  In this paper, a joint task, spectrum, and transmit power allocation problem
is investigated for a wireless network in which the base stations (BSs) are
equipped with mobile edge computing (MEC) servers to jointly provide
computational and communication services to users. Each user can request one
computational task from three types of computational tasks. Since the data size
of each computational task is different, as the requested computational task
varies, the BSs must adjust their resource (subcarrier and transmit power) and
task allocation schemes to effectively serve the users. This problem is
formulated as an optimization problem whose goal is to minimize the maximal
computational and transmission delay among all users. A multi-stack
reinforcement learning (RL) algorithm is developed to solve this problem. Using
the proposed algorithm, each BS can record the historical resource allocation
schemes and users' information in its multiple stacks to avoid learning the
same resource allocation scheme and users' states, thus improving the
convergence speed and learning efficiency. Simulation results illustrate that
the proposed algorithm can reduce the number of iterations needed for
convergence and the maximal delay among all users by up to 18% and 11.1%
compared to the standard Q-learning algorithm.


  Baryon acoustic oscillation data from the first year of the Dark Energy
Spectroscopic Instrument (DESI) provide near percent-level precision of cosmic
distances in seven bins over the redshift range $z=0.1$-$4.2$. We use this
data, together with other distance probes, to constrain the cosmic expansion
history using some well-motivated physical classes of dark energy. In
particular, we explore three physics-focused behaviors of dark energy from the
equation of state and energy density perspectives: the thawing class (matching
many simple quintessence potentials), emergent class (where dark energy comes
into being recently, as in phase transition models), and mirage class (where
phenomenologically the distance to CMB last scattering is close to that from a
cosmological constant $\Lambda$ despite dark energy dynamics). All three
classes fit the data at least as well as $\Lambda$CDM, and indeed can improve
on it by $\Delta\chi^2\approx -5$ to $-17$ for the combination of DESI BAO with
CMB and supernova data, while having one more parameter. The mirage class does
essentially as well as $w_0w_a$CDM while having one less parameter. These
classes of dynamical behaviors highlight worthwhile avenues for further
exploration into the nature of dark energy.


  Let Gamma be a torsion-free group which is hyperbolic relative to a
collection of free abelian subgroups. We construct Makanin-Razborov diagrams
for Gamma. We also prove that every system of equations over Gamma is
equivalent to a finite subsystem, and a number of structural results about
Gamma-limit groups.


  We consider the design of identical one-bit probabilistic quantizers for
distributed estimation in sensor networks. We assume the parameter-range to be
finite and known and use the maximum Cram\'er-Rao Lower Bound (CRB) over the
parameter-range as our performance metric. We restrict our theoretical analysis
to the class of antisymmetric quantizers and determine a set of conditions for
which the probabilistic quantizer function is greatly simplified. We identify a
broad class of noise distributions, which includes Gaussian noise in the
low-SNR regime, for which the often used threshold-quantizer is found to be
minimax-optimal. Aided with theoretical results, we formulate an optimization
problem to obtain the optimum minimax-CRB quantizer. For a wide range of noise
distributions, we demonstrate the superior performance of the new quantizer -
particularly in the moderate to high-SNR regime.


  Oscillations of flagella and cilia play an important role in biology, which
motivates the idea of functional mimicry as part of bio-inspired applications.
Nevertheless, it still remains challenging to drive their artificial
counterparts to oscillate via a steady, homogeneous stimulus. Combining theory
and simulations, we demonstrate a strategy to achieve this goal by using an
elasto-electro-hydrodynamic instability. In particular, we show that applying a
uniform DC electric field can produce self-oscillatory motion of a microrobot
composed of a dielectric particle and an elastic filament. Upon tuning the
electric field and filament elasticity, the microrobot exhibits three distinct
behaviors: a stationary state, undulatory swimming and steady spinning, where
the swimming behavior stems from an instability emerging through a Hopf
bifurcation. Our results imply the feasibility of engineering self-oscillations
by leveraging the elasto-viscous response to control the type of bifurcation
and the form of instability. We anticipate that our strategy will be useful in
a broad range of applications imitating self-oscillatory natural phenomena and
biological processes.


  A family F is intersecting if any two members have a nonempty intersection.
Erdos, Ko, and Rado showed that |F|\leq {n-1\choose k-1} holds for an
intersecting family of k-subsets of [n]:={1,2,3,...,n}, n\geq 2k. For n> 2k the
only extremal family consists of all k-subsets containing a fixed element. Here
a new proof is presented. It is even shorter than the classical proof of Katona
using cyclic permutations, or the one found by Daykin applying the
Kruskal-Katona theorem.


  QED processes at electron-positron colliders are considerd. We present
differential cross-sections for large-angle Bhabha scattering, annihilation
into muons and photons. Radiative corrections in the first order are taken into
account exactly. Leading logarithmic contributions are calculated in all orders
by means of the structure-function method. An accuracy of the calculation can
be estimated about 0.2%.


  We provide succinct covariant amplitude decompositions of 2-body weak
hadronic decays, with which to compare data, including exclusive rates,
helicity amplitudes and polarizations. For weak decays, the systematic
dependence of these amplitudes on masses and quantum numbers of participating
particles are determined within a factor of about two by the CKM angles and the
Fermi constant so theoretical models need to be much more accurate if they are
to be convincing.


  The distance-dependent interaction of an emitter with a plasmonic
nanoparticle or surface forms the basis of the field of plexitonics.
Semiconductor quantum dots (QDs) are robust emitters due to their
photostability, and offer the possibility of understanding the fundamental
photophysics between one emitter and one metal nanoparticle. A key enabling
challenge is the formation of systems containing both QDs and plasmonic
nanoparticles in high purity. We present the translation of DNA-based
self-assembly techniques to assemble metal and semiconductor nanocrystals into
discrete hybrid structures, including dimers, of high purity. This method gives
control over the interparticle separation, geometry, and ratio of QD:metal
nanoparticle, as well as the spectral properties of the metal/QD components in
the assembly to allow investigation of plasmon-exciton interaction. The hybrid
assemblies show the expected enhancement in steady-state photoluminescence
accompanied by an increase in the QD emission rate for assemblies with a strong
overlap between the QD emission and localised surface plasmon resonance. In
contrast, lengthening of the QD emission lifetime (a reduction of the emission
rate) of up to 1.7-fold, along with an enhancement in steady-state PL of 15-75%
is observed upon detuning of the QD and metal nanoparticle spectral properties.
This understood in terms of the Purcell effect, where the gold nanoparticle
acts as a damped, nanoscale cavity. Considering the metal nanoparticle using
generalised nonlocal optical response theory (GNOR) and the QD as an open
quantum system, the response is driven by the interference experienced by the
emitter for parallel and perpendicular field orientations. This provides a
mechanism for control of the emission rate of a QD by a metal nanoparticle
across a much wider range of lifetimes than previously understood.


  We develop the theory of veering triangulations on oriented surfaces adapted
to moduli spaces of half-translation surfaces. We use veering triangulations to
give a coding of the Teichm\"uller flow on connected components of strata of
quadratic differentials. We prove that this coding, given by a countable shift,
has an approximate product structure and a roof function with exponential
tails. This makes it conducive to the study of the dynamics of Teichm\"uller
flow.


  The goal of this small note is to give a more concise proof of a result due
to Berthelot, Esnault, and R\"ulling. For a regular, proper, and flat scheme
$X$ over a discrete valuation ring of mixed characteristic $(0,p)$, it relates
the vanishing of the cohomology of the structure sheaf of the generic fibre of
$X$ with the vanishing of the Witt vector cohomology of its special fibre. We
use as a critical ingredient results and constructions by Beilinson and
Nekov\'a\v{r}--Nizio{\l} related to the $h$-topos over a $p$-adic field.


  We investigate theoretically the collective radiance characteristics of an
atomic ensemble with the simultaneous decay of two atoms. We show that the
two-atom decay can significantly suppress the steady-state collective radiance
of the atoms, expanding the region of subradiance. In the steady-state
subradiance regime, the system is in an entangled state, and the mean
populations of the system in the excited state and ground state of the atoms
are almost equal. The processes of the two-atom decay can be demonstrated by
the population distribution of the system state on the Dicke ladder. Moreover,
we show the correlation property of the emitted light from the atomic ensemble,
where the correlation function is rewritten in the presence of the two-atom
decay. We find that the emitted photons of steady state only show bunching in
the case of two-atom decay. This work broadens the realm of collective
radiance, with potential applications for quantum information processing.


  At the inner edge of a protoplanetary disk solids are illuminated by stellar
light. This illumination heats the solids and creates temperature gradients
along their surfaces. Interactions with ambient gas molecules lead to a radial
net gas flow. Every illuminated solid particle within the edge is an individual
small gas pump transporting gas inward. In total the inner edge can provide
local mass flow rates as high as $\dot{M} = 10^{-5} M_{\odot}$ yr$^{-1}$.


  There are two ways to compute Poincar\'e-Dulac normal forms of systems of
ODEs. Under the original approach used by Poincar\'e the normalizing
transformation is explicitly computed. On each step, the normalizing procedure
requires the substitution of a polynomial to a series. Under the other
approach, a normal form is computed using Lie transformations. In this case,
the changes of coordinates are performed as actions of certain infinitesimal
generators. In both cases, on each step the homological equation is solved in
the vector space of polynomial vector fields $V^n_j$ where each component of
the vector field is a homogeneous polynomial of degree $j$. We present the
third way of computing normal forms of polynomial systems of ODEs where the
coefficients of all terms are parameters. Although we use Lie transforms the
homological equation is solved not in $V^n_j$ but in the vector space of
polynomial vector fields where each component is a homogeneous polynomial in
the parameters of the system. It is shown that the space of the parameters is a
kind of dual space and, the computation of normal forms can be performed in the
space of parameters treated as the space of generalized vector fields. The
approach provides a simple way to parallelize the normal form computations
opening the way to compute normal forms up to higher order than under
previously known two approaches.


  Advances in AI have led to new types of technical debt in software
engineering projects. AI-based competition platforms face challenges due to
rapid prototyping and a lack of adherence to software engineering principles by
participants, resulting in technical debt. Additionally, organizers often lack
methods to evaluate platform quality, impacting sustainability and
maintainability. In this research, we identify and categorize types of
technical debt in AI systems through a scoping review. We develop a
questionnaire for assessing technical debt in AI competition platforms,
categorizing debt into various types, such as algorithm, architectural, code,
configuration, data etc. We introduce Accessibility Debt, specific to AI
competition platforms, highlighting challenges participants face due to
inadequate platform usability. Our framework for managing technical debt aims
to improve the sustainability and effectiveness of these platforms, providing
tools for researchers, organizers, and participants.


  We study the propagation of cold-atom wave packets in an interferometer with
a Mach-Zehnder topology based on the dynamical phase of Bloch oscillation in a
weakly forced optical lattice with a narrow potential barrier that functions as
a cold-atom wave packet splitter. We calculate analytically the atomic wave
function, and show that the expected number of atoms in the two outputs of the
interferometer oscillates rapidly as a function of the angle between the
potential barrier and the forcing direction with period proportional to the
external potential difference across a lattice spacing divided by the lattice
band energy scale. The interferometer can be used as a high precision force
probe whose principle of operation is different from current interferometers
based on the overall position of Bloch oscillating wave packets.


  Until now, there have been developed many arbitrated quantum signature
schemes implemented with a help of a trusted third party. In order to guarantee
the unconditional security, most of them take advantage of the optimal quantum
one-time encryption method based on Pauli operators. However, we in this paper
point out that the previous schemes only provides a security against total
break and actually show that there exists a simple existential forgery attack
to validly modify the transmitted pair of message and signature. In addition,
we also provide a simple method to recover the security against the proposed
attack.


  General cylindrical waves are the simplest axisymmetrical gravitational waves
that contain both $+$ and $\times$ modes of polarization. In this paper, we
have studied the evolution of general cylindrical gravitational waves in the
realm of the characteristic scheme with a numerical code based on the
Galerkin-Collocation method. The investigation consists of the numerical
realization of concepts such as Bondi mass and the news functions adapted to
cylindrical symmetry. The Bondi mass decays due to the presence of the news
functions associated with both polarization modes. We have interpreted that
each polarization mode as channels from which mass is extracted. Under this
perspective, we have presented the enhancement effect of the polarization mode
$+$ due to the nonlinear interaction with the mode $\times$. After discussing
the role of matter in cylindrical symmetry, we have extended the numerical code
to include electromagnetic fields.


  We connect topological changes that can occur in $3$-space via surgery, with
black hole formation, the formation of wormholes and new generalizations of
these phenomena, including relationships between quantum entanglement and
wormhole formation. By considering the initial manifold as the $3$-dimensional
spatial section of spacetime, we describe the changes of topology occurring in
these processes by determining the resulting $3$-manifold and its fundamental
group. As these global changes are induced by local processes, we use the local
form of Morse functions to provide an algebraic formulation of their temporal
evolution and propose a potential energy function which, in some cases, could
give rise to the local forces related to surgery. We further show how this
topological perspective gives new insight for natural phenomena exhibiting
surgery, in all dimensions, while emphasizing the $3$-dimensional case, which
describes cosmic phenomena. This work makes new bridges between topology and
natural sciences and creates a platform for exploring geometrical physics.


  A stability criterion is derived in general relativity for self-similar
solutions with a scalar field and those with a stiff fluid, which is a perfect
fluid with the equation of state $P=\rho$. A wide class of self-similar
solutions turn out to be unstable against kink mode perturbation. According to
the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be
a critical solution for the spherical collapse of a stiff fluid if we allow
sufficiently small discontinuity in the density gradient field in the initial
data sets. The self-similar scalar-field solution, which was recently found
numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19}
6359), is also unstable. Both the flat Friedmann universe with a scalar field
and that with a stiff fluid suffer from kink instability at the particle
horizon scale.


  In this paper, we study the geometry of $GT-$varieties $X_{d}$ with group a
finite cyclic group $\Gamma \subset \mathrm{GL}(n+1,\mathbb{K})$ of order $d$.
We prove that the homogeneous ideal $\mathrm{I}(X_{d})$ of $X_{d}$ is generated
by binomials of degree at most $3$ and we provide examples reaching this bound.
We give a combinatorial description of the canonical module of the homogeneous
coordinate ring of $X_{d}$ and we show that it is generated by monomial
invariants of $\Gamma$ of degree $d$ and $2d$. This allows us to characterize
the Castelnuovo-Mumford regularity of the homogeneous coordinate ring of $X_d$.
Finally, we compute the cohomology table of the normal bundle of the so called
$RL-$varieties. They are projections of the Veronese variety
$\nu_{d}(\mathbb{P}^{n}) \subset \mathbb{P}^{\binom{n+d}{n}-1}$ which naturally
arise from level $GT-$varieties.


  From FORTRAN to NumPy, arrays have revolutionized how we express computation.
However, arrays in these, and almost all prominent systems, can only handle
dense rectilinear integer grids. Real world arrays often contain underlying
structure, such as sparsity, runs of repeated values, or symmetry. Support for
structured data is fragmented and incomplete. Existing frameworks limit the
array structures and program control flow they support to better simplify the
problem.
  In this work, we propose a new programming language, Finch, which supports
both flexible control flow and diverse data structures. Finch facilitates a
programming model which resolves the challenges of computing over structured
arrays by combining control flow and data structures into a common
representation where they can be co-optimized. Finch automatically specializes
control flow to data so that performance engineers can focus on experimenting
with many algorithms. Finch supports a familiar programming language of loops,
statements, ifs, breaks, etc., over a wide variety of array structures, such as
sparsity, run-length-encoding, symmetry, triangles, padding, or blocks. Finch
reliably utilizes the key properties of structure, such as structural zeros,
repeated values, or clustered non-zeros. We show that this leads to dramatic
speedups in operations such as SpMV and SpGEMM, image processing, graph
analytics, and a high-level tensor operator fusion interface.


  We analyze how the spectrum of synchrotron and inverse Compton radiation from
a narrow relativistic jet changes with the observation angle. It is shown that
diversity of acceleration mechanisms (in particular, taking the converter
mechanism (Derishev et al. 2003) into account) allows for numerous
modifications of the observed spectrum. In general, the off-axis emission in
GeV-TeV energy range appears to be brighter, has a much harder spectrum and a
much higher cut-off frequency compared to the values derived from Doppler
boosting considerations alone. The magnitude of these effects depends on the
details of particle acceleration mechanisms, what can be used to discriminate
between different models.
  One of the implications is the possibility to explain high-latitude
unidentified EGRET sources as off-axis but otherwise typical relativistic-jet
sources, such as blazars. We also discuss the broadening of beam pattern in
application to bright transient jet sources, such as Gamma-Ray Bursts.


  This paper proposes a neuro-rough model based on multi-layered perceptron and
rough set. The neuro-rough model is then tested on modelling the risk of HIV
from demographic data. The model is formulated using Bayesian framework and
trained using Monte Carlo method and Metropolis criterion. When the model was
tested to estimate the risk of HIV infection given the demographic data it was
found to give the accuracy of 62%. The proposed model is able to combine the
accuracy of the Bayesian MLP model and the transparency of Bayesian rough set
model.


  Heat-capacity (C) and ac susceptibility measurements have been performed on
the spin-chain compounds, Sr3ZnRhO6 and Ca3NiMnO6, to establish their magnetic
behavior and to explore whether there are magnetic frustration effects due to
antiferromagnetic coupling of the chains arranged in a triangular fashion.
While the paramagnetic Curie temperatures have been known to be large with a
negative sign, as though antiferromagnetic interaction is very strong, the
results establish that (i) the former apparently undergoes inhomogeneous
magnetic ordering only around 15 K, however without spin-glass anomalies, and
(ii) the latter orders antiferromagnetically at a relatively low temperature
(17 K). Thus, the magnetic frustration manifests differently in these
compounds.


  We study the critical bosonic O(N) vector model with quenched random mass
disorder in the large N limit. Due to the replicated action which is sometimes
not bounded from below, we avoid the replica trick and adopt a traditional
approach to directly compute the disorder averaged physical observables. At
$N=\infty$, we can exactly solve the disordered model. The resulting low energy
behavior can be described by two scale invariant theories, one of which has an
intrinsic scale. At finite $N$, we find that the previously proposed attractive
disordered fixed point at $d=2$ continues to exist at $d=2+\epsilon$ spatial
dimensions. We also studied the system in the $3<d<4$ spatial dimensions where
the disorder is relevant at the Gaussian fixed point. However, no physical
attractive fixed point is found right below four spatial dimensions.
Nevertheless, the stable fixed point at $2+\epsilon$ dimensions can still
survive at $d=3$ where the system has experimental realizations. Some critical
exponents are predicted in order to be checked by future numerics and
experiments.


  Following our recent conjecture to model the phenomenona of
antiferromagnetism and superconductivity by quantum symmetry groups, we propose
in the present note three toy models, namely, one based on SO_{q}(3) the other
two constructed with the SO_{q}(4) and SO_{q}(5) quantum groups. Possible
motivations and rationale for these choices are outlined. One of the prime
motivations underlying our proposal is the experimental observation of stripe
structure [phase] in high T_c superconductivity [HTSC] materials. A number of
experimental techniques have recently observed that the CuO_{2} are rather
inhomogeneous, providing evidence for phase separation into a two component
system. i.e. carrier-rich and carrier-poor regions. In particular, extended
x-ray absorption fine structure [EXAFS] demonstrated that these domains forms
stripes of undistorted and distorted local structures alternating with
mesoscopic length scale comparable with coherence length in HTSC.
  Evidence for our conjecture is discussed.


  Mixed Boolean-Arithmetic (MBA) obfuscation is a common technique used to
transform simple expressions into semantically equivalent but more complex
combinations of boolean and arithmetic operators. Its widespread usage in DRM
systems, malware, and software protectors is well documented. In 2021, Liu et
al. proposed a groundbreaking method of simplifying linear MBAs, utilizing a
hidden two-way transformation between 1-bit and n-bit variables. In 2022,
Reichenwallner et al. proposed a similar but more effective method of
simplifying linear MBAs, SiMBA, relying on a similar but more involved theorem.
However, because current linear MBA simplifiers operate in 1-bit space, they
cannot handle expressions which utilize constants inside of their bitwise
operands, e.g. (x&1), (x&1111) + (y&1111). We propose an extension to SiMBA
that enables simplification of this broader class of expressions. It surpasses
peer tools, achieving efficient simplification of a class of MBAs that current
simplifiers struggle with.


  Side-channel attacks on practical quantum key distribution systems compromise
its security. Although some of these attacks can be taken into account, the
general recipe of how to eliminate all side-channel flaws is still missing. In
this work, we propose a method for estimation of the total passive side-channel
information leakage from the Alice's light source. The method relies on
Hong-Ou-Mandel interference between different signals emitted by Alice, which
reveals their overall mode mismatch without the necessity to measure all
individual degrees of freedom independently. We include experimental values of
interference visibility in the security proof for the decoy-state BB84
protocol, and lower-bound the secure key rate for realistic light sources. The
obtained results provide a tool that can be used for certification of the
current QKD systems and pave the way towards the loophole-free design of the
future ones.


  Z_2-graded Schwinger terms for neutral particles in 1 and 3 space dimensions
are considered.


  We report our progress in data analysis on two-point correlation functions of
the $B$ meson using sequential Bayesian method. The data set of measurement is
obtained using the Oktay-Kronfeld (OK) action for the bottom quarks (valence
quarks) and the HISQ action for the light quarks on the MILC HISQ lattices. We
find that the old initial guess for the $\chi^2$ minimizer in the fitting code
is poor enough to slow down the analysis somewhat. In order to find a better
initial guess, we adopt the Newton method. We find that the Newton method
provides a natural test to check whether the $\chi^2$ minimizer finds a local
minimum or the global minimum, and it also reduces the number of iterations
dramatically.


  We study the evolution of cooperation in structured populations within
popular models of social dilemmas, whereby simple coevolutionary rules are
introduced that may enhance players abilities to enforce their strategy on the
opponent. Coevolution thus here refers to an evolutionary process affecting the
teaching activity of players that accompanies the evolution of their
strategies. Particularly, we increase the teaching activity of a player after
it has successfully reproduced, yet we do so depending on the disseminated
strategy. We separately consider coevolution affecting either only the
cooperators or only the defectors, and show that both options promote
cooperation irrespective of the applied game. Opposite to intuitive reasoning,
however, we reveal that the coevolutionary promotion of players spreading
defection is, in the long run, more beneficial for cooperation than the
likewise promotion of cooperators. We explain the contradictory impact of the
two considered coevolutionary rules by examining the differences between
resulting heterogeneities that segregate participating players, and
furthermore, demonstrate that the influential individuals completely determine
the final outcome of the games. Our findings are immune to changes defining the
type of considered social dilemmas and highlight that the heterogeneity of
players, resulting in a positive feedback mechanism, is a fundamental property
promoting cooperation in groups of selfish individuals.


  Motivated by the projectable Horava--Lifshitz model/mimetic matter scenario,
we consider a particular modification of standard gravity, which manifests as
an imperfect low pressure fluid. While practically indistinguishable from a
collection of non-relativistic weakly interacting particles on cosmological
scales, it leaves drastically different signatures in the Solar system. The
main effect stems from gravitational focusing of the flow of Imperfect Dark
Matter passing near the Sun. This entails strong amplification of Imperfect
Dark Matter energy density compared to its average value in the surrounding
halo. The enhancement is many orders of magnitude larger than in the case of
Cold Dark Matter, provoking deviations of the metric in the second order in the
Newtonian potential. Effects of gravitational focusing are prominent enough to
substantially affect the planetary dynamics. Using the existing bound on the
PPN parameter $\beta_{PPN}$, we deduce a stringent constraint on the unique
constant of the model.


  A central design problem in game theoretic analysis is the estimation of the
players' utilities. In many real-world interactive situations of human decision
making, including human driving, the utilities are multi-objective in nature;
therefore, estimating the parameters of aggregation, i.e., mapping of
multi-objective utilities to a scalar value, becomes an essential part of game
construction. However, estimating this parameter from observational data
introduces several challenges due to a host of unobservable factors, including
the underlying modality of aggregation and the possibly boundedly rational
behaviour model that generated the observation. Based on the concept of
rationalisability, we develop algorithms for estimating multi-objective
aggregation parameters for two common aggregation methods, weighted and
satisficing aggregation, and for both strategic and non-strategic reasoning
models. Based on three different datasets, we provide insights into how human
drivers aggregate the utilities of safety and progress, as well as the
situational dependence of the aggregation process. Additionally, we show that
irrespective of the specific solution concept used for solving the games, a
data-driven estimation of utility aggregation significantly improves the
predictive accuracy of behaviour models with respect to observed human
behaviour.


  Privacy definitions provide ways for trading-off the privacy of individuals
in a statistical database for the utility of downstream analysis of the data.
In this paper, we present Blowfish, a class of privacy definitions inspired by
the Pufferfish framework, that provides a rich interface for this trade-off. In
particular, we allow data publishers to extend differential privacy using a
policy, which specifies (a) secrets, or information that must be kept secret,
and (b) constraints that may be known about the data. While the secret
specification allows increased utility by lessening protection for certain
individual properties, the constraint specification provides added protection
against an adversary who knows correlations in the data (arising from
constraints). We formalize policies and present novel algorithms that can
handle general specifications of sensitive information and certain count
constraints. We show that there are reasonable policies under which our privacy
mechanisms for k-means clustering, histograms and range queries introduce
significantly lesser noise than their differentially private counterparts. We
quantify the privacy-utility trade-offs for various policies analytically and
empirically on real datasets.


  Spin wave excitations were measured in the ferromagnetic phase of
Nd$_{1/2}$Sr$_{1/2}$MnO$_{3}$ by neutron scattering. This compound is located
in proximity to the A-type antiferromagnetic state, and it shows a clear
anisotropy and anomalous softening of the spin wave excitations. The softening
in the ferromagnetic phase is induced by the orbital ordering.


  I classify spacelike self-similar shrinking solutions of the mean curvature
flow in pseudo-euclidean space in arbitrary codimension, if the mean curvature
vector is not a null vector and the principal normal vector is parallel in the
normal bundle. Moreover, I exclude the existence of such self-shrinkers in
several cases. The classification is analogous to the existing classifications
in the euclidean case of Huisken and Smoczyk.


  This paper is the next installment of our analysis of length-commensurable
locally symmetric spaces begun in Publ. math. IHES 109(2009), 113-184. For a
Riemannian manifold $M$, we let $L(M)$ be the weak length spectrum of $M$, i.e.
the set of lengths of all closed geodesics in $M$, and let $\mathcal{F}(M)$
denote the subfield of $\mathbb{R}$ generated by $L(M)$. Let now $M_i$ be an
arithmetically defined locally symmetric space associated with a simple
algebraic $\mathbb{R}$-group $G_i$ for $i = 1, 2$. Assuming Schanuel's
conjecture from transcendental number theory, we prove (under some minor
technical restrictions) the following dichotomy: either $M_1$ and $M_2$ are
length-commensurable, i.e. $\mathbb{Q} \cdot L(M_1) = \mathbb{Q} \cdot L(M_2)$,
or the compositum $\mathcal{F}(M_1)\mathcal{F}(M_2)$ has infinite transcendence
degree over $\mathcal{F}(M_i)$ for at least one $i = 1$ or $2$ (which means
that the sets $L(M_1)$ and $L(M_2)$ are very different).


  We review the present state of understanding of solid friction at low
velocities and for systems with negligibly small wear effects.
  We first analyze in detail the behavior of friction at interfaces between
wacroscopic hard rough solids, whose main dynamical features are well described
by the Rice-Ruina rate and state dependent constitutive law. We show that it
results from two combined effects : (i) the threshold rheology of
nanometer-thick junctions jammed under confinement into a soft glassy structure
(ii) geometric aging, i.e. slow growth of the real arrea of contact via
asperity creep interrupted by sliding.
  Closer analysis leads to identifying a second aging-rejuvenation process, at
work within the junctions themselves. We compare the effects of structural
aging at such multicontact, very highly confined, interfaces with those met
under different confinement levels, namely boundary lubricated contacts and
extended adhesive interfaces involving soft materials (hydrogels, elastomers).
This leads us to propose a classification of frictional junctions in terms of
the relative importance of jamming and adsoprtion-induced metastability.


  We construct periodic approximations to the free energies of Ising models on
fractal lattices of dimension smaller than two, in the case of zero external
magnetic field, using a generalization of the combinatorial method of Feynman
and Vodvickenko. Our procedure is applicable to any fractal obtained by the
removal of sites of a periodic two dimensional lattice. As a first application,
we compute estimates for the critical temperatures of many different Sierpinski
carpets and we compare them to known Monte Carlo estimates. The results show
that our method is capable of determining the critical temperature with,
possibly, arbitrary accuracy and paves the way to determine $T_c$ for any
fractal of dimension below two. Critical exponents are more difficult to
determine since the free energy of any periodic approximation still has a
logarithmic singularity at the critical point implying $\alpha = 0$. We also
compute the correlation length as a function of the temperature and extract the
relative critical exponent. We find $\nu=1$ for all periodic approximation, as
expected from universality.


  We prove an equivalence result between the validity of a pointwise Hardy
inequality in a domain and uniform capacity density of the complement. This
result is new even in Euclidean spaces, but our methods apply in general metric
spaces as well. We also present a new transparent proof for the fact that
uniform capacity density implies the classical integral version of the Hardy
inequality in the setting of metric spaces. In addition, we consider the
relations between the above concepts and certain Hausdorff content conditions.


  We consider an optimization problem related to semi-active damping of
vibrating systems. The main problem is to determine the best damping matrix
able to minimize influence of the input on the output of the system. We use a
minimization criteria based on the $\mathcal{H}_2$ system norm.
  The objective function is non-convex and the associated optimization problem
typically requires a large number of objective function evaluations. We propose
an optimization approach that calculates `interpolatory' reduced order models,
allowing for significant acceleration of the optimization process.
  In our approach, we use parametric model reduction (PMOR) based on the
Iterative Rational Krylov Algorithm, which ensures good approximations relative
to the $\mathcal{H}_2$ system norm, aligning well with the underlying damping
design objectives. For the parameter sampling that occurs within each PMOR
cycle, we consider approaches with predetermined sampling and approaches using
adaptive sampling, and each of these approaches may be combined with three
possible strategies for internal reduction. In order to preserve important
system properties, we maintain second-order structure, which through the use of
modal coordinates, allows for very efficient implementation.
  The methodology proposed here provides a significant acceleration of the
optimization process; the gain in efficiency is illustrated in numerical
experiments.


  Personalized recommender systems are increasingly important as more content
and services become available and users struggle to identify what might
interest them. Thanks to the ability for providing rich information, knowledge
graphs (KGs) are being incorporated to enhance the recommendation performance
and interpretability. To effectively make use of the knowledge graph, we
propose a recommendation model in the hyperbolic space, which facilitates the
learning of the hierarchical structure of knowledge graphs. Furthermore, a
hyperbolic attention network is employed to determine the relative importances
of neighboring entities of a certain item. In addition, we propose an adaptive
and fine-grained regularization mechanism to adaptively regularize items and
their neighboring representations. Via a comparison using three real-world
datasets with state-of-the-art methods, we show that the proposed model
outperforms the best existing models by 2-16% in terms of NDCG@K on Top-K
recommendation.


  We generalize the cohomology theory for linear cycle sets introduced by Lebed
and Vendramin. Our cohomology classifies extensions of linear cycle sets by
trivial ideals, whereas the cohomology of Lebed and Vendramin only deals with
central ideals $I$ (which are automatically trivial). Therefore our theory
gives an analog to the theory of extensions of braces by trivial ideals
constructed by Bachiller, but from a cohomological point of view. We also study
the general notions of extensions of linear cycle sets and the equivalence of
extensions.


  Enfant terrible of charmonium spectroscopy, the resonance $X(3872)$,
generated a stream of interpretations and ushered in a new exotic $XYZ$
spectroscopy. In th meantime, many (if not all) characteristics of $X(3872)$
are rather ambiguous. We construct spectra of decays of the resonance $X(3872)$
with good analytical and unitary properties which allows to define the
branching ratio of the $X(3872) \to D^{*0}\bar D^0 + c.c.$ decay studying only
one more decay, for example, the $X(3872)\to\pi^+\pi^- J/\psi(1S)$ decay. We
next define the range of values of the coupling constant of the $X(3872)$
resonance with the $D^{*0}\bar D^0$ system. Finally, we show that our spectra
are effective means of selection of models for the resonance $X(3872)$.


  Recent improvements in object detection have shown potential to aid in tasks
where previous solutions were not able to achieve. A particular area is
assistive devices for individuals with visual impairment. While
state-of-the-art deep neural networks have been shown to achieve superior
object detection performance, their high computational and memory requirements
make them cost prohibitive for on-device operation. Alternatively, cloud-based
operation leads to privacy concerns, both not attractive to potential users. To
address these challenges, this study investigates creating an efficient object
detection network specifically for OLIV, an AI-powered assistant for object
localization for the visually impaired, via micro-architecture design
exploration. In particular, we formulate the problem of finding an optimal
network micro-architecture as an numerical optimization problem, where we find
the set of hyperparameters controlling the MobileNetV2-SSD network
micro-architecture that maximizes a modified NetScore objective function for
the MSCOCO-OLIV dataset of indoor objects. Experimental results show that such
a micro-architecture design exploration strategy leads to a compact deep neural
network with a balanced trade-off between accuracy, size, and speed, making it
well-suited for enabling on-device computer vision driven assistive devices for
the visually impaired.


  BCJ relation reveals a dual between color structures and kinematic structure
and can be used to reduce the number of independent color-ordered amplitudes at
tree level. Refer to the loop-level in Yang-Mills theory, we investigate the
similar BCJ relation in this paper. Four-point 1-loop example in N = 4 SYM can
hint about the relation of integrands. Five-point example implies that the
general formula can be proven by unitary- cut method. We will then prove a
'general' BCJ relation for 1-loop integrands by D-dimension unitary cut, which
can be regarded as a non-trivial generalization of the (fundamental)BCJ
relation given by Boels and Isermann in [arXiv:1109.5888 [hep-th]] and
[arXiv:1110.4462 [hep-th]].


  There have been many efforts in the last three decades to embed the empirical
MOND program into a robust theoretical framework. While many such theories can
explain the profile of galactic rotation curves, they usually cannot explain
the evolution 15 the primordial fluctuations and the formation of
large-scale-structures in the Universe. The Aether Scalar Tensor (AeST) theory
seems to have overcome this difficulty, thereby providing the first compelling
example of an extension of general relativity able to successfully challenge
the particle dark matter hypothesis. Here we study the phenomenology of this
theory in the quasistatic weak-field regime and specifically for the idealised
case of spherical isolated sources.
  We find the existence of three distinct gravitational regimes, that is,
Newtonian, MOND and a third regime characterised by the presence of
oscillations in the gravitational potential which do not exist in the
traditional MOND paradigm. We identify the transition scales between these
three regimes and discuss their dependence on the boundary conditions and other
parameters in the theory. Aided by analytical and numerical solutions, we
explore the dependence of these solutions on the theory parameters. Our results
could help in searching for interesting observable phenomena at low redshift
pertaining to galaxy dynamics as well as lensing observations, however, this
may warrant proper N-body simulations that go beyond the idealised case of
spherical isolated sources.


  The elementary excitations of a model Hamiltonian that captures the low
energy behavior of a simple two-fold degenerate Hubbard Hamiltonian with Hund's
rule coupling, is studied. The phase diagram in the mean-field limit and in a
two-site approach reveals a rich variety of phases where both the orbital and
the spin degrees of freedom are ordered. We show that besides usual spin waves
(magnons) there exist also orbital waves (orbitons) and, most interestingly, in
a completely ferromagnetically coupled system, a combined spin-orbital
excitation which can be visualized as a bound state of magnons and orbitons.
For a completely degenerate system the bound states are found to be the lowest
lying elementary excitations, both in one- and two-dimensions. Finally we
extend our treatment to almost-degenerate systems. This can serve as an example
that the elementary excitations in orbitally degenerate strongly correlated
electron systems in general carry both spin and orbital character.


  In recent years a tentative description of the short-range part of hadron
interactions with constituent quark interchange has been developed providing an
alternative approach to meson physics. Quark interchange plays a role, for
example, in the nucleon-nucleon ($NN$) phase-shifts and cross-section. In heavy
ion collision simulations at intermediate energies one of the main features is
the $NN$ cross-section in the collisional term, where in most cases it is an
input adjusted to the free space value. In this paper we introduce the quark
degrees of freedom to the $NN$ cross-section in the Vlasov-Uehling-Uhlenbeck
(VUU) model and explore the possibility that these effects appear in the
observables at lower energies.


  The first output-sensitive algorithm for the Maximal Clique Listing problem
was given by Tsukiyama et.al. in 1977. As any algorithm falling within the
Reverse Search paradigm, it performs a DFS visit of a directed tree (the
RS-tree) having the objects to be listed (i.e. maximal cliques) as its nodes.
In a recursive implementation, the RS-tree corresponds to the recursion tree of
the algorithm. The time delay is given by the cost of generating the next child
of a node, and Tsukiyama showed it is $O(mn)$. In 2004, Makino and Uno
sharpened the time delay to $O(n^{\omega})$ by generating all the children of a
node in one single shot performed by computing a \emph{square} fast matrix
multiplication. In this paper, we further improve the asymptotics for the
exploration of the same RS-tree by grouping the offsprings' computation even
further. Our idea is to rely on rectangular fast matrix multiplication in order
to compute all children of $n^2$ nodes in one shot. According to the current
upper bounds on fast matrix multiplication, with this the time delay improves
from $O(n^{2.3728639})$ to $O(n^{2.093362})$.


  We recently discovered the X-ray/optical outbursting source 3XMM
J215022.4-055108. It was best explained as the tidal disruption of a star by an
intermediate-mass black hole of mass of a few tens of thousand solar masses in
a massive star cluster at the outskirts of a large barred lenticular galaxy at
D_L=247 Mpc. However, we could not completely rule out a Galactic cooling
neutron star as an alternative explanation for the source. In order to further
pin down the nature of the source, we have obtained new multiwavelength
observations by XMM-Newton and Hubble Space Telescope (HST). The optical
counterpart to the source in the new HST image is marginally resolved, which
rules out the Galactic cooling neutron star explanation for the source and
suggests a star cluster of half-light radius ~27 pc. The new XMM-Newton
observation indicates that the luminosity was decaying as expected for a tidal
disruption event and that the disk was still in the thermal state with a
super-soft X-ray spectrum. Therefore, the new observations confirm the source
as one of the best intermediate-mass black hole candidates.


  Quantum computing is an emerging technology that has the potential to
revolutionize fields such as cryptography, machine learning, optimization, and
quantum simulation. However, a major challenge in the realization of quantum
algorithms on actual machines is ensuring that the gates in a quantum circuit
(i.e., corresponding operations) match the topology of a targeted architecture
so that the circuit can be executed while, at the same time, the resulting
costs (e.g., in terms of the number of additionally introduced gates, fidelity,
etc.) are kept low. This is known as the quantum circuit mapping problem. This
summary paper provides an overview of QMAP, an open-source tool that is part of
the Munich Quantum Toolkit (MQT) and offers efficient, automated, and
accessible methods for tackling this problem. To this end, the paper first
briefly reviews the problem. Afterwards, it shows how QMAP can be used to
efficiently map quantum circuits to quantum computing architectures from both a
user's and a developer's perspective. QMAP is publicly available as open-source
at https://github.com/cda-tum/qmap.


  We prove that there exists an extremal function to the Airy Strichartz
inequality, $e^{-t\partial_x^3}: L^2(\mathbb{R})\to L^8_{t,x}(\mathbb{R}^2)$ by
using the linear profile decomposition. Furthermore we show that, if $f$ is an
extremiser, then $f$ is extremely fast decaying in Fourier space and so $f$ can
be extended to be an entire function on the whole complex domain. The rapid
decay of the Fourier transform of extremisers is established with a bootstrap
argument which relies on a refined bilinear Airy Strichartz estimate and a
weighted Strichartz inequality.


  When studying boundary value problems for some partial differential equations
arising in applied mathematics, we often have to study the solution of a system
of partial differential equations satisfied by hypergeometric functions and
find explicit linearly independent solutions for the system. In this study, we
construct self-similar solutions of some model degenerate partial differential
equations of the second, third, and fourth order. These self-similar solutions
are expressed in terms of hypergeometric functions.


  We survey recent developments in the study of (worst-case) one-way functions
having strong algebraic and security properties. According to [RS93], this line
of research was initiated in 1984 by Rivest and Sherman who designed two-party
secret-key agreement protocols that use strongly noninvertible, total,
associative one-way functions as their key building blocks. If commutativity is
added as an ingredient, these protocols can be used by more than two parties,
as noted by Rabi and Sherman [RS93] who also developed digital signature
protocols that are based on such enhanced one-way functions.
  Until recently, it was an open question whether one-way functions having the
algebraic and security properties that these protocols require could be created
from any given one-way function. Recently, Hemaspaandra and Rothe [HR99]
resolved this open issue in the affirmative, by showing that one-way functions
exist if and only if strong, total, commutative, associative one-way functions
exist.
  We discuss this result, and the work of Rabi, Rivest, and Sherman, and recent
work of Homan [Hom99] that makes progress on related issues.


  Spectral clustering is a popular algorithm that clusters points using the
eigenvalues and eigenvectors of Laplacian matrices derived from the data. For
years, spectral clustering has been working mysteriously. This paper explains
spectral clustering by dividing it into two categories based on whether the
graph Laplacian is fully connected or not. For a fully connected graph, this
paper demonstrates the dimension reduction part by offering an objective
function: the covariance between the original data points' similarities and the
mapped data points' similarities. For a multi-connected graph, this paper
proves that with a proper $k$, the first $k$ eigenvectors are the indicators of
the connected components. This paper also proves there is an equivalence
between spectral embedding and PCA.


  In this article, we introduce the concepts of Weyl mean equicontinuity and
Weyl mean sensitivity of a random dynamical system associated to an infinite
countable discrete amenable group action. We obtain the dichotomy result to
Weyl mean equicontinuity and Weyl mean sensitivity of a random dynamical system
when the corresponding skew product transformation is minimal and \Omega is
finite.


  We present the light curves obtained during an eight-year program of optical
spectroscopic monitoring of nine Seyfert 1 galaxies: 3C 120, Akn 120, Mrk 79,
Mrk 110, Mrk 335, Mrk 509, Mrk 590, Mrk 704, and Mrk 817. All objects show
significant variability in both the continuum and emission-line fluxes. We use
cross-correlation analysis to derive the sizes of the broad Hbeta-emitting
regions based on emission-line time delays, or lags. We successfully measure
time delays for eight of the nine sources, and find values ranging from about
two weeks to a little over two months. Combining the measured lags and widths
of the variable parts of the emission lines allows us to make virial mass
estimates for the active nucleus in each galaxy. The virial masses are in the
range 10^{7-8} solar masses.


  I propose that if the universe was born as a baby universe on the other side
of the event horizon of a black hole existing in a parent universe, then the
corresponding white hole provides the absolute inertial frame of reference in
the universe. The principle of relativity then allows to construct an infinity
of other inertial frames. Consequently, this scenario could give the origin of
inertia and complete Einstein's general theory of relativity by making it
consistent with Mach's principle.


  The ratio of convexity radius over injectivity radius may be made arbitrarily
small within the class of compact Riemannian manifolds of any fixed dimension
at least two. This is proved using Gulliver's method of constructing manifolds
with focal points but no conjugate points. The approach is suggested by a
characterization of the convexity radius that resembles a classical result of
Klingenberg about the injectivity radius.


  Weyl semimetals are intriguing topological states of matter that support
various anomalous magneto-transport phenomena. One such phenomenon is a
negative longitudinal ($\mathbf{\nabla} T \parallel \mathbf{B}$)
magneto-thermal resistivity, which arises due to chiral magnetic effect (CME).
In this paper we show that another fascinating effect induced by CME is the
planar thermal Hall effect (PTHE), i.e., appearance of an in-plane transverse
temperature gradient when the current due to $\mathbf{\nabla} T$ and the
magnetic field $\mathbf{B}$ are not aligned with each other. Using
semiclassical Boltzmann transport formalism in the relaxation time
approximation we compute both longitudinal magneto-thermal conductivity (LMTC)
and planar thermal Hall conductivity (PTHC) for a time reversal symmetry
breaking WSM. We find that both LMTC and PTHC are quadratic in B in type-I WSM
whereas each follows a linear-B dependence in type-II WSM in a configuration
where $\mathbf{\nabla} T$ and B are applied along the tilt direction. In
addition, we investigate the Wiedemann-Franz law for an inversion symmetry
broken WSM (e.g., WTe$_{2}$) and find that this law is violated in these
systems due to both chiral anomaly and CME.


  To solve nonlinear problems, we construct two kinds of greedy capped
nonlinear Kaczmarz methods by setting a capped threshold and introducing an
effective probability criterion for selecting a row of the Jacobian matrix. The
capped threshold and probability criterion are mainly determined by the maximum
residual and maximum distance rules. The block versions of the new methods are
also presented. We provide the convergence analysis of these methods and their
numerical results behave quite well.


  We investigate the ratchet dynamics of nonlinear Klein-Gordon kinks in a
periodic, asymmetric lattice of point-like inhomogeneities. We explain the
underlying rectification mechanism within a collective coordinate framework,
which shows that such system behaves as a rocking ratchet for point particles.
Careful attention is given to the kink width dynamics and its role in the
transport. We also analyze the robustness of our kink rocking ratchet in the
presence of noise. We show that the noise activates unidirectional motion in a
parameter range where such motion is not observed in the noiseless case. This
is subsequently corroborated by the collective variable theory. An explanation
for this new phenomenom is given.


  The photorecombination spectrum of 48Ti18+ was measured employing the merged
electron-ion beams technique at a heavy-ion storage ring. The experimental
electron-ion collision energy range 0-80 eV comprises all dielectronic
recombination (DR) resonances associated with 2s->2p (Delta N =0) core
excitations as well as trielectronic recombination (TR) resonances that involve
2s2->2p2 core double-excitations. At low collision energies DR resonances are
observed that are associated with the excitation of metastable 2s2p 3P0 primary
ions with nearly infinite lifetime for the isotope 48Ti with zero nuclear spin.
For the isotope 47Ti with nonzero nuclear spin hyperfine quenching of these
resonances occurs. The procedure for obtaining the associated time constant
from a recombination measurement is outlined.


  The exactness equation for Lepage 2-forms, associated with variational
systems of ordinary differential equations on smooth manifolds, is analyzed
with the aim to construct a concrete global variational principle. It is shown
that locally variational systems defined by homogeneous functions of degree $c
\neq 0, 1$ are automatically globally variational. A new constructive method of
finding a global Lagrangian is described for these systems, which include for
instance the geodesic equations in Riemann and Finsler geometry.


  The prize-collecting Steiner tree problem PCSTP is a well-known
generalization of the classical Steiner tree problem in graphs, with a large
number of practical applications. It attracted particular interest during the
latest (11th) DIMACS Challenge and since then a number of PCSTP solvers have
been introduced in the literature, some of which drastically improved on the
best results achieved at the Challenge. The following article aims to further
advance the state of the art. It introduces new techniques and algorithms for
PCSTP, involving various forms of reductions of PCSTP instances to equivalent
problems---which for example allows to decrease the problem size or to obtain a
better IP formulation. Several of the new techniques and algorithms provably
dominate previous approaches. Further theoretical properties of the new
components, such as their complexity, are discussed, and their profound
interaction is described. Finally, the new developments also translate into a
strong computational performance: the resulting exact solver outperforms all
previous approaches---both in terms of run-time and solvability---and can solve
formerly intractable benchmark instances from the 11th DIMACS Challenge to
optimality.


  To address the 'memory wall' problem in NN hardware acceleration, we
introduce HALO-CAT, a software-hardware co-design optimized for Hidden Neural
Network (HNN) processing. HALO-CAT integrates Layer-Penetrative Tiling (LPT)
for algorithmic efficiency, reducing intermediate result sizes. Furthermore,
the architecture employs an activation-localized computing-in-memory approach
to minimize data movement. This design significantly enhances energy
efficiency, achieving a 14.2x reduction in activation memory capacity and a
17.8x decrease in energy consumption, with only a 1.5% loss in accuracy,
compared to traditional HNN processors.


  By applying a relativistic mean-field description of neutron star matter with
density dependent couplings, we analyse the properties of two different matter
compositions: nucleonic matter with delta baryons and nucleonic matter with
hyperons and delta baryons. The delta-meson couplings are allowed to vary
within a wide range of values obtained by experimental data, while the
hyperon-meson couplings are fitted to hypernuclear properties. Neutron star
properties with no deconfinement phase transition are studied. It is verified
that many models are excluded because the effective nucleon mass becomes zero
before the maximum mass configuration is attained. Hyperon-free with
delta-dominated composition compact stars are possible, the deltic stars. It is
found that with a convenient choice of parameters the existence of deltic stars
with 80% of delta baryons at the center of the star is possible. However, the
presence of hyperons lowers the delta baryon fraction to values below 20% at
the center and below 30% at 2-3 saturation densities. It is discussed that in
the presence of delta baryons, the hyperon softening is not so drastic because
deltas couple more strongly to the $\omega$-meson, and the stiffness of the
equation of state is determined by the $\omega$-dominance at high densities.
The speed of sound reflects very well this behavior. The compactness of the
pulsar RX J0720.4-3125 imposes $x_{\sigma\Delta}>x_{\omega\Delta}>1$ and favors
$x_{\rho\Delta}>1$.


  The MOSCAB experiment (Materia OSCura A Bolle) uses a new technique for Dark
Matter search. The Geyser technique is applied to the construction of a
prototype detector with a mass of 0.5 kg and the encouraging results are
reported here; an accent is placed on a big detector of 40 kg in construction
at the Milano-Bicocca University and INFN.


  Machine learning has become widely used in astronomy. Gaussian Process (GP)
regression in particular has been employed a number of times to fit or
re-sample supernova (SN) light-curves, however by their nature typical GP
models are not suited to fit SN photometric data and they will be prone to
over-fitting. Recently GP re-sampling was used in the context of studying the
morphologies of type II and IIb SNe and they were found to be clearly distinct
with respect to four parameters: the rise time (t$_{\rm rise}$), the magnitude
difference between 40 and 30 days post explosion ($\Delta m_{\rm 40-30}$), the
earliest maximum (post-peak) of the first derivative (dm1) and minimum of the
second derivative (dm2). Here we take a close look at GP regression and its
limitations in the context of SN light-curves in general, and we also discuss
the uncertainties on these specific parameters, finding that dm1 and dm2 cannot
give reliable astrophysical information. We do reproduce the clustering in
t$_{\rm rise}$--$\Delta m_{\rm 40-30}$ space although it is not as clear cut as
previously presented. The best strategy to accurately populate the t$_{\rm
rise}$-- $\Delta m_{\rm 40-30}$ space will be to use an expanded sample of high
quality light-curves (such as those in the ATLAS transient survey) and
analytical fitting methods. Finally, using the BPASS fiducial models, we
predict that future photometric studies will reveal clear clustering of the
type IIb and II light curve morphologies with a distinct continuum of
transitional events.


  Quiescent galaxies at $z \gtrsim 2$ are compact and have weak or absent
emission lines, making it difficult to spatially resolve their kinematics and
stellar populations using ground-based spectroscopy. Gravitationally lensed
examples provide a promising route forward, but such objects are very rare. We
describe a search in the fields of 232 galaxy clusters that has uncovered five
bright ($H_{\rm AB} < 20$) lensed galaxies with red near-infrared colors. These
include MRG-M0138, the brightest lensed galaxy known in the near-infrared.
Analysis of near-infrared spectra and multiband photometry confirms that all
are quiescent galaxies at z=1.95-2.64 with stellar ages of 0.5-1.4 Gyr
(corresponding to formation epochs $z_{\rm form} \simeq 3-4$) and stellar
masses of $10^{11.6-12.8} \mu^{-1} M_{\odot}$, where $\mu$ is the
magnification. In three cases we derive lens models and reconstruct the source
structure; these galaxies are massive ($M_* \gtrsim 10^{11.0} M_{\odot}$) and
follow the mass--size relation defined by unlensed samples. In two of these
three galaxies, the main structural component is an inclined disk. Weak
emission lines are detected in four of five galaxies with high ratios
[NII]/H$\alpha$~2-6 that are inconsistent with a star formation origin. Based
on the line ratios, the H$\alpha$ equivalent widths, and the distribution and
kinematics of the gas, we infer that shocks are likely present in at least two
galaxies and could be present in all of the line emitters. We speculate that
these could be analogs of local galaxies in which AGN jet-driven outflows are
thought to heat the interstellar medium and suppress star formation. In further
papers we will present spatially resolved measurements of the stellar
populations and kinematics of this unique sample.


  Hella et al. (PODC 2012, Distributed Computing 2015) identified seven
different models of distributed computing - one of which is the port-numbering
model - and provided a complete classification of their computational power
relative to each other. However, one of their simulation results involves an
additive overhead of $2\Delta-2$ communication rounds, and it was not clear, if
this is actually optimal. In this paper we give a positive answer: there is a
matching linear-in-$\Delta$ lower bound. This closes the final gap in our
understanding of the models, with respect to the number of communication
rounds.


  If T is an iteration tree on K and F is a countably certified extender that
coheres with the final model of T, then F is on the extender sequence of the
final model of T. Several applications of maximality are proved, including:
  o K computes successors of weakly compact cardinals correctly.
  o K^c is an iterate of K.
  o (with Mitchell) If alpha is a cardinal > aleph_1, then K-restriction-alpha
is universal for mice of height alpha.
  Other results in this paper, when combined with work of Woodin, imply:
  o If square-kappa-finite fails and kappa is a singular, strong limit
cardinal, then Inductive Determinacy holds.
  o If square-kappa-finite fails and kappa is a weakly compact cardinal, then
L(R)-determinacy holds.


  Graph homologies are powerful tools to compute the rational homotopy group of
the space of long embeddings. Two graph homologies have been invented from two
approaches to study the space of long embeddings: the hairy graph homology from
embedding calculus, and BCR graph homology from configuration space integral.
In this paper, we construct a monomorphism from the top hairy graph homology to
the top BCR graph homology, though the latter graph homology is quite modified.
This map and its left inverse are analogs of PBW isomorphism between the space
of open Jacobi diagrams and the space of Jacobi diagrams on the unit circle, in
the theory of Vassiliev knot invariants.


  Latent user representations are widely adopted in the tech industry for
powering personalized recommender systems. Most prior work infers a single high
dimensional embedding to represent a user, which is a good starting point but
falls short in delivering a full understanding of the user's interests. In this
work, we introduce PinnerSage, an end-to-end recommender system that represents
each user via multi-modal embeddings and leverages this rich representation of
users to provides high quality personalized recommendations. PinnerSage
achieves this by clustering users' actions into conceptually coherent clusters
with the help of a hierarchical clustering method (Ward) and summarizes the
clusters via representative pins (Medoids) for efficiency and interpretability.
PinnerSage is deployed in production at Pinterest and we outline the several
design decisions that makes it run seamlessly at a very large scale. We conduct
several offline and online A/B experiments to show that our method
significantly outperforms single embedding methods.


  We present multi-frequency observations with the Very Long Baseline Array of
the compact double radio source B2 2050+36. Our observations are at 0.33, 0.61,
1.67, 2.3, and 8.4 GHz, with the 0.61 GHz observations forming the third epoch
of observation of this source at that frequency. At 0.61 GHz, the structure of
B2 2050+36 is dominated by two components 56 mas apart. Within the
uncertainties of the various measurements, this separation has remained
unchanged for the past 16 years. Any differential image wander caused by
refractive interstellar scattering is less than 4 mas. Both the lack of
differential image wander and the frequency dependence of the angular diameter
of B2 2050+36 below 1 GHz indicate that the electron density power spectrum
along this line of sight has a spectral index near the Kolmogorov value, with a
value of 4 being highly unlikely. We conclude that diffractive scattering
dominates along this line of sight; results in the literature indicate that
this conclusion also holds true for the line of sight to the pulsar PSR
B2020+28 (8.7 deg. from B2 2050+36). Comparison of our 1.67 GHz observations
with those obtained 21 years previously place a limit on the projected linear
separation velocity of the two components of c.


  This paper describes our efforts in predicting current and future
psychological health from childhood essays within the scope of the CLPsych-2018
Shared Task. We experimented with a number of different models, including
recurrent and convolutional networks, Poisson regression, support vector
regression, and L1 and L2 regularized linear regression. We obtained the best
results on the training/development data with L2 regularized linear regression
(ridge regression) which also got the best scores on main metrics in the
official testing for task A (predicting psychological health from essays
written at the age of 11 years) and task B (predicting later psychological
health from essays written at the age of 11).


  We propose Cognitive Databases, an approach for transparently enabling
Artificial Intelligence (AI) capabilities in relational databases. A novel
aspect of our design is to first view the structured data source as meaningful
unstructured text, and then use the text to build an unsupervised neural
network model using a Natural Language Processing (NLP) technique called word
embedding. This model captures the hidden inter-/intra-column relationships
between database tokens of different types. For each database token, the model
includes a vector that encodes contextual semantic relationships. We seamlessly
integrate the word embedding model into existing SQL query infrastructure and
use it to enable a new class of SQL-based analytics queries called cognitive
intelligence (CI) queries. CI queries use the model vectors to enable complex
queries such as semantic matching, inductive reasoning queries such as
analogies, predictive queries using entities not present in a database, and,
more generally, using knowledge from external sources. We demonstrate unique
capabilities of Cognitive Databases using an Apache Spark based prototype to
execute inductive reasoning CI queries over a multi-modal database containing
text and images. We believe our first-of-a-kind system exemplifies using AI
functionality to endow relational databases with capabilities that were
previously very hard to realize in practice.


  Theoretical studies of nonequilibrium systems are complicated by the lack of
a general framework. In this work we first show that a transformation
introduced by Ao recently (J. Phys. A {\bf 37}, L25 (2004)) is related to
previous works of Graham (Z. Physik B {\bf 26}, 397 (1977)) and Eyink {\it et
al.} (J. Stat. Phys. {\bf 83}, 385 (1996)), which can also be viewed as the
generalized application of the Helmholtz theorem in vector calculus. We then
show that systems described by ordinary stochastic differential equations with
white noise can be mapped to thermostated Hamiltonian systems. A steady-state
of a dissipative system corresponds to the equilibrium state of the
corresponding Hamiltonian system. These results provides a solid theoretical
ground for corresponding studies on nonequilibrium dynamics, especially on
nonequilibrium steady state. The mapping permits the application of established
techniques and results for Hamiltonian systems to dissipative non-Hamiltonian
systems, those for thermodynamic equilibrium states to nonequilibrium steady
states. We discuss several implications of the present work.


  In this article, we study the dynamic variant and the equilibrium variant of
the model of Rydberg atoms on a square ladder. In the dynamic case, we obtain
the jamming limit for all values of $b \ge 1$, where $b$ represents the
so-called blockade range of a Rydberg atom. In the equilibrium case, we derive
the complexity function for all values of $b \ge 1$. By comparing these
results, we highlight significant differences in the behavior of the two models
as $b$ approaches infinity.


  Since the introduction of Bitcoin in 2008, many other cryptocurrencies have
been introduced and gained popularity. Lack of interoperability and scalability
amongst these cryptocurrencies was and still is, acting as a significant
impediment to the general adoption of cryptocurrencies and coloured tokens.
Atomic Swaps, a smart exchange protocol for cryptocurrencies, is designed to
facilitate a wallet-to-wallet transfer enabling direct trades amongst different
cryptocurrencies. Since swaps between cryptocurrencies are still relatively
unknown, this article will investigate the operation and market development
thus far and query the advantages they offer and the future challenges they
face. The paper contains detailed literature and technology reviews, followed
by the main analysis and findings.


  We discuss the chirally symmetric solution of the massless, quenched,
Dyson-Schwinger equation for the fermion propagator in three and four
dimensions. The solutions are manifestly gauge covariant. We consider a gauge
covariance constraint on the fermion--gauge-boson vertex, which motivates a
vertex Ansatz that both satisfies the Ward identity when the fermion self-mass
is zero and ensures gauge covariance of the fermion propagator.


  Multiple and single measurements of quantum states of mesoscopic
superconducting loops are carried out in order to investigate a possibility of
macroscopic quantum superposition and of creation of a superconductor quantum
register. Asymmetric superconducting rings are used in order to be convinced
that single measurement gives result corresponding to one of permitted states
and multiple one gives an average value on these states. We have measured
magnetic dependencies of resistance, rectified voltage and critical current on
these rings. The observed quantum oscillations of the resistance and the
rectified voltage, corresponding to multiple measurement of quantum states,
give evidence of two permitted states at the magnetic flux inside the ring
divisible by half of the flux quantum. But the observed quantum oscillations of
the critical current, corresponding to single measurement, not only does not
confirm these two quantum states, but are in a direct contradiction with the
observed oscillations of the resistance. It is assumed that the observed
contradiction between the results of measurements made on the same ring can
testify to violation of the principle of realism on the mesoscopic level that
is a necessary condition for an opportunity of creation of a quantum computer.


  The fact that every compact oriented 4-manifold admits spin$^c$ structures
was proved long ago by Hirzebruch and Hopf. However, the usual proof is neither
direct nor transparent. This article gives a new proof using twistor spaces
that is simpler and more geometric. After using these ideas to clarify various
aspects of four-dimensional geometry, we then explain how related ideas can be
used to understand both spin and spin$^c$ structures in any dimension.


  We consider a definition of the Fukaya category of a singular hypersurface
proposed by Auroux, given by localizing the Fukaya category of a nearby fiber
at Seidel's natural transformation, and show that this possesses several
desirable properties. Firstly, we prove an A-side analog of Orlov's derived
Kn\"orrer periodicity theorem by showing that Auroux' category is derived
equivalent to the Fukaya-Seidel category of a higher-dimensional
Landau-Ginzburg model. Secondly, we describe how this definition should imply
homological mirror symmetry at various large complex structure limits, in the
context of forthcoming work of Abouzaid-Auroux and Abouzaid-Gross-Siebert.


  An exact algorithm is used to investigate the distributions of the
degeneracies of low-energy excited states for the bimodal Ising spin glass on
the brickwork lattice. Since the distributions are extreme and do not
self-average, we base our conclusions on the most likely values of the
degeneracies. Our main result is that the degeneracy of the first excited state
per ground state and per spin is finite in the thermodynamic limit. This is
very different from the same model on a square lattice where a divergence
proportional to the linear lattice size is expected. The energy gap for the
brickwork lattice is obviously 2J on finite systems and predicted to be the
same in the thermodynamic limit. Our results suggest that a 2J gap is universal
for planar bimodal Ising spin glasses. The distribution of the second
contribution to the internal energy has a mode close to zero and we predict
that the low-temperature specific heat is dominated by the leading term
proportional to $T^{-2} \exp(-2J/kT)$.


  We apply the Desnanot-Jacobi identity to give an alternative proof of the
determinants whose entries are rising powers of the Fibonacci numbers given by
Prodinger. We then generalize the determinants to include entries that are
rising powers of the terms in a second order linear recurrence.


  Electronic diodes, which enable the rectification of an electrical energy
flux, have played a crucial role in the development of current microelectronics
after the invention of semiconductor p-n junctions. Analogously, signal
rectification at specific target wavelengths has recently become a key goal in
optical communication and signal processing. Here we propose a genuinely
quantum device with the essential rectifying features being demonstrated in a
general model of a nonlinear-linear junction of coupled resonators. It is shown
that such a surprisingly simple structure is a versatile valve and may be
alternatively tuned to behave as: a photonic diode, a single or two-photon
rectified source turning a classical input into a quantum output depending on
the input frequency, or a quantum photonic splitter. Given the relevance of
non-reciprocal operations in integrated circuits, the nonlinear-linear junction
realises a crucial building component in prospective quantum photonic
applications.


  Active matter consumes energy from the environment and transforms it into
mechanical work. Notable examples from biology include cell division, bacterial
swarms, and muscle contraction. In this work, we investigate the nature of
active matter systems using the powerful effective field theory toolbox. This
allows us to construct the most general theory without ambiguity up to a given
order in the derivative expansion. Our primary focus is active nematics --
liquid crystal systems that spontaneously break rotational but not
translational symmetry -- in two spatial dimensions. (Such spontaneous symmetry
breaking is allowed if the nematic is embedded in a higher dimensional space.)
While we focus on this one particular class of physical system, the tools
developed here can in principle be applied to any active matter system. Our
theories give unambiguous predictions for the relationship between fluctuations
and equations of motion in the presence of activity, generalizing the standard
fluctuation-dissipation relations characteristic of passive systems.


  $ \newcommand{\schs}{\scriptstyle{\mathsf{S}}_1} $For all $n \ge 1$, we give
an explicit construction of $m \times m$ matrices $A_1,\ldots,A_n$ with $m =
2^{\lfloor n/2 \rfloor}$ such that for any $d$ and $d \times d$ matrices
$A'_1,\ldots,A'_n$ that satisfy \[ \|A'_i-A'_j\|_{\schs} \,\leq\,
\|A_i-A_j\|_{\schs}\,\leq\, (1+\delta) \|A'_i-A'_j\|_{\schs} \] for all
$i,j\in\{1,\ldots,n\}$ and small enough $\delta = O(n^{-c})$, where $c> 0$ is a
universal constant, it must be the case that $d \ge 2^{\lfloor n/2\rfloor -1}$.
This stands in contrast to the metric theory of commutative $\ell_p$ spaces, as
it is known that for any $p\geq 1$, any $n$ points in $\ell_p$ embed exactly in
$\ell_p^d$ for $d=n(n-1)/2$.
  Our proof is based on matrices derived from a representation of the Clifford
algebra generated by $n$ anti-commuting Hermitian matrices that square to
identity, and borrows ideas from the analysis of nonlocal games in quantum
information theory.


  In this paper, we study the class of indecomposable involutive solutions of
the Yang-Baxter equation of finite primitive level, recently introduced by
Ced\'o and Okni\'nski in \cite{cedo2021constructing}. We give a group-theoretic
characterization of these solutions by means of displacements groups and we
apply this result to compute and enumerate the ones having small size. For some
classes of indecomposable involutive solutions recently studied in literature,
we compute the exact value of the primitive level. Some relationships with
other families of solutions also are discussed. Finally, following
\cite[Question 3.2]{cedo2021constructing}, we completely describe the ones
having primitive level $2$ by left braces.


  In this paper, we develop discrete versions of Darboux transformations and
Crum's theorems for two second order difference equations. The difference
equations are discretised versions (using Darboux transformations) of the
spectral problems of the KdV quation, and of the modified KdV equation or
sine-Gordon equation. Considering the discrete dynamics created by Darboux
transformations for the difference equations, one obtains the lattice potential
KdV equation, the lattice potential modified KdV equation and the lattice
Schwarzian KdV equation, that are prototypes of integrable lattice equations.
It turns out that, along the discretisation processes using Darboux
transformations, two families of integrable systems (the KdV family, and the
modified KdV or sine-Gordon family), including their continuous, semi-discrete
and lattice versions, are explicitly constructed. As direct applications of the
discrete Crum's theorems, multi-soliton solutions of the lattice equations are
obtained.


  Current state-of-the-art models for sentiment analysis make use of word order
either explicitly by pre-training on a language modeling objective or
implicitly by using recurrent neural networks (RNNs) or convolutional networks
(CNNs). This is a problem for cross-lingual models that use bilingual
embeddings as features, as the difference in word order between source and
target languages is not resolved. In this work, we explore reordering as a
pre-processing step for sentence-level cross-lingual sentiment classification
with two language combinations (English-Spanish, English-Catalan). We find that
while reordering helps both models, CNNS are more sensitive to local
reorderings, while global reordering benefits RNNs.


  In this work we present novel differentially private identity
(goodness-of-fit) testers for natural and widely studied classes of
multivariate product distributions: Gaussians in $\mathbb{R}^d$ with known
covariance and product distributions over $\{\pm 1\}^{d}$. Our testers have
improved sample complexity compared to those derived from previous techniques,
and are the first testers whose sample complexity matches the order-optimal
minimax sample complexity of $O(d^{1/2}/\alpha^2)$ in many parameter regimes.
We construct two types of testers, exhibiting tradeoffs between sample
complexity and computational complexity. Finally, we provide a two-way
reduction between testing a subclass of multivariate product distributions and
testing univariate distributions, and thereby obtain upper and lower bounds for
testing this subclass of product distributions.


  In this paper the usual $Z_2$ graded Lie algebra is generalized to a new
form, which may be called $Z_{2,2}$ graded Lie algebra. It is shown that there
exists close connections between the $Z_{2,2}$ graded Lie algebra and
parastatistics, so the $Z_{2,2}$ can be used to study and analyse various
symmetries and supersymmetries of the paraparticle systems.


  This review examines the properties of graphene from an experimental
perspective. The intent is to review the most important experimental results at
a level of detail appropriate for new graduate students who are interested in a
general overview of the fascinating properties of graphene. While some
introductory theoretical concepts are provided, including a discussion of the
electronic band structure and phonon dispersion, the main emphasis is on
describing relevant experiments and important results as well as some of the
novel applications of graphene. In particular, this review covers graphene
synthesis and characterization, field-effect behavior, electronic transport
properties, magneto-transport, integer and fractional quantum Hall effects,
mechanical properties, transistors, optoelectronics, graphene-based sensors,
and biosensors. This approach attempts to highlight both the means by which the
current understanding of graphene has come about and some tools for future
contributions.


  Without using the $L^2$ extension theorem, we provide a new proof of the
equality part in Suita's conjecture, which states that for any open Riemann
surface admitting a Green's function, the Bergman kernel and the logarithmic
capacity coincide at one point if and only if the surface is biholomorphic to a
disc possibly less a relatively closed polar set. In comparison with Guan and
Zhou's proof, our proof essentially depends on Maitani and Yamaguchi's
variation formula for the Bergman kernel, and we explore the harmonicity in
such variations. As applications, we characterize the above surface by the
constant Gaussian curvature property of the Bergman kernel or metric, and also
find the relations with disc quotients. Additionally, we obtain results on
planar domains without the Bergman-completeness assumption.


  In this work, we investigate the possibility that the galaxy rotation curves
can be explained in the framework of modified gravity models that introduce a
Yukawa term in the gravitational potential. We include dark matter and assume
that the fifth-force couples differently to dark matter and to baryons. We aim
at constraining the modified gravity parameters $\beta$ and $\lambda$, that is,
the strength and the range of the Yukawa fifth force, respectively, using a set
of 40 galaxy rotation curves data from the SPARC catalogue. We include baryonic
gas, disk and bulge components, along with a NFW halo of dark matter. Each
galaxy rotation curve is modeled with three free parameters, beside the two
global Yukawa parameter. We find that the inclusion of the Yukawa term improves
the $\chi^2$ from $680.75$ to $536.23$ for $655$ degrees of freedom. As global
best-fit we obtain $\beta = 0.34\pm0.04$ and $\lambda = 5.61\pm0.91$kpc and a
dark matter content on average 20\% smaller than without the Yukawa term. The
Bayesian evidence in favor of a NFW profile plus Yukawa term is higher than
8$\sigma$ with respect to the standard gravity parametrization.


  We present a comprehensive characterization of 26 CME-driven compressive
waves known as Coronal Bright Fronts (CBFs) observed in the low solar corona
between 2010 and 2017. These CBFs have been found to be associated with SEP
events near Earth, indicating their importance in understanding space weather
phenomena. The aim of this study is to analyze and describe the early dynamics
of CBFs using a physics-based heliospheric SEP forecasting system known as the
SPREAdFAST framework. This framework utilizes a chain of data-driven analytic
and numerical models to predict SEP fluxes at multiple locations in the inner
heliosphere by considering their acceleration at CMEs near the Sun and
subsequent interplanetary transport. To estimate the time-dependent plasma and
compression parameters of the CBFs, we utilized sequences of base-difference
images obtained from the AIA instrument on board the SDO satellite, and
measurements of the height-time profiles of the CMEs obtained from the LASCO
instrument on board the SOHO satellite. We employed kinematic measurements and
plasma model results to derive these parameters. The SPREAdFAST framework
facilitated the analysis and correlation of these observations with SEP events
near Earth. Our analysis yielded statistical relations and distributions for
both the shocks and plasma parameters associated with the 26 CBFs investigated.
By combining the observations from the AIA and LASCO instruments, as well as
the data products from the SPREAdFAST framework, we obtained a comprehensive
understanding of the early dynamics of CBFs, including their temporal
evolution, plasma properties, and compressional characteristics. These findings
contribute to the growing body of knowledge in the field and have implications
for space weather forecasting and the study of SEP events.


  We study the scaling properties of heat transfer $Nu$ in turbulent thermal
convection at large Prandtl number $Pr$ using a quasi-linear theory. We show
that two regimes arise, depending on the Reynolds number $Re$. At low Reynolds
number, $Nu Pr^{-1/2}$ and $Re$ are a function of $Ra Pr^{-3/2}$. At large
Reynolds number $Nu Pr^{1/3}$ and $Re Pr$ are function only of $Ra Pr^{2/3}$
(within logarithmic corrections). In practice, since $Nu$ is always close to
$Ra^{1/3}$, this corresponds to a much weaker dependence of the heat transfer
in the Prandtl number at low Reynolds number than at large Reynolds number.
This difference may solve an existing controversy between measurements in SF6
(large $Re$) and in alcohol/water (lower $Re$). We link these regimes with a
possible global bifurcation in the turbulent mean flow. We further show how a
scaling theory could be used to describe these two regimes through a single
universal function. This function presents a bimodal character for intermediate
range of Reynolds number. We explain this bimodality in term of two dissipation
regimes, one in which fluctuation dominate, and one in which mean flow
dominates. Altogether, our results provide a six parameters fit of the curve
$Nu(Ra,Pr)$ which may be used to describe all measurements at $Pr\ge 0.7$.


  A new ultra low-level counting setup has been installed in the
shallow-underground laboratory Felsenkeller in Dresden, Germany. It includes a
high-purity germanium detector (HPGe) of 163\% relative efficiency within
passive and active shields. The passive shield consists of 45m rock overburden
(140 meters water equivalent), 40 cm of low-activity concrete, and a lead and
copper castle enclosed by an anti-radon box. The passive shielding alone is
found to reduce the background rate to rates comparable to other
shallow-underground laboratories. An additional active veto is given by five
large plastic scintillation panels surrounding the setup. It further reduces
the background rate by more than one order of magnitude down to 116$\pm$1
kg$^{-1}$ d$^{-1}$ in an energy interval of 40-2700 keV. This low background
rate is unprecedented for shallow-underground laboratories and close to deep
underground laboratories.


  We introduce a new electronic aromaticity index, AV1245, consisting in the
average of the 4-center MCI values along the ring that keep a positional
relationship of 1,2,4,5. AV1245 measures the extent of transferability of the
delocalized electrons between bonds 1-2 and 4-5, which is expected to be large
in conjugated circuits and, therefore, in aromatic molecules. A new algorithm
for the calculation of MCI for large rings is also introduced and used to
produce the data for the calibration of the new aromaticity index. AV1245 does
not rely on reference values, does not suffer from large numerical precision
errors, and it does not present any limitation on the nature of atoms, the
molecular geometry or the level of calculation. It is a size-extensive measure
with a small computational cost that grows linearly with the number of ring
members. Therefore, it is specially suitable to study the aromaticity of large
molecular rings as those occurring in belt-shaped M\"obius structures or
porphyrins.


  Experimental noise often contains valuable information on the interactions of
a system with its environment but establishing a relation between the measured
time fluctuations and relevant physical observables is rarely apparent. Here,
we leverage a multi-dimensional and multi-sensor analysis of spectral diffusion
to investigate the dynamics of carriers in charge traps surrounding color
center clusters in diamond. Working with nitrogen-vacancy (NV) centers sharing
the same diffraction-limited volume, we establish statistical correlations in
the spectral changes we measure as we recursively probe the optical resonances
of the cluster, which we subsequently exploit to unveil proximal traps. By
simultaneously co-monitoring the spectra of multiple NVs in the set, we show
the ability to deterministically induce Stark shifts in the observed optical
resonances, hence allowing us to identify electrostatically coupled sets of
emitters. These cross-correlated measurements allow us to determine the
relative three-dimensional positions of interacting NVs in a cluster as well as
the location and charge sign of proximal traps. Our results can be generalized
to other color centers and open intriguing opportunities for the microscopic
characterization of photo-carrier dynamics in semiconductors and for the
manipulation of nanoscale spin-qubit clusters connected via electric fields.


  In a model of relativistic heavy ion collisions wherein the unconfined
quark-gluon plasma is condensed into glass, we derive the Vogel-Fulcher-Tammann
cooling law. This law is well known to hold true in condensed matter glasses.
The high energy plasma is initially created in a very hot negative temperature
state and cools down to the Hagedorn glass temperature at an ever decreasing
rate. The cooling rate is largely determined by the QCD string tension derived
from hadronic Regge trajectories. The ultimately slow relaxation time is a
defining characteristic of a color glass condensate.


  To improve the poor performance of distributed operation and non-scalability
of centralized operation in traditional cell-free massive MIMO, we propose a
cell-free distributed collaborative (CFDC) massive multiple-input
multiple-output (MIMO) system based on a novel two-layer model to take
advantages of the distributed cloud-edge-end collaborative architecture in
beyond 5G (B5G) internet of things (IoT) environment to provide strong
flexibility and scalability. We further ultilize the proposed CFDC massive MIMO
system to support the low altitude three-dimensional (3-D) coverage scenario
with unmanned aerial vehicles (UAVs), while accounting for 3-D Rician channel
estimation, user-centric association and different scalable receiving schemes.
Since coexisted UAVs and ground users (GUEs) cause greater interference, we
ultilize user-centric association strategy and minimum-mean-square error (MMSE)
channel state information (CSI) estimation to obtain the estimated CSI of UAVs
and GUEs. Under the CFDC scenarios, scalable receiving schemes as maximum ratio
combing (MRC), partial zero-forcing (P-ZF) and partial minimum-mean-square
error (P-MMSE) can be performed at edge servers and the closed-form expressions
for uplink spectral efficiency (SE) are derived. Based on the derived
expressions, we propose an efficient power control algorithm by solving a
multi-objective optimization problem (MOOP) between maximizing the average SE
of UAVs and GUEs simultaneously with Deep Q-Network (DQN). Numerical results
verify the accuracy of the derived closed-form expressions and the
effectiveness of the coexisted UAVs and GUEs transmission scheme in CFDC
massive MIMO systems. The SE analysis under various system parameters offers
numerous flexibilities for system optimization.


  We calculate the ionisation fraction in protostellar disk models using two
different gas-phase chemical networks, and examine the effect of turbulent
mixing by modelling the diffusion of chemical species vertically through the
disk. The aim is to determine in which regions of the disk gas can couple to a
magnetic field and sustain MHD turbulence. We find that the effect of diffusion
depends crucially on the elemental abundance of heavy metals (magnesium)
included in the chemical model. In the absence of heavy metals, diffusion has
essentially no effect on the ionisation structure of the disks, as the
recombination time scale is much shorter than the turbulent diffusion time
scale. When metals are included with an elemental abundance above a threshold
value, the diffusion can dramatically reduce the size of the magnetically
decoupled region, or even remove it altogther. For a complex chemistry the
elemental abundance of magnesium required to remove the dead zone is 10(-10) -
10(-8). We also find that diffusion can modify the reaction pathways, giving
rise to dominant species when diffusion is switched on that are minor species
when diffusion is absent. This suggests that there may be chemical signatures
of diffusive mixing that could be used to indirectly detect turbulent activity
in protoplanetary disks. We find examples of models in which the dead zone in
the outer disk region is rendered deeper when diffusion is switched on. Overall
these results suggest that global MHD turbulence in protoplanetary disks may be
self-sustaining under favourable circumstances, as turbulent mixing can help
maintain the ionisation fraction above that necessary to ensure good coupling
between the gas and magnetic field.


  We developed a novel design of a Micro Pixel Chamber ($\mu$-PIC) with
resistive electrodes for a charged-particle-tracking detector in high-rate
applications. Diamond-Like Carbon (DLC) thin film is used for the cathodes. The
resistivity can be controlled flexibly ($\mathrm{10^{5-7}k\Omega/sq.}$) at high
uniformity. The fabrication-process was greatly improved and the resistive
$\mu$-PIC could be operated at 10$\times$10 $\mathrm{cm^2}$. Resistors for the
HV bias and capacitors for the AC coupling were completely removed by applying
PCB and carbon-sputtering techniques, and the resistive $\mu$-PIC became a very
compact detector. The performances of our new resistive $\mu$-PIC were measured
in various ways. Consequently, it was possible to attain high gas gains
($\mathrm{> 10^{4}}$), high detection efficiency, and position resolution
exceeding 100 $\mu$m. The spark current was suppressed, and the new resistive
$\mu$-PIC was operated stably under fast-neutrons irradiation. These features
offer solutions for a charged-particle-tracking detector in future high-rate
applications.