  The problem of recovering the topology and cable parameters of an electrical
network from power and voltage data at all nodes is a problem of fitting both
an algebraic variety and a graph. The problem is often ill-posed. In case there
are multiple electrical networks which fit the data up to a given tolerance, we
seek a solution in which the graph and therefore the algebraic equations
associated with the electrical network are sparse, i.e. with few edges and
terms. We propose an algorithm for recovering simultaneously a sparse topology
and the cable parameters of any network, combining in an iterative procedure
the resolution of non-negative linear regression problems, which are convex,
and techniques of spectral graph sparsification. The algorithm is tested on
several electrical networks.


  Explaining deep learning model inferences is a promising venue for scientific
understanding, improving safety, uncovering hidden biases, evaluating fairness,
and beyond, as argued by many scholars. One of the principal benefits of
counterfactual explanations is allowing users to explore "what-if" scenarios
through what does not and cannot exist in the data, a quality that many other
forms of explanation such as heatmaps and influence functions are inherently
incapable of doing. However, most previous work on generative explainability
cannot disentangle important concepts effectively, produces unrealistic
examples, or fails to retain relevant information. We propose a novel approach,
DISSECT, that jointly trains a generator, a discriminator, and a concept
disentangler to overcome such challenges using little supervision. DISSECT
generates Concept Traversals (CTs), defined as a sequence of generated examples
with increasing degrees of concepts that influence a classifier's decision. By
training a generative model from a classifier's signal, DISSECT offers a way to
discover a classifier's inherent "notion" of distinct concepts automatically
rather than rely on user-predefined concepts. We show that DISSECT produces CTs
that (1) disentangle several concepts, (2) are influential to a classifier's
decision and are coupled to its reasoning due to joint training (3), are
realistic, (4) preserve relevant information, and (5) are stable across similar
inputs. We validate DISSECT on several challenging synthetic and realistic
datasets where previous methods fall short of satisfying desirable criteria for
interpretability and show that it performs consistently well and better than
existing methods. Finally, we present experiments showing applications of
DISSECT for detecting potential biases of a classifier and identifying spurious
artifacts that impact predictions.


  We study the two point correlation function of two nucleon currents
sandwiched between the vacuum and the rho meson state. The light cone QCD sum
rules are derived both for $\rho NN$ vector and tensor couplings
simultaneously. The contribution from the excited states and the continuum is
subtracted cleanly through the double Borel transform with respect to the two
external momenta, $p_1^2$, $p^2_2=(p-q)^2$. Our results are $g_\rho =(2.5\pm
0.2)$, $\kappa_\rho =(8.0\pm 2.0), in good agreement with the values used in
the nuclear forces.


  Large Language Models (LLMs) have achieved remarkable performance across a
wide variety of natural language tasks. However, they have been shown to suffer
from a critical limitation pertinent to 'hallucination' in their output. Recent
research has focused on investigating and addressing this problem for a variety
of tasks such as biography generation, question answering, abstractive
summarization, and dialogue generation. However, the crucial aspect pertaining
to 'negation' has remained considerably underexplored. Negation is important
because it adds depth and nuance to the understanding of language and is also
crucial for logical reasoning and inference. In this work, we address the above
limitation and particularly focus on studying the impact of negation in LLM
hallucinations. Specifically, we study four tasks with negation: 'false premise
completion', 'constrained fact generation', 'multiple choice question
answering', and 'fact generation'. We show that open-source state-of-the-art
LLMs such as LLaMA-2-chat, Vicuna, and Orca-2 hallucinate considerably on all
these tasks involving negation which underlines a critical shortcoming of these
models. Addressing this problem, we further study numerous strategies to
mitigate these hallucinations and demonstrate their impact.


  Given a directed graph $G$ and a pair of nodes $s$ and $t$, an \emph{$s$-$t$
bridge} of $G$ is an edge whose removal breaks all $s$-$t$ paths of $G$ (and
thus appears in all $s$-$t$ paths). Computing all $s$-$t$ bridges of $G$ is a
basic graph problem, solvable in linear time.
  In this paper, we consider a natural generalisation of this problem, with the
notion of "safety" from bioinformatics. We say that a walk $W$ is \emph{safe}
with respect to a set $\mathcal{W}$ of $s$-$t$ walks, if $W$ is a subwalk of
all walks in $\mathcal{W}$. We start by considering the maximal safe walks when
$\mathcal{W}$ consists of: all $s$-$t$ paths, all $s$-$t$ trails, or all
$s$-$t$ walks of $G$. We show that the first two problems are immediate
linear-time generalisations of finding all $s$-$t$ bridges, while the third
problem is more involved. In particular, we show that there exists a compact
representation computable in linear time, that allows outputting all maximal
safe walks in time linear in their length.
  We further generalise these problems, by assuming that safety is defined only
with respect to a subset of \emph{visible} edges. Here we prove a dichotomy
between the $s$-$t$ paths and $s$-$t$ trails cases, and the $s$-$t$ walks case:
the former two are NP-hard, while the latter is solvable with the same
complexity as when all edges are visible. We also show that the same complexity
results hold for the analogous generalisations of \emph{$s$-$t$ articulation
points} (nodes appearing in all $s$-$t$ paths).
  We thus obtain the best possible results for natural "safety"-generalisations
of these two fundamental graph problems. Moreover, our algorithms are simple
and do not employ any complex data structures, making them ideal for use in
practice.


  We implement a two-qubit entangling M{\o}lmer-S{\o}rensen interaction by
transporting two co-trapped $^{40}\mathrm{Ca}^{+}$ ions through a stationary,
bichromatic optical beam within a surface-electrode Paul trap. We describe a
procedure for achieving a constant Doppler shift during the transport which
uses fine temporal adjustment of the moving confinement potential. The fixed
interaction duration of the ions transported through the laser beam as well as
the dynamically changing ac Stark shift require alterations to the calibration
procedures used for a stationary gate. We use the interaction to produce Bell
states with fidelities commensurate to those of stationary gates performed in
the same system. This result establishes the feasibility of actively
incorporating ion transport into quantum information entangling operations.


  In the realm of Delone sets in locally compact, second countable, Hausdorff
groups, we develop a dynamical systems approach in order to study the
continuity behavior of measured quantities arising from point sets. A special
focus is both on the autocorrelation, as well as on the density of states for
random bounded operators. It is shown that for uniquely ergodic limit systems,
the latter measures behave continuously with respect to the Chabauty-Fell
convergence of hulls. In the special situation of Euclidean spaces, our results
complement recent developments in describing spectra as topological limits: we
show that the measured quantities under consideration can be approximated via
periodic analogs.


  In image dehazing task, haze density is a key feature and affects the
performance of dehazing methods. However, some of the existing methods lack a
comparative image to measure densities, and others create intermediate results
but lack the exploitation of their density differences, which can facilitate
perception of density. To address these deficiencies, we propose a
density-aware dehazing method named Density Feature Refinement Network
(DFR-Net) that extracts haze density features from density differences and
leverages density differences to refine density features. In DFR-Net, we first
generate a proposal image that has lower overall density than the hazy input,
bringing in global density differences. Additionally, the dehazing residual of
the proposal image reflects the level of dehazing performance and provides
local density differences that indicate localized hard dehazing or high density
areas. Subsequently, we introduce a Global Branch (GB) and a Local Branch (LB)
to achieve density-awareness. In GB, we use Siamese networks for feature
extraction of hazy inputs and proposal images, and we propose a Global Density
Feature Refinement (GDFR) module that can refine features by pushing features
with different global densities further away. In LB, we explore local density
features from the dehazing residuals between hazy inputs and proposal images
and introduce an Intermediate Dehazing Residual Feedforward (IDRF) module to
update local features and pull them closer to clear image features. Sufficient
experiments demonstrate that the proposed method achieves results beyond the
state-of-the-art methods on various datasets.


  We present recent results from the Laboratory for Cosmological Data Mining
(http://lcdm.astro.uiuc.edu) at the National Center for Supercomputing
Applications (NCSA) to provide robust classifications and photometric redshifts
for objects in the terascale-class Sloan Digital Sky Survey (SDSS). Through a
combination of machine learning in the form of decision trees, k-nearest
neighbor, and genetic algorithms, the use of supercomputing resources at NCSA,
and the cyberenvironment Data-to-Knowledge, we are able to provide improved
classifications for over 100 million objects in the SDSS, improved photometric
redshifts, and a full exploitation of the powerful k-nearest neighbor
algorithm. This work is the first to apply the full power of these algorithms
to contemporary terascale astronomical datasets, and the improvement over
existing results is demonstrable. We discuss issues that we have encountered in
dealing with data on the terascale, and possible solutions that can be
implemented to deal with upcoming petascale datasets.


  We provide a variety of results for (quasi)convex, law-invariant functionals
defined on a general Orlicz space, which extend well-known results in the
setting of bounded random variables. First, we show that Delbaen's
representation of convex functionals with the Fatou property, which fails in a
general Orlicz space, can be always achieved under the assumption of
law-invariance. Second, we identify the range of Orlicz spaces where the
characterization of the Fatou property in terms of norm lower semicontinuity by
Jouini, Schachermayer and Touzi continues to hold. Third, we extend Kusuoka's
representation to a general Orlicz space. Finally, we prove a version of the
extension result by Filipovi\'{c} and Svindland by replacing norm lower
semicontinuity with the (generally non-equivalent) Fatou property. Our results
have natural applications to the theory of risk measures.


  Supersymmetrizable theories, such as M(em)branes and associated matrix-models
related to Yang-Mills theory, possess r-matrices


  This research delves into the comparative advantages of Generative AI
chatbots (GenAIbots) -- ChatGPT, Bing Chat, Bard, and Claude -- in the context
of Chemistry education, framed within a constructivist perspective. Our primary
objective was to identify which of these four AI tools is more effective for
enhancing Chemistry learning. Employing a single-case study approach, we
scrutinised interaction logs between the AI systems and a simulated student
persona during Chemistry learning simulations, incorporating Content Analysis
methodology to delve deeper into the discourse. Our findings underscore these
tools' potential as "agents-to-think-with", enhancing critical thinking,
problem-solving, comprehension, creativity, and tailored learning. Especially
noteworthy is their ability to stimulate learners through Socratic-like
questioning, aligning with constructionist principles. The research emphasises
the pivotal role of prompt crafting to coax desired responses from GenAIbots,
engendering iterative reflections. It also highlights the need for robust
educator training to infuse these technologies into educational settings.
Conclusively, while ChatGPT, Bing Chat, Bard, and Claude are poised to enrich
Chemistry education by fostering dynamic, inclusive learning experiences,
ChatGPT stood out, decisively surpassing Bing Chat in its performance. Bard and
Claude trailed closely, with all three showcasing a more in-depth, precise, and
nuanced understanding, underscoring ChatGPT's adeptness at contextual
comprehension.


  Let $L\subseteq \mathbb{R}^{n}$ an even lattice and $T_{L}=\mathbb{R}^{n}/L$
the associated torus. Associated with $L$ we construct $T_{L}$--kernel on a
hyperfinite factor type $\mathcal{A}_{L}$, i.e. a monomorphism
$T_{L}\to\mathsf{Out}(\mathcal{A}_{L})$, and compute Sutherland's obstruction
class in $H^{3}_{\mathrm{Borel}}(T_{L},\mathbb{T})\cong H^{4}(BT_{L}
,\mathbb{Z})$, which is an invariant of the $T_{L}$--kernel and an obstruction
to the existence of a twisted crossed product by $T_{L}$. As a Corollary, we
obtain that for any $n$-torus $T$ any class in
$H^{3}_{\mathrm{Borel}}(T,\mathbb{T})$ arises as an obstruction for a
$T$-kernel on the hyperfinite type III${}_{1}$ factor $R$. The construction is
an analogue of the construction of Vaughan Jones for finite groups on the
hyperfinite type II${}_{1}$ factor but is also motivated by and has
applications to conformal nets. Namely, there is an associated local extension
$\mathcal{A}_{L}\supseteq \mathcal{A}_{\mathbb{R}^n}$ of conformal nets and the
$T_{L}$--kernel corresponds to a family of $T_{L^\ast}$--twisted sectors
representations whose anomaly (obstruction) can be identified with the inner
product on $L$ seen as a class in $H^{4}(BT_{L},\mathbb{Z})\cong
\operatorname{Sym}^{2}(L,\mathbb{Z})$.


  We construct a hyperbolic group with a finitely presented subgroup, which has
infinitely many conjugacy classes of finite-order elements.
  We also use a version of Morse theory with high dimensional horizontal cells
and use handle cancellation arguments to produce other examples of subgroups of
CAT(0) groups with infinitely many conjugacy classes of finite-order elements.


  Herein, we report the reversible structural transition of single-layer VSe2
grown on Au(111) through alternating thermal annealing and Se replenishment.
Using scanning tunneling microscopy (STM) and angle-resolved photoemission
spectroscopy (ARPES), we demonstrate the epitaxial growth of high-quality VSe2
on Au(111) with the octahedral (1T) structure and the Se-vacancy-induced
transformation of VSe2 from the metallic moir\'e (1T) phase to the
semiconducting (2H) phase. With convincing agreement between the experimental
results and DFT calculations, the nanostructure near the grain boundary in the
defective intermediate phase is confirmed, as well as the reaction pathway with
Se gradually depleting at elevated temperatures. Importantly, it is revealed
that the density of the linear Se defects plays a crucial role in the formation
of the 2H domain phase due to the increment of the in-plane lattice parameter
after Se desorption and the better thermal stability of the 2H phase compared
to the 1T phase. The proper control of the density of Se atoms in the topmost
Se layer of VSe2 could feasibly manipulate the ratio between the 1T phase and
the 2H phase in the steak-shaped domain, which is regarded as a good platform
for 2D homojunctions in nanoelectronics.


  The field of 'explainable' artificial intelligence (XAI) has produced highly
cited methods that seek to make the decisions of complex machine learning (ML)
methods 'understandable' to humans, for example by attributing 'importance'
scores to input features. Yet, a lack of formal underpinning leaves it unclear
as to what conclusions can safely be drawn from the results of a given XAI
method and has also so far hindered the theoretical verification and empirical
validation of XAI methods. This means that challenging non-linear problems,
typically solved by deep neural networks, presently lack appropriate remedies.
Here, we craft benchmark datasets for three different non-linear classification
scenarios, in which the important class-conditional features are known by
design, serving as ground truth explanations. Using novel quantitative metrics,
we benchmark the explanation performance of a wide set of XAI methods across
three deep learning model architectures. We show that popular XAI methods are
often unable to significantly outperform random performance baselines and edge
detection methods. Moreover, we demonstrate that explanations derived from
different model architectures can be vastly different; thus, prone to
misinterpretation even under controlled conditions.


  This letter proposes a new spoof surface plasmon transmission line (SSP-TL)
using capacitor loading techniques. This new SSP-TL features flexible and
reconfigurable dispersion control and highly selective filtering performance
without resorting to configuration change. Moreover, it requires much smaller
line width than the conventional SSP-TLs for achieving a extremely slow wave
(or a highly confined field), which is quite useful for a compact system. To
illustrate the design principle, several examples are designed within the
frequency range of 2-8 GHz. Both numerical and experimental results are given
in comparison with the conventional SSP-TL. It is demonstrated that the
proposed technique provides a better performance in size reduction and
dispersion reconfigurability.


  This technical note describes a set of baseline tools for automatic
processing of Danish text. The tools are machine-learning based, using natural
language processing models trained over previously annotated documents. They
are maintained at ITU Copenhagen and will always be freely available.


  Starting from any unital colored PROP $P$, we define a category $P(P)$ of
shapes called $P$-propertopes. Presheaves on $P(P)$ are called $P$-propertopic
sets. For $0 \leq n \leq \infty$ we define and study $n$-time categorified
$P$-algebras as $P$-propertopic sets with some lifting properties. Taking
appropriate PROPs $P$, we obtain higher categorical versions of polycategories,
2-fold monoidal categories, topological quantum field theories, and so on.


  In recent years, lead-free solder alloys based on tin, silver, or copper have
gained popularity over lead-based solder alloys due to their improved
mechanical and electrical properties and their non-toxic nature. In our
previous studies, we examined the stress-strain behavior of SAC305 under
varying cooling rates. This study extends our investigation to various
lead-free solder materials, including Sn, Sn-Ag, and SAC305, to compare their
relative mechanical and cyclic properties. We employed molecular dynamics to
model the atomistic behavior. Initially, the models were melted at a constant
rate and then cooled at various rates, including 2.5 K/ps, 10 K/ps, 50 K/ps,
and 100 K/ps. Additionally, exponential cooling was used to replicate
real-world cooling scenarios.. We utilized a set of modified embedded atomic
model (MEAM) interatomic potentials for the tensile test and cyclic loading.
The tensile test has been conducted until fracture occurs at a constant strain
rate. Furthermore, we investigated the cyclic loading behavior within a strain
range of -10% to 10% for 10 cycles. The results indicated that cooling rates
significantly influenced mechanical properties, with slower rates (2.5 K/ps and
10 K/ps) showing substantial differences, while the differences between higher
rates (50 K/ps and 100 K/ps) were less pronounced. The ultimate strength,
Young's modulus, modulus of resilience, and coefficient of thermal expansion
exhibited a negative correlation with increasing cooling rates, while the
modulus of toughness increased, indicating improved impact resistance. To
assess energy dissipation during cyclic loading, we examined the hysteresis
loop area and stress amplitude. After a certain number of cycles, the energy
lost during each cycle reached a stable level.


  We present a new set of basis functions for H(curl)-conforming,
H(div)-conforming, and L2 -conforming finite elements of arbitrary order on a
tetrahedron. The basis functions are expressed in terms of Bernstein
polynomials and augment the natural H1 -conforming Bernstein basis. The basis
functions respect the differential operators, namely, the gradients of the
high-order H1 -conforming Bernstein-Bezier basis functions form part of the
H(curl)-conforming basis, and the curl of the high-order, non-gradients
H(curl)-conforming basis functions form part of the H(div)-conforming basis,
and the divergence of the high-order, non-curl H(div)-conforming basis
functions form part of the L2-conforming basis. Procedures are given for the
efficient computation of the mass and stiffness matrices with these basis
functions without using quadrature rules for (piece-wise) constant coefficients
on affine tetrahedra. Numerical results are presented to illustrate the use of
the basis to approximate representative problems.


  Let $E=\mathbb{Q}\big(\sqrt{-d}\big)$ be an imaginary quadratic field for a
square-free positive integer $d$, and let $\mathcal{O}$ be its ring of
integers. For each positive integer $m$, let $I_m$ be the free Hermitian
lattice over $\mathcal{O}$ with an orthonormal basis, let $\mathfrak{S}_d(1)$
be the set consisting of all positive definite integral unary Hermitian
lattices over $\mathcal{O}$ that can be represented by some $I_m$, and let
$g_d(1)$ be the least positive integer such that all Hermitian lattices in
$\mathfrak{S}_d(1)$ can be uniformly represented by $I_{g_d(1)}$. The main
results of this work provide an algorithm to calculate the explicit form of
$\mathfrak{S}_d(1)$ and the exact value of $g_d(1)$ for every imaginary
quadratic field $E$, which can be viewed as a natural extension of the
Pythagoras number in the lattice setting.


  I review the main properties of four-dimensional strings constructed with
free-fermions on the world-sheet. In particular I discuss possible model
independent low energy predictions related to the existence of states with
fractional electric charges, the computation of the string unification scale,
the string model building, and the perturbative approach to supersymmetry
breaking which makes the spectacular prediction of a new large dimension at the
TeV scale.


  We put forward an idea that physical phenomena have to be treated in
5-dimensional space where the fifth coordinate is the interval S. Thus, we
considered the (1+4) extended space G(T;X,Y,Z,S). In addition to Lorentz
transformations (T;X), (T;Y), (T;Z) which are in (1+3)-dimensional Minkowski
space, in the proposed (1+4)d extended space two other types of transformations
exist in planes (T,S); (X,S), (Y,S), (Z,S) that converts massive particles into
massless and vice versa. We also consider energy-momentum-mass 5-d space which
is conjugated to the time-coordinates-interval (T;X,Y,Z,S) space. The mass in
above mentioned 5-d energy-momentum-mass space corresponds to the interval S in
5-d space (T,X,Y,Z,S). Well known energy-momentum 4-vector P(1+3)=(E/c;
px,py,pz) in the Minkowski (T;X,Y,Z) space is transformed to the the 5-vector -
P(1+4)=(E/c; px,py,pz,mc) in the extended space G(T;X,Y,Z,S) and becomes
isotropic for 5-vectors of the massive as well as for the massless particles.


  Gromov's compactness theorem for pseudo-holomorphic curves is a foundational
result in symplectic geometry. It controls the compactness of the moduli space
of pseudo-holomorphic curves with bounded area in a symplectic manifold.
  In this paper, we prove the analog of Gromov's compactness theorem in
non-archimedean analytic geometry. We work in the framework of Berkovich
spaces.
  First, we introduce a notion of K\"ahler structure in non-archimedean
analytic geometry using metrizations of virtual line bundles. Second, we
introduce formal stacks and non-archimedean analytic stacks. Then we construct
the moduli stack of non-archimedean analytic stable maps using formal models,
Artin's representability criterion and the geometry of stable curves. Finally,
we reduce the non-archimedean problem to the known compactness results in
algebraic geometry. The motivation of this paper is to provide the foundations
for non-archimedean enumerative geometry.


  Applying assignment methods to compute user-equilibrium route choice is very
common in traffic planning. It is common sense that vehicular traffic arranges
in a user-equilibrium based on generalized costs in which travel time is a
major factor. Surprisingly travel time has not received much attention for the
route choice of pedestrians. In microscopic simulations of pedestrians the
vastly dominating paradigm for the computation of the preferred walking
direction is set into the direction of the (spatially) shortest path. For
situations where pedestrians have travel time as primary determinant for their
walking behavior it would be desirable to also have an assignment method in
pedestrian simulations. To apply existing (road traffic) assignment methods
with simulations of pedestrians one has to reduce the nondenumerably many
possible pedestrian trajectories to a small subset of routes which represent
the main, relevant, and significantly distinguished routing alternatives. All
except one of these routes will mark detours, i.e. not the shortest connection
between origin and destination. The proposed assignment method is intended to
work with common operational models of pedestrian dynamics. These - as
mentioned before - usually send pedestrians into the direction of the spatially
shortest path. Thus, all detouring routes have to be equipped with intermediate
destinations, such that pedestrians can do a detour as a piecewise connection
of segments on which they walk into the direction of the shortest path. One has
then to take care that the transgression from one segment to the following one
no artifacts are introduced into the pedestrian trajectory.


  Assistive robot arms try to help their users perform everyday tasks. One way
robots can provide this assistance is shared autonomy. Within shared autonomy,
both the human and robot maintain control over the robot's motion: as the robot
becomes confident it understands what the human wants, it intervenes to
automate the task. But how does the robot know these tasks in the first place?
State-of-the-art approaches to shared autonomy often rely on prior knowledge.
For instance, the robot may need to know the human's potential goals
beforehand. During long-term interaction these methods will inevitably break
down -- sooner or later the human will attempt to perform a task that the robot
does not expect. Accordingly, in this paper we formulate an alternate approach
to shared autonomy that learns assistance from scratch. Our insight is that
operators repeat important tasks on a daily basis (e.g., opening the fridge,
making coffee). Instead of relying on prior knowledge, we therefore take
advantage of these repeated interactions to learn assistive policies. We
introduce SARI, an algorithm that recognizes the human's task, replicates
similar demonstrations, and returns control when unsure. We then combine
learning with control to demonstrate that the error of our approach is
uniformly ultimately bounded. We perform simulations to support this error
bound, compare our approach to imitation learning baselines, and explore its
capacity to assist for an increasing number of tasks. Finally, we conduct three
user studies with industry-standard methods and shared autonomy baselines,
including a pilot test with a disabled user. Our results indicate that learning
shared autonomy across repeated interactions matches existing approaches for
known tasks and outperforms baselines on new tasks. See videos of our user
studies here: https://youtu.be/3vE4omSvLvc


  We show that perturbation theory may give reasonable numbers for the decays
of the bottomonium and charmonium ground states to $e^+e^-$ and to
$\gamma\gamma$. To reach this conclusion it is important to perform the
resummation of logs. In particular, we obtain the value $\Gamma(\eta_b (1S) \to
\gamma\gamma)=0.35 \pm 0.1 ({\rm th.}) \pm 0.05 (\lQ)$ KeV.


  To implement the previously formulated principles of sustainable economic
development, all non-negative solutions of the linear system of equations and
inequalities, which are satisfied by the vector of real consumption, are
completely described. It is established that the vector of real consumption
with the minimum level of excess supply is determined by the solution of some
quadratic programming problem. The necessary and sufficient conditions are
established under which the economic system, described by the "input-output"
production model, functions in the mode of sustainable development. A complete
description of the equilibrium states for which markets are partially cleared
in the economy model of production "input-output" is given, on the basis that
all solutions of system of linear equations and inequalities are completely
described. The existence of a family of taxation vectors in the "input-output"
model of production, under which the economic system is able to function in the
mode of sustainable development, is proved. Restrictions were found for the
vector of taxation in the economic system, under which the economic system is
able to function in the mode of sustainable development. The axioms of the
aggregated description of the economy is proposed.


  This paper is concerned with some properties of the generalized GARCH models,
obtained by extending GARCH models with exogenous variables, the so-called
GARCH extended (GARCHX) models. For these, we establish sufficient conditions
for some properties such as stationarity, existence of moments, ergodicity,
geometric ergodicity, consistence and asymptotic normality of likelihood
estimators of the model parameters. For some of these properties we show that
the conditions that we propose are also necessary. We further provide examples
and applications to illustrate and highlight the importance of our findings.


  In this article, the new black hole solutions to the
Einstein-power-Maxwell-dilaton gravity theory have been investigated in a
four-dimensional space-time. The coupled scalar, electromagnetic and
gravitational field equations have been solved in a static and spherically
symmetric geometry. It has been shown that dilatonic potential, as the solution
to the scalar field equation, can be written in the form of a generalized
Liouville potential. Also, three classes of novel charged dilaton black hole
solutions, in the presence of power law nonlinear electrodynamics, have been
constructed out which are asymptotically non-flat and non-AdS. The conserved
and thermodynamic quantities have been calculated from geometrical and
thermodynamical approaches, separately. Since the results of these two
alternative approaches are identical one can argue that the first law of black
hole thermodynamics is valid for all of the new black hole solutions. The
thermodynamic stability or phase transition of the black holes have been
studied, making use of the canonical ensemble method. The points of type-1 and
type-2 phase transitions as well as the ranges at which the black holes are
stable have been indicated by considering the heat capacity of the new black
hole solutions. The global stability of the black holes have been studied
through the grand canonical ensemble method. Regarding the Gibbs free energy of
the black holes, the points of Hawking-Page phase transition and ranges of the
horizon radii at which the black holes are globally stable have been
determined.


  Superconducting cosmic strings can give transient electromagnetic signatures
that we argue are most evident at radio frequencies. We investigate the three
different kinds of radio bursts from cusps, kinks, and kink-kink collisions on
superconducting strings. We find that the event rate is dominated by kink
bursts in a range of parameters that are of observational interest, and can be
quite high (several a day at 1 Jy flux) for a canonical set of parameters. In
the absence of events, the search for radio transients can place stringent
constraints on superconducting cosmic strings.


  We perform individual-based Monte Carlo simulations in a community consisting
of two predator species competing for a single prey species, with the purpose
of studying biodiversity stabilization in this simple model system. Predators
are characterized with predation efficiency and death rates, to which Darwinian
evolutionary adaptation is introduced. Competition for limited prey abundance
drives the populations' optimization with respect to predation efficiency and
death rates. We study the influence of various ecological elements on the final
state, finding that both indirect competition and evolutionary adaptation are
insufficient to yield a stable ecosystem. However, stable three-species
coexistence is observed when direct interaction between the two predator
species is implemented.


  If S and S' are two finite sets of Coxeter generators for a right-angled
Coxeter group W, then the Coxeter systems (W,S) and (W,S') are equivalent.


  The reason for the horizontal turn of the Tunguska-1908 bolide trajectory
remains difficult to understand. It finds explanation, however, in the New
Explosive Cosmogony of minor bodies as having been caused by an explosion of a
part (M up to 10^12 g) of the comet nucleus whose ices contained products of
its electrolysis, 2H2+O2. In detonation, this part was repelled from the more
massive unexploded nucleus remnant, changed the direction of its own motion by
~10^o and imparted its kinetic energy, in expanding and slowing down, to the
air in producing an effect of a high-altitude explosion. Because there are no
traces of a fall of the more massive remnant, one comes to the conclusion that
on passing through the Earth's atmosphere it again entered a heliocentric orbit
(the hypothesis of V.Vernadskiy, 1932). A search for this comet,
P/Tunguska-1908, among the 6077 known NEAs shows the 2005NB56 object to be the
most appropriate candidate for a number of its parameters (a size is ~ 170 m, P
= 2.106 y, e = 0.473 and i = 6.8^o). Back integration of its orbit made without
allowing for non-gravitational effects suggests that it had passed the Earth on
June 27, 1908 at a distance of 0.06945 AU. It is quite possible that a proper
inclusion of even fairly weak non-gravitational forces would make its orbit fit
in parameters that of the Tunguska bolide.


  Warning: This paper contains memes that may be offensive to some readers.
  Multimodal Internet Memes are now a ubiquitous fixture in online discourse.
One strand of meme-based research is the classification of memes according to
various affects, such as sentiment and hate, supported by manually compiled
meme datasets. Understanding the unique characteristics of memes is crucial for
meme classification. Unlike other user-generated content, memes spread via
memetics, i.e. the process by which memes are imitated and transformed into
symbols used to create new memes. In effect, there exists an ever-evolving pool
of visual and linguistic symbols that underpin meme culture and are crucial to
interpreting the meaning of individual memes. The current approach of training
supervised learning models on static datasets, without taking memetics into
account, limits the depth and accuracy of meme interpretation. We argue that
meme datasets must contain genuine memes, as defined via memetics, so that
effective meme classifiers can be built. In this work, we develop a meme
identification protocol which distinguishes meme from non-memetic content by
recognising the memetics within it. We apply our protocol to random samplings
of the leading 7 meme classification datasets and observe that more than half
(50. 4\%) of the evaluated samples were found to contain no signs of memetics.
Our work also provides a meme typology grounded in memetics, providing the
basis for more effective approaches to the interpretation of memes and the
creation of meme datasets.


  Unmanned aerial vehicles (UAVs) are emerging as enablers for supporting many
applications and services, such as precision agriculture, search and rescue,
temporary network deployment or coverage extension, and security. UAVs are
being considered for integration into emerging 5G networks as aerial users or
network support nodes. We propose to leverage UAVs in 5G to assist in the
prevention, detection, and recovery of attacks on 5G networks. Specifically, we
consider jamming, spoofing, eavesdropping and the corresponding mitigation
mechanisms that are enabled by the versatility of UAVs. We introduce the hot
zone, safe zone and UAV-based secondary authorization entity, among others, to
increase the resilience and confidentiality of 5G radio access networks and
services. We present simulation results and discuss open issues and research
directions, including the need for experimental evaluation and a research
platform for prototyping and testing the proposed technologies.


  In this paper, we show that a multi-mode antenna (MMA) is an interesting
alternative to a conventional phased antenna array for direction-of-arrival
(DoA) estimation. By MMA we mean a single physical radiator with multiple
ports, which excite different characteristic modes. In contrast to phased
arrays, a closed-form mathematical model of the antenna response, like a
steering vector, is not straightforward to define for MMAs. Instead one has to
rely on calibration measurement or electromagnetic field (EMF) simulation data,
which is discrete. To perform DoA estimation, array interpolation technique
(AIT) and wavefield modeling (WM) are suggested as methods with inherent
interpolation capabilities, fully taking antenna nonidealities like mutual
coupling into account. We present a non-coherent DoA estimator for low-cost
receivers and show how coherent DoA estimation and joint DoA and polarization
estimation can be performed with MMAs. Utilizing these methods, we assess the
DoA estimation performance of an MMA prototype in simulations for both 2D and
3D cases. The results show that WM outperforms AIT for high SNR. Coherent
estimation is superior to non-coherent, especially in 3D, because non-coherent
suffers from estimation ambiguities. In conclusion, DoA estimation with a
single MMA is feasible and accurate.


  In this paper, we revisit a classic example of probabilistic cellular
automaton (PCA) on {0, 1} Z , namely, addition modulo 2 of the states of the
left-and right-neighbouring cells, followed by either preserving the result of
the addition, with probability p, or flipping it, with probability 1 -- p. It
is well-known that, for any value of p $\in$]0, 1[, this PCA is ergodic. We
show that, for p sufficiently close to 1, no coupling of the PCA dynamics based
on the composition of i.i.d. random functions of nearest-neighbour states (we
call this a basic i.i.d. coupling), can be successful, where successful means
that, for any given cell, the probability that every possible initial condition
leads to the same state after t time steps, goes to 1 as t goes to infinity. In
particular, this precludes the possibility of a CFTP scheme being based on such
a coupling. This property stands in sharp contrast with the case of monotone
PCA, for which, as soon as ergodicity holds, there exists a successful basic
i.i.d. coupling.


  In contemporary scientific research, understanding the distinction between
correlation and causation is crucial. While correlation is a widely used
analytical standard, it does not inherently imply causation. This paper
addresses the potential for misinterpretation in relying solely on correlation,
especially in the context of nonlinear dynamics. Despite the rapid development
of various correlation research methodologies, including machine learning, the
exploration into mining causal correlations between variables remains ongoing.
Empirical Dynamic Modeling (EDM) emerges as a data-driven framework for
modeling dynamic systems, distinguishing itself by eschewing traditional
formulaic methods in data analysis. Instead, it reconstructs dynamic system
behavior directly from time series data. The fundamental premise of EDM is that
dynamic systems can be conceptualized as processes where a set of states,
governed by specific rules, evolve over time in a high-dimensional space. By
reconstructing these evolving states, dynamic systems can be effectively
modeled. Using EDM, this paper explores the detection of causal relationships
between variables within dynamic systems through their time series data. It
posits that if variable X causes variable Y, then the information about X is
inherent in Y and can be extracted from Y's data. This study begins by
examining the dialectical relationship between correlation and causation,
emphasizing that correlation does not equate to causation, and the absence of
correlation does not necessarily indicate a lack of causation.


  We show that, if g is more than or equal to 2, the virtual cohomological
dimension of the mapping class group of a 3-dimensional handlebody of genus g
is equal to 4g-5 and the Euler number of it is equal to 0.


  At the spin transition point of $\nu=2/3$ quantum Hall states, nuclear spins
in a two-dimensional electron gas are polarized by an electric current. Using
GaAs/AlGaAs double-quantum-well samples, we first observed the spatial
diffusion of nuclear spin polarization between the two layers when the nuclear
spin polarization is current-induced in one layer. By numerical simulation, we
estimated the diffusion constant of the nuclear spin polarization to be $15 \pm
7$\,nm$^2$/s.


  Riemann normal coordinates (RNC) are unsuitable for \kahler manifolds since
they are not holomorphic. Instead, \kahler normal coordinates (KNC) can be
defined as holomorphic coordinates. We prove that KNC transform as a
holomorphic tangent vector under holomorphic coordinate transformations, and
therefore that they are natural extensions of RNC to the case of \kahler
manifolds. The KNC expansion provides a manifestly covariant background field
method preserving the complex structure in supersymmetric nonlinear sigma
models.


  Jets plus missing transverse energy is one of the main search channels for
new physics at the LHC. A major limitation lies in our understanding of QCD
backgrounds. Using jet merging we can describe the number of jets in typical
background channels in terms of a staircase scaling, including theory
uncertainties. The scaling parameter depends on the particles in the final
state and on cuts applied. Measuring the staircase scaling will allow us to
also predict the effective mass for Standard Model backgrounds. Based on both
observables we propose an analysis strategy avoiding model specific cuts which
returns information about the color charge and the mass scale of the underlying
new physics.


  The existence of closed loops of degeneracies in crystals has been intimately
connected to associated crystal symmetries, raising the question: what is the
minimum symmetry required for topological character, and can one find an
example? Triclinic CaAs$_3$, in space group $P{\bar 1}$ with only a center of
inversion, has been found to display, without need for tuning, a nodal loop of
accidental degeneracies with topological character, centered on one face of the
Brillouin zone that is otherwise fully gapped. The small loop is very flat in
energy, yet is cut four times by the Fermi energy, a condition that results in
an intricate repeated touching of inversion related pairs of Fermi surfaces at
Weyl points. Spin-orbit coupling lifts the fourfold degeneracy along the loop,
leaving trivial Kramers pairs. With its single nodal loop that emerges without
protection from any point group symmetry, CaAs$_3$ represents the primal
"hydrogen atom" of nodal loop systems.


  We measure the band structure of nickel along various high-symmetry lines of
the bulk Brillouin zone with angle-resolved photoelectron spectroscopy. The
Gutzwiller theory for a nine-band Hubbard model whose tight-binding parameters
are obtained from non-magnetic density-functional theory resolves most of the
long-standing discrepancies between experiment and theory on nickel. Thereby we
support the view of itinerant ferromagnetism as induced by atomic correlations.


  Many statistical estimators are defined as the fixed point of a
data-dependent operator, with estimators based on minimizing a cost function
being an important special case. The limiting performance of such estimators
depends on the properties of the population-level operator in the idealized
limit of infinitely many samples. We develop a general framework that yields
bounds on statistical accuracy based on the interplay between the deterministic
convergence rate of the algorithm at the population level, and its degree of
(in)stability when applied to an empirical object based on $n$ samples. Using
this framework, we analyze both stable forms of gradient descent and some
higher-order and unstable algorithms, including Newton's method and its
cubic-regularized variant, as well as the EM algorithm. We provide applications
of our general results to several concrete classes of models, including
Gaussian mixture estimation, non-linear regression models, and informative
non-response models. We exhibit cases in which an unstable algorithm can
achieve the same statistical accuracy as a stable algorithm in exponentially
fewer steps -- namely, with the number of iterations being reduced from
polynomial to logarithmic in sample size $n$.


  It is proved that triangle-free intersection graphs of $n$ L-shapes in the
plane have chromatic number $O(\log\log n)$. This improves the previous bound
of $O(\log n)$ (McGuinness, 1996) and matches the known lower bound
construction (Pawlik et al., 2013).


  We report the first high-resolution X-ray spectra of two high-redshift
quasars, S5 0836+710 and PKS 2149-306, obtained with the Chandra High Energy
Transmission Grating Spectrometer (HETGS). The primary goal of this observation
is to use the high spectral resolving power of the HETGS to detect X-ray
absorption produced by a hot intergalactic medium. The continuum of both
quasars can be fitted by absorbed power laws. The power law photon index
(Gamma) of S5 0836+710 is consistent with that found in previous observations
with ROSAT and ASCA, while the power law of PKS 2149-306 is harder than found
in a previous observation by ASCA. Excess continuum absorption above the
Galactic value is found in S5 0836+710, as evidenced in ASCA and ROSAT
observations. No significant emission or absorption feature is detected in
either source at 3 sigma level. Based on the detection limits we constrain the
properties of possible emitters and absorbers. The upper limit of the
equivalent width of Fe K emission lines could be as low as ~ 10 eV. Absorbers
with a column density higher than 8e16 cm^{-2} for O VIII or 5e16 cm^{-2} for
Si XIV would have been detected. We propose a method to constrain the
cosmological parameters (namely Omega_0 and Omega_b) via the X-ray forest
theory, but current data do not give significant constraints. However, we
estimate that observing ~ 7 bright quasars should give at least one O VIII and
more O VII absorption lines at 95% possibility. We also find that combined with
the constraints from the distortion of the CMB spectrum, the X-ray
Gunn-Peterson test can marginally constrain a uniform, enriched IGM.


  We investigate Siegel modular varieties in positive characteristic with
Iwahori level structure. On these spaces, we have the Newton stratification,
and the Kottwitz-Rapoport stratification; one would like to understand how
these stratifications are related to each other. We give a simple description
of all KR strata which are entirely contained in the supersingular locus as
disjoint unions of Deligne-Lusztig varieties. We also give an explicit
numerical description of the KR stratification in terms of abelian varieties.


  The recent emergence of the hybrid quantum-classical neural network (HQCNN)
architecture has garnered considerable attention due to the potential
advantages associated with integrating quantum principles to enhance various
facets of machine learning algorithms and computations. However, the current
investigated serial structure of HQCNN, wherein information sequentially passes
from one network to another, often imposes limitations on the trainability and
expressivity of the network. In this study, we introduce a novel architecture
termed Parallel Proportional Fusion of Quantum and Spiking Neural Networks
(PPF-QSNN). The dataset information is simultaneously fed into both the spiking
neural network and the variational quantum circuits, with the outputs
amalgamated in proportion to their individual contributions. We systematically
assess the impact of diverse PPF-QSNN parameters on network performance for
image classification, aiming to identify the optimal configuration. Numerical
results on the MNIST dataset unequivocally illustrate that our proposed
PPF-QSNN outperforms both the existing spiking neural network and the serial
quantum neural network across metrics such as accuracy, loss, and robustness.
This study introduces a novel and effective amalgamation approach for HQCNN,
thereby laying the groundwork for the advancement and application of quantum
advantage in artificial intelligent computations.


  This study provides a comprehensive test of the head-related impulse response
(HRIR) to an auditory spatial speller brain-computer interface (BCI) paradigm,
including a comparison with a conventional virtual headphone-based spatial
auditory modality. Five BCI-naive users participated in an experiment based on
five Japanese vowels. The auditory evoked potentials obtained produced
encouragingly good and stable P300-responses in online BCI experiments. Our
case study indicates that the auditory HRIR spatial sound paradigm reproduced
with headphones could be a viable alternative to established multi-loudspeaker
surround sound BCI-speller applications.


  Permanent electric dipole moments (EDMs) of fundamental particles provide
powerful probes for physics beyond the Standard Model. We propose to search for
the EDM of strange and charm baryons at LHC, extending the ongoing experimental
program on the neutron, muon, atoms, molecules and light nuclei. The EDM of
strange $\Lambda$ baryons, selected from weak decays of charm baryons produced
in pp collisions at LHC, can be determined by studying the spin precession in
the magnetic field of the detector tracking system. A test of CPT symmetry can
be performed by measuring the magnetic dipole moment of $\Lambda$ and
$\overline{\Lambda}$ baryons. For short-lived $\Lambda_c^+$ and $\Xi_c^+$
baryons, to be produced in a fixed-target experiment using the 7 TeV LHC beam
and channeled in a bent crystal, the spin precession is induced by the intense
electromagnetic field between crystal atomic planes. The experimental layout
based on the LHCb detector and the expected sensitivities in the coming years
are discussed.


  We present the first determination of parton distributions of the nucleon at
NLO and NNLO based on a global data set which includes LHC data: NNPDF2.3. Our
data set includes, besides the deep inelastic, Drell-Yan, gauge boson
production and jet data already used in previous global PDF determinations, all
the relevant LHC data for which experimental systematic uncertainties are
currently available: ATLAS and LHCb W and Z lepton rapidity distributions from
the 2010 run, CMS W electron asymmetry data from the 2011 run, and ATLAS
inclusive jet cross-sections from the 2010 run. We introduce an improved
implementation of the FastKernel method which allows us to fit to this extended
data set, and also to adopt a more effective minimization methodology. We
present the NNPDF2.3 PDF sets, and compare them to the NNPDF2.1 sets to assess
the impact of the LHC data. We find that all the LHC data are broadly
consistent with each other and with all the older data sets included in the
fit. We present predictions for various standard candle cross-sections, and
compare them to those obtained previously using NNPDF2.1, and specifically
discuss the impact of ATLAS electroweak data on the determination of the
strangeness fraction of the proton. We also present collider PDF sets,
constructed using only data from HERA, Tevatron and LHC, but find that this
data set is neither precise nor complete enough for a competitive PDF
determination.


  Spin-charge conversion via inverse spin Hall effect (ISHE) is essential for
enabling various applications of spintronics. The spin Hall response usually
follows a universal scaling relation with longitudinal electric resistivity and
has mild temperature dependence because elementary excitations play only a
minor role in resistivity and hence ISHE. Here we report that the ISHE of
metallic glasses shows nearly two orders of magnitude enhancements with
temperature increase from a threshold of 80-100 K to glass transition points.
As electric resistivity changes only marginally in the temperature range, the
anomalous temperature dependence is in defiance of the prevailing scaling law.
Such a giant temperature enhancement can be well described by a two-level
thermal excitation model of glasses and disappears after crystallization,
suggesting a new mechanism which involves unique thermal excitations of
glasses. This finding may pave new ways to achieve high spin-charge conversion
efficiency at room and higher temperatures for spintronic devices and to detect
structure and dynamics of glasses using spin currents.


  We investigate degenerate special-Hermitian metrics on compact complex
manifolds, in particular, degenerate K\"ahler and locally conformally K\"ahler
metrics on special classes of non-K\"ahler manifolds.


  We uncover the connection between the Fitness-Complexity algorithm, developed
in the economic complexity field, and the Sinkhorn-Knopp algorithm, widely used
in diverse domains ranging from computer science and mathematics to economics.
Despite minor formal differences between the two methods, both converge to the
same fixed-point solution up to normalization. The discovered connection allows
us to derive a rigorous interpretation of the Fitness and the Complexity
metrics as the potentials of a suitable energy function. Under this
interpretation, high-energy products are unfeasible for low-fitness countries,
which explains why the algorithm is effective at displaying nested patterns in
bipartite networks. We also show that the proposed interpretation reveals the
scale invariance of the Fitness-Complexity algorithm, which has practical
implications for the algorithm's implementation in different datasets. Further,
analysis of empirical trade data under the new perspective reveals three
categories of countries that might benefit from different development
strategies.


  We develop a fourth order simulation algorithm for solving the stochastic
Langevin equation. The method consists of identifying solvable operators in the
Fokker-Planck equation, factorizing the evolution operator for small time steps
to fourth order and implementing the factorization process numerically. A key
contribution of this work is to show how certain double commutators in the
factorization process can be simulated in practice. The method is general,
applicable to the multivariable case, and systematic, with known procedures for
doing fourth order factorizations. The fourth order convergence of the
resulting algorithm allowed very large time steps to be used. In simulating the
Brownian dynamics of 121 Yukawa particles in two dimensions, the converged
result of a first order algorithm can be obtained by using time steps 50 times
as large. To further demostrate the versatility of our method, we derive two
new classes of fourth order algorithms for solving the simpler Kramers equation
without requiring the derivative of the force. The convergence of many fourth
order algorithms for solving this equation are compared.


  We study the binding energies of spin-isospin saturated nuclei with nucleon
number $8 \le A \le 100$ in semiclassical Monte Carlo many-body simulations.
The model Hamiltonian consists of, (i) nucleon kinetic energy, (ii) a
nucleon-nucleon interaction potential, and (iii) an effective Pauli potential
which depends on density. The basic ingredients of the nucleon-nucleon
potential are, a short-range repulsion, and a medium-range attraction. Our
results demonstrate that one can always expect to obtain the empirical binding
energies for a set of nuclei by introducing a proper density dependent Pauli
potential. The present work suggests a simple, pragmatic procedure for
modelling a set of nuclei calibrated by the empirical binding energies for a
given NN interaction potential. Then, each set of modelled nuclei can be tested
by studying other properties of nuclei in semiclassical simulations.


  Inversionless gain is observed in a V-type inhomogeneously broadened system
without introducing any incoherent pumping and only by changing the collisional
dephasing decay rate. In this system sub-Doppler linewidth is achieved with
off-resonance pump detuning.


  We present a heuristic algorithm to compute the ideal class group, and a
generator of a principal ideal in $\mathbb{Q}(\zeta_{p^s})$ in time
$2^{O(n^{1/2+\varepsilon})}$ for $n:= deg(K)$ and arbitrarily small
$\varepsilon$. This yields an attack on the schemes relying on the hardness of
finding a short generator of a principal ideal such as such as the homomorphic
encryption scheme of Vercauteren and Smart, and the multilinear maps of Garg,
Gentry and Halevi. We rely on the work from Cramer, Ducas, Peikert and Regev.
They proved that finding a short generator polynomially reduces to finding an
arbitrary one. The complexity is better than when we rely on the work of Biasse
and Fieker on the PIP, which yields an attack in time $2^{n^{2/3+\varepsilon}}$
for arbitrarily small $\varepsilon >0$.
  $\textbf{Since Sep. 30 2016}$ We present practical improvements to our
methods. Moreover, we describe a variant that solves the PIP on input ideal $I$
of norm less than $2^{n^b}$ in time $2^{O\left(n^{c+o(1)}\right)}$ for $2/5 < c
< 1/2$ and $b\leq 7c -2$ given a one time precomputation of cost
$2^{O(n^{2-3c+\varepsilon})}$ for an arbitrarily small $\varepsilon$. This also
solves $\gamma$-SVP in principal ideals of $\mathbb{Q}(\zeta_{p^s})$ for
$\gamma\in e^{\tilde{O}(\sqrt{n})}$. On principal ideals of norm less than
$2^{n^b}$, we can leverage the precomputation to achieve a better asymptotic
run time than the BKZ algorithm.


  Reconstructing visual stimuli from brain recordings has been a meaningful and
challenging task. Especially, the achievement of precise and controllable image
reconstruction bears great significance in propelling the progress and
utilization of brain-computer interfaces. Despite the advancements in complex
image reconstruction techniques, the challenge persists in achieving a cohesive
alignment of both semantic (concepts and objects) and structure (position,
orientation, and size) with the image stimuli. To address the aforementioned
issue, we propose a two-stage image reconstruction model called MindDiffuser.
In Stage 1, the VQ-VAE latent representations and the CLIP text embeddings
decoded from fMRI are put into Stable Diffusion, which yields a preliminary
image that contains semantic information. In Stage 2, we utilize the CLIP
visual feature decoded from fMRI as supervisory information, and continually
adjust the two feature vectors decoded in Stage 1 through backpropagation to
align the structural information. The results of both qualitative and
quantitative analyses demonstrate that our model has surpassed the current
state-of-the-art models on Natural Scenes Dataset (NSD). The subsequent
experimental findings corroborate the neurobiological plausibility of the
model, as evidenced by the interpretability of the multimodal feature employed,
which align with the corresponding brain responses.


  Regular path queries (RPQs) the ubiquitous mechanism for querying data graphs
of partially known structure. RPQs are in essence regular expressions over the
edge symbols. The answer to an RPQ on a given graph (database) is the set of
pairs of objects, which are connected by paths spelling words in the language
of the regular path query. Often the database edges come with a weights
assoaciated to them. Such weights can distances, levels of discomfort,
multiplicities, etc. We model weights using semiring frameworks.


  Suppose that party A collects private information about its users, where each
user's data is represented as a bit vector. Suppose that party B has a
proprietary data mining algorithm that requires estimating the distance between
users, such as clustering or nearest neighbors. We ask if it is possible for
party A to publish some information about each user so that B can estimate the
distance between users without being able to infer any private bit of a user.
Our method involves projecting each user's representation into a random,
lower-dimensional space via a sparse Johnson-Lindenstrauss transform and then
adding Gaussian noise to each entry of the lower-dimensional representation. We
show that the method preserves differential privacy---where the more privacy is
desired, the larger the variance of the Gaussian noise. Further, we show how to
approximate the true distances between users via only the lower-dimensional,
perturbed data. Finally, we consider other perturbation methods such as
randomized response and draw comparisons to sketch-based methods. While the
goal of releasing user-specific data to third parties is more broad than
preserving distances, this work shows that distance computations with privacy
is an achievable goal.


  Different aspects of relativity, mainly in a canonical formulation, relevant
for the question "Is spacetime nothing more than a mathematical space (which
describes the evolution in time of the ordinary three-dimensional world) or is
it a mathematical model of a real four-dimensional world with time entirely
given as the fourth dimension?" are presented. The availability as well as
clarity of the arguments depend on which framework is being used, for which
currently special relativity, general relativity and some schemes of quantum
gravity are available. Canonical gravity provides means to analyze the field
equations as well as observable quantities, the latter even in coordinate
independent form. This allows a unique perspective on the question of
dimensionality since the space-time manifold does not play a prominent role.
After re-introducing a Minkowski background into the formalism, one can see how
distinguished coordinates of special relativity arise, where also the nature of
time is different from that in the general perspective. Just as it is of
advantage to extend special to general relativity, general relativity itself
has to be extended to some theory of quantum gravity. This suggests that a
final answer has to await a thorough formulation and understanding of a
fundamental theory of space-time. Nevertheless, we argue that current insights
into quantum gravity do not change the picture of the role of time obtained
from general relativity.


  Consider a binary decision making process where a single machine learning
classifier replaces a multitude of humans. We raise questions about the
resulting loss of diversity in the decision making process. We study the
potential benefits of using random classifier ensembles instead of a single
classifier in the context of fairness-aware learning and demonstrate various
attractive properties: (i) an ensemble of fair classifiers is guaranteed to be
fair, for several different measures of fairness, (ii) an ensemble of unfair
classifiers can still achieve fair outcomes, and (iii) an ensemble of
classifiers can achieve better accuracy-fairness trade-offs than a single
classifier. Finally, we introduce notions of distributional fairness to
characterize further potential benefits of random classifier ensembles.


  We investigate the possibility of using future photometric and radio surveys
to constrain the power spectrum of primordial fluctuations that is predicted by
inflationary models with a violation of the slow-roll phase. We forecast
constraints with a Fisher analysis on the amplitude of the parametrized
features on ultra-large scales, in order to assess whether these could be
distinguishable over the cosmic variance. We find that the next generation of
photometric and radio surveys has the potential to test these models at a
sensitivity better than current CMB experiments and that the synergy between
galaxy and CMB observations is able to constrain models with many extra
parameters. In particular, an SKA continuum survey with a huge sky coverage and
a flux threshold of a few $\mu$Jy could confirm the presence of a new phase in
the early Universe at more than 3$\sigma$.


  A group is $\textit{finitely axiomatizable}$ (FA) in a class $\mathcal{C}$ if
it can be determined up to isomorphism within $\mathcal{C}$ by a sentence in
the first-order language of group theory. We show that profinite groups of
various kinds are FA in the class of profinite groups. Reasons why certain
groups cannot be FA are also discussed.


  Developing safe and useful general-purpose AI systems will require us to make
progress on scalable oversight: the problem of supervising systems that
potentially outperform us on most skills relevant to the task at hand.
Empirical work on this problem is not straightforward, since we do not yet have
systems that broadly exceed our abilities. This paper discusses one of the
major ways we think about this problem, with a focus on ways it can be studied
empirically. We first present an experimental design centered on tasks for
which human specialists succeed but unaided humans and current general AI
systems fail. We then present a proof-of-concept experiment meant to
demonstrate a key feature of this experimental design and show its viability
with two question-answering tasks: MMLU and time-limited QuALITY. On these
tasks, we find that human participants who interact with an unreliable
large-language-model dialog assistant through chat -- a trivial baseline
strategy for scalable oversight -- substantially outperform both the model
alone and their own unaided performance. These results are an encouraging sign
that scalable oversight will be tractable to study with present models and
bolster recent findings that large language models can productively assist
humans with difficult tasks.


  The non-linear evolution of one-dimensional perturbations in a
three-dimensional expanding Universe is considered. A general Lagrangian scheme
is derived, and compared to two previously introduced approximate models. These
models are simulated with heap-based event-driven numerical procedure, that
allows for the study of large systems, averaged over many realizations of
random initial conditions. One of the models is shown to be qualitatively, and,
in some respects, concerning mass aggregation, quantitatively similar to the
adhesion model.


  We consider multi-access coded caching problem introduced by Hachem et.al.,
where each user has access to $L$ neighboring caches in a cyclic wrap-around
fashion. We focus on the deterministic schemes for a specific class of
multi-access coded caching problem based on the concept of PDA. We construct
new PDAs which specify the delivery scheme for the specific class of
multi-access coded caching problem discussed in this paper. For the proposed
scheme, the coding gain is larger than that of the state-of-the-art while the
sub-packetization level varies only linearly with the number of users. Hence,
we achieve a lower transmission rate with the least sub-packetization level
compared to the existing schemes.


  The general scheme of two-level parallelization (TLP) for direct simulation
Monte Carlo of unsteady gas flows on shared memory multiprocessor computers has
been described. The high efficient algorithm of parallel independent runs is
used on the first level. The data parallelization is employed for the second
one. Two versions of TLP algorithm are elaborated with static and dynamic load
balancing. The method of dynamic processor reallocation is used for dynamic
load balancing. Two gasdynamic unsteady problems were used to study speedup and
efficiency of the algorithms. The conditions of efficient application field for
the algorithms have been determined.


  Ultraluminous X-ray sources (ULXs) are a class of accreting compact objects
with X-ray luminosities above 1e39 erg/s. The ULX population counts several
hundreds objects but only a minor fraction is well studied. Here we present a
detailed analysis of all ULXs hosted in the galaxy NGC 7456. It was observed in
X-rays only once in the past (in 2005) by XMM-Newton, but the observation was
short and strongly affected by high background. In 2018, we obtained a new,
deeper (~90 ks) XMM-Newton observation that allowed us to perform a detailed
characterization of the ULXs hosted in the galaxy. ULX-1 and ULX-2, the two
brightest objects (Lx~(6-10)e39 erg/s), have spectra that can be described by a
two-thermal component model as often found in ULXs. ULX-1 shows also one order
of magnitude in flux variability on short-term timescales (hundreds to thousand
ks). The other sources (ULX-3 and ULX-4) show flux changes of at least an order
of magnitude, and these objects may be candidate transient ULXs although longer
X-ray monitoring or further studies are required to ascribe them to the ULX
population. In addition, we found a previously undetected source that might be
a new candidate ULX (labelled as ULX-5) with a luminosity of ~1e39 erg/s and
hard power-law spectral shape, whose nature is still unclear and for which a
background Active Galactic Nucleus cannot be excluded. We discuss the
properties of all the ULXs in NGC 7456 within the framework of super-Eddington
accretion onto stellar mass compact objects. Although no pulsations were
detected, we cannot exclude that the sources host neutron stars.


  We have systematically investigated the optical properties of the InP1-xBix
ternary alloys with 0<x<2.46%, using high resolution polarized Raman scattering
measurement. Both InP-like and InBi-like optical vibration modes (LO) were
identified in all the samples, suggesting most of the Bi-atoms are incorporated
into the lattice sites to substitute P-atoms. And the intensity of the
InBi-like Raman modes increase exponentially as Bi-content increasing. Linearly
red-shift of the InP-like longitudinal optical vibration modes was observed to
be 1.1 cm-1 of percent Bi, while that of the InP-like optical vibration
overtones (2LO) were nearly doubled. In addition, through comparing the
difference between the Z(X,X)Z and Z(X,Y)Z Raman spectra, Longitudinal Optical
Plasmon Coupled (LOPC) modes are identified in all the samples, and their
intensities are found to be proportional to the electron concentrations.


  We study the numerical stability of polynomial based encoding methods, which
has emerged to be a powerful class of techniques for providing straggler and
fault tolerance in the area of coded computing. Our contributions are as
follows: 1) We construct new codes for matrix multiplication that achieve the
same fault/straggler tolerance as the previously constructed MatDot Codes and
Polynomial Codes. Unlike previous codes that use polynomials expanded in a
monomial basis, our codes uses a basis of orthogonal polynomials. 2) We show
that the condition number of every $m \times m$ sub-matrix of an $m \times n, n
\geq m$ Chebyshev-Vandermonde matrix, evaluated on the $n$-point Chebyshev
grid, grows as $O(n^{2(n-m)})$ for $n > m$. An implication of this result is
that, when Chebyshev-Vandermonde matrices are used for coded computing, for a
fixed number of redundant nodes $s=n-m,$ the condition number grows at most
polynomially in the number of nodes $n$. 3) By specializing our orthogonal
polynomial based constructions to Chebyshev polynomials, and using our
condition number bound for Chebyshev-Vandermonde matrices, we construct new
numerically stable techniques for coded matrix multiplication. We empirically
demonstrate that our constructions have significantly lower numerical errors
compared to previous approaches which involve inversion of Vandermonde
matrices. We generalize our constructions to explore the trade-off between
computation/communication and fault-tolerance. 4) We propose a numerically
stable specialization of Lagrange coded computing. Motivated by our condition
number bound, our approach involves the choice of evaluation points and a
suitable decoding procedure that involves inversion of an appropriate
Chebyshev-Vandermonde matrix. Our approach is demonstrated empirically to have
lower numerical errors as compared to standard methods.


  Several differential equation models have been proposed to explain the
formation of patterns characteristic of the grid cell network. Understanding
the effect of noise on these models is one of the key open questions in
computational neuroscience. In the present work, we continue the analysis of an
SDE system commonly proposed for this aim, which we initiated in a previous
paper. We show that the fluctuations of the empirical measure associated to the
particle system around its mean field limit converge to the solution of a
Langevin SPDE. The interaction between different columns of neurons along the
cortex prescribes a peculiar scaling regime.


  Two-component mixtures of Bose-Einstein condensates are shown to support
solitary wave complexes that move with a constant velocity preserving their
form. I obtain the families of such solitary wave complexes in two-dimensional
two-component mixture condensates. These solutions are classified according to
the structure of the wavefunction in each component. I show that these
complexes nucleate from the surface of the disk when it moves supercritically,
therefore, suggesting a mechanism by which these waves can be obtained in
condensates by a moving laser beam. The condition for such a nucleation is
derived analytically. The flow for supercritical disk velocities is computed
numerically. The process of a boundary layer separation with emission of either
vortex pairs in each component or a vortex pair in one component and a ``slaved
wave'' in the other component is elucidated.


  Deep neural networks have revolutionized medical image analysis and disease
diagnosis. Despite their impressive performance, it is difficult to generate
well-calibrated probabilistic outputs for such networks, which makes them
uninterpretable black boxes. Bayesian neural networks provide a principled
approach for modelling uncertainty and increasing patient safety, but they have
a large computational overhead and provide limited improvement in calibration.
In this work, by taking skin lesion classification as an example task, we show
that by shifting Bayesian inference to the functional space we can craft
meaningful priors that give better calibrated uncertainty estimates at a much
lower computational cost.


  PINOCCHIO (PINpointing Orbit-Crossing Collapsed Hierarchical Objects) is a
new algorithm for identifying dark matter halos in a given numerical
realisation of the linear density field in a hierarchical universe (Monaco et
al. 2001). It is shown that Lagrangian perturbation theory, and in particular
its ellipsoidal truncation, is able to predict accurately the collapse, in the
orbit-crossing sense, of generic mass elements. Some points that have undergone
orbit crossing are assigned to the network of filaments and sheets that
connects the halos; it is demonstrated that this network resembles closely that
found in N-body simulations. The code generates a catalogue of dark matter
halos with known mass, position, velocity, merging history and angular
momentum. It is shown that the predictions of the code are very accurate when
compared with the results of large N-body simulations that cover a range of
cosmological models, box sizes and numerical resolutions. The mass function is
recovered with an accuracy of better than 10 per cent in number density for
halos with at least 30-50 particles. A similar accuracy is reached in the
estimate of the correlation length r_0. The good agreement is still valid on
the object-by-object level, with 70-100 per cent of the objects with more than
50 particles in the simulations also identified by our algorithm. For these
objects the masses are recovered with an error of 20-40 per cent, and positions
and velocities with a root mean square error of ~1-2 Mpc (0.5-2 grid lengths)
and ~100 km/s, respectively. The recovery of the angular momentum of halos is
considerably noisier and accuracy at the statistical level is achieved only by
introducing free parameters. The algorithm requires negligible computer time as
compared with performing a numerical $N$-body simulation.


  I argue that the most interesting goal facing researchers in automated
reasoning is being able to solve problems that cannot currently be solved by
existing tools and methods. This may appear obvious, and is clearly not an
original thought, but focusing on this as a primary goal allows us to examine
other goals in a new light. Many successful theorem provers employ a portfolio
of different methods for solving problems. This changes the landscape on which
we perform our research: solving problems that can already be solved may not
improve the state of the art and a method that can solve a handful of problems
unsolvable by current methods, but generally performs poorly on most problems,
can be very useful. We acknowledge that forcing new methods to compete against
portfolio solvers can stifle innovation. However, this is only the case when
comparisons are made at the level of total problems solved. We propose a
movement towards focussing on unique solutions in evaluation and competitions
i.e. measuring the potential contribution to a portfolio solver. This state of
affairs is particularly prominent in first-order logic, which is undecidable.
When reasoning in a decidable logic there can be a focus on optimising a
decision procedure and measuring average solving times. But in a setting where
solutions are difficult to find, average solving times lose meaning, and whilst
improving the efficiency of a technique can move potential solutions within
acceptable time limits, in general, complementary strategies may be more
successful.


  We describe the equivariant cobordism ring of smooth toric varieties. This
equivariant description is used to compute the ordinary cobordism ring of such
varieties.


  Transport through a one-dimensional wire of interacting electrons connected
to semi infinite leads is investigated using a bosonization approach. The
dynamic nonlocal conductivity is rigorously expressed in terms of the
transmission. For abrupt variations of the interaction parameters at the
junctions, an incident electron is transmitted as a sequence of partial
charges: the central wire acts as a Fabry-P\'erot resonator. The dc conductance
is shown to be given by the total transmission which turns out to be perfect.
When the wire has a tendency towards superconducting order, partial Andreev
reflection of an incident electron occurs. Finally, we study the role of a weak
barrier at one contact or inside the wire by a renormalization group method at
finite temperature. We compute the conductance in the presence of localized or
extended disorder, and compare our results to recent experiments on quantum
wires.


  We focus on understanding the influence of the two-component coupling in
ferronematics, a colloidal suspension of magnetic nanoparticles in nematic
liquid crystals. Using coarse-grained Landau-de Gennes free energies, we study
the ordering dynamics of this complex fluid and present a range of analytical
and numerical results. Our main observations are: (i) slaved coarsening for
quench temperatures $T$ intermediate to the critical temperatures of the
uncoupled components, (ii) slower growth similar to the Lifshitz-Slyozov law
($L \sim t^{1/3}$) for symmetric magneto-nematic coupling, (iii) sub-domain
morphologies dominated by interfacial defects for asymmetric coupling
strengths. These novel results will serve to guide future experiments on this
technologically important system.


  Black hole entropy is a robust prediction of quantum gravity with no
established phenomenological consequences to date. We use the
Bekenstein-Hawking entropy formula and general-relativistic statistical
mechanics to determine the probability distribution of random geometries
uniformly sampled in phase space. We show that this statistics (in the limit
$\hbar\to 0$) is relevant to large curvature perturbations, resulting in a
population of primordial black holes with zero natal spin. In principle, the
identification of such a population at LIGO, Virgo, and future gravitational
wave observatories could provide the first observational evidence for the
statistical nature of black hole entropy.


  In an $L_\infty$-framework, we present a few extension theorems for linear
operators. We focus the attention on majorant preserving and sandwich
preserving types of extensions. These results are then applied to the study of
price systems derived by a reasonable restriction of the class of equivalent
martingale measures applicable. First we consider equivalent martingale
measures with bounds on densities and the corresponding prices bounded by
linear minorant and majorant. Then we consider prices bounded by bid-ask
dynamics. Finally we study price systems consistent with no-good-deal pricing
measures for given bounds on the Sharpe ratio. Within this study we introduce
the definition of dynamic no-good-deal pricing measure.


  This paper studies separating invariants: mappings on $D$ dimensional domains
which are invariant to an appropriate group action, and which separate orbits.
The motivation for this study comes from the usefulness of separating
invariants in proving universality of equivariant neural network architectures.
  We observe that in several cases the cardinality of separating invariants
proposed in the machine learning literature is much larger than the dimension
$D$. As a result, the theoretical universal constructions based on these
separating invariants is unrealistically large. Our goal in this paper is to
resolve this issue.
  We show that when a continuous family of semi-algebraic separating invariants
is available, separation can be obtained by randomly selecting $2D+1 $ of these
invariants. We apply this methodology to obtain an efficient scheme for
computing separating invariants for several classical group actions which have
been studied in the invariant learning literature. Examples include matrix
multiplication actions on point clouds by permutations, rotations, and various
other linear groups.
  Often the requirement of invariant separation is relaxed and only generic
separation is required. In this case, we show that only $D+1$ invariants are
required. More importantly, generic invariants are often significantly easier
to compute, as we illustrate by discussing generic and full separation for
weighted graphs. Finally we outline an approach for proving that separating
invariants can be constructed also when the random parameters have finite
precision.


  Colloidal spheres synthesized from polymer gels swell by absorbing molecules
from solution. The resulting change in size can be monitored with nanometer
precision using holographic video microscopy. When the absorbate is chemically
similar to the polymer matrix, swelling is driven primarily by the entropy of
mixing, and is limited by the surface tension of the swelling sphere and by the
elastic energy of the polymer matrix. We demonstrate though a combination of
optical micromanipulation and holographic particle characterization that the
degree of swelling of a single polymer bead can be used to measure the monomer
concentration in situ with spatial resolution comparable to the size of the
sphere.


  Deep neural networks (DNNs) have been widely used in various video analytic
tasks. These tasks demand real-time responses. Due to the limited processing
power on mobile devices, a common way to support such real-time analytics is to
offload the processing to an edge server. This paper examines how to speed up
the edge server DNN processing for multiple clients. In particular, we observe
batching multiple DNN requests significantly speeds up the processing time.
Based on this observation, we first design a novel scheduling algorithm to
exploit the batching benefits of all requests that run the same DNN. This is
compelling since there are only a handful of DNNs and many requests tend to use
the same DNN. Our algorithms are general and can support different objectives,
such as minimizing the completion time or maximizing the on-time ratio. We then
extend our algorithm to handle requests that use different DNNs with or without
shared layers. Finally, we develop a collaborative approach to further improve
performance by adaptively processing some of the requests or portions of the
requests locally at the clients. This is especially useful when the network
and/or server is congested. Our implementation shows the effectiveness of our
approach under different request distributions (e.g., Poisson, Pareto, and
Constant inter-arrivals).


  We present a theoretical framework to describe polarons from first principles
within a many-body Green's function formalism. Starting from a general
electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in
which the phonon-mediated self-energy is composed by two distinct terms. One
term is the Fan-Migdal self-energy and describes dynamic electron-phonon
processes, the other term is a new contribution to the self-energy originating
from the static displacements of the atomic nuclei in the polaronic ground
state. The lowest-order approximation to the present theory yields the standard
many-body perturbation theory approach to electron-phonon interactions in the
limit of large polarons, and the ab initio polaron equations introduced in [Sio
et al., Phys. Rev. B 99, 235139 (2019); Phys. Rev. Lett. 122, 246403 (2019)] in
the limit of small polarons. A practical recipe to implement the present
unifying formalism in first-principles calculations is outlined. We apply our
method to the Fr\"ohlich model, and obtain remarkably accurate polaron energies
at all couplings, in line with Feynman's polaron theory and diagrammatic Monte
Carlo calculations. We also recover the well-known results of Fr\"ohlich and
Pekar at weak and strong coupling, respectively. The present approach enables
predictive many-body calculations of polarons in real materials at all
couplings.


  We prove the strong Atiyah conjecture for right-angled Artin groups and
right-angled Coxeter groups. More generally, we prove it for groups which are
certain finite extensions or elementary amenable extensions of such groups.


  Networks observed in the real world often have many short loops. This
violates the tree-like assumption that underpins the majority of random graph
models and most of the methods used for their analysis. In this paper we sketch
possible research routes to be explored in order to make progress on networks
with many short loops, involving old and new random graph models and ideas for
novel mathematical methods. We do not present conclusive solutions of problems,
but aim to encourage and stimulate new activity and in what we believe to be an
important but under-exposed area of research. We discuss in more detail the
Strauss model, which can be seen as the `harmonic oscillator' of `loopy' random
graphs, and a recent exactly solvable immunological model that involves random
graphs with extensively many cliques and short loops.


  We list 4d interacting $\mathcal{N}=2$ SCFT with minimal flavor central
charge from the theory space constructed using 6d $(2,0)$ theory. For $ADE$ and
$C_N$ flavor groups, our theory saturates the bound found using bootstrap
method, but other cases have higher values. We find interesting rank one SCFTs
with $B_3, G_2, F_4, C_4\times U(1), C_1\times U(1)$ flavor symmetry. Many
physical properties of these theories are also studied.


  In this paper, the Penrose process is being used to extract rotational energy
from regular black holes. Initially, we consider the rotating Simpson-Visser
regular spacetime which describes the class of geometries of the Kerr black
hole's mimickers. The Penrose process is then studied through conformally
transformed rotating singular and regular black hole solutions. These both
Simpson-Visser and conformally transformed geometries depend on mass, spin, and
an additional regularisation parameter $l$. In both cases, we investigate how
the spin and regularisation parameter $l$ affects the configuration of an
ergoregion and event horizons. Surprisingly, we find that the energy extraction
efficiency from the event horizon surface is not dependent on the
regularisation parameter $l$ in the Simpson-Visser regular spacetimes and hence
it does not vary from the Kerr black hole case. While, in the conformally
transformed singular and regular black holes, we obtain the efficiency rate of
extracted energies are extremely high compared to the Kerr black hole scenario.
This distinct signature of the conformally transformed singular and regular
black holes would be useful to distinguish them from the Kerr black hole in
observation.


  Using a multiple-scale asymptotic approach, we have derived the complex cubic
Ginzburg-Landau equation for amplified and nonlinearly saturated surface
plasmon polaritons propagating and diffracting along a metal-dielectric
interface. An important feature of our method is that it explicitly accounts
for nonlinear terms in the boundary conditions, which are critical for a
correct description of nonlinear surface waves. Using our model we have
analyzed filamentation and discussed bright and dark spatially localized
structures of plasmons.


  Given a pair $(M,X)$, where $X$ is a smooth submanifold in a closed smooth
manifold $M$, we study the operation, which takes each operator $D$ on the
ambient manifold to a certain operator on the submanifold. The latter operator
is called the trace of $D$. More precisely, we study traces of operators,
associated with actions of compact Lie groups on $M$. We show that traces of
such operators are localized at special submanifolds in $X$ and study the
structure of the traces on these submanifolds.


  We show new radio data and a re-analysis of old data for the Narrow Line
Seyfert 1 (NLSy1) galaxy RGB J0044+193. This galaxy has previously been
suggested to be both radio loud, and highly variable in the radio. As most NLSy
1 galaxies are radio quiet, this was interpreted as possible evidence that this
AGN's jet was beamed toward the observer. This object was probably never either
radio loud and nor variable -- the one exception to this rule is a marginal
detection of the object in the 1987 Green Bank survey, which we argue may have
been spurious.


  Random braids that are formed by multiplying randomly chosen permutation
braids are studied by analyzing their behavior under Garside's weighted
decomposition and cycling. Using this analysis, we propose a polynomial-time
algorithm to the conjugacy problem that is successful for random braids in
overwhelming probability. As either the braid index or the number of
permutation-braid factors increases, the success probability converges to 1 and
so, contrary to the common belief, the distribution of hard instances for the
conjugacy problem is getting sparser. We also prove a conjecture by Birman and
Gonz\'{a}lez-Meneses that any pseudo-Anosov braid can be made to have a special
weighted decomposition after taking power and cycling. Moreover we give
polynomial upper bounds for the power and the number of iterated cyclings
required.


  With the aim to propose a non parametric hypothesis test, this paper carries
out a study on the Matching Error (ME), a comparison index of two partitions
obtained from the same data set, using for example two clustering methods. This
index is related to the misclassifica-tion error in supervised learning. Some
properties of the ME and, especially, its distribution function for the case of
two independent partitions are analyzed. Extensive simulations show the
efficiency of the ME and we propose a hypothesis test based on it.


  Solving Perspective-n-Point (PnP) problems is a traditional way of estimating
object poses. Given outlier-contaminated data, a pose of an object is
calculated with PnP algorithms of n = {3, 4} in the RANSAC-based scheme.
However, the computational complexity considerably increases along with n and
the high complexity imposes a severe strain on devices which should estimate
multiple object poses in real time. In this paper, we propose an efficient
method based on 1-point RANSAC for estimating a pose of an object on the
ground. In the proposed method, a pose is calculated with 1-DoF
parameterization by using a ground object assumption and a 2D object bounding
box as an additional observation, thereby achieving the fastest performance
among the RANSAC-based methods. In addition, since the method suffers from the
errors of the additional information, we propose a hierarchical robust
estimation method for polishing a rough pose estimate and discovering more
inliers in a coarse-to-fine manner. The experiments in synthetic and real-world
datasets demonstrate the superiority of the proposed method.


  Performance models are well-known instruments to understand the scaling
behavior of parallel applications. They express how performance changes as key
execution parameters, such as the number of processes or the size of the input
problem, vary. Besides reasoning about program behavior, such models can also
be automatically derived from performance data. This is called empirical
performance modeling. While this sounds simple at the first glance, this
approach faces several serious interrelated challenges, including expensive
performance measurements, inaccuracies inflicted by noisy benchmark data, and
overall complex experiment design, starting with the selection of the right
parameters. The more parameters one considers, the more experiments are needed
and the stronger the impact of noise. In this paper, we show how taint
analysis, a technique borrowed from the domain of computer security, can
substantially improve the modeling process, lowering its cost, improving model
quality, and help validate performance models and experimental setups.


  This paper presents the design of an integral controller for vehicle platoons
with actuator dynamics. The proposed controller ensures string stability with
disturbances and simultaneously compensates for constant disturbances through
integral action. Sufficient conditions for string stability are satisfied by
the use of a suitable state transformation. The proposed controller guarantees
disturbance string stability for a prescribed time constant of the actuator
dynamics, and we show through simulation that platoons with faster dynamics are
also made disturbance string stable.


  The off-shell entropy for a massless scalar field in a D-dimensional
Rindler-like space-time is investigated within the conical Euclidean approach
in the manifold $C_\be\times\M^N$, $C_\be$ being the 2-dimensional cone, making
use of the zeta-function regularisation. Due to the presence of conical
singularities, it is shown that the relation between the zeta-function and the
heat kernel is non trivial and, as first pointed out by Cheeger, requires a
separation between small and large eigenvalues of the Laplace operator. As a
consequence, in the massless case, the (naive) non existence of the Mellin
transform is by-passed by the Cheeger's analytical continuation of the
zeta-function on manifold with conical singularities. Furthermore, the
continuous spectrum leads to the introduction of smeared traces. In general, it
is pointed out that the presence of the divergences may depend on the smearing
function and they arise in removing the smearing cutoff. With a simple choice
of the smearing function, horizon divergences in the thermodynamical quantities
are recovered and these are similar to the divergences found by means of
off-shell methods like the brick wall model, the optical conformal
transformation techniques or the canonical path integral method.


  Large language models (LLMs) have significantly advanced the field of natural
language processing (NLP) through their extensive parameters and comprehensive
data utilization. However, existing LLMs lack a dedicated memory unit, limiting
their ability to explicitly store and retrieve knowledge for various tasks. In
this paper, we propose RET-LLM a novel framework that equips LLMs with a
general write-read memory unit, allowing them to extract, store, and recall
knowledge from the text as needed for task performance. Inspired by Davidsonian
semantics theory, we extract and save knowledge in the form of triplets. The
memory unit is designed to be scalable, aggregatable, updatable, and
interpretable. Through qualitative evaluations, we demonstrate the superiority
of our proposed framework over baseline approaches in question answering tasks.
Moreover, our framework exhibits robust performance in handling temporal-based
question answering tasks, showcasing its ability to effectively manage
time-dependent information.


  Inter-package conflicts require the presence of two or more packages in a
particular configuration, and thus tend to be harder to detect and localize
than conventional (intra-package) defects. Hundreds of such inter-package
conflicts go undetected by the normal testing and distribution process until
they are later reported by a user. The reason for this is that current
meta-data is not fine-grained and accurate enough to cover all common types of
conflicts. A case study of inter-package conflicts in Debian has shown that
with more detailed package meta-data, at least one third of all package
conflicts could be prevented relatively easily, while another one third could
be found by targeted testing of packages that share common resources or
characteristics. This paper reports the case study and proposes ideas to detect
inter-package conflicts in the future.