs which includes applications such as
max-cut, community detection in the stochastic block model, robust PCA, phase
retrieval and synchronization of rotations. We show that the low-rank
Burer--Monteiro formulation of SDPs in that class almost never has any spurious
local optima.


  We consider the problem of decomposing a real-valued symmetric tensor as the
sum of outer products of real-valued vectors. Algebraic methods exist for
computing complex-valued decompositions of symmetric tensors, but here we focus
on real-valued decompositions, both unconstrained and nonnegative, for problems
with low-rank structure. We discuss when solutions exist and how to formulate
the mathematical program. Numerical results show the properties of the proposed
formulations (including one that ignores symmetry) on a set of test problems
and illustrate that these straightforward formulations can be effective even
though the problem is nonconvex.


  Reaching distributed average consensus quickly and accurately over a network
through iterative dynamics represents an important task in numerous distributed
applications. Suitably designed filters applied to the state values can
significantly improve the convergence rate. For constant networks, these
filters can be viewed in terms of graph signal processing as polynomials in a
single matrix, the consensus iteration matrix, with filter response evaluated
at its eigenvalues. For random, time-varying networks, filter design becomes
more complicated, involving eigendecompositions of sums and products of random,
time-varying iteration matrices. This paper focuses on deriving an estimate for
the Gram matrix of error in the state vectors over a filtering window for
large-scale, stationary, switching random networks. The result depends on the
moments of the empirical spectral distribution, which can be estimated through
Monte-Carlo simulation. This work then defines a quadratic objective function
to minimize the expected consensus estimate error norm. Simulation results
provide support for the approximation.


  Designing cyber defense systems to account for cognitive biases in human
decision making has demonstrated significant success in improving performance
against human attackers. However, much of the attention in this area has
focused on relatively simple accounts of biases in human attackers, and little
is known about adversarial behavior or how defenses could be improved by
disrupting attacker's behavior. In this work, we present a novel model of human
decision-making inspired by the cognitive faculties of Instance-Based Learning
Theory, Theory of Mind, and Transfer of Learning. This model functions by
learning from both roles in a security scenario: defender and attacker, and by
making predictions of the opponent's beliefs, intentions, and actions. The
proposed model can better defend against attacks from a wide range of opponents
compared to alternatives that attempt to perform optimally without accounting
for human biases. Additionally, the proposed model performs better against a
range of human-like behavior by explicitly modeling human transfer of learning,
which has not yet been applied to cyber defense scenarios. Results from
simulation experiments demonstrate the potential usefulness of cognitively
inspired models of agents trained in attack and defense roles and how these
insights could potentially be used in real-world cybersecurity.


  Josephson junctions have been shown to be a promising solid-state system for
implementation of quantum computation. The significant two-qubit gates are
generally realized by the capacitive coupling between the nearest neighbour
qubits. We propose an effective Hamiltonian to describe charge qubits coupled
through the cavity. We find that nontrivial two-qubit gates may be achieved by
this coupling. The ability to interconvert localized charge qubits and flying
qubits in the proposed scheme implies that quantum network can be constructed
using this large scalable solid-state system.


  Neural Collapse (NC) is a geometric structure recently observed in the final
layer of neural network classifiers. In this paper, we investigate the
interrelationships between batch normalization (BN), weight decay, and
proximity to the NC structure. Our work introduces the geometrically intuitive
intra-class and inter-class cosine similarity measure, which encapsulates
multiple core aspects of NC. Leveraging this measure, we establish theoretical
guarantees for the emergence of NC under the influence of last-layer BN and
weight decay, specifically in scenarios where the regularized cross-entropy
loss is near-optimal. Experimental evidence substantiates our theoretical
findings, revealing a pronounced occurrence of NC in models incorporating BN
and appropriate weight-decay values. This combination of theoretical and
empirical insights suggests a greatly influential role of BN and weight decay
in the emergence of NC.


  We develop a theory of magnetooscillations in the photoconductivity of a
two-dimensional electron gas observed in recent experiments. The effect is
governed by a change of the electron distribution function induced by the
microwave radiation. We analyze a nonlinearity with respect to both the dc
field and the microwave power, as well as the temperature dependence determined
by the inelastic relaxation rate.


  We compute the Hochschild homology of the crossed product $\Bbb C[S_n]\ltimes
A^{\otimes n}$ in terms of the Hochschild homology of the associative algebra
$A$ (over $\Bbb C$). It allows us to compute the Hochschild (co)homology of
$\Bbb C[W]\ltimes A^{\otimes n}$ where $A$ is the $q$-Weyl algebra or any its
degeneration and $W$ is the Weyl group of type $A_{n-1}$ or $B_n$. For a
deformation quantization $A_+$ of an affine symplectic variety $X$ we show that
the Hochschild homology of $S^n A$, $A=A_+[\hbar^{-1}]$ is additively
isomorphic to the Chen-Ruan orbifold cohomology of $S^nX$ with coefficients in
$\Bbb C((\hbar))$. We prove that for $X$ satisfying $H^1(X,\Bbb C)=0$ (or $A\in
VB(d)$) the deformation of $S^nX$ ($\Bbb C[S_n]\ltimes A^{\otimes n}$) which
does not come from deformations of $X$ ($A$) exists if and only if $\dim X=2$
($d=2$). In particular if $A$ is $q$-Weyl algebra (its trigonometric or
rational degeneration) then the corresponding nontrivial deformations yield the
double affine Hecke algebras of type $A_{n-1}$ (its trigonometric or rational
versions) introduced by Cherednik.


  An open problem in neuroscience is to explain the functional role of
oscillations in neural networks, contributing, for example, to perception,
attention, and memory. Cross-frequency coupling (CFC) is associated with
information integration across populations of neurons. Impaired CFC is linked
to neurological disease. It is unclear what role CFC has in information
processing and brain functional connectivity. We construct a model of CFC which
predicts a computational role for observed $\theta - \gamma$ oscillatory
circuits in the hippocampus and cortex. Our model predicts that the complex
dynamics in recurrent and feedforward networks of coupled oscillators performs
robust information storage and pattern retrieval. Based on phasor associative
memories (PAM), we present a novel oscillator neural network (ONN) model that
includes subharmonic injection locking (SHIL) and which reproduces experimental
observations of CFC. We show that the presence of CFC increases the memory
capacity of a population of neurons connected by plastic synapses. CFC enables
error-free pattern retrieval whereas pattern retrieval fails without CFC. In
addition, the trade-offs between sparse connectivity, capacity, and information
per connection are identified. The associative memory is based on a
complex-valued neural network, or phasor neural network (PNN). We show that for
values of $Q$ which are the same as the ratio of $\gamma$ to $\theta$
oscillations observed in the hippocampus and the cortex, the associative memory
achieves greater capacity and information storage than previous models. The
novel contributions of this work are providing a computational framework based
on oscillator dynamics which predicts the functional role of neural
oscillations and connecting concepts in neural network theory and dynamical
system theory.


  A magic labelling of a graph $G$ with magic sum $s$ is a labelling of the
edges of $G$ by nonnegative integers such that for each vertex $v\in V$, the
sum of labels of all edges incident to $v$ is equal to the same number $s$.
Stanley gave remarkable results on magic labellings, but the distinct labelling
case is much more complicated. We consider the complete construction of all
magic labellings of a given graph $G$. The idea is illustrated in detail by
dealing with three regular graphs. We give combinatorial proofs. The structure
result was used to enumerate the corresponding magic distinct labellings.


  As is known from QED, a possible solution to the ghost-pole trouble can be
obtained by imposing the $Q^2$-analyticity imperative. Here, the pole is
compensated by the $\alpha$ non-analytic contribution that results in finite
coupling renormalization.
  We apply this idea to QCD and arrive at the $Q^2$ analytic
$\bar{\alpha}_s(Q)$. This solution corresponds to perturbation expansion, obeys
AF and, due to non-perturbative contribution, has a regular IR behaviour. It
does not contain any adjustable parameter and has a finite IR limit
$\bar{\alpha}_s(0)$ which depends only on group symmetry factors. In the
one-loop approximation it is equal to $4\pi/\beta_0 \simeq 1.40\,$ and turns
out to be surprisingly stable with respect to higher order corrections. On the
other hand, the IR behaviour of our new analytic solution agrees with recent
global low energy experimental estimates of $\bar{\alpha}_s(Q^2)$.


  AI technologies are being increasingly tested and applied in critical
environments including healthcare. Without an effective way to detect and
mitigate AI induced inequalities, AI might do more harm than good, potentially
leading to the widening of underlying inequalities. This paper proposes a
generic allocation-deterioration framework for detecting and quantifying AI
induced inequality. Specifically, AI induced inequalities are quantified as the
area between two allocation-deterioration curves. To assess the framework's
performance, experiments were conducted on ten synthetic datasets (N>33,000)
generated from HiRID - a real-world Intensive Care Unit (ICU) dataset, showing
its ability to accurately detect and quantify inequality proportionally to
controlled inequalities. Extensive analyses were carried out to quantify health
inequalities (a) embedded in two real-world ICU datasets; (b) induced by AI
models trained for two resource allocation scenarios. Results showed that
compared to men, women had up to 33% poorer deterioration in markers of
prognosis when admitted to HiRID ICUs. All four AI models assessed were shown
to induce significant inequalities (2.45% to 43.2%) for non-White compared to
White patients. The models exacerbated data embedded inequalities significantly
in 3 out of 8 assessments, one of which was >9 times worse.
  The codebase is at https://github.com/knowlab/DAindex-Framework.


  Recently, inversion methods have focused on additional high-rate information
in the generator (e.g., weights or intermediate features) to refine inversion
and editing results from embedded latent codes. Although these techniques gain
reasonable improvement in reconstruction, they decrease editing capability,
especially on complex images (e.g., containing occlusions, detailed
backgrounds, and artifacts). A vital crux is refining inversion results,
avoiding editing capability degradation. To tackle this problem, we introduce
Domain-Specific Hybrid Refinement (DHR), which draws on the advantages and
disadvantages of two mainstream refinement techniques to maintain editing
ability with fidelity improvement. Specifically, we first propose
Domain-Specific Segmentation to segment images into two parts: in-domain and
out-of-domain parts. The refinement process aims to maintain the editability
for in-domain areas and improve two domains' fidelity. We refine these two
parts by weight modulation and feature modulation, which we call Hybrid
Modulation Refinement. Our proposed method is compatible with all latent code
embedding methods. Extension experiments demonstrate that our approach achieves
state-of-the-art in real image inversion and editing. Code is available at
https://github.com/caopulan/Domain-Specific_Hybrid_Refinement_Inversion.


  Let $H_r(n,p)$ denote the maximum number of Hamiltonian cycles in an
$n$-vertex $r$-graph with density $p \in (0,1)$. The expected number of
Hamiltonian cycles in the random $r$-graph model $G_r(n,p)$ is
$E(n,p)=p^n(n-1)!/2$ and in the random graph model $G_r(n,m)$ with
$m=p\binom{n}{r}$ it is, in fact, slightly smaller than $E(n,p)$. For graphs,
$H_2(n,p)$ is proved to be only larger than $E(n,p)$ by a polynomial factor and
it is an open problem whether a quasi-random graph with density $p$ can be
larger than $E(n,p)$ by a polynomial factor. For hypergraphs (i.e. $r \ge 3$)
the situation is drastically different. For all $r \ge 3$ it is proved that
$H_r(n,p)$ is larger than $E(n,p)$ by an {\em exponential} factor and,
moreover, there are quasi-random $r$-graphs with density $p$ whose number of
Hamiltonian cycles is larger than $E(n,p)$ by an exponential factor.


  Taking advantage of the impressive sensitivity of Spitzer to detect massive
galaxies at high redshift, we study the mid-infrared environments of powerful,
high-redshift radio galaxies at 1.2<z<3. Galaxy cluster member candidates were
isolated using a single Spitzer/IRAC mid-infrared color criterion,
[3.6]-[4.5]>-0.1 (AB), in the fields of 48 radio galaxies at 1.2<z<3. This
simple IRAC color selection is effective at identifying galaxies at z>1.2.
Using a counts-in-cell analysis, we identify a field as overdense when 15 or
more red IRAC sources are found within 1arcmin (i.e.,~0.5Mpc at 1.2<z<3) of the
radio galaxy to the 5sigma flux density limits of our IRAC data (f3.6=11.0uJy,
f4.5=13.4uJy). We find that radio galaxies lie preferentially in medium to
dense regions, with 73% of the targeted fields denser than average. Our
(shallow) 120s data permit the rediscovery of previously known clusters and
protoclusters associated with radio galaxies as well as the discovery of new
promising galaxy cluster candidates at z>1.2.


  In this paper we prove that Arnold Surfaces of all real algebraic curves of
even degree with non-empty real part are standard (Rokhlin's Conjecture). There
is an obvious connection with classification of Arnold Surfaces up to isotopy
of S^4 and Hilbert's Sixteen Problem on the arrangements of connected real
components of curves. First, we consider some M-curves, i.e curves of a
prescribed degree having the greatest possible number of connected real
components, and prove that Arnold surfaces of these curves are standard.
Afterwards, we exhibit a procedure of modification "perestroika" of these
M-curves which allows to prove the Rokhlin's Conjecture.


  We devise a new formulation for the vertex coloring problem. Different from
other formulations, decision variables are associated with the pairs of
vertices. Consequently, colors will be distinguishable. Although the objective
function is fractional, it can be replaced by a piece-wise linear convex
function. Numerical experiments show that our formulation has significantly
good performance for dense graphs.


  Quantum optics did not, and could not, flourish without the laser. The
present paper is not about the principles of laser construction, still less a
history of how the laser was invented. Rather, it addresses the question: what
are the fundamental features that distinguish laser light from thermal light?
The obvious answer, "laser light is coherent", is, I argue, so vague that it
must be put aside at the start, albeit to revisit later. A more specific,
quantum theoretic, version, "laser light is in a coherent state", is simply
wrong in this context: both laser light and thermal light can equally well be
described by coherent states, with amplitudes that vary stochastically in
space. Instead, my answer to the titular question is that four principles are
needed: high directionality, monochromaticity, high brightness, and stable
intensity. Combining the first three of these principles suffices to show, in a
quantitative way --- involving, indeed, very large dimensionless quantities (up
to $\sim10^{51}$) --- that a laser must be constructed very differently from a
light bulb. This quantitative analysis is quite simple, and is easily relatable
to "coherence", yet is not to be found in any text-books on quantum optics to
my knowledge. The fourth principle is the most subtle and, perhaps
surprisingly, is the only one related to coherent states in the quantum optics
sense: it implies that the description in terms of coherent states is the only
simple description of a laser beam. Interestingly, this leads to the (not, as
it turns out, entirely new) prediction that narrowly filtered laser beams are
indistinguishable from similarly filtered thermal beams. I hope that other
educators find this material useful, it may contain surprises even for
researchers who have been in the field longer than I have.


  The third edition of the "international - Traveling Workshop on Interactions
between Sparse models and Technology" (iTWIST) took place in Aalborg, the 4th
largest city in Denmark situated beautifully in the northern part of the
country, from the 24th to 26th of August 2016. The workshop venue was at the
Aalborg University campus. One implicit objective of this biennial workshop is
to foster collaboration between international scientific teams by disseminating
ideas through both specific oral/poster presentations and free discussions. For
this third edition, iTWIST'16 gathered about 50 international participants and
features 8 invited talks, 12 oral presentations, and 12 posters on the
following themes, all related to the theory, application and generalization of
the "sparsity paradigm": Sparsity-driven data sensing and processing (e.g.,
optics, computer vision, genomics, biomedical, digital communication, channel
estimation, astronomy); Application of sparse models in non-convex/non-linear
inverse problems (e.g., phase retrieval, blind deconvolution, self
calibration); Approximate probabilistic inference for sparse problems; Sparse
machine learning and inference; "Blind" inverse problems and dictionary
learning; Optimization for sparse modelling; Information theory, geometry and
randomness; Sparsity? What's next? (Discrete-valued signals; Union of
low-dimensional spaces, Cosparsity, mixed/group norm, model-based,
low-complexity models, ...); Matrix/manifold sensing/processing (graph,
low-rank approximation, ...); Complexity/accuracy tradeoffs in numerical
methods/optimization; Electronic/optical compressive sensors (hardware).


  In this work, we study magnetoelastic interactions by means of ultrasound
experiments in $\alpha$-RuCl$_3$ -- a prototypical material for the Kitaev spin
model on the honeycomb lattice, with a possible spin-liquid state featuring
Majorana fermions and $\mathbb{Z}_{2}$-flux excitations. We present results of
the temperature and in-plane magnetic-field dependence of the sound velocity
and sound attenuation for several longitudinal and transverse phonon modes
propagating along high-symmetry crystallographic directions. A comprehensive
data analysis above the ordered state provides strong evidence of phonon
scattering by Majorana fermions. This scattering depends sensitively on the
value of the phonon velocities relative to the characteristic velocity of the
low-energy fermionic excitations describing the spin dynamics of the underlying
Kitaev magnet. Moreover, our data displays a distinct reduction of anisotropy
of the sound attenuation, consistent with randomization, generated by thermally
excited $\mathbb{Z}_2$ visons. We demonstrate the potential of phonon dynamics
as a promising probe for uncovering fractionalized excitations in
$\alpha$-RuCl$_3$ and provide new insights into the $H$-$T$ phase diagram of
this material.


  In this paper, we establish gradient continuity for solutions to \[
(\partial_t - \operatorname{div}(A(x) \nabla u))^s =f,\ s \in (1/2, 1), \] when
$f$ belongs to the scaling critical function space $L(\frac{n+2}{2s-1}, 1)$.
Our main results Theorems 1.1 and 1.2 can be seen as a nonlocal generalization
of a well-known result of Stein in the context of fractional heat type
operators and sharpens some of the previous gradient continuity results which
deals with $f$ in subcritical spaces. Our proof is based on an appropriate
adaptation of compactness arguments, which has its roots in a fundamental work
of Caffarelli in [13].


  The transition of a standard thin disk to a radiatively inefficient accretion
flow (RIAF) is expected to occur, when the accretion rate is close to the
critical rate. The radiative efficiencies of accretion flows accreting at rates
lower than the critical accretion rate become significantly lower than that of
standard thin disks. It is believed that the initial transition radius is small
just after the accretion mode transition, and then the transition radius
increases with decreasing accretion rate, as suggested by some theoretical
models and observations. Based on such variable transition radius models, we
derive how the dimensionless accretion rate evolves with time from the observed
Eddington ratio distribution for a sample of low-luminosity active galactic
nuclei in the local universe. The derived time-dependent accretion rates show a
rapid decrease after the transition of the standard thin accretion disk to a
RIAF, which is consistent with that derived from the hard X-ray background.


  Toward a partial classification of monomial ideals with $d$-linear
resolution, in this paper, some classes of $d$-uniform clutters which do not
have linear resolution, but every proper subclutter of them has a $d$-linear
resolution, are introduced and the regularity and Betti numbers of circuit
ideals of such clutters are computed. Also, it is proved that for given two
$d$-uniform clutters $\mathcal{C}_1, \mathcal{C}_2$, the Castelnuovo-Mumford
regularity of the ideal $I(\bar{\mathcal{C}_1 \cup \mathcal{C}_2})$ is equal to
the maximum of regularities of $I(\bar{\C}_1)$ and $I(\bar{\C}_2)$, whenever
$V(\mathcal{C}_1) \cap V(\mathcal{C}_2)$ is a clique or ${\rm
SC}(\mathcal{C}_1) \cap {\rm SC}(\mathcal{C}_2)=\emptyset$.
  As applications, alternative proofs are given for Fr\"oberg's Theorem on
linearity of edge ideal of graphs with chordal complement as well as for
linearity of generalized chordal hypergraphs defined by Emtander. Finally, we
find minimal free resolutions of the circuit ideal of a triangulation of a
pseudo-manifold and a homology manifold explicitly.


  Machine learning involves expensive data collection and training procedures.
Model owners may be concerned that valuable intellectual property can be leaked
if adversaries mount model extraction attacks. As it is difficult to defend
against model extraction without sacrificing significant prediction accuracy,
watermarking instead leverages unused model capacity to have the model overfit
to outlier input-output pairs. Such pairs are watermarks, which are not sampled
from the task distribution and are only known to the defender. The defender
then demonstrates knowledge of the input-output pairs to claim ownership of the
model at inference. The effectiveness of watermarks remains limited because
they are distinct from the task distribution and can thus be easily removed
through compression or other forms of knowledge transfer.
  We introduce Entangled Watermarking Embeddings (EWE). Our approach encourages
the model to learn features for classifying data that is sampled from the task
distribution and data that encodes watermarks. An adversary attempting to
remove watermarks that are entangled with legitimate data is also forced to
sacrifice performance on legitimate data. Experiments on MNIST, Fashion-MNIST,
CIFAR-10, and Speech Commands validate that the defender can claim model
ownership with 95\% confidence with less than 100 queries to the stolen copy,
at a modest cost below 0.81 percentage points on average in the defended
model's performance.


  We deform the Dorfman's and Sokolov's Hamiltonian operators by the
quasi-Miura transformation coming from the topological field theory and
investigate the deformed operators.


  In this work, we discuss techniques for coherently detecting turbo coded
orthogonal frequency division multiplexed (OFDM) signals, transmitted through
frequency selective Rayleigh (the magnitude of each channel tap is Rayleigh
distributed) fading channels having a uniform power delay profile. The channel
output is further distorted by a carrier frequency and phase offset, besides
additive white Gaussian noise (AWGN). A new frame structure for OFDM,
consisting of a known preamble, cyclic prefix, data and known postamble is
proposed, which has a higher throughput compared to the earlier work. A robust
turbo decoder is proposed, which functions effectively over a wide range of
signal-to-noise ratio (SNR). The key contribution to the good performance of
the practical coherent receiver is due to the use of a long preamble (512 QPSK
symbols), which is perhaps not specified in any of the current wireless
communication standards. We have also shown from computer simulations that, it
is possible to obtain even better BER performance, using a better code. A
simple and approximate Cramer-Rao bound on the variance of the frequency offset
estimation error for coherent detection, is derived. The proposed algorithms
are well suited for implementation on a DSP-platform.


  Rotating convective turbulence is ubiquitously found across geophysical
settings, such as surface and subsurface oceans, planetary atmospheres, molten
metal planetary cores, magma chambers, and magma oceans. Depending on the
thermal and material properties of the system, buoyant convection can be driven
thermally or compositionally, where a Prandtl number ($Pr = \nu / \kappa_i$)
defines the characteristic diffusion properties of the system, with $\kappa_i =
\kappa_T$ representing thermal diffusion and $\kappa_i = \kappa_C$ representing
chemical diffusion. These numbers vary widely for geophysical systems; for
example, the liquid iron undergoing thermal-compositional convection in Earth's
core is defined by $Pr_T \approx 0.1$ and $Pr_C \approx 100$, while a
thermally-driven liquid silicate magma ocean is defined by $Pr_T \approx 100$.
Currently, most numerical and laboratory data for rotating convective flows
exists at $Pr = O(1)$; high $Pr$ rotating convection relevant to
compositionally-driven core flow and other systems is less commonly studied.
Here, we address this deficit by carrying out a broad suite of rotating
convection experiments made over a range of $Pr$ values, employing water and
three different silicone oils as our working fluids ($Pr = $ 6, 41, 206, and
993). Using measurements of flow velocities (Reynolds, $Re$) and heat transfer
efficiency (Nusselt, $Nu$), a baroclinic torque balance is found to describe
the turbulence regardless of Prandtl number so long as $Re$ is sufficiently
large ($Re \gtrsim 10$). Estimated turbulent scales are found to remain close
to onset scales in all experiments, a result that may extrapolate to planetary
settings. Lastly, we use our data to build $Pr$-dependent predictive
nondimensional and dimensional scaling relations for rotating convective
velocities that can be applied across a broad range of geophysical fluid
dynamical settings.


  Brain networks in fMRI are typically identified using spatial independent
component analysis (ICA), yet mathematical constraints such as sparse coding
and positivity both provide alternate biologically-plausible frameworks for
generating brain networks. Non-negative Matrix Factorization (NMF) would
suppress negative BOLD signal by enforcing positivity. Spatial sparse coding
algorithms ($L1$ Regularized Learning and K-SVD) would impose local
specialization and a discouragement of multitasking, where the total observed
activity in a single voxel originates from a restricted number of possible
brain networks.
  The assumptions of independence, positivity, and sparsity to encode
task-related brain networks are compared; the resulting brain networks for
different constraints are used as basis functions to encode the observed
functional activity at a given time point. These encodings are decoded using
machine learning to compare both the algorithms and their assumptions, using
the time series weights to predict whether a subject is viewing a video,
listening to an audio cue, or at rest, in 304 fMRI scans from 51 subjects.
  For classifying cognitive activity, the sparse coding algorithm of $L1$
Regularized Learning consistently outperformed 4 variations of ICA across
different numbers of networks and noise levels (p$<$0.001). The NMF algorithms,
which suppressed negative BOLD signal, had the poorest accuracy. Within each
algorithm, encodings using sparser spatial networks (containing more
zero-valued voxels) had higher classification accuracy (p$<$0.001). The success
of sparse coding algorithms may suggest that algorithms which enforce sparse
coding, discourage multitasking, and promote local specialization may capture
better the underlying source processes than those which allow inexhaustible
local processes such as ICA.


  The chemical equilibration of heavy quarks in a quark-gluon plasma proceeds
via annihilation or pair creation. For temperatures T much below the heavy
quark mass M, when kinetically equilibrated heavy quarks move very slowly, the
annihilation in the colour singlet channel is enhanced because the quark and
antiquark attract each other which increases their probability to meet, whereas
the octet contribution is suppressed. This is the so-called Sommerfeld effect.
It has not been taken into account in previous calculations of the chemical
equilibration rate, which are therefore incomplete for T < alphas^2 M. We
compute the leading-order equilibration rate in this regime; there is a large
enhancement in the singlet channel, but the rate is dominated by the octet
channel, and therefore the total effect is small. In the course of the
computation we demonstrate how operators that represent the annihilation of
heavy quarks in non-relativistic QCD can be incorporated into the
imaginary-time formalism.


  Machine learning (ML) is moving towards edge devices. However, ML models with
high computational demands and energy consumption pose challenges for ML
inference in resource-constrained environments, such as the deep sea. To
address these challenges, we propose a battery-free ML inference and model
personalization pipeline for microcontroller units (MCUs). As an example, we
performed fish image recognition in the ocean. We evaluated and compared the
accuracy, runtime, power, and energy consumption of the model before and after
optimization. The results demonstrate that, our pipeline can achieve 97.78%
accuracy with 483.82 KB Flash, 70.32 KB RAM, 118 ms runtime, 4.83 mW power, and
0.57 mJ energy consumption on MCUs, reducing by 64.17%, 12.31%, 52.42%, 63.74%,
and 82.67%, compared to the baseline. The results indicate the feasibility of
battery-free ML inference on MCUs.


  A recent line of work has shown that an overparametrized neural network can
perfectly fit the training data, an otherwise often intractable nonconvex
optimization problem. For (fully-connected) shallow networks, in the best case
scenario, the existing theory requires quadratic over-parametrization as a
function of the number of training samples. This paper establishes that linear
overparametrization is sufficient to fit the training data, using a simple
variant of the (stochastic) gradient descent. Crucially, unlike several related
works, the training considered in this paper is not limited to the lazy regime
in the sense cautioned against in [1, 2]. Beyond shallow networks, the
framework developed in this work for over-parametrization is applicable to a
variety of learning problems.


  Cosmic Reionization On Computers (CROC) is a long-term program of numerical
simulations of cosmic reionization. Its goal is to model fully
self-consistently (albeit not necessarily from the first principles) all
relevant physics, from radiative transfer to gas dynamics and star formation,
in simulation volumes of up to 100 comoving Mpc, and with spatial resolution
approaching 100 pc in physical units. In this method paper we describe our
numerical method, the design of simulations, and the calibration of numerical
parameters. Using several sets (ensembles) of simulations in 20 Mpc/h and 40
Mpc/h boxes with spatial resolution reaching 125 pc at z=6, we are able to
match the observed galaxy UV luminosity functions at all redshifts between 6
and 10, as well as obtain reasonable agreement with the observational
measurements of the Gunn-Peterson optical depth at z<6.


  We analyze the tunneling of a particle through a repulsive potential
resulting from an inverted harmonic oscillator in the quantum mechanical phase
space described by the Wigner function. In particular, we solve the partial
differential equations in phase space determining the Wigner function of an
energy eigenstate of the inverted oscillator. The reflection or transmission
coefficients $R$ or $T$ are then given by the total weight of all classical
phase space trajectories corresponding to energies below, or above the top of
the barrier given by the Wigner function.


  Matrix factorization is a widely adopted recommender system technique that
fits scalar rating values by dot products of user feature vectors and item
feature vectors. However, the formulation of matrix factorization as a scalar
fitting problem is not friendly to side information incorporation or multi-task
learning. In this paper, we replace the scalar values of the user rating matrix
by matrices, and fit the matrix values by matrix products of user feature
matrix and item feature matrix. Our framework is friendly to multitask learning
and side information incorporation. We use popularity data as side information
in our paper in particular to enhance the performance of matrix factorization
techniques. In the experiment section, we prove the competence of our method
compared with other approaches using both accuracy and fairness metrics. Our
framework is an ideal substitute for tensor factorization in context-aware
recommendation and many other scenarios.


  We describe Sunyaev-Zel'dovich (SZ) effect measurements and analysis of the
intracluster medium (ICM) pressure profiles of a set of 45 massive galaxy
clusters imaged using Bolocam at the Caltech Submillimeter Observatory. We have
used masses determined from Chandra X-ray observations to scale each cluster's
profile by the overdensity radius R500 and the mass-and-redshift-dependent
normalization factor P500. We deproject the average pressure profile of our
sample into 13 logarithmically spaced radial bins between 0.07R500 and 3.5R500.
We find that a generalized Navarro, Frenk, and White (gNFW) profile describes
our data with sufficient goodness-of-fit and best-fit parameters (C500, alpha,
beta, gamma, P0 = 1.18, 0.86, 3.67, 0.67, 4.29). We also use the X-ray data to
define cool-core and disturbed subsamples of clusters, and we constrain the
average pressure profiles of each of these subsamples. We find that given the
precision of our data the average pressure profiles of disturbed and cool-core
clusters are consistent with one another at R>~0.15R500, with cool-core systems
showing indications of higher pressure at R<~0.15R500. In addition, for the
first time, we place simultaneous constraints on the mass scaling of cluster
pressure profiles, their ensemble mean profile, and their radius-dependent
intrinsic scatter between 0.1R500 and 2.0R500. The scatter among profiles is
minimized at radii between ~0.2R500 and ~0.5R500, with a value of ~20%. The
best-fit mass scaling has a power-law slope of 0.49, which is shallower than
the nominal prediction of 2/3 from self-similar hydrostatic equilibrium models.
These results for the intrinsic scatter and mass scaling are largely consistent
with previous analyses, most of which have relied heavily on X-ray derived
pressures of clusters at significantly lower masses and redshifts compared to
our sample.


  We analyse the reheating in the modification of \nuMSM (Standard Model with
three right handed neutrinos with masses below the electroweak scale) where the
sterile neutrino providing the Dark Matter is generated in decays of the
additional inflaton field. We deduce that due to rather inefficient transfer of
energy from the inflaton to the Standard Model sector reheating tends to happen
at very low temperature, thus providing strict bounds on the coupling between
the inflaton and the Higgs particles. This in turn translates to the bound on
the inflaton mass, which appears to be very light 0.1 GeV <~ m_I <~ 10 GeV, or
slightly heavier then two Higgs masses 300 GeV <~ m_I <~ 1000 GeV.


  We are investigating a prototype virtual pinhole positron emission tomography
(VP-PET) system for small animal imaging applications. The PET detector modules
were made up of 1.3 mm lutetium-yttrium oxyorthosilicate (LYSO) arrays, and the
insert detectors consists of 0.6 mm pixelated Cadmium Zinc Telluride (CdZnTe).
To validate the imaging experiment, we conducted a Monte Carlo simulation for
the VP-PET system in Geant4 Application for Emission Tomography (GATE). For a
point source of Na-22 with 0.5 mm diameter, the filtered back-projection (FBP)
algorithm reconstructed PET image shows a resolution of 0.7 mm
full-width-at-half-maximum (FWHM). The system sensitivity is 0.46 cps/kBq at
the center of field view (CFOV) of the PET system with a source activity of
0.925 MBq and an energy resolution of 350-650 keV. A rod source phantom and a
Derenzo phantom with F-18 were also simulated to investigate the PET imaging
capability. GATE simulation indicated that two point sources with 0.5 mm
diameter 2 mm apart could be clearly separated using 0.6 mm pixelated CdZnTe
detectors as insert devices in a VP-PET system.


  We prove a Thomas--Yau-type conjecture for monotone Lagrangian tori
satisfying a symmetry condition in the complex projective plane
$\mathbb{CP}^2$. We show that such tori exist for all time under Lagrangian
mean curvature flow with surgery, undergoing at most a finite number of
surgeries before flowing to a minimal Clifford torus in infinite time.
Furthermore, we show that we can construct a torus with any finite number of
surgeries before convergence. Along the way, we prove many interesting
subsidiary results and develop methods which should be useful in studying
Lagrangian mean curvature flow in non-Calabi--Yau manifolds, even in
non-symmetric cases.


  This paper is concerned with the interpretation of velocity eigenstates for
unstable quantons, their relationship to space like momentum eigenstates for
such quantons and the explanation of Shirokovs contracting lifetimes for such
velocity eigenstates. It is an elaboration of a portion of the authors earlier
study.


  The main result of this letter is that SOC naturally arises as a result of
memory effects. We show that memory effects provide the mechanism for self
organization. A general procedure to investigate this issue in models that
display self organized critical behaviour is proposed and applied to some
example. The simplest class of models exhibiting self organized criticality
through this mechanism is introduced and discussed in some detail. PACS:
02.50-r, 05.40+j, 05.40jk


  We analyze an extended model of the Iterated Prisoner's Dilemma where agents
decide to play based on the data from their limited memory or recommendations.
The cooperators can decide whether to play with the matched opponent or not.
The agents' decisions are directly linked to their level of optimism since they
decide to play if they believe the opponent has a high probability of
cooperating. Optimism is precisely tuned by parameters optimism threshold and
tolerance. Our experiment showed that being optimistic is better for
cooperators as it leads to more accurate exploration in the multi-agent system,
which tolerates the vulnerability against defectors.


  We use a rectangular pulse to freeze the possibility of estimating the
coherent parameters ($\theta,\phi$) of a single qubit and the encoded
information. It is shown that, as the possibility of estimating the parameters
increases, the amount of encoded information decreases. The pulse strength and
the detuning between the qubit and the pulse have a different effect on the
estimation degree and the encoded information. We show that if the weight
parameter, $\theta$ is estimated, the encoded information depends on the
initial state settings. Meanwhile, the encoded information doesn't depend on
the estimated phase parameter,$\phi$. These results may be useful in the
context of quantum cryptography, teleportation and secure communication.


  To reduce cost, datacenter network operators are exploring blocking network
designs. An example of such a design is a "spine-free" form of a Fat-Tree, in
which pods directly connect to each other, rather than via spine blocks. To
maintain application-perceived performance in the face of dynamic workloads,
these new designs must be able to reconfigure routing and the inter-pod
topology. Gemini is a system designed to achieve these goals on commodity
hardware while reconfiguring the network infrequently, rendering these blocking
designs practical enough for deployment in the near future. The key to Gemini
is the joint optimization of topology and routing, using as input a robust
estimation of future traffic derived from multiple historical traffic matrices.
Gemini "hedges" against unpredicted bursts, by spreading these bursts across
multiple paths, to minimize packet loss in exchange for a small increase in
path lengths. It incorporates a robust decision algorithm to determine when to
reconfigure, and whether to use hedging. Data from tens of production fabrics
allows us to categorize these as either low-or high-volatility; these
categories seem stable. For the former, Gemini finds topologies and routing
with near-optimal performance and cost. For the latter, Gemini's use of
multi-traffic-matrix optimization and hedging avoids the need for frequent
topology reconfiguration, with only marginal increases in path length. As a
result, Gemini can support existing workloads on these production fabrics using
a spine-free topology that is half the cost of the existing topology on these
fabrics.


  Turbulent transport provides the main contribution to particle and energy
losses in tokamak plasmas, which control is of paramount importance for
forthcoming reactors such as the Divertor-Tokamak-Test (DTT) facility under
construction at ENEA Frascati. In this work we investigate the characteristic
features of drift turbulence at the plasma edge through 3D electro-static fluid
simulations. We outline the crucial role of the diffusion coefficient for the
emerging turbulent spectra and for the excitation of vortex structures or zonal
flows. Moreover, the impact of adding a poloidal magnetic component is
discussed considering also a radial shear, and the emergence of anisotropic
spectral features is emphasized. The analysis is extended to the case with
Dirichlet boundary conditions along the radial direction, instead of the
periodic ones usually employed in such kind of analyses.


  We introduce Neural Deformation Graphs for globally-consistent deformation
tracking and 3D reconstruction of non-rigid objects. Specifically, we
implicitly model a deformation graph via a deep neural network. This neural
deformation graph does not rely on any object-specific structure and, thus, can
be applied to general non-rigid deformation tracking. Our method globally
optimizes this neural graph on a given sequence of depth camera observations of
a non-rigidly moving object. Based on explicit viewpoint consistency as well as
inter-frame graph and surface consistency constraints, the underlying network
is trained in a self-supervised fashion. We additionally optimize for the
geometry of the object with an implicit deformable multi-MLP shape
representation. Our approach does not assume sequential input data, thus
enabling robust tracking of fast motions or even temporally disconnected
recordings. Our experiments demonstrate that our Neural Deformation Graphs
outperform state-of-the-art non-rigid reconstruction approaches both
qualitatively and quantitatively, with 64% improved reconstruction and 62%
improved deformation tracking performance.


  It is shown that Cooper pairs are a solution of the bipolaron problem for
model Fr\"{o}hlich Hamiltonian. The total energy of a pair for the initial
Fr\"{o}hlich Hamiltonian is found. Differences between the solutions for the
model and initial two-particle problems are discussed.


  Given an $m$-tuple of weights $\vec{v}=(v_1,\dots,v_m)$, we characterize the
classes of pairs $(w,\vec{v})$ involved with the boundedness properties of the
multilinear fractional integral operator from
$\prod_{i=1}^mL^{p_i}\left(v_i^{p_i}\right)$ into suitable Lipschitz spaces
associated to a parameter $\delta$, $\mathcal{L}_w(\delta)$. Our results
generalize some previous estimates not only for the linear case but also for
the unweighted problem in the multilinear context. We emphasize the study
related to the range of the parameters involved with the problem described
above, which is optimal in the sense that they become trivial outside of the
region obtained.
  We also exhibit nontrivial examples of pairs of weights in this region.


  We present the first two-loop calculation of the heavy quark energy shift in
lattice nonrelativistic QCD (NRQCD). This calculation allow us to extract a
preliminary prediction of $m_b(m_b, n_f = 5) = 4.25(12)$ GeV for the mass of
the b quark from lattice NRQCD simulations performed with a lattice of spacing
$a=0.12$fm. Our result is an improvement on a previous determination of the b
quark mass from unquenched lattice NRQCD simulations, which was limited by the
use of one-loop expressions for the energy shift. Our value is in good
agreement with recent results of $m_b(m_b) = 4.163(16)$ GeV from QCD sum rules
and $m_b(m_b, n_f = 5) = 4.170(25)$ GeV from realistic lattice simulations
using highly-improved staggered quarks. We employ a mixed strategy to simplify
our calculation. Ghost, gluon and counterterm contributions to the energy shift
and mass renormalisation are extracted from quenched high-beta simulations
whilst fermionic contributions are calculated using automated lattice
perturbation theory. Our results demonstrate the effectiveness of such a
strategy.


  The question whether a nonlinear localized mode (discrete soliton/breather)
can be mobile in a lattice has a standard interpretation in terms of the
Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases,
the PN barrier for strongly localized solutions becomes large, rendering these
essentially immobile. Several ways to improve the mobility by reducing the
PN-barrier have been proposed during the last decade, and the first part gives
a brief review of such scenarios in 1D and 2D. We then proceed to discuss two
recently discovered novel mobility scenarios. The first example is the 2D
Kagome lattice, where the existence of a highly degenerate, flat linear band
allows for a very small PN-barrier and mobility of highly localized modes in a
small-power regime. The second example is a 1D waveguide array in an active
medium with intrinsic (saturable) gain and damping, where exponentially
localized, travelling discrete dissipative solitons may exist as stable
attractors. Finally, using the framework of an extended Bose-Hubbard model, we
show that while quantum fluctuations destroy the mobility of slowly moving,
strongly localized classical modes, coherent mobility of rapidly moving states
survives even in a strongly quantum regime.


  We assume that, within the dense clusters of neurons that can be found in
nuclei, cells may interconnect via soma-to-soma interactions, in addition to
conventional synaptic connections. We illustrate this idea with a multi-layer
architecture (MLA) composed of multiple clusters of recurrent sub-networks of
spiking Random Neural Networks (RNN) with dense soma-to-soma interactions, and
use this RNN-MLA architecture for deep learning. The inputs to the clusters are
first normalised by adjusting the external arrival rates of spikes to each
cluster. Then we apply this architecture to learning from multi-channel
datasets. Numerical results based on both images and sensor based data, show
the value of this novel architecture for deep learning.


  Due to detector malfunctions and communication failures, missing data is
ubiquitous during the collection of traffic data. Therefore, it is of vital
importance to impute the missing values to facilitate data analysis and
decision-making for Intelligent Transportation System (ITS). However, existing
imputation methods generally perform zero pre-filling techniques to initialize
missing values, introducing inevitable noises. Moreover, we observe prevalent
over-smoothing interpolations, falling short in revealing the intrinsic
spatio-temporal correlations of incomplete traffic data. To this end, we
propose Mask-Aware Graph imputation Network: MagiNet. Our method designs an
adaptive mask spatio-temporal encoder to learn the latent representations of
incomplete data, eliminating the reliance on pre-filling missing values.
Furthermore, we devise a spatio-temporal decoder that stacks multiple blocks to
capture the inherent spatial and temporal dependencies within incomplete
traffic data, alleviating over-smoothing imputation. Extensive experiments
demonstrate that our method outperforms state-of-the-art imputation methods on
five real-world traffic datasets, yielding an average improvement of 4.31% in
RMSE and 3.72% in MAPE.


  Advances in our understanding of the physical universe have impacted
dramatically on how we view ourselves. Right at the core of all modern thinking
about the universe is the assumption that dynamics is an elemental feature that
exists without question. However, ongoing research into the quantum nature of
time is challenging this view: my recently-introduced quantum theory of time
suggests that dynamics may be a phenomenological consequence of a fundamental
violation of time reversal symmetry. I show here that there is consistency
between the new theory and the block universe view. I also discuss the new
theory in relation to the human experience of existing in the present moment,
able to reflect on the past and contemplate a future that is yet to happen.


  We present electron-tunneling spectroscopy of slightly overdoped Bi2212
single crystals with Tc = 87 - 90 K in a temperature range between 14 K and 290
K using a break-junction technique. The pseudogap which has been detected above
Tc appears at T* = 280 K. The analysis of the spectra shows that there is a
contribution to the pseudogap above Tc, which disappears approximately at 110 -
115 K. We associate this contribution with the presence of incoherent Cooper
pairs.


  We performed a Penning trap mass measurement of $^{61}{\rm Zn}$ at the
National Superconducting Cyclotron Laboratory and NuShellX calculations of the
$^{61}{\rm Zn}$ and $^{62}{\rm Ga}$ structure using the GXPF1A Hamiltonian to
obtain improved estimates of the $^{61}{\rm Zn}(p,\gamma)^{62}{\rm Ga}$ and
$^{60}{\rm Cu}(p,\gamma)^{61}{\rm Zn}$ reaction rates. Surveying astrophysical
conditions for type-I X-ray bursts with the code MESA, implementing our
improved reaction rates, and taking into account updated nuclear masses for
$^{61}{\rm V}$ and $^{61}{\rm Cr}$ from the recent literature, we refine the
neutrino luminosity from the important mass number $A=61$ urca cooling source
in accreted neutron star crusts. This improves our understanding of the thermal
barrier between deep heating in the crust and the shallow depths where extra
heat is needed to explain X-ray superbursts, as well as the expected signature
of crust urca neutrino emission in light curves of cooling transients.


  An important dividing line in the class of unstable theories is being
NSOP$_1$, which is more general than being simple. In NSOP$_1$ theories forking
independence may not be as well-behaved as in stable or simple theories, so it
is replaced by another independence notion, called Kim-independence. We
generalise Kim-independence over models in NSOP$_1$ theories to positive logic
-- a proper generalisation of first-order logic where negation is not built in,
but can be added as desired. For example, an important application is that we
can add hyperimaginary sorts to a positive theory to get another positive
theory, preserving NSOP$_1$ and various other properties. We prove that, in a
thick positive NSOP$_1$ theory, Kim-independence over existentially closed
models has all the nice properties that it is known to have in a first-order
NSOP$_1$ theory. We also provide a Kim-Pillay style theorem, characterising
which thick positive theories are NSOP$_1$ by the existence of a certain
independence relation. Furthermore, this independence relation must then be the
same as Kim-independence. Thickness is the mild assumption that being an
indiscernible sequence is type-definable.
  In first-order logic Kim-independence is defined in terms of Morley sequences
in global invariant types. These may not exist in thick positive theories. We
solve this by working with Morley sequences in global Lascar-invariant types,
which do exist in thick positive theories. We also simplify certain tree
constructions that were used in the study of Kim-independence in first-order
theories. In particular, we only work with trees of finite height.


  In this paper we study the homogeneous interiors of black holes possessing
SU(2) Yang-Mills fields subject to corrections inspired by loop quantum
gravity. The systems studied possess both magnetic and induced electric
Yang-Mills fields. We consider the system of equations both with and without
Wilson loop corrections to the Yang-Mills potential. The structure of the
Yang-Mills Hamiltonian along with the restriction to homogeneity allows for an
anomaly free effective quantization. In particular we study the bounce which
replaces the classical singularity and the behavior of the Yang-Mills fields in
the quantum corrected interior, which possesses topology $R\times S^{2}$.
Beyond the bounce the magnitude of the Yang-Mills electric field asymptotically
grows monotonically. This results in an ever expanding $R$ sector even though
the two-sphere volume is asymptotically constant. The results are similar with
and without Wilson loop corrections on the Yang-Mills potential.


  We present a new method GTSNE to visualize high-dimensional data points in
the two dimensional map. The technique is a variation of t-SNE that produces
better visualizations by capturing both the local neighborhood structure and
the macro structure in the data. This is particularly important for
high-dimensional data that lie on continuous low-dimensional manifolds. We
illustrate the performance of GTSNE on a wide variety of datasets and compare
it the state of art methods, including t-SNE and UMAP. The visualizations
produced by GTSNE are better than those produced by the other techniques on
almost all of the datasets on the macro structure preservation.


  We prove that, for $X$, $Y$, $A$ and $B$ matrices with entries in a
non-commutative ring such that $[X_{ij},Y_{k\ell}]=-A_{i\ell} B_{kj}$,
satisfying suitable commutation relations (in particular, $X$ is a Manin
matrix), the following identity holds: $ \mathrm{coldet} X \mathrm{coldet} Y =
< 0 | \mathrm{coldet} (a A + X (I-a^{\dagger} B)^{-1} Y) |0 > $. Furthermore,
if also $Y$ is a Manin matrix, $ \mathrm{coldet} X \mathrm{coldet} Y =\int
\mathcal{D}(\psi, \psi^{\dagger}) \exp [ \sum_{k \geq 0} \frac{1}{k+1}
(\psi^{\dagger} A \psi)^{k} (\psi^{\dagger} X B^k Y \psi) ] $. Notations: $ < 0
|$, $| 0 >$, are respectively the bra and the ket of the ground state,
$a^{\dagger}$ and $a$ the creation and annihilation operators of a quantum
harmonic oscillator, while $\psi^{\dagger}_i$ and $\psi_i$ are Grassmann
variables in a Berezin integral. These results should be seen as a
generalization of the classical Cauchy-Binet formula, in which $A$ and $B$ are
null matrices, and of the non-commutative generalization, the Capelli identity,
in which $A$ and $B$ are identity matrices and
$[X_{ij},X_{k\ell}]=[Y_{ij},Y_{k\ell}]=0$.


  Magnetic fields are present on all scales in the Universe. While we
understand the processes which amplify the fields fairly well, we do not have a
"natural" mechanism to generate the small initial seed fields. By using fully
relativistic cosmological perturbation theory and going beyond the usual
confines of linear theory we show analytically how magnetic fields are
generated. This is the first analytical calculation of the magnetic field at
second order, using gauge-invariant cosmological perturbation theory, and
including all the source terms. To this end, we have rederived the full set of
governing equations independently. Our results suggest that magnetic fields of
the order of $10^{-30}$ G can be generated (although this depends on the small
scale cut-off of the integral), which is largely in agreement with previous
results that relied upon numerical calculations. These fields are likely too
small to act as the primordial seed fields for dynamo mechanisms.


  The low-spin structure of the semimagic 64Ni nucleus has been considerably
expanded: combining four experiments, several 0+ and 2+ excited states were
identified below 4.5 MeV, and their properties established. The Monte Carlo
shell model accounts for the results and unveils an unexpectedly complex
landscape of coexisting shapes: a prolate 0+ excitation is located at a
surprisingly high energy (3463 keV), with a collective 2+ state 286 keV above
it, the first such observation in Ni isotopes. The evolution in excitation
energy of the prolate minimum across the neutron N = 40 subshell gap highlights
the impact of the monopole interaction and its variation in strength with N.