  Programming embedded systems applications involve writing concurrent,
event-driven and timing-aware programs. Traditionally, such programs are
written in low-level machine-oriented programming languages like C or Assembly.
We present an alternative by introducing Synchron, an API that offers
high-level abstractions to the programmer while supporting the low-level
infrastructure in an associated runtime system and one-time-effort drivers.
Embedded systems applications exhibit the general characteristics of being (i)
concurrent, (ii) I/O-bound and (iii) timing-aware. To address each of these
concerns, the Synchron API consists of three components: (1) a Concurrent ML
(CML) inspired message-passing concurrency model, (2) a message-passing--based
I/O interface that translates between low-level interrupt based and
memory-mapped peripherals, and (3) a timing operator, $syncT$, that marries
CML's $sync$ operator with timing windows inspired from the TinyTimber kernel.
We implement the Synchron API as the bytecode instructions of a virtual machine
called SynchronVM. SynchronVM hosts a Caml-inspired functional language as its
frontend language, and the backend of the VM supports the STM32F4 and NRF52
microcontrollers, with RAM in the order of hundreds of kilobytes. We illustrate
the expressiveness of the Synchron API by showing examples of expressing state
machines commonly found in embedded systems. The timing functionality is
demonstrated through a music programming exercise. Finally, we provide
benchmarks on the response time, jitter rates, memory, and power usage of the
SynchronVM.


  We observed the H2CO(110-111) absorption lines and H110{\alpha} radio
recombination lines (RRL) toward 180 NH3 sources using the Nanshan 25-m radio
telescope. In our observation, 138 sources were found to have H2CO lines and 36
have H110{\alpha} RRLs. Among the 138 detected H2CO sources, 38 sources were
first detected. The detection rates of H2CO have a better correlation with
extinction than with background continuum radiation. Line center velocities of
H2CO and NH3 agree well. The line width ratios of H2CO and NH3 are generally
larger than 1 and are similar to that of 13CO. The correlation between column
densities of H2CO and extinction is better than that between NH3 and
extinction. These line width relation and column density relation indicate H2CO
is distributed on a larger scale than that of NH3, being similar to the regions
of 13CO. The abundance ratios between NH3 and H2CO were found to be different
in local clouds and other clouds.


  We prove that Schubert varieties are globally F-regular in the sense of Karen
Smith. We apply this result to the category of equivariant and holonomic
D-modules on flag varieties in positive characteristic. Here recent results of
Blickle are shown to imply that the simple D-modules coincide with local
cohomology sheaves with support in Schubert varieties. Using a local
Grothendieck-Cousin complex we prove that the decomposition of local cohomology
sheaves with support in Schubert cells is multiplicity free.


  We present a detailed analysis of how to implement the computation of modular
symbols for a given elliptic curve by using numerical approximations. This
method turns out to be more efficient than current implementation as the
conductor of the curve increases.


  This paper contains several results concerning circle action on
almost-complex and smooth manifolds. More precisely, we show that, for an
almost-complex manifold $M^{2mn}$(resp. a smooth manifold $N^{4mn}$), if there
exists a partition $\lambda=(\lambda_{1},...,\lambda_{u})$ of weight $m$ such
that the Chern number $(c_{\lambda_{1}}... c_{\lambda_{u}})^{n}[M]$ (resp.
Pontrjagin number $(p_{\lambda_{1}}... p_{\lambda_{u}})^{n}[N]$) is nonzero,
then \emph{any} circle action on $M^{2mn}$ (resp. $N^{4mn}$) has at least $n+1$
fixed points. When an even-dimensional smooth manifold $N^{2n}$ admits a
semi-free action with isolated fixed points, we show that $N^{2n}$ bounds,
which generalizes a well-known fact in the free case. We also provide a
topological obstruction, in terms of the first Chern class, to the existence of
semi-free circle action with \emph{nonempty} isolated fixed points on
almost-complex manifolds. The main ingredients of our proofs are Bott's residue
formula and rigidity theorem.


  The effect of anomalous magnetic moment of quarks on thermodynamic properties
of the chiral condensate is studied, using of a two-flavor Nambu--Jona-Lasinio
model at finite temperature $T$, chemical potential $\mu$, and in the presence
of a uniform magnetic field $eB$. To this purpose, the Schwinger linear-in-$B$
ansatz for the quark anomalous magnetic moment in term of the nonperturbative
Bohr magneton is considered. In a two-dimensional flavor space, it leads to the
correction $\hat{T}_{Sch}=\hat{\kappa}\hat{Q} eB$ in the energy dispersion
relation of quarks. Here, $\hat{Q}$ is the quark charge matrix. We consider
three different sets for $\hat{\kappa}$, and numerically determine the
dependence of the constituent quark mass on $T,\mu$ and $eB$ for fixed
$\hat{\kappa}$. By exploring the complete phase portrait of this model in
$T$-$\mu$, $\mu$-$eB$, and $T$-$eB$ phase spaces for various fixed $eB$, $T$,
$\mu$ and $\hat{\kappa}$, we observe that inverse magnetic catalysis occurs for
large enough $\hat{\kappa}$. Moreover, in the regime of weak magnetic fields,
the phenomenon of reentrance of chiral symmetry broken and restored phases
occurs for $T, \mu$ and $eB$ dependent $\hat{\kappa}$.


  An accurate theoretical template for the galaxy power spectrum is a key for
the success of ongoing and future spectroscopic surveys. We examine to what
extent the Effective Field Theory of Large Scale Structure is able to provide
such a template and correctly estimate cosmological parameters. To that end, we
initiate a blinded challenge to infer cosmological parameters from the
redshift-space power spectrum of high-resolution mock catalogs mimicking the
BOSS galaxy sample but covering a hundred times larger cumulative volume. This
gigantic simulation volume allows us to separate systematic bias due to
theoretical modeling from the statistical error due to sample variance. The
challenge task was to measure three unknown input parameters used in the
simulation: the Hubble constant, the matter density fraction, and the
clustering amplitude. We present analyses done by two independent teams, who
have fitted the mock simulation data generated by yet another independent
group. This allows us to avoid any confirmation bias by analyzers and pin down
possible tuning of the specific EFT implementations. Both independent teams
have recovered the true values of the input parameters within sub-percent
statistical errors corresponding to the total simulation volume.


  In this article, the theory of hierarchical evolutive systems of Ehresmann
and Vandremeersch [Bull. Math. Bio. 49, 13-50 (1987)] is improved by
considering the categories of the theory as fuzzy sets whose elements are the
composite objects formed by the arrows and corresponding vertices of their
embedded graphs. This way each category can be represented as a point in the
states space [0.1]**N. The introduction of a diffeomorphism, that acts in this
context as a functor between categories, allows to define a measure preserving
dynamical system. In particular, we apply this formalism to describe a living
single cell. We propose for its state at a given time a hirerchical category
with three levels (molecular, coarse-grained and cellular levels) related by
adequate colimits. Each level involves the main functional and structural
modules in which the cell can be partitioned. The time evolution of the cell is
drived by a transformation which is a N-dimensional generalization of the
Ricker map whose parameters we propose to be determined by requiring that, as
hallmark of its behavior, the living cell to evolve at the edge of chaos. From
the dynamical point of view this property manifests in the fact that the
largest Lyapunov exponent is equal to zero. Since in a rather complete model of
the living cell the huge number of involved parameters can make of the
calculations a hard task, we also propose a toy model, with fewer parameters to
be determined, which emphasizes the cellular fission.


  Using the relative entropy of total correlation, we derive an expression
relating the mutual information of $n$-partite pure states to the sum of the
mutual informations and entropies of its marginals and analyze some of its
implications. Besides, by utilizing the extended strong subadditivity of von
Neumann entropy, we obtain generalized monogamy relations for the total
correlation in three-partite mixed states. These inequalities lead to a tight
lower bound for this correlation in terms of the sum of the bipartite mutual
informations. We use this bound to propose a measure for residual three-partite
total correlation and discuss the non-applicability of this kind of quantifier
to measure genuine multiparty correlations.


  A detailed analysis of the electro-optical response of single as well as
coupled semiconductor quantum dots is presented. This is based on a realistic
---i.e., fully tridimensional--- description of Coulomb-correlated few-electron
states, obtained via a direct-diagonalization approach. More specifically, we
investigate the combined effect of static electric fields and ultrafast
sequences of multicolor laser pulses in the few-carrier, i.e., low-excitation,
regime. In particular, we show how the presence of a properly tailored static
field may give rise to significant electron-hole charge separation; these
field-induced dipoles, in turn, may introduce relevant exciton-exciton
couplings, which are found to induce significant ---both intra- and
inter-dot--- biexcitonic splittings. We finally show that such few-exciton
systems constitute an ideal semiconductor-based hardware for an all optical
implementation of quantum information processing.


  We consider the construction of locally conservative fluxes by means of a
simple post-processing technique obtained from the finite element solutions of
advection diffusion equations. It is known that a naive calculation of fluxes
from these solutions yields non-conservative fluxes. We consider two finite
element methods: the usual continuous Galerkin finite element (CGFEM) for
solving non dominating advection diffusion equations and the streamline
upwind/Petrov-Galerkin (SUPG) for solving advection dominated problems. We then
describe the post-processing technique for constructing conservative fluxes
from the numerical solutions of the general variational formulation. The
post-processing technique requires solving an auxiliary Neumann boundary value
problem on each element independently and it produces a locally conservative
flux on a vertex centered dual mesh relative to the finite element mesh. We
provide a convergence analysis for the post-processing technique. Performance
of the technique and the convergence behavior are demonstrated through
numerical examples including a set of test problems for advection diffusion
equations, advection dominated equations, and drift-diffusion equations.


  The two-nucleon momentum distributions have been calculated for nuclei up to
A=40 and various values of the relative and center-of-mass momenta and angle
between them. For complex nuclei a parameter-free linked-cluster expansion,
based upon a realistic local two-nucleon interaction of the Argonne family and
variational wave function featuring central, tensor, spin and iso-spin
correlations, has been used. The obtained results show that: 1) independently
of the mass number A, at values of the relative momentum k_rel> 2 fm^{-1} the
proton-neutron momentum distributions for back-to-back (BB) nucleons (K_cm=0)
exhibit the factorization property n_A^{pn}(k_rel,K_cm=0)=C_A^{pn} n_D(k_rel)
n_{cm}^{pn}(K_cm=0), where n_D is the deuteron momentum distribution,
n_{cm}^{pn}(K_{cm}=0) the momentum distribution of the c.m. motion of the pair
and C_A^{pn} the nuclear contact measuring the number of BB pn pairs with
deuteron-like momenta; 2) the values of the proton-neutron nuclear contact
C_A^{pn} are obtained in a model-independent way from the ratio
n_A^{pn}(k_rel,K_cm=0)/n_D(k_rel) n_{cm}^{pn}(K_cm=0); 3) also the
K_cm-integrated pn momentum distributions divided by the deuteron momentum
distribution exhibits a constant behavior equal to C_A^{pn}, but only at very
high values of k_{rel}> 3.5fm^{-1}, where the relative momentum distribution is
entirely governed by BB short-range correlated nucleons; 4) the absolute value
of the number of pn and pp short-range correlated pairs is calculated,
illustrating that the high values (K_cm>1 fm^{-1}) of the pair c.m. momentum
appreciably reduce the dominance of the pn over pp pairs produced by the tensor
force when K_cm=0; 5) calculations are in good agreement with the VMC
calculations for light nuclei and with available experimental on the processes
A(e,e'pn)X and A(e,e'pp)X.


  We have observed an extended region surrounding the first discovered galactic
superluminal source GRS 1915+105, seeking evidence of interaction between the
relativistic ejecta of that object and the interstellar medium. We find two
radio sources axisymmetrically aligned along the sub-arcsecond relativistic
ejecta of GRS 1915+105 and roughly 17' distant from it, which coincide with the
luminous IRAS sources 19124+1106 and 19132+1035. We have observed these sources
at centimeter (VLA), millimeter (IRAM 30m), and infrared (ISO, UKIRT, ESO/MPI
2.2m) wavelengths in both line and continuum emission. At centimeter
wavelengths a non-thermal jet-like feature aligned along the outflow axis is
located adjacent to the inner edge of the southern source. Strong density
enhancements are found in the millimeter tracers CO and H13CO+ at the positions
of both sources and some of the morphology is reminiscent of shock-like
interactions; however, linewidths are narrow. At infrared wavelengths strong
hydrogen recombination lines and weak lines of molecular hydrogen are observed
at the southern source. We discuss these results as possible evidence of the
sought-after interaction, both in terms of the regions undergoing ongoing
shock-heating and in terms of them being locations of shock-induced star
formation. The evidence for each of these is inconclusive. Millimeter line
mapping of a portion of W 50 where the relativistic jets of the X-ray binary SS
433 interact with the interstellar medium shows roughly similar morphology as
GRS 1915+105, suggesting that the phenomena observed at the IRAS sources may
not be unusual for such a long distance interaction.


  We study a one-dimensional (1d) XXZ spin-chain in a random field on the
metallic side of the many-body localization transition by level statistics. For
a fixed interaction, and intermediate disorder below the many-body localization
transition, we find that, asymptotically, the number variance grows faster than
linear with a disorder dependent exponent. This is consistent with the
existence of an anomlaous Thouless energy in the spectrum. In non-interacting
disordered metals this is an energy scale related to the typical time for a
particle to diffuse across the sample. In the interacting case it seems related
to a more intricate anomalous diffusion process. This interpretation is not
fully consistent with recent claims that, for intermediate disorder, level
statistics are described by a plasma model with power-law decaying interactions
whose number variance grows slower than linear. As disorder is further
increased, still on the metallic side, the Thouless energy is gradually washed
out. In the range of sizes we can explore, level statistics are scale invariant
and approach Poisson statistics at the many-body localization transition.
Slightly below the many-body localization transition, spectral correlations,
well described by critical statistics, are quantitatively similar to those of a
high dimensional, non-interacting, disordered conductor at the Anderson
transition.


  In this article, we prove a new functional limit theorem for the partial sum
sequence $S_{[nt]}=\sum_{i=1}^{[nt]}X_i$ corresponding to a linear sequence of
the form $X_i=\sum_{j \in \bZ}c_j \xi_{i-j}$ with i.i.d. innovations
$(\xi_i)_{i \in \bZ}$ and real-valued coefficients $(c_j)_{j \in \bZ}$. This
weak convergence result is obtained in space $\bD[0,1]$ endowed with the
$S$-topology introduced in Jakubowski (1992), and the limit process is a linear
fractional stable motion (LFSM). One of our result provides an extension of the
results of Avram and Taqqu (1992) to the case when the coefficients $(c_j)_{j
\in \bZ}$ may not have the same sign. The proof of our result relies on the
recent criteria for convergence in Skorokhod's $M_1$-topology (due to Louhichi
and Rio (2011)), and a result which connects the weak $S$-convergence of the
sum of two processes with the weak $M_1$-convergence of the two individual
processes. Finally, we illustrate our results using some examples and computer
simulations.


  We consider a queuing network that opens at a specified time, where customers
are non-atomic and belong to different classes. Each class has its own route,
and as is typical in the literature, the costs are a linear function of waiting
and service completion time. We restrict ourselves to a two class, two queue
network: this simplification is well motivated as the diversity in solution
structure as a function of problem parameters is substantial even in this
simple setting (e.g., a specific routing structure involves eight different
regimes), suggesting a combinatorial blow up as the number of queues, routes
and customer classes increase. We identify the unique Nash equilibrium customer
arrival profile when the customer linear cost preferences are different. This
profile is a function of problem parameters including the size of each class,
service rates at each queue, and customer cost preferences. When customer cost
preferences match, under certain parametric settings, the equilibrium arrival
profiles may not be unique and may lie in a convex set. We further make a
surprising observation that in some parametric settings, customers in one class
may arrive in disjoint intervals. Further, the two classes may arrive in
contiguous intervals or in overlapping intervals, and at varying rates within
an interval, depending upon the problem parameters.


  Efficient authoring of vast virtual environments hinges on algorithms that
are able to automatically generate content while also being controllable. We
propose a method to automatically generate furniture layouts for indoor
environments. Our method is simple, efficient, human-interpretable and amenable
to a wide variety of constraints. We model the composition of rooms into
classes of objects and learn joint (co-occurrence) statistics from a database
of training layouts. We generate new layouts by performing a sequence of
conditional sampling steps, exploiting the statistics learned from the
database. The generated layouts are specified as 3D object models, along with
their positions and orientations. We show they are of equivalent perceived
quality to the training layouts, and compare favorably to a state-of-the-art
method. We incorporate constraints using a general mechanism -- rejection
sampling -- which provides great flexibility at the cost of extra computation.
We demonstrate the versatility of our method by applying a wide variety of
constraints relevant to real-world applications.


  We present results of long-term daily monitoring of a sample of Galactic
radio-emitting X-ray binaries showing relativistic jets (RJXRB): SS433, Cyg
X-3, and GRS 1915+105, with the RATAN-600 radio telescope in the 0.6-22 GHz
range. We carried out the modeling calculations to understand the temporal
(1--100 days) and spectral (1-22 GHz) dependence. We tested the finite jet
segment models and we found that the geometry of the conical hollow jets is
responsible for either a power law or an exponential decay of the flares. SS433
was monitored for 100 days in 1997 and 120 days in 1999. From the quiescent
radio light curves, we obtained clear evidence of a 6.04-day 10-15% modulation.
Three powerful flares (up to 13 Jy) from Cyg X-3 were detected in April 2000.


  If the magnetic moment of unstable tau neutrinos with the mass of $O$(MeV) is
in the region of $10^{-8}\mu_{B} \lesssim \mu_{\nu_{\tau}} \lesssim
10^{-6}\mu_{B}$, it is compatible with the present experimental and
cosmological bounds.
  It is pointed out here, that if the tau neutrino has such a large magnetic
moment and can oscillate into a neutrino of another flavour the results from
$\nu e$ scattering experiment at LAMPF constrain the tau neutrino mixing angles
to $sin^{2}2\theta_{e \tau} \lesssim 2\times 10^{-6} - 2\times 10^{-2}$ and
$sin^{2}2\theta_{\mu\tau} \lesssim 10^{-6} - 10^{-2}$ depending on the magnetic
moment value in the allowed region.


  We solve the 2+1-dimensional Teukolsky equation numerically for the Weyl
scalars $\psi_0$ and $\psi_4$ along a time-like geodesic approaching the Cauchy
horizon of a rapidly rotating perturbed Kerr black hole. We find that both the
amplitude and frequency of the Weyl scalars agree with the results of linear
perturbation analysis. We then model a physical object by a simple damped
harmonic oscillator, which is driven by an external force that mimics the tidal
force experienced by the infalling object. We use this model to find the total
deformation of the object at the Cauchy horizon, and the resonant effect when
the driving force's frequency matches the internal frequency of the oscillator
that models the object.


  We discuss pore dynamics in osmotically stressed vesicles. A set of equations
which govern the liposomal size, internal solute concentration, and pore
diameter is solved numerically. We find that dependent on the internal solute
concentration and vesicle size, liposomes can stay pore-free, nucleate a short
lived pore, or nucleate a long-lived pore. The phase diagram of pore stability
is constructed, and the different scaling regimes are deduced analytically.


  Continuing the scaling of quantum computers hinges on building classical
control hardware pipelines that are scalable, extensible, and provide real time
response. The instruction set architecture (ISA) of the control processor
provides functional abstractions that map high-level semantics of quantum
programming languages to low-level pulse generation by hardware. In this paper,
we provide a methodology to quantitatively assess the effectiveness of the ISA
to encode quantum circuits for intermediate-scale quantum devices with
O($10^2$) qubits. The characterization model that we define reflects
performance, the ability to meet timing constraint implications, scalability
for future quantum chips, and other important considerations making them useful
guides for future designs. Using our methodology, we propose scalar (QUASAR)
and vector (qV) quantum ISAs as extensions and compare them with other ISAs in
metrics such as circuit encoding efficiency, the ability to meet real-time gate
cycle requirements of quantum chips, and the ability to scale to more qubits.


  For a general subcritical second-order elliptic operator $P$ in a domain
$\Omega \subset \mathbb{R}^n$ (or noncompact manifold), we construct
Hardy-weight $W$ which is optimal in the following sense. The operator $P -
\lambda W$ is subcritical in $\Omega$ for all $\lambda < 1$, null-critical in
$\Omega$ for $\lambda = 1$, and supercritical near any neighborhood of infinity
in $\Omega$ for any $\lambda > 1$. Moreover, if $P$ is symmetric and $W>0$,
then the spectrum and the essential spectrum of $W^{-1}P$ are equal to
$[1,\infty)$, and the corresponding Agmon metric is complete.
  Our method is based on the theory of positive solutions and applies to both
symmetric and nonsymmetric operators. The constructed Hardy-weight is given by
an explicit simple formula involving two distinct positive solutions of the
equation $Pu=0$, the existence of which depends on the subcriticality of $P$ in
$\Omega$.


  The set $\mathcal{E}'(\mathbb{R})$ of all compactly distributions, with the
operations of addition, convolution, multiplication by complex scalars, and
with the strong dual topology is a topological algebra. In this article, it is
shown that the topological stable rank of $\mathcal{E}'(\mathbb{R})$ is 2.


  The A-hypergeometric system studied by I.M. Gelfand, M.I. Graev, A.V.
Zelevinsky and the author, is defined for a set A of characters of an algebraic
torus. In this paper we propose a generalization of the theory where the torus
is replaced by an arbitrary reductive group H and A is a set of irreducible
representations of H. The functions are thus defined on the space M_A of
functions on H spanned by the matrix elements of representations from A. The
properties of the system are related to the geometry of a certain algebraic
variety X_A, which belongs to the class of group compactifications studied by
De Concini and Procesi. We develop the theory of Euler integral representations
for these generalized hypergeometric functions (with integrals taken over
cycles in H). We also construct the analogs of hypergeometric series, by
expanding the delta-function along a subgroup into a power series and taking
the termwise Fourier transform.


  In this work, we tackle two vital tasks in automated driving systems, i.e.,
driver intent prediction and risk object identification from egocentric images.
Mainly, we investigate the question: what would be good road scene-level
representations for these two tasks? We contend that a scene-level
representation must capture higher-level semantic and geometric representations
of traffic scenes around ego-vehicle while performing actions to their
destinations. To this end, we introduce the representation of semantic regions,
which are areas where ego-vehicles visit while taking an afforded action (e.g.,
left-turn at 4-way intersections). We propose to learn scene-level
representations via a novel semantic region prediction task and an automatic
semantic region labeling algorithm. Extensive evaluations are conducted on the
HDD and nuScenes datasets, and the learned representations lead to
state-of-the-art performance for driver intention prediction and risk object
identification.


  Multi-source transfer learning is an effective solution to data scarcity by
utilizing multiple source tasks for the learning of the target task. However,
access to source data and model details is limited in the era of commercial
models, giving rise to the setting of multi-source-free (MSF) transfer learning
that aims to leverage source domain knowledge without such access. As a newly
defined problem paradigm, MSF transfer learning remains largely underexplored
and not clearly formulated. In this work, we adopt an information theoretic
perspective on it and propose a framework named H-ensemble, which dynamically
learns the optimal linear combination, or ensemble, of source models for the
target task, using a generalization of maximal correlation regression. The
ensemble weights are optimized by maximizing an information theoretic metric
for transferability. Compared to previous works, H-ensemble is characterized
by: 1) its adaptability to a novel and realistic MSF setting for few-shot
target tasks, 2) theoretical reliability, 3) a lightweight structure easy to
interpret and adapt. Our method is empirically validated by ablation studies,
along with extensive comparative analysis with other task ensemble and transfer
learning methods. We show that the H-ensemble can successfully learn the
optimal task ensemble, as well as outperform prior arts.


  The universality of the point cloud format enables many 3D applications,
making the compression of point clouds a critical phase in practice. Sampled as
discrete 3D points, a point cloud approximates 2D surface(s) embedded in 3D
with a finite bit-depth. However, the point distribution of a practical point
cloud changes drastically as its bit-depth increases, requiring different
methodologies for effective consumption/analysis. In this regard, a
heterogeneous point cloud compression (PCC) framework is proposed. We unify
typical point cloud representations -- point-based, voxel-based, and tree-based
representations -- and their associated backbones under a learning-based
framework to compress an input point cloud at different bit-depth levels.
Having recognized the importance of voxel-domain processing, we augment the
framework with a proposed context-aware upsampling for decoding and an enhanced
voxel transformer for feature aggregation. Extensive experimentation
demonstrates the state-of-the-art performance of our proposal on a wide range
of point clouds.


  To seek reliable information sources for news events, we introduce a novel
task of expert recommendation, which aims to identify trustworthy sources based
on their previously quoted statements. To achieve this, we built a novel
dataset, called NewsQuote, consisting of 23,571 quote-speaker pairs sourced
from a collection of news articles. We formulate the recommendation task as the
retrieval of experts based on their likelihood of being associated with a given
query. We also propose a multi-layer ranking framework employing Large Language
Models to improve the recommendation performance. Our results show that
employing an in-context learning based LLM ranker and a multi-layer
ranking-based filter significantly improve both the predictive quality and
behavioural quality of the recommender system.


  We study the accuracy of the bound-state parameters obtained with the method
of dispersive sum rules, one of the most popular theoretical approaches in
nonperturbative QCD and hadron physics. We make use of a quantum-mechanical
potential model since it provides the only possibility to probe the reliability
and the accuracy of this method: one obtains the bound-state parameters from
sum rules and compares these results with the exact values calculated from the
Schr\"odinger equation. We investigate various possibilities to fix the crucial
ingredient of the method of sum rules -- the effective continuum threshold --
and propose modifications which lead to a remarkable improvement of the
accuracy of the extracted ground-state parameters compared to the standard
procedures adopted in the method. Although the rigorous control of systematic
uncertainties in the method of sum rules remains unfeasible, the application of
the proposed procedures in QCD promises a considerable increase of the actual
accuracy of the extracted hadron parameters.


  The star ASAS J174600-2321.3 was found to exhibit peculiar photometric
variability (conspicuous brightening of about 4 magnitudes (V), fast luminosity
declines, intrinsic pulsations). It was rejected as an RCB candidate in recent
investigations on spectroscopic grounds. We have collected and present all
available data from public sky surveys, photometric catalogues, and the
literature. From an analysis of these data, we have identified ASAS
J174600-2321.3 as a long-period eclipsing binary (Porb = 1011.5 days). The
primary star, which is probably a white dwarf, is currently in outburst and
exhibits the spectral characteristics of a reddened, early F-type supergiant;
the secondary star is a giant of spectral type late M. We discuss the possible
origin of the observed brightening, which is related to the primary component.
ASAS J174600-2321.3 is most certainly an eclipsing symbiotic binary - probably
a symbiotic nova of GCVS type NC - that is currently in outburst. However,
further photometric and spectroscopic data are needed to confirm this.


  The study of high contrast imaged brown dwarfs and exoplanets depends
strongly on evolutionary models. To estimate the mass of a directly imaged
substellar object, its extracted photometry or spectrum is used and adjusted
with model spectra together with the estimated age of the system. These models
still need to be properly tested and constrained. HD 4747B is a brown dwarf
close to the H burning mass limit, orbiting a nearby, solar-type star and has
been observed with the radial velocity method over almost two decades now. Its
companion was also recently detected by direct imaging, allowing a complete
study of this particular object. We aim to fully characterize HD 4747B by
combining a well constrained dynamical mass and a study of its observed
spectral features in order to test evolutionary models for substellar objects
and characterize its atmosphere. We combine the radial velocity measurements of
HIRES and CORALIE taken over two decades and high contrast imaging of several
epochs from NACO, NIRC2 and SPHERE to obtain a dynamical mass. From the SPHERE
data we obtain a low resolution spectrum of the companion from Y to H band, as
well as two narrow band-width photometric measurements in the K band. A study
of the primary star allows in addition to constrain the age of the system as
well as its distance. Thanks to the new SPHERE epoch and NACO archival data
combined with previous imaging data and high precision radial velocity
measurements, we have been able to derive a well constrained orbit. We derive a
dynamical mass of mB=70.0$\pm$1.6 MJup which is higher than a previous study,
but in better agreement with the models. By comparing the object with known
brown dwarfs spectra, we derive a spectral type of L9 and an effective
temperature of 1350$\pm$50 K. With a retrieval analysis we constrain the oxygen
and carbon abundances and compare them with the ones from the HR 8799 planets.


  The hydrogenated $\rm{Sb}$ monolayer epitaxially grown on a $\rm{LaFeO_3}$
substrate is a novel type of two-dimensional material hosting quantum
spin-quantum anomalous Hall (QS-QAH) states. For a device formed by $\rm{Sb}$
monolayer ribbon, the QAH edge states, belong to a single valley, are located
at opposite edges of the ribbon. The QSH edge states, on the other hand, belong
to the other valley and are distributed in a very narrow region at the same
edge. In this paper, we find such material can be used to fabricate perfect
valley filter. Adopting scattering matrix method and Green's function method,
the valley resolved transport and spatial distribution of local current are
calculated, in the present of Anderson disorder, edge defects and edge
deformations. The numerical results demonstrate that, in the presence of above
three types of disorder with moderate strength, the carriers can flow
disspationless with nearly perfect valley polarization. Moreover, when the
device becomes longer, the transport current does not decrease while the valley
filter works even better. The origin is that the disorder can destroy the QSH
edge states, but the valley-polarized QAH edge states can well hold.


  Cluster radioactivity is described as a very mass asymmetric fission process.
The reflection symmetry breaking octupole moment has been used in a mean field
HFB theory as leading coordinate instead of the quadrupole moment usually used
in standard fission calculations. The procedure has been applied to the study
of the ``very mass asymmetric fission barrier'' of several even-even Thorium
isotopes. The masses of the emitted clusters as well as the corresponding
half-lives have been evaluated on those cases where experimental data exist.


  In this paper we provide a classification of plane symmetric kinematic
self-similar perfect fluid and dust solutions. In the perfect fluid and dust
cases, kinematic self-similar vectors for the tilted, orthogonal and parallel
cases have been explored in the first, second, zeroth and infinite kinds with
different equations of state. We obtain total of eleven plane symmetric
kinematic self-similar solutions out of which six are independent. The perfect
fluid case gives two solutions for infinite tilted and infinite orthogonal
kinds. In the dust case, we have four independent solutions in the first
orthogonal, infinite tilted, infinite orthogonal and infinite parallel kinds.
The remaining cases provide contradiction. It is interesting to mention that
some of these solutions turn out to be vacuum.


  The arithmetic complexity counts the number of algebraically independent
entries in the periodic continued fraction $\theta=[b_1,\dots, b_N,
\overline{a_1,\dots,a_k}]$. If $\mathscr{A}_{\theta}$ is a noncommutative torus
corresponding to the rational elliptic curve $\mathscr{E}(K)$, then the rank of
$\mathscr{E}(K)$ is given by a simple formula $r(\mathscr{E}(K))=
c(\mathscr{A}_{\theta})-1$, where $c(\mathscr{A}_{\theta})$ is the arithmetic
complexity of $\theta$. We prove that $c(\mathscr{A}_{\theta})$ is equal to the
dimension of the Brock-Elkies-Jordan variety of $\theta$ introduced in [1].
Following Zagier and Lemmermeyer, we evaluate the Shafarevich-Tate group of
$\mathscr{E}(K)$.


  Trial-based economic evaluations are typically performed on cross-sectional
variables, derived from the responses for only the completers in the study,
using methods that ignore the complexities of utility and cost data (e.g.
skewness and spikes). We present an alternative and more efficient Bayesian
parametric approach to handle missing longitudinal outcomes in economic
evaluations, while accounting for the complexities of the data. We specify a
flexible parametric model for the observed data and partially identify the
distribution of the missing data with partial identifying restrictions and
sensitivity parameters. We explore alternative nonignorable scenarios through
different priors for the sensitivity parameters, calibrated on the observed
data. Our approach is motivated by, and applied to, data from a trial assessing
the cost-effectiveness of a new treatment for intellectual disability and
challenging behaviour.


  One of the variants to proof the generalized Ito-Wentzell's formula is
introduced and examined in this paper. The relationship between different
representations of the generalized Ito-Wentzell's formula/ is considered.


  The formation of fragments in proton-induced reactions at low relativistic
energies within a combination of a covariant dynamical transport model and a
statistical approach is investigated. In particular, we discuss in detail the
applicability and limitations of such a hybrid model by comparing data on
fragmentation at low relativistic $SIS/GSI$-energies.


  We present a new analysis of relationships between disease incidence and the
prevalence of an experimentally defined state of `recent infection'. This leads
to a clean separation between biological parameters (properties of disease
progression as reflected in a test for recent infection), which need to be
calibrated, and epidemiological state variables, which are estimated in a
cross-sectional survey. The framework takes into account the possibility that
details of the assay and host/pathogen chemistry leave a (knowable) fraction of
the population in the recent category for all times. This systematically
addresses an issue which is the source of some controversy about the
appropriate use of the BED assay for defining recent HIV infection. Analysis of
relative contributions of error arising variously from statistical
considerations and simplifications of general expressions indicate that
statistical error dominates heavily over all sources of bias for realistic
epidemiological and biological scenarios. Numerical calculations validate the
approximations made in analytical relations.


  Among the states of $^{12}$C, there is an important subset of $K$=0 and
$K$=$I$ planar intrinsic states in which the intrinsic motion of the nucleons
are confined in the planar region defined by the three-alpha cluster or by
their generated toroid. The intrinsic nuclear densities of these states are
toroidal in nature. We study these $^{12}$C toroidal states from the
generator-coordinate viewpoints in both the alpha cluster model and the
toroidal shell model. Numerical solutions in the toroidal mean field
approximation are examined to pave the way for future extensions and
refinements.


  Investigation of a TMD-metal interface is essential for the effective
functioning of monolayer TMD based field effect transistors (FETs). In this
work, we employ Density Functional Theory (DFT) calculations to analyze the
modulation of the electronic structure of monolayer WS2 with chlorine doping
and the relative changes in the contact properties when interfaced with gold
and palladium. We initially examine the atomic and electronic structures of
pure and doped monolayer WS2 supercell and explore the formation of mid gap
states with band splitting near the conduction band edge. Further we analyze
the contact nature of the pure supercell with Au and Pd. We find that while Au
is physiosorped and forms n-type contact, Pd is chemisorped and forms p-type
contact with a higher valence electron density. Next, we study the interface
formed between the Cl-doped supercell and metals and observe a reduction in the
Schottky barrier height (SBH) in comparison to the pure supercell. This
reduction found is higher for Pd in comparison to Au which is further validated
by examining the charge transfer occurring at the interface. Our study confirms
that Cl doping is an efficient mechanism to reduce the n-SBH for both Au and Pd
which form different types of contact with WS2.


  Several recent publications report advances in training optimal decision
trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in
integer programming and a growing interest in addressing the inherent
suboptimality of heuristic approaches such as CART. In this paper, we propose a
novel MIP formulation, based on a 1-norm support vector machine model, to train
a multivariate ODT for classification problems. We provide cutting plane
techniques that tighten the linear relaxation of the MIP formulation, in order
to improve run times to reach optimality. Using 36 data-sets from the
University of California Irvine Machine Learning Repository, we demonstrate
that our formulation outperforms its counterparts in the literature by an
average of about 10% in terms of mean out-of-sample testing accuracy across the
data-sets. We provide a scalable framework to train multivariate ODT on large
data-sets by introducing a novel linear programming (LP) based data selection
method to choose a subset of the data for training. Our method is able to
routinely handle large data-sets with more than 7,000 sample points and
outperform heuristics methods and other MIP based techniques. We present
results on data-sets containing up to 245,000 samples. Existing MIP-based
methods do not scale well on training data-sets beyond 5,500 samples.


  By using coupling method, a Bismut type derivative formula is established for
the Markov semigroup associated to a class of hyperdissipative stochastic
Navier-Stokes/Burgers equations. As applications, gradient estimates,
dimension-free Harnack inequality, strong Feller property, heat kernel
estimates and some properties of the invariant probability measure are derived.


  We use advanced statistical tools of time-series analysis to characterize the
dynamical complexity of the transition to optical wave turbulence in a fibre
laser. Ordinal analysis and the horizontal visibility graph applied to the
experimentally measured laser output intensity reveal the presence of temporal
correlations during the transition from the laminar to the turbulent lasing
regimes. Both methods unveil coherent structures with well defined time-scales
and strong correlations both, in the timing of the laser pulses and in their
peak intensities. Our approach is generic and may be used in other complex
systems that undergo similar transitions involving the generation of extreme
fluctuations.


  We consider the group of smooth diffeomorphisms of the circle. We show that
any recurrent $f$ (in the sense that $\{f^n\}_{n \in Z}$ is not discrete) is in
fact a distortion element (in the sense that its iterates can be written as
short compositions involving finitely many smooth diffeomorphisms). Thus
rotations are distortion elements.


  We introduce a variation of the classical Ricci flow equation that modifies
the unit volume constraint of that equation to a scalar curvature constraint.
The resulting equations are named the Conformal Ricci Flow Equations because of
the role that conformal geometry plays in constraining the scalar curvature.
These equations are analogous to the incompressible Navier-Stokes equations of
fluid mechanics inasmuch as a conformal pressure arises as a Lagrange
multiplier to conformally deform the metric flow so as to maintain the scalar
curvature constraint. The equilibrium points are Einstein metrics with a
negative Einstein constant and the conformal pressue is shown to be zero at an
equilibrium point and strictly positive otherwise. The geometry of the
conformal Ricci flow is discussed as well as the remarkable analytic fact that
the constraint force does not lose derivatives and thus analytically the
conformal Ricci equation is a bounded perturbation of the classical
unnormalized Ricci equation. That the constraint force does not lose
derivatives is exactly analogous to the fact that the real physical pressure
force that occurs in the Navier-Stokes equations is a bounded function of the
velocity. Using a nonlinear Trotter product formula, existence and uniqueness
of solutions to the conformal Ricci flow equations is proven. Lastly, we
discuss potential applications to Perelman's proposed implementation of
Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.


  We show that phantom dark energy, if it is described by a K-essence theory,
has three fundamental problems: first, its hamiltonian is unbounded from below.
Second, classical stability precludes the equation of state from crossing the
``Lambda-barrier'', $w_\Lambda=-1$. Finally, both the equation of state and the
sound speed are unbounded -- the first, from below, the second, from above --
if the kinetic term is not bounded by dynamics.


  We investigate the magneto-optical properties of two-dimensional
nonsymmorphic Dirac semimetals in the presence of antiferromagnetic order.
Using the Kubo formula, we calculate the conductivity tensor of two-dimensional
CuMnAs, a prototype antiferromagnetic Dirac material, as a function of light
frequency. From the finite-frequency conductivity tensor, we derive the dynamic
dielectric function and magnetic linear dichroism, demonstrating how they are
influenced by the orientation of the N{\'e}el order parameter. Adjusting the
N{\'e}el vector changes both the sign and amplitude of the system's
magneto-optical response. We propose that magnetic linear dichroism
spectroscopy is a powerful technique for determining the orientation of the
N{\'e}el vector.


  The detailed workings of the central engines of powerful quasars remain a
mystery. This is primarily due to the fact that, at their cosmological
distances, the inner regions of these quasars are spatially unresolvable.
Reverberation mapping is now beginning to unlock the physics of the Broad
Emission Line Region (BELR) in nearby, low-luminosity quasars, however it is
still unknown whether this gas is dominated by virial motion, by outflows, or
infall. The challenge is greater for more distant, powerful sources due to the
very long response time of the BELR to changes in the continuum. We present a
new technique for probing the kinematic properties of the BELR and accretion
disk of high-z quasars using differential microlensing, and show how
substantial information can be gained through a single observation of a
strongly-lensed quasar using integral field spectroscopy. We apply this
technique to GMOS IFU observations of the multiply-imaged quasar Q2237+0305,
and find that the observed microlensing signature in the CIII] broad emission
line favours gravitationally-dominated dynamics over an accelerating outflow.


  We present high-resolution single crystal time-of-flight neutron scattering
measurements on the candidate quantum spin liquid pyrochlore Tb2Ti2O7 at low
temperature and in a magnetic field. At ~70 mK and in zero field, Tb2Ti2O7
reveals diffuse magnetic elastic scattering at (1/2,1/2,1/2) positions in
reciprocal space, consistent with short-range correlated regions based on a
two-in, two-out spin ice configuration on a doubled conventional unit cell.
This elastic scattering is separated from very low-energy magnetic inelastic
scattering by an energy gap of ~0.06-0.08 meV. The elastic signal disappears
under the application of small magnetic fields and upon elevating temperature.
Pinch-point-like elastic diffuse scattering is observed near (1,1,1) and
(0,0,2) in zero field at ~70 mK, in agreement with Fennell et al. (Ref. 1),
supporting the quantum spin ice interpretation of Tb2Ti2O7.


  Topological semimetals are currently attracting increasing interest due to
their potential applications in topological qubits and low-power electronics,
which are closely related to their thermal transport properties. In this work,
by solving the Boltzmann transport equation based on first-principles
calculations, we systematically investigate the phonon transport properties of
topological semimetal WC and WN. The predicted room-temperature lattice thermal
conductivities of WC (WN) along a and c directions are 1140.64 (7.47)
$\mathrm{W m^{-1} K^{-1}}$ and 1214.69 (5.39) $\mathrm{W m^{-1} K^{-1}}$.
Considering the similar crystal structure of WC and WN, it is quite interesting
to find that the thermal conductivity of WC is more than two orders of
magnitude higher than that of WN. It is found that, different from WN, the
large acoustic-optical (a-o) gap prohibits the
acoustic+acoustic$\rightarrow$optical (aao) scattering, which gives rise to
very long phonon lifetimes, leading to ultrahigh lattice thermal conductivity
in WC. For WN, the lack of a-o gap is due to soft phonon modes in optical
branches, which can provide more scattering channels for aao scattering,
producing very short phonon lifetimes. Further deep insight can be attained
from their different electronic structures. Distinctly different from that in
WC, the density of states (DOS) of WN at the Fermi level becomes very sharp,
which leads to destabilization of WN, producing soft phonon modes. It is found
that the small shear modulus $G$ and $C_{44}$ limit the stability of WN,
compared with WC. Our works provide valuable information for phonon transports
in WC and WN, and motivate further experimental works to study their lattice
thermal conductivities.


  We describe our experiences in using SPIN to verify parts of the Multi
Purpose Daemon (MPD) parallel process management system. MPD is a distributed
collection of processes connected by Unix network sockets. MPD is dynamic:
processes and connections among them are created and destroyed as MPD is
initialized, runs user processes, recovers from faults, and terminates. This
dynamic nature is easily expressible in the SPIN/PROMELA framework but poses
performance and scalability challenges. We present here the results of
expressing some of the parallel algorithms of MPD and executing both simulation
and verification runs with SPIN.


  Liquid Helium is used widely, from hospitals to characterization of materials
at low temperatures. Many experiments at low temperatures require liquid
Helium, particularly when vibration isolation precludes the use of cryocoolers
and when one needs to cool heavy equipment such as superconducting coils. Here
we describe methods to simplify the operations required to use liquid Helium by
eliminating the use of high pressure bottles, avoiding blockage and improving
heating and cooling rates. First we show a simple and very low cost method to
transfer liquid Helium from a transport container into a cryostat that uses a
manual pump having pumping and pressurizing ports, giving a liquid Helium
transfer rate of about 100 liters an hour. Second, we describe a closed cycle
circuit of Helium gas cooled in an external liquid nitrogen bath that allows
precooling a cryogenic experiment without inserting liquid nitrogen into the
cryostat, eliminating problems associated to the presence of nitrogen around
superconducting magnets. And third, we show a sliding seal assembly and an
inner vacuum chamber design that allows inserting large experiments into liquid
Helium.


  Let $G$ be a linear split algebraic group. The degenerate Eisenstein series
associated to a maximal parabolic subgroup $E_{P}(f^{0},s,g)$ with the
spherical section $f^{0}$ is studied in the first part of the thesis. In this
part, we study the poles of $E_{P}(f^{0},s,g)$ in the region $\operatorname{Re}
s >0$. We determine when the leading term in the Laurent expansion of
  $E_{P}(f^{0},s,g)$ around $s=s_0$ is square integrable. The second part is
devoted to finding identities between the leading terms of various Eisenstein
series at different points. We present an algorithm to find this data and
implement it on \textit{SAGE}. While both parts can be applied to a general
algebraic group, we restrict ourself to the case where $G$ is split exceptional
group of type $F_4,E_6,E_7$, and obtain new results.


  Restriction categories were introduced to provide an axiomatic setting for
the study of partially defined mappings; they are categories equipped with an
operation called restriction which assigns to every morphism an endomorphism of
its domain, to be thought of as the partial identity that is defined to just
the same degree as the original map. In this paper, we show that restriction
categories can be identified with \emph{enriched categories} in the sense of
Kelly for a suitable enrichment base. By varying that base appropriately, we
are also able to capture the notions of join and range restriction category in
terms of enriched category theory.


  Locomotion via cyclic moves presents a challenge to mesoscopic objects in
overdamped environments, where time reversibility may prevent directed motion.
Most reported cyclic movers exploit anisotropic drag to push themselves
forward. Under an oscillating drive, however, anisotropic drag enables
locomotion only if the objects can change their shape. Here, we present a
strategy that unexpectedly enables structurally invariant objects to move under
oscillating fields. The objects are self-assembled clusters of magnetic
particles that exhibit an off-centered dipole moment. By theoretical modeling
and in experiments with magnetic Janus particles, we demonstrate that the
interaction between such anisotropic particles in the cluster breaks time
reversibility. Experimentally, we show that the magnetic configuration of a
cluster determines its motion path. We realize stirrers and steerable movers
with helical or directed path using the same particle system. The presented
strategy based on internal interactions establishes a counterpart to locomotion
via anisotropic drag.


  We present a quantum theoretical analysis of the electroluminescence from an
intersubband transition of a quantum well structure embedded in a planar
microcavity. By using a cluster factorization method, we have derived a closed
set of dynamical equations for the quantum well carrier and cavity photon
occupation numbers, the correlation between the cavity field and the
intersubband polarization, as well as polarization-polarization contributions.
In order to model the electrical excitation, we have considered electron
population tunneling from an injector and into an extractor contact. The
tunneling rates have been obtained by considering the bare electronic states in
the quantum well and the limit of validity of this approximation (broad-band
injection) are discussed in detail. We apply the present quantum model to
provide a comprehensive description of the electronic transport and optical
properties of an intersubband microcavity light emitting diode, accounting for
non-radiative carrier relaxation and Pauli blocking. We study the enhancement
of the electroluminescence quantum efficiency passing from the weak to the
strong polariton coupling regime.


  We present multicolor light curves of SN 1998bw which appeared in ESO184-G82
in close temporal and spacial association with GRB 980425. They are based on
observations done at Cerro Tololo Inter-American Observatory and data from the
literature. The CTIO photometry reaches ~86 days after the GRB in $U$ and ~160
days after the GRB in BV(RI)_C. The observations in U extend by about 30 days
the previously known coverage, and determine the slope of the early exponential
tail.
  We calibrate a large set of local standards in common with those of previous
studies and use them to transform published observations of the SN to our
realization of the standard photometric system. We show that the photometry
from different sources merges smoothly and provide a unified set of 300
observations of the SN in five bands. Using the extensive set of spectra in
public domain we compute extinction and K corrections, and build
quasi-bolometric unreddened rest frame light curves. We provide low degree
piecewise spline fits to these light curves with daily sampling. They reach ~86
rest frame days after the GRB with U band coverage, and ~498 rest frame days
after the GRB without U.


  We present a relativistic symmetry analysis of the allowed pairing states in
the noncentroymmetric superconductor LaNiC$_2$. The case of zero spin-orbit
coupling (SOC) is discussed first and then the evolution of the
symmetry-allowed superconducting instabilities as SOC is adiabatically turned
on is described. In addition to mixing singlet with triplet pairing, SOC splits
some triplet pairing states with degenerate order parameter spaces into
non-degenerate pairing states with different critical temperatures. We address
the breaking of time-reversal symmetry (TRS) detected in recent muon spin
relaxation experiments and show that it is only compatible with such
non-unitary triplet pairing states. In particular, an alternative scenario
featuring conventional singlet pairing with a small admixture of triplet
pairing is shown to be incompatible with the experimental data.


  Let K be the field of fractions of a Henselian discrete valuation ring O_K.
Let X_K/K be a smooth proper geometrically connected scheme admitting a regular
model X/O_K. We show that the index \delta(X_K/K) of X_K/K can be explicitly
computed using data pertaining only to the special fiber X_k/k of the model X.
  We give two proofs of this theorem, using two moving lemmas. One moving lemma
pertains to horizontal 1-cycles on a regular projective scheme X over the
spectrum of a semi-local Dedekind domain, and the second moving lemma can be
applied to 0-cycles on an FA-scheme X which need not be regular.
  The study of the local algebra needed to prove these moving lemmas led us to
introduce an invariant \gamma(A) of a singular local ring (A, \m): the greatest
common divisor of all the Hilbert-Samuel multiplicities e(Q,A), over all
\m-primary ideals Q in \m. We relate this invariant \gamma(A) to the index of
the exceptional divisor in a resolution of the singularity of Spec(A), and we
give a new way of computing the index of a smooth subvariety X_K/K of P^n_K
over any field K, using the invariant \gamma of the local ring at the vertex of
a cone over X.


  The bosonisation technique is used to calculate the resonant Raman spectrum
of a quantum wire with two electronic sub-bands occupied. Close to resonance,
the cross section at frequencies in the region of the inter sub-band
transitions shows distinct peaks in parallel polarisation of the incident and
scattered light that are signature of collective higher order spin density
excitations. This is in striking contrast to the conventional selection rule
for non-resonant Raman scattering according to which spin modes can appear only
in perpendicular polarisation. We predict a new selection rule for the
excitations observed near resonance, namely that, apart from charge density
excitations, only spin modes with positive group velocities can appear as peaks
in the spectra in parallel configuration close to resonance. The results are
consistent with all of the presently available experimental data.


  Several recent works have proposed a class of algorithms for the offline
reinforcement learning (RL) problem that we will refer to as return-conditioned
supervised learning (RCSL). RCSL algorithms learn the distribution of actions
conditioned on both the state and the return of the trajectory. Then they
define a policy by conditioning on achieving high return. In this paper, we
provide a rigorous study of the capabilities and limitations of RCSL, something
which is crucially missing in previous work. We find that RCSL returns the
optimal policy under a set of assumptions that are stronger than those needed
for the more traditional dynamic programming-based algorithms. We provide
specific examples of MDPs and datasets that illustrate the necessity of these
assumptions and the limits of RCSL. Finally, we present empirical evidence that
these limitations will also cause issues in practice by providing illustrative
experiments in simple point-mass environments and on datasets from the D4RL
benchmark.


  A major challenge in monocular 3D object detection is the limited diversity
and quantity of objects in real datasets. While augmenting real scenes with
virtual objects holds promise to improve both the diversity and quantity of the
objects, it remains elusive due to the lack of an effective 3D object insertion
method in complex real captured scenes. In this work, we study augmenting
complex real indoor scenes with virtual objects for monocular 3D object
detection. The main challenge is to automatically identify plausible physical
properties for virtual assets (e.g., locations, appearances, sizes, etc.) in
cluttered real scenes. To address this challenge, we propose a physically
plausible indoor 3D object insertion approach to automatically copy virtual
objects and paste them into real scenes. The resulting objects in scenes have
3D bounding boxes with plausible physical locations and appearances. In
particular, our method first identifies physically feasible locations and poses
for the inserted objects to prevent collisions with the existing room layout.
Subsequently, it estimates spatially-varying illumination for the insertion
location, enabling the immersive blending of the virtual objects into the
original scene with plausible appearances and cast shadows. We show that our
augmentation method significantly improves existing monocular 3D object models
and achieves state-of-the-art performance. For the first time, we demonstrate
that a physically plausible 3D object insertion, serving as a generative data
augmentation technique, can lead to significant improvements for discriminative
downstream tasks such as monocular 3D object detection. Project website:
https://gyhandy.github.io/3D-Copy-Paste/


  Higher order random walks (HD-walks) on high dimensional expanders (HDX) have
seen an incredible amount of study and application since their introduction by
Kaufman and Mass [KM16], yet their broader combinatorial and spectral
properties remain poorly understood. We develop a combinatorial
characterization of the spectral structure of HD-walks on two-sided
local-spectral expanders [DK17], which offer a broad generalization of the
well-studied Johnson and Grassmann graphs. Our characterization, which shows
that the spectra of HD-walks lie tightly concentrated in a few combinatorially
structured strips, leads to novel structural theorems such as a tight
$\ell_2$-characterization of edge-expansion, as well as to a new understanding
of local-to-global algorithms on HDX.
  Towards the latter, we introduce a spectral complexity measure called
Stripped Threshold Rank, and show how it can replace the (much larger)
threshold rank in controlling the performance of algorithms on structured
objects. Combined with a sum-of-squares proof of the former
$\ell_2$-characterization, we give a concrete application of this framework to
algorithms for unique games on HD-walks, in many cases improving the state of
the art [RBS11, ABS15] from nearly-exponential to polynomial time (e.g. for
sparsifications of Johnson graphs or of slices of the $q$-ary hypercube). Our
characterization of expansion also holds an interesting connection to hardness
of approximation, where an $\ell_\infty$-variant for the Grassmann graphs was
recently used to resolve the 2-2 Games Conjecture [KMS18]. We give a reduction
from a related $\ell_\infty$-variant to our $\ell_2$-characterization, but it
loses factors in the regime of interest for hardness where the gap between
$\ell_2$ and $\ell_\infty$ structure is large. Nevertheless, we open the door
for further work on the use of HDX in hardness of approximation and unique
games.


  In this article, we construct SL$_k$-friezes using Pl\"ucker coordinates,
making use of the cluster structure on the homogeneous coordinate ring of the
Grassmannian of $k$-spaces in $n$-space via the Pl\"ucker embedding. When this
cluster algebra is of finite type, the SL$_k$-friezes are in bijection with the
so-called mesh friezes of the corresponding Grassmannian cluster category.
These are collections of positive integers on the AR-quiver of the category
with relations inherited from the mesh relations on the category. In these
finite type cases, many of the SL$_k$-friezes arise from specialising a cluster
to 1. These are called unitary. We use Iyama-Yoshino reduction to analyse the
non-unitary friezes. With this, we provide an explanation for all known friezes
of this kind. An appendix by Cuntz and Plamondon proves that there are 868
friezes of type $E_6$.


  Designing a good transfer channel for arbitrary quantum states in spin chains
implies optimizing a cost function, usually the averaged fidelity of
transmission. The fidelity of transmission measures how much the transferred
state resembles the state prepared at the beginning of the transfer protocol.
When averaged over all the possible initial states, the figure of merit
quantifies the quality of the protocol. There are proposals for optimizing a
given Hamiltonian to accomplish a particular task. The transfer of quantum
states is one of them. In particular, we consider the design of Heisenberg spin
chains using a genetic algorithm. This very efficient algorithm allows us to
study different properties of Hamiltonians with good to excellent transfer
ability. One apparent drawback of using a random search method is that it
results in exchange coefficient strengths that change abruptly from site to
site. Modifying the cost function, we obtain Hamiltonians with exchange
coefficients varying smoothly along the chain length. Our results show that the
smoothed Hamiltonians have the same, or less, transfer ability than the rough
ones, and both kinds show similar robustness against static disorder. By
studying the statistical properties of the eigenvalues of Hamiltonians with
varying transfer abilities, we determine the ensemble of random matrices to
which the spectra belong.


  Non-associtive algebras is a research direction gaining much attention these
days. New developments show that associative algebras and some not-associative
structures can be unified at the level of Yang-Baxter structures. In this
paper, we present a unification for associative algebras, Jordan algebras and
Lie algebras. The (quantum) Yang-Baxter equation and related structures are
interesting topics, because they have applications in many areas of
mathematics, physics and computer science. Several new interpretations and
results are presented below.


  Many frameworks for emotional text-to-speech (E-TTS) rely on human-annotated
emotion labels that are often inaccurate and difficult to obtain. Learning
emotional prosody implicitly presents a tough challenge due to the subjective
nature of emotions. In this study, we propose a novel approach that leverages
text awareness to acquire emotional styles without the need for explicit
emotion labels or text prompts. We present TEMOTTS, a two-stage framework for
E-TTS that is trained without emotion labels and is capable of inference
without auxiliary inputs. Our proposed method performs knowledge transfer
between the linguistic space learned by BERT and the emotional style space
constructed by global style tokens. Our experimental results demonstrate the
effectiveness of our proposed framework, showcasing improvements in emotional
accuracy and naturalness. This is one of the first studies to leverage the
emotional correlation between spoken content and expressive delivery for
emotional TTS.


  We present a construction of closed 7-manifolds of holonomy G_2, which
generalises Kovalev's twisted connected sums by taking quotients of the pieces
in the construction before gluing. This makes it possible to realise a wider
range of topological types, and Crowley, Goette and the author arXiv:1505.02734
use this to exhibit examples of closed 7-manifolds with disconnected moduli
space of holonomy G_2 metrics.


  The LoRa physical layer is one of the most promising Low Power Wide-Area
Network (LPWAN) technologies for future Internet of Things (IoT) applications.
It provides a flexible adaptation of coverage and data rate by allocating
different Spreading Factors (SFs) and transmit powers to end-devices. We focus
on improving throughput fairness while reducing energy consumption. Whereas
most existing methods assume perfect SF orthogonality and ignore the harmful
effects of inter-SF interferences, we formulate a joint SF and power allocation
problem to maximize the minimum uplink throughput of end-devices, subject to
co-SF and inter-SF interferences, and power constraints. This results into a
mixed-integer non-linear optimization, which, for tractability, is split into
two sub-problems: firstly, the SF assignment for fixed transmit powers, and
secondly, the power allocation given the previously obtained assignment
solution. For the first sub-problem, we propose a low-complexity many-to-one
matching algorithm between SFs and end-devices. For the second one, given its
intractability, we transform it using two types of constraints approximation: a
linearized and a quadratic version. Our performance evaluation demonstrates
that the proposed joint SF allocation and power optimization enables to
drastically enhance various performance objectives such as throughput, fairness
and power consumption, and that it outperforms baseline schemes.


  Alignment between real and virtual objects is a challenging task required for
the deployment of Mixed Reality (MR) into manufacturing, medical, and
construction applications. To face this challenge, a series of methods have
been proposed. While many approaches use dynamic augmentations such as
animations, arrows, or text to assist users, they require tracking the position
of real objects. In contrast, when tracking of the real objects is not
available or desired, alternative approaches use virtual replicas of real
objects to allow for interactive, perceptual virtual-to-real, and/or
real-to-virtual alignment. In these cases, the accuracy achieved strongly
depends on the quality of the perceptual information provided to the user. This
paper proposes a novel set of perceptual alignment concepts that go beyond the
use of traditional visualization of virtual replicas, introducing the concept
of COMPLEMENTARY TEXTURES to improve interactive alignment in MR applications.
To showcase the advantages of using COMPLEMENTARY TEXTURES, we describe three
different implementations that provide highly salient visual cues when
misalignment is observed; or present semantic augmentations that, when combined
with a real object, provide contextual information that can be used during the
alignment process. The authors aim to open new paths for the community to
explore rather than describing end-to-end solutions. The objective is to show
the multitude of opportunities such concepts could provide for further research
and development.


  Relativistic phenomena (orbital precession, Shapiro delay, and/or orbital
decay) have been measured in Arecibo timing observations of four pulsar-white
dwarf binaries, leading to constraints on the neutron star masses. We have
detected the decay of the PSR J0751+1807 orbit due to gravitational radiation
emission, the first such measurement in a binary with a low mass ratio
(m_2/m_1<<1). Timing data constrains the mass of this pulsar to bet between 1.6
and 2.8 solar masses. Masses of the other pulsars are in marginal agreement
with the canonical pulsar mass of 1.35 solar masses, but higher values are
preferred.


  We establish exponential inequalities for a class of V-statistics under
strong mixing conditions. Our theory is developed via a novel kernel expansion
based on random Fourier features and the use of a probabilistic method. This
type of expansion is new and useful for handling many notorious classes of
kernels.


  An analysis of the propagation of non stationary waves in the adiabatic
region of stellar interior is presented. An equation of motion with an
effective potential is derived, similar to the Zerilli equation known in the
propagation of gravitational waves. The Huyghens principle is violated in this
case and the energy diffusion outward null cones is expected. Numerical
calculations demonstrate that the diffusion is weak for the case of standard
Solar model; thus no significant effect corresponding to quasinormal modes can
be expected. The likely reason for the absence of stronger features is the
restriction of our analysis to adiabatic regions only, where the breakdown of
the Huyghens principle is insignificant.


  Magnetar giant flares (MGFs) have been long proposed to contribute at least a
sub-sample of the observed short gamma-ray bursts (GRBs). The recent discovery
of the short GRB 200415A in the nearby galaxy NGC 253 established a
textbook-version connection between these two phenomena. Unlike previous
observations of the Galactic MGFs, the unsaturated instrument spectra of GRB
200415A provide for the first time an opportunity to test the theoretical
models with the observed $\gamma$-ray photons. This paper proposed a new
readily fit-able model for the MGFs, which invokes an expanding fireball
Comptonized by the relativistic magnetar wind at photosphere radius. In this
model, a large amount of energy is released from the magnetar crust due to the
magnetic reconnection or the starquakes of the star surface and is injected
into confined field lines, forming a trapped fireball bubble. After breaking
through the shackles and expanding to the photospheric radius, the thermal
photons of the fireball are eventually Comptonized by the relativistic
$e^{\pm}$ pairs in the magnetar wind region, which produces additional
higher-energy gamma-ray emission. The model predicts a modified thermal-like
spectrum characterized by a low-energy component in the Rayleigh-Jeans regime,
a smooth component affected by coherent Compton scattering (CC) in the
intermediate energy range, and a high-energy tail due to the inverse Compton
process. By performing a Monte-Carlo fit to the observational spectra of GRB
200415A, we found that the observation of the burst is entirely consistent with
our model predictions.


  I examine the role of final state interactions in cold nuclear matter in
modifying hadron production on nuclear targets with leptonic or hadronic beams.
I demonstrate the extent to which available experimental data in
electron-nucleus collisions can give direct information on final state effects
in hadron-nucleus and nucleus-nucleus collisions. For hadron-nucleus
collisions, a theoretical estimate based on a parton energy loss model tested
in lepton-nucleus collisions shows a large effect on mid-rapidity hadrons at
fixed target experiments. At RHIC energy, the effect is large for negative
rapidity hadrons, but mild at midrapidity. This final state cold hadron
quenching needs to be taken into account in jet tomographic analysis of the
medium created in nucleus-nucleus collisions.


  We report on simulations of mildly turbulent convection in spherical wedge
geometry with varying density stratification. We vary the density contrast
within the convection zone by a factor of 20 and study the influence of
rotation on the solutions. We demonstrate that the size of convective cells
decreases and the anisotropy of turbulence increases as the stratification is
increased. Differential rotation is found to change from anti-solar (slow
equator) to solar-like (fast equator) at roughly the same Coriolis number for
all stratifications. The largest stratification runs, however, are sensitive to
changes of the Reynolds number. Evidence for a near-surface shear layer is
found in runs with strong stratification and large Reynolds numbers.


  Earth observation (EO) applications involving complex and heterogeneous data
sources are commonly approached with machine learning models. However, there is
a common assumption that data sources will be persistently available. Different
situations could affect the availability of EO sources, like noise, clouds, or
satellite mission failures. In this work, we assess the impact of missing
temporal and static EO sources in trained models across four datasets with
classification and regression tasks. We compare the predictive quality of
different methods and find that some are naturally more robust to missing data.
The Ensemble strategy, in particular, achieves a prediction robustness up to
100%. We evidence that missing scenarios are significantly more challenging in
regression than classification tasks. Finally, we find that the optical view is
the most critical view when it is missing individually.


  Electromagnetically induced absorption (EIA) was observed on a sample of $%
^{85}Rb$ in a magneto-optical trap using low intensity cw copropagating pump
and probe optical fields. At moderate trapping field intensity, the EIA
spectrum is determined by the Zeeman effect produced on the atomic ground-state
by the trapping quadrupolar magnetic field. The use of EIA spectroscopy for the
magnetic field mapping of cold atomic samples is illustrated.


  In this paper, we show the spectral convergence result of
$\overline{\partial}$-Laplacians when $(X,\omega)$ is a compact toric
symplectic manifold equipped with the natural prequantum line bundle $L$. We
consider a family $\{ J_s\}_s$ of $\omega$-compatible complex structures
tending to the large complex structure limit, and obtain the spectral
convergence of $\overline{\partial}$-Laplacians acting on $L^k$.


  ALICE is a unique opportunity for studying low Pt physics and minimum bias
events, and consequently for hunting substructures in strong interactions. The
general question concerning global event properties in pp and ppbar physics is
indeed whether substructures can be seen in the data in a model-independent
way. In other terms, can we identify the interface between perturbative and
non-perturbative regimes?


  Consider an ensemble of $N\times N$ non-Hermitian matrices in which all
entries are independent identically distributed complex random variables of
mean zero and absolute mean-square one. If the entry distributions also possess
bounded densities and finite $(4+\epsilon)$ moments, then Z. D. Bai [Ann.
Probab. 25 (1997) 494--529] has shown the ensemble to satisfy the circular law:
after scaling by a factor of $1/\sqrt{N}$ and letting $N\to \infty$, the
empirical measure of the eigenvalues converges weakly to the uniform measure on
the unit disk in the complex plane. In this note, we investigate fluctuations
from the circular law in a more restrictive class of non-Hermitian matrices for
which higher moments of the entries obey a growth condition. The main result is
a central limit theorem for linear statistics of type
$X_N(f)=\sum_{k=1}^Nf(\lambda_k)$ where $\lambda_1,\lambda_2,...,\lambda_N$
denote the ensemble eigenvalues and the test function $f$ is analytic on an
appropriate domain. The proof is inspired by Bai and Silverstein [Ann. Probab.
32 (2004) 533--605], where the analogous result for random sample covariance
matrices is established.


  The performance of GNNs degrades as they become deeper due to the
over-smoothing. Among all the attempts to prevent over-smoothing, residual
connection is one of the promising methods due to its simplicity. However,
recent studies have shown that GNNs with residual connections only slightly
slow down the degeneration. The reason why residual connections fail in GNNs is
still unknown. In this paper, we investigate the forward and backward behavior
of GNNs with residual connections from a novel path decomposition perspective.
We find that the recursive aggregation of the median length paths from the
binomial distribution of residual connection paths dominates output
representation, resulting in over-smoothing as GNNs go deeper. Entangled
propagation and weight matrices cause gradient smoothing and prevent GNNs with
residual connections from optimizing to the identity mapping. Based on these
findings, we present a Universal Deep GNNs (UDGNN) framework with cold-start
adaptive residual connections (DRIVE) and feedforward modules. Extensive
experiments demonstrate the effectiveness of our method, which achieves
state-of-the-art results over non-smooth heterophily datasets by simply
stacking standard GNNs.


  The main goal of this paper is to design multiscale basis functions within
GMsFEM framework such that the convergence of method is independent of the
contrast and linearly decreases with respect to mesh size if oversampling size
is appropriately chosen. We would like to show a mesh-dependent convergence
with a minimal number of basis functions. Our construction starts with an
auxiliary multiscale space by solving local spectral problems. In auxiliary
multiscale space, we select the basis functions that correspond to small
(contrast-dependent) eigenvalues. These basis functions represent the channels
(high-contrast features that connect the boundaries of the coarse block). Using
the auxiliary space, we propose a constraint energy minimization to construct
multiscale spaces. The minimization is performed in the oversampling domain,
which is larger than the target coarse block. The constraints allow handling
non-decaying components of the local minimizers. If the auxiliary space is
correctly chosen, we show that the convergence rate is independent of the
contrast (because the basis representing the channels are included in the
auxiliary space) and is proportional to the coarse-mesh size (because the
constrains handle non-decaying components of the local minimizers). The
oversampling size weakly depends on the contrast as our analysis shows. The
convergence theorem requires that channels are not aligned with the coarse
edges, which hold in many applications, where the channels are oblique with
respect to the coarse-mesh geometry. The numerical results confirm our
theoretical results. In particular, we show that if the oversampling domain
size is not sufficiently large, the errors are large. To remove the
contrast-dependence of the oversampling size, we propose a modified
construction for basis functions and present numerical results and the
analysis.


  This paper deals with the definition and optimization of augmentation spaces
for faster convergence of the conjugate gradient method in the resolution of
sequences of linear systems. Using advanced convergence results from the
literature, we present a procedure based on a selection of relevant
approximations of the eigenspaces for extracting, selecting and reusing
information from the Krylov subspaces generated by previous solutions in order
to accelerate the current iteration. Assessments of the method are proposed in
the cases of both linear and nonlinear structural problems.


  A phase detection sequence is a length-$n$ cyclic sequence, such that the
location of any length-$k$ contiguous subsequence can be determined from a
noisy observation of that subsequence. In this paper, we derive bounds on the
minimal possible $k$ in the limit of $n\to\infty$, and describe some sequence
constructions. We further consider multiple phase detection sequences, where
the location of any length-$k$ contiguous subsequence of each sequence can be
determined simultaneously from a noisy mixture of those subsequences. We study
the optimal trade-offs between the lengths of the sequences, and describe some
sequence constructions. We compare these phase detection problems to their
natural channel coding counterparts, and show a strict separation between the
fundamental limits in the multiple sequence case. Both adversarial and
probabilistic noise models are addressed.


  We demonstrate that the size of the electric-field-induced Rashba spin
splitting in an 80 nm wide modulation-doped InGaSb quantum well can depend
strongly on the spatial variation of the electric field. In a slightly
asymmetric quantum well it can be an order of magnitude stronger than for the
average uniform electric field. For even smaller asymmetry spin subbands can
have wave functions and/or expectation values of the spin direction that are
completely changed as the in-plane wave vector varies. The Dresselhaus effect
can give an anticrossing at which the spin rapidly flips.


  We present low-temperature thermal conductivity measurements on the cuprate
Tl_2Ba_2CuO_{6+delta} throughout the overdoped regime. In the T -> 0 limit, the
thermal conductivity due to d-wave nodal quasiparticles provides a bulk
measurement of the superconducting gap, Delta. We find Delta to decrease with
increasing doping, with a magnitude consistent with spectroscopic measurements
(photoemission and tunneling). This argues for a pure and simple d-wave
superconducting state in the overdoped region of the phase diagram, which
appears to extend into the underdoped regime down to a hole concentration of
0.1 hole/Cu. As hole concentration is decreased, the gap-to-Tc ratio increases,
showing that the suppression of the superconducting transition temperature Tc
(relative to the gap) begins in the overdoped regime.


  In supporting Wifi networks it is useful to identify the type of client
device connecting to an AP. Knowing the type of client can guide
troubleshooting steps, allow searches for known issues, or allow specific
workarounds to be implemented in the AP. For support purposes a passive method
which analyzes normal traffic is preferable to active methods, which often send
obscure combinations of packet options which might trigger client bugs. We have
developed a method of passive client identification which observes the contents
of Wifi management frames including Probes and Association requests. We show
that the management frames populated by modern Wifi chipsets and device drivers
are quite distinguishable, making it possible in many cases to identify the
model of the device. Supplementing information from the Wifi management frames
with additional information from DHCP further extends the set of clients which
can be distinguished.


  Next generation (5G) cellular networks are expected to be supported by an
extensive infrastructure with many-fold increase in the number of cells per
unit area compared to today. The total energy consumption of base transceiver
stations (BTSs) is an important issue for both economic and environmental
reasons. In this paper, an optimization-based framework is proposed for
energy-efficient global radio resource management in heterogeneous wireless
networks. Specifically, with stochastic arrivals of known rates intended for
users, the smallest set of BTSs is activated with jointly optimized user
association and spectrum allocation to stabilize the network first and then
minimize the delay. The scheme can be carried out periodically on a relatively
slow timescale to adapt to aggregate traffic variations and average channel
conditions. Numerical results show that the proposed scheme significantly
reduces the energy consumption and increases the quality of service compared to
existing schemes in the literature.


  Mixing processes such as convection, overshooting and rotational mixing have
long been known to affect the evolutionary properties of low-mass stars. While
modeling a 1.2 Msun star, we encountered a semiconvective region outside the
fully convective core, reminiscent of the well-known situation for massive
stars. In this study we focus on low-mass stars presenting convective cores
and, by applying different prescriptions for the determination of the
convective boundaries and using different mixing descriptions for the dynamical
processes in the core, we look for the effects of semiconvective mixing in the
interior structure of the stars and its observable quantities. With this
purpose, we have constructed different sets of evolutionary models using a
stellar evolution code (GARSTEC), and analyzed the models looking for imprints
of these processes.


  A Littlewood polynomial is a polynomial in $\mathbb{C}[z]$ having all of its
coefficients in $\{-1,1\}$. There are various old unsolved problems, mostly due
to Littlewood and Erd\H{o}s, that ask for Littlewood polynomials that provide a
good approximation to a function that is constant on the complex unit circle,
and in particular have small $L^q$ norm on the complex unit circle. We consider
the Fekete polynomials \[ f_p(z)=\sum_{j=1}^{p-1}(j\mid p)\,z^j, \] where $p$
is an odd prime and $(\,\cdot\mid p)$ is the Legendre symbol (so that
$z^{-1}f_p(z)$ is a Littlewood polynomial). We give explicit and recursive
formulas for the limit of the ratio of $L^q$ and $L^2$ norm of $f_p(z)$ when
$q$ is an even positive integer and $p\to\infty$. To our knowledge, these are
the first results that give these limiting values for specific sequences of
nontrivial Littlewood polynomials and infinitely many $q$. Similar results are
given for polynomials obtained by cyclically permuting the coefficients of
Fekete polynomials and for Littlewood polynomials whose coefficients are
obtained from additive characters of finite fields. These results vastly
generalise earlier results on the $L^4$ norm of these polynomials.


  Radon-Nikodym (RN) derivative between two measures arises naturally in the
affine structure of the space of probability measures with densities. Entropy,
free energy, relative entropy, and entropy production as mathematical concepts
associated with RN derivatives are introduced. We identify a simple equation
that connects two measures with densities as a possible mathematical basis of
the entropy balance equation that is central in nonequilibrium thermodynamics.
Application of this formalism to Gibbsian canonical distribution yields many
results in classical thermomechanics. An affine structure based on the
canonical represenation and two divergences are introduced in the space of
probability measures. It is shown that thermodynamic work, as a conditional
expectation, is indictive of the RN derivative between two energy
represenations being singular. The entropy divergence and the heat divergence
yield respectively a Massieu-Planck potential based and a generalized Carnot
inequalities.


  We study the Einstein gravity and dust system in three spacetime dimensions
as an example of a non-perturbative quantum gravity model with local degrees of
freedom. We derive the Hamiltonian theory in the dust time gauge and show that
it has a rich class of exact solutions. These include the
Ba\~nados-Teitelboim-Zanelli black hole, static solutions with naked
singularities and travelling wave solutions with dynamical horizons. We give a
complete quantization of the wave sector of the theory, including a definition
of a self-adjoint spacetime metric operator. This operator is used to
demonstrate the quantization of deficit angle and the fluctuation of dynamical
horizons.


  We analyze, within the wavelet theory framework, the wandering over a screen
of the centroid of a laser beam after it has propagated through a time-changing
laboratory-generated turbulence. Following a previous work (Fractals 12 (2004)
223) two quantifiers are used, the Hurst parameter, $H$, and the Normalized
Total Wavelet Entropy, $\text{NTWS}$. The temporal evolution of both
quantifiers, obtained from the laser spot data stream is studied and compared.
This allows us to extract information of the stochastic process associated to
the turbulence dynamics.


  We present a scheme for on-chip optical transduction of strain and
displacement of Graphene-based Nano-Electro-Mechanical Systems (NEMS). A
detailed numerical study on the feasibility of three silicon-photonic
integrated circuit configurations is presented: Mach-Zehnder
Interferometer(MZI), micro-ring resonator and ring-loaded MZI. An index-sensing
based technique using a Mach-Zehnder Interferometer loaded with a ring
resonator with a moderate Q-factor of 2400 can yield a sensitivity of 28
fm/sqrt(Hz), and 6.5E-6 %/sqrt(Hz) for displacement and strain respectively.
Though any phase sensitive integrated photonic device could be used for optical
transduction, here we show that optimal sensitivity is achievable by combining
resonance with phase sensitivity.


  Spontaneous breaking of Lorentz invariance compatible with observational
limits may realistically take place in the context of string theories, possibly
endowing the photon with a mass. In this process the conformal symmetry of the
electromagnetic action is broken allowing for the possibility of generating
large scale ($\sim Mpc$) magnetic fields within inflationary scenarios. We show
that for reheating temperatures safe from the point of view of the gravitino
and moduli problem, $T_{RH} \laq 10^{9} GeV$ for $m_{3/2} \approx 1 TeV$, the
strength of the generated seed fields is, in our mechanism, consistent with
amplification by the galactic dynamo processes and can be even as large as to
explain the observed galactic magnetic fields through the collapse of
protogalactic clouds.


  Thoth is a tool designed to combine many different types of speed reading
technology. The largest insight is using natural language parsing for more
optimal rapid serial visual presentation and more effective reading
information.


  Wiles' proof of Fermat's last theorem initiated a powerful new approach
towards the resolution of certain Diophantine equations over $\mathbb{Q}$.
Numerous novel obstacles arise when extending this approach to the resolution
of Diophantine equations over totally real number fields. We give an extensive
overview of these obstacles as well as providing a survey of existing methods
and results in this area.


  In view of the upcoming observations with the Event Horizon Telescope (EHT),
we present our thoughts on the immediate environment of an astrophysical black
hole. We are concerned that two approximations used in general relativistic
magnetohydrodynamic numerical simulations, namely numerical density floors
implemented near the base of the black hole jet, and a magnetic field that
comes from large distances, may mislead our interpretation of the observations.
We predict that three physical processes will manifest themselves in EHT
observations, namely dynamic pair formation just above the horizon,
electromagnetic energy dissipation along the boundary of the black hole jet,
and a region of weak magnetic field separating the black hole jet from the disk
wind.


  We show that Laplacian and symmetric diagonally dominant (SDD) matrices can
be well approximated by linear-sized sparse Cholesky factorizations. We show
that these matrices have constant-factor approximations of the form $L L^{T}$,
where $L$ is a lower-triangular matrix with a number of nonzero entries linear
in its dimension. Furthermore linear systems in $L$ and $L^{T}$ can be solved
in $O (n)$ work and $O(\log{n}\log^2\log{n})$ depth, where $n$ is the dimension
of the matrix.
  We present nearly linear time algorithms that construct solvers that are
almost this efficient. In doing so, we give the first nearly-linear work
routine for constructing spectral vertex sparsifiers---that is, spectral
approximations of Schur complements of Laplacian matrices.


  To understand the mechanisms by which Fe and Cr additions increase the
corrosion rate of irradiated Zr alloys, a combination of experimental (atom
probe tomography, x-ray diffraction and thermoelectric power measurements) and
modelling (density functional theory) techniques are employed to investigate
the non-equilibrium solubility and clustering of Fe and Cr in binary Zr alloys.
Cr occupies both interstitial and substitutional sites in the {\alpha}-Zr
lattice, Fe favours interstitial sites, and a low-symmetry site that was not
previously modelled is found to be the most favourable for Fe. Lattice
expansion as a function of alloying concentration (in the dilute regime) is
strongly anisotropic for Fe additions, expanding the $c$-axis while contracting
the $a$-axis. Defect clusters are observed at higher solution concentrations,
which induce a smaller amount of lattice strain compared to the dilute defects.
In the presence of a Zr vacancy, all two-atom clusters are more soluble than
individual point defects and as many as four Fe or three Cr atoms could be
accommodated in a single Zr vacancy. The Zr vacancy is critical for the
increased solubility of defect clusters, the implications for irradiation
induced microstructure changes in Zr alloys are discussed.


  Emulation of gauge fields for ultracold atoms provides access to a class of
exotic states arising in strong magnetic fields. Here we report on the
experimental realisation of tunable staggered gauge fields in a periodically
driven triangular lattice. For maximal staggered magnetic fluxes, the doubly
degenerate superfluid ground state breaks both a discrete Z2 (Ising) symmetry
and a continuous U(1) symmetry. By measuring an Ising order parameter, we
observe a thermally driven phase transition from an ordered antiferromagnetic
to an unordered paramagnetic state and textbook-like magnetisation curves. Both
the experimental and theoretical analysis of the coherence properties of the
ultracold gas demonstrate the strong influence of the Z2 symmetry onto the
condensed phase.