  Research over the years has shown that the formation of the Fe$_3$Si phase in
FINEMET (Fe-Si-Nb-B-Cu) alloys leads to superior soft magnetic properties. In
this work, we use a CALPHAD approach to derive Fe-Si phase diagrams to identify
the composition-temperature domain where the Fe$_3$Si phase can be stabilized.
Thereafter, we have developed a precipitation model capable of simulating the
nucleation and growth of Fe$_3$Si nanocrystals via Langer-Schwartz theory. For
optimum magnetic properties, prior work suggests that it is desirable to
precipitate Fe$_3$Si nanocrystals with 10-15 nm diameter and with the
crystalline volume fraction of about 70 \%. Based on our parameterized model,
we simulated the nucleation and growth of Fe$_3$Si nanocrystals by isothermal
annealing of Fe$_{72.89}$Si$_{16.21}$B$_{6.90}$Nb$_{3}$Cu$_{1}$ (composition in
atomic \%). In numerical experiments, the alloys were annealed at a series of
temperatures from 490 to 550 \degree C for two hours to study the effect of
holding time on mean radius, volume fraction, size distribution, nucleation
rate, number density, and driving force for the growth of Fe$_3$Si
nanocrystals. With increasing annealing temperature, the mean radius of
Fe$_3$Si nanocrystals increases, while the volume fraction decreases. We have
also studied the effect of composition variations on the nucleation and growth
of Fe$_3$Si nanocrystals. As Fe content decreases, it is possible to achieve
the desired mean radius and volume fraction within one hour holding time. The
CALPHAD approach presented here can provide efficient exploration of the
nanocrystalline morphology for most FINEMET systems, for cases in which the
optimization of one or more material properties or process variables are
desired.


  The distribution of stars around a massive black hole (MBH) has been
addressed in stellar dynamics for the last four decades by a number of authors.
Because of its proximity, the centre of the Milky Way is the only observational
test case where the stellar distribution can be accurately tested. Past
observational work indicated that the brightest giants in the Galactic Centre
(GC) may show a density deficit around the central black hole, not a cusp-like
distribution, while we theoretically expect the presence of a stellar cusp. We
here present a solution to this long-standing problem. We performed
direct-summation $N-$body simulations of star clusters around massive black
holes and compared the results of our simulations with new observational data
of the GC's nuclear cluster. We find that after a Hubble time, the distribution
of bright stars as well as the diffuse light follow power-law distributions in
projection with slopes of $\Gamma \approx 0.3$ in our simulations. This is in
excellent agreement with what is seen in star counts and in the distribution of
the diffuse stellar light extracted from adaptive-optics (AO) assisted
near-infrared observations of the GC. Our simulations also confirm that there
exists a missing giant star population within a projected radius of a few
arcsec around Sgr A*. Such a depletion of giant stars in the innermost 0.1 pc
could be explained by a previously present gaseous disc and collisions, which
means that a stellar cusp would also be present at the innermost radii, but in
the form of degenerate compact cores.


  We prove that if S is a closed compact surface of negative Euler
characteristic, and if R is a quasi-Fuchsian representation in PSL(2,C), then
the deformation space M(k,R) of branched projective structures on S with total
branching order k and holonomy R is connected, as soon as k>0. Equivalently,
two branched projective structures with the same quasi-Fuchsian holonomy and
the same number of branch points are related by a movement of branch points. In
particular grafting annuli are obtained by moving branch points. In the
appendix we give an explicit atlas for the space M(k,R). It is shown to be a
smooth complex manifold modeled on Hurwitz spaces.


  We present new generalizations of Olson's theorem and of a consequence of
Alon's Combinatorial Nullstellensatz. These enable us to extend some of their
combinatorial applications with conditions modulo primes to conditions modulo
prime powers. We analyze computational search problems corresponding to these
kinds of combinatorial questions and we prove that the problem of finding
degree-constrained subgraphs modulo $2^d$ such as $2^d$-divisible subgraphs and
the search problem corresponding to the Combinatorial Nullstellensatz over
$\mathbb{F}_2$ belong to the complexity class Polynomial Parity Argument (PPA).


  We present large-scale ($\sim$ 2000 square arcminutes), deep ($\sim$ 20
$\mu$Jy), high-resolution ($\sim$ 1$''$) radio observations of the Ophiuchus
star-forming complex obtained with the Karl G.\ Jansky Very Large Array at
$\lambda$ = 4 and 6 cm. In total, 189 sources were detected, 56 of them
associated with known young stellar sources, and 4 with known extragalactic
objects; the other 129 remain unclassified, but most of them are most probably
background quasars. The vast majority of the young stars detected at radio
wavelengths have spectral types K or M, although we also detect 4 objects of
A/F/B types and 2 brown dwarf candidates. At least half of these young stars
are non-thermal (gyrosynchrotron) sources, with active coronas characterized by
high levels of variability, negative spectral indices, and (in some cases)
significant circular polarization. As expected, there is a clear tendency for
the fraction of non-thermal sources to increase from the younger (Class 0/I or
flat spectrum) to the more evolved (Class III or weak line T Tauri) stars. The
young stars detected both in X-rays and at radio wavelengths broadly follow a
G\"udel-Benz relation, but with a different normalization than the most
radio-active types of stars. Finally, we detect a $\sim$ 70 mJy compact
extragalactic source near the center of the Ophiuchus core, which should be
used as gain calibrator for any future radio observations of this region.


  In this paper, we introduce a thinness in sense to a type of relative
capacity for weighted variable exponent Sobolev space. Moreover, we reveal some
properties of this thinness and consider the relationship with finely open and
finely closed sets. We discuss fine topology and compare this topology with
Euclidean one. Finally, we give some information about importance of the fine
topology in the potential theory.


  Consider a set of items and a set of $m$ colors, where each item is
associated to one color. Consider also $n$ computational agents connected by a
ring. Each agent holds a subset of the items and items of the same color can be
held by different agents. We analyze the problem of distributively assigning
colors to agents in such a way that (a) each color is assigned to one agent
only and (b) the number of different colors assigned to each agent is minimum.
Since any color assignment requires the items be distributed according to it
(e.g. all items of the same color are to be held by only one agent), we define
the cost of a color assignment as the amount of items that need to be moved,
given an initial allocation. We first show that any distributed algorithm for
this problem requires a message complexity of $\Omega(n\cdot m)$ and then we
exhibit an optimal message complexity algorithm for synchronous rings that in
polynomial time determines a color assignment with cost at most three times the
optimal. We also discuss solutions for the asynchronous setting. Finally, we
show how to get a better cost solution at the expenses of either the message or
the time complexity.


  In solving real-world problems like changing healthcare-seeking behaviors,
designing interventions to improve downstream outcomes requires an
understanding of the causal links within the system. Causal Bayesian Networks
(BN) have been proposed as one such powerful method. In real-world
applications, however, confidence in the results of BNs are often moderate at
best. This is due in part to the inability to validate against some ground
truth, as the DAG is not available. This is especially problematic if the
learned DAG conflicts with pre-existing domain doctrine. At the policy level,
one must justify insights generated by such analysis, preferably accompanying
them with uncertainty estimation. Here we propose a causal extension to the
datasheet concept proposed by Gebru et al (2018) to include approximate BN
performance expectations for any given dataset. To generate the results for a
prototype Causal Datasheet, we constructed over 30,000 synthetic datasets with
properties mirroring characteristics of real data. We then recorded the results
given by state-of-the-art structure learning algorithms. These results were
used to populate the Causal Datasheet, and recommendations were automatically
generated dependent on expected performance. As a proof of concept, we used our
Causal Datasheet Generation Tool (CDG-T) to assign expected performance
expectations to a maternal health survey we conducted in Uttar Pradesh, India.


  The decays of the X(3872) to P-wave quarkonia are calculated under the
assumption that it is a shallow bound state of neutral charmed mesons. The
X(3872) is described using an effective theory of nonrelativistic D mesons and
pions (X-EFT). We calculate X(3872) decays by first matching heavy hadron
chiral perturbation theory (HHchiPT) amplitudes for D^0 bar{D}^{*0} -> chi_{cJ}
+ (pi^0,pi+pi) onto local operators in X-EFT, and then using these operators to
calculate the X(3872) decays. This procedure reproduces the factorization
theorems for X(3872) decays to conventional quarkonia previously derived using
the operator product expansion. For single pion decays, we find nontrivial
dependence on the pion energy from HHchiPT diagrams with virtual D mesons. This
nontrivial energy dependence can potentially modify heavy quark symmetry
predictions for the relative sizes of decay rates. At leading order, decays to
final states with two pions are dominated by the final state chi_{c1} + pi^0 +
pi^0, with a branching fraction just below that for the decay to chi_{c1} +
pi^0. Decays to all other final states with two pions are highly suppressed.


  We investigate the impact of multiple distributed intelligent reflecting
surfaces (IRSs), which are deployed and optimized by a mobile operator (MO), on
the performance of user equipments (UEs) served by other co-existing
out-of-band (OOB) MOs that do not control the IRSs. We show that, under
round-robin scheduling, in mmWave frequencies, the ergodic sum spectral
efficiency (SE) of an OOB MO increases logarithmically in the total number of
IRS elements with a pre-log factor that increases with the ratio of the number
of OOB paths through the IRS to the number of elements at an IRS. We further
show that the maximum achievable SE of the OOB MO scales log-linearly with the
total IRS elements, with a pre-log factor of $1$. Then, we specify the minimum
number of IRSs as a function of the channel parameters and design a distributed
IRS system in which an OOB MO almost surely obtains the maximum SE. Finally, we
prove that the outage probability at an OOB UE decreases exponentially as the
number of IRSs increases, even though they are randomly configured from the OOB
UE's viewpoint. We numerically verify our theory and conclude that distributed
IRSs always help every MO, but the MO controlling the IRSs benefits the most.


  Using combinatorial arguments, we determine an upper bound on achievable
rates of stabilizer codes used over the quantum erasure channel. This allows us
to recover the no-cloning bound on the capacity of the quantum erasure channel,
R is below 1-2p, for stabilizer codes: we also derive an improved upper bound
of the form : R is below 1-2p-D(p) with a function D(p) that stays positive for
0 < p < 1/2 and for any family of stabilizer codes whose generators have
weights bounded from above by a constant - low density stabilizer codes.
  We obtain an application to percolation theory for a family of self-dual
tilings of the hyperbolic plane. We associate a family of low density
stabilizer codes with appropriate finite quotients of these tilings. We then
relate the probability of percolation to the probability of a decoding error
for these codes on the quantum erasure channel. The application of our upper
bound on achievable rates of low density stabilizer codes gives rise to an
upper bound on the critical probability for these tilings.


  Accurate quantum control is a key technology for realizing quantum
information processing, such as quantum communication and quantum computation.
In reality, a quantum state under control suffers from undesirable effects
caused by systematic errors. A composite pulse (CP) is used to eliminate the
effects of systematic errors during control. One qubit control, which is the
most fundamental in quantum control, is typically affected by two errors: pulse
length error (PLE) and off-resonance error (ORE). In this study, we focus on
ORE-robust CPs and systematically construct ORE-robust symmetric CPs with three
elementary operations. We find an infinitely large number of ORE-robust CPs and
evaluate their performance according to gate infidelity and operation time,
both of which are important for the realization of accurate quantum control.


  To realise the goals of active matter at the micro- and nano-scale, the next
generation of microrobots must be capable of autonomously sensing and
responding to their environment to carry out pre-programmed tasks. Memory
effects are proposed to have a significant effect on the dynamics of responsive
robotic systems, drawing parallels to strategies used in nature across all
length-scales. Inspired by the integral feedback control mechanism by which
E.coli are proposed to sense their environment, we develop a numerical
responsive active Brownian particle (rABP) model in which the rABPs
continuously react to changes in the physical parameters dictated by their
local environment. The resulting generated time series are then used to
classify and characterise their response, leading to the identification of
conditional heteroscedasticity in their physics. We then train recurrent neural
networks (RNNs) capable of quantitatively describing the responsiveness of
rABPs using their 2-D trajectories. We believe that our proposed strategy to
determine the parameters governing the dynamics of rABPs can be applied to
guide the design of microrobots with physical intelligence encoded during their
fabrication.


  The significance of intelligent sensing systems is growing in the realm of
smart services. These systems extract relevant signal features and generate
informative representations for particular tasks. However, building the feature
extraction component for such systems requires extensive domain-specific
expertise or data. The exceptionally rapid development of foundation models is
likely to usher in newfound abilities in such intelligent sensing. We propose a
new scheme for sensing model, which we refer to as semi-generalist sensing
model (SGSM). SGSM is able to semiautomatically solve various tasks using
relatively less task-specific labeled data compared to traditional systems.
Built through the analysis of the common theoretical model, SGSM can depict
different modalities, such as the acoustic and Wi-Fi signal. Experimental
results on such two heterogeneous sensors illustrate that SGSM functions across
a wide range of scenarios, thereby establishing its broad applicability. In
some cases, SGSM even achieves better performance than sensor-specific
specialized solutions. Wi-Fi evaluations indicate a 20\% accuracy improvement
when applying SGSM to an existing sensing model.


  Hadron spectra and hadronic moments in the decay $B \to X_s \ell^+ \ell^-$
are calculated taking into account both the short-distance and long-distance
contributions in the decay amplitude using a Fermi motion (FM) model to
incorporate the $B$-meson wave-function effects. The measured branching ratios
for the inclusive decays $B \to X_s+ (J/\psi,\psi^\prime,...)\to X_s \ell^+
\ell^-$ are used to fix the normalization of the long-distance contribution.
The momentum distribution of the $J/\psi$ measured by the CLEO collaboration is
fitted in the FM model which is then used to calculate the hadronic spectra
from the resonant contribution also away from the $J/\psi$-resonance. We also
study the effect of various descriptions of the resonant and non-resonant
$c\bar{c}$ contributions in $B \to X_s \ell^+ \ell^-$ existing in the
literature on the hadron energy and invariant mass spectra, and in the
Forward-Backward asymmetry. Selective cuts on the hadron and dilepton invariant
masses can be used to reduce the $B\bar{B}$ background and resonant
contribution and, as an example, we work out the hadron spectra with the
experimental cuts used by the CLEO collaboration in searching for the decay $B
\to X_s \ell^+ \ell^-$. We show that data from the forthcoming B facilities
could be used effectively to measure the short-distance contribution in $B \to
X_s \ell^+ \ell^-$, enabling precise determination of the FM model and heavy
quark effective theory parameters $\lambda_1$ and $\bar{\Lambda}$.


  Model independent reconstructions of dark energy have received some
attention. The approach that addresses the reconstruction of the dimensionless
coordinate distance and its two first derivatives using a polynomial fit in
different redshift windows is well developed
\cite{DalyDjorgovski1,DalyDjorgovski2,DalyDjorgovski3}. In this work we offer
new insights into the problem by focusing on two types of observational probes:
SNeIa and GRBs. Our results allow to highlight some of the intrinsic weaknesses
of the method. One of the directions we follow is to consider updated
observational samples. Our results indicate than conclusions on the main dark
energy features as drawn from this method are intimately related to the
features of the samples themselves (which are not quite ideal). This is
particularly true of GRBs, which manifest themselves as poor performers in this
context. In contrast to original works, we conclude they cannot be used for
cosmological purposes, and the state of the art does not allow to regard them
on the same quality basis as SNeIa. The next direction we contribute to is the
question of how the adjusting of some parameters (window width, overlap,
selection criteria) affect the results. We find again there is a considerable
sensitivity to these features. Then, we try to establish what is the current
redshift range for which one can make solid predictions on dark energy
evolution. Finally, we strengthen the former view that this model is modest in
the sense it provides only a picture of the global trend. But, on the other
hand, we believe it offers an interesting complement to other approaches given
that it works on minimal assumptions.


  We propose a new class of distribution-based clustering algorithms, called
k-groups, based on energy distance between samples. The energy distance
clustering criterion assigns observations to clusters according to a
multi-sample energy statistic that measures the distance between distributions.
The energy distance determines a consistent test for equality of distributions,
and it is based on a population distance that characterizes equality of
distributions. The k-groups procedure therefore generalizes the k-means method,
which separates clusters that have different means. We propose two k-groups
algorithms: k-groups by first variation; and k-groups by second variation. The
implementation of k-groups is partly based on Hartigan and Wong's algorithm for
k-means. The algorithm is generalized from moving one point on each iteration
(first variation) to moving $m$ $(m > 1)$ points. For univariate data, we prove
that Hartigan and Wong's k-means algorithm is a special case of k-groups by
first variation. The simulation results from univariate and multivariate cases
show that our k-groups algorithms perform as well as Hartigan and Wong's
k-means algorithm when clusters are well-separated and normally distributed.
Moreover, both k-groups algorithms perform better than k-means when data does
not have a finite first moment or data has strong skewness and heavy tails. For
non--spherical clusters, both k-groups algorithms performed better than k-means
in high dimension, and k-groups by first variation is consistent as dimension
increases. In a case study on dermatology data with 34 features, both k-groups
algorithms performed better than k-means.


  Existential rules have been proposed for representing ontological knowledge,
specifically in the context of Ontology- Based Data Access. Entailment with
existential rules is undecidable. We focus in this paper on conditions that
ensure the termination of a breadth-first forward chaining algorithm known as
the chase. Several variants of the chase have been proposed. In the first part
of this paper, we propose a new tool that allows to extend existing acyclicity
conditions ensuring chase termination, while keeping good complexity
properties. In the second part, we study the extension to existential rules
with nonmonotonic negation under stable model semantics, discuss the relevancy
of the chase variants for these rules and further extend acyclicity results
obtained in the positive case.


  Lehel conjectured that in every $2$-coloring of the edges of $K_n$, there is
a vertex disjoint red and blue cycle which span $V(K_n)$. \L uczak, R\"odl, and
Szemer\'edi proved Lehel's conjecture for large $n$, Allen gave a different
proof for large $n$, and finally Bessy and Thomass\'e gave a proof for all $n$.
  Balogh, Bar\'at, Gerbner, Gy\'arf\'as, and S\'ark\"ozy proposed a significant
strengthening of Lehel's conjecture where $K_n$ is replaced by any graph $G$
with $\delta(G)> 3n/4$; if true, this minimum degree condition is essentially
best possible. We prove that their conjecture holds when
$\delta(G)>(3/4+o(1))n$. Our proof uses Szemer\'edi's regularity lemma along
with the absorbing method of R\"odl, Ruci\'nski, and Szemer\'edi by first
showing that the graph can be covered with monochromatic subgraphs having
certain robust expansion properties.


  In order to describe the dynamics of monochromatic surface waves in deep
water, we derive a nonlinear and dispersive system of equations for the free
surface elevation and the free surface velocity from the Euler equations in
infinite depth. From it, and using a multiscale perturbative methods, an
asymptotic model for small-aspect-ratio waves is derived. The model is shown to
be completely integrable. The Lax pair, the first conserved quantities as well
as the symmetries are exhibited. Theoretical and numerical studies reveal that
it supports periodic progressive Stokes waves which peak and break in finite
time. Comparison between the limiting wave solution of the asymptotic model and
classical irrotational results is performed.


  The existence of contextuality in quantum mechanics is a fundamental
departure from the classical description of the world. Currently, the quest to
identify scenarios which cannot be more contextual than quantum theory is at
the forefront of research in quantum contextuality. In this work, we
experimentally test two inequalities, which are capable of revealing fully
contextual quantum correlations, on a Hilbert space of dimension 8 and 4
respectively, on an NMR quantum information processor. The projectors
associated with the contextuality inequalities are first reformulated in terms
of Pauli operators, which can be determined in an NMR experiment. We also
analyze the behavior of each inequality under rotation of the underlying
quantum state, which unitarily transforms it to another pure state.


  Simulators play a crucial role in autonomous driving, offering significant
time, cost, and labor savings. Over the past few years, the number of
simulators for autonomous driving has grown substantially. However, there is a
growing concern about the validity of algorithms developed and evaluated in
simulators, indicating a need for a thorough analysis of the development status
of the simulators.
  To bridge the gap in research, this paper analyzes the evolution of
simulators and explains how the functionalities and utilities have developed.
Then, the existing simulators are categorized based on their task
applicability, providing researchers with a taxonomy to swiftly assess a
simulator's suitability for specific tasks. Recommendations for select
simulators are presented, considering factors such as accessibility,
maintenance status, and quality. Recognizing potential hazards in simulators
that could impact the confidence of simulation experiments, the paper dedicates
substantial effort to identifying and justifying critical issues in actively
maintained open-source simulators. Moreover, the paper reviews potential
solutions to address these issues, serving as a guide for enhancing the
credibility of simulators.


  In the past few decades, many works have been devoted to the study of
exceptional points (EPs), i.e., exotic degeneracies of non-Hermitian systems.
The usual approach in those studies involves the introduction of a
phenomenological effective non-Hermitian Hamiltonian (NHH), where the gain and
losses are incorporated as the imaginary frequencies of fields and from which
the Hamiltonian EPs (HEPs) are derived. Although this approach can provide
valid equations of motion for the fields in the classical limit, its
application in the derivation of EPs in the quantum regime is questionable.
Recently, a framework [Minganti {\it et al.},
\href{https://doi.org/10.1103/PhysRevA.100.062131}{Phys. Rev. A {\bf 100},
062131 (2019)}], which allows one to determine quantum EPs from a Liouvillian
EP (LEP), rather than from an NHH, has been proposed. Compared to the NHHs, a
Liouvillian naturally includes quantum noise effects via quantum-jump terms,
thus allowing one to consistently determine its EPs purely in the quantum
regime. In this work we study a non-Hermitian system consisting of coupled
cavities with unbalanced gain and losses, where the gain is far from
saturation, i.e, the system is assumed to be linear. We apply both formalisms,
based on an NHH and a Liouvillian within the Scully-Lamb laser theory, to
determine and compare the corresponding HEPs and LEPs in the semiclassical and
quantum regimes. {Our results indicate that, although the overall spectral
properties of the NHH and the corresponding Liouvillian for a given system can
differ substantially, their LEPs and HEPs occur for the same combination of
system parameters.}


  Necessary and sufficient conditions are derived for a social choice
correspondence to be the one that selects the Pareto optimal alternatives.


  The paper presents several quantum models constructed with the formalism of
algebraic geometry. The Universe is presented as a presheaf on the "space of
ultimation" (i.e. the branching future) with values in certain category which
enhances the category opposite to C*-algebras. Given models show the
possibility to derive ordinary space-times (of both Special and General
Relativity) from ultrametric spaces.


  Intrinsic triferroicity is essential and highly sought for novel device
applications, such as high-density multistate data storage. So far, the
intrinsic triferroicity has only been discussed in three-dimensional systems.
Herein on basis of first-principles, we report the intrinsic triferroicity in
two-dimensional lattice. Being exfoliatable from the layered bulk, single-layer
FeO2H is shown to be an intrinsically triferroic semiconductor, presenting
antiferromagnetism, ferroelasticity and ferroelectricity simultaneously.
Moreover, the directional control of its ferroelectric polarization is
achievable by 90{\deg} reversible ferroelastic switching. In addition,
single-layer FeO2H is identified to harbor in-plane piezoelectric effect. The
unveiled phenomena and mechanism of triferroics in this two-dimensional system
not only broaden the scientific and technological impact of triferroics but
also enable a wide range of nanodevice applications.


  We present six nearly full-sky maps made from data taken by radiometers on
the Juno satellite during its 5-year flight to Jupiter. The maps represent
integrated emission over $\sim 4\%$ passbands spaced approximately in octaves
between 600 MHz and 21.9 GHz. Long time-scale offset drifts are removed in all
bands, and, for the two lowest frequency bands, gain drifts are also removed
from the maps via a self-calibration algorithm similar to the NPIPE pipeline
used by the Planck collaboration. We show that, after this solution is applied,
residual noise in the maps is consistent with thermal radiometer noise. We
verify our map solutions with several consistency tests and end-to-end
simulations. We also estimate the level of pixelization noise and polarization
leakage via simulations.


  Online discussion forums are complex webs of overlapping subcommunities
(macrolevel structure, across threads) in which users enact different roles
depending on which subcommunity they are participating in within a particular
time point (microlevel structure, within threads). This sub-network structure
is implicit in massive collections of threads. To uncover this structure, we
develop a scalable algorithm based on stochastic variational inference and
leverage topic models (LDA) along with mixed membership stochastic block (MMSB)
models. We evaluate our model on three large-scale datasets,
Cancer-ThreadStarter (22K users and 14.4K threads), Cancer-NameMention(15.1K
users and 12.4K threads) and StackOverFlow (1.19 million users and 4.55 million
threads). Qualitatively, we demonstrate that our model can provide useful
explanations of microlevel and macrolevel user presentation characteristics in
different communities using the topics discovered from posts. Quantitatively,
we show that our model does better than MMSB and LDA in predicting user reply
structure within threads. In addition, we demonstrate via synthetic data
experiments that the proposed active sub-network discovery model is stable and
recovers the original parameters of the experimental setup with high
probability.


  Sanchez, Viader, Paradis and Carrillo (2016) proved that there exists an
increasing continuous singular function $f$ on $[0,1]$ such that the set $A_f$
of points where $f$ has a nonzero finite derivative has Hausdorff dimension 1
in each subinterval of $[0,1]$. We prove a stronger (and optimal) result
showing that a set $A_f$ as above can contain any prescribed $F_{\sigma}$ null
subset of $[0,1]$.


  We report the first application of complex symmetric wavelets to the
numerical simulation of a nonlinear signal propagation model. This model is the
so-called nonlinear Schrodinger equation that describes, for instance, the
evolution of the electric field amplitude in nonlinear optical fibers. We
propose and study a new way to implement a global space-time adaptive grid,
based on interpolation properties of higher-order scaling functions.


  Missing value imputation in machine learning is the task of estimating the
missing values in the dataset accurately using available information. In this
task, several deep generative modeling methods have been proposed and
demonstrated their usefulness, e.g., generative adversarial imputation
networks. Recently, diffusion models have gained popularity because of their
effectiveness in the generative modeling task in images, texts, audio, etc. To
our knowledge, less attention has been paid to the investigation of the
effectiveness of diffusion models for missing value imputation in tabular data.
Based on recent development of diffusion models for time-series data
imputation, we propose a diffusion model approach called "Conditional
Score-based Diffusion Models for Tabular data" (TabCSDI). To effectively handle
categorical variables and numerical variables simultaneously, we investigate
three techniques: one-hot encoding, analog bits encoding, and feature
tokenization. Experimental results on benchmark datasets demonstrated the
effectiveness of TabCSDI compared with well-known existing methods, and also
emphasized the importance of the categorical embedding techniques.


  We use the newly introduced conformable fractional derivative, which is
different from the Caputo and Riemann-Liouville fractional derivatives, to
reformulate several common boundary value problems, including those with
conjugate, right-focal, and Lidstone conditions. With the fractional
differential equation and fractional boundary conditions established, we find
the corresponding Green's functions and prove their positivity under
appropriate assumptions.


  Prediction queries are widely used across industries to perform advanced
analytics and draw insights from data. They include a data processing part
(e.g., for joining, filtering, cleaning, featurizing the datasets) and a
machine learning (ML) part invoking one or more trained models to perform
predictions. These parts have so far been optimized in isolation, leaving
significant opportunities for optimization unexplored. We present Raven, a
production-ready system for optimizing prediction queries. Raven follows the
enterprise architectural trend of collocating data and ML runtimes. It relies
on a unified intermediate representation that captures both data and ML
operators in a single graph structure to unlock two families of optimizations.
First, it employs logical optimizations that pass information between the data
part (and the properties of the underlying data) and the ML part to optimize
each other. Second, it introduces logical-to-physical transformations that
allow operators to be executed on different runtimes (relational, ML, and DNN)
and hardware (CPU, GPU). Novel data-driven optimizations determine the runtime
to be used for each part of the query to achieve optimal performance. Our
evaluation shows that Raven improves performance of prediction queries on
Apache Spark and SQL Server by up to 13.1x and 330x, respectively. For complex
models where GPU acceleration is beneficial, Raven provides up to 8x speedup
compared to state-of-the-art systems.


  Carbon nanotube quantum dots allow accurate control of electron charge, spin
and valley degrees of freedom in a material which is atomically perfect and can
be grown isotopically pure. These properties underlie the unique potential of
carbon nanotubes for quantum information processing, but developing nanotube
charge, spin, or spin-valley qubits requires efficient readout techniques as
well as understanding and extending quantum coherence in these devices. Here,
we report on microwave spectroscopy of a carbon nanotube charge qubit in which
quantum information is encoded in the spatial position of an electron. We
combine radio-frequency reflectometry measurements of the quantum capacitance
of the device with microwave manipulation to drive transitions between the
qubit states. This approach simplifies charge-state readout and allows us to
operate the device at an optimal point where the qubit is first-order
insensitive to charge noise. From these measurements, we are able to quantify
the degree of charge noise experienced by the qubit and obtain an inhomogeneous
charge coherence of 5 ns. We use a chopped microwave signal whose duty-cycle
period is varied to measure the decay of the qubit states, yielding a charge
relaxation time of 48 ns.


  The tunnel magnetoresistance (TMR) in the magnetic tunnel junction (MTJ) with
embedded nanoparticles (NPs) was calculated in range of the quantum-ballistic
model. The simulation was performed for electron tunneling through the
insulating layer with embedded magnetic and nonmagnetic NPs within the approach
of the double barrier subsystem connected in parallel to the single barrier
one. This model can be applied for both MTJs with in-plane magnetization and
perpendicular one. We also calculated the in-plane component of the spin
transfer torque (STT) versus the applied voltage in MTJs with magnetic NPs and
determined that its value can be much larger than in single barrier system
(SBS) for the same tunneling thickness. The reported simulation reproduces
experimental data of the TMR suppression and peak-like TMR anomalies at low
voltages available in literature.


  The prior knowledge (a.k.a. priors) integrated into the design of a machine
learning system strongly influences its generalization abilities. In the
specific context of deep learning, some of these priors are poorly understood
as they implicitly emerge from the successful heuristics and tentative
approximations of biological brains involved in deep learning design. Through
the lens of supervised image classification problems, this thesis investigates
the implicit integration of a natural clustering prior composed of three
statements: (i) natural images exhibit a rich clustered structure, (ii) image
classes are composed of multiple clusters and (iii) each cluster contains
examples from a single class. The decomposition of classes into multiple
clusters implies that supervised deep learning systems could benefit from
unsupervised clustering to define appropriate decision boundaries. Hence, this
thesis attempts to identify implicit clustering abilities, mechanisms and
hyperparameters in deep learning systems and evaluate their relevance for
explaining the generalization abilities of these systems. We do so through an
extensive empirical study of the training dynamics as well as the neuron- and
layer-level representations of deep neural networks. The resulting collection
of experiments provides preliminary evidence for the relevance of the natural
clustering prior for understanding deep learning.


  Power prediction is crucial to the efficiency and reliability of Photovoltaic
(PV) systems. For the model-chain-based (also named indirect or physical) power
prediction, the conversion of ground environmental data (plane-of-array
irradiance and module temperature) to the output power is a fundamental step,
commonly accomplished through physical modeling. The core of the physical model
lies in the parameters. However, traditional parameter estimation either relies
on datasheet information that cannot reflect the system's current health status
or necessitates additional I-V characterization of the entire array, which is
not commonly available. To address this, our paper introduces PVPro, a dynamic
physical modeling method for irradiance-to-power conversion. It extracts model
parameters from the recent production data without requiring I-V curve
measurements. This dynamic model, periodically-updated (as short as daily), can
closely capture the actual health status, enabling precise power estimation. To
evaluate the performance, PVPro is compared with the smart persistence, nominal
physical, and various machine learning models for day-ahead power prediction.
The results indicate that PVPro achieves an outstanding power estimation
performance with the average nMAE =1.4% across four field PV systems, reducing
the error by 17.6% compared to the best of other techniques. Furthermore, PVPro
demonstrates robustness across different seasons and weather conditions. More
importantly, PVPro can also perform well with a limited amount of historical
production data (3 days), rendering it applicable for new PV systems. The tool
is available as a Python package at: https://github.com/DuraMAT/pvpro.


  The synthesis of ultralow-noise microwaves is of both scientific and
technological relevance for timing, metrology, communications and
radio-astronomy. Today, the lowest reported phase noise signals are obtained
via optical frequency-division using mode-locked laser frequency combs.
Nonetheless, this technique ideally requires high repetition rates and tight
comb stabilisation. Here, a soliton microcomb with a 14 GHz repetition rate is
generated with an ultra-stable pump laser and used to derive an ultralow-noise
microwave reference signal, with an absolute phase noise level below -60 dBc/Hz
at 1 Hz offset frequency and -135 dBc/Hz at 10 kHz. This is achieved using a
transfer oscillator approach, where the free-running microcomb noise (which is
carefully studied and minimised) is cancelled via a combination of electronic
division and mixing. Although this proof-of-principle uses an auxiliary comb
for detecting the microcomb's offset frequency, we highlight the prospects of
this method with future self-referenced integrated microcombs and electro-optic
combs, that would allow for ultralow-noise microwave and sub-terahertz signal
generators.


  The variations in metallicity and spatial patterns within star-forming
regions of galaxies result from diverse physical processes unfolding throughout
their evolutionary history, with a particular emphasis in recent events.
Analysing MaNGA and \textsc{eagle} galaxies, we discovered an additional
dependence of the mass-metallicity relation (MZR) on metallicity gradients
($\nabla_{{\rm (O/H)}}$). Two regimes emerged for low and high stellar mass
galaxies, distinctly separated at approximately ${\rm M_{\star}} >10^{9.75}$.
  Low-mass galaxies with strong positive $\nabla_{{\rm (O/H)}}$ appear less
enriched than the MZR median, while those with strong negative gradients are
consistently more enriched in both simulated and observed samples.
Interestingly, low-mass galaxies with strong negative $\nabla_{{\rm (O/H)}}$
exhibit high star-forming activity, regardless of stellar surface density or
$\nabla_{{\rm (O/H)}}$. In contrast, a discrepancy arises for massive galaxies
between MaNGA and \textsc{eagle} datasets. The latter exhibit a notable
anticorrelation between specific star formation rate and stellar surface
density, independent of $\nabla_{{\rm (O/H)}}$, while MaNGA galaxies show this
trend mainly for strong positive $\nabla_{{\rm (O/H)}}$. Further investigation
indicates that galaxies with strong negative gradients tend to host smaller
central black holes in observed datasets, a trend not replicated in
simulations. These findings suggest disparities in metallicity recycling and
mixing history between observations and simulations, particularly in massive
galaxies with varying metallicity gradients. These distinctions could
contribute to a more comprehensive understanding of the underlying physics.


  The onset of long-form egocentric datasets such as Ego4D and EPIC-Kitchens
presents a new challenge for the task of Temporal Sentence Grounding (TSG).
Compared to traditional benchmarks on which this task is evaluated, these
datasets offer finer-grained sentences to ground in notably longer videos. In
this paper, we develop an approach for learning to ground sentences in these
datasets using only narrations and their corresponding rough narration
timestamps. We propose to artificially merge clips to train for temporal
grounding in a contrastive manner using text-conditioning attention. This Clip
Merging (CliMer) approach is shown to be effective when compared with a high
performing TSG method -- e.g. mean R@1 improves from 3.9 to 5.7 on Ego4D and
from 10.7 to 13.0 on EPIC-Kitchens. Code and data splits available from:
https://github.com/keflanagan/CliMer


  Ultracold atoms trapped in laser-generated optical lattices serve as a
versatile platform for quantum simulations. However, as these lattices are
infinitely stiff, they do not allow to emulate phonon degrees of freedom. This
restriction can be lifted in emerged optical lattices inside multimode
cavities. Motivated by recent experimental progress in multimode cavity QED, we
propose a scheme to implement and study supersolid and droplet states with
phonon-like lattice excitations by coupling a Bose gas to many longitudinal
modes of a ring cavity. The interplay between contact collisional and
tunable-range cavity-mediated interactions leads to a rich phase diagram, which
includes elastic supersolid as well as insulating droplet phases exhibiting
roton-type mode softening for a continuous range of momenta across the
superradiant phase transition. The non-trivial dynamic response of the system
to local density perturbations further proves the existence of phonon-like
modes.


  We present a preliminary measurement of \rone, \rtwo and \rhosq which are the
three parameters used to characterize the $B\rar D^*\ell\bar\nu_e$ form factors
($A_1$, $V$, and $A_2$). We use $85 \times 10^6$ $B\bar B$-pairs accumulated on
the \upsfs resonance at PEP-II. In this analysis we use the decay mode $\bar
B^0\rar D^{+*}e^-\bar\nu$ and its charge conjugate. The $D^{*+}$ is
reconstructed in the channel $D^{*+}\to D^0\pi^+$ and the $D^0$ in the channel
$\dtokpi$. We parameterize the \ff s in terms of their ratios (determined by
the parameters $R_1$ and $R_2$) and the common slope $\rhosq$ in the variable
$w$ (a quantity related to the momentum transfer in the decay process). These
parameters are determined via an unbinned maximum likelihood fit to the
distributions in four kinematic variables (three decay angles and $w$). The
results are $R_1= 1.328 \pm 0.055\pm 0.025\pm 0.025$ and $R_2=0.920 \pm
0.044\pm 0.020\pm 0.013 $ for the ratios and $\rhosq= 0.769\pm 0.039 \pm
0.019\pm 0.032 $ for the slope. The stated errors are the statistical
uncertainty from the data, statistical uncertainty from the size of the Monte
Carlo sample and the systematic uncertainty, respectively.


  During a core-collapse supernova (SN), axion-like particles (ALPs) could be
produced through the Primakoff process and subsequently convert into gamma rays
in the magnetic field of the Milky Way. Using a sample of well studied
extragalactic SNe at optical wavelengths, we estimate the time of the core
collapse and search for a coincident gamma-ray burst with the Fermi Large Area
Telescope (LAT). Under the assumption that at least one SN was contained within
the LAT field of view, we exclude photon-ALP couplings within a factor of
$\sim$5 of previous limits from SN1987A. With the increasing number of SNe
observed with optical surveys, our results demonstrate the potential to probe
ALP dark matter with combined optical and gamma-ray observations. We also
provide preliminary results for the estimation of explosion times of 15
close-by SNe observed recently with ZTF. Our findings show that the explosion
time can be estimated within one day (statistical uncertainty only) making them
promising targets for a follow-up LAT analysis.


  Let $\mathfrak{g}$ be the $p$-dimensional Witt algebra over an algebraically
closed field $k$ of characteristic $p>3$. Let $\mathscr{N}={x\in\ggg\mid
x^{[p]}=0}$ be the nilpotent variety of $\mathfrak{g}$, and
$\mathscr{C}(\mathscr{N}):=\{(x,y)\in \mathscr{N}\times\mathscr{N}\mid
[x,y]=0\}$ the nilpotent commuting variety of $\mathfrak{g}$. As an analogue of
Premet's result in the case of classical Lie algebras [A. Premet, Nilpotent
commuting varieties of reductive Lie algebras. Invent. Math., 154, 653-683,
2003.], we show that the variety $\mathscr{C}(\mathscr{N})$ is reducible and
equidimensional. Irreducible components of $\mathscr{C}(\mathscr{N})$ and their
dimension are precisely given. Furthermore, the nilpotent commuting varieties
of Borel subalgebras are also determined.


  Recently, the interplay between spin and lattice degrees of freedom has
gained a lot of attention due to its importance for various fundamental
phenomena as well as for spintronic and magnonic applications. Examples are
ultrafast angular momentum transfer between the spin and lattice subsystems
during ultrafast demagnetization, frustration driven by structural distortions
in transition metal oxides, or in acoustically driven spin-wave resonances. In
this work, we provide a systematic analysis of spin-lattice interactions for
ferro- and antiferromagnetic materials and focus on the role of lattice
symmetries and dimensions, magnetic order, and the relevance of spin-lattice
interactions for angular momentum transfer as well as magnetic frustration. For
this purpose, we use a recently developed scheme which allows an efficient
calculation of spin-lattice interaction tensors from first principles. In
addition to that, we provide a more accurate and self consistent scheme to
calculate ab initio spin lattice interactions by using embedded clusters which
allows to benchmark the performance of the scheme introduced previously.


  In this paper, we extend the work in
\cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic
conditions on the second fundamental form, and we also give an $L^{6}-$norm
bound for the difference between general data and Extreme Kerr data or Extreme
Kerr-Newman data by proving convexity of the renormalized Dirichlet energy when
the target has non-positive curvature. In particular, we give the first proof
of the strict mass/angular momentum/charge inequality for axisymmetric
Einstein/Maxwell data which is not identical with the extreme Kerr-Newman
solution.


  We investigate the behavior of the dc voltage drop in a periodically driven
double barrier structure (DBS) sensed by voltages probes that are weakly
coupled to the system. We find that the four terminal resistance $R_{4t}$
measured with the probes located outside the DBS results identical to the
resistance measured in the same structure under a stationary bias voltage
difference between left and right reservoirs. This result, valid beyond the
adiabatic pumping regime, can be taken as an indication of the universal
character of $R_{4t}$ as a measure of the resistive properties of a sample,
irrespectively of the mechanism used to induce the transport.


  Market-based conservation instruments, such as payments, auctions or tradable
permits, are environmental policies that create financial incentives for
landowners to engage in voluntary conservation on their land. But what if
ecological processes operate across property boundaries and land use decisions
on one property influence ecosystem functions on neighboring sites? This paper
examines how to account for such spatial externalities when designing
market-based conservation instruments. We use an agent-based model to analyze
different spatial metrics and their implications on land use decisions in a
dynamic cost environment. The model contains a number of alternative submodels
which differ in incentive design and social interactions of agents, the latter
including coordinating as well as cooperating behavior of agents. We find that
incentive design and social interactions have a strong influence on the spatial
allocation and the costs of the conservation market.


  Given a topological space X denote by exp_k(X) the space of non-empty subsets
of X of size at most k, topologised as a quotient of X^k. This space may be
regarded as a union over 0 < l < k+1 of configuration spaces of l distinct
unordered points in X. In the special case X=S^1 we show that: (1) exp_k(S^1)
has the homotopy type of an odd dimensional sphere of dimension k or k-1; (2)
the natural inclusion of exp_{2k-1}(S^1) h.e. S^{2k-1} into exp_2k(S^1) h.e.
S^{2k-1} is multiplication by two on homology; (3) the complement
exp_k(S^1)-exp_{k-2}(S^1) of the codimension two strata in exp_k(S^1) has the
homotopy type of a (k-1,k)-torus knot complement; and (4) the degree of an
induced map exp_k(f): exp_k(S^1)-->exp_k(S^1) is (deg f)^[(k+1)/2] for f:
S^1-->S^1. The first three results generalise known facts that exp_2(S^1) is a
Moebius strip with boundary exp_1(S^1), and that exp_3(S^1) is the three-sphere
with exp_1(S^1) inside it forming a trefoil knot.


  The ground state parameters of the two-dimensional S=1/2 antiferromagnetic
Heisenberg model are calculated using the Stochastic Series Expansion quantum
Monte Carlo method for L*L lattices with L up to 16. The finite-size results
for the energy E, the sublattice magnetization M, the long-wavelength
susceptibility chi_perp(q=2*pi/L), and the spin stiffness rho_s, are
extrapolated to the thermodynamic limit using fits to polynomials in 1/L,
constrained by scaling forms previously obtained from renormalization group
calculations for the nonlinear sigma model and chiral perturbation theory. The
results are fully consistent with the predicted leading finite-size corrections
and are of sufficient accuracy for extracting also subleading terms. The
subleading energy correction (proportional to 1/L^4) agrees with chiral
perturbation theory to within a statistical error of a few percent, thus
providing the first numerical confirmation of the finite-size scaling forms to
this order. The extrapolated ground state energy per spin, E=-0.669437(5), is
the most accurate estimate reported to date. The most accurate Green's function
Monte Carlo (GFMC) result is slightly higher than this value, most likely due
to a small systematic error originating from ``population control'' bias in
GFMC. The other extrapolated parameters are M=0.3070(3), rho_s = 0.175(2),
chi_perp = 0.0625(9), and the spinwave velocity c=1.673(7). The statistical
errors are comparable with those of the best previous estimates, obtained by
fitting loop algorithm quantum Monte Carlo data to finite-temperature scaling
forms. Both M and rho_s obtained from the finite-T data are, however, a few
error bars higher than the present estimates. It is argued that the T=0
extrapolations performed here are less sensitive to effects of neglected


  Fairness-aware classification models have gained increasing attention in
recent years as concerns grow on discrimination against some demographic
groups. Most existing models require full knowledge of the sensitive features,
which can be impractical due to privacy, legal issues, and an individual's fear
of discrimination. The key challenge we will address is the group dependency of
the unavailability, e.g., people of some age range may be more reluctant to
reveal their age. Our solution augments general fairness risks with
probabilistic imputations of the sensitive features, while jointly learning the
group-conditionally missing probabilities in a variational auto-encoder. Our
model is demonstrated effective on both image and tabular datasets, achieving
an improved balance between accuracy and fairness.


  The path integral quantization method is applied to a relativistically
covariant version of the Hopfield model, which represents a very interesting
mesoscopic framework for the description of the interaction between quantum
light and dielectric quantum matter, with particular reference to the context
of analogue gravity. In order to take into account the constraints occurring in
the model, we adopt the Faddeev-Jackiw approach to constrained quantization in
the path integral formalism. In particular we demonstrate that the propagator
obtained with the Faddeev-Jackiw approach is equivalent to the one which, in
the framework of Dirac canonical quantization for constrained systems, can be
directly computed as the vacuum expectation value of the time ordered product
of the fields. Our analysis also provides an explicit example of quantization
of the electromagnetic field in a covariant gauge and coupled with the
polarization field, which is a novel contribution to the literature on the
Faddeev-Jackiw procedure.


  In this article we introduce a hyperbolic metric on the (normalized) space of
stability conditions on projective K3 surfaces $X$ with Picard rank $\rho (X)
=1$. And we show that all walls are geodesic in the normalized space with
respect to the hyperbolic metric. Furthermore we demonstrate how the hyperbolic
metric is helpful for us by discussing mainly three topics. We first make a
study of so called Bridgeland's conjecture. In the second topic we prove a
famous Orlov's theorem without the global Torelli theorem. In the third topic
we give an explicit example of stable complexes in large volume limits by using
the hyperbolic metric. Though Bridgeland's conjecture may be well-known for
algebraic geometers, we would like to start from the review of it.


  We study the nonlinear dynamics of series arrays of Josephson junctions in
the large-N limit, where N is the number of junctions in the array. The
junctions are assumed to be identical, overdamped, driven by a constant bias
current and globally coupled through a common load. Previous simulations of
such arrays revealed that their dynamics are remarkably simple, hinting at the
presence of some hidden symmetry or other structure. These observations were
later explained by the discovery of (N - 3) constants of motion, each choice of
which confines the resulting flow in phase space to a low-dimensional invariant
manifold. Here we show that the dimensionality can be reduced further by
restricting attention to a special family of states recently identified by Ott
and Antonsen. In geometric terms, the Ott-Antonsen ansatz corresponds to an
invariant submanifold of dimension one less than that found earlier. We derive
and analyze the flow on this submanifold for two special cases: an array with
purely resistive loading and another with resistive-inductive-capacitive
loading. Our results recover (and in some instances improve) earlier findings
based on linearization arguments.


  We explore further the classical QGP using methods from classical liquids.
The partition function of an ensemble of SU(N_c) colored charge spheres is
constructed. We analyze it using a cumulant expansion (low density) and a loop
expansion (high temperature) after resumming the Debye screening effects. The
pertinent free energies are derived in both limits and compared to recent
molecular dynamics results.


  Cataclysmic variables can experience short optical brightenings, which are
commonly attributed to phenomena such as dwarf novae outbursts, micronovae,
donor flares or magnetic gating bursts. Since these events exhibit similar
observational characteristics, their identification has often been ambiguous.
In particular, magnetic gating bursts and micronovae have been suggested as
alternative interpretations of the same phenomena. Here we show that the
timescales and energies separate the optical brightenings into separate
clusters consistent with their different classifications. This suggest that
micronovae and magnetic gating bursts are in fact separate phenomena. Based on
our finding we develop diagnostic diagrams that can distinguish between these
bursts/flares based on their properties. We demonstrate the effectiveness of
this approach on observations of a newly identified intermediate polar, CTCV
J0333-4451, which we classify as a magnetic gating system. CTCV J0333-4451 is
the third high spin-to-orbital period ratio intermediate polar with magnetic
gating, suggesting that these bursts are common among these rare systems.


  Deep neural networks (DNNs) have shown promising results for acoustic echo
cancellation (AEC). But the DNN-based AEC models let through all near-end
speakers including the interfering speech. In light of recent studies on
personalized speech enhancement, we investigate the feasibility of personalized
acoustic echo cancellation (PAEC) in this paper for full-duplex communications,
where background noise and interfering speakers may coexist with acoustic
echoes. Specifically, we first propose a novel backbone neural network termed
as gated temporal convolutional neural network (GTCNN) that outperforms
state-of-the-art AEC models in performance. Speaker embeddings like d-vectors
are further adopted as auxiliary information to guide the GTCNN to focus on the
target speaker. A special case in PAEC is that speech snippets of both parties
on the call are enrolled. Experimental results show that auxiliary information
from either the near-end speaker or the far-end speaker can improve the
DNN-based AEC performance. Nevertheless, there is still much room for
improvement in the utilization of the finite-dimensional speaker embeddings.


  We report a careful finite size scaling study of the metal insulator
transition in Anderson's model of localisation. We focus on the estimation of
the critical exponent $\nu$ that describes the divergence of the localisation
length. We verify the universality of this critical exponent for three
different distributions of the random potential: box, normal and Cauchy. Our
results for the critical exponent are consistent with the measured values
obtained in experiments on the dynamical localisation transition in the quantum
kicked rotor realised in a cold atomic gas.


Our universe is a deforming Lie group.


  With recent advancements in deep neural networks (DNNs), we are able to solve
traditionally challenging problems. Since DNNs are compute intensive,
consumers, to deploy a service, need to rely on expensive and scarce compute
resources in the cloud. This approach, in addition to its dependability on
high-quality network infrastructure and data centers, raises new privacy
concerns. These challenges may limit DNN-based applications, so many
researchers have tried optimize DNNs for local and in-edge execution. However,
inadequate power and computing resources of edge devices along with small
number of requests limits current optimizations applicability, such as batch
processing. In this paper, we propose an approach that utilizes aggregated
existing computing power of Internet of Things (IoT) devices surrounding an
environment by creating a collaborative network. In this approach, IoT devices
cooperate to conduct single-batch inferencing in real time. While exploiting
several new model-parallelism methods and their distribution characteristics,
our approach enhances the collaborative network by creating a balanced and
distributed processing pipeline. We have illustrated our work using many
Raspberry Pis with studying DNN models such as AlexNet, VGG16, Xception, and
C3D.


  Fundamental quantum electrodynamical (QED) processes such as spontaneous
emission and electron-photon scattering encompass a wealth of phenomena that
form one of the cornerstones of modern science and technology. Conventionally,
calculations in QED and in other field theories assume that incoming particles
are single-momentum states. The possibility that coherent superposition states,
i.e. "shaped wavepackets", will alter the result of fundamental scattering
processes is thereby neglected, and is instead assumed to sum to an incoherent
(statistical) distribution in the incoming momentum. Here, we show that
free-electron wave-shaping can be used to engineer quantum interferences that
alter the results of scattering processes in QED. Specifically, the
interference of two or more pathways in a QED process (such as photon emission)
enables precise control over the rate of that process. As an example, we apply
our concept to Bremsstrahlung, a ubiquitous phenomenon that occurs, for
instance, in X-ray sources for state-of-the-art medical imaging, security
scanning, materials analysis, and astrophysics. We show that free electron
wave-shaping can be used to tailor both the spatial and the spectral
distribution of emitted photons, enhancing their directionality and
monochromaticity, and adding more degrees of freedom that make emission
processes like Bremsstrahlung more versatile. The ability to tailor the
spatiotemporal attributes of photon emission via quantum interference provides
a new degree of freedom in shaping radiation across the entire electromagnetic
spectrum. More broadly, the ability to tailor general QED processes through the
shaping of free electrons opens up new avenues of control in processes ranging
from optical excitation processes (e.g., plasmon and phonon emission) in
electron microscopy to free electron lasing in the quantum regime.


  A velocity-map-imaging spectrometer is demonstrated to characterize the
normalized transverse emittance of photoemitted electron bunches. The
two-dimensional (2D) projected velocity distribution images of photoemitted
electrons are recorded by the detection system and analyzed to obtain the
normalized transverse emittance. With the presented distribution function of
the electron photoemission angles a mathematical method is implemented to
reconstruct the three-dimensional (3D) velocity distribution curve. As a first
example, multiphoton emission from a planar Au surface is studied via
irradiation at a glancing angle by intense 45 fs laser pulses at a central
wavelength of 800 nm. The reconstructed energy distribution agrees very well
with the Berglund-Spicer theory of photoemission. The normalized transverse
emittance of the intrinsic electron bunch is characterized to be 0.52 and 0.05
$\pi \cdot mm \cdot mrad$ in $X$- and $Y$-directions, respectively.


  Synthesis remains a challenge for advancing materials science. A key focus of
this challenge is how to enable selective synthesis, particularly as it
pertains to metastable materials. This perspective addresses the question: how
can ``spectator'' elements, such as those found in double ion exchange
(metathesis) reactions, enable selective materials synthesis? By observing
reaction pathways as they happen (\emph{in situ}) and calculating their
energetics using modern computational thermodynamics, we observe transient,
crystalline intermediates that suggest that many reactions attain a local
thermodynamic equilibrium dictated by local chemical potentials far before
achieving a global equilibrium set by the average composition. Using this
knowledge, one can thermodynamically ``shortcut'' unfavorable intermediates by
including additional elements beyond those of the desired target, providing
access to a greater number of intermediates with advantageous energetics and
selective phase nucleation. Ultimately, data-driven modeling that unites
first-principles approaches with experimental insights will refine the accuracy
of emerging predictive retrosynthetic models for complex materials synthesis.


  Measurements of CP asymmetries in B decays will soon be made at $B$ factories
and hadron machines. In light of this, we review and update the profile of the
CKM unitarity triangle and the resulting CP asymmetries in B decays. This is
done both in the standard model and in several variants of the minimal
supersymmetric standard model (MSSM), which are characterized by a single phase
in the quark flavour mixing matrix. After imposing present constraints on the
parameters of these models, the predicted ranges of $\sin 2 \beta$ in the
standard model and in the MSSM are found to be similar. However, these theories
may be distinguished by future precise measurements of the other two
CP-violating phases $\alpha$ and $\gamma$.


  Free-form strong-lensing (SL) mass reconstructions typically suffer from
overfitting, which manifest itself as false-positive small-scale fluctuations.
We present a new free-form MAximum-entropy ReconStruction (${\tt MARS}$) method
without the assumption that light traces mass (LTM). The ${\tt MARS}$ algorithm
enables us to achieve excellent convergence in source positions ~0.001$"$,
minimize spurious small-scale fluctuations, and provide a quasi-unique solution
independently of initial conditions. Our method is tested with the publicly
available synthetic SL data ${\tt FF-SIMS}$ and the comparison with the truth
shows that the reconstruction quality is on a par with those of the
best-performing LTM methods published in the literature, which have been
demonstrated to outperform the existing free-form methods. In terms of the
radial mass profile reconstruction, we achieve $<1$% agreements with the truth
for the regions constrained by the multiple images. Finally, we apply ${\tt
MARS}$ to A1689 and find that the cluster mass in the SL regime is dominated by
the primary halo centered on the brightest cluster galaxy and the weaker
secondary halo also coincident with the bright cluster member ~160 kpc
northeast. Within the SL field, the A1689 radial profile is well-described by a
Navarro-Frenk-White (NFW) profile with $c_{200}=5.53\pm0.77$ and
$r_s=538^{+90}_{-100}$ kpc and we find no evidence that A1689 is
over-concentrated.


  We study the Schwarz overlapping domain decomposition method applied to the
Poisson problem on a special family of domains, which by construction consist
of a union of a large number of fixed-size subdomains. These domains are
motivated by applications in computational chemistry where the subdomains
consist of van der Waals balls. As is usual in the theory of domain
decomposition methods, the rate of convergence of the Schwarz method is related
to a stable subspace decomposition. We derive such a stable decomposition for
this family of domains and analyze how the stability "constant" depends on
relevant geometric properties of the domain. For this, we introduce new
descriptors that are used to formalize the geometry for the family of domains.
We show how, for an increasing number of subdomains, the rate of convergence of
the Schwarz method depends on specific local geometry descriptors and on one
global geometry descriptor. The analysis also naturally provides lower bounds
in terms of the descriptors for the smallest eigenvalue of the Laplace
eigenvalue problem for this family of domains.


  This paper describes a 720-vertex connected planar graph G such that cop1(G),
denoting the minimum number of cops needed to catch the robber in the
1-cop-move game on G, is at least 4 and at most 7. Furthermore, G has a
connected subgraph H such that cop1(H) is exactly 4, meaning that 4 cops are
barely sufficient to catch the robber in the 1-cop-move game on H. This is a
significant improvement over the graph given by Gao and Yang in 2017.


  Let $G$ be the special linear group of degree $2$ over an algebraically
closed field $K$. Let $E$ be the natural module and $S^rE$ the $r$th symmetric
power. We consider here, for $r,s\geq 0$, the tensor product of $S^rE$ and the
dual of $S^sE$. In characteristic zero this tensor product decomposes according
to the Clebsch-Gordan formula. We consider here the situation when $K$ is a
field of positive characteristic. We show that each indecomposable component
occurs with multiplicity one and identify which modules occur for given $r$ and
$s$.


  Map retrieval, the problem of similarity search over a large collection of 2D
pointset maps previously built by mobile robots, is crucial for autonomous
navigation in indoor and outdoor environments. Bag-of-words (BoW) methods
constitute a popular approach to map retrieval; however, these methods have
extremely limited descriptive ability because they ignore the spatial layout
information of the local features. The main contribution of this paper is an
extension of the bag-of-words map retrieval method to enable the use of spatial
information from local features. Our strategy is to explicitly model a unique
viewpoint of an input local map; the pose of the local feature is defined with
respect to this unique viewpoint, and can be viewed as an additional invariant
feature for discriminative map retrieval. Specifically, we wish to determine a
unique viewpoint that is invariant to moving objects, clutter, occlusions, and
actual viewpoints. Hence, we perform scene parsing to analyze the scene
structure, and consider the "center" of the scene structure to be the unique
viewpoint. Our scene parsing is based on a Manhattan world grammar that imposes
a quasi-Manhattan world constraint to enable the robust detection of a scene
structure that is invariant to clutter and moving objects. Experimental results
using the publicly available radish dataset validate the efficacy of the
proposed approach.


  Recent advances in modeling and control of crowds of pedestrians are briefly
surveyed in this paper. Possibilities of applying fractional calculus in the
modeling of crowd of pedestrians have been shortly reviewed and discussed from
different aspects such as descriptions of motion, interactions of long range
and effects of memory. Control of the crowd of pedestrians have also been
formulated using the framework of Cyber-Physical Systems and been realized
using networked Segways with onboard emergency response personnels to regulate
the velocity and flux of the crowd. Platform for verification of the
theoretical results are also provided in this paper.


  Bidirectional cargo transport by molecular motors in cells is a complex
phenomenon, in which the cargo (usually a vesicle) alternately moves in
retrograde and anterograde directions. In this case, teams of oppositely
pulling motors (eg., kinesin and dynein) bind to the cargo simultaneously, and
`coordinate' their activity such that the motion consists of spells of
positively and negatively directed segments, separated by pauses of varying
duration. A set of recent experiments have analyzed the bidirectional motion of
endosomes in the amoeba D. discoideum in detail. It was found that in between
directional switches, a team of 5-6 dyneins stall a cargo against a stronger
kinesin in tug of war, which lasts for almost a second. As the mean detachment
time of a kinesin under its stall load was also observed to be ~ 1s, we infer
that the collective detachment time of the dynein assembly must also be
similar. Here, we analyze this inference from a modeling perspective, using
experimentally measured single-molecule parameters as inputs. We find that the
commonly assumed exponential load-dependent detachment rate is inconsistent
with observations, as it predicts that a 5-dynein assembly will detach under
its combined stall load in less than a hundredth of a second. A modified model
where the load-dependent unbinding rate is assumed to saturate at stall-force
level for super-stall loads gives results which are in agreement with
experimental data. Our analysis suggests that the load-dependent detachment of
a dynein in a team is qualitatively different at sub-stall and super-stall
loads, a conclusion which is likely to have implications in other situations
involving collective effects of many motors.


  We discuss the relative rates of different charmonium states and introduce an
improved model for mapping the continuous ccbar mass spectrum on the physical
charmonium resonances.


  We improve upon the local bound in the depth aspect for sup-norms of newforms
on $D^\times$ where $D$ is an indefinite quaternion division algebra over
$\mathbb{Q}$. Our sup-norm bound implies a depth-aspect subconvexity bound for
$L(1/2, f \times \theta_\chi)$, where $f$ is a (varying) newform on $D^\times$
of level $p^n$, and $\theta_\chi$ is an (essentially fixed) automorphic form on
$\mathrm{GL}_2$ obtained as the theta lift of a Hecke character $\chi$ on a
quadratic field.
  For the proof, we augment the amplification method with a novel filtration
argument and a recent counting result proved by the second-named author to
reduce to showing strong quantitative decay of matrix coefficients of local
newvectors along compact subsets, which we establish via $p$-adic stationary
phase analysis. Furthermore, we prove a general upper bound in the level aspect
for sup-norms of automorphic forms belonging to \emph{any} family whose
associated matrix coefficients have such a decay property.


  Quantum computing has emerged as a promising field with the potential to
revolutionize various domains by harnessing the principles of quantum
mechanics. As quantum hardware and algorithms continue to advance, developing
high-quality quantum software has become crucial. However, testing quantum
programs poses unique challenges due to the distinctive characteristics of
quantum systems and the complexity of multi-subroutine programs. This paper
addresses the specific testing requirements of multi-subroutine quantum
programs. We begin by investigating critical properties by surveying existing
quantum libraries and providing insights into the challenges of testing these
programs. Building upon this understanding, we focus on testing criteria and
techniques based on the whole testing process perspective, spanning from unit
testing to integration testing. We delve into various aspects, including IO
analysis, quantum relation checking, structural testing, behavior testing,
integration of subroutine pairs, and test case generation. We also introduce
novel testing principles and criteria to guide the testing process. We conduct
comprehensive testing on typical quantum subroutines, including diverse mutants
and randomized inputs, to evaluate our proposed approach. The analysis of
failures provides valuable insights into the effectiveness of our testing
methodology. Additionally, we present case studies on representative
multi-subroutine quantum programs, demonstrating the practical application and
effectiveness of our proposed testing principles and criteria.


  The Diophantine problem for a monoid $M$ is the decision problem to decide
whether any given system of equations has a solution in $M$. In this note, we
give a simple example of a context-free, word-hyperbolic, finitely presented,
special monoid $M$ with trivial group of units, and such that the Diophantine
problem is undecidable in $M$. This answers two questions asked by Garreta &
Gray in 2019, and shows that the decidability of the Diophantine problem in
hyperbolic groups, as proved by Dahmani & Guirardel, does not generalise to
word-hyperbolic monoids.


  We have assumed that in a physical universe a blackhole is created some
where. We conjecture that this blackhole will then separate itself from the
physical universe and will build up an extra dimensional entity associated with
the physical universe. The extra dimensional entity we suppose to be orthogonal
to the physical universe. We further conjecture that this blackhole is a
Schwartzschild blackhole. We assume that this physical universe and the
blackhole span a seven dimensional space with a common time coordinate. We then
generate the Einstein equation. Using the time-blackhole and the time-time
component of the equation we show that the Hubble parameter is positive and
time dependent if we conjecture that both scale factor and the radius of the
blackhole reduces exponetially. Under the same assumption we have also
calculated the deacceleration parameter and shown that under certain constrain
the universe accelerates.


  The aim of this article is to introduce a method for recovering functions,
defined on the $n - 1$ dimensional unit sphere $\Bbb S^{n - 1}$, using their
spherical transform, which integrates functions on $n - 2$ dimensional
subspheres, on a prescribed family of subspheres of integration. This family of
subspheres is obtained as follows, we take a spheroid $\Sigma$ inside $\Bbb
S^{n - 1}$ which contains the points $\pm e_{n}$ and then each subsphere of
integration is obtained by the intersection of a hyperplane, which is tangent
to $\Sigma$, with $\Bbb S^{n - 1}$. In particular, we obtain as a limiting
case, by shrinking the spheroid into its main axis, a method for recovering
functions in case where the subspheres of integration pass through a common
point in $\Bbb S^{n - 1}$.


  Detection of many compact binary coalescences (CBCs) is one of the primary
goals of the present and future ground-based gravitational-wave (GW) detectors.
While increasing the detectors' sensitivities will be crucial in achieving
this, efficient data analysis strategies can play a vital role. With given
computational power in hand, efficient data analysis techniques can expand the
size and dimensionality of the parameter space to search for a variety of GW
sources. Matched filtering based analyses that depend on modeled signals to
produce adequate signal-to-noise ratios for signal detection may miss them if
the parameter space is too restrained. Specifically, the CBC search is
currently limited to non-precessing binaries only, where the spins of the
components are either aligned or anti-aligned to the orbital angular momentum.
A hierarchical search for CBCs is thus well motivated. The first stage of this
search is performed by matched filtering coarsely sampled data with a coarse
template bank to look for candidate events. These candidates are then followed
up for a finer search around the vicinity of an event's parameter space.
Performing such a search leads to enormous savings in computational cost. Here
we report the first successful implementation of the hierarchical search as a
PyCBC-based production pipeline to perform a complete analysis of LIGO
observing runs. With this, we analyze Advanced LIGO's first and second
observing run data. We recover all the events detected by the PyCBC (flat)
search in the first GW catalog, GWTC-1, published by the LIGO-Virgo
collaboration, with nearly the same significance using a scaled background. In
the analysis, we get an impressive factor of 20 reduction in computation
compared to the flat search. With a standard injection study, we show that the
sensitivity of the hierarchical search remains comparable to the flat search
within the error bars.


  The rho-meson mass shift, width broadening, and spectral density at finite
temperature and nucleon density are estimated using a general formula which
relates the self-energy to the real and imaginary parts of the forward
scattering amplitude on the constituents of the medium. We saturate the
scattering amplitude at low energies with resonances, while at high energies a
Regge approach is taken in combination with vector meson dominance;
experimental data is used wherever possible. The main result is that the
rho-meson becomes increasingly broad with increasing nucleon density. The
spectral density is suppressed in the resonance region 600 < M < 900 MeV and
enhanced in the subresonance region M < 600 MeV.


  We consider a variation of $O(N)$-symmetric vector models in which the vector
components are Grassmann numbers. We show that these theories generate the same
sort of random polymer models as the $O(N)$ vector models and that they lie in
the same universality class in the large-$N$ limit. We explicitly construct the
double-scaling limit of the theory and show that the genus expansion is an
alternating Borel summable series that otherwise coincides with the topological
expansion of the bosonic models. We also show how the fermionic nature of these
models leads to an explicit solution even at finite-$N$ for the generating
functions of the number of random polymer configurations.


  Monitoring concurrent programs typically rely on collecting traces to
abstract program executions. However, existing approaches targeting general
behavioral properties are either not tailored for online monitoring, are no
longer maintained, or implement naive instrumentation that often leads to
unsound verdicts. We first define the notion of when a trace is representative
of a concurrent execution. We then present a non-blocking vector clock
algorithm to collect sound concurrent traces on the fly reflecting the partial
order between events. Moreover, concurrent events in the representative trace
pose a soundness problem for monitors synthesized from total order formalisms.
For this, we extract a causal dependence relation from the monitor to check if
the trace has the needed orderings and define the conditions to decide at
runtime when a collected trace is monitorable. We implement our contributions
in a tool, FACTS, which instruments programs compiling to Java bytecode,
constructs sound representative traces, and warns the monitor about
non-monitorable traces. We evaluate our work and compare it with existing
approaches.


  With the recently published Cosmic Microwave Background data from Planck we
address the optimized binning of the primordial power spectrum. As an important
modification to the usual binning of the primordial spectrum, along with the
spectral amplitude of the bins, we allow the position of the bins also to vary.
This technique enables us to address the location of the possible broad
physical features in the primordial spectrum with relatively smaller number of
bins compared to the analysis performed earlier. This approach is in fact a
reconstruction method looking for broad features in the primordial spectrum and
avoiding fitting noise in the data. Performing Markov Chain Monte Carlo
analysis we present samples of the allowed primordial spectra with broad
features consistent with Planck data. To test how realistic it is to have
step-like features in primordial spectrum we revisit an inflationary model,
proposed by A. A. Starobinsky which can address the similar features obtained
from the binning of the spectrum. Using the publicly available code BINGO, we
numerically calculate the local $f_{\rm NL}$ for this model in equilateral and
arbitrary triangular configurations of wavevectors and show that the obtained
non-Gaussianity for this model is consistent with Planck results. In this paper
we have also considered different spectral tilts at different bins to identify
the cosmological scale that the spectral index needs to have a red tilt and it
is interesting to report that spectral index cannot be well constrained up to
$k \sim 0.01~ {\rm Mpc}^{-1}$.


  Polymer additives can substantially reduce the drag of turbulent flows and
the upper limit, the so called "maximum drag reduction" (MDR) asymptote is
universal, i.e. independent of the type of polymer and solvent used. Until
recently, the consensus was that, in this limit, flows are in a marginal state
where only a minimal level of turbulence activity persists. Observations in
direct numerical simulations using minimal sized channels appeared to support
this view and reported long "hibernation" periods where turbulence is
marginalized. In simulations of pipe flow we find that, indeed, with increasing
Weissenberg number (Wi), turbulence expresses long periods of hibernation if
the domain size is small. However, with increasing pipe length, the temporal
hibernation continuously alters to spatio-temporal intermittency and here the
flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an
increase in Wi, the flow fully relaminarises, in agreement with recent
experiments. At even larger Wi, a different instability is encountered causing
a drag increase towards MDR. Our findings hence link earlier minimal flow unit
simulations with recent experiments and confirm that the addition of polymers
initially suppresses Newtonian turbulence and leads to a reverse transition.
The MDR state on the other hand results from a separate instability and the
underlying dynamics corresponds to the recently proposed state of
elasto-inertial-turbulence (EIT).


  IoT devices and sensor networks present new opportunities for measuring,
monitoring, and guiding scientific experiments. Sensors, cameras, and
instruments can be combined to provide previously unachievable insights into
the state of ongoing experiments. However, IoT devices can vary greatly in the
type, volume, and velocity of data they generate, making it challenging to
fully realize this potential. Indeed, synergizing diverse IoT data streams in
near-real time can require the use of machine learning (ML). In addition, new
tools and technologies are required to facilitate the collection, aggregation,
and manipulation of sensor data in order to simplify the application of ML
models and in turn, fully realize the utility of IoT devices in laboratories.
Here we will demonstrate how the use of the Argonne-developed Manufacturing
Data and Machine Learning (MDML) platform can analyze and use IoT devices in a
manufacturing experiment. MDML is designed to standardize the research and
operational environment for advanced data analytics and AI-enabled automated
process optimization by providing the infrastructure to integrate AI in
cyber-physical systems for in situ analysis. We will show that MDML is capable
of processing diverse IoT data streams, using multiple computing resources, and
integrating ML models to guide an experiment.


  We construct axisymmetric Schwarzschild models to measure the mass profile of
the local group dwarf galaxy Fornax. These models require no assumptions to be
made about the orbital anisotropy of the stars, as is the case for commonly
used Jeans models. We test a variety of parameterizations of dark matter
density profiles and find cored models with uniform density rho_c = (1.6 +/-
0.1) x 10^-2 M_sun pc^-3 fit significantly better than the cuspy halos
predicted by cold dark matter simulations. We also construct models with an
intermediate-mass black hole, but are unable to make a detection. We place a
1-sigma upper limit on the mass of a potential intermediate-mass black hole at
M_BH < 3.2 x 10^4 M_sun.


  Using renormalization group techniques, we study spectral and transport
properties of a spinless interacting quantum dot consisting of two levels
coupled to metallic reservoirs. For strong Coulomb repulsion $U$ and an applied
Aharonov-Bohm phase $\phi$, we find a large direct tunnel splitting
$|\Delta|\sim (\Gamma/\pi)|\cos(\phi/2)|\ln(U/\omega_c)$ between the levels of
the order of the level broadening $\Gamma$. As a consequence we discover a
many-body resonance in the spectral density that can be measured via the
absorption power. Furthermore, for $\phi=\pi$, we show that the system can be
tuned into an effective Anderson model with spin-dependent tunneling.


  We study the maximal number of pairwise distinct columns in a
$\Delta$-modular integer matrix with $m$ rows. Recent results by Lee et al.
provide an asymptotically tight upper bound of $O(m^2)$ for fixed $\Delta$. We
complement this and obtain an upper bound of the form $O(\Delta)$ for fixed
$m$, and with the implied constant depending polynomially on $m$.


  Charm fragmentation and dijet angular distributions have been measured in
$D^*$ photoproduction at HERA. Charm fragmentation and its property of
universality is evaluated in terms of measurement of $P_v$, the ratio of
vector/(vector + pseudoscalar) mesons. Angular distributions of dijets, with at
least one of the jets associated with a $D^{*\pm}$ meson, have been measured
for samples enriched in direct or resolved photon events. The differential
cross section shows a steep rise for resolved events in the photon direction,
providing strong evidence that the bulk of the resolved photon cross section is
due to the charm content of the photon. The shallower rise for direct events as
well as for resolved photon events in the proton direction are consistent with
the quark exchange diagrams.


  In the sciences in general, the phrase "route to chaos" has come to refer to
a metaphor when some physical, biological, economic, or social system
transitions from one exhibiting order to one displaying randomness (or chaos).
Sometimes the goal is to understand which universal mechanisms explain that
transition, and how one can describe systems that operate in a region between
order and complete chaos. In other words, the goal is to understand the
mathematical processes by which a system evolves from one whose recurrent set
is finite towards another one exhibiting chaotic behavior as parameters
governing the behavior of the system are varied. This has only been understood
for one-dimensional dynamics. The present note exposes new approaches that
allow one to move away from those limitations. A tentative global framework
toward describing a large class of two-dimensional dynamics, inspired partially
by the developments in the one-dimensional theory of interval maps is
discussed. More precisely, we present a class of intermediate smooth dynamics
between one and higher dimensions. In this setting, it could be possible to
develop a similar one-dimensional type approach and in particular to understand
the transition from zero entropy to positive entropy.


  Structure-induced features of the wave functions for the quantum systems on
complex networks are discussed in this paper. For a quantum system on a
network, the state corresponding to the eigenvalue close to the center of the
spectrum is used as the representative state to display the impacts of the
structure on the wave functions. We consider the Erdos-Renyi, the WS small
world and the growing randomly network (GRN) models. It is found that the
probability distribution functions (PDF) of the representative state's
components can be described with a power-law with an exponential cutoff in a
unified way. For Erdos-Renyi networks, with the increase of the connectivity
probability $p_{ER} $ the PDF turns from power-law-dominated to
exponential-dominated functions. For the WS networks in a special region of the
rewiring probability $p_r \in (0,0.2)$, where this model can capture the
features of real world networks, and the GRN networks, the PDFs obey almost a
perfect power-law. These characteristics can be used as the structure
measurements of complex networks. They can also provide useful information on
dynamical processes on complex networks.


  Using the example of such a complicated problem as the Cauchy problem for the
Navier-Stokes equation, we show how the Poincar\'e-Riemann-Hilbert boundary
value problem enables us to construct effective estimates of solutions for this
case. The apparatus of the three-dimensional inverse problem of quantum
scattering theory is developing for this. In which it is shown that the unitary
scattering operator can be studied as a solution of the
Poincar\'e-Riemann-Hilbert boundary-value problem. This allows us to go on to
study the potential in the Schrodinger equation, which we consider as a
velocity component in the Navier-Stokes equation. The same scheme of reduction
of Riemann integral equations for the zeta-function to the
Poincar\'e-Riemann-Hilbert boundary-value problem allows us to construct
effective estimates that describe the behavior of the zeros of the zeta
function very well.


  A "no-knowledge" measurement of an open quantum system yields no information
about any system observable; it only returns noise input from the environment.
Surprisingly, performing such a no-knowledge measurement can be advantageous.
We prove that a system undergoing no-knowledge monitoring has reversible noise,
which can be cancelled by directly feeding back the measurement signal. We show
how no-knowledge feedback control can be used to cancel decoherence in an
arbitrary quantum system coupled to a Markovian reservoir that is being
monitored. Since no-knowledge feedback does not depend on the system state or
Hamiltonian, such decoherence cancellation is guaranteed to be general, robust
and can operate in conjunction with any other quantum control protocol. As an
application, we show that no-knowledge feedback could be used to improve the
performance of dissipative quantum computers subjected to local loss.


  Galaxy clustering on small scales is significantly under-predicted by
sub-halo abundance matching (SHAM) models that populate (sub-)haloes with
galaxies based on peak halo mass, $M_{\rm peak}$. SHAM models based on the peak
maximum circular velocity, $V_{\rm peak}$, have had much better success. The
primary reason $M_{\rm peak}$ based models fail is the relatively low abundance
of satellite galaxies produced in these models compared to those based on
$V_{\rm peak}$. Despite success in predicting clustering, a simple $V_{\rm
peak}$ based SHAM model results in predictions for galaxy growth that are at
odds with observations. We evaluate three possible remedies that could "save"
mass-based SHAM: (1) SHAM models require a significant population of "orphan"
galaxies as a result of artificial disruption/merging of sub-haloes in modern
high resolution dark matter simulations; (2) satellites must grow significantly
after their accretion; and (3) stellar mass is significantly affected by halo
assembly history. No solution is entirely satisfactory. However, regardless of
the particulars, we show that popular SHAM models based on $M_{\rm peak}$
cannot be complete physical models as presented. Either $V_{\rm peak}$ truly is
a better predictor of stellar mass at $z\sim 0$ and it remains to be seen how
the correlation between stellar mass and $V_{\rm peak}$ comes about, or SHAM
models are missing vital component(s) that significantly affect galaxy
clustering.


  We study the ground state energy of a gas of $N$ fermions confined to a unit
box in $d$ dimensions. The particles interact through a 2-body potential with
strength scaled in an $N$-dependent way as $N^{-\alpha}v$, where $\alpha\in
\mathbb R$ and $v$ is a function of positive type satisfying a mild regularity
assumption. Our focus is on the strongly interacting case $\alpha<1-\frac2d$.
We contrast our result with existing results in the weakly interacting case
$\alpha>1-\frac2d$, and the transition happening at the mean-field scaling
$\alpha=1-\frac2d$. Our proof is an adaptation of the bosonization technique
used to treat the mean-field case.


  We give a lower bound of the hyperbolic and the Hausdorff dimension of the
Julia set of meromorphic functions of finite order under very general
conditions.


  The financial turmoil surrounding the Great Recession called for
unprecedented intervention by Central Banks: unconventional policies affected
various areas in the economy, including stock market volatility. In order to
evaluate such effects, by including Markov Switching dynamics within a recent
Multiplicative Error Model, we propose a model--based classification of the
dates of a Central Bank's announcements to distinguish the cases where the
announcement implies an increase or a decrease in volatility, or no effect. In
detail, we propose two smoothed probability--based classification methods,
obtained as a by--product of the model estimation, which provide very similar
results to those coming from a classical k--means clustering procedure. The
application on four Eurozone market volatility series shows a successful
classification of 144 European Central Bank announcements.


  The cumulant generating function of time-averaged current is studied from an
operational viewpoint. Specifically, for interacting Brownian particles under
non-equilibrium conditions, we show that the first derivative of the cumulant
generating function is equal to the expectation value of the current in a
modified system with an extra force added, where the modified system is
characterized by a variational principle. The formula reminds us of Einstein's
fluctuation theory in equilibrium statistical mechanics. Furthermore, since the
formula leads to the fluctuation-dissipation relation when the linear response
regime is focused on, it is regarded as an extension of the linear response
theory to that valid beyond the linear response regime. The formula is also
related to previously known theories such as the Donsker-Varadhan theory, the
additivity principle, and the least dissipation principle, but it is not
derived from them. Examples of its application are presented for a driven
Brownian particle on a ring subject to a periodic potential.